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lfunc_lfunctions • Show schema
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{'Lhash': '645536799136739825323888265751', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.48486195287192946, 0.0], 'a4': [0.0, 0.0], 'a5': [1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-0.48486195287192946, 0.0], 'a8': [0.0, 0.0], 'a9': [-2.764908886657219, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 77.29518915659945, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-1.0, 0]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 5, 11], 'central_character': '9680.1', 'coefficient_field': 'CDF', 'conductor': 9680, 'conductor_radical': 110, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.48486195287192946, 0], [3.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0.48486195287192946, 0], [7.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [5.2800469337852896, 0], [13.0, 0]], [[1.0, 0], [2.4848619528719293, 0], [17.0, 0]], [[1.0, 0], [4.734632792401078, 0], [19.0, 0]], [[1.0, 0], [4.249770839529148, 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'4.25326122194598661344793578469473', '4.93426243357501218821942298246212', '5.63778862520529089286875274799459', '6.43364966222057861442194262640896', '6.81536576017082901890951337773766', '7.941809611955504436540984422370946'], 'prelabel': '2-9680-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.791768261083742, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.50923874372048305079146366620', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.13366419772419433811967890920', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.37912396688920701217631372703', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 77.29518915659945, 'bad_primes': [2, 5, 11], 'central_character': '1.1', 'conductor': 9680, 'conductor_radical': 110, 'degree': 2, 'index': 30, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/9680/2/a/cg/1/2'], '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': '2-9680-1.1-c1-0-30', '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': '2-9680-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.791768261083742, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.50923874372048305079146366620', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '645536799136739825323888265751', 'Lhash_array': ['645536799136739825323888265751'], 'label': '2-9680-1.1-c1-0-30', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9680/2/a/cg/1/2'}