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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_45.13', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.8660254037844386, 0.5], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.5, 0.8660254037844386], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.8660254037844386, 0.5], 'a8': [-7.040766286173228e-31, 1.0], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 4.835921615758126, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [5, [1]]], 'bad_primes': [3, 5], 'central_character': '45.13', 'coeff_info': ['x^12 - 1', '0.866025403784439 + 0.500000000000000*I', '\\\\zeta_{12}'], 'conductor': 45, 'conductor_radical': 15, 'conjugate': 'dirichlet_L_45.7', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^1', 0, 'a^2', 0, 0, 'a^1', 'a^3', 0, 0, 'a^4', 0, 'a^11', 'a^2', 0, 'a^4', 'a^9', 0, 'a^6', 0, 0, 'a^5', 'a^11', 0, 0, 'a^0', 0, 'a^3', 'a^10', 0, 'a^8', 'a^5', 0, 'a^10', 0, 0, 'a^9', 'a^7', 0, 0, 'a^8', 0, 'a^7', 'a^6', 0, 'a^0', 'a^1', 0, 'a^2', 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'0.370030112513420242664871772147+0.929019760733487065660313306094*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.18967368219', 'prec': 44}, 'spectral_label': 'r1-0', 'st_group': 'mu(12)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.66210406738430354146586613947+0.715214240089227471923203859376*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.43040465758', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '4.41542201284', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '5.67126081963', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 4.835921615758126, 'bad_primes': [3, 5], 'central_character': '45.13', 'conductor': 45, 'conductor_radical': 15, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/45/13'], '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': '1-45-45.13-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-45-45.13-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.835921615758126, 'root_angle': 0.1896736821903861, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.43040465758', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_45.13', 'Lhash_array': ['dirichlet_L_45.13'], 'label': '1-45-45.13-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/45/13'}
Lfunction data - 1-45-45.13-r1-0-0