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lfunc_lfunctions • Show schema
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{'Lhash': '585397664425513417660765307594', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.8740320488976422, 0.0], 'a4': [0.0, 0.0], 'a5': [0.0, 3.7024591736438324], 'a6': [0.0, 0.0], 'a7': [-1.4142135623730951, 2.23606797749979], 'a8': [0.0, 0.0], 'a9': [-2.23606797749979, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.154596021106726, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [1.4142135623730951, -2.23606797749979]]]], 'bad_primes': [2, 7], 'central_character': '896.895', 'coefficient_field': 'CDF', 'conductor': 896, 'conductor_radical': 14, 'conjugate': '2889443163545496341422335147790', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.8740320488976422, 0], [3.0, 0]], [[1.0, 0], [0, -3.7024591736438324], [-5.0, 0]], [[1.0, 0], [1.4142135623730951, -2.23606797749979]], [[1.0, 0], [0, 3.23606797749979], [-11.0, 0]], [[1.0, 0], [0, 0.8740320488976422], [-13.0, 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'4.51888826610682980342043049708110', '5.07064852660337654481152238512980', '6.36029762837596688212028724828445', '7.36861625374541787083698736802486', '8.239686129346459957581591073653193', '8.958429788299529436309075805729982', '9.588093383301745468038758600711155'], 'prelabel': '2-896-28.27-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.6748076605817332, 'root_angle': -0.820491482014312, 'root_number': '-0.8451542547285167 - 0.5345224838248486*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.410245741007', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.46179733147297661444400625252', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.96340014655408535178794482379', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.37962029258533855201715818439', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.154596021106726, 'bad_primes': [2, 7], 'central_character': '28.27', 'conductor': 896, 'conductor_radical': 14, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/896/2/f/b/895/6'], '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': '2-896-28.27-c1-0-4', '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': '2-896-28.27-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.6748076605817332, 'root_angle': -0.410245741007156, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.46179733147297661444400625252', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '585397664425513417660765307594', 'Lhash_array': ['585397664425513417660765307594'], 'label': '2-896-28.27-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/896/2/f/b/895/6'}