Table lfunc_lfunctions
L-functions
{'Lhash': '2094827276471439748156262771685,2509605659784249995147328155830', 'a10': 0, 'a2': 0, 'a3': 1, 'a4': 0, 'a5': 6, 'a6': 0, 'a7': 4, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.2067378401294855, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [1]], [3, [1, -1, 1]], [13, [1, 5, 13]]], 'bad_primes': [2, 3, 13], 'central_character': '312.1', 'coefficient_field': '1.1.1.1', 'conductor': 97344, 'conductor_radical': 78, 'degree': 4, 'euler_factors': [[1], [1, -1, 1], [1, -6, 19, -30, 25], [1, -4, 9, -28, 49], [1, 4, 5, 44, 121], [1, 5, 13], [1, 3, -8, 51, 289], [1, -4, -3, -76, 361], [1, -8, 41, -184, 529], [1, -5, -4, -145, 841], [1, 16, 126, 496, 961], [1, 7, 12, 259, 1369], [1, -9, 40, -369, 1681], [1, 8, 21, 344, 1849], [1, 8, 110, 376, 2209], [1, 10, 131, 530, 2809], [1, 4, -43, 236, 3481], [1, -5, -36, -305, 3721], [1, 8, -3, 536, 4489], [1, -4, -55, -284, 5041], [1, -22, 267, -1606, 5329], [1, 8, 174, 632, 6241], [1, 0, 166, 0, 6889], [1, -6, -53, -534, 7921], [1, -14, 99, -1358, 9409], [1, 11, 20, 1111, 10201], [1, 8, 222, 824, 10609], [1, 8, -43, 856, 11449], [1, 36, 542, 3924, 11881], [1, -9, -32, -1017, 12769]], 'euler_factors_factorization': [[1], [[[1, -1, 1], 1]], [[[1, -3, 5], 2]], [[[1, -5, 7], 1], [[1, 1, 7], 1]], [[[1, 4, 5, 44, 121], 1]], [[[1, 5, 13], 1]], [[[1, 3, -8, 51, 289], 1]], [[[1, -4, -3, -76, 361], 1]], [[[1, -8, 41, -184, 529], 1]], [[[1, -5, -4, -145, 841], 1]], [[[1, 8, 31], 2]], [[[1, 7, 12, 259, 1369], 1]], [[[1, -9, 40, -369, 1681], 1]], [[[1, -5, 43], 1], [[1, 13, 43], 1]], [[[1, 4, 47], 2]], [[[1, 5, 53], 2]], [[[1, 4, -43, 236, 3481], 1]], [[[1, -5, -36, -305, 3721], 1]], [[[1, 8, -3, 536, 4489], 1]], [[[1, -4, -55, -284, 5041], 1]], [[[1, -11, 73], 2]], [[[1, 4, 79], 2]], [[[1, 0, 83], 2]], [[[1, -6, -53, -534, 7921], 1]], [[[1, -19, 97], 1], [[1, 5, 97], 1]], [[[1, 11, 20, 1111, 10201], 1]], [[[1, 4, 103], 2]], [[[1, 8, -43, 856, 11449], 1]], [[[1, 18, 109], 2]], [[[1, -9, -32, -1017, 12769], 1]]], 'gamma_factors': [[], [0, 0]], 'group': 'GL2', 'id': 9881124, 'index': 35, 'label': '4-312e2-1.1-c1e2-0-35', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/312/2/q/c', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 10}, 'plot_values': [3.0729583977083093, 3.076974391152456, 3.0840923585200692, 3.09642195915684, 3.1119266258068756, 3.1275593312575602, 3.1404429067627975, 3.1475663044007414, 3.1452745193665788, 3.1297735010527923, 3.0973185878556597, 3.04437618720293, 2.967847377286481, 2.8651910248591888, 2.734809333650459, 2.5760285474942823, 2.389536040799219, 2.1772077503639222, 1.9425271262181134, 1.6902193971197488, 1.4265603555943436, 1.1588049419698225, 0.8953092889664953, 0.6447800553337665, 0.4161707006924713, 0.2178344197084391, 0.05722159100955358, 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1.0014365760001926, 0.7562679724686251, 0.40453539218558354, 0.03736450181839392, -0.25366962979819563, -0.3957624215395273, -0.3565417742358992, -0.15177079676071342, 0.1571445559038803, 0.47996437090990046, 0.7199611155310444, 0.8057117964370202, 0.7102603178511149, 0.4720734808448199, 0.18836553651530882, 0.004989405518463068, 0.08227424601870524, 0.5590658800704456, 1.5144363824222926, 2.9365451841030032, 4.710655162263714, 6.626573431207085, 8.403913353534112, 9.746690771326552, 10.38429988913982, 10.145858682212909, 8.976397794097858, 6.985322636849431, 4.409871625909119, 1.6083915556244377, -1.0194451868146557, -3.0829760483460253, -4.279917038755358, -4.4440754038762815, -3.5778115129218397, -1.8502898489117363, 0.43027633731736126, 2.8791904576922662, 5.091570087416284, 6.732193754380043, 7.566919080547615, 7.526857909905879, 6.680783041314843, 5.241766701112117, 3.492151724071873, 1.7450557805882516, 0.26958489527960106, -0.7486859136576538, -1.2364824290313756, 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'2.61987270067235914312200550889760', '3.24299268288688182379717532261899', '4.68413657355429970066777703792965', '5.00051044922080561458393268027477', '5.53061107605458742488750484563449', '5.56754534870062268907340746090597', '6.80747266974240587771543573211069', '6.87345100907401027477054771785720', '7.87525592776815281158952278370292', '7.915936716857834631976966885766461', '8.893177391750017321594638484442971', '9.109819490646681994508145771920870', '9.721404877693394660012466115517609', '9.746521821197915874565769412383293', '10.58718193668514673289818130812161', '10.88746238257520542034844996986251', '11.13206431393542394912977985171667', '11.97203891351371068805972167805653'], 'prelabel': '4-312e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.5783955597580568, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 1744232417556367228, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.65252734159892672478220869023', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '1.97972979252517803365857623707', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '2.61987270067235914312200550890', 'prec': 100}}