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lfunc_lfunctions • Show schema
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{'Lhash': '599061566080881286986807240172', 'a10': [4.969808862334437, -0.10132962622829421], 'a2': [-1.3877351349029912, -0.2723806075251636], 'a3': [-0.7037642981038793, -2.7573212938874594], 'a4': [1.8516176092884455, 0.7559842782577831], 'a5': [-3.4345890734307005, 0.7471491198650939], 'a6': [0.22559759399795942, 4.018123384815858], 'a7': [-0.12528921835778847, 0.694431450233189], 'a8': [-2.3636393558233277, -1.5534506736948828], 'a9': [-4.4744995617378, 2.4432616099190057], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.685348623915166, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.3877351349029912, 0.2723806075251636]]], [89, [[1.0, 0], [5.2015828021028465, -7.870421612141747]]]], 'bad_primes': [2, 89], 'central_character': '712.171', 'coefficient_field': 'CDF', 'conductor': 712, 'conductor_radical': 178, 'conjugate': '1067618710250936749759928965933', 'degree': 2, 'euler_factors': [[[1.0, 0], 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[-7.801435287497711, -4.2599059575743325], [42.71062457899221, 66.45902909366332]], [[1.0, 0], [-2.8568144919665106, 5.707188313112391], [-49.7400463204418, -66.44492299672191]], [[1.0, 0], [5.2015828021028465, -7.870421612141747]], [[1.0, 0], [-16.310246544733783, -10.481958982295009], [40.295256261182985, 88.23430354938829]], [[1.0, 0], [-0.7972044971706124, -1.924621909054116], [-71.4177848998413, 71.4177848998413]], [[1.0, 0], [-11.47929792986257, -14.24493973518974], [-21.8942248239566, 100.64612719502944]], [[1.0, 0], [3.1820941125052156, -14.62785055734518], [-97.33062350293346, -44.44940639120185]], [[1.0, 0], [-0.7226315130060221, -1.9374500647359085], [-82.37670360461415, 71.37982000003608]], [[1.0, 0], [0.4029359945846157, -1.210628922525913], [-90.46116022445273, -67.71837631578221]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 7, 'label': '2-712-712.171-c1-0-7', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': 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'2-712-712.171-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.3843969098946523, 'root_angle': 0.10920251506968594, 'root_number': '0.9417264799352277 + 0.3363796025159746*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0546012575348', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.47257624930168099352229059089', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.02401950616094740519349382799', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.11457597148884472957149356389', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.685348623915166, 'bad_primes': [2, 89], 'central_character': '712.171', 'conductor': 712, 'conductor_radical': 178, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/712/2/bf/c/171/6'], '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': '2-712-712.171-c1-0-7', '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': '2-712-712.171-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.3843969098946523, 'root_angle': 0.05460125753484297, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.47257624930168099352229059089', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '599061566080881286986807240172', 'Lhash_array': ['599061566080881286986807240172'], 'label': '2-712-712.171-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/712/2/bf/c/171/6'}