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lfunc_lfunctions • Show schema
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{'Lhash': '983239761578244730650222261769', 'a10': [0, 0], 'a2': [0.8660254037844386, -0.5], 'a3': [0.8660254037844386, 0.5], 'a4': [0.5, -0.8660254037844386], 'a5': [0, 0], 'a6': [1.0, 0], 'a7': [-0.8660254037844386, 2.5], 'a8': [0, -1.0], 'a9': [0.5, 0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.384292212234444, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.8660254037844386, 0.5]]], [3, [[1.0, 0], [-0.8660254037844386, -0.5]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0.8660254037844386, -2.5]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '1050.949', 'coefficient_field': 'CDF', 'conductor': 1050, 'conductor_radical': 210, 'conjugate': '2540308093454615238461973955816', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8660254037844386, 0.5]], [[1.0, 0], [-0.8660254037844386, -0.5]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.8660254037844386, -2.5]], [[1.0, 0], [3.0, -5.196152422706632], 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'sign_arg': {'__RealLiteral__': 0, 'data': '-0.1772980952124961', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.77563940836790596139122098489', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.74456253382226711071637230133', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.37970273041077530920096457158', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.384292212234444, 'bad_primes': [2, 3, 5, 7], 'central_character': '35.4', 'conductor': 1050, 'conductor_radical': 210, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1050/2/o/h/949/2'], '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': '2-1050-35.4-c1-0-8', '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': '2-1050-35.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.8955642303762565, 'root_angle': -0.1772980952124961, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.77563940836790596139122098489', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '983239761578244730650222261769', 'Lhash_array': ['983239761578244730650222261769'], 'label': '2-1050-35.4-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1050/2/o/h/949/2'}