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lfunc_lfunctions • Show schema
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{'Lhash': '273258984910925616612531414514', 'a10': [0, 0], 'a2': [-2.549145961047532, 0], 'a3': [0, 3.346781578996862], 'a4': [4.4981451307249465, 0], 'a5': [0, 0], 'a6': [0, -8.531434744608134], 'a7': [0, 0], 'a8': [-6.368136570098056, 0], 'a9': [-8.20094693751273, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.999140307798303, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [0, 0]]], [23, [[1.0, 0], [-4.795831523312719, 0]]]], 'bad_primes': [7, 23], 'central_character': '1127.1126', 'coefficient_field': 'CDF', 'conductor': 1127, 'conductor_radical': 161, 'conjugate': '2433784440965518809207607854305', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.549145961047532, 0], [2.0, 0]], [[1.0, 0], [0, -3.346781578996862], [-3.0, 0]], [[1.0, 0], [0, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-11.0, 0]], [[1.0, 0], [0, -6.770862083361707], [-13.0, 0]], [[1.0, 0], [0, 0], [17.0, 0]], [[1.0, 0], [0, 0], 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'7.62537264241238050497832295304087', '8.191206582225484632439265772284014', '8.990749632574807053057190339079381'], 'prelabel': '2-1127-161.160-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.9998567145445967, 'root_angle': 0.5500398164377889, 'root_number': '-0.1565580108156215421545904255253269822922515178137538237 + 0.9876687649457462356957853427012008439154843628296922565*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.27501990821889444', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.21556333019660758790878453055', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.15468526990917564733860842361', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.23488961508807332227161259283', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.999140307798303, 'bad_primes': [7, 23], 'central_character': '161.160', 'conductor': 1127, 'conductor_radical': 161, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1127/2/c/b/1126/3'], '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': '2-1127-161.160-c1-0-4', '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': '2-1127-161.160-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.9998567145445967, 'root_angle': 0.27501990821889444, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.21556333019660758790878453055', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '273258984910925616612531414514', 'Lhash_array': ['273258984910925616612531414514'], 'label': '2-1127-161.160-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1127/2/c/b/1126/3'}