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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_539.130', 'a10': [0.07473009358642425, 0.9972037971811801], 'a2': [0.8875857890045541, 0.4606424504506323], 'a3': [0.7910710346563412, -0.6117242991150064], 'a4': [0.5756170656856735, 0.8177193856644314], 'a5': [0.5256837698105047, 0.8506800656873396], 'a6': [0.9839295885986297, -0.17855689479863665], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.1342332658176555, 0.9909497617679347], 'a9': [0.2515867637445085, -0.9678347484506665], 'algebraic': True, 'analytic_conductor': 2.503105476724276, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [11, [1]]], 'bad_primes': [7, 11], 'central_character': '539.130', 'coeff_info': ['x^105 - 1', '0.998210129767735 + 0.0598041539450342*I', '\\\\zeta_{105}'], 'conductor': 539, 'conductor_radical': 77, 'conjugate': 'dirichlet_L_539.170', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^8', 'a^94', 'a^16', 'a^17', 'a^102', 0, 'a^24', 'a^83', 'a^25', 0, 'a^5', 'a^78', 0, 'a^6', 'a^32', 'a^82', 'a^91', 'a^14', 'a^33', 0, 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'primitive': True, 'rational': False, 'root_analytic_conductor': 2.503105476724276, 'root_angle': 0.1008202848963796, 'root_number': '0.805976816182776829134965044813+0.591947102177107013158141463832*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.100820284896', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(105)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '2.29702811771713290249790047475+0.520234636138571078145551009422*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.66151901107', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.95037960427', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.1858408663', 'prec': 40}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 2.503105476724276, 'bad_primes': [7, 11], 'central_character': '539.130', 'conductor': 539, 'conductor_radical': 77, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/539/130'], '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': '1-539-539.130-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': '1-539-539.130-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.503105476724276, 'root_angle': 0.1008202848963796, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.66151901107', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_539.130', 'Lhash_array': ['dirichlet_L_539.130'], 'factors': ['1-539-539.130-r0-0-0'], 'label': '1-539-539.130-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/539/130'}
Lfunction data - 1-539-539.130-r0-0-0