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lfunc_lfunctions • Show schema
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{'Lhash': '1869896694169903873480716555425', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0.8660254037844386, 0.5], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [2.0907702751760278, 1.6213203435596426], 'a8': [0, 0], 'a9': [0.5, 0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 16.768584424468887, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-0.8660254037844386, -0.5]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-2.0907702751760278, -1.6213203435596426]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '2100.949', 'coefficient_field': 'CDF', 'conductor': 2100, 'conductor_radical': 210, 'conjugate': '986175240092375024146284224812', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.8660254037844386, -0.5]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.0907702751760278, -1.6213203435596426]], [[1.0, 0], [-2.1213203435596424, 3.6742346141747673], [-5.5, 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True, 'rational': False, 'root_analytic_conductor': 4.0949462053205155, 'root_angle': 0.21104738015662117, 'root_number': '0.78813400351945421134413487064431138686171422263757274359 + 0.61550369007536984611803436650997984950069516238754618121*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.10552369007831058', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.47508839883264783770891687683', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.99237552250492068938053354448', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.48259487610441857146031951067', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 16.768584424468887, 'bad_primes': [2, 3, 5, 7], 'central_character': '35.4', 'conductor': 2100, 'conductor_radical': 210, 'degree': 2, 'index': 19, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2100/2/bc/f/949/4'], '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': '2-2100-35.4-c1-0-19', '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': '2-2100-35.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.0949462053205155, 'root_angle': 0.10552369007831058, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.47508839883264783770891687683', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1869896694169903873480716555425', 'Lhash_array': ['1869896694169903873480716555425'], 'label': '2-2100-35.4-c1-0-19', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2100/2/bc/f/949/4'}