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lfunc_lfunctions • Show schema
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{'Lhash': '807651930000691605855003598078', 'a10': [-0.2928932188134525, 0.5073059361772883], 'a2': [-0.5, -0.8660254037844386], 'a3': [-1.2071067811865475, 2.0907702751760278], 'a4': [-0.5, 0.8660254037844386], 'a5': [-0.2928932188134525, -0.5073059361772883], 'a6': [2.414213562373095, 0], 'a7': [0, 0], 'a8': [1.0, 0], 'a9': [-1.4142135623730951, -2.449489742783178], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.607873337894029, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.5, 0.8660254037844386]]], [7, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [0.5, -0.8660254037844386]]]], 'bad_primes': [2, 7, 11], 'central_character': '1078.67', 'coefficient_field': 'CDF', 'conductor': 1078, 'conductor_radical': 154, 'conjugate': '1435169735718098483487476299576', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [1.2071067811865475, -2.0907702751760278], [-1.5, -2.598076211353316]], [[1.0, 0], 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'8.625613493641034964049706320499433', '9.599912921802389419726505640466193'], 'prelabel': '2-1078-7.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.9339177455910432, 'root_angle': -0.3736792394412256, 'root_number': '0.3865135727591552881869185769990697126707082293252108640 - 0.9222837188593069656715137745867251124838836430784361633*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.1868396197206128', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.63712503260384284201440131060', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.78676092649032180415758147830', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.40756788457424491678596021631', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.607873337894029, 'bad_primes': [2, 7, 11], 'central_character': '7.4', 'conductor': 1078, 'conductor_radical': 154, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1078/2/e/m/67/1'], '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': '2-1078-7.4-c1-0-6', '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': '2-1078-7.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.9339177455910432, 'root_angle': -0.1868396197206128, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.63712503260384284201440131060', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '807651930000691605855003598078', 'Lhash_array': ['807651930000691605855003598078'], 'label': '2-1078-7.4-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1078/2/e/m/67/1'}