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lfunc_lfunctions • Show schema
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{'Lhash': '1005481441056077616293689315670,1609770567710601155989805208242', 'a10': 0, 'a2': 2, 'a3': 0, 'a4': 3, 'a5': 0, 'a6': 0, 'a7': -2, 'a8': 4, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 365.42857651126263, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -2, 1]], [3, [1]], [7, [1, 2, 1]], [19, [1, -2, 1]]], 'bad_primes': [2, 3, 7, 19], 'central_character': '2394.1', 'coefficient_field': '1.1.1.1', 'conductor': 5731236, 'conductor_radical': 798, 'degree': 4, 'euler_factors': [[1, -2, 1], [1], [1, 0, -2, 0, 25], [1, 2, 1], [1, -4, 14, -44, 121], [1, 0, 14, 0, 169], [1, 8, 38, 136, 289], [1, -2, 1], [1, -4, 38, -92, 529], [1, -12, 94, -348, 841], [1, 0, 14, 0, 961], [1, -20, 174, -740, 1369], [1, -4, 86, -164, 1681], [1, 0, 38, 0, 1849], [1, 8, 62, 376, 2209], [1, 4, 110, 212, 2809], [1, 8, 134, 472, 3481], [1, -4, 78, -244, 3721], [1, -12, 158, -804, 4489], [1, -8, 110, -568, 5041], [1, -20, 246, -1460, 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12769], 1]]], 'gamma_factors': [[], [0, 0]], 'group': 'GL2', 'index': 15, 'label': '4-2394e2-1.1-c1e2-0-15', 'leading_term': '7.42601535975389941643566620528865211313949525380794561121600000000000000000000000000000000', '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}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/2394/2/a/x', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.029296875', 'prec': 37}, 'plot_values': [7.426015359753899, 7.410911376557498, 7.379046822841405, 7.3198574630200195, 7.2357542644728445, 7.128584286041588, 6.997427589802464, 6.841921447356441, 6.662240184639735, 6.458474681583844, 6.230760418984088, 5.979420099295774, 5.704968174902618, 5.408127151482164, 5.089877375658512, 4.751470443383655, 4.394476685886337, 4.020785570362912, 3.6326378713436718, 3.232626554388384, 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'4.82765091075040148017849262651338', '4.87709161993679250703606891524276', '5.83723660437817179087812207865403', '5.98159371006717615689971220032713', '6.61077543430544603923983161339255', '6.68304401168267273880138709452247', '6.78261303430059598583977675594256', '7.48811881540264659913874606408741', '8.000370395302103329151571202216778', '8.297782014101703106788659932132835', '8.775042265480180355137739906589453', '9.285055372263357549392046008433686'], 'prelabel': '4-2394e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.3722061072065825, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 313432750866255337, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.793184999774424812735472750690', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.26988506724232690547654711275', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.31142045400819991841852134076', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 365.42857651126263, 'bad_primes': [2, 3, 7, 19], 'central_character': '1.1', 'conductor': 5731236, 'conductor_radical': 798, 'degree': 4, 'dirichlet_coefficients': [1, 2, 0, 3, 0, 0, -2, 4, 0, 0, 4, 0, 0, -4, 0, 5, -8, 0, 2, 0, 0, 8, 4, 0, 2, 0, 0, -6, 12, 0, 0, 6, 0, -16, 0, 0, 20, 4, 0, 0, 4, 0, 0, 12, 0, 8, -8, 0, 3, 4, 0, 0, -4, 0, 0, -8, 0, 24, -8, 0, 4, 0, 0, 7, 0, 0, 12, -24, 0, 0, 8, 0, 20, 40, 0, 6, -8, 0, -4, 0, 0, 8, -16, 0, 0, 0, 0, 16, 4, 0, 0, 12, 0, -16, 0, 0, 16, 6, 0, 6], 'euler11': [1, -4, 14, -44, 121], 'euler13': [1, 0, 14, 0, 169], 'euler17': [1, 8, 38, 136, 289], 'euler19': [1, -2, 1, 0, 0], 'euler2': [1, -2, 1, 0, 0], 'euler23': [1, -4, 38, -92, 529], 'euler29': [1, -12, 94, -348, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 0, 14, 0, 961], 'euler37': [1, -20, 174, -740, 1369], 'euler41': [1, -4, 86, -164, 1681], 'euler43': [1, 0, 38, 0, 1849], 'euler47': [1, 8, 62, 376, 2209], 'euler5': [1, 0, -2, 0, 25], 'euler53': [1, 4, 110, 212, 2809], 'euler59': [1, 8, 134, 472, 3481], 'euler61': [1, -4, 78, -244, 3721], 'euler67': [1, -12, 158, -804, 4489], 'euler7': [1, 2, 1, 0, 0], 'euler71': [1, -8, 110, -568, 5041], 'euler73': [1, -20, 246, -1460, 5329], 'euler79': [1, 4, 54, 316, 6241], 'euler83': [1, 16, 230, 1328, 6889], 'euler89': [1, -4, 182, -356, 7921], 'euler97': [1, -16, 246, -1552, 9409], 'euler_factors': [[1, -2, 1, 0, 0], [1, 0, 0, 0, 0], [1, 0, -2, 0, 25], [1, 2, 1, 0, 0], [1, -4, 14, -44, 121], [1, 0, 14, 0, 169], [1, 8, 38, 136, 289], [1, -2, 1, 0, 0], [1, -4, 38, -92, 529], [1, -12, 94, -348, 841], [1, 0, 14, 0, 961], [1, -20, 174, -740, 1369], [1, -4, 86, -164, 1681], [1, 0, 38, 0, 1849], [1, 8, 62, 376, 2209], [1, 4, 110, 212, 2809], [1, 8, 134, 472, 3481], [1, -4, 78, -244, 3721], [1, -12, 158, -804, 4489], [1, -8, 110, -568, 5041], [1, -20, 246, -1460, 5329], [1, 4, 54, 316, 6241], [1, 16, 230, 1328, 6889], [1, -4, 182, -356, 7921], [1, -16, 246, -1552, 9409]], 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2394/2/a/x'], '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': '4-2394e2-1.1-c1e2-0-15', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-2394e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.3722061072065825, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 313432750866255337, 'z1': {'__RealLiteral__': 0, 'data': '0.793184999774424812735472750690', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1005481441056077616293689315670,1609770567710601155989805208242', 'Lhash_array': ['1005481441056077616293689315670', '1609770567710601155989805208242'], 'label': '4-2394e2-1.1-c1e2-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2394/2/a/x'}