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lfunc_lfunctions • Show schema
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{'Lhash': '349175037817271026156025289266', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.625688919646985, -1.6150892779753658], 'a4': [1.8169305436390473, 0.8359206897735668], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-2.225429618799654, 0.2292830512147813], 'a8': [0.0, 0.0], 'a9': [-2.2170267516619773, 2.0210869309396715], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.354222026159927, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.625688919646985, 1.6150892779753658]]], [307, [[1.0, 0], [16.63110847439972, -5.514184519287494]]]], 'bad_primes': [3, 307], 'central_character': '921.137', 'coefficient_field': 'CDF', 'conductor': 921, 'conductor_radical': 921, 'conjugate': '2347015190095082388633929548998', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [-1.8169305436390473, -0.8359206897735668]], [[1.0, 0], [0.625688919646985, 1.6150892779753658]], [[1.0, 0], [0, 0], [4.932693023118298, 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7.787323989581649], [14.504680359793447, 108.03061717707727]], [[1.0, 0], [0, 0], [-109.58705377195606, 27.562250372246616]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 13, 'label': '2-921-921.137-c1-0-13', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/921/2/x/a/137/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.6353185495325869, 0.36186242054388507, 0.06409190397891426, -0.2630498500768022, -0.622131199795626, -1.0112743856711142, -1.422898048548587, -1.8432489805662498, -2.2527196532391134, -2.626927371585201, -2.9385214119246763, -3.159648302303787, -3.264935322630197, -3.234760072774202, -3.0584792723333285, -2.7372145345915433, -2.285757314768356, -1.7331765740383005, -1.1218016432254947, -0.5044110418158583, 0.06032380280451344, 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'4.70561722203200915783961805021269', '5.32710734177077210179014419984605', '6.51000629640533828378502864769748', '6.92010681346693263179225379532292', '8.182935352721247697293081601337102', '9.343899254242111844487112702521679', '10.07180666398959891948449219716917'], 'prelabel': '2-921-921.137-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.7118668894619304, 'root_angle': -0.6064359606406056, 'root_number': '-0.3281820911997533 - 0.9446144795712994*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.30321798032', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.27545053641311345183642444791', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.48563279589513937670939979715', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.23020019541403596484935073468', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.354222026159927, 'bad_primes': [3, 307], 'central_character': '921.137', 'conductor': 921, 'conductor_radical': 921, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/921/2/x/a/137/1'], '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': '2-921-921.137-c1-0-13', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-921-921.137-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.7118668894619304, 'root_angle': -0.3032179803203028, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.27545053641311345183642444791', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '349175037817271026156025289266', 'Lhash_array': ['349175037817271026156025289266'], 'label': '2-921-921.137-c1-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/921/2/x/a/137/1'}