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lfunc_lfunctions • Show schema
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{'Lhash': '3699507233268962663409781138159', 'a10': [44008696178719870000000, 0.0], 'a2': [7368513.332482818, 0.0], 'a3': [-57533690087.64158, 0.0], 'a4': [19110616642145.043, 0.0], 'a5': [5972533968923573.0, 0.0], 'a6': [-423937762477721540, 0.0], 'a7': [-13575407698885376000, 0.0], 'a8': [-118439681311981140000, 0.0], 'a9': [355812788549952900000, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12.825572607427626, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '22.5', 'prec': 14}, 'bad_lfactors': [], 'bad_primes': [], 'central_character': '1.1', 'coefficient_field': 'CDF', 'conductor': 1, 'conductor_radical': 1, 'conjugate': '3699507233268962663409781138159', 'degree': 2, 'euler_factors': [[[1.0, 0], [-7368513.332482818, 0], [35184372088832.0, 0]], [[1.0, 0], [57533690087.64158, 0], [2954312706550833600000, 0]], [[1.0, 0], [-5972533968923573.0, 0], [28421709430404005000000000000000, 0]], [[1.0, 0], [13575407698885376000, 0], 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{'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c45-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.91839662490823476782717262862', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.33002238531523506864245254531', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.13161181216014691666479320551', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 12.825572607427626, 'bad_primes': [], 'central_character': '1.1', 'conductor': 1, 'conductor_radical': 1, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1/46/a/a/1/3'], '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': '2-1-1.1-c45-0-1', 'motivic_weight': 45, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [45], 'order_of_vanishing': 1, 'prelabel': '2-1-1.1-c45-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.581280861287987, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c45-0', 'z1': {'__RealLiteral__': 0, 'data': '2.91839662490823476782717262862', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3699507233268962663409781138159', 'Lhash_array': ['3699507233268962663409781138159'], 'label': '2-1-1.1-c45-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1/46/a/a/1/3'}