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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_507.395', 'a10': [0.7485107481711011, 0.6631226582407952], 'a2': [-0.23931566428755777, -0.970941817426052], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.8854560256532099, 0.46472317204376856], 'a5': [-0.8229838658936564, 0.5680647467311558], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.6631226582407952, -0.7485107481711011], 'a8': [0.6631226582407952, 0.7485107481711011], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 2.3544981014827604, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [13, [1]]], 'bad_primes': [3, 13], 'central_character': '507.395', 'coeff_info': ['x^52 - 1', '0.992708874098054 + 0.120536680255323*I', '\\\\zeta_{52}'], 'conductor': 507, 'conductor_radical': 39, 'conjugate': 'dirichlet_L_507.86', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^37', 0, 'a^22', 'a^21', 0, 'a^33', 'a^7', 0, 'a^6', 'a^15', 0, 0, 'a^18', 0, 'a^44', 'a^20', 0, 'a^39', 'a^43', 0, 'a^0', 'a^0', 0, 'a^42', 0, 0, 'a^3', 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'185.53083456480953349722366914705', '185.948469638389820163994484550205', '186.74418618199350503035710248612', '187.46738376854573456707343139989', '188.11497272387503234658726068288', '188.72568733290115188593866613077', '189.84031091723117091731622332667', '190.30817886230554936595555491786', '190.94499257791313210163792174427', '191.14483362410893925673719154867', '191.9541503304274090203951354856', '192.71590034614859692796023965599', '193.39304858278797519949128237201', '193.91130384525986604288217996992', '194.649337020000677610323090809944', '194.97736829717120931254919088987', '195.67913418645426480733315574722', '196.549597518829281853616663292679', '197.542732830601570329038314778355', '197.92277662020907341675977827973', '198.85130332298780302411661519563', '199.19212830248498499689689966854', '199.73986128486291574940877386326'], 'prelabel': '1-507-507.395-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.3544981014827604, 'root_angle': -0.2958579881656805, 'root_number': '-0.284163872904746090570666013726-0.958775726296705589804718322842*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.295857988166', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(52)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.598401111240773247603737373401-0.285114491310055034467569072204*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.498009286223', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.14549561275', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.18640430749', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 2.3544981014827604, 'bad_primes': [3, 13], 'central_character': '507.395', 'conductor': 507, 'conductor_radical': 39, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/507/395'], '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': '1-507-507.395-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': '1-507-507.395-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.3544981014827604, 'root_angle': -0.2958579881656805, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.498009286223', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_507.395', 'Lhash_array': ['dirichlet_L_507.395'], 'factors': ['1-507-507.395-r0-0-0'], 'label': '1-507-507.395-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/507/395'}
Lfunction data - 1-507-507.395-r0-0-0