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lfunc_lfunctions • Show schema
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{'Lhash': '995089342102655141596079739705', 'a10': [0.0, 0.0], 'a2': [-0.9659258262890683, -0.25881904510252074], 'a3': [1.331951230073507, 1.1072063586819179], 'a4': [0.8660254037844386, 0.5], 'a5': [0.0, 0.0], 'a6': [-1.0, -1.4142135623730951], 'a7': [-0.2837630714848505, 1.0590182000932615], 'a8': [-0.7071067811865476, -0.7071067811865476], 'a9': [0.5481881585886564, 2.949489742783178], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.593268090957619, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.9659258262890683, 0.25881904510252074]]], [3, [[1.0, 0], [-1.331951230073507, -1.1072063586819179]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '450.257', 'coefficient_field': 'CDF', 'conductor': 450, 'conductor_radical': 30, 'conjugate': '2647035819399797707835861615484', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.9659258262890683, 0.25881904510252074]], [[1.0, 0], 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'7.55703022481491181026247470829508', '8.093077146260975022401179856683963', '8.726648252456857748864249732865124', '10.07419653926218956342135259164359', '10.50409851319560368478885006637769'], 'prelabel': '2-450-45.32-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8955917521865353, 'root_angle': -0.5211739164113796, 'root_number': '-0.06647077398924046 - 0.9977883724544355*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.260586958206', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.78498707918688162994646362320', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.52668089245270803036630115122', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.50612487407875756643298282684', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.593268090957619, 'bad_primes': [2, 3, 5], 'central_character': '45.32', 'conductor': 450, 'conductor_radical': 30, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/450/2/p/a/257/1'], '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': '2-450-45.32-c1-0-1', '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': '2-450-45.32-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8955917521865353, 'root_angle': -0.2605869582056898, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.78498707918688162994646362320', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '995089342102655141596079739705', 'Lhash_array': ['995089342102655141596079739705'], 'label': '2-450-45.32-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/450/2/p/a/257/1'}