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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1300.987', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.5877852522924731, -0.8090169943749475], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-5.8869658587496495e-30, 1.0], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-0.30901699437494745, 0.9510565162951535], 'algebraic': True, 'analytic_conductor': 6.037174619186565, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [5, [1]], [13, [1]]], 'bad_primes': [2, 5, 13], 'central_character': '1300.987', 'coeff_info': ['x^20 - 1', '0.951056516295154 + 0.309016994374947*I', '\\\\zeta_{20}'], 'conductor': 1300, 'conductor_radical': 130, 'conjugate': 'dirichlet_L_1300.623', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^13', 0, 0, 0, 'a^25', 0, 'a^6', 0, 'a^24', 0, 0, 0, 0, 0, 'a^17', 0, 'a^22', 0, 'a^18', 0, 'a^29', 0, 0, 0, 'a^19', 0, 'a^18', 0, 'a^12', 0, 'a^17', 0, 0, 0, 'a^11', 0, 0, 0, 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{'__RealLiteral__': 0, 'data': '0.23', 'prec': 14}, 'spectral_label': 'r0-0', 'st_group': 'mu(20)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.830460654337199426662782572839+0.0549171980334445701567362537610*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.26073431002', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.09920181491', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.01342620944', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 6.037174619186565, 'bad_primes': [2, 5, 13], 'central_character': '1300.987', 'conductor': 1300, 'conductor_radical': 130, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1300/987'], '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': '1-1300-1300.987-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': '1-1300-1300.987-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.037174619186565, 'root_angle': 0.23, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.26073431002', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1300.987', 'Lhash_array': ['dirichlet_L_1300.987'], 'factors': ['1-1300-1300.987-r0-0-0'], 'label': '1-1300-1300.987-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1300/987'}
Lfunction data - 1-1300-1300.987-r0-0-0