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lfunc_lfunctions • Show schema
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{'Lhash': '1511944803642098563685558746290', 'a10': [-0.769420224406413, 0.0], 'a2': [-0.19565626780522913, 0.0], 'a3': [-0.2597884275521169, 0.0], 'a4': [-1.9617186248685285, 0.0], 'a5': [3.9325099729099984, 0.0], 'a6': [0.050829234153836354, 0.0], 'a7': [0.0, 0.0], 'a8': [0.7751350802362409, 0.0], 'a9': [-2.9325099729099984, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.086470608755563, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [7, 13], 'central_character': '637.1', 'coefficient_field': 'CDF', 'conductor': 637, 'conductor_radical': 91, 'conjugate': '1511944803642098563685558746290', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.19565626780522913, 0], [2.0, 0]], [[1.0, 0], [0.2597884275521169, 0], [3.0, 0]], [[1.0, 0], [-3.9325099729099984, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-4.506273929511182, 0], [11.0, 0]], [[1.0, 0], [-1.0, 0]], 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'5.22509066933486439733252162204295', '6.02883304303346113051358692948091', '6.69757501810445103551369381232272', '8.392307526431928522157372431684519', '8.975133828205401973565169243250317', '9.572817839349911366904369790831692', '10.36110620479067596003155069243623'], 'prelabel': '2-637-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2553205113144257, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.19271414644531081978401165037', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.63643294720511834793319575028', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.12836263864436883298067059119', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.086470608755563, 'bad_primes': [7, 13], 'central_character': '1.1', 'conductor': 637, 'conductor_radical': 91, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/637/2/a/l/1/2'], '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': '2-637-1.1-c1-0-11', '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': '2-637-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2553205113144257, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.19271414644531081978401165037', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1511944803642098563685558746290', 'Lhash_array': ['1511944803642098563685558746290'], 'label': '2-637-1.1-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/637/2/a/l/1/2'}