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lfunc_lfunctions • Show schema
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{'Lhash': '1496796112709840696010586054732', 'a10': [11.103280198474403, 4.265832180887906], 'a2': [-1.625890400986364, -3.6546518854715013], 'a3': [-3.6742346141747673, 3.6742346141747673], 'a4': [-10.712960807960801, 11.88412683906966], 'a5': [-2.1026780198217807, 2.1026780198217807], 'a6': [19.401951250517058, 7.454145670199877], 'a7': [84.82762346533538, 0.0], 'a8': [60.850446703395, 19.82985466404846], 'a9': [0.0, -27.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.961758228024529, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.625890400986364, 3.6546518854715013]]], [3, [[1.0, 0], [3.6742346141747673, -3.6742346141747673]]]], 'bad_primes': [2, 3], 'central_character': '48.19', 'coefficient_field': 'CDF', 'conductor': 48, 'conductor_radical': 6, 'conjugate': '1860174346446182717527609003612', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.625890400986364, 3.6546518854715013]], [[1.0, 0], 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2.2275004440009725, 'root_angle': 0.09203464851698563, 'root_number': '0.9584907585570613 + 0.28512359734106385*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0460173242585', 'prec': 50}, 'spectral_label': 'c4-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.18076393640357654506399985421', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.80254516463027911975774976188', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.93075221726187382988688678997', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.961758228024529, 'bad_primes': [2, 3], 'central_character': '16.3', 'conductor': 48, 'conductor_radical': 6, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/48/5/l/a/19/6'], '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': '2-48-16.3-c4-0-5', 'motivic_weight': 4, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [4], 'order_of_vanishing': 0, 'prelabel': '2-48-16.3-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2275004440009725, 'root_angle': 0.046017324258492816, 'self_dual': False, 'spectral_label': 'c4-0', 'z1': {'__RealLiteral__': 0, 'data': '1.18076393640357654506399985421', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1496796112709840696010586054732', 'Lhash_array': ['1496796112709840696010586054732'], 'label': '2-48-16.3-c4-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/48/5/l/a/19/6'}