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lfunc_lfunctions • Show schema
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{'Lhash': '7369236946008198962403401542710', 'a10': [2.0, 3.4641016151377544], 'a2': [-1.0, -1.7320508075688772], 'a3': [0.0, 1.7320508075688772], 'a4': [-2.0, 3.4641016151377544], 'a5': [-2.0, 0.0], 'a6': [3.0, -1.7320508075688772], 'a7': [0.0, -6.928203230275509], 'a8': [8.0, 0.0], 'a9': [-3.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.3269763172323563, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, 1.7320508075688772]]], [3, [[1.0, 0], [0, -1.7320508075688772]]]], 'bad_primes': [2, 3], 'central_character': '12.7', 'coefficient_field': 'CDF', 'conductor': 12, 'conductor_radical': 6, 'conjugate': '5130036913272786842859115661272', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 1.7320508075688772]], [[1.0, 0], [0, -1.7320508075688772]], [[1.0, 0], [2.0, 0], [25.0, 0]], [[1.0, 0], [0, 6.928203230275509], [-49.0, 0]], [[1.0, 0], [0, -6.928203230275509], [-121.0, 0]], [[1.0, 0], [-2.0, 0], [169.0, 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'16.10483807261337693382380385118476', '17.62690934090527446578915444830030', '18.74904406917276109914630132478598', '19.63454363885461930623749185310238'], 'prelabel': '2-12-4.3-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5718184303013993, 'root_angle': 0.08333333333333334, 'root_number': '0.8660254037844386 + 0.5*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0833333333333', 'prec': 50}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '5.81330292801615233284569326855', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '7.71002150047828499977504048565', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '9.174383214369402603361117159153', 'prec': 107}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.3269763172323563, 'bad_primes': [2, 3], 'central_character': '4.3', 'conductor': 12, 'conductor_radical': 6, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/12/3/d/a/7/1'], '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': '2-12-4.3-c2-0-1', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-12-4.3-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5718184303013993, 'root_angle': 0.08333333333333334, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '5.81330292801615233284569326855', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '7369236946008198962403401542710', 'Lhash_array': ['7369236946008198962403401542710'], 'factors': ['2-12-4.3-c2-0-1'], 'label': '2-12-4.3-c2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/12/3/d/a/7/1'}