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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 1, 'A4': 0, 'A5': 1, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 1, 'Lhash': '68482071992267504', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 647.7464611966268, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [5, [1, -1]], [13, [1]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '81120.1', 'coefficient_field': '1.1.1.1', 'conductor': 81120, 'conductor_radical': 390, 'degree': 2, 'euler_factors': [[1], [1, -1], [1, -1], [1, 0, 7], [1, 0, 11], [1], [1, -2, 17], [1, 4, 19], [1, 4, 23], [1, 6, 29], [1, -8, 31], [1, -6, 37], [1, -2, 41], [1, 4, 43], [1, 0, 47], [1, -6, 53], [1, 0, 59], [1, 2, 61], [1, -8, 67], [1, 0, 71], [1, 6, 73], [1, -4, 79], [1, 12, 83], [1, 6, 89], [1, -10, 97]], 'gamma_factors': [[], [0]], 'index': 45, 'label': '2-81120-1.1-c1-0-45', 'leading_term': '8.90396391604', 'load_key': 'Cremona', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'EllipticCurve/Q/81120/bw', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 2.047572185215824, 3.065537609399372, 2.392674648027309, 0.3941814957987337, -1.413463592224979, -1.52224225144454, -0.02919186808668552, 1.256069282241152, 0.8076590604219953, -0.6365737939406886, -0.841004234461232, 0.9156517698658379, 2.515098831487753, 1.681761267017042, -0.6189263402472688, -1.180074711801607, 0.8026017666189786, 2.147895064814363, 0.2206891045178973, -2.721968693689345, -2.425043293628291, 0.9163614673576154, 2.663116345855198, 0.7877843553145424, -0.9918201624862164, 0.6265846122329535, 2.917129594732804, 1.599703643584222, -1.808951393469096, -2.327309085456129, 0.2206214781688824, 1.242112953145707, -0.4149085197836698, -0.7730509296203766, 1.510815945620848, 2.419459981498792, 0.1265652145004282, -1.444990716223215, -0.08650460903302686, 0.5259785780650051, -1.536548670776423, -1.883638662775347, 1.679997054547183, 3.591058959766556, 0.1541398626948006, -2.904219250154393, -0.2934776883264644, 3.123468822901753, 1.257048058509605, -2.226702506642146, -1.389467412069263, 1.089801608985713, 0.3608159715286528, -0.905079531989057, 1.019296633255293, 2.724685521572223, 1.006308817984828, -0.3281923289691705, 1.028543375737819, 0.6547557005728428, -2.5301428674096, -2.76552630271938, 0.4270616996944216, 0.125934414388272, -3.907903054330579, -4.13659322774763, -0.520486399112855, -0.4043323447149999, -2.944105126652352, -1.107945072676559, 2.899539625913495, 1.91877178775375, -1.255370551071595, -0.249861046872612, 1.490194697567643, -0.8004313353250126, -2.379535857582441, 0.1717026173617372, 1.210285781308533, -1.175871432835872, -0.9425231132488319, 2.026567930399696, 1.612238434773722, -0.7825255377299948, -0.1125091086451134, 0.3180485658442266, -2.575386555215653, -2.741680794386909, 1.419854778785197, 1.659648782630969, -2.3751657369191, -1.518008765539172, 2.868914556165088, 1.4432956739438, -2.906787976331935, -1.770632991942681, 0.7924780811176321, -1.335309209758108, -2.873491522352952, -0.444533129316698, 0.07034758836001229, -1.861698405939608, -0.8984648794684083, 0.6279700558235907, -0.953166588277619, -0.7774701637296493, 2.011161763791162, 0.1699754554868187, -4.390541827261637, -3.090349757095599, 0.3573213849582823, -1.162152075553413, -1.72152043274333, 2.488671069575821, 2.524188581052736, -2.860791818692121, -3.420502748731227, 0.2767066985536774, -0.1164852219150308, -1.614644327745931], 'positive_zeros': ['1.045066424038222', '1.754158038611956', '2.386814308111070', '2.891829258888078', '3.678358053122505', '4.166273207819739', '4.767005696842333', '5.435318063106905', '6.075456167161358', '6.441943862994995', '7.112849666345933', '7.728870873610708', '8.194887524372763', '8.601909948785004', '9.261466086680797', '9.762074352989412', '10.08469652282787', '10.64848741660731', '11.25818331348163', '11.76624682756786', '12.32565592024860', '12.86856791243216', '13.29482660406583', '13.65565925963003', '14.36889030188838', '14.59094997377176', '15.05843550732988', '15.71210762164745', '16.00957803461084', '16.80730327575816', '16.95003660105104', '17.56090716414661', '18.12938199798701', '18.52296178769008', '18.93840232723025', '19.48589720054396', '19.88532855772851'], 'prelabel': '2-81120-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 25.450863663078838, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 68482071992267504, 'z1': {'__RealLiteral__': 0, 'data': '1.045066424038222', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '1.754158038611956', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.386814308111070', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 647.7464611966268, 'bad_primes': [2, 3, 5, 13], 'central_character': '1.1', 'conductor': 81120, 'conductor_radical': 390, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, -4, 0, 0, 0, -4, 0, 1, 0, 1, 0, -6, 0, 8, 0, 0, 0, 0, 0, 6, 0, 0, 0, 2, 0, -4, 0, 1, 0, 0, 0, -7, 0, 2, 0, 6, 0, 0, 0, -4, 0, 0, 0, -2, 0, 0, 0, 0, 0, 8, 0, -4, 0, 0, 0, -6, 0, 1, 0, 0, 0, 4, 0, 1, 0, -12, 0, 2, 0, -6, 0, -6, 0, 0, 0, 8, 0, -4, 0, 10, 0, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, 0, 0], 'euler17': [1, -2, 17], 'euler19': [1, 4, 19], 'euler2': [1, 0, 0], 'euler23': [1, 4, 23], 'euler29': [1, 6, 29], 'euler3': [1, -1, 0], 'euler31': [1, -8, 31], 'euler37': [1, -6, 37], 'euler41': [1, -2, 41], 'euler43': [1, 4, 43], 'euler47': [1, 0, 47], 'euler5': [1, -1, 0], 'euler53': [1, -6, 53], 'euler59': [1, 0, 59], 'euler61': [1, 2, 61], 'euler67': [1, -8, 67], 'euler7': [1, 0, 7], 'euler71': [1, 0, 71], 'euler73': [1, 6, 73], 'euler79': [1, -4, 79], 'euler83': [1, 12, 83], 'euler89': [1, 6, 89], 'euler97': [1, -10, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, -1, 0], [1, 0, 7], [1, 0, 11], [1, 0, 0], [1, -2, 17], [1, 4, 19], [1, 4, 23], [1, 6, 29], [1, -8, 31], [1, -6, 37], [1, -2, 41], [1, 4, 43], [1, 0, 47], [1, -6, 53], [1, 0, 59], [1, 2, 61], [1, -8, 67], [1, 0, 71], [1, 6, 73], [1, -4, 79], [1, 12, 83], [1, 6, 89], [1, -10, 97]], 'index': 45, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/81120/bw'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-81120-1.1-c1-0-45', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-81120-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 25.450863663078838, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 68482071992267504, 'z1': {'__RealLiteral__': 0, 'data': '1.045066424038222', 'prec': 57}}
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lfunc_instances • Show schema
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{'Lhash': '68482071992267504', 'Lhash_array': ['68482071992267504'], 'label': '2-81120-1.1-c1-0-45', 'type': 'ECQ', 'url': 'EllipticCurve/Q/81120/bw'}