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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_967.135', 'a10': [-0.7997432346737522, 0.6003422012432275], 'a2': [-0.5334082164798489, -0.8458579517813772], 'a3': [-0.4073307573478526, -0.913280709376052], 'a4': [-0.4309513491835733, 0.9023751629100049], 'a5': [-0.08121461226236834, -0.9966966372748898], 'a6': [-0.5552321774399664, 0.831695394441543], 'a7': [-0.7418377371099133, 0.6705794298959991], 'a8': [0.9931541975950378, -0.11681070070570036], 'a9': [-0.6681633082368496, 0.7440146460426628], 'algebraic': True, 'analytic_conductor': 4.490729120579545, 'analytic_normalization': 0, 'bad_lfactors': [[967, [1]]], 'bad_primes': [967], 'central_character': '967.135', 'coeff_info': ['x^483 - 1', '0.999915388507649 + 0.0130082983359933*I', '\\\\zeta_{483}'], 'conductor': 967, 'conductor_radical': 967, 'conjugate': 'dirichlet_L_967.659', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^319', 'a^330', 'a^155', 'a^356', 'a^166', 'a^185', 'a^474', 'a^177', 'a^192', 'a^246', 'a^2', 'a^398', 'a^21', 'a^203', 'a^310', 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'primitive': True, 'rational': False, 'root_analytic_conductor': 4.490729120579545, 'root_angle': -0.5676485631059428, 'root_number': '-0.210928006979502050705936993715-0.977501598910024870033921982238*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.283824281553', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(483)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.490830893595248515830401117169-0.389254032303409022549853875005*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.709397136298', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.54116972301', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.76124867387', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.490729120579545, 'bad_primes': [967], 'central_character': '967.135', 'conductor': 967, 'conductor_radical': 967, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/967/135'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, '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': '1-967-967.135-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-967-967.135-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.490729120579545, 'root_angle': -0.2838242815529714, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.709397136298', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_967.135', 'Lhash_array': ['dirichlet_L_967.135'], 'label': '1-967-967.135-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/967/135'}