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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_837.214', 'a10': [0.30901699437494745, -0.9510565162951535], 'a2': [-0.6156614753256583, 0.7880107536067219], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.24192189559966773, -0.9702957262759965], 'a5': [-0.9396926207859084, 0.3420201433256687], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.4383711467890774, -0.898794046299167], 'a8': [0.9135454576426009, 0.4067366430758002], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 3.8870116586608887, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [31, [1]]], 'bad_primes': [3, 31], 'central_character': '837.214', 'coeff_info': ['x^45 - 1', '0.990268068741570 + 0.139173100960065*I', '\\\\zeta_{45}'], 'conductor': 837, 'conductor_radical': 93, 'conjugate': 'dirichlet_L_837.661', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^16', 0, 'a^32', 'a^20', 0, 'a^37', 'a^3', 0, 'a^36', 'a^22', 0, 'a^14', 'a^8', 0, 'a^19', 'a^3', 0, 'a^36', 'a^7', 0, 'a^38', 'a^23', 0, 'a^40', 'a^30', 0, 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'195.38217728043910566310509767506', '195.787764563215473834570077958355', '196.77538140134941628765337096877', '197.00763353566861313489558607637', '198.02354185401258352728601904114', '198.44387641247737900274577127818', '198.743086536476567595381161157568', '199.39758184789675923100770107164'], 'prelabel': '1-837-837.214-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8870116586608887, 'root_angle': 0.25752104475103715, 'root_number': '-0.0472385315782651124271063575297+0.998883637434475772976160768076*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.257521044751', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(45)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.588397243351220980750477685280+0.222587562075475895594967302041*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.887641949395', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.26516496861', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.77271382994', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 3.8870116586608887, 'bad_primes': [3, 31], 'central_character': '837.214', 'conductor': 837, 'conductor_radical': 93, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/837/214'], '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': '1-837-837.214-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': '1-837-837.214-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8870116586608887, 'root_angle': 0.25752104475103715, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.887641949395', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_837.214', 'Lhash_array': ['dirichlet_L_837.214'], 'factors': ['1-837-837.214-r0-0-0'], 'label': '1-837-837.214-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/837/214'}
Lfunction data - 1-837-837.214-r0-0-0