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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_15.8', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [-7.040766286173228e-31, 1.0], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-1.0, -1.4081532572346456e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [2.9010907910729803e-30, -1.0], 'a8': [2.9010907910729803e-30, -1.0], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 0.06965970714446038, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [5, [1]]], 'bad_primes': [3, 5], 'central_character': '15.8', 'coeff_info': ['x^4 - 1', '6.12323399573677e-17 + 1.00000000000000*I', '\\\\zeta_{4}'], 'conductor': 15, 'conductor_radical': 15, 'conjugate': 'dirichlet_L_15.2', 'degree': 1, 'dirichlet_coefficients': [1, 'I', 0, -1, 0, 0, '-I', '-I', 0, 0, -1, 0, 'I', 1, 0, 1, 'I', 0, -1, 0, 0, '-I', '-I', 0, 0, -1, 0, 'I', 1, 0, 1, 'I', 0, -1, 0, 0, '-I', '-I', 0, 0, -1, 0, 'I', 1, 0, 1, 'I', 0, -1, 0, 0, '-I', '-I', 0, 0, -1, 0, 'I', 1, 0, 1, 'I', 0, -1, 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'197.1013578368705251988068997065', '198.25254278940855331017960846466', '198.90776268240691215119556041574'], 'prelabel': '1-15-15.8-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.06965970714446038, 'root_angle': 0.32379180882521663, 'root_number': '0.525731112119133606025669084848+0.850650808352039932181540497063*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.161895904413', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(4)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.738566632162963626893918351164+0.316802644588479147434743885696*I']], 'z1': {'__RealLiteral__': 0, 'data': '4.4067002398', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '6.59078267022', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '8.2645016539', 'prec': 40}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.06965970714446038, 'bad_primes': [3, 5], 'central_character': '15.8', 'conductor': 15, 'conductor_radical': 15, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/15/8'], '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': '1-15-15.8-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': '1-15-15.8-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.06965970714446038, 'root_angle': 0.16189590441260832, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '4.4067002398', 'prec': 40}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_15.8', 'Lhash_array': ['dirichlet_L_15.8'], 'label': '1-15-15.8-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/15/8'}