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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_143.7', 'a10': [-0.5, -0.8660254037844386], 'a2': [-0.7431448254773942, -0.6691306063588582], 'a3': [-0.10452846326765347, 0.9945218953682733], 'a4': [0.10452846326765347, 0.9945218953682733], 'a5': [0.9510565162951535, 0.30901699437494745], 'a6': [0.7431448254773942, -0.6691306063588582], 'a7': [0.9945218953682733, -0.10452846326765347], 'a8': [0.5877852522924731, -0.8090169943749475], 'a9': [-0.9781476007338057, -0.20791169081775934], 'algebraic': True, 'analytic_conductor': 0.6640892081105222, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]], [13, [1]]], 'bad_primes': [11, 13], 'central_character': '143.7', 'coeff_info': ['x^60 - 1', '0.994521895368273 + 0.104528463267653*I', '\\\\zeta_{60}'], 'conductor': 143, 'conductor_radical': 143, 'conjugate': 'dirichlet_L_143.41', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^37', 'a^16', 'a^14', 'a^3', 'a^53', 'a^59', 'a^51', 'a^32', 'a^40', 0, 'a^30', 0, 'a^36', 'a^19', 'a^28', 'a^8', 'a^9', 'a^41', 'a^17', 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'190.49601297397808962390833096468', '191.74490762700093400775197127562', '192.14984888412744073012356615333', '192.65269939066907164233466383139', '193.50831282179506868498470315010', '194.10198737889646105910347680631', '194.61746448598429794043197966104', '195.77364857927148385172715429982', '197.08835705415347221196207734841', '197.48528257728073128094566940413', '198.388328219749451646683212281711', '198.763549173698396891127694148210', '199.45656667078201536587931326447'], 'prelabel': '1-143-143.7-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6640892081105222, 'root_angle': 0.1860760221144695, 'root_number': '0.833946659958388159576760695251+0.551845058276549678366980627453*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0930380110572', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(60)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.882537213509730861702747370402+0.116011637331472705681575744915*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.68560080492', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.06812207847', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.46053038207', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.6640892081105222, 'bad_primes': [11, 13], 'central_character': '143.7', 'conductor': 143, 'conductor_radical': 143, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/143/7'], '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': '1-143-143.7-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': '1-143-143.7-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6640892081105222, 'root_angle': 0.09303801105723475, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.68560080492', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_143.7', 'Lhash_array': ['dirichlet_L_143.7'], 'label': '1-143-143.7-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/143/7'}
Lfunction data - 1-143-143.7-r0-0-0