Table lfunc_lfunctions
L-functions
{'Lhash': '2313068217588659866373525307073', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [190.5484840028542, 0], 'a6': [0, 0], 'a7': [0, -4097.7443115610295], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 117.32503969760468, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '4.0', 'prec': 7}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '288.127', 'coefficient_field': 'CDF', 'conductor': 288, 'conductor_radical': 6, 'conjugate': '100595201649575992426292164033', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-190.5484840028542, 0], [390625.0, 0]], [[1.0, 0], [0, 4097.7443115610295], [-5764801.0, 0]], [[1.0, 0], [0, 8804.590813398949], [-214358881.0, 0]], [[1.0, 0], [2752.5922525766114, 0], [815730721.0, 0]], [[1.0, 0], [96418.55168436287, 0], [6975757441.0, 0]], [[1.0, 0], [0, -5160.348318936832], [-16983563041.0, 0]], [[1.0, 0], [0, 482342.82997560076], [-78310985281.0, 0]], [[1.0, 0], [1153436.4463917585, 0], [500246412961.0, 0]], [[1.0, 0], [0, -421771.36999763985], [-852891037441.0, 0]], [[1.0, 0], [-2094955.8538463998, 0], [3512479453921.0, 0]], [[1.0, 0], [-1119388.8909035882, 0], [7984925229121.0, 0]], [[1.0, 0], [0, -1000784.6202420453], [-11688200277601.0, 0]], [[1.0, 0], [0, -4110537.6114821145], [-23811286661761.0, 0]], [[1.0, 0], [-8869123.34767778, 0], [62259690411361.0, 0]], [[1.0, 0], [0, -17277551.250037894], [-146830437604321.0, 0]], [[1.0, 0], [-19968445.15034912, 0], [191707312997281.0, 0]], [[1.0, 0], [0, 6643098.948566904], [-406067677556641.0, 0]], [[1.0, 0], [0, 16136768.22653249], [-645753531245761.0, 0]], [[1.0, 0], [2881259.315523727, 0], [806460091894081.0, 0]], [[1.0, 0], [0, -4800143.916889434], [-1517108809906561.0, 0]], [[1.0, 0], [0, 21500897.233864147], [-2252292232139041.0, 0]], [[1.0, 0], [88990907.96124883, 0], [3936588805702081.0, 0]], [[1.0, 0], [-88970079.21122077, 0], [7837433594376961.0, 0]], [[1.0, 0], [44059339.61382462, 0], [10828567056280800, 0]], [[1.0, 0], [0, 27932579.26296568], [-12667700813876160, 0]], [[1.0, 0], [0, -124580759.46635996], [-17181861798319200, 0]], [[1.0, 0], [215414824.11201525, 0], [19925626416901920, 0]], [[1.0, 0], [-95121791.83041678, 0], [26584441929064320, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 23241263, 'index': 39, 'label': '2-288-4.3-c8-0-39', 'leading_term': '0.369468793815812675773262621821720418085676302725267529', 'load_key': 'CMFs-workshop', 'motivic_weight': 8, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [8], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/288/9/g/e/127/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0703125', 'prec': 20}, 'plot_values': [0.36946879381581266, 0.7192388107791394, 1.0807738416703019, 1.4447981301951018, 1.8019297890220953, 2.1429317573077995, 2.4589599363993195, 2.741802339758165, 2.984103236229707, 3.1795665364363974, 3.323133069485729, 3.4111269187338737, 3.441366626343422, 3.413237829796814, 3.3277247497709284, 3.187398895441587, 2.9963643750174223, 2.7601602777264964, 2.4856217072312514, 2.1807021713253176, 1.8542611420185848, 1.5158216648810885, 1.1753038863999843, 0.8427412519198372, 0.5279868733707813, 0.24041814539064513, -0.011351927288880483, -0.21974806380761425, -0.37848215049464284, -0.4827705713640217, -0.5295117957308313, -0.517417447510686, -0.4470911896833925, -0.32105110344119103, -0.14369279828843323, 0.07880777879744186, 0.3386510045007461, 0.6266269391622605, 0.9323806544412762, 1.2447228833599633, 1.5519775470850998, 1.842356095476864, 2.104347232214735, 2.3271095443873735, 2.500853878374131, 2.6172020468607404, 2.669508652162254, 2.653133490576183, 2.5656531668184064, 2.4070021843965277, 2.1795358559405082, 1.888009846875764, 1.5394739576785401, 1.1430807783465549, 0.7098130125872697, 0.2521364553272336, -0.21641130627213528, -0.6816835369726152, -1.129422901039479, -1.5457784311368301, -1.9178219742773257, -2.2340443781868005, -2.4848116288541227, -2.6627618812311344, -2.7631258543331385, -2.783955371326808, -2.726247862750913, -2.593958331112892, -2.3938944796258297, -2.135495289209789, -1.8304981135076597, -1.4925041599250592, -1.136456832097583, -0.7780516185904176, -0.4330998222663187, -0.11687124753877597, 0.15655716440178036, 0.3749189695283425, 0.5283147179349015, 0.609681495863615, 0.6151524843675684, 0.5442874319473701, 0.4001598803110832, 0.18929276715693008, -0.07855956348293534, -0.3907781457498173, -0.7323833382539413, -1.0866577056813653, -1.4358635732358063, -1.7620258183539566, -2.0477464344755028, -2.277014756099893, -2.4359761599762817, -2.513622675490288, -2.502371294479681, -2.398499831764025, -2.2024158334697903, -1.9187410589288374, -1.5562021945583717, -1.1273273483722657, -0.6479571216577898, -0.13658822345226665, 0.3864237691139848, 0.8997682431796884, 1.3821494535459335, 1.81327748133162, 2.174832799927721, 2.451356834791143, 2.6310231037070344, 2.706248072556115, 2.6741076202230274, 2.5365337174537763, 2.3002762188306995, 1.976626077452306, 1.580908273417535, 1.1317647020733064, 0.6502585747913157, 0.15884193059005675, -0.3197639308130415, -0.763719403398923, -1.1531900716543202, -1.471383742926564, -1.705444954771443, -1.8471569049359546, -1.8934096086202303, -1.8464044179493573, -1.7135783177535442, -1.5072459889478584, -1.2439727591921705, -0.9437064345201249, -0.6287098031257499, -0.3223475298472279, -0.04779049739305974, 0.1732932044205486, 0.3219889337880654, 0.3832574805152612, 0.34686340189860604, 0.20805385140624036, -0.032055456035706684, -0.3664152050033646, -0.7823091225964559, -1.261944657240658, -1.7833415632989884, -2.3214747495796053, -2.8496122433381337, -3.3407765735477883, -3.769249102174511, -4.112032452186482, -4.350186582802836, -4.469959365909212, -4.463642558799537, -4.330098399319171, -4.074919954041353, -3.7102088773987236, -3.253976252379792, -2.7291944192604483, -2.162548842187721, -1.5829578225125125, -1.019943053617316, -0.5019446139959776, -0.054679248752932015, 0.30035976948088666, 0.5471694056756147, 0.6761906592033937, 0.6848871123916607, 0.5779074588885575, 0.3668157353446789, 0.06939903683338917, -0.2914114496422181, -0.6889458182290269, -1.0944456768748287, -1.4788609936831867, -1.814684342859789, -2.0777089298517093, -2.248599373185166, -2.3141738356115367, -2.268312299162915, -2.112427707714849, -1.8554631089331732, -1.5134072475087046, -1.1083514968731794, -0.6671406503353002, -0.21969700760745456, 0.20288040464219506, 0.5703232995745013, 0.8551810274279708, 1.0346585894931166, 1.0921846773493282, 1.0186038719128143, 0.8129095607895696, 0.48246245596081894, 0.04267209767182997, -0.4838466239367433, -1.0685953420557934, -1.6789137098536169, -2.2799941188085064, -2.8370620939917695, -3.317581714917714, -3.693341390587698, -3.9422808514858603, -4.049935146977664, -4.01039495533177, -3.826713228083153, -3.51072418334687, -3.082279613253552, -2.5679468022992102, -1.9992494028223042, -1.4105648111200022, -0.8368166349701468, -0.311116879541722, 0.13748178085024093, 0.4859684380342929, 0.7189518127669824, 0.8297200786505154, 0.8207032926148331, 0.7032992883129371, 0.4970675252408423, 0.22833947605794763, -0.07166439261591184, -0.36908508921070793, -0.629889357352275, -0.8223766744541915, -0.9195522772083949, -0.9011962073153926, -0.7554772057274725, -0.47999014885898056, -0.08213470772162433, 0.4212015779758385, 1.004643703775796, 1.635952085725543, 2.2781615648038733, 2.892091646327483, 3.439054306630498, 3.8835689069046766, 4.195890385020934, 4.354167439938227, 4.3460713700523215, 4.169772082151723, 3.834183159924211, 3.3584496365331624, 2.770706592321644, 2.106189962572132, 1.4048290700189858, 0.7084897725478987, 0.05806469358297053, -0.5093794507402122, -0.9631891336489683, -1.2812547298397918, -1.4515249745037184, -1.4727892609101216, -1.3546648639036374, -1.1167845898088116, -0.7872399043186834, -0.40039083536407677, 0.005797388798054266, 0.3926937084211415, 0.7239964126259486], 'positive_zeros': ['1.82468908796494252273435696500527', '2.43747695332861021884932182172366', '3.90509292331087347797170848874925', '5.30197377789616428254873467673883', '5.88694047487533508899256577944006', '7.11996116103432388814544720112324', '8.249530882905910822798157131295240', '9.294915479948522843559717178795258', '9.695175302812170052735561901136629', '11.25966264497629297405339380911913'], 'prelabel': '2-288-4.3-c8-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.831668370920736, 'root_angle': -0.375, 'root_number': '-0.70710678118654752440084436210484903928483593768847403659 - 0.70710678118654752440084436210484903928483593768847403659*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.375', 'prec': 10}, 'spectral_label': 'c8-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.82468908796494252273435696501', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.43747695332861021884932182172', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.90509292331087347797170848875', 'prec': 100}}