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lfunc_lfunctions • Show schema
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{'Lhash': '1275142315715061603176701845604', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [-0.8660254037844386, 0.5], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [1.3660254037844386, 0.36602540378443865], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.7590778842147967, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 13], 'central_character': '1521.1333', 'coefficient_field': 'CDF', 'conductor': 1521, 'conductor_radical': 39, 'conjugate': '1855635811064171877185991229589', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [0.8660254037844386, -0.5]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [0, 1.0]], [[1.0, 0], [-1.3660254037844386, -0.36602540378443865], [0.8660254037844386, 0.5]], [[1.0, 0], [0, 0], [-0.8660254037844386, 0.5]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], 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'3.83953811371073736117525611212286', '4.64762352851899894365460135792211', '5.19795534094704571975896521049736', '6.17477414005074460699207809920745', '7.30603228816637395553731706193641', '8.027026064507285190245537838032517', '8.827211079583198201941644455174056', '9.431850757414943487974547202952977'], 'prelabel': '2-39e2-13.7-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8712507585160524, 'root_angle': -0.2643320903572995, 'root_number': '0.67456299872691227719333155837809 - 0.73821728559317530078333243074324*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.13216604517864974', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.00590992146060072376580203962', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.27257178374952788949614248738', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.83953811371073736117525611212', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.7590778842147967, 'bad_primes': [3, 13], 'central_character': '13.7', 'conductor': 1521, 'conductor_radical': 39, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1521/1/bd/c/1333/1'], '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': '2-39e2-13.7-c0-0-1', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-39e2-13.7-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8712507585160524, 'root_angle': -0.13216604517864974, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.00590992146060072376580203962', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1275142315715061603176701845604', 'Lhash_array': ['1275142315715061603176701845604'], 'label': '2-39e2-13.7-c0-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1521/1/bd/c/1333/1'}