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lfunc_lfunctions • Show schema
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{'Lhash': '789269776779666140811430635363', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.841082670492394, 0.0], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-3.292579941397383, 0.0], 'a8': [0.0, 0.0], 'a9': [-2.292579941397383, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 35.13417688936339, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 5, 11], 'central_character': '4400.1', 'coefficient_field': 'CDF', 'conductor': 4400, 'conductor_radical': 110, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.841082670492394, 0], [3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [3.292579941397383, 0], [7.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [1.0, 0], [13.0, 0]], [[1.0, 0], [-1.158917329507606, 0], [17.0, 0]], [[1.0, 0], [1.317834659015212, 0], [19.0, 0]], [[1.0, 0], [-3.841082670492394, 0], [23.0, 0]], [[1.0, 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0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 10, 'label': '2-4400-1.1-c1-0-10', 'leading_term': '1.42608821594265790334830435930', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/4400/2/a/bz/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [1.426088215942658, 1.4168441585505442, 1.3890593691019266, 1.3425839771393528, 1.2771942577788378, 1.192629872192994, 1.088642512099032, 0.9650528911607982, 0.8218126792911286, 0.6590678879358759, 0.4772203402383287, 0.27698413851133574, 0.05943441147036063, -0.1739539651135246, -0.42127956239179676, -0.6802009873834812, -0.9479379544560103, -1.2212875448087426, -1.4966559796732235, -1.7701058469689077, -2.037418322730987, -2.294169515363669, -2.535819634679765, -2.7578132551179886, -2.9556885136966367, 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'6.08790685641803955600470608792862', '7.01934943310234496166760715482333', '7.57029346361662135394477736185666', '8.499796190904944813884249249918661'], 'prelabel': '2-4400-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.927408952431357, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.62262407057399335576134861925', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.23124593233089065195915240682', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.95516537506063791040877134856', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 35.13417688936339, 'bad_primes': [2, 5, 11], 'central_character': '1.1', 'conductor': 4400, 'conductor_radical': 110, 'degree': 2, 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4400/2/a/bz/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': '2-4400-1.1-c1-0-10', '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': '2-4400-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.927408952431357, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.62262407057399335576134861925', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '789269776779666140811430635363', 'Lhash_array': ['789269776779666140811430635363'], 'factors': ['2-4400-1.1-c1-0-10'], 'label': '2-4400-1.1-c1-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4400/2/a/bz/1/2'}