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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_45.23', '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': [2.9010907910729803e-30, -1.0], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 0.20897912143338113, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [5, [1]]], 'bad_primes': [3, 5], 'central_character': '45.23', 'coeff_info': ['x^12 - 1', '0.866025403784439 + 0.500000000000000*I', '\\\\zeta_{12}'], 'conductor': 45, 'conductor_radical': 15, 'conjugate': 'dirichlet_L_45.2', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^7', 0, 'a^2', 0, 0, 'a^1', 'a^9', 0, 0, 'a^10', 0, 'a^11', 'a^8', 0, 'a^4', 'a^3', 0, 'a^6', 0, 0, 'a^5', 'a^5', 0, 0, 'a^6', 0, 'a^3', 'a^4', 0, 'a^8', 'a^11', 0, 'a^10', 0, 0, 'a^9', 'a^1', 0, 0, 'a^2', 0, 'a^7', 'a^0', 0, 'a^0', 'a^7', 0, 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'data': '-0.0603263178096', 'prec': 54}, 'spectral_label': 'r0-0', 'st_group': 'mu(12)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.744002717043410104583391127125-0.118015263599899694433943171080*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.75276955785', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.713936602', 'prec': 37}, 'z3': {'__RealLiteral__': 0, 'data': '6.060925271', 'prec': 37}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.20897912143338113, 'bad_primes': [3, 5], 'central_character': '45.23', 'conductor': 45, 'conductor_radical': 15, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/45/23'], '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': '1-45-45.23-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': '1-45-45.23-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.20897912143338113, 'root_angle': -0.06032631780961391, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.75276955785', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_45.23', 'Lhash_array': ['dirichlet_L_45.23'], 'label': '1-45-45.23-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/45/23'}
Lfunction data - 1-45-45.23-r0-0-0