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lfunc_lfunctions • Show schema
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{'Lhash': '26235599252381400828330010080', 'a10': [3.1005850305536864, 1.790123602035495], 'a2': [-0.8660254037844386, 0.5], 'a3': [0.8660254037844386, 0.5], 'a4': [0.5, -0.8660254037844386], 'a5': [-1.790123602035495, -3.1005850305536864], 'a6': [-1.0, 0], 'a7': [-1.038776172338852, -2.433299008297386], 'a8': [0, 1.0], 'a9': [0.5, 0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.725778966191955, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.8660254037844386, -0.5]]], [3, [[1.0, 0], [-0.8660254037844386, -0.5]]], [7, [[1.0, 0], [1.038776172338852, 2.433299008297386]]], [29, [[1.0, 0], [-5.279580892406078, 1.0611435343725388]]]], 'bad_primes': [2, 3, 7, 29], 'central_character': '1218.1159', 'coefficient_field': 'CDF', 'conductor': 1218, 'conductor_radical': 1218, 'conjugate': '1668030336812367017660892348230', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.8660254037844386, -0.5]], [[1.0, 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'3.72113359266963505608302408150420', '5.06687030705446220310302770413253', '6.48479264063910833312862600276749', '7.14114701200944357178279112594936', '7.64727462583370074418965819138191', '8.673188771057523277953088697458754', '9.299393933041410248372271329965796'], 'prelabel': '2-1218-203.144-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.1186181180439445, 'root_angle': -0.41903052801114293, 'root_number': '-0.8733558997266613566994594826202393932122674391347958425 - 0.4870826135396682721284994935980117055055139050152594003*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.4190305280111429', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.02069623857524929241943157098', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.39139519370011405551626166950', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.70186937114518748712201818048', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.725778966191955, 'bad_primes': [2, 3, 7, 29], 'central_character': '203.144', 'conductor': 1218, 'conductor_radical': 1218, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1218/2/p/b/1159/8'], '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': '2-1218-203.144-c1-0-0', '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': '2-1218-203.144-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.1186181180439445, 'root_angle': -0.41903052801114293, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.02069623857524929241943157098', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '26235599252381400828330010080', 'Lhash_array': ['26235599252381400828330010080'], 'factors': ['2-1218-203.144-c1-0-0'], 'label': '2-1218-203.144-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1218/2/p/b/1159/8'}