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lfunc_lfunctions • Show schema
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{'Lhash': '1926028597200970677869604978879', 'a10': [8.055247193829187, 4.650699135746259], 'a2': [-2.1544823880892787, 1.2438909867276526], 'a3': [-1.0868654821224477, 1.3486005427000016], 'a4': [2.094529573724587, -3.6278316396465673], 'a5': [-1.8694158834533463, -3.2379232906174544], 'a6': [0.6641204796944232, -4.257478294812314], 'a7': [1.0649643854145021, -2.421951869422411], 'a8': [0.0, 5.4459018858514945], 'a9': [-0.6374468475414784, -2.9314947580644644], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.875119614032244, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.0868654821224477, -1.3486005427000016]]], [7, [[1.0, 0], [-1.0649643854145021, 2.421951869422411]]], [41, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [3, 7, 41], 'central_character': '861.206', 'coefficient_field': 'CDF', 'conductor': 861, 'conductor_radical': 861, 'conjugate': '373918349458219992717224340308', 'degree': 2, 'euler_factors': 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'3.43315005884183411676769719365510', '5.38985993962259865209273480252779', '6.49562047368139579483412377397965', '7.46369347648634939577578149930010', '7.899494822718021975735874449500364', '8.567598847232634169584254832242008', '9.926973021993293436702538039658564', '10.53813064119942548329009616218836'], 'prelabel': '2-861-21.17-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.622044929827146, 'root_angle': 0.6407752016490115, 'root_number': '-0.4279816134086744 + 0.9037874410413701*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.320387600825', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.51936866266951325336468552392', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.63080830687022347359562210458', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.43315005884183411676769719366', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.875119614032244, 'bad_primes': [3, 7, 41], 'central_character': '21.17', 'conductor': 861, 'conductor_radical': 861, 'degree': 2, 'index': 76, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/861/2/s/a/206/4'], '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': '2-861-21.17-c1-0-76', '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': '2-861-21.17-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.622044929827146, 'root_angle': 0.32038760082450574, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.51936866266951325336468552392', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1926028597200970677869604978879', 'Lhash_array': ['1926028597200970677869604978879'], 'label': '2-861-21.17-c1-0-76', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/861/2/s/a/206/4'}