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lfunc_lfunctions • Show schema
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{'Lhash': '2269060090635352558904197737325', 'a10': [3.2779726325672023, 0.0], 'a2': [0.21369989565587372, 0.0], 'a3': [3.0, 0.0], 'a4': [-7.954332354596668, 0.0], 'a5': [15.33914007073641, 0.0], 'a6': [0.6410996869676212, 0.0], 'a7': [-32.39277706513322, 0.0], 'a8': [-3.409439159436438, 0.0], 'a9': [9.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 29.913968372910507, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-3.0, 0]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 13], 'central_character': '507.1', 'coefficient_field': 'CDF', 'conductor': 507, 'conductor_radical': 39, 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.21369989565587372, 0], [8.0, 0]], [[1.0, 0], [-3.0, 0]], [[1.0, 0], [-15.33914007073641, 0], [125.0, 0]], [[1.0, 0], [32.39277706513322, 0], [343.0, 0]], [[1.0, 0], [-29.592525961687937, 0], [1331.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [78.19578890299314, 0], [4913.0, 0]], [[1.0, 0], 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'4.04538958921835453191936902635154', '5.45451904917329249283037474091418', '6.28763258395917733760005805906427', '7.13264498436737702351484202719323', '8.865635419859896923804469691028390', '9.105186734350332148537019929154381', '9.830628141224935646256469721190053'], 'prelabel': '2-507-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.469366359361064, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.78997279709947531183025095688', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.16566454193906547594355214523', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.04538958921835453191936902635', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 29.913968372910507, 'bad_primes': [3, 13], 'central_character': '1.1', 'conductor': 507, 'conductor_radical': 39, 'degree': 2, 'index': 65, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/507/4/a/o/1/6'], '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': '2-507-1.1-c3-0-65', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-507-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.469366359361064, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.78997279709947531183025095688', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2269060090635352558904197737325', 'Lhash_array': ['2269060090635352558904197737325'], 'label': '2-507-1.1-c3-0-65', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/507/4/a/o/1/6'}