Bessel function J_0 31 terms Bessel function J_1 30 terms Bessel function J_2 29 terms Bessel function J_3 28 terms Bessel function J_4 27 terms Bessel function J_5 26 terms Bessel function J_6 25 terms Bessel function J_7 24 terms Bessel function J_8 23 terms Bessel function J_9 22 terms Bessel function J_10 21 terms Bessel function J_11 20 terms Bessel function J_12 19 terms Bessel function J_13 18 terms Bessel function J_14 17 terms Bessel function J_15 16 terms Bessel function J_16 15 terms Bessel function J_17 14 terms Bessel function J_18 13 terms Bessel function J_19 12 terms Bessel function J_20 11 terms expansion for a/r 1 current order 31 current number of terms 2 current order 60 current number of terms 3 current order 88 current number of terms 4 current order 115 current number of terms 5 current order 141 current number of terms 6 current order 166 current number of terms 7 current order 190 current number of terms 8 current order 213 current number of terms 9 current order 235 current number of terms 10 current order 256 current number of terms 11 current order 276 current number of terms 12 current order 295 current number of terms 13 current order 313 current number of terms 14 current order 330 current number of terms 15 current order 346 current number of terms 16 current order 361 current number of terms 17 current order 375 current number of terms 18 current order 388 current number of terms 19 current order 400 current number of terms 20 current order 411 current number of terms all number of terms for function a/r is 411 expansion for cos(v) 1 current order 32 current number of terms 2 current order 62 current number of terms 3 current order 91 current number of terms 4 current order 119 current number of terms 5 current order 146 current number of terms 6 current order 172 current number of terms 7 current order 197 current number of terms 8 current order 221 current number of terms 9 current order 244 current number of terms 10 current order 266 current number of terms 11 current order 287 current number of terms 12 current order 307 current number of terms 13 current order 326 current number of terms 14 current order 344 current number of terms 15 current order 361 current number of terms 16 current order 377 current number of terms 17 current order 392 current number of terms 18 current order 406 current number of terms 19 current order 419 current number of terms 20 current order 431 current number of terms all number of terms for function cos(v) is 431 expansion for sin(v) 1 current order 31 current number of terms 1 current order 31 current number of terms 2 current order 61 current number of terms 2 current order 61 current number of terms 3 current order 90 current number of terms 3 current order 90 current number of terms 4 current order 118 current number of terms 4 current order 118 current number of terms 5 current order 145 current number of terms 5 current order 145 current number of terms 6 current order 171 current number of terms 6 current order 171 current number of terms 7 current order 196 current number of terms 7 current order 196 current number of terms 8 current order 220 current number of terms 8 current order 220 current number of terms 9 current order 243 current number of terms 9 current order 243 current number of terms 10 current order 265 current number of terms 10 current order 265 current number of terms 11 current order 286 current number of terms 11 current order 286 current number of terms 12 current order 306 current number of terms 12 current order 306 current number of terms 13 current order 325 current number of terms 13 current order 325 current number of terms 14 current order 343 current number of terms 14 current order 343 current number of terms 15 current order 360 current number of terms 15 current order 360 current number of terms 16 current order 376 current number of terms 16 current order 376 current number of terms 17 current order 391 current number of terms 17 current order 391 current number of terms 18 current order 405 current number of terms 18 current order 405 current number of terms 19 current order 418 current number of terms 19 current order 418 current number of terms all number of terms for function sin(v) is 418 to compare expansion for a/r maximum power of eccentricity is 2 v max e e M a/r dif num t 1 2 0.0010 245.0 0.9995767400901242 -0.0000000011394746 3 1 2 0.0010 46.0 1.0006946225467731 0.0000000009241892 3 1 2 0.0010 86.0 1.0000687659646676 0.0000000002410078 3 1 2 0.0010 166.0 0.9990305865070171 0.0000000007142998 3 1 2 0.0010 225.0 0.9992928941013643 -0.0000000008825508 3 1 2 0.0010 303.0 1.0005442311183872 0.0000000011799848 3 2 2 0.0050 164.0 0.9952148138349818 0.0000000788877305 3 2 2 0.0050 157.0 0.9954148060084122 0.0000000361835871 3 2 2 0.0050 179.0 0.9950256221052394 0.0000001241896541 3 2 2 0.0050 193.0 0.9951505257907836 0.0000000937364477 3 2 2 0.0050 13.0 1.0048944145631301 -0.0000000943880465 3 2 2 0.0050 108.0 0.9984348086190439 -0.0000001190157780 3 3 2 0.0200 211.0 0.9830456309803136 -0.0000011883692415 3 3 2 0.0200 298.0 1.0091562893528839 0.0000094647414456 3 3 2 0.0200 64.0 1.0085119039806464 0.0000092543650049 3 3 2 0.0200 290.0 1.0065259336761445 0.0000080514131213 3 3 2 0.0200 209.0 0.9827198596389680 -0.0000002860760627 3 3 2 0.0200 108.0 0.9935037457258199 -0.0000076924110688 3 4 2 0.1000 67.0 1.0310678034390929 0.0010587257052446 3 4 2 0.1000 185.0 0.9093509688853899 0.0008776388355576 3 4 2 0.1000 158.0 0.9141208887263093 0.0003541238203985 3 4 2 0.1000 183.0 0.9091845334898716 0.0008977319883538 3 4 2 0.1000 2.0 1.1110182786692516 -0.0011035554647437 3 4 2 0.1000 80.0 1.0075305730595873 0.0004373184992466 3 5 2 0.2000 33.0 1.1795733246052769 0.0044302547068399 3 5 2 0.2000 118.0 0.8922675712345798 -0.0085295999305878 3 5 2 0.2000 209.0 0.8458092932687161 0.0004635358727330 3 5 2 0.2000 253.0 0.9162571088949043 -0.0078929527416533 3 5 2 0.2000 336.0 1.2103215735526638 -0.0008472577697893 3 5 2 0.2000 214.0 0.8505442097766340 -0.0013674605510058 3 6 2 0.7000 1.0 3.3202605020989763 -1.1306656102501455 3 6 2 0.7000 270.0 0.7215270981226794 -0.2115270981226794 3 6 2 0.7000 59.0 0.9047415946224492 0.2257439920495022 3 6 2 0.7000 23.0 1.6320515434630991 0.3526844554785178 3 6 2 0.7000 181.0 0.5882480596516592 0.2015600589782239 3 6 2 0.7000 199.0 0.5928895575688011 0.1313727087789709 3 to compare expansion for a/r maximum power of eccentricity is 4 v max e e M a/r dif num t 1 4 0.0010 323.0 1.0007989106431857 0.0000000000000014 7 1 4 0.0010 246.0 0.9995925953471802 0.0000000000000020 7 1 4 0.0010 82.0 1.0001382113657412 -0.0000000000000013 7 1 4 0.0010 133.0 0.9993179328417061 -0.0000000000000004 7 1 4 0.0010 40.0 1.0007662174317291 0.0000000000000012 7 1 4 0.0010 63.0 1.0004534015463747 -0.0000000000000018 7 2 4 0.0050 301.0 1.0025633047417182 -0.0000000000041733 7 2 4 0.0050 186.0 0.9950517265652368 0.0000000000025293 7 2 4 0.0050 148.0 0.9957707461481143 -0.0000000000045386 7 2 4 0.0050 335.0 1.0045476305787349 0.0000000000034386 7 2 4 0.0050 333.0 1.0044697349449834 0.0000000000039160 7 2 4 0.0050 244.0 0.9977928970515831 0.0000000000058051 7 3 4 0.0200 214.0 0.9835716226166466 -0.0000000046257669 7 3 4 0.0200 84.0 1.0016966746598561 -0.0000000030586396 7 3 4 0.0200 85.0 1.0013470307624181 -0.0000000025449792 7 3 4 0.0200 183.0 0.9804174801384276 0.0000000029894181 7 3 4 0.0200 8.0 1.0201972295320033 -0.0000000021881097 7 3 4 0.0200 273.0 1.0006477133045986 -0.0000000014713728 7 4 4 0.1000 257.0 0.9693456559232819 0.0000194504993174 7 4 4 0.1000 206.0 0.9161131818285222 -0.0000103014034890 7 4 4 0.1000 296.0 1.0365341261765384 -0.0000205728986305 7 4 4 0.1000 152.0 0.9172329953951660 -0.0000116390276578 7 4 4 0.1000 119.0 0.9473498680638388 0.0000132511875610 7 4 4 0.1000 210.0 0.9184350389182397 -0.0000126594545439 7 5 4 0.2000 323.0 1.1643143670264494 0.0004581062981647 7 5 4 0.2000 187.0 0.8340535709148978 0.0002054805984626 7 5 4 0.2000 277.0 0.9848036840012538 -0.0001877126751308 7 5 4 0.2000 341.0 1.2244303002358279 0.0002459054098627 7 5 4 0.2000 265.0 0.9477092353439461 0.0004137415273207 7 5 4 0.2000 71.0 1.0273256251766651 -0.0006696552495990 7 6 4 0.7000 320.0 1.1473863985545064 -0.0665739103000242 7 6 4 0.7000 230.0 0.6225017365697936 -0.0827328874715219 7 6 4 0.7000 16.0 2.0239591618609683 0.3539193704242300 7 6 4 0.7000 75.0 0.7912035262786665 -0.0889567718275252 7 6 4 0.7000 6.0 2.9514499410545349 -0.2374715434477787 7 6 4 0.7000 132.0 0.6196331615913637 -0.1031470161630402 7 to compare expansion for a/r maximum power of eccentricity is 6 v max e e M a/r dif num t 1 6 0.0010 69.0 1.0003576237579307 0.0000000000000000 13 1 6 0.0010 0.0 1.0010010010010010 -0.0000000000000000 13 1 6 0.0010 13.0 1.0009752696118460 0.0000000000000000 13 1 6 0.0010 29.0 1.0008751495751916 0.0000000000000000 13 1 6 0.0010 170.0 0.9990161310891386 0.0000000000000000 13 1 6 0.0010 44.0 1.0007193738558034 0.0000000000000000 13 2 6 0.0050 113.0 0.9980291153974127 -0.0000000000000002 13 2 6 0.0050 273.0 1.0002367949413791 0.0000000000000001 13 2 6 0.0050 57.0 1.0027128788857880 -0.0000000000000001 13 2 6 0.0050 333.0 1.0044697349449834 0.0000000000000001 13 2 6 0.0050 149.0 0.9957259204792118 -0.0000000000000000 13 2 6 0.0050 191.0 0.9951149414840152 -0.0000000000000000 13 3 6 0.0200 142.0 0.9843408053268723 0.0000000000017537 13 3 6 0.0200 209.0 0.9827198596389680 -0.0000000000012310 13 3 6 0.0200 231.0 0.9873388917482848 0.0000000000036522 13 3 6 0.0200 37.0 1.0160787410929921 -0.0000000000015531 13 3 6 0.0200 321.0 1.0156210107571205 -0.0000000000022725 13 3 6 0.0200 150.0 0.9828802290193336 -0.0000000000009700 13 4 6 0.1000 139.0 0.9265063077882208 0.0000001882361385 13 4 6 0.1000 182.0 0.9091325203325457 0.0000000864600834 13 4 6 0.1000 150.0 0.9184350389182397 -0.0000000799278106 13 4 6 0.1000 208.0 0.9172329953951660 -0.0000001132428761 13 4 6 0.1000 104.0 0.9678453579514934 -0.0000004069812394 13 4 6 0.1000 45.0 1.0696878488589864 -0.0000003182943370 13 5 6 0.2000 47.0 1.1238547959259586 -0.0000429306718293 13 5 6 0.2000 346.0 1.2358090795291412 0.0000150096252255 13 5 6 0.2000 78.0 1.0018932369507415 0.0000462707077575 13 5 6 0.2000 36.0 1.1681978909107048 -0.0000203988834519 13 5 6 0.2000 256.0 0.9235950516679212 -0.0000487879480238 13 5 6 0.2000 181.0 0.8333480237750625 0.0000105397263196 13 6 6 0.7000 16.0 2.0239591618609683 0.2553381427719833 13 6 6 0.7000 350.0 2.5341262461163857 0.1898553342642242 13 6 6 0.7000 105.0 0.6732300319050133 -0.1720805416362722 13 6 6 0.7000 274.0 0.7376140630420878 -0.0976418746034885 13 6 6 0.7000 94.0 0.7069275517557318 -0.2296449293350511 13 6 6 0.7000 248.0 0.6558792149366664 -0.0362977089885217 13 to compare expansion for a/r maximum power of eccentricity is 8 v max e e M a/r dif num t 1 8 0.0010 79.0 1.0001898811762218 0.0000000000000000 21 1 8 0.0010 289.0 1.0003247791600905 0.0000000000000000 21 1 8 0.0010 137.0 0.9992687168529165 -0.0000000000000000 21 1 8 0.0010 325.0 1.0008194936697300 0.0000000000000000 21 1 8 0.0010 228.0 0.9993307658576943 -0.0000000000000000 21 1 8 0.0010 155.0 0.9990943348222454 -0.0000000000000000 21 2 8 0.0050 56.0 1.0027864525445835 0.0000000000000000 21 2 8 0.0050 213.0 0.9958168500413997 0.0000000000000000 21 2 8 0.0050 299.0 1.0024106518622263 0.0000000000000000 21 2 8 0.0050 247.0 0.9980291153974127 0.0000000000000000 21 2 8 0.0050 230.0 0.9967818518286516 -0.0000000000000000 21 2 8 0.0050 354.0 1.0049971819298362 -0.0000000000000000 21 3 8 0.0200 169.0 0.9807318661752857 -0.0000000000000006 21 3 8 0.0200 248.0 0.9922287678727977 0.0000000000000005 21 3 8 0.0200 0.0 1.0204081632653061 -0.0000000000000005 21 3 8 0.0200 283.0 1.0041337998323404 -0.0000000000000043 21 3 8 0.0200 206.0 0.9822693304631657 0.0000000000000005 21 3 8 0.0200 286.0 1.0051667093001774 -0.0000000000000036 21 4 8 0.1000 80.0 1.0075305730595873 -0.0000000081690041 21 4 8 0.1000 275.0 0.9987291075013221 -0.0000000044801010 21 4 8 0.1000 122.0 0.9437325601968588 -0.0000000061884571 21 4 8 0.1000 13.0 1.1072313035890334 0.0000000017193804 21 4 8 0.1000 197.0 0.9120956083147637 -0.0000000016258694 21 4 8 0.1000 208.0 0.9172329953951660 0.0000000015608788 21 5 8 0.2000 286.0 1.0162200167462296 -0.0000041421906724 21 5 8 0.2000 328.0 1.1832608711134792 -0.0000021965285379 21 5 8 0.2000 282.0 1.0018932369507415 -0.0000042907184091 21 5 8 0.2000 352.0 1.2452822459256598 0.0000002686007148 21 5 8 0.2000 74.0 1.0162200167462296 -0.0000041421906724 21 5 8 0.2000 161.0 0.8386589697658947 -0.0000006967482804 21 6 8 0.7000 141.0 0.6084966997623370 0.0939966152423018 21 6 8 0.7000 104.0 0.6759477219158302 0.1168387195349886 21 6 8 0.7000 131.0 0.6210486546185979 -0.0226889055395300 21 6 8 0.7000 225.0 0.6156065684047488 0.0433495370083803 21 6 8 0.7000 147.0 0.6025644909463816 0.0741420369467310 21 6 8 0.7000 78.0 0.7750438467316507 -0.1842837782072537 21 to compare expansion for a/r maximum power of eccentricity is 10 v max e e M a/r dif num t 1 10 0.0010 228.0 0.9993307658576943 -0.0000000000000000 31 1 10 0.0010 21.0 1.0009343239652554 0.0000000000000000 31 1 10 0.0010 56.0 1.0005588171257288 0.0000000000000000 31 1 10 0.0010 344.0 1.0009621103769504 0.0000000000000000 31 1 10 0.0010 304.0 1.0005588171257288 0.0000000000000000 31 1 10 0.0010 14.0 1.0009711793890712 -0.0000000000000000 31 2 10 0.0050 288.0 1.0015247413833643 0.0000000000000000 31 2 10 0.0050 225.0 0.9964645757483716 -0.0000000000000000 31 2 10 0.0050 354.0 1.0049971819298362 -0.0000000000000000 31 2 10 0.0050 308.0 1.0030721205577778 0.0000000000000000 31 2 10 0.0050 244.0 0.9977928970515831 0.0000000000000000 31 2 10 0.0050 2.0 1.0050220180959831 0.0000000000000000 31 3 10 0.0200 249.0 0.9925438156692191 0.0000000000000000 31 3 10 0.0200 161.0 0.9814008876153227 -0.0000000000000000 31 3 10 0.0200 172.0 0.9805720391867985 -0.0000000000000000 31 3 10 0.0200 213.0 0.9833913700622404 0.0000000000000000 31 3 10 0.0200 215.0 0.9837567386221650 -0.0000000000000000 31 3 10 0.0200 129.0 0.9873388917482848 -0.0000000000000000 31 4 10 0.1000 72.0 1.0219521872564930 0.0000000000522355 31 4 10 0.1000 343.0 1.1045281633218656 0.0000000000063197 31 4 10 0.1000 156.0 0.9150757644679907 0.0000000000316252 31 4 10 0.1000 6.0 1.1102773839789205 0.0000000000038737 31 4 10 0.1000 344.0 1.1052673107963259 0.0000000000116433 31 4 10 0.1000 153.0 0.9166627989634529 0.0000000000412279 31 5 10 0.2000 356.0 1.2488127249842104 -0.0000000080138626 31 5 10 0.2000 112.0 0.9047910735167424 0.0000001917044024 31 5 10 0.2000 200.0 0.8392369959122477 0.0000000136676843 31 5 10 0.2000 29.0 1.1939565499432339 -0.0000000940495482 31 5 10 0.2000 309.0 1.1072801382799136 -0.0000000098572916 31 5 10 0.2000 176.0 0.8335684218312217 0.0000000064926582 31 6 10 0.7000 335.0 1.5488025371105617 -0.1002185428850204 31 6 10 0.7000 18.0 1.8929237885092868 -0.0974845125244093 31 6 10 0.7000 7.0 2.8466562773538598 0.0756469684784216 31 6 10 0.7000 133.0 0.6182546828314210 -0.1102229122384101 31 6 10 0.7000 127.0 0.6270925752448754 -0.0506739957033217 31 6 10 0.7000 46.0 1.0512039052062233 0.0084210035045635 31 to compare expansion for a/r maximum power of eccentricity is 12 v max e e M a/r dif num t 1 12 0.0010 75.0 1.0002579521928086 -0.0000000000000000 43 1 12 0.0010 309.0 1.0006291113971630 0.0000000000000000 43 1 12 0.0010 171.0 0.9990132618377609 -0.0000000000000000 43 1 12 0.0010 252.0 0.9996901749380815 -0.0000000000000000 43 1 12 0.0010 39.0 1.0007773532639766 0.0000000000000000 43 1 12 0.0010 283.0 1.0002240515253156 0.0000000000000000 43 2 12 0.0050 62.0 1.0023332306108149 0.0000000000000000 43 2 12 0.0050 354.0 1.0049971819298362 -0.0000000000000000 43 2 12 0.0050 130.0 0.9967818518286516 -0.0000000000000000 43 2 12 0.0050 21.0 1.0046865299384090 0.0000000000000000 43 2 12 0.0050 77.0 1.0011021941136618 0.0000000000000000 43 2 12 0.0050 211.0 0.9957259204792118 0.0000000000000000 43 3 12 0.0200 141.0 0.9845449066125488 0.0000000000000000 43 3 12 0.0200 38.0 1.0158523296088685 -0.0000000000000000 43 3 12 0.0200 266.0 0.9982109597550260 -0.0000000000000000 43 3 12 0.0200 131.0 0.9868311572333555 0.0000000000000000 43 3 12 0.0200 9.0 1.0201413445746861 0.0000000000000000 43 3 12 0.0200 238.0 0.9892356352737227 0.0000000000000000 43 4 12 0.1000 191.0 0.9103493625025662 -0.0000000000001717 43 4 12 0.1000 218.0 0.9240613297260037 -0.0000000000009813 43 4 12 0.1000 337.0 1.0992466461639656 -0.0000000000005341 43 4 12 0.1000 302.0 1.0473702323604039 0.0000000000004382 43 4 12 0.1000 46.0 1.0680580014436096 -0.0000000000014534 43 4 12 0.1000 184.0 0.9092573502356086 0.0000000000000030 43 5 12 0.2000 328.0 1.1832608711134792 0.0000000086241485 43 5 12 0.2000 196.0 0.8371053390362785 0.0000000006292578 43 5 12 0.2000 264.0 0.9448730209404420 0.0000000288292844 43 5 12 0.2000 5.0 1.2481471917689539 0.0000000005134853 43 5 12 0.2000 326.0 1.1758311061390831 0.0000000104616165 43 5 12 0.2000 59.0 1.0743680951809990 0.0000000115253475 43 6 12 0.7000 338.0 1.6777118021040706 -0.0291070122071749 43 6 12 0.7000 315.0 1.0656435262833895 -0.1927128439447023 43 6 12 0.7000 338.0 1.6777118021040706 -0.0291070122071749 43 6 12 0.7000 216.0 0.6053887574296657 -0.0625151882225216 43 6 12 0.7000 92.0 0.7140519934717104 0.2355801932174908 43 6 12 0.7000 44.0 1.0806697603838394 -0.1861311170115739 43 to compare expansion for a/r maximum power of eccentricity is 14 v max e e M a/r dif num t 1 14 0.0010 276.0 1.0001035499565019 0.0000000000000000 57 1 14 0.0010 217.0 0.9992016406290807 0.0000000000000000 57 1 14 0.0010 173.0 0.9990084232187283 0.0000000000000000 57 1 14 0.0010 286.0 1.0002747884380975 0.0000000000000000 57 1 14 0.0010 148.0 0.9991523904976253 -0.0000000000000000 57 1 14 0.0010 147.0 0.9991617364484940 -0.0000000000000000 57 2 14 0.0050 303.0 1.0027128788857880 0.0000000000000000 57 2 14 0.0050 353.0 1.0049871044635679 0.0000000000000000 57 2 14 0.0050 166.0 0.9951705059963266 0.0000000000000000 57 2 14 0.0050 257.0 0.9988528675845884 0.0000000000000000 57 2 14 0.0050 353.0 1.0049871044635679 0.0000000000000000 57 2 14 0.0050 71.0 1.0016080178509038 0.0000000000000000 57 3 14 0.0200 76.0 1.0044791673562872 -0.0000000000000000 57 3 14 0.0200 336.0 1.0185403677038036 0.0000000000000000 57 3 14 0.0200 264.0 0.9975213010352886 -0.0000000000000000 57 3 14 0.0200 22.0 1.0188341128589543 0.0000000000000000 57 3 14 0.0200 216.0 0.9839466725282574 0.0000000000000000 57 3 14 0.0200 282.0 1.0037875147355248 0.0000000000000000 57 4 14 0.1000 266.0 0.9835158968617861 -0.0000000000000682 57 4 14 0.1000 101.0 0.9723926328682325 -0.0000000000000390 57 4 14 0.1000 351.0 1.1092407820277291 0.0000000000000021 57 4 14 0.1000 71.0 1.0237727011892201 -0.0000000000000584 57 4 14 0.1000 306.0 1.0544561212267022 0.0000000000000474 57 4 14 0.1000 345.0 1.1059645648157559 -0.0000000000000040 57 5 14 0.2000 236.0 0.8810561798566203 -0.0000000013494347 57 5 14 0.2000 182.0 0.8333920971719074 0.0000000000168036 57 5 14 0.2000 126.0 0.8776037792327643 -0.0000000011216477 57 5 14 0.2000 73.0 1.0198885992767916 -0.0000000008517876 57 5 14 0.2000 109.0 0.9115568623133125 0.0000000019866111 57 5 14 0.2000 355.0 1.2481471917689539 0.0000000000420268 57 6 14 0.7000 358.0 3.2820858104577111 -0.0061056208574831 57 6 14 0.7000 22.0 1.6777118021040706 0.0516398996730427 57 6 14 0.7000 49.0 1.0110908699422883 0.1802186439144362 57 6 14 0.7000 242.0 0.6431101602744458 -0.0881341022397311 57 6 14 0.7000 311.0 1.0110908699422883 0.1802186439144362 57 6 14 0.7000 273.0 0.7334430955340661 -0.0410552763212049 57 to compare expansion for a/r maximum power of eccentricity is 16 v max e e M a/r dif num t 1 16 0.0010 331.0 1.0008751495751916 0.0000000000000000 73 1 16 0.0010 189.0 0.9990132618377609 -0.0000000000000000 73 1 16 0.0010 7.0 1.0009935173744319 0.0000000000000000 73 1 16 0.0010 90.0 0.9999990000016667 -0.0000000000000000 73 1 16 0.0010 285.0 1.0002579521928086 -0.0000000000000000 73 1 16 0.0010 312.0 1.0006690250828405 0.0000000000000000 73 2 16 0.0050 355.0 1.0050057145326983 0.0000000000000000 73 2 16 0.0050 31.0 1.0042975519712825 0.0000000000000000 73 2 16 0.0050 318.0 1.0037182422299063 0.0000000000000000 73 2 16 0.0050 61.0 1.0024106518622263 0.0000000000000000 73 2 16 0.0050 11.0 1.0049314185212892 -0.0000000000000000 73 2 16 0.0050 211.0 0.9957259204792118 0.0000000000000000 73 3 16 0.0200 281.0 1.0034404219775350 0.0000000000000000 73 3 16 0.0200 49.0 1.0130571092286811 0.0000000000000000 73 3 16 0.0200 96.0 0.9975213010352886 -0.0000000000000000 73 3 16 0.0200 121.0 0.9895208542574694 0.0000000000000000 73 3 16 0.0200 274.0 1.0009973411838621 0.0000000000000000 73 3 16 0.0200 34.0 1.0167277156452699 -0.0000000000000000 73 4 16 0.1000 204.0 0.9150757644679907 -0.0000000000000001 73 4 16 0.1000 356.0 1.1107400758570167 0.0000000000000000 73 4 16 0.1000 315.0 1.0696878488589864 0.0000000000000006 73 4 16 0.1000 252.0 0.9620042723228157 -0.0000000000000014 73 4 16 0.1000 101.0 0.9723926328682325 0.0000000000000004 73 4 16 0.1000 134.0 0.9309829173009518 -0.0000000000000005 73 5 16 0.2000 296.0 1.0543179731093378 -0.0000000000023252 73 5 16 0.2000 351.0 1.2440430102902372 0.0000000000016092 73 5 16 0.2000 282.0 1.0018932369507415 -0.0000000000852771 73 5 16 0.2000 335.0 1.2072133046145660 0.0000000000244151 73 5 16 0.2000 231.0 0.8726870529719687 -0.0000000000581691 73 5 16 0.2000 223.0 0.8610780140522219 -0.0000000000171995 73 6 16 0.7000 295.0 0.8558051894750491 0.2055201323557852 73 6 16 0.7000 163.0 0.5919538722724934 0.0079754937132265 73 6 16 0.7000 80.0 0.7649571442384913 -0.2901454990573262 73 6 16 0.7000 245.0 0.6492689395204227 0.1074410651256223 73 6 16 0.7000 236.0 0.6320444580331692 0.0308162031905539 73 6 16 0.7000 47.0 1.0373183639855512 0.0855532796494007 73 to compare expansion for a/r maximum power of eccentricity is 18 v max e e M a/r dif num t 1 18 0.0010 223.0 0.9992687168529165 -0.0000000000000000 91 1 18 0.0010 177.0 0.9990023640017918 0.0000000000000000 91 1 18 0.0010 27.0 1.0008915943734444 0.0000000000000000 91 1 18 0.0010 330.0 1.0008665252946965 -0.0000000000000000 91 1 18 0.0010 68.0 1.0003738861793395 0.0000000000000000 91 1 18 0.0010 346.0 1.0009711793890712 -0.0000000000000000 91 2 18 0.0050 54.0 1.0029310573022629 -0.0000000000000000 91 2 18 0.0050 79.0 1.0009307866070976 -0.0000000000000000 91 2 18 0.0050 190.0 0.9950993475942893 0.0000000000000000 91 2 18 0.0050 52.0 1.0030721205577778 0.0000000000000000 91 2 18 0.0050 302.0 1.0026384884898983 0.0000000000000000 91 2 18 0.0050 315.0 1.0035354225849951 0.0000000000000000 91 3 18 0.0200 80.0 1.0030926312774433 -0.0000000000000000 91 3 18 0.0200 50.0 1.0127776648152660 0.0000000000000000 91 3 18 0.0200 149.0 0.9830456309803136 0.0000000000000000 91 3 18 0.0200 165.0 0.9810225561163684 0.0000000000000000 91 3 18 0.0200 156.0 0.9819948206166274 0.0000000000000000 91 3 18 0.0200 110.0 0.9928613866722429 0.0000000000000000 91 4 18 0.1000 241.0 0.9473498680638388 -0.0000000000000000 91 4 18 0.1000 324.0 1.0834100063107812 0.0000000000000000 91 4 18 0.1000 95.0 0.9818854816653619 -0.0000000000000000 91 4 18 0.1000 281.0 1.0093140958988717 0.0000000000000000 91 4 18 0.1000 350.0 1.1088049478217295 -0.0000000000000000 91 4 18 0.1000 145.0 0.9217985983853544 0.0000000000000000 91 5 18 0.2000 343.0 1.2293343627996841 0.0000000000001570 91 5 18 0.2000 112.0 0.9047910735167424 -0.0000000000022260 91 5 18 0.2000 36.0 1.1681978909107048 0.0000000000011899 91 5 18 0.2000 252.0 0.9138879100126688 0.0000000000119932 91 5 18 0.2000 322.0 1.1603911052927261 0.0000000000035852 91 5 18 0.2000 145.0 0.8515858469042395 0.0000000000009066 91 6 18 0.7000 328.0 1.3229744406046419 -0.0052169418729405 91 6 18 0.7000 214.0 0.6034749898113578 0.0261194986391425 91 6 18 0.7000 156.0 0.5957059640210532 -0.0109526410154533 91 6 18 0.7000 280.0 0.7649571442384913 0.2845305066826978 91 6 18 0.7000 293.0 0.8413705245681957 -0.1845059139814616 91 6 18 0.7000 298.0 0.8791412535218840 0.1476916435329510 91 to compare expansion for a/r maximum power of eccentricity is 20 v max e e M a/r dif num t 1 20 0.0010 188.0 0.9990106922898089 0.0000000000000000 111 1 20 0.0010 54.0 1.0005874750909113 0.0000000000000000 111 1 20 0.0010 21.0 1.0009343239652554 0.0000000000000000 111 1 20 0.0010 92.0 0.9999641030628567 0.0000000000000000 111 1 20 0.0010 50.0 1.0006426129056868 0.0000000000000000 111 1 20 0.0010 108.0 0.9996901749380815 -0.0000000000000000 111 2 20 0.0050 300.0 1.0024873512545685 -0.0000000000000000 111 2 20 0.0050 125.0 0.9971237115406736 -0.0000000000000000 111 2 20 0.0050 203.0 0.9954148060084122 0.0000000000000000 111 2 20 0.0050 174.0 0.9950517265652368 0.0000000000000000 111 2 20 0.0050 64.0 1.0021763197280381 0.0000000000000000 111 2 20 0.0050 351.0 1.0049623284589456 0.0000000000000000 111 3 20 0.0200 158.0 0.9817412969677465 0.0000000000000000 111 3 20 0.0200 46.0 1.0138716119503900 -0.0000000000000000 111 3 20 0.0200 255.0 0.9944839780730295 0.0000000000000000 111 3 20 0.0200 194.0 0.9809416183939668 -0.0000000000000000 111 3 20 0.0200 232.0 0.9875986630332924 -0.0000000000000000 111 3 20 0.0200 313.0 1.0136041794589283 0.0000000000000000 111 4 20 0.1000 57.0 1.0491548653411401 0.0000000000000000 111 4 20 0.1000 140.0 0.9256711352073344 0.0000000000000000 111 4 20 0.1000 1.0 1.1110878983944988 -0.0000000000000000 111 4 20 0.1000 312.0 1.0647460575197020 -0.0000000000000000 111 4 20 0.1000 257.0 0.9693456559232819 -0.0000000000000000 111 4 20 0.1000 206.0 0.9161131818285222 -0.0000000000000000 111 5 20 0.2000 277.0 0.9848036840012538 -0.0000000000015563 111 5 20 0.2000 168.0 0.8354523089314167 0.0000000000000118 111 5 20 0.2000 70.0 1.0310926061819229 0.0000000000004806 111 5 20 0.2000 315.0 1.1321049336114464 -0.0000000000005015 111 5 20 0.2000 350.0 1.2426647954481870 -0.0000000000000138 111 5 20 0.2000 55.0 1.0907386637614142 0.0000000000008102 111 6 20 0.7000 5.0 3.0517073537897610 0.0030599259190960 111 6 20 0.7000 72.0 0.8087205004104631 0.2993609565296140 111 6 20 0.7000 188.0 0.5890537003750700 0.0001388080613721 111 6 20 0.7000 295.0 0.8558051894750491 -0.1350371797495821 111 6 20 0.7000 352.0 2.7406338859328705 -0.0054265347985115 111 6 20 0.7000 85.0 0.7418896423522091 -0.2114694921274627 111 to compare expansion for a/r maximum power of eccentricity is 22 v max e e M a/r dif num t 1 22 0.0010 60.0 1.0004994988120015 0.0000000000000000 131 1 22 0.0010 126.0 0.9994119068731486 0.0000000000000000 131 1 22 0.0010 315.0 1.0007071058959690 0.0000000000000000 131 1 22 0.0010 162.0 0.9990497519584656 0.0000000000000000 131 1 22 0.0010 88.0 1.0000339018123485 0.0000000000000000 131 1 22 0.0010 189.0 0.9990132618377609 -0.0000000000000000 131 2 22 0.0050 321.0 1.0038908508056272 -0.0000000000000000 131 2 22 0.0050 141.0 0.9961195431697016 0.0000000000000000 131 2 22 0.0050 92.0 0.9998005796917615 0.0000000000000000 131 2 22 0.0050 82.0 1.0006717755014911 0.0000000000000000 131 2 22 0.0050 302.0 1.0026384884898983 0.0000000000000000 131 2 22 0.0050 110.0 0.9982708755987658 -0.0000000000000000 131 3 22 0.0200 85.0 1.0013470307624181 0.0000000000000000 131 3 22 0.0200 343.0 1.0194624525712728 0.0000000000000000 131 3 22 0.0200 66.0 1.0078581343117915 0.0000000000000000 131 3 22 0.0200 22.0 1.0188341128589543 0.0000000000000000 131 3 22 0.0200 345.0 1.0196703851002273 0.0000000000000000 131 3 22 0.0200 237.0 0.9889538342301445 0.0000000000000000 131 4 22 0.1000 327.0 1.0875349661509500 0.0000000000000000 131 4 22 0.1000 141.0 0.9248561277803004 0.0000000000000000 131 4 22 0.1000 335.0 1.0971793292535520 0.0000000000000000 131 4 22 0.1000 325.0 1.0848129314690287 0.0000000000000000 131 4 22 0.1000 58.0 1.0473702323604039 -0.0000000000000000 131 4 22 0.1000 163.0 0.9120956083147637 -0.0000000000000000 131 5 22 0.2000 80.0 0.9949457121163425 0.0000000000000738 131 5 22 0.2000 109.0 0.9115568623133125 0.0000000000001328 131 5 22 0.2000 268.0 0.9564541466418038 0.0000000000000809 131 5 22 0.2000 243.0 0.8942626430032898 -0.0000000000001376 131 5 22 0.2000 30.0 1.1904564156256977 -0.0000000000000206 131 5 22 0.2000 111.0 0.9070086042546107 0.0000000000001265 131 6 22 0.7000 138.0 0.6118987492708944 0.0414053174031911 131 6 22 0.7000 343.0 1.9562457296176466 -0.1115544277536620 131 6 22 0.7000 147.0 0.6025644909463816 -0.0242323826954077 131 6 22 0.7000 104.0 0.6759477219158302 0.1779424231267863 131 6 22 0.7000 305.0 0.9429637990048892 -0.1773458345654082 131 6 22 0.7000 48.0 1.0239567057855231 0.0385906446171041 131 to compare expansion for a/r maximum power of eccentricity is 24 v max e e M a/r dif num t 1 24 0.0010 349.0 1.0009825551887537 0.0000000000000000 151 1 24 0.0010 332.0 1.0008835067923013 0.0000000000000000 151 1 24 0.0010 303.0 1.0005442311183872 0.0000000000000000 151 1 24 0.0010 292.0 1.0003738861793395 0.0000000000000000 151 1 24 0.0010 179.0 0.9990011506981893 -0.0000000000000000 151 1 24 0.0010 328.0 1.0008484862427342 0.0000000000000000 151 2 24 0.0050 269.0 0.9998877618684898 0.0000000000000000 151 2 24 0.0050 165.0 0.9951919373956524 0.0000000000000000 151 2 24 0.0050 201.0 0.9953506271673956 0.0000000000000000 151 2 24 0.0050 359.0 1.0050243486823364 0.0000000000000000 151 2 24 0.0050 53.0 1.0030020428459257 -0.0000000000000000 151 2 24 0.0050 299.0 1.0024106518622263 0.0000000000000000 151 3 24 0.0200 90.0 0.9996002664662922 -0.0000000000000000 151 3 24 0.0200 111.0 0.9925438156692191 0.0000000000000000 151 3 24 0.0200 67.0 1.0075280025807290 -0.0000000000000000 151 3 24 0.0200 264.0 0.9975213010352886 -0.0000000000000000 151 3 24 0.0200 255.0 0.9944839780730295 0.0000000000000000 151 3 24 0.0200 354.0 1.0202894073032956 0.0000000000000000 151 4 24 0.1000 261.0 0.9754997438161936 0.0000000000000000 151 4 24 0.1000 19.0 1.1029264482289734 -0.0000000000000000 151 4 24 0.1000 150.0 0.9184350389182397 -0.0000000000000000 151 4 24 0.1000 57.0 1.0491548653411401 0.0000000000000000 151 4 24 0.1000 114.0 0.9537459263819251 0.0000000000000000 151 4 24 0.1000 48.0 1.0647460575197020 -0.0000000000000000 151 5 24 0.2000 127.0 0.8759301363328813 0.0000000000001457 151 5 24 0.2000 76.0 1.0089859795101419 0.0000000000001939 151 5 24 0.2000 358.0 1.2497026871408830 -0.0000000000001845 151 5 24 0.2000 161.0 0.8386589697658947 0.0000000000001208 151 5 24 0.2000 330.0 1.1904564156256977 -0.0000000000000418 151 5 24 0.2000 131.0 0.8695817040910687 0.0000000000000791 151 6 24 0.7000 315.0 1.0656435262833895 -0.1376052540510271 151 6 24 0.7000 213.0 0.6025644909463816 0.0347060455264564 151 6 24 0.7000 250.0 0.6605512366992809 0.1107465521380393 151 6 24 0.7000 205.0 0.5963525733560747 -0.0193653928663198 151 6 24 0.7000 202.0 0.5944966827856131 -0.0222130237877680 151 6 24 0.7000 213.0 0.6025644909463816 0.0347060455264564 151 to compare expansion for cos(v) maximum power of eccentricity is 2 v max e e M cos(v) dif num t 1 2 0.0010 8.0 0.9902292439733893 0.0000000001511819 5 1 2 0.0010 264.0 -0.1065061431088648 -0.0000000025208826 5 1 2 0.0010 135.0 -0.7081051915298049 0.0000000013335151 5 1 2 0.0010 182.0 -0.9993932575010006 0.0000000000097128 5 1 2 0.0010 135.0 -0.7081051915298049 0.0000000013335151 5 1 2 0.0010 78.0 0.2059972523137577 -0.0000000021127020 5 2 2 0.0050 143.0 -0.8022249692702005 0.0000001867242937 5 2 2 0.0050 133.0 -0.6873062577329961 0.0000001537358198 5 2 2 0.0050 198.0 -0.9520012970872578 0.0000000827682791 5 2 2 0.0050 245.0 -0.4307930707195395 -0.0000000762671168 5 2 2 0.0050 110.0 -0.3508162346248393 -0.0000001546354118 5 2 2 0.0050 152.0 -0.8851298901172858 0.0000001548137323 5 3 2 0.0200 245.0 -0.4548446523315770 -0.0000045167632398 5 3 2 0.0200 86.0 0.0298471123694256 -0.0000209506741845 5 3 2 0.0200 16.0 0.9580867029450010 0.0000044959261356 5 3 2 0.0200 238.0 -0.5580029490193399 0.0000022603721740 5 3 2 0.0200 18.0 0.9470679018065005 0.0000054823073508 5 3 2 0.0200 325.0 0.8054953720585246 0.0000119881067544 5 4 2 0.1000 108.0 -0.4761577040041243 -0.0011831074348816 5 4 2 0.1000 257.0 -0.4034780063595090 -0.0017418988535935 5 4 2 0.1000 260.0 -0.3580058371766028 -0.0020330605701654 5 4 2 0.1000 130.0 -0.7442756097584060 0.0010973287067221 5 4 2 0.1000 282.0 0.0099314903071578 -0.0023259358636486 5 4 2 0.1000 3.0 0.9979328410236990 0.0000257948334086 5 5 2 0.2000 356.0 0.9943010799242100 0.0004428438552574 5 5 2 0.2000 24.0 0.8095435530527861 0.0106242450145421 5 5 2 0.2000 121.0 -0.7447984188745861 0.0039810738422620 5 5 2 0.2000 99.0 -0.5043184756260038 -0.0148581692581677 5 5 2 0.2000 224.0 -0.8604239687853167 0.0105452360885536 5 5 2 0.2000 224.0 -0.8604239687853167 0.0105452360885536 5 6 2 0.7000 299.0 -0.7820310362849977 -0.6218486626261609 5 6 2 0.7000 120.0 -0.9628379515047125 0.2397129515047125 5 6 2 0.7000 340.0 -0.1329717002633740 0.6665148740243350 5 6 2 0.7000 182.0 -0.9999627945299464 0.0015508012652435 5 6 2 0.7000 330.0 -0.4239634411675994 0.4625923411158662 5 6 2 0.7000 77.0 -0.8600756241032552 -0.7150462882355752 5 to compare expansion for cos(v) maximum power of eccentricity is 4 v max e e M cos(v) dif num t 1 4 0.0010 254.0 -0.2774842560709222 0.0000000000000012 10 1 4 0.0010 26.0 0.8984089293871026 0.0000000000000010 10 1 4 0.0010 191.0 -0.9816998390436178 0.0000000000000006 10 1 4 0.0010 214.0 -0.8296618008511702 -0.0000000000000000 10 1 4 0.0010 282.0 0.2059972523137577 0.0000000000000026 10 1 4 0.0010 324.0 0.8083247520893944 -0.0000000000000004 10 2 4 0.0050 96.0 -0.1144072558928394 0.0000000000130604 10 2 4 0.0050 190.0 -0.9851059778801175 0.0000000000014708 10 2 4 0.0050 245.0 -0.4307930707195395 -0.0000000000060866 10 2 4 0.0050 159.0 -0.9348513196567249 0.0000000000036181 10 2 4 0.0050 190.0 -0.9851059778801175 0.0000000000014708 10 2 4 0.0050 180.0 -1.0000000000000000 0.0000000000000000 10 3 4 0.0200 307.0 0.5756055059052161 -0.0000000111259136 10 3 4 0.0200 348.0 0.9763397149816150 0.0000000020908128 10 3 4 0.0200 183.0 -0.9987343426813905 0.0000000001517909 10 3 4 0.0200 288.0 0.2723459575478414 0.0000000017311000 10 3 4 0.0200 300.0 0.4693254315115437 -0.0000000096365437 10 3 4 0.0200 306.0 0.5609073911936467 -0.0000000111876990 10 4 4 0.1000 350.0 0.9771689834351221 0.0000054116920976 10 4 4 0.1000 66.0 0.2256261980409658 -0.0000115571776608 10 4 4 0.1000 64.0 0.2616878491477306 -0.0000180366828875 10 4 4 0.1000 52.0 0.4735872514188702 -0.0000359070405649 10 4 4 0.1000 309.0 0.4906428868829772 -0.0000354967128957 10 4 4 0.1000 318.0 0.6371745363522530 -0.0000213526726089 10 5 4 0.2000 77.0 -0.1739759117992860 0.0010571390028230 10 5 4 0.2000 173.0 -0.9965428596084904 0.0000633034833332 10 5 4 0.2000 249.0 -0.6463586995778689 -0.0004705630096775 10 5 4 0.2000 321.0 0.5508720207512278 -0.0005837496182656 10 5 4 0.2000 226.0 -0.8471415986190301 -0.0006248385165500 10 5 4 0.2000 102.0 -0.5423346218815131 0.0004503445445280 10 6 4 0.7000 291.0 -0.8254949655282931 0.4273387640024393 10 6 4 0.7000 212.0 -0.9902013146934966 0.0886681070323539 10 6 4 0.7000 296.0 -0.7995593452162747 0.2229286251685013 10 6 4 0.7000 100.0 -0.9276968516505007 0.0318878650709949 10 6 4 0.7000 141.0 -0.9852381187445831 -0.0190164058958479 10 6 4 0.7000 241.0 -0.9614457170707511 -0.3954691878033145 10 to compare expansion for cos(v) maximum power of eccentricity is 6 v max e e M cos(v) dif num t 1 6 0.0010 45.0 0.7061051888631431 0.0000000000000000 17 1 6 0.0010 121.0 -0.5165058437189148 0.0000000000000000 17 1 6 0.0010 115.0 -0.4242594866158520 -0.0000000000000000 17 1 6 0.0010 135.0 -0.7081051915298049 -0.0000000000000000 17 1 6 0.0010 284.0 0.2400379249983334 -0.0000000000000000 17 1 6 0.0010 222.0 -0.7440388011610759 0.0000000000000000 17 2 6 0.0050 300.0 0.4924578141574227 0.0000000000000005 17 2 6 0.0050 20.0 0.9385103772607604 0.0000000000000000 17 2 6 0.0050 294.0 0.3983528981757386 0.0000000000000005 17 2 6 0.0050 13.0 0.9738584405532072 0.0000000000000001 17 2 6 0.0050 2.0 0.9993785091061411 0.0000000000000000 17 2 6 0.0050 11.0 0.9812590471652319 0.0000000000000001 17 3 6 0.0200 210.0 -0.8756461536137074 -0.0000000000028182 17 3 6 0.0200 5.0 0.9958767356018363 0.0000000000002959 17 3 6 0.0200 11.0 0.9801042451808735 0.0000000000010295 17 3 6 0.0200 275.0 0.0473245975056577 -0.0000000000102755 17 3 6 0.0200 100.0 -0.2121210475121309 -0.0000000000048192 17 3 6 0.0200 213.0 -0.8500993242892256 -0.0000000000038669 17 4 6 0.1000 115.0 -0.5709367263242782 0.0000007135583907 17 4 6 0.1000 131.0 -0.7543163293497671 -0.0000000069067338 17 4 6 0.1000 63.0 0.2796803888275807 0.0000007598685574 17 4 6 0.1000 287.0 0.0993290906546117 0.0000001609876990 17 4 6 0.1000 152.0 -0.9193933455878567 -0.0000001362043190 17 4 6 0.1000 134.0 -0.7832691187205770 -0.0000001645357173 17 5 6 0.2000 246.0 -0.6777517941461749 0.0000869887914125 17 5 6 0.2000 135.0 -0.8538629228979680 -0.0000281457087803 17 5 6 0.2000 267.0 -0.4232009661693509 -0.0000932393102521 17 5 6 0.2000 322.0 0.5698773054050852 -0.0000497665158481 17 5 6 0.2000 86.0 -0.3199800604426133 -0.0001147161182200 17 5 6 0.2000 288.0 -0.0867646229713530 0.0000170156638793 17 6 6 0.7000 28.0 -0.3786054193529967 -0.3458757749860511 17 6 6 0.7000 5.0 0.7948153577611116 0.0880476784554190 17 6 6 0.7000 359.0 0.9904755086721113 0.0047289918367617 17 6 6 0.7000 218.0 -0.9860163203692475 -0.1827364342134351 17 6 6 0.7000 350.0 0.4177205507419381 0.1466539106274591 17 6 6 0.7000 193.0 -0.9984209316604257 0.0440884611316216 17 to compare expansion for cos(v) maximum power of eccentricity is 8 v max e e M cos(v) dif num t 1 8 0.0010 122.0 -0.5313559206224471 -0.0000000000000000 26 1 8 0.0010 17.0 0.9561334250714312 -0.0000000000000000 26 1 8 0.0010 314.0 0.6936218521504998 0.0000000000000000 26 1 8 0.0010 19.0 0.9453061346343447 0.0000000000000000 26 1 8 0.0010 64.0 0.4367538922315057 0.0000000000000000 26 1 8 0.0010 14.0 0.9701784178917950 -0.0000000000000000 26 2 8 0.0050 40.0 0.7618768906104397 0.0000000000000000 26 2 8 0.0050 103.0 -0.2344207474202398 -0.0000000000000000 26 2 8 0.0050 40.0 0.7618768906104397 0.0000000000000000 26 2 8 0.0050 161.0 -0.9465673375023914 0.0000000000000000 26 2 8 0.0050 245.0 -0.4307930707195395 -0.0000000000000000 26 2 8 0.0050 284.0 0.2324817763452396 -0.0000000000000000 26 3 8 0.0200 124.0 -0.5859972303056160 0.0000000000000008 26 3 8 0.0200 235.0 -0.5997288814405579 0.0000000000000017 26 3 8 0.0200 305.0 0.5460390520135160 0.0000000000000014 26 3 8 0.0200 329.0 0.8461362781069276 -0.0000000000000016 26 3 8 0.0200 165.0 -0.9684926453039098 0.0000000000000002 26 3 8 0.0200 170.0 -0.9859622466046385 0.0000000000000004 26 4 8 0.1000 201.0 -0.9546230023603792 -0.0000000014882015 26 4 8 0.1000 47.0 0.5574633427732774 0.0000000097576959 26 4 8 0.1000 350.0 0.9771689834351221 0.0000000008701687 26 4 8 0.1000 122.0 -0.6570476540510982 -0.0000000007614904 26 4 8 0.1000 237.0 -0.6686137610256468 0.0000000009407310 26 4 8 0.1000 230.0 -0.7442756097584060 0.0000000084644798 26 5 8 0.2000 262.0 -0.4912706819412948 0.0000015619780015 26 5 8 0.2000 306.0 0.2553423281581983 0.0000008754323918 26 5 8 0.2000 337.0 0.8240297040374111 -0.0000017237884885 26 5 8 0.2000 105.0 -0.5786693968317485 -0.0000058067081569 26 5 8 0.2000 29.0 0.7309914397275228 -0.0000019452452067 26 5 8 0.2000 210.0 -0.9358707301798567 -0.0000015581934522 26 6 8 0.7000 350.0 0.4177205507419381 0.0442932202818934 26 6 8 0.7000 301.0 -0.7694025524893584 -0.4941635024420574 26 6 8 0.7000 327.0 -0.4835212620082034 0.1899417968773750 26 6 8 0.7000 91.0 -0.9056433232862782 0.3241695195955378 26 6 8 0.7000 289.0 -0.8348676213638235 -0.1046898042311234 26 6 8 0.7000 170.0 -0.9990674109771221 0.0189528654570875 26 to compare expansion for cos(v) maximum power of eccentricity is 10 v max e e M cos(v) dif num t 1 10 0.0010 153.0 -0.8914179137369363 0.0000000000000000 37 1 10 0.0010 59.0 0.5135669003540925 0.0000000000000000 37 1 10 0.0010 139.0 -0.7555689468214452 -0.0000000000000000 37 1 10 0.0010 255.0 -0.2606839820212337 -0.0000000000000000 37 1 10 0.0010 293.0 0.3890349811511623 -0.0000000000000000 37 1 10 0.0010 354.0 0.9944999939841866 0.0000000000000000 37 2 10 0.0050 322.0 0.7841865728478399 0.0000000000000000 37 2 10 0.0050 198.0 -0.9520012970872578 -0.0000000000000000 37 2 10 0.0050 243.0 -0.4618888341559182 -0.0000000000000000 37 2 10 0.0050 298.0 0.4616344560099180 0.0000000000000000 37 2 10 0.0050 296.0 0.4302530640089886 -0.0000000000000000 37 2 10 0.0050 353.0 0.9923959571912687 0.0000000000000000 37 3 10 0.0200 98.0 -0.1781336725792848 -0.0000000000000000 37 3 10 0.0200 236.0 -0.5859972303056160 -0.0000000000000000 37 3 10 0.0200 318.0 0.7246248887926350 0.0000000000000000 37 3 10 0.0200 277.0 0.0822673297098785 -0.0000000000000000 37 3 10 0.0200 219.0 -0.7924455675048097 0.0000000000000000 37 3 10 0.0200 353.0 0.9919245704838264 0.0000000000000000 37 4 10 0.1000 269.0 -0.2140136688657981 -0.0000000003675472 37 4 10 0.1000 211.0 -0.9012382966198205 0.0000000000361109 37 4 10 0.1000 110.0 -0.5040900128677242 0.0000000002899157 37 4 10 0.1000 322.0 0.6971953837740718 0.0000000001092609 37 4 10 0.1000 203.0 -0.9455787944154232 -0.0000000000314466 37 4 10 0.1000 152.0 -0.9193933455878567 -0.0000000000004649 37 5 10 0.2000 107.0 -0.6019658773044594 0.0000006403580493 37 5 10 0.2000 140.0 -0.8850811057010510 0.0000001782094888 37 5 10 0.2000 118.0 -0.7171156580740169 -0.0000001465653070 37 5 10 0.2000 125.0 -0.7793004835948951 -0.0000004014477152 37 5 10 0.2000 119.0 -0.7265170370038092 -0.0000002193006943 37 5 10 0.2000 5.0 0.9911065204909789 0.0000000112323975 37 6 10 0.7000 12.0 0.2790174225478123 -0.0472482942946663 37 6 10 0.7000 196.0 -0.9976022964655103 -0.0130631245319198 37 6 10 0.7000 105.0 -0.9380752624692046 0.4476599645449812 37 6 10 0.7000 302.0 -0.7627794040800327 0.1121959282351151 37 6 10 0.7000 233.0 -0.9716896951787337 -0.2074890664568867 37 6 10 0.7000 245.0 -0.9555326297779777 -0.0537209436776808 37 to compare expansion for cos(v) maximum power of eccentricity is 12 v max e e M cos(v) dif num t 1 12 0.0010 121.0 -0.5165058437189148 0.0000000000000000 50 1 12 0.0010 257.0 -0.2268488853181269 0.0000000000000000 50 1 12 0.0010 323.0 0.7979098442750837 0.0000000000000000 50 1 12 0.0010 213.0 -0.8392627132424880 0.0000000000000000 50 1 12 0.0010 295.0 0.4209739126475212 0.0000000000000000 50 1 12 0.0010 308.0 0.6144178322189649 0.0000000000000000 50 2 12 0.0050 314.0 0.6894432745437623 0.0000000000000000 50 2 12 0.0050 96.0 -0.1144072558928394 0.0000000000000000 50 2 12 0.0050 26.0 0.8968527788665845 0.0000000000000000 50 2 12 0.0050 270.0 -0.0099996666816659 -0.0000000000000000 50 2 12 0.0050 157.0 -0.9220158723476028 -0.0000000000000000 50 2 12 0.0050 52.0 0.6094087509527741 0.0000000000000000 50 3 12 0.0200 343.0 0.9527333795122143 0.0000000000000000 50 3 12 0.0200 130.0 -0.6655899363611611 0.0000000000000000 50 3 12 0.0200 161.0 -0.9495836369861692 -0.0000000000000000 50 3 12 0.0200 267.0 -0.0921115328770177 0.0000000000000000 50 3 12 0.0200 87.0 0.0123727109638401 0.0000000000000000 50 3 12 0.0200 232.0 -0.6398188215960474 -0.0000000000000000 50 4 12 0.1000 290.0 0.1533921535579188 -0.0000000000053066 50 4 12 0.1000 207.0 -0.9250382902618159 0.0000000000006909 50 4 12 0.1000 295.0 0.2436674023651719 0.0000000000009109 50 4 12 0.1000 140.0 -0.8358557614473890 -0.0000000000013404 50 4 12 0.1000 104.0 -0.4183309562802157 -0.0000000000070225 50 4 12 0.1000 142.0 -0.8517928357125631 -0.0000000000005309 50 5 12 0.2000 246.0 -0.6777517941461749 0.0000000141830655 50 5 12 0.2000 128.0 -0.8034018174432768 0.0000000000033271 50 5 12 0.2000 81.0 -0.2406682373329503 0.0000000045652952 50 5 12 0.2000 269.0 -0.3946503590615294 0.0000000571021472 50 5 12 0.2000 277.0 -0.2729423167939818 0.0000000293059993 50 5 12 0.2000 270.0 -0.3800919782276370 0.0000000621135380 50 6 12 0.7000 346.0 0.1550991822633989 -0.0541582080148110 50 6 12 0.7000 302.0 -0.7627794040800327 0.2952454465477677 50 6 12 0.7000 204.0 -0.9945570833560898 0.0048517600431389 50 6 12 0.7000 351.0 0.4918508708718561 -0.0128970904973941 50 6 12 0.7000 56.0 -0.7488663474459622 0.3915947802418419 50 6 12 0.7000 254.0 -0.9400097354198005 -0.3353543455313485 50 to compare expansion for cos(v) maximum power of eccentricity is 14 v max e e M cos(v) dif num t 1 14 0.0010 208.0 -0.8833875254776867 -0.0000000000000000 65 1 14 0.0010 264.0 -0.1065061431088648 -0.0000000000000000 65 1 14 0.0010 314.0 0.6936218521504998 0.0000000000000000 65 1 14 0.0010 258.0 -0.2098243390085786 0.0000000000000000 65 1 14 0.0010 203.0 -0.9208095636495115 0.0000000000000000 65 1 14 0.0010 147.0 -0.8392627132424880 0.0000000000000000 65 2 14 0.0050 178.0 -0.9994028710356730 0.0000000000000000 65 2 14 0.0050 129.0 -0.6353173086715969 0.0000000000000000 65 2 14 0.0050 223.0 -0.7359668268738379 -0.0000000000000000 65 2 14 0.0050 283.0 0.2154333117617827 -0.0000000000000000 65 2 14 0.0050 163.0 -0.9571504468817227 0.0000000000000000 65 2 14 0.0050 134.0 -0.6997925903827670 0.0000000000000000 65 3 14 0.0200 19.0 0.9410924101370629 0.0000000000000000 65 3 14 0.0200 24.0 0.9066475778361028 0.0000000000000000 65 3 14 0.0200 274.0 0.0298471123694256 0.0000000000000000 65 3 14 0.0200 58.0 0.5004643420195709 -0.0000000000000000 65 3 14 0.0200 27.0 0.8824218932539631 0.0000000000000000 65 3 14 0.0200 74.0 0.2382321308228648 0.0000000000000000 65 4 14 0.1000 129.0 -0.7340412015180071 0.0000000000000641 65 4 14 0.1000 197.0 -0.9702534776838394 -0.0000000000000020 65 4 14 0.1000 109.0 -0.4902073006977513 0.0000000000000317 65 4 14 0.1000 200.0 -0.9588380561762404 0.0000000000000022 65 4 14 0.1000 103.0 -0.4034780063595090 0.0000000000001534 65 4 14 0.1000 292.0 0.1895094548659757 -0.0000000000000250 65 5 14 0.2000 33.0 0.6619519581053291 -0.0000000007638841 65 5 14 0.2000 298.0 0.0989063834520137 -0.0000000039412655 65 5 14 0.2000 232.0 -0.8034018174432768 0.0000000019183772 65 5 14 0.2000 24.0 0.8095435530527861 0.0000000004348113 65 5 14 0.2000 235.0 -0.7793004835948951 0.0000000010012531 65 5 14 0.2000 129.0 -0.8111021457345501 0.0000000019813431 65 6 14 0.7000 142.0 -0.9860163203692475 -0.0918926692696252 65 6 14 0.7000 336.0 -0.2707594219612266 0.0513645176112773 65 6 14 0.7000 359.0 0.9904755086721113 0.0007970109782823 65 6 14 0.7000 254.0 -0.9400097354198005 0.1701162893798398 65 6 14 0.7000 342.0 -0.0494412398003767 0.0430374317684475 65 6 14 0.7000 190.0 -0.9990674109771221 -0.0018901194646806 65 to compare expansion for cos(v) maximum power of eccentricity is 16 v max e e M cos(v) dif num t 1 16 0.0010 253.0 -0.2941995374860848 0.0000000000000000 82 1 16 0.0010 190.0 -0.9848679269924628 0.0000000000000000 82 1 16 0.0010 214.0 -0.8296618008511702 0.0000000000000000 82 1 16 0.0010 276.0 0.1025498529519036 -0.0000000000000000 82 1 16 0.0010 170.0 -0.9848679269924628 0.0000000000000000 82 1 16 0.0010 292.0 0.3728858054533534 0.0000000000000000 82 2 16 0.0050 253.0 -0.3014866136871322 -0.0000000000000000 82 2 16 0.0050 354.0 0.9944114000575815 -0.0000000000000000 82 2 16 0.0050 184.0 -0.9976121686255968 -0.0000000000000000 82 2 16 0.0050 134.0 -0.6997925903827670 0.0000000000000000 82 2 16 0.0050 279.0 0.1466623088220324 0.0000000000000000 82 2 16 0.0050 307.0 0.5953935589709025 -0.0000000000000000 82 3 16 0.0200 265.0 -0.1266758796189227 -0.0000000000000000 82 3 16 0.0200 255.0 -0.2956907759099843 -0.0000000000000000 82 3 16 0.0200 105.0 -0.2956907759099843 0.0000000000000000 82 3 16 0.0200 227.0 -0.7027467681481302 -0.0000000000000000 82 3 16 0.0200 276.0 0.0647997994996094 0.0000000000000000 82 3 16 0.0200 49.0 0.6325943192494792 0.0000000000000000 82 4 16 0.1000 135.0 -0.7925280218395764 0.0000000000000007 82 4 16 0.1000 258.0 -0.3884711769645979 -0.0000000000000033 82 4 16 0.1000 270.0 -0.1973804172533883 0.0000000000000037 82 4 16 0.1000 91.0 -0.2140136688657981 0.0000000000000034 82 4 16 0.1000 93.0 -0.2469233087217559 0.0000000000000022 82 4 16 0.1000 181.0 -0.9998970115872075 0.0000000000000000 82 5 16 0.2000 355.0 0.9911065204909789 0.0000000000007671 82 5 16 0.2000 253.0 -0.6019658773044594 -0.0000000000272071 82 5 16 0.2000 209.0 -0.9401153923101628 -0.0000000000229100 82 5 16 0.2000 204.0 -0.9591103991173997 0.0000000000103661 82 5 16 0.2000 138.0 -0.8730683981352599 0.0000000000876486 82 5 16 0.2000 97.0 -0.4780344411183792 -0.0000000002156421 82 6 16 0.7000 175.0 -0.9997673319918714 0.0006887612160115 82 6 16 0.7000 55.0 -0.7415549464392950 -0.0839103690025085 82 6 16 0.7000 251.0 -0.9455502118754813 0.3221792726449363 82 6 16 0.7000 96.0 -0.9184732860248985 -0.3785480817460646 82 6 16 0.7000 188.0 -0.9994037325838776 -0.0005281185361131 82 6 16 0.7000 351.0 0.4918508708718561 -0.0123973600938587 82 to compare expansion for cos(v) maximum power of eccentricity is 18 v max e e M cos(v) dif num t 1 18 0.0010 222.0 -0.7440388011610759 0.0000000000000000 101 1 18 0.0010 89.0 0.0154529397611942 0.0000000000000000 101 1 18 0.0010 139.0 -0.7555689468214452 -0.0000000000000000 101 1 18 0.0010 122.0 -0.5313559206224471 -0.0000000000000000 101 1 18 0.0010 228.0 -0.6702334730715931 0.0000000000000000 101 1 18 0.0010 9.0 0.9876392881547163 0.0000000000000000 101 2 18 0.0050 160.0 -0.9408501303021299 0.0000000000000000 101 2 18 0.0050 203.0 -0.9220158723476028 -0.0000000000000000 101 2 18 0.0050 263.0 -0.1317070074882785 0.0000000000000000 101 2 18 0.0050 7.0 0.9923959571912687 0.0000000000000000 101 2 18 0.0050 32.0 0.8452129842294422 0.0000000000000000 101 2 18 0.0050 259.0 -0.2004239572090530 0.0000000000000000 101 3 18 0.0200 326.0 0.8160512279505914 0.0000000000000000 101 3 18 0.0200 316.0 0.6994019765924338 -0.0000000000000000 101 3 18 0.0200 324.0 0.7946821381133911 0.0000000000000000 101 3 18 0.0200 249.0 -0.3926600928524273 0.0000000000000000 101 3 18 0.0200 171.0 -0.9886251738952954 0.0000000000000000 101 3 18 0.0200 166.0 -0.9725379126695384 0.0000000000000000 101 4 18 0.1000 224.0 -0.8015898762538612 -0.0000000000000000 101 4 18 0.1000 192.0 -0.9851738096054168 -0.0000000000000000 101 4 18 0.1000 76.0 0.0455494822226499 0.0000000000000001 101 4 18 0.1000 35.0 0.7396480215433843 0.0000000000000000 101 4 18 0.1000 340.0 0.9104442788477637 0.0000000000000000 101 4 18 0.1000 54.0 0.4391156001443522 0.0000000000000000 101 5 18 0.2000 101.0 -0.5298500442862223 0.0000000000345265 101 5 18 0.2000 61.0 0.1181613146346016 0.0000000000055968 101 5 18 0.2000 38.0 0.5698773054050852 0.0000000000054353 101 5 18 0.2000 103.0 -0.5546323495251739 0.0000000000227601 101 5 18 0.2000 1.0 0.9996430760100407 0.0000000000000039 101 5 18 0.2000 7.0 0.9826264284615780 -0.0000000000000449 101 6 18 0.7000 112.0 -0.9507165719747145 -0.3167118634336251 101 6 18 0.7000 302.0 -0.7627794040800327 0.1563772722420412 101 6 18 0.7000 152.0 -0.9925483864193373 -0.0262567930289402 101 6 18 0.7000 53.0 -0.7261632492289652 0.3475806147653295 101 6 18 0.7000 340.0 -0.1329717002633740 -0.0095107515133274 101 6 18 0.7000 162.0 -0.9969597008525368 0.0071911461475899 101 to compare expansion for cos(v) maximum power of eccentricity is 20 v max e e M cos(v) dif num t 1 20 0.0010 247.0 -0.3924242961327206 0.0000000000000000 121 1 20 0.0010 267.0 -0.0543302406420699 0.0000000000000000 121 1 20 0.0010 221.0 -0.7555689468214452 -0.0000000000000000 121 1 20 0.0010 166.0 -0.9704125235694246 0.0000000000000000 121 1 20 0.0010 83.0 0.1198985098844834 0.0000000000000000 121 1 20 0.0010 182.0 -0.9993932575010006 -0.0000000000000000 121 2 20 0.0050 1.0 0.9998446147238677 0.0000000000000000 121 2 20 0.0050 49.0 0.6503209877555691 0.0000000000000000 121 2 20 0.0050 289.0 0.3165955300915091 0.0000000000000000 121 2 20 0.0050 290.0 0.3331561034264503 -0.0000000000000000 121 2 20 0.0050 188.0 -0.9904596211645659 0.0000000000000000 121 2 20 0.0050 78.0 0.1983218498678759 -0.0000000000000000 121 3 20 0.0200 94.0 -0.1094162314438022 -0.0000000000000000 121 3 20 0.0200 48.0 0.6463656729414199 0.0000000000000000 121 3 20 0.0200 287.0 0.2553229903608195 -0.0000000000000000 121 3 20 0.0200 284.0 0.2038687844672336 -0.0000000000000000 121 3 20 0.0200 80.0 0.1345697112466156 0.0000000000000000 121 3 20 0.0200 316.0 0.6994019765924338 -0.0000000000000000 121 4 20 0.1000 342.0 0.9271020374586374 -0.0000000000000000 121 4 20 0.1000 169.0 -0.9875413112245947 -0.0000000000000000 121 4 20 0.1000 177.0 -0.9990731184502714 0.0000000000000000 121 4 20 0.1000 144.0 -0.8669279862687999 0.0000000000000000 121 4 20 0.1000 249.0 -0.5178039514338940 0.0000000000000000 121 4 20 0.1000 316.0 0.6058608913744618 0.0000000000000000 121 5 20 0.2000 117.0 -0.7075393135842088 -0.0000000000020221 121 5 20 0.2000 158.0 -0.9656780253434669 -0.0000000000002788 121 5 20 0.2000 88.0 -0.3504106770103843 0.0000000000025741 121 5 20 0.2000 165.0 -0.9840926140084089 0.0000000000008249 121 5 20 0.2000 180.0 -1.0000000000000000 0.0000000000011436 121 5 20 0.2000 297.0 0.0797592205183968 -0.0000000000004171 121 6 20 0.7000 25.0 -0.3001581515337337 0.0862308829029957 121 6 20 0.7000 208.0 -0.9925483864193373 -0.0630896605127100 121 6 20 0.7000 68.0 -0.8206053212754855 0.4694760943005215 121 6 20 0.7000 175.0 -0.9997673319918714 -0.0224694741753837 121 6 20 0.7000 139.0 -0.9836100085813011 -0.1380066573161792 121 6 20 0.7000 348.0 0.2790174225478123 0.0337834721047028 121 to compare expansion for cos(v) maximum power of eccentricity is 22 v max e e M cos(v) dif num t 1 22 0.0010 239.0 -0.5165058437189148 -0.0000000000000000 141 1 22 0.0010 285.0 0.2569519348563962 0.0000000000000000 141 1 22 0.0010 194.0 -0.9704125235694246 0.0000000000000000 141 1 22 0.0010 163.0 -0.9564753511381390 0.0000000000000000 141 1 22 0.0010 284.0 0.2400379249983334 -0.0000000000000000 141 1 22 0.0010 71.0 0.3237788353113687 -0.0000000000000000 141 2 22 0.0050 54.0 0.5811968051660706 0.0000000000000000 141 2 22 0.0050 7.0 0.9923959571912687 0.0000000000000000 141 2 22 0.0050 124.0 -0.5660227574777327 -0.0000000000000000 141 2 22 0.0050 74.0 0.2663686783275309 -0.0000000000000000 141 2 22 0.0050 37.0 0.7949809682705151 -0.0000000000000000 141 2 22 0.0050 58.0 0.5226845055372089 0.0000000000000000 141 3 22 0.0200 58.0 0.5004643420195709 -0.0000000000000000 141 3 22 0.0200 229.0 -0.6781787614768922 0.0000000000000000 141 3 22 0.0200 115.0 -0.4548446523315770 0.0000000000000000 141 3 22 0.0200 206.0 -0.9061788634509786 0.0000000000000000 141 3 22 0.0200 23.0 0.9141370818727089 -0.0000000000000000 141 3 22 0.0200 74.0 0.2382321308228648 0.0000000000000000 141 4 22 0.1000 132.0 -0.7641626185634250 0.0000000000000000 141 4 22 0.1000 46.0 0.5737742142917351 0.0000000000000000 141 4 22 0.1000 222.0 -0.8191201720758857 -0.0000000000000000 141 4 22 0.1000 155.0 -0.9357167757036782 -0.0000000000000000 141 4 22 0.1000 309.0 0.4906428868829772 -0.0000000000000000 141 4 22 0.1000 68.0 0.1895094548659757 -0.0000000000000000 141 5 22 0.2000 255.0 -0.5786693968317485 -0.0000000000004912 141 5 22 0.2000 301.0 0.1569668568687950 0.0000000000011180 141 5 22 0.2000 252.0 -0.6133380319391897 0.0000000000002319 141 5 22 0.2000 82.0 -0.2568959863875977 -0.0000000000002547 141 5 22 0.2000 329.0 0.6970713904954834 -0.0000000000006236 141 5 22 0.2000 169.0 -0.9914557676502105 -0.0000000000004275 141 6 22 0.7000 36.0 -0.5347064552774603 0.0597023571586067 141 6 22 0.7000 266.0 -0.9135242122922526 0.1407511901040397 141 6 22 0.7000 253.0 -0.9418997101558226 -0.4509057866963948 141 6 22 0.7000 267.0 -0.9109599200978628 -0.0190283463882796 141 6 22 0.7000 161.0 -0.9966090366284449 -0.1598435394198871 141 6 22 0.7000 178.0 -0.9999627945299464 -0.1316709505040827 141 to compare expansion for cos(v) maximum power of eccentricity is 24 v max e e M cos(v) dif num t 1 24 0.0010 159.0 -0.9338367429834487 -0.0000000000000000 161 1 24 0.0010 207.0 -0.8914179137369363 0.0000000000000000 161 1 24 0.0010 340.0 0.9394581697839270 -0.0000000000000000 161 1 24 0.0010 29.0 0.8741487000420432 0.0000000000000000 161 1 24 0.0010 75.0 0.2569519348563962 0.0000000000000000 161 1 24 0.0010 308.0 0.6144178322189649 0.0000000000000000 161 2 24 0.0050 38.0 0.7841865728478399 0.0000000000000000 161 2 24 0.0050 282.0 0.1983218498678759 0.0000000000000000 161 2 24 0.0050 152.0 -0.8851298901172858 -0.0000000000000000 161 2 24 0.0050 75.0 0.2494619808662766 -0.0000000000000000 161 2 24 0.0050 11.0 0.9812590471652319 -0.0000000000000000 161 2 24 0.0050 269.0 -0.0274470651113790 -0.0000000000000000 161 3 24 0.0200 108.0 -0.3446827886235238 0.0000000000000000 161 3 24 0.0200 29.0 0.8648375240727957 0.0000000000000000 161 3 24 0.0200 183.0 -0.9987343426813905 -0.0000000000000000 161 3 24 0.0200 172.0 -0.9910094814438126 -0.0000000000000000 161 3 24 0.0200 33.0 0.8263458371138435 0.0000000000000000 161 3 24 0.0200 51.0 0.6044706904137169 0.0000000000000000 161 4 24 0.1000 337.0 0.8825417970232595 0.0000000000000000 161 4 24 0.1000 230.0 -0.7442756097584060 0.0000000000000000 161 4 24 0.1000 58.0 0.3689653003679984 0.0000000000000000 161 4 24 0.1000 355.0 0.9942639606861432 0.0000000000000000 161 4 24 0.1000 9.0 0.9814837420745183 0.0000000000000000 161 4 24 0.1000 60.0 0.3334171377119625 0.0000000000000000 161 5 24 0.2000 315.0 0.4341036813349425 0.0000000000005665 161 5 24 0.2000 56.0 0.2158006563630800 0.0000000000003567 161 5 24 0.2000 129.0 -0.8111021457345501 0.0000000000007238 161 5 24 0.2000 253.0 -0.6019658773044594 0.0000000000001523 161 5 24 0.2000 98.0 -0.4912706819412948 -0.0000000000000413 161 5 24 0.2000 173.0 -0.9965428596084904 -0.0000000000005911 161 6 24 0.7000 264.0 -0.9184732860248985 -0.2531997715627899 161 6 24 0.7000 120.0 -0.9628379515047125 -0.1648459049669879 161 6 24 0.7000 215.0 -0.9882109833852330 0.2181925193393094 161 6 24 0.7000 259.0 -0.9298705624466733 -0.2039856343919970 161 6 24 0.7000 112.0 -0.9507165719747145 0.0436605448379175 161 6 24 0.7000 227.0 -0.9781287310799647 -0.1643890833590459 161 to compare expansion for sin(v) maximum power of eccentricity is 2 v max e e M sin(v) dif num t 1 2 0.0010 213.0 -0.5437261242214295 0.0000000000738175 4 1 2 0.0010 187.0 -0.1216277176944601 -0.0000000003433554 4 1 2 0.0010 222.0 -0.6681364099993272 0.0000000008809991 4 1 2 0.0010 15.0 0.2593196147028041 -0.0000000005718190 4 1 2 0.0010 234.0 -0.8080655795041243 0.0000000018912234 4 1 2 0.0010 247.0 -0.9197843072181319 0.0000000021717202 4 2 2 0.0050 107.0 0.9534704094870831 -0.0000002368439363 4 2 2 0.0050 194.0 -0.2395879956263139 -0.0000000694162620 4 2 2 0.0050 269.0 -0.9996232583412471 0.0000000187923649 4 2 2 0.0050 279.0 -0.9891866189809640 -0.0000001413451052 4 2 2 0.0050 270.0 -0.9999500020832320 0.0000000020832319 4 2 2 0.0050 228.0 -0.7381726694237089 0.0000001782559926 4 3 2 0.0200 71.0 0.9572398353747666 0.0000159506638468 4 3 2 0.0200 351.0 -0.1627678043599906 0.0000034557701421 4 3 2 0.0200 183.0 -0.0502962498479849 -0.0000012150541889 4 3 2 0.0200 237.0 -0.8201926887045546 0.0000161691014954 4 3 2 0.0200 81.0 0.9931133210068303 0.0000087156207133 4 3 2 0.0200 120.0 0.8484188871757163 -0.0000171003582910 4 4 2 0.1000 175.0 0.0717116127759775 0.0002284137133490 4 4 2 0.1000 145.0 0.4855770455760209 -0.0001219995758853 4 4 2 0.1000 123.0 0.7436098698693686 -0.0018723274260245 4 4 2 0.1000 93.0 0.9690350249655068 -0.0007078387984961 4 4 2 0.1000 2.0 0.0428630110017837 -0.0001172923092559 4 4 2 0.1000 8.0 0.1705242596787820 -0.0004294005358144 4 5 2 0.2000 198.0 -0.2129326781979736 -0.0041174356622286 4 5 2 0.2000 136.0 0.5095788397684154 -0.0056701605328195 4 5 2 0.2000 233.0 -0.6059071825763712 0.0113496968388588 4 5 2 0.2000 105.0 0.8155622166152502 -0.0152635993996940 4 5 2 0.2000 120.0 0.6772593902296652 -0.0147499563345696 4 5 2 0.2000 236.0 -0.6369194736964666 0.0129789610074096 4 6 2 0.7000 329.0 -0.8955986963675892 -0.5671746499594870 4 6 2 0.7000 54.0 0.6791587077624742 0.6190774298300118 4 6 2 0.7000 174.0 0.0258877114728405 0.0586316077455648 4 6 2 0.7000 316.0 -0.7673518162024649 -0.7387039418800179 4 6 2 0.7000 253.0 -0.3358942333657687 0.5279530395176303 4 6 2 0.7000 206.0 -0.1130062135919622 -0.1250096413911032 4 to compare expansion for sin(v) maximum power of eccentricity is 4 v max e e M sin(v) dif num t 1 4 0.0010 266.0 -0.9974229044073526 -0.0000000000000015 9 1 4 0.0010 147.0 0.5437261242214295 -0.0000000000000020 9 1 4 0.0010 215.0 -0.5726373287553236 0.0000000000000022 9 1 4 0.0010 266.0 -0.9974229044073526 -0.0000000000000015 9 1 4 0.0010 75.0 0.9664241838724620 -0.0000000000000042 9 1 4 0.0010 100.0 0.9844638981421235 0.0000000000000033 9 2 4 0.0050 347.0 -0.2271557566148731 0.0000000000010664 9 2 4 0.0050 194.0 -0.2395879956263139 -0.0000000000009100 9 2 4 0.0050 232.0 -0.7831536950860393 0.0000000000004222 9 2 4 0.0050 210.0 -0.4956870419696338 0.0000000000051985 9 2 4 0.0050 311.0 -0.7596595374801931 -0.0000000000027574 9 2 4 0.0050 128.0 0.7831536950860393 -0.0000000000004222 9 3 4 0.0200 182.0 -0.0335383750245980 -0.0000000004035390 9 3 4 0.0200 67.0 0.9343908414566790 -0.0000000125690741 9 3 4 0.0200 280.0 -0.9909041289726280 0.0000000104002151 9 3 4 0.0200 71.0 0.9572398353747666 -0.0000000137076144 9 3 4 0.0200 301.0 -0.8745324804530595 0.0000000065967238 9 3 4 0.0200 268.0 -0.9972010365909448 -0.0000000028353241 9 4 4 0.1000 50.0 0.8616122945500173 0.0000030443042845 9 4 4 0.1000 41.0 0.7577723340577155 0.0000216274959295 9 4 4 0.1000 344.0 -0.3352017370555463 0.0000012016648183 9 4 4 0.1000 18.0 0.3748090342294903 0.0000010170422727 9 4 4 0.1000 250.0 -0.8636511210708973 -0.0000393407167938 9 4 4 0.1000 339.0 -0.4327256117487008 -0.0000051741689977 9 5 4 0.2000 353.0 -0.1855944559755042 0.0001461673720808 9 5 4 0.2000 237.0 -0.6471172014615516 -0.0001822640600355 9 5 4 0.2000 236.0 -0.6369194736964666 -0.0000993162194281 9 5 4 0.2000 131.0 0.5636586561912986 -0.0003886475199699 9 5 4 0.2000 44.0 0.8910968108261348 0.0004862171845255 9 5 4 0.2000 311.0 -0.9349612933269660 -0.0000506753003855 9 6 4 0.7000 245.0 -0.2948853903291619 -0.1964850997766973 9 6 4 0.7000 93.0 0.4124948775140068 0.4594608504396930 9 6 4 0.7000 298.0 -0.6156058245711601 0.5843056356854398 9 6 4 0.7000 346.0 -0.9878989035631252 -0.1516157956409720 9 6 4 0.7000 234.0 -0.2410327517390346 0.1184570132059588 9 6 4 0.7000 140.0 0.1757428060524024 -0.2391078038379905 9 to compare expansion for sin(v) maximum power of eccentricity is 6 v max e e M sin(v) dif num t 1 6 0.0010 263.0 -0.9923023119009926 0.0000000000000000 16 1 6 0.0010 302.0 -0.8489462636542664 -0.0000000000000000 16 1 6 0.0010 102.0 0.9777390995350514 -0.0000000000000000 16 1 6 0.0010 142.0 0.6146916691385776 0.0000000000000000 16 1 6 0.0010 140.0 0.6418032144639653 0.0000000000000000 16 1 6 0.0010 311.0 -0.7556997991144261 0.0000000000000000 16 2 6 0.0050 193.0 -0.2227719103328528 0.0000000000000000 16 2 6 0.0050 30.0 0.5043473320814053 0.0000000000000001 16 2 6 0.0050 313.0 -0.7363430530376068 0.0000000000000004 16 2 6 0.0050 36.0 0.5925543838688769 -0.0000000000000000 16 2 6 0.0050 300.0 -0.8703363150387862 0.0000000000000001 16 2 6 0.0050 22.0 0.3780974495273683 0.0000000000000001 16 3 6 0.0200 43.0 0.7020524841782766 -0.0000000000047899 16 3 6 0.0200 298.0 -0.8991544965267769 -0.0000000000001937 16 3 6 0.0200 37.0 0.6212461507118811 -0.0000000000010513 16 3 6 0.0200 232.0 -0.7685257806550443 -0.0000000000068082 16 3 6 0.0200 61.0 0.8912333197596834 -0.0000000000008546 16 3 6 0.0200 134.0 0.6994110378718041 0.0000000000059631 16 4 6 0.1000 226.0 -0.6216827870053108 -0.0000004241172210 16 4 6 0.1000 40.0 0.7444812861816535 -0.0000002783065793 16 4 6 0.1000 44.0 0.7955706004516146 -0.0000004644391034 16 4 6 0.1000 92.0 0.9730654163139518 -0.0000003197034506 16 4 6 0.1000 253.0 -0.8869095169503943 0.0000007180040664 16 4 6 0.1000 92.0 0.9730654163139518 -0.0000003197034506 16 5 6 0.2000 356.0 -0.1066084539872409 0.0000041802249940 16 5 6 0.2000 238.0 -0.6572413324066175 -0.0000465314624926 16 5 6 0.2000 41.0 0.8587426335951686 -0.0000509117783016 16 5 6 0.2000 85.0 0.9525169786952365 0.0000311348743888 16 5 6 0.2000 113.0 0.7446394325077719 -0.0000283754284089 16 5 6 0.2000 67.0 0.9999904432913685 0.0000789553903685 16 6 6 0.7000 153.0 0.1174245313743554 -0.1070257994410882 16 6 6 0.7000 281.0 -0.4972299114779589 -0.2060461521587733 16 6 6 0.7000 221.0 -0.1803090430862876 -0.0572993288377911 16 6 6 0.7000 342.0 -0.9987770340806809 -0.2478096393594719 16 6 6 0.7000 29.0 0.9156799788842142 -0.0851985662200871 16 6 6 0.7000 232.0 -0.2315071920668361 -0.2822477123953899 16 to compare expansion for sin(v) maximum power of eccentricity is 8 v max e e M sin(v) dif num t 1 8 0.0010 229.0 -0.7537192660226032 0.0000000000000000 25 1 8 0.0010 350.0 -0.1739906088265812 0.0000000000000000 25 1 8 0.0010 111.0 0.9329099703757305 0.0000000000000000 25 1 8 0.0010 160.0 0.3413780301640108 -0.0000000000000000 25 1 8 0.0010 154.0 0.4375838525020912 0.0000000000000000 25 1 8 0.0010 319.0 -0.6570496657222030 -0.0000000000000000 25 2 8 0.0050 305.0 -0.8238396223306075 -0.0000000000000000 25 2 8 0.0050 271.0 -0.9999722198794781 -0.0000000000000000 25 2 8 0.0050 79.0 0.9834549868003762 -0.0000000000000000 25 2 8 0.0050 348.0 -0.2099574222663869 0.0000000000000000 25 2 8 0.0050 179.0 0.0172789926311049 0.0000000000000000 25 2 8 0.0050 191.0 -0.1889470455813917 0.0000000000000000 25 3 8 0.0200 40.0 0.6626426460535444 -0.0000000000000029 25 3 8 0.0200 165.0 0.2490421570582683 -0.0000000000000007 25 3 8 0.0200 162.0 0.2975125879573765 -0.0000000000000009 25 3 8 0.0200 314.0 -0.7393665177861869 -0.0000000000000000 25 3 8 0.0200 212.0 -0.5122052749237618 -0.0000000000000020 25 3 8 0.0200 81.0 0.9931133210068303 -0.0000000000000088 25 4 8 0.1000 165.0 0.2139807620275573 -0.0000000012529554 25 4 8 0.1000 19.0 0.3943231694217651 0.0000000020677468 25 4 8 0.1000 298.0 -0.9546788855219405 -0.0000000093358914 25 4 8 0.1000 252.0 -0.8793599040879228 -0.0000000071194607 25 4 8 0.1000 295.0 -0.9698588541765288 -0.0000000039660684 25 4 8 0.1000 323.0 -0.7025795314026694 0.0000000064652823 25 5 8 0.2000 303.0 -0.9805805502808514 -0.0000067176546106 25 5 8 0.2000 62.0 0.9950967426900981 0.0000040063704448 25 5 8 0.2000 54.0 0.9668507100120219 0.0000065018982908 25 5 8 0.2000 164.0 0.1894292506601416 -0.0000006656326309 25 5 8 0.2000 148.0 0.3752310462896960 0.0000015205912990 25 5 8 0.2000 129.0 0.5849045299746008 -0.0000022814910162 25 6 8 0.7000 356.0 -0.5076242499659889 0.0230453907723691 25 6 8 0.7000 357.0 -0.3950038560047785 0.0256761169144510 25 6 8 0.7000 303.0 -0.6546438260969702 -0.2566856835995235 25 6 8 0.7000 111.0 0.3151722127969656 -0.1739286886076822 25 6 8 0.7000 77.0 0.5101665618436748 -0.4503792077324754 25 6 8 0.7000 107.0 0.3358942333657687 0.0359353474191050 25 to compare expansion for sin(v) maximum power of eccentricity is 10 v max e e M sin(v) dif num t 1 10 0.0010 195.0 -0.2583196135600692 0.0000000000000000 36 1 10 0.0010 216.0 -0.5868347517270315 0.0000000000000000 36 1 10 0.0010 94.0 0.9974229044073526 0.0000000000000000 36 1 10 0.0010 103.0 0.9739299683395738 0.0000000000000000 36 1 10 0.0010 143.0 0.6008542855592614 0.0000000000000000 36 1 10 0.0010 317.0 -0.6829962006730074 -0.0000000000000000 36 2 10 0.0050 60.0 0.8703363150387862 0.0000000000000000 36 2 10 0.0050 338.0 -0.3780974495273683 -0.0000000000000000 36 2 10 0.0050 346.0 -0.2442828506726447 0.0000000000000000 36 2 10 0.0050 247.0 -0.9168782107485950 0.0000000000000000 36 2 10 0.0050 148.0 0.5254416720630855 -0.0000000000000000 36 2 10 0.0050 196.0 -0.2730025586232172 -0.0000000000000000 36 3 10 0.0200 166.0 0.2327445131907030 -0.0000000000000000 36 3 10 0.0200 212.0 -0.5122052749237618 -0.0000000000000000 36 3 10 0.0200 210.0 -0.4829532209867944 -0.0000000000000000 36 3 10 0.0200 84.0 0.9978982843881487 0.0000000000000000 36 3 10 0.0200 225.0 -0.6871864735767872 0.0000000000000000 36 3 10 0.0200 239.0 -0.8392487320005487 -0.0000000000000000 36 4 10 0.1000 310.0 -0.8616122945500173 -0.0000000000959560 36 4 10 0.1000 313.0 -0.8302015547227332 -0.0000000001563122 36 4 10 0.1000 109.0 0.8716058755783054 0.0000000000715945 36 4 10 0.1000 92.0 0.9730654163139518 -0.0000000001762590 36 4 10 0.1000 104.0 0.9082946719086710 -0.0000000001990132 36 4 10 0.1000 74.0 0.9966845255972758 0.0000000001880677 36 5 10 0.2000 330.0 -0.6999510756706390 0.0000001421022761 36 5 10 0.2000 21.0 0.5241496342907693 -0.0000000304901190 36 5 10 0.2000 317.0 -0.8808241670468400 -0.0000003406721504 36 5 10 0.2000 138.0 0.4875977565345552 -0.0000001851950885 36 5 10 0.2000 256.0 -0.8238941191535404 0.0000003167902525 36 5 10 0.2000 188.0 -0.0949320330821194 0.0000000048967707 36 6 10 0.7000 194.0 -0.0605149256455664 0.0194947254343380 36 6 10 0.7000 267.0 -0.4124948775140068 0.4997063093793610 36 6 10 0.7000 298.0 -0.6156058245711601 0.3084705691001565 36 6 10 0.7000 198.0 -0.0779188993506727 0.0175715952264359 36 6 10 0.7000 275.0 -0.4597433454444952 -0.0126128546869043 36 6 10 0.7000 331.0 -0.9156799788842142 0.0559635816354477 36 to compare expansion for sin(v) maximum power of eccentricity is 12 v max e e M sin(v) dif num t 1 12 0.0010 63.0 0.8918145833505165 0.0000000000000000 49 1 12 0.0010 192.0 -0.2075054329945062 0.0000000000000000 49 1 12 0.0010 75.0 0.9664241838724620 -0.0000000000000000 49 1 12 0.0010 105.0 0.9654241873485215 -0.0000000000000000 49 1 12 0.0010 50.0 0.7670291414758624 0.0000000000000000 49 1 12 0.0010 242.0 -0.8821176673151602 -0.0000000000000000 49 2 12 0.0050 6.0 0.1055744639366953 0.0000000000000000 49 2 12 0.0050 253.0 -0.9534704094870831 0.0000000000000000 49 2 12 0.0050 25.0 0.4264664581428231 -0.0000000000000000 49 2 12 0.0050 226.0 -0.7143460859033084 0.0000000000000000 49 2 12 0.0050 357.0 -0.0528618729464432 -0.0000000000000000 49 2 12 0.0050 191.0 -0.1889470455813917 0.0000000000000000 49 3 12 0.0200 221.0 -0.6364074401393815 0.0000000000000000 49 3 12 0.0200 176.0 0.0670405515271746 0.0000000000000000 49 3 12 0.0200 201.0 -0.3452565258210016 0.0000000000000000 49 3 12 0.0200 15.0 0.2690513003957138 0.0000000000000000 49 3 12 0.0200 302.0 -0.8657571497636724 -0.0000000000000000 49 3 12 0.0200 10.0 0.1806565417946635 0.0000000000000000 49 4 12 0.1000 205.0 -0.3527522015051250 -0.0000000000005824 49 4 12 0.1000 26.0 0.5246722009495639 -0.0000000000005582 49 4 12 0.1000 66.0 0.9742139491700880 0.0000000000063529 49 4 12 0.1000 106.0 0.8942510044912235 -0.0000000000012691 49 4 12 0.1000 320.0 -0.7444812861816535 -0.0000000000014620 49 4 12 0.1000 6.0 0.1282172779898738 0.0000000000000230 49 5 12 0.2000 73.0 0.9945212373744252 -0.0000000024737184 49 5 12 0.2000 186.0 -0.0712225748779125 0.0000000001142946 49 5 12 0.2000 293.0 -0.9999904432913685 -0.0000000498635592 49 5 12 0.2000 49.0 0.9349612933269660 -0.0000000317747343 49 5 12 0.2000 51.0 0.9491100351273503 -0.0000000337376959 49 5 12 0.2000 106.0 0.8071035625526333 -0.0000000161368281 49 6 12 0.7000 106.0 0.3411476180717032 -0.2909603467032108 49 6 12 0.7000 60.0 0.6309583604852956 0.4479950195895090 49 6 12 0.7000 116.0 0.2898770489579531 -0.1581732196213470 49 6 12 0.7000 48.0 0.7308427955473313 -0.3241266256294838 49 6 12 0.7000 349.0 -0.9380076578583777 -0.0230726311466295 49 6 12 0.7000 90.0 0.4298771255033790 0.3931215686378575 49 to compare expansion for sin(v) maximum power of eccentricity is 14 v max e e M sin(v) dif num t 1 14 0.0010 115.0 0.9055406606091489 0.0000000000000000 64 1 14 0.0010 102.0 0.9777390995350514 -0.0000000000000000 64 1 14 0.0010 8.0 0.1394490745035258 0.0000000000000000 64 1 14 0.0010 62.0 0.8837757380533646 0.0000000000000000 64 1 14 0.0010 358.0 -0.0349693403380050 0.0000000000000000 64 1 14 0.0010 312.0 -0.7441393569396625 0.0000000000000000 64 2 14 0.0050 300.0 -0.8703363150387862 0.0000000000000000 64 2 14 0.0050 332.0 -0.4736344851860986 -0.0000000000000000 64 2 14 0.0050 102.0 0.9760699514786443 0.0000000000000000 64 2 14 0.0050 127.0 0.7938220376864106 -0.0000000000000000 64 2 14 0.0050 170.0 0.1719482839253052 -0.0000000000000000 64 2 14 0.0050 199.0 -0.3225062411390418 0.0000000000000000 64 3 14 0.0200 305.0 -0.8377597231164678 -0.0000000000000000 64 3 14 0.0200 117.0 0.8744614914276975 0.0000000000000000 64 3 14 0.0200 346.0 -0.2515323002309079 0.0000000000000000 64 3 14 0.0200 126.0 0.7898665818634789 0.0000000000000000 64 3 14 0.0200 185.0 -0.0837667591526778 -0.0000000000000000 64 3 14 0.0200 203.0 -0.3766237434964444 -0.0000000000000000 64 4 14 0.1000 140.0 0.5489491288409204 0.0000000000000254 64 4 14 0.1000 123.0 0.7436098698693686 -0.0000000000000860 64 4 14 0.1000 188.0 -0.1146188547876465 0.0000000000000010 64 4 14 0.1000 159.0 0.2978169292777955 0.0000000000000057 64 4 14 0.1000 298.0 -0.9546788855219405 -0.0000000000000014 64 4 14 0.1000 30.0 0.5935268907429099 0.0000000000000206 64 5 14 0.2000 217.0 -0.4318848302584137 0.0000000000146002 64 5 14 0.2000 229.0 -0.5636586561912986 -0.0000000004806357 64 5 14 0.2000 16.0 0.4107574320618329 -0.0000000001390490 64 5 14 0.2000 283.0 -0.9847499084100526 -0.0000000023415400 64 5 14 0.2000 307.0 -0.9613923717360391 -0.0000000026584760 64 5 14 0.2000 55.0 0.9718633015450817 0.0000000031382680 64 6 14 0.7000 16.0 0.9989401781033162 -0.0467019805636787 64 6 14 0.7000 263.0 -0.3898904085285330 0.3817794923410173 64 6 14 0.7000 156.0 0.1041931281142278 0.0094468974262903 64 6 14 0.7000 232.0 -0.2315071920668361 0.0295298709349155 64 6 14 0.7000 153.0 0.1174245313743554 -0.0156597696612481 64 6 14 0.7000 9.0 0.8706794592860203 0.0126062675336574 64 to compare expansion for sin(v) maximum power of eccentricity is 16 v max e e M sin(v) dif num t 1 16 0.0010 25.0 0.4233850234785601 0.0000000000000000 81 1 16 0.0010 29.0 0.4856583678006649 -0.0000000000000000 81 1 16 0.0010 189.0 -0.1561258214822475 -0.0000000000000000 81 1 16 0.0010 230.0 -0.7650595291797778 -0.0000000000000000 81 1 16 0.0010 134.0 0.7183405341179398 -0.0000000000000000 81 1 16 0.0010 249.0 -0.9329099703757305 0.0000000000000000 81 2 16 0.0050 151.0 0.4805868344911823 0.0000000000000000 81 2 16 0.0050 282.0 -0.9801369515863504 0.0000000000000000 81 2 16 0.0050 350.0 -0.1753685998677904 0.0000000000000000 81 2 16 0.0050 86.0 0.9982105194184590 0.0000000000000000 81 2 16 0.0050 246.0 -0.9098013325770840 0.0000000000000000 81 2 16 0.0050 208.0 -0.4653440422106655 -0.0000000000000000 81 3 16 0.0200 163.0 0.2814306236594330 -0.0000000000000000 81 3 16 0.0200 219.0 -0.6099426387308729 0.0000000000000000 81 3 16 0.0200 3.0 0.0544798738424023 -0.0000000000000000 81 3 16 0.0200 19.0 0.3381494870355628 0.0000000000000000 81 3 16 0.0200 44.0 0.7147285324783086 -0.0000000000000000 81 3 16 0.0200 253.0 -0.9445182916096590 -0.0000000000000000 81 4 16 0.1000 221.0 -0.5613366568206583 -0.0000000000000003 81 4 16 0.1000 158.0 0.3116309927638518 -0.0000000000000000 81 4 16 0.1000 204.0 -0.3391011145375198 0.0000000000000001 81 4 16 0.1000 230.0 -0.6678726051566668 0.0000000000000011 81 4 16 0.1000 164.0 0.2280546594612416 0.0000000000000001 81 4 16 0.1000 283.0 -0.9996159138776423 -0.0000000000000002 81 5 16 0.2000 14.0 0.3627574810857205 -0.0000000000063340 81 5 16 0.2000 107.0 0.7985218109488760 -0.0000000003660997 81 5 16 0.2000 102.0 0.8401625782600867 -0.0000000000880198 81 5 16 0.2000 326.0 -0.7650344889555276 0.0000000000612377 81 5 16 0.2000 234.0 -0.6163122755521260 0.0000000000280000 81 5 16 0.2000 44.0 0.8910968108261348 0.0000000000965974 81 6 16 0.7000 173.0 0.0302067979772528 -0.0014781408090259 81 6 16 0.7000 210.0 -0.1307305816521937 0.0233331387051627 81 6 16 0.7000 134.0 0.2033481872183125 -0.0776033546659428 81 6 16 0.7000 107.0 0.3358942333657687 -0.4271506407906649 81 6 16 0.7000 261.0 -0.3788169221715888 -0.0506895673768954 81 6 16 0.7000 57.0 0.6546438260969702 -0.4010267043017364 81 to compare expansion for sin(v) maximum power of eccentricity is 18 v max e e M sin(v) dif num t 1 18 0.0010 312.0 -0.7441393569396625 0.0000000000000000 100 1 18 0.0010 67.0 0.9212229824753152 0.0000000000000000 100 1 18 0.0010 168.0 0.2075054329945062 -0.0000000000000000 100 1 18 0.0010 134.0 0.7183405341179398 -0.0000000000000000 100 1 18 0.0010 37.0 0.6027768081213076 0.0000000000000000 100 1 18 0.0010 39.0 0.6302989897769034 -0.0000000000000000 100 2 18 0.0050 76.0 0.9726007524505428 -0.0000000000000000 100 2 18 0.0050 198.0 -0.3060939893957062 0.0000000000000000 100 2 18 0.0050 289.0 -0.9485606308117981 0.0000000000000000 100 2 18 0.0050 154.0 0.4344489670740730 0.0000000000000000 100 2 18 0.0050 226.0 -0.7143460859033084 0.0000000000000000 100 2 18 0.0050 37.0 0.6066343710075076 0.0000000000000000 100 3 18 0.0200 257.0 -0.9649247058714876 -0.0000000000000000 100 3 18 0.0200 340.0 -0.3551504414832548 0.0000000000000000 100 3 18 0.0200 163.0 0.2814306236594330 -0.0000000000000000 100 3 18 0.0200 109.0 0.9326455411405321 0.0000000000000000 100 3 18 0.0200 235.0 -0.8002032671553255 0.0000000000000000 100 3 18 0.0200 219.0 -0.6099426387308729 0.0000000000000000 100 4 18 0.1000 78.0 0.9999506815339839 -0.0000000000000000 100 4 18 0.1000 156.0 0.3391011145375198 -0.0000000000000000 100 4 18 0.1000 144.0 0.4984334124273005 0.0000000000000000 100 4 18 0.1000 193.0 -0.1857306716382163 -0.0000000000000000 100 4 18 0.1000 281.0 -0.9999696539792749 -0.0000000000000000 100 4 18 0.1000 67.0 0.9782199008880098 0.0000000000000000 100 5 18 0.2000 143.0 0.4318848302584137 0.0000000000002116 100 5 18 0.2000 123.0 0.6471172014615516 0.0000000000055644 100 5 18 0.2000 250.0 -0.7720731308412513 -0.0000000000079939 100 5 18 0.2000 152.0 0.3293417547134994 0.0000000000004198 100 5 18 0.2000 86.0 0.9474242771425807 0.0000000000305924 100 5 18 0.2000 286.0 -0.9925123993685558 0.0000000000330969 100 6 18 0.7000 122.0 0.2603150810186195 0.0952852418603624 100 6 18 0.7000 75.0 0.5233413279275834 -0.1557496048385078 100 6 18 0.7000 2.0 0.2707044041396803 -0.0003033229337743 100 6 18 0.7000 277.0 -0.4720283548713967 -0.5943061723268509 100 6 18 0.7000 333.0 -0.9352625642411737 0.0652088939400142 100 6 18 0.7000 73.0 0.5367654767229330 -0.4402120083788975 100 to compare expansion for sin(v) maximum power of eccentricity is 20 v max e e M sin(v) dif num t 1 20 0.0010 138.0 0.6681364099993272 -0.0000000000000000 119 1 20 0.0010 187.0 -0.1216277176944601 -0.0000000000000000 119 1 20 0.0010 95.0 0.9960190922389031 0.0000000000000000 119 1 20 0.0010 111.0 0.9329099703757305 0.0000000000000000 119 1 20 0.0010 221.0 -0.6550691311603166 0.0000000000000000 119 1 20 0.0010 94.0 0.9974229044073526 0.0000000000000000 119 2 20 0.0050 134.0 0.7143460859033084 0.0000000000000000 119 2 20 0.0050 247.0 -0.9168782107485950 0.0000000000000000 119 2 20 0.0050 90.0 0.9999500020832320 -0.0000000000000000 119 2 20 0.0050 27.0 0.4580534726737553 -0.0000000000000000 119 2 20 0.0050 318.0 -0.6741112205283948 -0.0000000000000000 119 2 20 0.0050 13.0 0.2271557566148731 -0.0000000000000000 119 3 20 0.0200 258.0 -0.9693185229157357 0.0000000000000000 119 3 20 0.0200 37.0 0.6212461507118811 -0.0000000000000000 119 3 20 0.0200 97.0 0.9869479376544797 0.0000000000000000 119 3 20 0.0200 85.0 0.9988795635465406 -0.0000000000000000 119 3 20 0.0200 253.0 -0.9445182916096590 -0.0000000000000000 119 3 20 0.0200 29.0 0.5020518468800175 -0.0000000000000000 119 4 20 0.1000 319.0 -0.7577723340577155 0.0000000000000000 119 4 20 0.1000 88.0 0.9864976185703583 0.0000000000000000 119 4 20 0.1000 125.0 0.7226799054704353 0.0000000000000000 119 4 20 0.1000 60.0 0.9427794080695453 -0.0000000000000000 119 4 20 0.1000 293.0 -0.9782199008880098 -0.0000000000000000 119 4 20 0.1000 131.0 0.6565111387297962 -0.0000000000000000 119 5 20 0.2000 89.0 0.9308720802230737 0.0000000000003101 119 5 20 0.2000 34.0 0.7650344889555276 0.0000000000031416 119 5 20 0.2000 191.0 -0.1304433240650203 0.0000000000018748 119 5 20 0.2000 279.0 -0.9706074384317538 0.0000000000007854 119 5 20 0.2000 99.0 0.8635177329634081 0.0000000000012124 119 5 20 0.2000 224.0 -0.5095788397684154 -0.0000000000023193 119 6 20 0.7000 132.0 0.2126684878853791 0.1378764090395135 119 6 20 0.7000 149.0 0.1351840926900312 0.0096624600509861 119 6 20 0.7000 76.0 0.5167234879162912 0.1156858707773581 119 6 20 0.7000 113.0 0.3049769114777812 0.3509631137739308 119 6 20 0.7000 294.0 -0.5858881708323775 0.0387256981378664 119 6 20 0.7000 52.0 0.6959844314572450 0.3703815173228954 119 to compare expansion for sin(v) maximum power of eccentricity is 22 v max e e M sin(v) dif num t 1 22 0.0010 67.0 0.9212229824753152 0.0000000000000000 138 1 22 0.0010 219.0 -0.6283426957731536 0.0000000000000000 138 1 22 0.0010 224.0 -0.6936592089145954 -0.0000000000000000 138 1 22 0.0010 91.0 0.9998107974717781 -0.0000000000000000 138 1 22 0.0010 337.0 -0.3914511771711454 -0.0000000000000000 138 1 22 0.0010 87.0 0.9987320778717090 0.0000000000000000 138 2 22 0.0050 246.0 -0.9098013325770840 0.0000000000000000 138 2 22 0.0050 86.0 0.9982105194184590 0.0000000000000000 138 2 22 0.0050 314.0 -0.7243396794228343 0.0000000000000000 138 2 22 0.0050 333.0 -0.4580534726737553 -0.0000000000000000 138 2 22 0.0050 288.0 -0.9539578631671118 0.0000000000000000 138 2 22 0.0050 343.0 -0.2951832040651584 -0.0000000000000000 138 3 22 0.0200 347.0 -0.2339273300354606 0.0000000000000000 138 3 22 0.0200 142.0 0.5964549573552714 -0.0000000000000000 138 3 22 0.0200 69.0 0.9464152129220912 0.0000000000000000 138 3 22 0.0200 358.0 -0.0363303017044621 -0.0000000000000000 138 3 22 0.0200 153.0 0.4380930680727510 0.0000000000000000 138 3 22 0.0200 260.0 -0.9772433991602892 -0.0000000000000000 138 4 22 0.1000 305.0 -0.9067277508748045 0.0000000000000000 138 4 22 0.1000 173.0 0.1003318052092182 0.0000000000000000 138 4 22 0.1000 82.0 0.9981654316702840 0.0000000000000000 138 4 22 0.1000 352.0 -0.1705242596787820 0.0000000000000000 138 4 22 0.1000 253.0 -0.8869095169503943 -0.0000000000000000 138 4 22 0.1000 29.0 0.5767343413710454 0.0000000000000000 138 5 22 0.2000 148.0 0.3752310462896960 -0.0000000000027418 138 5 22 0.2000 65.0 0.9991254279954991 0.0000000000031378 138 5 22 0.2000 217.0 -0.4318848302584137 -0.0000000000006467 138 5 22 0.2000 140.0 0.4654368231360783 0.0000000000026745 138 5 22 0.2000 81.0 0.9706074384317538 0.0000000000009777 138 5 22 0.2000 208.0 -0.3293417547134994 0.0000000000007030 138 6 22 0.7000 32.0 0.8854734084340427 -0.2397649359410674 138 6 22 0.7000 216.0 -0.1576034848995455 -0.0770201664539316 138 6 22 0.7000 24.0 0.9626470461281344 0.2213132111129758 138 6 22 0.7000 77.0 0.5101665618436748 -0.0127873343451555 138 6 22 0.7000 1.0 0.1376890217872232 0.0585731763732629 138 6 22 0.7000 180.0 -0.0000000000000000 0.0000000000000000 138 to compare expansion for sin(v) maximum power of eccentricity is 24 v max e e M sin(v) dif num t 1 24 0.0010 83.0 0.9927861538757883 0.0000000000000000 157 1 24 0.0010 305.0 -0.8200913093678398 0.0000000000000000 157 1 24 0.0010 322.0 -0.6166322595790259 0.0000000000000000 157 1 24 0.0010 277.0 -0.9927861538757883 0.0000000000000000 157 1 24 0.0010 175.0 0.0869823092269815 -0.0000000000000000 157 1 24 0.0010 50.0 0.7670291414758624 0.0000000000000000 157 2 24 0.0050 92.0 0.9989922474758977 0.0000000000000000 157 2 24 0.0050 214.0 -0.5545722809177679 0.0000000000000000 157 2 24 0.0050 164.0 0.2730025586232172 0.0000000000000000 157 2 24 0.0050 70.0 0.9428716830776627 0.0000000000000000 157 2 24 0.0050 196.0 -0.2730025586232172 -0.0000000000000000 157 2 24 0.0050 217.0 -0.5970218577903374 -0.0000000000000000 157 3 24 0.0200 291.0 -0.9464152129220912 0.0000000000000000 157 3 24 0.0200 135.0 0.6871864735767872 0.0000000000000000 157 3 24 0.0200 16.0 0.2864783929722753 -0.0000000000000000 157 3 24 0.0200 35.0 0.5926020634391168 0.0000000000000000 157 3 24 0.0200 94.0 0.9939960202619708 0.0000000000000000 157 3 24 0.0200 169.0 0.1834913283991008 0.0000000000000000 157 4 24 0.1000 188.0 -0.1146188547876465 -0.0000000000000000 157 4 24 0.1000 219.0 -0.5364622231219645 -0.0000000000000000 157 4 24 0.1000 145.0 0.4855770455760209 -0.0000000000000000 157 4 24 0.1000 46.0 0.8190135230958657 0.0000000000000000 157 4 24 0.1000 252.0 -0.8793599040879228 0.0000000000000000 157 4 24 0.1000 275.0 -0.9936424559478662 -0.0000000000000000 157 5 24 0.2000 116.0 0.7163051868823392 -0.0000000000004171 157 5 24 0.2000 235.0 -0.6266504258905140 -0.0000000000004748 157 5 24 0.2000 198.0 -0.2129326781979736 0.0000000000001780 157 5 24 0.2000 168.0 0.1422628370827590 -0.0000000000022945 157 5 24 0.2000 20.0 0.5022894950393250 -0.0000000000032889 157 5 24 0.2000 26.0 0.6266638976434179 -0.0000000000008797 157 6 24 0.7000 141.0 0.1711895130334649 -0.0617231765243431 157 6 24 0.7000 136.0 0.1940893334339614 0.0198347448834939 157 6 24 0.7000 301.0 -0.6387642070614634 0.0975292794550984 157 6 24 0.7000 195.0 -0.0648589051109326 0.0012479130732344 157 6 24 0.7000 287.0 -0.5367654767229330 -0.1938623317523842 157 6 24 0.7000 262.0 -0.3843353246413814 0.0378772019977908 157 411 number of terms for function a/r 1 0 0 0 0 0 1.00000000000000000E+00 C 2 0 1 0 1 0 1.00000000000000000E+00 C 3 0 3 0 1 0 -1.25000000000000000E-01 C 4 0 5 0 1 0 5.20833333333333333E-03 C 5 0 7 0 1 0 -1.08506944444444444E-04 C 6 0 9 0 1 0 1.35633680555555556E-06 C 7 0 11 0 1 0 -1.13028067129629630E-08 C 8 0 13 0 1 0 6.72786113866843035E-11 C 9 0 15 0 1 0 -3.00350943690554926E-13 C 10 0 17 0 1 0 1.04288522114776016E-15 C 11 0 19 0 1 0 -2.89690339207711155E-18 C 12 0 21 0 1 0 6.58387134562979898E-21 C 13 0 23 0 1 0 -1.24694533061170435E-23 C 14 0 25 0 1 0 1.99830982469824415E-26 C 15 0 27 0 1 0 -2.74493107788220350E-29 C 16 0 29 0 1 0 3.26777509271690894E-32 C 17 0 31 0 1 0 -3.40393238824678015E-35 C 18 0 33 0 1 0 3.12861432743270234E-38 C 19 0 35 0 1 0 -2.55605745705286139E-41 C 20 0 37 0 1 0 1.86846305340121446E-44 C 21 0 39 0 1 0 -1.22925200881658846E-47 C 22 0 41 0 1 0 7.31697624295588372E-51 C 23 0 43 0 1 0 -3.95940272887223146E-54 C 24 0 45 0 1 0 1.95622664469971909E-57 C 25 0 47 0 1 0 -8.85972212273423503E-61 C 26 0 49 0 1 0 3.69155088447259793E-64 C 27 0 51 0 1 0 -1.41982726325869151E-67 C 28 0 53 0 1 0 5.05636489764491279E-71 C 29 0 55 0 1 0 -1.67207833916829127E-74 C 30 0 57 0 1 0 5.14802444325212828E-78 C 31 0 59 0 1 0 -1.47931736875061158E-81 C 32 0 2 0 2 0 1.00000000000000000E+00 C 33 0 4 0 2 0 -3.33333333333333334E-01 C 34 0 6 0 2 0 4.16666666666666666E-02 C 35 0 8 0 2 0 -2.77777777777777778E-03 C 36 0 10 0 2 0 1.15740740740740741E-04 C 37 0 12 0 2 0 -3.30687830687830688E-06 C 38 0 14 0 2 0 6.88932980599647266E-08 C 39 0 16 0 2 0 -1.09354441365023376E-09 C 40 0 18 0 2 0 1.36693051706279220E-11 C 41 0 20 0 2 0 -1.38073789602302242E-13 C 42 0 22 0 2 0 1.15061491335251868E-15 C 43 0 24 0 2 0 -8.04625813533229848E-18 C 44 0 26 0 2 0 4.78943936626922528E-20 C 45 0 28 0 2 0 -2.45612275193293604E-22 C 46 0 30 0 2 0 1.09648337139863216E-24 C 47 0 32 0 2 0 -4.29993478979855750E-27 C 48 0 34 0 2 0 1.49303291312449913E-29 C 49 0 36 0 2 0 -4.62239291989009020E-32 C 50 0 38 0 2 0 1.28399803330280283E-34 C 51 0 40 0 2 0 -3.21804018371629782E-37 C 52 0 42 0 2 0 7.31372769026431324E-40 C 53 0 44 0 2 0 -1.51422933545844994E-42 C 54 0 46 0 2 0 2.86785858988342792E-45 C 55 0 48 0 2 0 -4.98758015631900508E-48 C 56 0 50 0 2 0 7.99291691717789278E-51 C 57 0 52 0 2 0 -1.18413583958191004E-53 C 58 0 54 0 2 0 1.62656021920592038E-56 C 59 0 56 0 2 0 -2.07734383040347432E-59 C 60 0 58 0 2 0 2.47302836952794560E-62 C 61 0 3 0 3 0 1.12500000000000000E+00 C 62 0 5 0 3 0 -6.32812500000000001E-01 C 63 0 7 0 3 0 1.42382812500000000E-01 C 64 0 9 0 3 0 -1.77978515625000000E-02 C 65 0 11 0 3 0 1.43018450055803572E-03 C 66 0 13 0 3 0 -8.04478781563895090E-05 C 67 0 15 0 3 0 3.35199492318289621E-06 C 68 0 17 0 3 0 -1.07742693959450235E-07 C 69 0 19 0 3 0 2.75478478873594351E-09 C 70 0 21 0 3 0 -5.73913497653321565E-11 C 71 0 23 0 3 0 9.93311822861518093E-13 C 72 0 25 0 3 0 -1.45126727366130890E-14 C 73 0 27 0 3 0 1.81408409207663613E-16 C 74 0 29 0 3 0 -1.96235058037136120E-18 C 75 0 31 0 3 0 1.85516336379645492E-20 C 76 0 33 0 3 0 -1.54596946983037910E-22 C 77 0 35 0 3 0 1.14422082470998453E-24 C 78 0 37 0 3 0 -7.57204957528666232E-27 C 79 0 39 0 3 0 4.50717236624206090E-29 C 80 0 41 0 3 0 -2.42610952728340599E-31 C 81 0 43 0 3 0 1.18668400791036162E-33 C 82 0 45 0 3 0 -5.29769646388554297E-36 C 83 0 47 0 3 0 2.16723946249863121E-38 C 84 0 49 0 3 0 -8.15432908130755891E-41 C 85 0 51 0 3 0 2.83136426434290240E-43 C 86 0 53 0 3 0 -9.10081370681647200E-46 C 87 0 55 0 3 0 2.71576005840014085E-48 C 88 0 57 0 3 0 -7.54377794000039125E-51 C 89 0 4 0 4 0 1.33333333333333333E+00 C 90 0 6 0 4 0 -1.06666666666666667E+00 C 91 0 8 0 4 0 3.55555555555555555E-01 C 92 0 10 0 4 0 -6.77248677248677249E-02 C 93 0 12 0 4 0 8.46560846560846561E-03 C 94 0 14 0 4 0 -7.52498530276308055E-04 C 95 0 16 0 4 0 5.01665686850872037E-05 C 96 0 18 0 4 0 -2.60605551610842616E-06 C 97 0 20 0 4 0 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C 381 0 28 0 18 0 -3.37399617157768304E+02 C 382 0 30 0 18 0 1.89787284651244671E+02 C 383 0 32 0 18 0 -8.78444003242903908E+01 C 384 0 34 0 18 0 3.42086366647477001E+01 C 385 0 36 0 18 0 -1.14028788882492334E+01 C 386 0 38 0 18 0 3.29868996410067109E+00 C 387 0 40 0 18 0 -8.37598392138414915E-01 C 388 0 42 0 18 0 1.88459638231143356E-01 C 389 0 19 0 19 0 6.20417265088483562E+01 C 390 0 21 0 19 0 -2.79963290871178207E+02 C 391 0 23 0 19 0 6.01587785741043648E+02 C 392 0 25 0 19 0 -8.22625722168624078E+02 C 393 0 27 0 19 0 8.06977950279546991E+02 C 394 0 29 0 19 0 -6.06914666772742630E+02 C 395 0 31 0 19 0 3.65160324508266817E+02 C 396 0 33 0 19 0 -1.81075380697093848E+02 C 397 0 35 0 19 0 7.56576532773737026E+01 C 398 0 37 0 19 0 -2.70956476519165740E+01 C 399 0 39 0 19 0 8.43235241581196830E+00 C 400 0 41 0 19 0 -2.30612062280918224E+00 C 401 0 20 0 20 0 8.22063524662432972E+01 C 402 0 22 0 20 0 -3.91458821267825224E+02 C 403 0 24 0 20 0 8.89679139245057328E+02 C 404 0 26 0 20 0 -1.28939005687689468E+03 C 405 0 28 0 20 0 1.34311464258009862E+03 C 406 0 30 0 20 0 -1.07449171406407890E+03 C 407 0 32 0 20 0 6.88776739784665962E+02 C 408 0 34 0 20 0 -3.64432137452204212E+02 C 409 0 36 0 20 0 1.62692918505448309E+02 C 410 0 38 0 20 0 -6.23344515346545246E+01 C 411 0 40 0 20 0 2.07781505115515082E+01 C 431 number of terms for function cos(v) 1 0 1 0 0 0 -1.00000000000000000E+00 C 2 0 0 0 1 0 1.00000000000000000E+00 C 3 0 2 0 1 0 -1.12500000000000000E+00 C 4 0 4 0 1 0 1.30208333333333333E-01 C 5 0 6 0 1 0 -5.31684027777777778E-03 C 6 0 8 0 1 0 1.09863281250000000E-04 C 7 0 10 0 1 0 -1.36763961226851852E-06 C 8 0 12 0 1 0 1.13700853243496473E-08 C 9 0 14 0 1 0 -6.75789623303748584E-11 C 10 0 16 0 1 0 3.01393828911702686E-13 C 11 0 18 0 1 0 -1.04578212453983727E-15 C 12 0 20 0 1 0 2.90348726342274135E-18 C 13 0 22 0 1 0 -6.59634079893591603E-21 C 14 0 24 0 1 0 1.24894364043640260E-23 C 15 0 26 0 1 0 -2.00105475577612636E-26 C 16 0 28 0 1 0 2.74819885297492041E-29 C 17 0 30 0 1 0 -3.27117902510515572E-32 C 18 0 32 0 1 0 3.40706100257421285E-35 C 19 0 34 0 1 0 -3.13117038488975520E-38 C 20 0 36 0 1 0 2.55792592010626260E-41 C 21 0 38 0 1 0 -1.86969230541003105E-44 C 22 0 40 0 1 0 1.22998370644088405E-47 C 23 0 42 0 1 0 -7.32093564568475595E-51 C 24 0 44 0 1 0 3.96135895551693117E-54 C 25 0 46 0 1 0 -1.95711261691199252E-57 C 26 0 48 0 1 0 8.86341367361870763E-61 C 27 0 50 0 1 0 -3.69297071173585662E-64 C 28 0 52 0 1 0 1.42033289974845600E-67 C 29 0 54 0 1 0 -5.05803697598408108E-71 C 30 0 56 0 1 0 1.67259314161261648E-74 C 31 0 58 0 1 0 -5.14950376062087889E-78 C 32 0 60 0 1 0 1.47931736875061158E-81 C 33 0 1 0 2 0 1.00000000000000000E+00 C 34 0 3 0 2 0 -1.33333333333333333E+00 C 35 0 5 0 2 0 3.75000000000000001E-01 C 36 0 7 0 2 0 -4.44444444444444444E-02 C 37 0 9 0 2 0 2.89351851851851852E-03 C 38 0 11 0 2 0 -1.19047619047619048E-04 C 39 0 13 0 2 0 3.37577160493827161E-06 C 40 0 15 0 2 0 -6.99868424736149604E-08 C 41 0 17 0 2 0 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8 0 3 0 -1.60180664062500000E-01 C 67 0 10 0 3 0 1.92280360630580358E-02 C 68 0 12 0 3 0 -1.51063237871442522E-03 C 69 0 14 0 3 0 8.37998730795724052E-05 C 70 0 16 0 3 0 -3.45973761714234644E-06 C 71 0 18 0 3 0 1.10497478748186179E-07 C 72 0 20 0 3 0 -2.81217613850127567E-09 C 73 0 22 0 3 0 5.83846615881936746E-11 C 74 0 24 0 3 0 -1.00782449559813118E-12 C 75 0 26 0 3 0 1.46940811458207526E-14 C 76 0 28 0 3 0 -1.83370759788034974E-16 C 77 0 30 0 3 0 1.98090221400932575E-18 C 78 0 32 0 3 0 -1.87062305849475871E-20 C 79 0 34 0 3 0 1.55741167807747895E-22 C 80 0 36 0 3 0 -1.15179287428527119E-24 C 81 0 38 0 3 0 7.61712129894908293E-27 C 82 0 40 0 3 0 -4.53143346151489496E-29 C 83 0 42 0 3 0 2.43797636736250960E-31 C 84 0 44 0 3 0 -1.19198170437424716E-33 C 85 0 46 0 3 0 5.31936885851052928E-36 C 86 0 48 0 3 0 -2.17539379157993877E-38 C 87 0 50 0 3 0 8.18264272395098793E-41 C 88 0 52 0 3 0 -2.84046507804971887E-43 C 89 0 54 0 3 0 9.12797130740047341E-46 C 90 0 56 0 3 0 -2.72330383634014124E-48 C 91 0 58 0 3 0 7.54377794000039125E-51 C 92 0 3 0 4 0 1.33333333333333333E+00 C 93 0 5 0 4 0 -2.40000000000000000E+00 C 94 0 7 0 4 0 1.42222222222222222E+00 C 95 0 9 0 4 0 -4.23280423280423280E-01 C 96 0 11 0 4 0 7.61904761904761905E-02 C 97 0 13 0 4 0 -9.21810699588477367E-03 C 98 0 15 0 4 0 8.02665098961395258E-04 C 99 0 17 0 4 0 -5.27726242011956298E-05 C 100 0 19 0 4 0 2.71464116261294392E-06 C 101 0 21 0 4 0 -1.12297976299544005E-07 C 102 0 23 0 4 0 3.81839636059842661E-09 C 103 0 25 0 4 0 -1.08637876252716178E-10 C 104 0 27 0 4 0 2.62487965304886228E-12 C 105 0 29 0 4 0 -5.45385466742999367E-14 C 106 0 31 0 4 0 9.84964229179596742E-16 C 107 0 33 0 4 0 -1.56060670083828650E-17 C 108 0 35 0 4 0 2.18700939044811776E-19 C 109 0 37 0 4 0 -2.73026382388135184E-21 C 110 0 39 0 4 0 3.05578088237650952E-23 C 111 0 41 0 4 0 -3.08375141676897184E-25 C 112 0 43 0 4 0 2.82036221790661824E-27 C 113 0 45 0 4 0 -2.34863693549405911E-29 C 114 0 47 0 4 0 1.78832587524234676E-31 C 115 0 49 0 4 0 -1.24989227950714206E-33 C 116 0 51 0 4 0 8.04692553282693369E-36 C 117 0 53 0 4 0 -4.78776471204312153E-38 C 118 0 55 0 4 0 2.64050334792431310E-40 C 119 0 57 0 4 0 -1.34719558567566995E-42 C 120 0 4 0 5 0 1.62760416666666667E+00 C 121 0 6 0 5 0 -3.32302517361111111E+00 C 122 0 8 0 5 0 2.45230538504464286E+00 C 123 0 10 0 5 0 -9.53989684897125083E-01 C 124 0 12 0 5 0 2.31324978115837550E-01 C 125 0 14 0 5 0 -3.84971302337747401E-02 C 126 0 16 0 5 0 4.68252131210475587E-03 C 127 0 18 0 5 0 -4.35200968464176776E-04 C 128 0 20 0 5 0 3.19497834362184967E-05 C 129 0 22 0 5 0 -1.90105408857930038E-06 C 130 0 24 0 5 0 9.35852871268165355E-08 C 131 0 26 0 5 0 -3.87634513155961673E-09 C 132 0 28 0 5 0 1.37006368499423299E-10 C 133 0 30 0 5 0 -4.18150198074972404E-12 C 134 0 32 0 5 0 1.11335888589102084E-13 C 135 0 34 0 5 0 -2.60916864710839555E-15 C 136 0 36 0 5 0 5.42388222468931231E-17 C 137 0 38 0 5 0 -1.00703469096949597E-18 C 138 0 40 0 5 0 1.68020629416800335E-20 C 139 0 42 0 5 0 -2.53306876480413036E-22 C 140 0 44 0 5 0 3.46772867004351269E-24 C 141 0 46 0 5 0 -4.33015230414581893E-26 C 142 0 48 0 5 0 4.95214313148751705E-28 C 143 0 50 0 5 0 -5.20637601706095216E-30 C 144 0 52 0 5 0 5.04914328648609626E-32 C 145 0 54 0 5 0 -4.53116721301187885E-34 C 146 0 56 0 5 0 3.74476629174535441E-36 C 147 0 5 0 6 0 2.02500000000000000E+00 C 148 0 7 0 6 0 -4.62857142857142858E+00 C 149 0 9 0 6 0 4.06808035714285715E+00 C 150 0 11 0 6 0 -1.95267857142857143E+00 C 151 0 13 0 6 0 5.98007812500000000E-01 C 152 0 15 0 6 0 -1.27811688311688311E-01 C 153 0 17 0 6 0 2.02202085024350650E-02 C 154 0 19 0 6 0 -2.46888992703724847E-03 C 155 0 21 0 6 0 2.40055458084246748E-04 C 156 0 23 0 6 0 -1.90457222942873453E-05 C 157 0 25 0 6 0 1.25731526083381303E-06 C 158 0 27 0 6 0 -7.01801765690233895E-08 C 159 0 29 0 6 0 3.35683242517650142E-09 C 160 0 31 0 6 0 -1.39165846290718115E-10 C 161 0 33 0 6 0 5.04980979634706779E-12 C 162 0 35 0 6 0 -1.61753670194409289E-13 C 163 0 37 0 6 0 4.60803937343606008E-15 C 164 0 39 0 6 0 -1.17526207709260411E-16 C 165 0 41 0 6 0 2.69943008332207507E-18 C 166 0 43 0 6 0 -5.61342281558704332E-20 C 167 0 45 0 6 0 1.06188437798036846E-21 C 168 0 47 0 6 0 -1.83528490928284043E-23 C 169 0 49 0 6 0 2.90952990133364263E-25 C 170 0 51 0 6 0 -4.24625605270497913E-27 C 171 0 53 0 6 0 5.72396572193404177E-29 C 172 0 55 0 6 0 -7.06662434806671823E-31 C 173 0 6 0 7 0 2.55314670138888889E+00 C 174 0 8 0 7 0 -6.46265258789062501E+00 C 175 0 10 0 7 0 6.57014183703763985E+00 C 176 0 12 0 7 0 -3.74706229700473110E+00 C 177 0 14 0 7 0 1.38889731792889862E+00 C 178 0 16 0 7 0 -3.64225461466502469E-01 C 179 0 18 0 7 0 7.14531118343643218E-02 C 180 0 20 0 7 0 -1.09109495564247458E-02 C 181 0 22 0 7 0 1.33608618410849318E-03 C 182 0 24 0 7 0 -1.34286518681483025E-04 C 183 0 26 0 7 0 1.12867029031088356E-05 C 184 0 28 0 7 0 -8.05575889093631802E-07 C 185 0 30 0 7 0 4.94578340341620616E-08 C 186 0 32 0 7 0 -2.64059821689838487E-09 C 187 0 34 0 7 0 1.23765412293408382E-10 C 188 0 36 0 7 0 -5.13438937665685072E-12 C 189 0 38 0 7 0 1.89890324703875026E-13 C 190 0 40 0 7 0 -6.30111291410992915E-15 C 191 0 42 0 7 0 1.88673121531916746E-16 C 192 0 44 0 7 0 -5.12397840719363543E-18 C 193 0 46 0 7 0 1.26800307904217260E-19 C 194 0 48 0 7 0 -2.87127979551480346E-21 C 195 0 50 0 7 0 5.97226564849817974E-23 C 196 0 52 0 7 0 -1.14508441029500632E-24 C 197 0 54 0 7 0 1.99747725540958738E-26 C 198 0 7 0 8 0 3.25079365079365080E+00 C 199 0 9 0 8 0 -9.02998236331569666E+00 C 200 0 11 0 8 0 1.04025396825396825E+01 C 201 0 13 0 8 0 -6.86497568275346052E+00 C 202 0 15 0 8 0 2.98883295031443180E+00 C 203 0 17 0 8 0 -9.31136419136419136E-01 C 204 0 19 0 8 0 2.18962120902156175E-01 C 205 0 21 0 8 0 -4.03724443872927958E-02 C 206 0 23 0 8 0 6.00581817331628367E-03 C 207 0 25 0 8 0 -7.37097510014852536E-04 C 208 0 27 0 8 0 7.59874356149433777E-05 C 209 0 29 0 8 0 -6.67793106663890635E-06 C 210 0 31 0 8 0 5.06533437943573340E-07 C 211 0 33 0 8 0 -3.35137737100944816E-08 C 212 0 35 0 8 0 1.95182001205601259E-09 C 213 0 37 0 8 0 -1.00856256840539709E-10 C 214 0 39 0 8 0 4.65633688091134392E-12 C 215 0 41 0 8 0 -1.93265370774767310E-13 C 216 0 43 0 8 0 7.25161846270034133E-15 C 217 0 45 0 8 0 -2.47199662769222082E-16 C 218 0 47 0 8 0 7.69035947907490786E-18 C 219 0 49 0 8 0 -2.19233473564213529E-19 C 220 0 51 0 8 0 5.74843454562553584E-21 C 221 0 53 0 8 0 -1.36057622381669487E-22 C 222 0 8 0 9 0 4.17041800362723215E+00 C 223 0 10 0 9 0 -1.26155144609723773E+01 C 224 0 12 0 9 0 1.62184238783105628E+01 C 225 0 14 0 9 0 -1.21458240952584651E+01 C 226 0 16 0 9 0 6.07524778303216686E+00 C 227 0 18 0 9 0 -2.19533267948150755E+00 C 228 0 20 0 9 0 6.03412424159425448E-01 C 229 0 22 0 9 0 -1.30869467539314165E-01 C 230 0 24 0 9 0 2.30223048279834997E-02 C 231 0 26 0 9 0 -3.35665204391999426E-03 C 232 0 28 0 9 0 4.12711165049227365E-04 C 233 0 30 0 9 0 -4.34086177151077009E-05 C 234 0 32 0 9 0 3.95280086057836494E-06 C 235 0 34 0 9 0 -3.14827121654311923E-07 C 236 0 36 0 9 0 2.21262927450405596E-08 C 237 0 38 0 9 0 -1.38279228171503022E-09 C 238 0 40 0 9 0 7.73678418271697198E-11 C 239 0 42 0 9 0 -3.89881329478702000E-12 C 240 0 44 0 9 0 1.77913667792133484E-13 C 241 0 46 0 9 0 -7.38743030362448996E-15 C 242 0 48 0 9 0 2.80341165623233019E-16 C 243 0 50 0 9 0 -9.76156712392791953E-18 C 244 0 52 0 9 0 3.03993439845506145E-19 C 245 0 9 0 10 0 5.38228891093474428E+00 C 246 0 11 0 10 0 -1.76147637085137085E+01 C 247 0 13 0 10 0 2.49746360450570520E+01 C 248 0 15 0 10 0 -2.09102133291948107E+01 C 249 0 17 0 10 0 1.18145039039116885E+01 C 250 0 19 0 10 0 -4.86193576292662079E+00 C 251 0 21 0 10 0 1.53201621696385707E+00 C 252 0 23 0 10 0 -3.83030653591908150E-01 C 253 0 25 0 10 0 7.80432345402108379E-02 C 254 0 27 0 10 0 -1.32327017975373925E-02 C 255 0 29 0 10 0 1.89882519416193451E-03 C 256 0 31 0 10 0 -2.33813972922296889E-04 C 257 0 33 0 10 0 2.49956491826999738E-05 C 258 0 35 0 10 0 -2.34304380668977083E-06 C 259 0 37 0 10 0 1.94242085128005418E-07 C 260 0 39 0 10 0 -1.43484458081629118E-08 C 261 0 41 0 10 0 9.50670763431466960E-10 C 262 0 43 0 10 0 -5.68282435814856817E-11 C 263 0 45 0 10 0 3.08094549949637668E-12 C 264 0 47 0 10 0 -1.52208616033223060E-13 C 265 0 49 0 10 0 6.88153826828446269E-15 C 266 0 51 0 10 0 -2.75261530731378507E-16 C 267 0 10 0 11 0 6.98013564040841670E+00 C 268 0 12 0 11 0 -2.45758942339379671E+01 C 269 0 14 0 11 0 3.80677469571552774E+01 C 270 0 16 0 11 0 -3.52166942683799707E+01 C 271 0 18 0 11 0 2.21784951317345084E+01 C 272 0 20 0 11 0 -1.02446907784321771E+01 C 273 0 22 0 11 0 3.64452676646583759E+00 C 274 0 24 0 11 0 -1.03376142734861737E+00 C 275 0 26 0 11 0 2.39965951960511024E-01 C 276 0 28 0 11 0 -4.65233486462687897E-02 C 277 0 30 0 11 0 7.65780746268158814E-03 C 278 0 32 0 11 0 -1.08472324751043828E-03 C 279 0 34 0 11 0 1.33734498611139986E-04 C 280 0 36 0 11 0 -1.44904408427765093E-05 C 281 0 38 0 11 0 1.39144068827373033E-06 C 282 0 40 0 11 0 -1.19278994687859296E-07 C 283 0 42 0 11 0 9.18702292318012054E-09 C 284 0 44 0 11 0 -6.39412824713395225E-10 C 285 0 46 0 11 0 4.04209863546707101E-11 C 286 0 48 0 11 0 -2.33159907570014402E-12 C 287 0 50 0 11 0 1.17502494027370857E-13 C 288 0 11 0 12 0 9.08883116883116884E+00 C 289 0 13 0 12 0 -3.42579020979020979E+01 C 290 0 15 0 12 0 5.75293049807335522E+01 C 291 0 17 0 12 0 -5.82484212929927216E+01 C 292 0 19 0 12 0 4.04502925645782788E+01 C 293 0 21 0 12 0 -2.07295852248591744E+01 C 294 0 23 0 12 0 8.22330653548132540E+00 C 295 0 25 0 12 0 -2.61229098589538344E+00 C 296 0 27 0 12 0 6.81668831230688817E-01 C 297 0 29 0 12 0 -1.49052951435281812E-01 C 298 0 31 0 12 0 2.77509495035870135E-02 C 299 0 33 0 12 0 -4.45777048288227657E-03 C 300 0 35 0 12 0 6.24704860057896890E-04 C 301 0 37 0 12 0 -7.71003263182566759E-05 C 302 0 39 0 12 0 8.44909362715667814E-06 C 303 0 41 0 12 0 -8.28011175461354458E-07 C 304 0 43 0 12 0 7.30243092061398611E-08 C 305 0 45 0 12 0 -5.82818527367327509E-09 C 306 0 47 0 12 0 4.23066757105961745E-10 C 307 0 49 0 12 0 -2.64416723191226090E-11 C 308 0 12 0 13 0 1.18747182955249270E+01 C 309 0 14 0 13 0 -4.77109217230912247E+01 C 310 0 16 0 13 0 8.63055232547221669E+01 C 311 0 18 0 13 0 -9.48928357166836916E+01 C 312 0 20 0 13 0 7.20248915708888590E+01 C 313 0 22 0 13 0 -4.05586881539999677E+01 C 314 0 24 0 13 0 1.77594743320160788E+01 C 315 0 26 0 13 0 -6.25138570622489409E+00 C 316 0 28 0 13 0 1.81368639166511115E+00 C 317 0 30 0 13 0 -4.42232961577635806E-01 C 318 0 32 0 13 0 9.20565041868860239E-02 C 319 0 34 0 13 0 -1.65724025545486538E-02 C 320 0 36 0 13 0 2.60830450845097353E-03 C 321 0 38 0 13 0 -3.62238053081987833E-04 C 322 0 40 0 13 0 4.47473667865095198E-05 C 323 0 42 0 13 0 -4.95124143820829483E-06 C 324 0 44 0 13 0 4.93754371302414661E-07 C 325 0 46 0 13 0 -4.46208849307646439E-08 C 326 0 48 0 13 0 3.41372999243966720E-09 C 327 0 13 0 14 0 1.55594486543227862E+01 C 328 0 15 0 14 0 -6.63869809251105548E+01 C 329 0 17 0 14 0 1.28657191060431539E+02 C 330 0 19 0 14 0 -1.52607174097340726E+02 C 331 0 21 0 14 0 1.25667768780990718E+02 C 332 0 23 0 14 0 -7.71389105279400177E+01 C 333 0 25 0 14 0 3.69668586852934772E+01 C 334 0 27 0 14 0 -1.42909355075296283E+01 C 335 0 29 0 14 0 4.56741546760534995E+00 C 336 0 31 0 14 0 -1.23013761944479892E+00 C 337 0 33 0 14 0 2.83528301252568319E-01 C 338 0 35 0 14 0 -5.66378774543664629E-02 C 339 0 37 0 14 0 9.91084415845885133E-03 C 340 0 39 0 14 0 -1.53303616501956015E-03 C 341 0 41 0 14 0 2.11271546491758133E-04 C 342 0 43 0 14 0 -2.61188833977039428E-05 C 343 0 45 0 14 0 2.91420272276120826E-06 C 344 0 47 0 14 0 -2.69935601919280160E-07 C 345 0 14 0 15 0 2.04385148736937879E+01 C 346 0 16 0 15 0 -9.22926687265235112E+01 C 347 0 18 0 15 0 1.90730511329937721E+02 C 348 0 20 0 15 0 -2.42705896515762162E+02 C 349 0 22 0 15 0 2.15479691287658069E+02 C 350 0 24 0 15 0 -1.43203362889068601E+02 C 351 0 26 0 15 0 7.45680368186650074E+01 C 352 0 28 0 15 0 -3.14212156107189310E+01 C 353 0 30 0 15 0 1.09762775057961873E+01 C 354 0 32 0 15 0 -3.23912975953110041E+00 C 355 0 34 0 15 0 8.19821065170578100E-01 C 356 0 36 0 15 0 -1.80195078920484743E-01 C 357 0 38 0 15 0 3.47573141179258601E-02 C 358 0 40 0 15 0 -5.93616346074937525E-03 C 359 0 42 0 15 0 9.04631158645839930E-04 C 360 0 44 0 15 0 -1.23842488930355993E-04 C 361 0 46 0 15 0 1.37602765478173326E-05 C 362 0 15 0 16 0 2.69060654164569509E+01 C 363 0 17 0 16 0 -1.28199488160765472E+02 C 364 0 19 0 16 0 2.81370618734190336E+02 C 365 0 21 0 16 0 -3.82269135346942099E+02 C 366 0 23 0 16 0 3.63945490842708511E+02 C 367 0 25 0 16 0 -2.60346192391186194E+02 C 368 0 27 0 16 0 1.46395133465798799E+02 C 369 0 29 0 16 0 -6.68047256276937096E+01 C 370 0 31 0 16 0 2.53363107565771699E+01 C 371 0 33 0 16 0 -8.13577089850089124E+00 C 372 0 35 0 16 0 2.24518692242899230E+00 C 373 0 37 0 16 0 -5.39061381882606288E-01 C 374 0 39 0 16 0 1.13771034297872320E-01 C 375 0 41 0 16 0 -2.12935919895434242E-02 C 376 0 43 0 16 0 3.56111815931377339E-03 C 377 0 45 0 16 0 -4.70891657429920448E-04 C 378 0 16 0 17 0 3.54881383570408616E+01 C 379 0 18 0 17 0 -1.77933582595718765E+02 C 380 0 20 0 17 0 4.13279216508269442E+02 C 381 0 22 0 17 0 -5.96962773044224684E+02 C 382 0 24 0 17 0 6.06638766321862248E+02 C 383 0 26 0 17 0 -4.64753679736204583E+02 C 384 0 28 0 17 0 2.80704948972696338E+02 C 385 0 30 0 17 0 -1.37945021468981763E+02 C 386 0 32 0 17 0 5.64700768753114064E+01 C 387 0 34 0 17 0 -1.96132056440297700E+01 C 388 0 36 0 17 0 5.86529727453483162E+00 C 389 0 38 0 17 0 -1.52863193917614609E+00 C 390 0 40 0 17 0 3.50751903305459371E-01 C 391 0 42 0 17 0 -7.14730768476519527E-02 C 392 0 44 0 17 0 1.11712921627752376E-02 C 393 0 17 0 18 0 4.68871834715659375E+01 C 394 0 19 0 18 0 -2.46774649850347039E+02 C 395 0 21 0 18 0 6.04659585795812832E+02 C 396 0 23 0 18 0 -9.25193415810358241E+02 C 397 0 25 0 18 0 9.99445444209911139E+02 C 398 0 27 0 18 0 -8.16423764974352932E+02 C 399 0 29 0 18 0 5.27186901809012974E+02 C 400 0 31 0 18 0 -2.77631684975535061E+02 C 401 0 33 0 18 0 1.22053036989038091E+02 C 402 0 35 0 18 0 -4.56115155529969335E+01 C 403 0 37 0 18 0 1.47015688523499045E+01 C 404 0 39 0 18 0 -4.13628835623908600E+00 C 405 0 41 0 18 0 1.02605803036955827E+00 C 406 0 43 0 18 0 -1.88459638231143356E-01 C 407 0 18 0 19 0 6.20417265088483562E+01 C 408 0 20 0 19 0 -3.42005017380026563E+02 C 409 0 22 0 19 0 8.81551076612221855E+02 C 410 0 24 0 19 0 -1.42421350790966773E+03 C 411 0 26 0 19 0 1.62960367244817107E+03 C 412 0 28 0 19 0 -1.41389261705228962E+03 C 413 0 30 0 19 0 9.72074991281009448E+02 C 414 0 32 0 19 0 -5.46235705205360665E+02 C 415 0 34 0 19 0 2.56733033974467550E+02 C 416 0 36 0 19 0 -1.02753300929290277E+02 C 417 0 38 0 19 0 3.55280000677285423E+01 C 418 0 40 0 19 0 -1.07384730386211505E+01 C 419 0 42 0 19 0 2.30612062280918224E+00 C 420 0 19 0 20 0 8.22063524662432972E+01 C 421 0 21 0 20 0 -4.73665173734068521E+02 C 422 0 23 0 20 0 1.28113796051288255E+03 C 423 0 25 0 20 0 -2.17906919612195201E+03 C 424 0 27 0 20 0 2.63250469945699330E+03 C 425 0 29 0 20 0 -2.41760635664417752E+03 C 426 0 31 0 20 0 1.76326845384874486E+03 C 427 0 33 0 20 0 -1.05320887723687017E+03 C 428 0 35 0 20 0 5.27125055957652521E+02 C 429 0 37 0 20 0 -2.25027370040102834E+02 C 430 0 39 0 20 0 8.31126020462060328E+01 C 431 0 41 0 20 0 -2.07781505115515082E+01 C 418 number of terms for function sin(v) 1 0 0 0 1 0 1.00000000000000000E+00 S 2 0 2 0 1 0 -8.75000000000000000E-01 S 3 0 4 0 1 0 8.85416666666666667E-02 S 4 0 6 0 1 0 -2.94053819444444445E-02 S 5 0 8 0 1 0 -1.84882269965277778E-02 S 6 0 10 0 1 0 -1.42342009367766204E-02 S 7 0 12 0 1 0 -1.12251499048196029E-02 S 8 0 14 0 1 0 -9.10600635770527173E-03 S 9 0 16 0 1 0 -7.56331843026340090E-03 S 10 0 18 0 1 0 -6.40488780099118893E-03 S 11 0 20 0 1 0 -5.51121295679417098E-03 S 12 0 22 0 1 0 -4.80574911557769951E-03 S 13 0 24 0 1 0 -4.23784773508599199E-03 S 14 0 26 0 1 0 -3.77295615413353293E-03 S 15 0 28 0 1 0 -3.38684549675461702E-03 S 16 0 30 0 1 0 -3.06210645935619503E-03 S 17 0 32 0 1 0 -2.78595674662171582E-03 S 18 0 34 0 1 0 -2.54882987571652952E-03 S 19 0 36 0 1 0 -2.34344309250750169E-03 S 20 0 38 0 1 0 -2.16416711989002343E-03 S 21 0 40 0 1 0 -2.00659084915225084E-03 S 22 0 42 0 1 0 -1.86721483744629192E-03 S 23 0 44 0 1 0 -1.74323169830263798E-03 S 24 0 46 0 1 0 -1.63236623219796740E-03 S 25 0 48 0 1 0 -1.53275734701274954E-03 S 26 0 50 0 1 0 -1.44286967947510226E-03 S 27 0 52 0 1 0 -1.36142663576348820E-03 S 28 0 54 0 1 0 -1.28735908753629858E-03 S 29 0 56 0 1 0 -1.21976565336874547E-03 S 30 0 58 0 1 0 -1.15788165263796246E-03 S 31 0 60 0 1 0 -1.10105462082398638E-03 S 32 0 1 0 2 0 1.00000000000000000E+00 S 33 0 3 0 2 0 -1.16666666666666667E+00 S 34 0 5 0 2 0 3.33333333333333334E-01 S 35 0 7 0 2 0 -5.27777777777777777E-02 S 36 0 9 0 2 0 -6.88657407407407405E-03 S 37 0 11 0 2 0 -8.03488756613756612E-03 S 38 0 13 0 2 0 -6.52894896384479717E-03 S 39 0 15 0 2 0 -5.45928591987206404E-03 S 40 0 17 0 2 0 -4.63093195217580344E-03 S 41 0 19 0 2 0 -3.98338039881523896E-03 S 42 0 21 0 2 0 -3.46898531980281294E-03 S 43 0 23 0 2 0 -3.05382212431642216E-03 S 44 0 25 0 2 0 -2.71376757913506298E-03 S 45 0 27 0 2 0 -2.43149106515438671E-03 S 46 0 29 0 2 0 -2.19435678616330300E-03 S 47 0 31 0 2 0 -1.99300466591584722E-03 S 48 0 33 0 2 0 -1.82039222816239638E-03 S 49 0 35 0 2 0 -1.67114197482592205E-03 S 50 0 37 0 2 0 -1.54109097596558898E-03 S 51 0 39 0 2 0 -1.42697543260629995E-03 S 52 0 41 0 2 0 -1.32620645966108483E-03 S 53 0 43 0 2 0 -1.23670838823111400E-03 S 54 0 45 0 2 0 -1.15680053610530063E-03 S 55 0 47 0 2 0 -1.08510963000759034E-03 S 56 0 49 0 2 0 -1.02050413734374804E-03 S 57 0 51 0 2 0 -9.62044461954368312E-04 S 58 0 53 0 2 0 -9.08944767349174773E-04 S 59 0 55 0 2 0 -8.60543420581158396E-04 S 60 0 57 0 2 0 -8.16279896726863980E-04 S 61 0 59 0 2 0 -7.75676574406850054E-04 S 62 0 2 0 3 0 1.12500000000000000E+00 S 63 0 4 0 3 0 -1.61718750000000000E+00 S 64 0 6 0 3 0 7.18945312500000000E-01 S 65 0 8 0 3 0 -1.57983398437500000E-01 S 66 0 10 0 3 0 1.23851231166294645E-02 S 67 0 12 0 3 0 -6.62356649126325325E-03 S 68 0 14 0 3 0 -4.33711818286350788E-03 S 69 0 16 0 3 0 -3.78990745848538919E-03 S 70 0 18 0 3 0 -3.27215831058621679E-03 S 71 0 20 0 3 0 -2.85480519598218176E-03 S 72 0 22 0 3 0 -2.51385136446332055E-03 S 73 0 24 0 3 0 -2.23275839844933259E-03 S 74 0 26 0 3 0 -1.99862264496459835E-03 S 75 0 28 0 3 0 -1.80161525732565975E-03 S 76 0 30 0 3 0 -1.63425431289877082E-03 S 77 0 32 0 3 0 -1.49081109289625622E-03 S 78 0 34 0 3 0 -1.36686075712920821E-03 S 79 0 36 0 3 0 -1.25895172685546171E-03 S 80 0 38 0 3 0 -1.16436429188272568E-03 S 81 0 40 0 3 0 -1.08093410170382580E-03 S 82 0 42 0 3 0 -1.00692233007771177E-03 S 83 0 44 0 3 0 -9.40919392763393653E-04 S 84 0 46 0 3 0 -8.81772895032001381E-04 S 85 0 48 0 3 0 -8.28533201018644880E-04 S 86 0 50 0 3 0 -7.80411927140648270E-04 S 87 0 52 0 3 0 -7.36749999458903128E-04 S 88 0 54 0 3 0 -6.96992853175263916E-04 S 89 0 56 0 3 0 -6.60671013986939010E-04 S 90 0 58 0 3 0 -6.27384770627000946E-04 S 91 0 3 0 4 0 1.33333333333333334E+00 S 92 0 5 0 4 0 -2.26666666666666667E+00 S 93 0 7 0 4 0 1.34444444444444445E+00 S 94 0 9 0 4 0 -4.08201058201058202E-01 S 95 0 11 0 4 0 6.90806878306878307E-02 S 96 0 13 0 4 0 -1.25709141681363904E-02 S 97 0 15 0 4 0 -2.44658166764648250E-03 S 98 0 17 0 4 0 -2.87270669818619557E-03 S 99 0 19 0 4 0 -2.47463956096803046E-03 S 100 0 21 0 4 0 -2.18848912957626967E-03 S 101 0 23 0 4 0 -1.94635141269842200E-03 S 102 0 25 0 4 0 -1.74284182381492938E-03 S 103 0 27 0 4 0 -1.57063257074642124E-03 S 104 0 29 0 4 0 -1.42385761393192955E-03 S 105 0 31 0 4 0 -1.29783315443452400E-03 S 106 0 33 0 4 0 -1.18884432580758676E-03 S 107 0 35 0 4 0 -1.09394164095331146E-03 S 108 0 37 0 4 0 -1.01077276391645056E-03 S 109 0 39 0 4 0 -9.37449960941508223E-04 S 110 0 41 0 4 0 -8.72447757640756727E-04 S 111 0 43 0 4 0 -8.14524488570227910E-04 S 112 0 45 0 4 0 -7.62662197071987211E-04 S 113 0 47 0 4 0 -7.16020455364340865E-04 S 114 0 49 0 4 0 -6.73900704681460829E-04 S 115 0 51 0 4 0 -6.35718553141999470E-04 S 116 0 53 0 4 0 -6.00982114599577121E-04 S 117 0 55 0 4 0 -5.69274956677981467E-04 S 118 0 57 0 4 0 -5.40242586332850536E-04 S 119 0 4 0 5 0 1.62760416666666667E+00 S 120 0 6 0 5 0 -3.18739149305555556E+00 S 121 0 8 0 5 0 2.34573606460813492E+00 S 122 0 10 0 5 0 -9.19854199444806134E-01 S 123 0 12 0 5 0 2.20259048180465205E-01 S 124 0 14 0 5 0 -4.00499477413105727E-02 S 125 0 16 0 5 0 2.07978854154927991E-03 S 126 0 18 0 5 0 -2.62286495856818054E-03 S 127 0 20 0 5 0 -1.92560086678695461E-03 S 128 0 22 0 5 0 -1.74937044110536472E-03 S 129 0 24 0 5 0 -1.56803741857363776E-03 S 130 0 26 0 5 0 -1.41455101911417802E-03 S 131 0 28 0 5 0 -1.28268166138585368E-03 S 132 0 30 0 5 0 -1.16893541543323873E-03 S 133 0 32 0 5 0 -1.07028472706558923E-03 S 134 0 34 0 5 0 -9.84239994375892696E-04 S 135 0 36 0 5 0 -9.08766769793520051E-04 S 136 0 38 0 5 0 -8.42204986638834797E-04 S 137 0 40 0 5 0 -7.83197336422907663E-04 S 138 0 42 0 5 0 -7.30629753293335209E-04 S 139 0 44 0 5 0 -6.83583371655820347E-04 S 140 0 46 0 5 0 -6.41296264305929887E-04 S 141 0 48 0 5 0 -6.03133132947989884E-04 S 142 0 50 0 5 0 -5.68561318205665112E-04 S 143 0 52 0 5 0 -5.37131777192660685E-04 S 144 0 54 0 5 0 -5.08463949169272552E-04 S 145 0 56 0 5 0 -4.82233662904533230E-04 S 146 0 5 0 6 0 2.02500000000000000E+00 S 147 0 7 0 6 0 -4.48392857142857143E+00 S 148 0 9 0 6 0 3.92343750000000000E+00 S 149 0 11 0 6 0 -1.88939732142857143E+00 S 150 0 13 0 6 0 5.77215401785714285E-01 S 151 0 15 0 6 0 -1.26352932224025974E-01 S 152 0 17 0 6 0 1.77377549208603898E-02 S 153 0 19 0 6 0 -4.17927353756734330E-03 S 154 0 21 0 6 0 -1.35736890896790544E-03 S 155 0 23 0 6 0 -1.45405449348015262E-03 S 156 0 25 0 6 0 -1.29701148589084302E-03 S 157 0 27 0 6 0 -1.17896170476721594E-03 S 158 0 29 0 6 0 -1.07503718627356884E-03 S 159 0 31 0 6 0 -9.84458180520669324E-04 S 160 0 33 0 6 0 -9.05157664853689941E-04 S 161 0 35 0 6 0 -8.35434901658750400E-04 S 162 0 37 0 6 0 -7.73854433407875031E-04 S 163 0 39 0 6 0 -7.19217214934549440E-04 S 164 0 41 0 6 0 -6.70524057201022675E-04 S 165 0 43 0 6 0 -6.26941812822640365E-04 S 166 0 45 0 6 0 -5.87774111421932576E-04 S 167 0 47 0 6 0 -5.52436897927188652E-04 S 168 0 49 0 6 0 -5.20438342388388178E-04 S 169 0 51 0 6 0 -4.91362482627617449E-04 S 170 0 53 0 6 0 -4.64855953717597908E-04 S 171 0 55 0 6 0 -4.40617227380799608E-04 S 172 0 6 0 7 0 2.55314670138888889E+00 S 173 0 8 0 7 0 -6.30308091905381945E+00 S 174 0 10 0 7 0 6.37510979734821085E+00 S 175 0 12 0 7 0 -3.63940682736934458E+00 S 176 0 14 0 7 0 1.34877605742254018E+00 S 177 0 16 0 7 0 -3.56622227375843545E-01 S 178 0 18 0 7 0 6.81602988863622451E-02 S 179 0 20 0 7 0 -1.21286907123532656E-02 S 180 0 22 0 7 0 -1.59026539125254056E-05 S 181 0 24 0 7 0 -1.33582637490805154E-03 S 182 0 26 0 7 0 -1.08558364526658769E-03 S 183 0 28 0 7 0 -1.00259706954986166E-03 S 184 0 30 0 7 0 -9.18203022356904729E-04 S 185 0 32 0 7 0 -8.44629122923080272E-04 S 186 0 34 0 7 0 -7.79608414356977103E-04 S 187 0 36 0 7 0 -7.22013907873844644E-04 S 188 0 38 0 7 0 -6.70813589800888850E-04 S 189 0 40 0 7 0 -6.25126840809687637E-04 S 190 0 42 0 7 0 -5.84205368331129962E-04 S 191 0 44 0 7 0 -5.47415238118563361E-04 S 192 0 46 0 7 0 -5.14219470457350621E-04 S 193 0 48 0 7 0 -4.84162532248531563E-04 S 194 0 50 0 7 0 -4.56857019402605197E-04 S 195 0 52 0 7 0 -4.31972447125579297E-04 S 196 0 54 0 7 0 -4.09225915908912237E-04 S 197 0 7 0 8 0 3.25079365079365080E+00 S 198 0 9 0 8 0 -8.84938271604938272E+00 S 199 0 11 0 8 0 1.01406701940035273E+01 S 200 0 13 0 8 0 -6.69053284164395275E+00 S 201 0 15 0 8 0 2.91347478310441274E+00 S 202 0 17 0 8 0 -9.10832333647148462E-01 S 203 0 19 0 8 0 2.12844422805622101E-01 S 204 0 21 0 8 0 -4.07709111979877073E-02 S 205 0 23 0 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0 9 0 2.16450229061073679E-02 S 230 0 26 0 9 0 -4.18732161818583505E-03 S 231 0 28 0 9 0 -4.11745100876089668E-04 S 232 0 30 0 9 0 -7.97491587640009190E-04 S 233 0 32 0 9 0 -6.94082351792637061E-04 S 234 0 34 0 9 0 -6.47367556456722545E-04 S 235 0 36 0 9 0 -6.01366567739883949E-04 S 236 0 38 0 9 0 -5.60387740033953966E-04 S 237 0 40 0 9 0 -5.23504154002407344E-04 S 238 0 42 0 9 0 -4.90249359300893708E-04 S 239 0 44 0 9 0 -4.60186181204942288E-04 S 240 0 46 0 9 0 -4.32933618927789725E-04 S 241 0 48 0 9 0 -4.08160108831869522E-04 S 242 0 50 0 9 0 -3.85577928026900462E-04 S 243 0 52 0 9 0 -3.64937556790353143E-04 S 244 0 9 0 10 0 5.38228891093474428E+00 S 245 0 11 0 10 0 -1.73701142125621293E+01 S 246 0 13 0 10 0 2.45057245111498584E+01 S 247 0 15 0 10 0 -2.04899180412779950E+01 S 248 0 17 0 10 0 1.15753666762506849E+01 S 249 0 19 0 10 0 -4.76787792052162549E+00 S 250 0 21 0 10 0 1.50237066088812726E+00 S 251 0 23 0 10 0 -3.77111834999440230E-01 S 252 0 25 0 10 0 7.58867587407291954E-02 S 253 0 27 0 10 0 -1.37963837941306215E-02 S 254 0 29 0 10 0 1.15162243477094626E-03 S 255 0 31 0 10 0 -8.96208047791745120E-04 S 256 0 33 0 10 0 -5.93427914685936102E-04 S 257 0 35 0 10 0 -5.77272186430839081E-04 S 258 0 37 0 10 0 -5.35831045374608900E-04 S 259 0 39 0 10 0 -5.00868169049891358E-04 S 260 0 41 0 10 0 -4.69049241627273305E-04 S 261 0 43 0 10 0 -4.40238104103875296E-04 S 262 0 45 0 10 0 -4.14080527554432347E-04 S 263 0 47 0 10 0 -3.90277851974685424E-04 S 264 0 49 0 10 0 -3.68565670859154751E-04 S 265 0 51 0 10 0 -3.48711994406652457E-04 S 266 0 10 0 11 0 6.98013564040841671E+00 S 267 0 12 0 11 0 -2.42850552489209498E+01 S 268 0 14 0 11 0 3.74413245278878554E+01 S 269 0 16 0 11 0 -3.45823316951191240E+01 S 270 0 18 0 11 0 2.17712994677720572E+01 S 271 0 20 0 11 0 -1.00612788220376270E+01 S 272 0 22 0 11 0 3.58033300306378871E+00 S 273 0 24 0 11 0 -1.01732328814522776E+00 S 274 0 26 0 11 0 2.35411702362890375E-01 S 275 0 28 0 11 0 -4.65019777768178262E-02 S 276 0 30 0 11 0 6.91046218916662112E-03 S 277 0 32 0 11 0 -1.66208861600770746E-03 S 278 0 34 0 11 0 -4.19856989806591982E-04 S 279 0 36 0 11 0 -5.29263514668574650E-04 S 280 0 38 0 11 0 -4.80073057136333454E-04 S 281 0 40 0 11 0 -4.51131791759266821E-04 S 282 0 42 0 11 0 -4.23346098586279069E-04 S 283 0 44 0 11 0 -3.98187339628287867E-04 S 284 0 46 0 11 0 -3.75245625841067125E-04 S 285 0 48 0 11 0 -3.54294415174902255E-04 S 286 0 50 0 11 0 -3.35120549260312806E-04 S 287 0 11 0 12 0 9.08883116883116884E+00 S 288 0 13 0 12 0 -3.39083316683316684E+01 S 289 0 15 0 12 0 5.66928328814043100E+01 S 290 0 17 0 12 0 -5.73033326673326674E+01 S 291 0 19 0 12 0 3.97731559155130584E+01 S 292 0 21 0 12 0 -2.03862800741275531E+01 S 293 0 23 0 12 0 8.08952080052300641E+00 S 294 0 25 0 12 0 -2.57217999314808210E+00 S 295 0 27 0 12 0 6.70787899101805465E-01 S 296 0 29 0 12 0 -1.47518549435306875E-01 S 297 0 31 0 12 0 2.68003942445371905E-02 S 298 0 33 0 12 0 -4.92990194810771633E-03 S 299 0 35 0 12 0 1.20657823682013978E-04 S 300 0 37 0 12 0 -5.40522971527783777E-04 S 301 0 39 0 12 0 -4.26932422013422537E-04 S 302 0 41 0 12 0 -4.09561292560933166E-04 S 303 0 43 0 12 0 -3.84437698369263066E-04 S 304 0 45 0 12 0 -3.62372958870179675E-04 S 305 0 47 0 12 0 -3.42107625323410083E-04 S 306 0 49 0 12 0 -3.23542857496631459E-04 S 307 0 12 0 13 0 1.18747182955249270E+01 S 308 0 14 0 13 0 -4.72868246411081916E+01 S 309 0 16 0 13 0 8.51887342721668464E+01 S 310 0 18 0 13 0 -9.34993344323292853E+01 S 311 0 20 0 13 0 7.09208689196374625E+01 S 312 0 22 0 13 0 -3.99364422636141217E+01 S 313 0 24 0 13 0 1.74907919644269793E+01 S 314 0 26 0 13 0 -6.16030505336282783E+00 S 315 0 28 0 13 0 1.78740410925547887E+00 S 316 0 30 0 13 0 -4.36744958663721571E-01 S 317 0 32 0 13 0 9.03380371253477934E-02 S 318 0 34 0 13 0 -1.68424812192207266E-02 S 319 0 36 0 13 0 2.12788210047488867E-03 S 320 0 38 0 13 0 -7.79233753497257117E-04 S 321 0 40 0 13 0 -3.51554743422733195E-04 S 322 0 42 0 13 0 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