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lfunc_lfunctions • Show schema
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{'Lhash': '1288156094721219196786530220497', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-2.732050807568877, 0.0], 'a4': [0.0, 0.0], 'a5': [-1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-3.9324421947611325, 0.0], 'a8': [0.0, 0.0], 'a9': [4.464101615137754, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 21.719309349788276, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [1.0, 0]]], [17, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 5, 17], 'central_character': '2720.1', 'coefficient_field': 'CDF', 'conductor': 2720, 'conductor_radical': 170, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [2.732050807568877, 0], [3.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [3.9324421947611325, 0], [7.0, 0]], [[1.0, 0], [3.171424549765285, 0], [11.0, 0]], [[1.0, 0], [-6.66449300233001, 0], [13.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [5.464101615137754, 0], [19.0, 0]], [[1.0, 0], [-8.811189679153948, 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0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 24, 'label': '2-2720-1.1-c1-0-24', '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': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/2720/2/a/j/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [-3.591603544156186e-61, 0.08347053790353529, 0.16602944922675178, 0.2467318961856892, 0.32456896346201247, 0.39844130608272, 0.4671391564551533, 0.5293301086783353, 0.5835556238251253, 0.6282367291729688, 0.6616889561580404, 0.6821461982554701, 0.6877928770667804, 0.6768035764507572, 0.6473891274680892, 0.5978479861742413, 0.5266216285797635, 0.43235258294763607, 0.31394362413715654, 0.1706165673762256, 0.001969022595056169, -0.19197258929764255, -0.4107054932071895, -0.6532102303576794, -0.9179192508353486, -1.202696059842715, -1.5048264232148716, 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'7.42553818777745498063716554343031', '8.581603594228114223029819875427832'], 'prelabel': '2-2720-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.660397981909729, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.01617598294774440242685360877', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.77787694037259001175994149787', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.73781477542649589653316398291', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 21.719309349788276, 'bad_primes': [2, 5, 17], 'central_character': '1.1', 'conductor': 2720, 'conductor_radical': 170, 'degree': 2, 'index': 24, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2720/2/a/j/1/1'], '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': '2-2720-1.1-c1-0-24', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-2720-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.660397981909729, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.01617598294774440242685360877', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1288156094721219196786530220497', 'Lhash_array': ['1288156094721219196786530220497'], 'factors': ['2-2720-1.1-c1-0-24'], 'label': '2-2720-1.1-c1-0-24', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2720/2/a/j/1/1'}