-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '916580978885696918877930284177,1737687784280919841995410322821,1796394385895011323046678462124,2443847594272730591209684519559,3001639094934461985314835992874,3677298143189256729572277748959', 'a10': 5, 'a2': -1, 'a3': 0, 'a4': 2, 'a5': -5, 'a6': 0, 'a7': 3, 'a8': 1, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11.81499295812559, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [7, [1, -3, 6, -7, 6, -3, 1]]], 'bad_primes': [3, 7], 'central_character': '189.1', 'coefficient_field': '1.1.1.1', 'conductor': 45579633110361, 'conductor_radical': 21, 'degree': 12, 'euler_factors': [[1, 1, -1, -4, -3, 2, 13, 4, -12, -32, -16, 32, 64], [1], [1, 5, 8, 7, 9, -62, -299, -310, 225, 875, 5000, 15625, 15625], [1, -3, 6, -7, 6, -3, 1], [1, 2, -10, 34, 48, -416, 31, -4576, 5808, 45254, -146410, 322102, 1771561], [1, 3, -33, -32, 981, 549, -13818, 7137, 165789, -70304, -942513, 1113879, 4826809], [1, -24, 324, -3030, 21600, -121956, 557683, -2073252, 6242400, -14886390, 27060804, -34076568, 24137569], [1, 6, 111, 520, 5181, 18894, 130503, 358986, 1870341, 3566680, 14465631, 14856594, 47045881], [1, 0, -36, 18, 468, -324, -5393, -7452, 247572, 219006, -10074276, 0, 148035889], [1, -1, -82, 31, 4425, -758, -148595, -21982, 3721425, 756059, -57997042, -20511149, 594823321], [1, -3, -60, 219, 1983, -4746, -51289, -147126, 1905663, 6524229, -55411260, -85887453, 887503681], [1, 6, 123, 948, 9285, 55410, 458183, 2050170, 12711165, 48019044, 230521803, 416063742, 2565726409], [1, 22, 206, 1802, 18432, 135116, 808243, 5539756, 30984192, 124195642, 582106766, 2548836422, 4750104241], [1, -3, -54, 569, 123, -13170, 115347, -566310, 227427, 45239483, -184615254, -441025329, 6321363049], [1, 9, -6, -531, -2433, 3438, 104623, 161586, -5374497, -55130013, -29278086, 2064105063, 10779215329], [1, -36, 792, -12258, 148572, -1444752, 11597011, -76571856, 417338748, -1824934266, 6249260952, -15055037748, 22164361129], [1, 9, -90, -459, 10161, 20556, -598421, 1212804, 35370441, -94268961, -1090562490, 6434318691, 42180533641], [1, -6, -126, 358, 12372, -11472, -838653, -699792, 46036212, 81259198, -1744575966, -5067577806, 51520374361], [1, 0, 6, 1366, 438, 4098, 1065603, 274566, 1966182, 410842258, 120906726, 0, 90458382169], [1, 18, 495, 6120, 93789, 850842, 9049831, 60409782, 472790349, 2190415320, 12578782095, 32476128318, 128100283921], [1, -6, 111, -1668, 14133, -123774, 1717463, -9035502, 75314757, -648880356, 3152204751, -12438429558, 151334226289], [1, 15, 36, -367, -3225, -51726, -676905, -4086354, -20127225, -180945313, 1402202916, 46155845985, 243087455521], [1, 12, -144, -582, 34812, 90444, -2656433, 7506852, 239819868, -332780034, -6833998224, 47268487716, 326940373369], [1, -4, 236, -1934, 37044, -243500, 4408699, -21671500, 293425524, -1363410046, 14807168876, -22336237796, 496981290961], [1, 3, -168, 573, 14223, -78504, -1297807, -7614888, 133824207, 522961629, -14872919208, 25762020771, 832972004929], [1, 13, -124, -1117, 24237, 84854, -2267747, 8570254, 247241637, -1150846217, -12903489724, 136631306513, 1061520150601], [1, -30, 324, -3562, 66678, -709374, 5510307, -73065522, 707386902, -3892293574, 36466485444, -347782222290, 1194052296529], [1, 14, 521, 6502, 128586, 1268542, 18047833, 135733994, 1472181114, 7965229586, 68292472121, 196357242298, 1500730351849], [1, 42, 1167, 24240, 399777, 5425638, 62017751, 591394542, 4749750537, 31391502960, 164731573887, 646222061058, 1677100110841], [1, -4, -31, -3068, 2658, 59092, 4505473, 6677396, 33940002, -4426807996, -5054468191, -73697407172, 2081951752609]], 'euler_factors_factorization': [[[[1, 1, -1, -4, -3, 2, 13, 4, -12, -32, -16, 32, 64], 1]], [1], [[[1, 5, 8, 7, 9, -62, -299, -310, 225, 875, 5000, 15625, 15625], 1]], [[[1, -1, 1], 3]], [[[1, 2, -10, 34, 48, -416, 31, -4576, 5808, 45254, -146410, 322102, 1771561], 1]], [[[1, 1, -12, 13, 169], 3]], [[[1, -12, 90, -435, 1530, -3468, 4913], 2]], [[[1, 3, 51, 107, 969, 1083, 6859], 2]], [[[1, 0, -36, 18, 468, -324, -5393, -7452, 247572, 219006, -10074276, 0, 148035889], 1]], [[[1, -1, -82, 31, 4425, -758, -148595, -21982, 3721425, 756059, -57997042, -20511149, 594823321], 1]], [[[1, -3, -60, 219, 1983, -4746, -51289, -147126, 1905663, 6524229, -55411260, -85887453, 887503681], 1]], [[[1, 3, 57, 303, 2109, 4107, 50653], 2]], [[[1, 22, 206, 1802, 18432, 135116, 808243, 5539756, 30984192, 124195642, 582106766, 2548836422, 4750104241], 1]], [[[1, -3, -54, 569, 123, -13170, 115347, -566310, 227427, 45239483, -184615254, -441025329, 6321363049], 1]], [[[1, 9, -6, -531, -2433, 3438, 104623, 161586, -5374497, -55130013, -29278086, 2064105063, 10779215329], 1]], [[[1, -18, 234, -1917, 12402, -50562, 148877], 2]], [[[1, 9, -90, -459, 10161, 20556, -598421, 1212804, 35370441, -94268961, -1090562490, 6434318691, 42180533641], 1]], [[[1, -6, -126, 358, 12372, -11472, -838653, -699792, 46036212, 81259198, -1744575966, -5067577806, 51520374361], 1]], [[[1, 0, 6, 1366, 438, 4098, 1065603, 274566, 1966182, 410842258, 120906726, 0, 90458382169], 1]], [[[1, 9, 207, 1197, 14697, 45369, 357911], 2]], [[[1, -3, 51, -681, 3723, -15987, 389017], 2]], [[[1, 15, 36, -367, -3225, -51726, -676905, -4086354, -20127225, -180945313, 1402202916, 46155845985, 243087455521], 1]], [[[1, 12, -144, -582, 34812, 90444, -2656433, 7506852, 239819868, -332780034, -6833998224, 47268487716, 326940373369], 1]], [[[1, -2, 116, -735, 10324, -15842, 704969], 2]], [[[1, 3, -168, 573, 14223, -78504, -1297807, -7614888, 133824207, 522961629, -14872919208, 25762020771, 832972004929], 1]], [[[1, 13, -124, -1117, 24237, 84854, -2267747, 8570254, 247241637, -1150846217, -12903489724, 136631306513, 1061520150601], 1]], [[[1, -30, 324, -3562, 66678, -709374, 5510307, -73065522, 707386902, -3892293574, 36466485444, -347782222290, 1194052296529], 1]], [[[1, 7, 236, 1599, 25252, 80143, 1225043], 2]], [[[1, 21, 363, 4497, 39567, 249501, 1295029], 2]], [[[1, -4, -31, -3068, 2658, 59092, 4505473, 6677396, 33940002, -4426807996, -5054468191, -73697407172, 2081951752609], 1]]], 'gamma_factors': [[], [0, 0, 0, 0, 0, 0]], 'group': 'GL2', 'index': 0, 'label': '12-189e6-1.1-c1e6-0-0', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1, 1, 1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/189/2/f/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0208333333333', 'prec': 50}, 'plot_values': [1.215868317769259, 1.2165798635986476, 1.2161972599835522, 1.2148319298039425, 1.2125878669076957, 1.2095600076157256, 1.2058324196619572, 1.2014331692772486, 1.1962054126636557, 1.1899402115659157, 1.1824207510054194, 1.173423181434524, 1.162717734003604, 1.1500701194012968, 1.135242299385701, 1.117992653769468, 1.0980773520981357, 1.0752522114049115, 1.0492748993317913, 1.0199011728253549, 0.9868706442630575, 0.949932815418027, 0.9088588212387975, 0.8634469763396018, 0.8135288224444607, 0.7589744924973655, 0.6996966681002879, 0.6356620252544697, 0.5668998148516448, 0.4935092012281467, 0.4156664627504749, 0.333632781769519, 0.24776340398181462, 0.15851033911628937, 0.0664253864799064, -0.027837390630948516, -0.12352090432245866, -0.2197648530667731, -0.3156068088776584, -0.40999649638363134, -0.5018078281056096, -0.5898521408429611, -0.6728946526876332, -0.7496742664999277, -0.8189303580919457, -0.8794356479641344, -0.9300267691228349, -0.9696363832713932, -0.9973272817646933, -1.0123311513967908, -1.0140983595125261, -1.0023300481068302, -0.9770081598489482, -0.9384246794337181, -0.8872067974752689, -0.8243427818896415, -0.7512139517031495, -0.6695806400317585, -0.5815665947616967, -0.48963823565477904, -0.3965724421624666, -0.3054174286147308, -0.21944619408534524, -0.14205915854315332, -0.0766898305419907, -0.02670605907020102, 0.004697875036264714, 0.014616787989773727, 0.0005647510163870022, -0.03938725379975958, -0.10648915683270352, -0.20119893865160343, -0.32308107799423463, -0.47071473926390256, -0.6416069774443479, -0.8321664294294414, -1.0377062732509, -1.252476699997179, -1.4697334815442857, -1.6818426384097371, -1.8804324963843113, -2.056610604655658, -2.2012046349324965, -2.305031766178824, -2.359194905042604, -2.3554141976436163, -2.286423868818036, -2.146301184891228, -1.930783132899254, -1.6375688187754043, -1.2665862252776054, -0.8202415985420763, -0.30367976119733975, 0.2752063717866425, 0.905814032973223, 1.5749327522430365, 2.2669405207307025, 2.9640769996106258, 3.6467974184828598, 4.294352635134116, 4.885390545233538, 5.39859813711917, 5.813389052269178, 6.110640783114822, 6.273520932516828, 6.288171373006119, 6.144328964797775, 5.83587867114732, 5.3612995825871685, 4.724037652223127, 3.932839889983731, 3.0015641397499824, 1.948906220927809, 0.7980030656932144, -0.4241382211128544, -1.6873487143573649, -2.9591639865292776, -4.206020430460513, -5.394393955393282, -6.4919350644892, -7.468600392363693, -8.297798873346412, -8.957632503954574, -9.431659803069373, -9.709472880998476, -9.787102193544337, -9.667186034723048, -9.359009681443894, -8.878500125663612, -8.247196399536376, -7.49122579595722, -6.640218192467889, -5.726080541541058, -4.7817642499768, -3.840055929029332, -2.9318005294205287, -2.0845534876910303, -1.32151487934949, -0.6606826650175098, -0.11426759513546952, 0.3116717990538875, 0.6173241104246096, 0.8087381571519633, 0.8971177610771532, 0.8978646818660692, 0.8294479675876313, 0.7121721532825436, 0.5666671122307329, 0.4124462679290013, 0.26660945957674603, 0.14273729464470808, 0.05004681997073662, -0.007163538444793001, -0.02975985123911226, -0.023568083114643815, 0.0012160409599577316, 0.03095314306298509, 0.04976520565904933, 0.04095804668173319, -0.011399139986407882, -0.12089315231004366, -0.2972959189480797, -0.5453042538993266, -0.8635851489591688, -1.2442209834607967, -1.6726295467325571, -2.127973197502059, -2.5840495819112483, -3.0106286451401694, -3.3752220679623752, -3.645307077137995, -3.7904595942330768, -3.784512339049983, -3.607614489260695, -3.2480163229712065, -2.703543909077305, -1.982722909881987, -1.1046517493151915, -0.09838642424100862, 0.9982294272420978, 2.1403404562402866, 3.278361138236047, 4.360760687747472, 5.337298972037485, 6.162059217884664, 6.796257379675788, 7.210696623920264, 7.387800058689226, 7.323207904503031, 7.025932451490591, 6.517738345651399, 5.8317904474795945, 5.010556384598884, 4.103154219563716, 3.1622411263617303, 2.240090782142126, 1.3850240987219062, 0.6382315456534942, 0.03110468198768649, -0.41675969525892365, -0.6988101064561146, -0.821594739470176, -0.8036956357962195, -0.6737301573197828, -0.4675434610721616, -0.22479343376678948, 0.014906184659104862, 0.21608789105361811, 0.35112852148831575, 0.4033383057257252, 0.3692195794749098, 0.2597199838867826, 0.10032782618578695, -0.0703591029662089, -0.20324671411869966, -0.2423702023925989, -0.12932556591557035, 0.19176242889921416, 0.7689762243289421, 1.6377318613549616, 2.8166729848716847, 4.304581816297594, 6.078583576697698, 8.093908704691216, 10.285608202827344, 12.571638932577201, 14.857232376712071, 17.04036489944353, 19.01794782615456, 20.69277540238841, 21.981474722892816, 22.819179161511094, 23.163453708093073, 22.997143358778683, 22.32956496055098, 21.19655805167076, 19.65975688957914, 17.800175727335485, 15.711959530291319, 13.496035063200157, 11.253475329845058, 9.079399498774185, 7.057735039560489, 5.254774126028681, 3.715756165457832, 2.4636854291274846, 1.499942377052881, 0.8066339456608499, 0.3503254864706752, 0.08648485926367952, -0.034963926735258936, -0.06397555725779734, -0.04525828543008432, -0.014153053332027883, 0.006097772374138767, 0.005426031837875379, -0.013658186077591393, -0.038274297469369674, -0.04871698572353494, -0.02291023805190063, 0.05881321709249762, 0.20925233156639825, 0.43073847773472435, 0.712912410728098, 1.0322818445269197, 1.3538953529021622, 1.6354121389834697, 1.832534721270323, 1.9057297415470549, 1.8277194530657186, 1.5909581222422808, 1.2143785656870598, 0.7484197665507243, 0.2766202482353179, -0.08548149620536695, -0.1946059938233819, 0.1126572059019217, 1.0089463564048518, 2.662138862643125, 5.2207558626372235, 8.799147330898965, 13.46332844015783, 19.218706380218674, 26.001280252342337, 33.675354935643476, 42.03512841091584, 50.81065456252978, 59.67875359073712, 68.27827357987847, 76.23149956644878, 83.17536269056423, 88.77953855014917, 92.7648624176859, 94.92114504067438, 95.12123000302412, 93.33402466616435, 89.63904645158541, 84.21088915529526, 77.30445695220054, 69.23903559980629, 60.37863386181546, 51.11215886888645, 41.83471875023039, 32.91411902272212, 24.667984377489525, 17.348060197853602, 11.12977466248593, 6.107836823311591, 2.297110921213232, -0.3628425709157688, -1.9953827706900302, -2.7702610299337667, -2.88510010076166, -2.5465703707962297, -1.9527565667398783, -1.27705821841378, -0.6562046047865788, -0.1829762724348892, 0.09624172297885893, 0.17921821460684093, 0.10145974642988746, -0.07345354653926682, -0.2655509030724311, -0.39084913624570466, -0.37318689078700784, -0.15436028361040105, 0.29871172760531733, 0.9903029270563527, 1.8954498883675965, 2.9626934077244584, 4.119570646169777, 5.280679346009563, 6.358451526364314, 7.271385141712835, 7.9513728973981035, 8.349749665946742, 8.441239923459925, 8.226217046409293, 7.731550385679003, 7.004475201368257, 6.10632725718838, 5.1061455050880085, 4.074083283221076, 3.075519579003373, 2.166132687329403, 1.3866010215541076, 0.7606582631591738, 0.295403749539329, -0.016794816498172705, -0.19519215047324176, -0.266872249974284, -0.26253770482088157, -0.21238671466122172, -0.1427736981940969, -0.07395128010187217, -0.019000890205386874, 0.016115461656069023, 0.031498555944892453, 0.03150972310172703, 0.022651873495500668, 0.01152089258090879, 0.0031553917593705196, 1.0656462274461318e-05, 0.0016756928688867467, 0.005351696778006095, 0.00692660241314637, 0.002396957303332619, -0.010662958674004984, -0.03189820114420761, -0.05748348780089669, -0.0801168843667274, -0.08975482506142114, -0.07502305017023607, -0.025120561684232483, 0.0681295754326366, 0.20845403022887893, 0.39373365080608136, 0.6153100986276682, 0.8581750511051707, 1.1022288151251887, 1.3248292969167803, 1.5033043840412106, 1.6176414652215214, 1.6531059663954606, 1.6023637939891637, 1.4669887129696335, 1.2581651206762698, 0.9948674314936669, 0.701472968152074, 0.40489850875794614, 0.13140589715145987, -0.09651434577767246, -0.26295293032042605, -0.36061104782836556, -0.3912033910727996, -0.36454550867669683, -0.29654704529274684, -0.20644671866377695, -0.11366402124155221, -0.034444855178447364, 0.020641546905217436, 0.04797839169249355, 0.0507643234764343, 0.037443988484013, 0.018909369683410296, 0.004829997528748708, -0.0002209848062658341, -5.5181780542913926e-05, -0.008858310556967354, -0.051303386162248416, -0.16044384467564998, -0.37336303436641055, -0.7249383445185407, -1.2404323179654042, -1.9279144809966315, -2.7718832707047127, -3.72990677370288, -4.732042820420176, -5.684227788402542, -6.476095823458751, -6.992931198693225, -7.131570764605282, -6.819313824628241, -6.0283787506592885, -4.788684615975991, -3.1968875986079013, -1.4193717664248338, 0.3123953198666673, 1.717125420225303, 2.487140465262526, 2.3154765615751205, 0.9263505056755053, -1.8932990152694646, -6.262721783673789, -12.178999774700191, -19.50751739820527, -27.981903967042598, -37.2141993937454, -46.71635229707902, -55.93279320650845, -64.28686626185295, -71.23031606294842, -76.28842577067864, -79.10010020944198, -79.44949508550341, -77.28942869110148, -72.75779814828006, -66.15882502985606, -57.93379598202758, -48.623411126049795, -38.822452975812865, -29.132035920100275, -20.112374903320138, -12.231805069846532, -5.832150756429835, -1.1088940100880935, 1.8945113437574004, 3.2785720226684587, 3.267161603240359, 2.1744479979805376, 0.3660315820788284, -1.7811694406705338, -3.9164795013824407, -5.74753297441825, -7.06509304313283, -7.753319185251897, -7.7888223916402515, -7.230319331810862, -6.2005344879862765, -4.863339689389925, -3.3986351357279574, -1.976235578050039, -0.7360149892478427, 0.22525305401058174, 0.8600122252494303, 1.1691671981455822, 1.1952137253710118, 1.009469019471266, 0.6974279060364953, 0.3444327311424305, 0.02337605926891285, -0.214193170534915, -0.342779304391892, -0.3624045697468539, -0.29393834213485137, -0.17179275627552687, -0.03538678464075444, 0.07918630131651368, 0.1460912989175711, 0.15381190644974554, 0.10582363216924154, 0.018329521751766525, -0.08426070803388894, -0.17514714529383452, -0.23124518914485262, -0.2381853049039996, -0.1930656989164463, -0.10468588874660859, 0.00866331698149679, 0.12336580684428317, 0.2158628020858647, 0.26811020804989416, 0.2716868619737116, 0.22975462931985036, 0.15640119172412023, 0.0733486598590048, 0.004429073774813527, -0.031251650438246355, -0.025891538600518748, 0.011995444000219374, 0.05531569913371544, 0.05973280257241872, -0.031040079869635976, -0.2764529429264134, -0.7279956490997483, -1.4172149790396622, -2.3446854360499705, -3.472156173348515, -4.720698757617869, -5.973453895936023, -7.083955203119848, -7.889909203861378, -8.231093500379595, -7.970408027097552, -7.016062952768095, -5.334105400123797, -2.956958766670567, 0.013792335788341964, 3.411994109425751, 7.019638741947891, 10.590284347890396, 13.874183181348073, 16.64172939353007, 18.705065422295874, 19.935530107126453, 20.277551127010486, 19.759815585004166, 18.482165766805917, 16.599019495658222, 14.300458932375674, 11.791017968954147, 9.269737959037094, 6.912946914475559, 4.85339262108347, 3.171466613219295, 1.895093018381961, 1.0058345310170098, 0.4498203246319878, 0.1513539479279756, 0.02712283531241452, -0.00010772548518635449, 0.008851664202848337, 0.015370030901376194, 0.0039042047133334315, -0.021442522614987233, -0.043579366000119295, -0.04069393232691438, 0.005601435080955295, 0.10379309798748793, 0.2488771029042851, 0.422508105793164, 0.5961845334984505, 0.7367027041004603, 0.8128367476570917, 0.8018944599611916, 0.695010294502637, 0.5000514616642957, 0.24014564390579302, -0.05025274114206004, -0.3312037989689619, -0.5641808261361844, -0.7188869539584531, -0.7789324618508041, -0.7443203019584099, -0.6306284111964965, -0.46541800162521973, -0.2825321617366578, -0.11531849421335369, 0.010141012809652948, 0.08007769045141835, 0.09500923064023675, 0.06856241903997576, 0.023435338876726053, -0.01469138915762795, -0.02417200199816484, 0.006242166864518993, 0.07368835923300351, 0.16096297477778773, 0.2400681148333731, 0.27915758258276474, 0.2518313141754103, 0.14667888346078678, -0.025202495951022533, -0.2266180030536468, -0.39603807854025835, -0.45549226246357594, -0.324664187579866, 0.062224398831341364, 0.7389490748302745, 1.6922276151175637, 2.852415169962736, 4.092859981790039, 5.240775870336584, 6.098412470018038, 6.471247383549512, 6.200551670270099, 5.1959566605467655, 3.4633273083849203, 1.1209657637833086, -1.6049030926457255, -4.39911241753137, -6.891132893561107, -8.701028808895165, -9.495264662172964, -9.050673416207433, -7.295741749732058, -4.333508757781601, -0.44391254851061324, 3.938127675622214, 8.266704319377164, 11.950171878359503, 14.442492651549093, 15.326939381966099, 14.385481772800379, 11.646257129587305, 7.402888707877989, 2.2025959117051124, -3.212734384043889, -7.995402849159623, -11.29911288052619, -12.392890686839154, -10.766642077999615, -6.212510184902156, 1.126322662929346, 10.752635616849147, 21.857542742347125, 33.4035305279812, 44.243730911307544, 53.2727191533291, 59.55250990596517, 62.420845623794094, 61.57035356199123, 57.08566682042558, 49.437723634156505, 39.432965128984804, 28.091066187950876, 16.51456411666484, 5.758212183162513, -3.29126635083587, -10.012633702174913, -14.117724474900873, -15.659449858651431, -14.99129682399941, -12.691631249586615, -9.463551725251431, -6.0256093744799974, -3.0061931916448033, -0.8504781354461649, 0.2313268299748578, 0.27474396966622555, -0.46662466540593794, -1.5811787818707708, -2.5817562492339463, -2.9985843337901943, -2.4650065733105695, -0.7831440751783355, 2.039394700945717, 5.787683950934589, 10.076297485018351, 14.409310073029364, 18.255830060436605, 21.130532340224352, 22.666685575881527, 22.673202546419855, 21.16776880343867, 18.363268319530746, 14.63115698010486, 10.44595424699773, 6.316997744771801, 2.7166590619020075, 0.013224962561221581, -1.5735236363616636, -1.990541662987896, -1.3457766677180183, 0.11934989057506301, 2.074462062991227, 4.157697162916543, 6.033462242615406, 7.437207615109418, 8.204863831959683, 8.284629820050636, 7.732258141636718, 6.692194838118958, 5.358907923749912, 3.9379254586529746, 2.611782229739939, 1.5144278063716592, 0.7172372061642893, 0.2272865841678372, -0.0027638515983159514, -0.055199429559255324, -0.024183014980713867, 0.006057686780555239, -0.022124742248356775, -0.13112995196907679, -0.3085535044578968, -0.5154263318100772, -0.6996069270222379, -0.811029490650879, -0.8155237681753155, -0.7042290175920625, -0.4953732104635563, -0.22972045494531557, 0.039015173696295126, 0.2566678438696319, 0.3813729553781838, 0.39376328089018403, 0.30063234167016245, 0.13260357013436827, -0.06344742785846107, -0.23571616403580903, -0.3402304767589088, -0.3524760443005548, -0.27364571897923917, -0.1303261939261337, 0.03194827047419835, 0.1601502954853495, 0.20805902947207283, 0.1505616214708168, -0.00626317017699525, -0.2221764037536047, -0.4276240127293178, -0.5359970902292821, -0.46183880928409754, -0.14286203751533919, 0.44144687744844174, 1.2580205515755214, 2.217706309765713, 3.183645308563125, 3.9900730970149505, 4.469971915366054, 4.487731298844699, 3.968920056045825, 2.92234586253616, 1.4500527106052186, -0.2576619555385064, -1.9431271850424414, -3.315457507515648, -4.092534372640255, -4.045258711942662, -3.0375219076155706, -1.054555073317713, 1.7901980073984167, 5.265367709571931, 9.04664838023137, 12.755345833234022, 16.005479513715883, 18.45747309543277, 19.87654229629671, 20.151240232211713, 19.299032560216435, 17.458852095369757, 14.868586850158001, 11.833113002294509, 8.685394064492295, 5.730189793529465, 3.206570280321947, 1.2661815154454639, -0.0344023813296471, -0.7277785177069536, -0.9187521245966394, -0.7566677179619206, -0.4039282542652437, -0.007880683822626949, 0.3200010913945022, 0.5154996132045276, 0.5633379929988501, 0.48866381627035227, 0.34190882623690255, 0.18143085821924013, 0.05762853891897431, 0.001509730157776794, 0.01945682083267513, 0.09476000196591168, 0.19490776122376738, 0.282058188285529, 0.3239135222537884, 0.30244232100128404, 0.21841604149018765, 0.09037680180431851, -0.05080520284350964, -0.17027154972942066, -0.23837631064426765, -0.23855300140114183, -0.17178291423725936, -0.0558988556914519, 0.07929256751625273, 0.1997985397447779, 0.27635253747886884, 0.29243931416602176, 0.24947406052781512, 0.16647244429386218, 0.07512388730991411, 0.011537335219776863, 0.006433244367615844, 0.0760621131570215, 0.21626404634769136, 0.40192412010253115, 0.5921317042285194, 0.7398698797664838, 0.8042085020441572, 0.762491589165552, 0.6197419619233075, 0.41045128464115044, 0.19291621442228155, 0.03679967040216639, 0.005826302409628789, 0.13891779531758602, 0.4338375764209575, 0.8382812008359941, 1.2515545263308876, 1.537520032746886, 1.5476408472098213, 1.1511092636032276, 0.2669023896721984, -1.1117936466339295, -2.90392466262795, -4.941452940831885, -6.986672128768327, -8.766318894119737, -10.021934362886112, -10.554655021866159, -10.262451421067583, -9.164279799475228, -7.404697932551522, -5.238201853111968, -2.993033004669884, -1.0032412022490178, 0.45746667100377186, 1.2329093988428137, 1.3248361586883748, 0.907788767266897, 0.3136254501311179, -0.014442341930055278, 0.4048621099165814, 2.003718852244194, 5.077897753682666, 9.714693275753401, 15.756028907515164, 22.79751313135078, 30.225052105194685, 37.28687103480063, 43.1913850659262, 47.224226392462796, 48.87787849728882, 47.91810602752991, 44.41707839680863, 38.74897896090915, 31.543106322383785, 23.60348006223987, 15.802141868049988, 8.940734277622402, 3.639998522099201, 0.2627084946095515, -1.1242054234941243, -0.744175699026546, 0.9375865463447778, 3.3017723755611303, 5.680180493285962, 7.461722738694282, 8.184046558428006, 7.598481849293595, 5.698187252651323, 2.699732239411347, -1.0061024064410842, -4.925622977470781, -8.544687773578186, -11.411896874840545, -13.212577591511145, -13.80002117201362, -13.19987147853021, -11.590935570551988, -9.265488397154403, -6.576851161221664, -3.879213790158884, -1.4706589797642122, 0.4403312211088521, 1.748863223480175, 2.45021039448849, 2.6232398387333307, 2.4051948989631784, 1.9534309210045364, 1.4142219173672674, 0.9018705191819002, 0.48838203498721466, 0.2033158870725175, 0.04127553259017497, -0.026115404685808804, -0.03570259026053266, -0.020814904907601607, -0.004116727990612413, 0.004277332460101001, 0.0043579379274101444, 0.001260532552331164, 4.7787709849318365e-05, 0.0022372611797810507, 0.005205493000545325, 0.004483187608960792, -0.002100967916727189, -0.01016468784844247, -0.006245284322312249, 0.03157079498464924, 0.12927478669524814, 0.30945728265430594, 0.583123427713189, 0.9426230526200792, 1.3576535779105046, 1.7761465296317607, 2.1307986478878234, 2.351744771712461, 2.3849345557498403, 2.2045611868566732, 1.8218111110449602, 1.2880696113782713, 0.6905319897755418, 0.14039818199562742, -0.2463542298402216, -0.3741074733957759, -0.18754776288094455, 0.3154696992362943, 1.0800748029411316, 2.000660429692161, 2.9377541125839937, 3.74377423012124, 4.290160892462683, 4.4908580209169005, 4.317936568647008, 3.8070470814992783, 3.051984551857592, 2.1838479623704363, 1.3440135250708534, 0.6562473010095773, 0.202957786998744, 0.010347692697366313, 0.04518876002658292, 0.22400957213361739, 0.43334910704680746, 0.556220254468176, 0.4992003332333907, 0.21413634924175365, -0.29180720168837165, -0.957785753807716, -1.6818005288155897, -2.3419796219872664, -2.8222501716936335, -3.038241494431289, -2.9584462574526205, -2.6063505018374156, -2.0527061688261705, -1.399527712226455, -0.7581716901255916, -0.2260069820238843, 0.13436218376114253, 0.30665000646026835, 0.31866537835187986, 0.22960480535554928, 0.11044470356969202, 0.022155025951376323, -0.003300391756083321, 0.02621610520786092, 0.06516367348876105, 0.04461099800737605, -0.10457999131355095, -0.4249342398658031, -0.9084604988358878, -1.4829746673558304, -2.0135111505015217, -2.3203716213808887, -2.211964280166376, -1.5272277277033952, -0.17819453118040807, 1.8181467554117667, 4.323387989872082, 7.082088629045471, 9.748836001738875, 11.938347229418907, 13.29683368513702, 13.55761108083046, 12.586642915375224, 10.411639206747465, 7.226969842562031, 3.372874015018946, -0.7146366459023485, -4.578630721445447, -7.808553673259618, -10.096463986997609, -11.275944663099313, -11.341318843852669, -10.446135859648326, -8.854528604405274, -6.884294930846283, -4.8510346982812385, -3.019497166316807, -1.5698755644515143, -0.5816936308019016, -0.03608842620761036, 0.15865878351864007, 0.13146635909022208, 0.012361553053351564, -0.09660273846741735, -0.13846089380673, -0.10372836720904471, -0.019209774210321485, 0.07125772492915236, 0.1274996620941435, 0.1289347289650813, 0.08126425686575585, 0.011769119434864127, -0.04425162254554322, -0.0607707836058833, -0.03586687036263658, 0.001723082575506696, -0.0018047713662713164, -0.10737516713490854, -0.3571423016475017, -0.7475583325539502, -1.2097202504040272, -1.6056567408745088, -1.7483508087992197, -1.4393824260605024, -0.5192478514581165, 1.078697211517785, 3.2834414264812404, 5.863507544542514, 8.442027231095407, 10.555706407219148, 11.73928824862535, 11.625016184466025, 10.040075736511936, 7.084841080244837, 3.1720906770246664, -1.02038859610765, -4.655526002048706, -6.888261635067327, -7.043093197732967, -4.790533959167597, -0.29770370187902895, 5.704900763170894, 11.960812443748951, 16.82672802325733, 18.50199704558738, 15.315704863094957, 6.014808000700377, -9.96604303967774, -32.3179615900118, -59.791007634922984, -90.2639987354527, -120.97673207468705, -148.9546020867405, -171.35891040772373, -185.83942920293106, -190.85019541100849, -185.8652619612743, -171.49054067884038, -149.45755518598074, -122.26402239620582, -92.79929562277619, -63.96710283732894, -38.324051338379846, -17.783431305897228, -3.4120843455254626, 4.6434443958713585, 7.060251841150678, 5.133743028212263, 0.5088928506600684, -5.109882220391163, -10.236251116505029, -13.80164342339335, -15.248938431952912, -14.52956682245478, -12.018289875469069, -8.37185773805554, -4.35752763787166, -0.6774647004247822, 2.1542059611881754, 3.874591409901762, 4.476249682870097, 4.16231369498787, 3.2677804816013016, 2.157524672808317, 1.1409014859023636, 0.41639239972762593, 0.05151691719530144, -0.0031520411001311277, 0.12639261019362782, 0.2914332897483276, 0.37131933958396174, 0.308397212515215, 0.12035281115486829, -0.11079776163301326, -0.26861227227816703, -0.24152957434917302, 0.04140257614482051, 0.5869390197585388, 1.331462841330533, 2.154000497920958, 2.9073803202591426, 3.453552889551495, 3.6949097946084763, 3.595300979960214, 3.186033873668327, 2.5568906671466696, 1.8343688951797328, 1.1464513439137183, 0.5926854183018114, 0.22498605223510634, 0.042122800134215224, -0.0015317928090726948, 0.024030084893529275, 0.050374963550379986, 0.03499367229568061, -0.023293559445422576, -0.08220669675895974, -0.0679324075745394, 0.10245690515756785, 0.49438702353673675, 1.1317174585308525, 1.9816179887898955, 2.95279308752628, 3.9099399093729184, 4.705602496188887, 5.20996139067637, 5.337406078124182, 5.065136277461783, 4.438676472685203, 3.56404279314657, 2.5871289522699037, 1.6559083516012487, 0.88891666085866, 0.35412843135642186, 0.06092102910789789, -0.03366581999295274, -0.006403088390727704, 0.05883674855072728, 0.09734505359299298, 0.08114994646557411, 0.023049701127836317, -0.03406385585753068, -0.03986099714725014, 0.0350095743698031, 0.1741663360096995, 0.30288207557632196, 0.29362444679987276, -0.0087273189195347, -0.7481594125123399, -2.012778381717585, -3.7937571033681503, -5.959180378553138, -8.251743592807454, -10.320331843788304, -11.794684983449576, -12.349722773415444, -11.76996427320239, -10.004514176301743, -7.1976687847852165, -3.68951385493064, 0.024638584296515362, 3.3948454471526155, 5.91412074945051, 7.205681141418395, 7.089342743863282, 5.6184802780290815, 3.0831991951895996, -0.05439626361734655, -3.2536419757417616, -5.996509754005447, -7.880232056159049, -8.685199787930193, -8.408485130565902, -7.247305353916891, -5.53929610592727, -3.678108643677102, -2.022898433748387, -0.8211439036077052, -0.16024660144890707, 0.041589433719994774, 0.0008553237143488436, 0.002884392259984635, 0.32069234581006284, 1.1374083041073544, 2.4933011199846815, 4.269703801092075, 6.211091081962898, 7.980267938980858, 9.234620492238685, 9.709917278263314, 9.296107142178359, 8.06003647391551, 6.231419964398255, 4.155749661837953, 2.221234078335657, 0.7749316534673785, 0.043587411855275246, 0.07876898714094453, 0.7474013683779338, 1.7631247137782295, 2.7504436017339278, 3.3296766766268773, 3.2079669697252573, 2.246337778795848, 0.4917548054390504, -1.829600183876374, -4.356046968837781, -6.662939773381662, -8.354122118054267, -9.142331632151638, -8.901461051994346, -7.685324266299131, -5.710891551409764, -3.312105390048677, -0.8725180564256203, 1.2563296361928815, 2.817002527180225, 3.6819696931934796, 3.860269994710748, 3.4772390002587237, 2.734191742057571, 1.853235508210608, 1.0276698427757307, 0.3879536544703237, -0.012065799979323256, -0.18834964790735778, -0.20387738457077656, -0.13874302053292778, -0.062099561379639505, -0.013852476032469536, -7.979628575949756e-05, -0.001867187625862848, 0.006907665551201281, 0.04108045770521825, 0.09253144434075743, 0.12972825727378992, 0.10972485174579506, 0.00043372886128548464, -0.19262457356441523, -0.40888631241639106, -0.5301721979881417, -0.39624077174268746, 0.16188235961511194, 1.2759881310802497, 2.991725884400833, 5.232187756086084, 7.7855506777710275, 10.322223982888275, 12.441816963156255, 13.745822094287512, 13.927681985126812, 12.844100719226379, 10.561851541616916, 7.368987635079311, 3.743106328894156, 0.278828694329688, -2.416265580602285, -3.834061569416645, -3.6612850803597885, -1.8440530266950177, 1.390947137616308, 5.569360721923384, 10.068202268006672, 14.22407755570151, 17.43912433243867, 19.27484660321145, 19.516993147504575, 18.211133927545884, 15.665921374160753, 12.344335636906266, 8.759893060760271, 5.386661704595165, 2.5872486739918665, 0.5711785834943514, -0.6166399766568822, -1.0858092942361854, -1.0450399180003316, -0.7342757768136988, -0.3645446519201759, -0.07748876813414826, 0.06932265907975603, 0.09228635165897013, 0.05140568948182679, 0.010234427128647758, -0.0006482413424241791, -0.005376305647828804, -0.08341126169351679, -0.34939342225299136, -0.9176515874996849, -1.8606802635078328, -3.173014467494393, -4.752590730988578, -6.410717408713117, -7.898971061901874, -8.951813514443266, -9.338261674750255, -8.911537454192842, -7.646863091508874, -5.6537899048888764, -3.152135968355354, -0.43477011655747655, 2.179517778984451, 4.396386676275303, 5.99468942261983, 6.8702811018732515, 7.033233085742923, 6.587524458515698, 5.700930152540235, 4.568983950617366, 3.3815234080862373, 2.2958610905060115, 1.4111113958225476, 0.7655514931954945, 0.3478269492004192, 0.11459715989779584, 0.009379480821644819, -0.021758131578022324, -0.020016557134867722, -0.01028326015260009, -0.003228890973401715, -0.0004662006092699038, -4.597876416556177e-06, 1.5834986648139947e-05, 6.78430543461368e-05, -9.778625468382876e-05, -0.0003244866098180414, -3.6702964062960764e-05, -0.00025991321037631025, -0.007391233112425845, -0.037218535833959114, -0.11702415342094462, -0.28364858924079617, -0.576233652939989, -1.0241594495776347, -1.6340504110816703, -2.3788768106489706, -3.192593859079617, -3.973531819232096, -4.597777880181998, -4.943444121181803, -4.925318449895072, -4.515634447809794, -3.754977004942015, -2.7503638309998797, -1.65793505367946, -0.6529901795143106, 0.10909400765361109, 0.5356877047276626, 0.621574168085284, 0.45169387232754166, 0.18092651851336863, -0.005999244774694362, 0.053057157541566195, 0.4453222220507388, 1.1475498827614843, 2.0177806219652634, 2.8194889627021724, 3.2767966165867155, 3.1520025330765495, 2.3200164434029324, 0.8247543615216684, -1.097706321476764, -3.040119276310689, -4.492047649295937, -4.948930911948558, -4.028067927072717, -1.5680365881268, 2.306705634481421, 7.173220196321616, 12.361356796717754, 17.080289825700635, 20.569195108430616, 22.240231954876375, 21.794368467846947, 19.286423508515462, 15.130571087560162, 10.038531299839574, 4.850883551447559, 0.36264833295530224, -2.830320607610369, -4.441172994355345, -4.5373774868034795, -3.513364516229625, -1.9813916529673352, -0.6105654495690576, 0.04325129196102089, -0.3201747232343554, -1.662013881531601, -3.6020640392669967, -5.498648561411926, -6.590486449995938, -6.170924100356872, -3.7581824521299945, 0.7745261755813658, 7.1480879618164765, 14.720823378862168, 22.59524431733776, 29.771726620606074, 35.32137979788698, 38.5564291628612, 39.178226875940894, 37.28129109221258, 33.29657567118665, 27.89106145761089, 21.836837232375053, 15.879919146607918, 10.62749907435584, 6.4494684257527695, 3.4636429536963074, 1.5767041979824563, 0.5568973435450948, 0.11787317224768482, -0.0063247594064122755, -0.010179903067419189, 0.0015001710855405564, 0.0005563991523861718, 0.0022904193201226026, 0.026955378006581814, 0.07045085051447586, 0.09427638775003734, 0.03663430197715118, -0.16087158239500635, -0.5215213010516284, -1.0095910219684128, -1.527318221951967, -1.9354969717005266, -2.0927614806472343, -1.9041492096688153, -1.3651476289151148, -0.5877647415308755, 0.2026699179477683, 0.7095531272548018, 0.6308722177464985, -0.2640070614006405, -2.0634005249074807, -4.668756507910464, -7.8002624509907985, -11.037991690377105, -13.893852052959064, -15.903464243958714, -16.718754258780592, -16.189097345870877, -14.416059765034214, -11.707219599129937, -8.50320133750459, -5.2889893974559765, -2.500425099544741, -0.44549775273378617, 0.7478126989004154, 1.1456665267575217, 0.9658191373165019, 0.504597392923541, 0.054910467858051176, -0.16571902512175274, -0.06195123025427395, 0.3302901829322572, 0.8721695367173401, 1.3760363480530997, 1.668679147026791, 1.6460983933456101, 1.3044464482349587, 0.7369538727011742, 0.102057293951032, -0.426895883390415, -0.7157551734571697, -0.712195223094365, -0.46351548209671883, -0.09918706062049731, 0.21026385932044567, 0.3064096916346257, 0.09393191368695503, -0.4253895136255089, -1.14938316903994, -1.9051790968920943, -2.4994007128456115, -2.775000964014805, -2.659065124680191, -2.188806611306523, -1.505702470026894, -0.8047336588874154, -0.2670551962017913, 0.005876605550995039, 0.0390922345473455, -0.003723706783098232, 0.1477844344061471, 0.7956142648961088, 2.175275384616324, 4.36009183730708, 7.193403823937968, 10.271507665143456, 12.996855119196349, 14.684935056724333, 14.7047056436566, 12.626043926677783, 8.341481463040305, 2.137557388932872, -5.307280262695139, -13.04084314282839, -20.00139128000755, -25.203837590147717, -27.91818329133544, -27.80811115919782, -25.001461204166347, -20.049512721216388, -13.81023466446301, -7.2840578855508955, -1.4321350487735183, 2.9921485044376945, 5.574759757727424, 6.2770448187728425, 5.389564073318074, 3.4307181365312127, 1.0153512958438262, -1.2763158893532067, -3.005473594232493, -3.942077391343475, -4.070231646394731, -3.54686355979791, -2.6316712783555385, -1.609003968586564, -0.7192557705754351, -0.10367619106143404, 0.20983940992298594, 0.28241508090970135, 0.21784592405193007, 0.11403434506754347, 0.030349424535399114, -0.01216970068196604, -0.01637369935990052, 0.003001947315112007], 'positive_zeros': ['0.72305490071213197993133300462903', '1.37079395849934071523478881277804', '1.41710530139108223374200000506374', '1.92785582544017823996418248886547', '2.36787573357677827298945058939756', '2.90087674200382295163118206297869', '3.16314228315911781210588835565190', '3.22831514581994555807523278061338', '3.30931639574839657528727667067262', '3.71026619993020913154436508201182', '4.12623441675620218959095665002343', '4.29029878668166145768455608950078', '4.42872773456760787609298956682866', '4.51028781951976494243216193421682', '5.19997247781623912807733440146271', '5.28305784153718558869712343548095', '5.32023169211293971085883323480311', '5.40355588632900731165398578473565', '5.70230577990157987499611332923739', '5.74539050755666355124291412163183', '6.43407349601293785210187713793704', '6.61596037103994374500080168714127', '6.67953172013841081901892474198803', '6.77926427235722744338350715869104', '7.24857727456283483338327968031807', '7.40556586467059982458664509031425', '7.54226528091218168519797834400023', '7.54485292373798744737431223323296', '7.63015493574724958754094281829778', '7.77756478730675404803854954085776', '8.136385171191023172850064171326842', '8.324270666363428317181482010906717', '8.455214660501816704549666128549488', '8.473742459181020037324169462356256', '8.477692004343374430021661413847475', '8.891878641754838243450151713282397', '8.987342120003008759873443637076416', '9.485599694935336306840876028608487', '9.587018857775626102008780839334008', '9.848614979075890418744003417621808', '10.00172540720294089708261259803857', '10.13079144974678962761684545254819', '10.23296004755962489788738481905587', '10.37347172104846352606767311281055', '10.54338980394135776316604592720944', '10.59866366337889658422000822088838', '10.66210608846542098329298094020740', '10.97907964720295928956633918573681', '11.45708913073124502125238040764671', '11.46056954701142528423273083573594', '11.52457526734605264945426642265687', '11.60248908723861822189116365324610', '11.82977032415539609169561522139515', '12.03956203602862854006344400817480', '12.13648112448905929139164286265250', '12.18481458758104423941083298143354', '12.33060537590815887426675337216355', '12.43500138911033343405462488753315', '12.67546146885602992690220911710866', '13.18470522057810808957206757751378'], 'prelabel': '12-189e6-1.1-c1e6-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.2284838615961546, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e6-0', 'trace_hash': 1817720159708592833, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.72305490071213197993133300463', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.37079395849934071523478881278', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.41710530139108223374200000506', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 11.81499295812559, 'bad_primes': [3, 7], 'central_character': '1.1', 'conductor': 45579633110361, 'conductor_radical': 21, 'degree': 12, 'dirichlet_coefficients': [1, -1, 0, 2, -5, 0, 3, 1, 0, 5, -2, 0, -3, -3, 0, 0, 24, 0, -6, -10, 0, 2, 0, 0, 17, 3, 0, 6, 1, 0, 3, 4, 0, -24, -15, 0, -6, 6, 0, -5, -22, 0, 3, -4, 0, 0, -9, 0, 3, -17, 0, -6, 36, 0, 10, 3, 0, -1, -9, 0, 6, -3, 0, -5, 15, 0, 0, 48, 0, 15, -18, 0, 6, 6, 0, -12, -6, 0, -15, 0, 0, 22, -12, 0, -120, -3, 0, -2, 4, 0, -9, 0, 0, 9, 30, 0, -3, -3, 0, 34], 'euler11': [1, 2, -10, 34, 48, -416, 31, -4576, 5808, 45254, -146410, 322102, 1771561], 'euler13': [1, 3, -33, -32, 981, 549, -13818, 7137, 165789, -70304, -942513, 1113879, 4826809], 'euler17': [1, -24, 324, -3030, 21600, -121956, 557683, -2073252, 6242400, -14886390, 27060804, -34076568, 24137569], 'euler19': [1, 6, 111, 520, 5181, 18894, 130503, 358986, 1870341, 3566680, 14465631, 14856594, 47045881], 'euler2': [1, 1, -1, -4, -3, 2, 13, 4, -12, -32, -16, 32, 64], 'euler23': [1, 0, -36, 18, 468, -324, -5393, -7452, 247572, 219006, -10074276, 0, 148035889], 'euler29': [1, -1, -82, 31, 4425, -758, -148595, -21982, 3721425, 756059, -57997042, -20511149, 594823321], 'euler3': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler31': [1, -3, -60, 219, 1983, -4746, -51289, -147126, 1905663, 6524229, -55411260, -85887453, 887503681], 'euler37': [1, 6, 123, 948, 9285, 55410, 458183, 2050170, 12711165, 48019044, 230521803, 416063742, 2565726409], 'euler41': [1, 22, 206, 1802, 18432, 135116, 808243, 5539756, 30984192, 124195642, 582106766, 2548836422, 4750104241], 'euler43': [1, -3, -54, 569, 123, -13170, 115347, -566310, 227427, 45239483, -184615254, -441025329, 6321363049], 'euler47': [1, 9, -6, -531, -2433, 3438, 104623, 161586, -5374497, -55130013, -29278086, 2064105063, 10779215329], 'euler5': [1, 5, 8, 7, 9, -62, -299, -310, 225, 875, 5000, 15625, 15625], 'euler53': [1, -36, 792, -12258, 148572, -1444752, 11597011, -76571856, 417338748, -1824934266, 6249260952, -15055037748, 22164361129], 'euler59': [1, 9, -90, -459, 10161, 20556, -598421, 1212804, 35370441, -94268961, -1090562490, 6434318691, 42180533641], 'euler61': [1, -6, -126, 358, 12372, -11472, -838653, -699792, 46036212, 81259198, -1744575966, -5067577806, 51520374361], 'euler67': [1, 0, 6, 1366, 438, 4098, 1065603, 274566, 1966182, 410842258, 120906726, 0, 90458382169], 'euler7': [1, -3, 6, -7, 6, -3, 1, 0, 0, 0, 0, 0, 0], 'euler71': [1, 18, 495, 6120, 93789, 850842, 9049831, 60409782, 472790349, 2190415320, 12578782095, 32476128318, 128100283921], 'euler73': [1, -6, 111, -1668, 14133, -123774, 1717463, -9035502, 75314757, -648880356, 3152204751, -12438429558, 151334226289], 'euler79': [1, 15, 36, -367, -3225, -51726, -676905, -4086354, -20127225, -180945313, 1402202916, 46155845985, 243087455521], 'euler83': [1, 12, -144, -582, 34812, 90444, -2656433, 7506852, 239819868, -332780034, -6833998224, 47268487716, 326940373369], 'euler89': [1, -4, 236, -1934, 37044, -243500, 4408699, -21671500, 293425524, -1363410046, 14807168876, -22336237796, 496981290961], 'euler97': [1, 3, -168, 573, 14223, -78504, -1297807, -7614888, 133824207, 522961629, -14872919208, 25762020771, 832972004929], 'euler_factors': [[1, 1, -1, -4, -3, 2, 13, 4, -12, -32, -16, 32, 64], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 5, 8, 7, 9, -62, -299, -310, 225, 875, 5000, 15625, 15625], [1, -3, 6, -7, 6, -3, 1, 0, 0, 0, 0, 0, 0], [1, 2, -10, 34, 48, -416, 31, -4576, 5808, 45254, -146410, 322102, 1771561], [1, 3, -33, -32, 981, 549, -13818, 7137, 165789, -70304, -942513, 1113879, 4826809], [1, -24, 324, -3030, 21600, -121956, 557683, -2073252, 6242400, -14886390, 27060804, -34076568, 24137569], [1, 6, 111, 520, 5181, 18894, 130503, 358986, 1870341, 3566680, 14465631, 14856594, 47045881], [1, 0, -36, 18, 468, -324, -5393, -7452, 247572, 219006, -10074276, 0, 148035889], [1, -1, -82, 31, 4425, -758, -148595, -21982, 3721425, 756059, -57997042, -20511149, 594823321], [1, -3, -60, 219, 1983, -4746, -51289, -147126, 1905663, 6524229, -55411260, -85887453, 887503681], [1, 6, 123, 948, 9285, 55410, 458183, 2050170, 12711165, 48019044, 230521803, 416063742, 2565726409], [1, 22, 206, 1802, 18432, 135116, 808243, 5539756, 30984192, 124195642, 582106766, 2548836422, 4750104241], [1, -3, -54, 569, 123, -13170, 115347, -566310, 227427, 45239483, -184615254, -441025329, 6321363049], [1, 9, -6, -531, -2433, 3438, 104623, 161586, -5374497, -55130013, -29278086, 2064105063, 10779215329], [1, -36, 792, -12258, 148572, -1444752, 11597011, -76571856, 417338748, -1824934266, 6249260952, -15055037748, 22164361129], [1, 9, -90, -459, 10161, 20556, -598421, 1212804, 35370441, -94268961, -1090562490, 6434318691, 42180533641], [1, -6, -126, 358, 12372, -11472, -838653, -699792, 46036212, 81259198, -1744575966, -5067577806, 51520374361], [1, 0, 6, 1366, 438, 4098, 1065603, 274566, 1966182, 410842258, 120906726, 0, 90458382169], [1, 18, 495, 6120, 93789, 850842, 9049831, 60409782, 472790349, 2190415320, 12578782095, 32476128318, 128100283921], [1, -6, 111, -1668, 14133, -123774, 1717463, -9035502, 75314757, -648880356, 3152204751, -12438429558, 151334226289], [1, 15, 36, -367, -3225, -51726, -676905, -4086354, -20127225, -180945313, 1402202916, 46155845985, 243087455521], [1, 12, -144, -582, 34812, 90444, -2656433, 7506852, 239819868, -332780034, -6833998224, 47268487716, 326940373369], [1, -4, 236, -1934, 37044, -243500, 4408699, -21671500, 293425524, -1363410046, 14807168876, -22336237796, 496981290961], [1, 3, -168, 573, 14223, -78504, -1297807, -7614888, 133824207, 522961629, -14872919208, 25762020771, 832972004929]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/189/2/f/a'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '12-189e6-1.1-c1e6-0-0', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '12-189e6-1.1-c1e6-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.2284838615961546, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e6-0', 'trace_hash': 1817720159708592833, 'z1': {'__RealLiteral__': 0, 'data': '0.72305490071213197993133300463', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '916580978885696918877930284177,1737687784280919841995410322821,1796394385895011323046678462124,2443847594272730591209684519559,3001639094934461985314835992874,3677298143189256729572277748959', 'Lhash_array': ['916580978885696918877930284177', '1737687784280919841995410322821', '1796394385895011323046678462124', '2443847594272730591209684519559', '3001639094934461985314835992874', '3677298143189256729572277748959'], 'label': '12-189e6-1.1-c1e6-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/189/2/f/a'}