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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_6004.47', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.9770169650018171, 0.21316155867941614], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [0.9985583705641418, 0.05367662970312159], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.040265940109415144, 0.9991889981715696], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [0.9091242998027237, 0.4165249182320398], 'algebraic': True, 'analytic_conductor': 27.882458779689337, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [19, [1]], [79, [1]]], 'bad_primes': [2, 19, 79], 'central_character': '6004.47', 'coeff_info': ['x^234 - 1', '0.999639527670885 + 0.0268479928100611*I', '\\\\zeta_{234}'], 'conductor': 6004, 'conductor_radical': 3002, 'conjugate': 'dirichlet_L_6004.511', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^242', 0, 'a^2', 0, 'a^294', 0, 'a^16', 0, 'a^297', 0, 'a^220', 0, 'a^244', 0, 'a^77', 0, 0, 0, 'a^68', 0, 'a^247', 0, 'a^4', 0, 'a^258', 0, 'a^205', 0, 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'spectral_label': 'r0-0', 'st_group': 'mu(234)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.75790420671960785656313672562+0.645277410534011463800015800468*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.37423337242', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.92322910936', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.54386440568', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 27.882458779689337, 'bad_primes': [2, 19, 79], 'central_character': '6004.47', 'conductor': 6004, 'conductor_radical': 3002, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/6004/47'], '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': '1-6004-6004.47-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': '1-6004-6004.47-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 27.882458779689337, 'root_angle': 0.24807292878522183, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.37423337242', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_6004.47', 'Lhash_array': ['dirichlet_L_6004.47'], 'label': '1-6004-6004.47-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/6004/47'}