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lfunc_lfunctions • Show schema
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{'Lhash': '2351686778199066485786170680152', 'a10': [-34.0, -58.88972745734183], 'a2': [2.0, 3.4641016151377544], 'a3': [-1.0, -1.7320508075688772], 'a4': [-4.0, 6.928203230275509], 'a5': [-17.0, 0.0], 'a6': [4.0, -6.928203230275509], 'a7': [10.0, -17.320508075688775], 'a8': [0.0, 0.0], 'a9': [11.5, -19.91858428704209], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.971322790970168, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[13, [[1.0, 0], [0, 0]]]], 'bad_primes': [13], 'central_character': '169.146', 'coefficient_field': 'CDF', 'conductor': 169, 'conductor_radical': 13, 'conjugate': '770185570598250832945978105699', 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.0, -3.4641016151377544], [-4.0, 6.928203230275509]], [[1.0, 0], [1.0, 1.7320508075688772], [-13.5, 23.382685902179844]], [[1.0, 0], [17.0, 0], [125.0, 0]], [[1.0, 0], [-10.0, 17.320508075688775], [-171.5, -297.04671349806245]], [[1.0, 0], [16.0, 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['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.85515376064640039874511519575', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.35636653765253081209316927232', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.50277853019225456721620594290', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.971322790970168, 'bad_primes': [13], 'central_character': '13.3', 'conductor': 169, 'conductor_radical': 13, 'degree': 2, 'index': 21, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/169/4/c/d/146/1'], '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': '2-13e2-13.3-c3-0-21', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-13e2-13.3-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.157740139873794, 'root_angle': 0.08537428472590003, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.85515376064640039874511519575', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2351686778199066485786170680152', 'Lhash_array': ['2351686778199066485786170680152'], 'factors': ['2-13e2-13.3-c3-0-21'], 'label': '2-13e2-13.3-c3-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/169/4/c/d/146/1'}