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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_6003.104', 'a10': [0.9898214418809327, -0.14231483827328514], 'a2': [-0.8145759520503357, 0.5800569095711982], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.32706796331742166, -0.9450008187146685], 'a5': [-0.8888354486549235, -0.4582265217274104], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.7860530947427875, -0.6181589862206052], 'a8': [0.28173255684142967, 0.9594929736144974], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 27.87781479921304, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [23, [1]], [29, [1]]], 'bad_primes': [3, 23, 29], 'central_character': '6003.104', 'coeff_info': ['x^132 - 1', '0.998867339183008 + 0.0475819158237423*I', '\\\\zeta_{132}'], 'conductor': 6003, 'conductor_radical': 2001, 'conjugate': 'dirichlet_L_6003.3521', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^53', 0, 'a^106', 'a^76', 0, 'a^80', 'a^27', 0, 'a^129', 'a^101', 0, 'a^118', 'a^1', 0, 'a^80', 'a^81', 0, 'a^51', 'a^50', 0, 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'-0.947780088025792763803206087989-0.318924606673458986183486835995*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(132)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.528828194357414317480028189514-0.106744645681483473444022009728*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.268072130063', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '0.737334848934', 'prec': 47}, 'z3': {'__RealLiteral__': 0, 'data': '1.75948324765', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 27.87781479921304, 'bad_primes': [3, 23, 29], 'central_character': '6003.104', 'conductor': 6003, 'conductor_radical': 2001, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/6003/104'], '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': '1-6003-6003.104-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': '1-6003-6003.104-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 27.87781479921304, 'root_angle': -0.4483391607698249, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.268072130063', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_6003.104', 'Lhash_array': ['dirichlet_L_6003.104'], 'label': '1-6003-6003.104-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/6003/104'}