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lfunc_lfunctions • Show schema
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{'Lhash': '1934525115762859829749027355197', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.848048096156426, -0.5299192642332049], 'a4': [0.9902680687415704, 0.13917310096006544], 'a5': [1.632885257981252, -1.1013950135347974], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [0.4383711467890774, 0.898794046299167], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.630445396272019, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.848048096156426, 0.5299192642332049]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 11], 'central_character': '3267.1334', 'coefficient_field': 'CDF', 'conductor': 3267, 'conductor_radical': 33, 'conjugate': '1566980522357752074409753179796', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [-0.9902680687415704, -0.13917310096006544]], [[1.0, 0], [0.848048096156426, 0.5299192642332049]], [[1.0, 0], [-1.632885257981252, 1.1013950135347974], [0.374606593415912, 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'4.38366274961087479552819070169770', '5.56580220840992990309777959413420', '5.98496456961289850757427377189898', '6.45756700865933892647559977038238', '7.09166011717856809910002653088316', '8.050913954674918186660609041387306', '9.410053394750038362495143994908422'], 'prelabel': '2-3267-297.146-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.27688895220846, 'root_angle': 0.30749641556449975, 'root_number': '0.56857111431836871766905220953244 + 0.82263411548681136067762462205249*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.15374820778224987', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.52607123399347225913304649564', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.40262458341313793041152527560', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.20307889884968796085697716315', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.630445396272019, 'bad_primes': [3, 11], 'central_character': '297.146', 'conductor': 3267, 'conductor_radical': 33, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3267/1/be/a/1334/1'], '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': '2-3267-297.146-c0-0-0', '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': '2-3267-297.146-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.27688895220846, 'root_angle': 0.15374820778224987, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.52607123399347225913304649564', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1934525115762859829749027355197', 'Lhash_array': ['1934525115762859829749027355197'], 'label': '2-3267-297.146-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3267/1/be/a/1334/1'}