Table lfunc_lfunctions
L-functions
{'Lhash': '418501930945558649126621712852', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [2.2122969668445, 0.32518015082508633], 'a6': [0, 0], 'a7': [0, 3.545677699309884], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 27.308837491277906, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-2.2122969668445, -0.32518015082508633]]], [19, [[1.0, 0], [-0.8637597431793923, 4.2724605447052015]]]], 'bad_primes': [2, 3, 5, 19], 'central_character': '3420.1189', 'coefficient_field': 'CDF', 'conductor': 3420, 'conductor_radical': 570, 'conjugate': '2083303451953451955950699435226', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.2122969668445, -0.32518015082508633]], [[1.0, 0], [0, -3.545677699309884], [-7.0, 0]], [[1.0, 0], [-1.81575245447762, 0], [11.0, 0]], [[1.0, 0], [2.7830770142149936, -1.6068102633324863], [6.5, -11.258330249197702]], [[1.0, 0], [6.92193022462161, 3.996378278497093], [8.5, 14.722431864335457]], [[1.0, 0], [-0.8637597431793923, 4.2724605447052015]], [[1.0, 0], [7.300255739138604, -4.214804616144783], [11.5, -19.91858428704209]], [[1.0, 0], [-4.291240457588874, -7.432646500039047], [-14.5, 25.11473670974872]], [[1.0, 0], [1.7087429855743461, 0], [31.0, 0]], [[1.0, 0], [0, -5.506076664478615], [-37.0, 0]], [[1.0, 0], [4.056944651241349, -7.026834259444817], [-20.5, -35.50704155516198]], [[1.0, 0], [4.353730346786404, 2.513627387696173], [21.5, 37.239092362730865]], [[1.0, 0], [-1.1683425449354383, 0.6745428828241677], [23.5, -40.703193977868615]], [[1.0, 0], [1.9220131700341123, -1.1096748211052008], [26.5, -45.89934640057525]], [[1.0, 0], [0.9607744688218776, -1.664110194614492], [-29.5, -51.09549882328188]], [[1.0, 0], [-2.8304659887669956, -4.902510901640116], [-30.5, 52.827549630850754]], [[1.0, 0], [8.043598338767527, -4.643973666140659], [33.5, -58.023702053557386]], [[1.0, 0], [-2.9436452847904393, 5.098543192717598], [-35.5, -61.48780366869514]], [[1.0, 0], [-2.8271581509231383, -1.6322605194771185], [36.5, 63.21985447626402]], [[1.0, 0], [-2.0873884248958223, 3.615462807050736], [-39.5, -68.41600689897065]], [[1.0, 0], [0, -6.302682320202565], [-83.0, 0]], [[1.0, 0], [2.7364568488983623, 4.739682295011794], [-44.5, 77.07626093681505]], [[1.0, 0], [6.912549496356132, 3.990962312507824], [48.5, 84.00446416709055]], [[1.0, 0], [2.467312738456173, 4.273511021167993], [-50.5, 87.4685657822283]], [[1.0, 0], [0, 5.562913997194314], [-103.0, 0]], [[1.0, 0], [0, 9.122513229954825], [-107.0, 0]], [[1.0, 0], [-7.572248121562514, 13.115518474064267], [-54.5, -94.39676901250381]], [[1.0, 0], [0, -4.46090526773478], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 23462014, 'index': 11, 'label': '2-3420-95.49-c1-0-11', 'leading_term': '1.229071845137506743741002236490539462386745295264049414', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/3420/2/bj/c/1189/10', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 24}, 'plot_values': [1.2290718451375067, 1.0456474261932596, 0.85942864985979, 0.6708553902005135, 0.48040986779515865, 0.28866756351910255, 0.0963430358141776, -0.09567211506522005, -0.28628129626986143, -0.4741664814033301, -0.6577841186854878, -0.8353736317788294, -1.0049782518036754, -1.1644775114696466, -1.31163041246619, -1.4441280269588002, -1.5596540929052667, -1.6559519933615472, -1.730896359748715, -1.7825674020811333, -1.8093259449725287, -1.8098870409681482, -1.7833899497231687, -1.7294622219284332, -1.6482756204787847, -1.5405916576177767, -1.4077946339196044, -1.2519102394025055, -1.0756080229061291, -0.8821863545190948, -0.675538895776543, -0.4601020489230719, -0.24078337195998556, -0.02287150956671755, 0.1880712125444129, 0.38633176724139306, 0.5661826031698155, 0.7220280512472212, 0.8485574439771012, 0.9409009489679812, 0.994783724034651, 1.006673716357103, 0.9739182713912244, 0.8948647047392445, 0.7689601344897157, 0.5968261806516744, 0.38030461510699826, 0.12247068715237024, -0.17238835273483116, -0.4988310700143921, -0.8503564857183765, -1.2195348710147291, -1.5981728210773112, -1.977509503429396, -2.348439766851858, -2.701758651756237, -3.0284208063644167, -3.3198074292625406, -3.567992669761525, -3.766000960809117, -3.908046566990868, -3.989746727041298, -4.0083001719695135, -3.962623511937789, -3.853439001862815, -3.683308500087743, -3.4566099972790765, -3.1794548732242576, -2.8595459858952115, -2.5059787488523746, -2.128989440751722, -1.7396570395898663, -1.349566806352128, -0.9704455794798297, -0.6137802072380872, -0.29043166960279193, -0.010258163541070255, 0.21823930376202702, 0.38823548482156234, 0.4948510158872504, 0.5353627095228924, 0.5093443368503361, 0.4187303701102447, 0.2677976885445445, 0.06306308738255915, -0.1869025237676363, -0.47173919864208846, -0.7796351417072956, -1.0977258464131563, -1.4125422970343025, -1.7104930022350924, -1.9783627784670705, -2.2038099420793182, -2.3758429776552132, -2.4852578802614955, -2.525018247837489, -2.490561824327423, -2.380019531050849, -2.194336008938358, -1.937284233524771, -1.615370736518607, -1.2376322272926101, -0.8153287910986031, -0.3615431719801014, 0.10930025462885833, 0.5819795317746902, 1.0410618071159734, 1.4715099081054903, 1.8592845633786208, 2.191917493683512, 2.4590310829347586, 2.6527818660801823, 2.768207609132444, 2.803461236709276, 2.7599191687486777, 2.6421566050900736, 2.457787753190627, 2.217174710645627, 1.9330144506281235, 1.6198188648704446, 1.2933078459230596, 0.9697397004159556, 0.6652065630788618, 0.3949247460238614, 0.17255097099656647, 0.009555106764658814, -0.0853216605904358, -0.10649732939951613, -0.05184663975518965, 0.0771505573985416, 0.27542010438274417, 0.5344666088882412, 0.8427046505114867, 1.1859367404256635, 1.5479597164323744, 1.9112749581109008, 2.25787245741621, 2.570054654559357, 2.8312632753350204, 3.0268713521240556, 3.1449032743013636, 3.17664811514604, 3.117135561032767, 2.9654493831982234, 2.7248603242267717, 2.4027682328380386, 2.0104519259703886, 1.5626341976492393, 1.0768782147588754, 0.5728398186910356, 0.07140758017156493, -0.40623154303377385, -0.8395587421391024, -1.2096774314814527, -1.5002098227081464, -1.6980927210041719, -1.7942331388211916, -1.7839901765449306, -1.667457220747767, -1.4495275338734195, -1.1397363504453926, -0.7518831891607793, -0.3034487326803592, 0.18516920319148375, 0.6915669030860964, 1.1923517538827595, 1.6642177285467517, 2.085028421795055, 2.4348555018848383, 2.6969217901965217, 2.8584020695259422, 2.911041013775786, 2.8515560619649136, 2.681803249391382, 2.408695481189908, 2.043874934567927, 1.6031536015648484, 1.1057478096019822, 0.5733432688463126, 0.02903622308180541, -0.5037968722879106, -1.0026444505132504, -1.4469615930930524, -1.8191718807756625, -2.105517271161518, -2.296711215226847, -2.3883599489793292, -2.3811286042155606, -2.2806418965310664, -2.0971230050943346, -1.8447881393113759, -1.5410274576257414, -1.2054147504806643, -0.8585979705725748, -0.5211297334605816, -0.2123008938331614, 0.050959044310787786, 0.25505369996284566, 0.39050890421547224, 0.4525334349763113, 0.4413175580912304, 0.3620494137843094, 0.22464449621491156, 0.04319921056794107, -0.16480509258465925, -0.379506961479779, -0.5798256518253776, -0.7447154029082976, -0.8544443682332246, -0.8918267515435161, -0.8433379610968682, -0.7000477634126975, -0.45831528466972576, -0.12020185666438417, 0.3064274728228387, 0.8081262170521301, 1.3664072235704627, 1.9585788607808823, 2.558836683076181, 3.1395556843945465, 3.6727160614597336, 4.1313867194851905, 4.491186116936384, 4.731639798160252, 4.837358199786223, 4.798966885126889, 4.613733859998268, 4.285854423877705, 3.8263722842824737, 3.252735426462407, 2.5880053990471557, 1.8597581202844622, 1.0987319205347768, 0.3372932904479139, -0.39219817928164535, -1.0590375840977744, -1.6357454007937025, -2.099474574595939, -2.4331757017328077, -2.6264547557566047, -2.6760744110832455, -2.586069586880509, -2.367469287510034, -2.03763894556579, -1.619279015840494, -1.1391352739055374, -0.6264929800693597, -0.11153977434498888, 0.37630991440206885, 0.8100335483153638, 1.166469756101266, 1.4275540239234916, 1.581249916290434, 1.6221224915045747, 1.5515213925079925, 1.3773639810549794, 1.113532506418359], 'positive_zeros': ['0.33013981208245476900717673736621', '1.68118355274023560090132626408722', '2.40854192454396165607609142294834', '3.86142123103576156009278691558604', '4.27925737308241366274684310250329', '5.26953992224519706792419125213897', '6.35145967539294700032855472333085', '6.52396740442437791227669259814442', '7.62456922042631335469926520194661', '8.258443101013099866688874203084745'], 'prelabel': '2-3420-95.49-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.225785825239866, 'root_angle': -0.395567544874056, 'root_number': '-0.7923356040194772273504603887888629705400989602069294256 - 0.6100854781119529176804487699831596372719008997383439108*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.395567544874056', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.33013981208245476900717673737', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '1.68118355274023560090132626409', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '2.40854192454396165607609142295', 'prec': 100}}