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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_196.183', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.2225209339563144, -0.9749279121818236], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [-0.2225209339563144, 0.9749279121818236], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-0.9009688679024191, -0.4338837391175581], 'algebraic': True, 'analytic_conductor': 21.063125259746503, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [7, [1]]], 'bad_primes': [2, 7], 'central_character': '196.183', 'coeff_info': ['x^14 - 1', '0.900968867902419 + 0.433883739117558*I', '\\\\zeta_{14}'], 'conductor': 196, 'conductor_radical': 14, 'conjugate': 'dirichlet_L_196.15', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^11', 0, 'a^4', 0, 0, 0, 'a^8', 0, 'a^13', 0, 'a^6', 0, 'a^15', 0, 'a^2', 0, 'a^7', 0, 0, 0, 'a^19', 0, 'a^8', 0, 'a^19', 0, 'a^2', 0, 'a^7', 0, 'a^10', 0, 0, 0, 'a^2', 0, 'a^17', 0, 'a^4', 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'190.5387585068509904254841095988', '191.60626423100403247332810302500', '191.98889467151132939583616259250', '192.99575989820901959320721086142', '194.11170261111788871889861311882', '194.34753739780875247330396227489', '195.29674117091900521387363229343', '195.75824523987325322283709112778', '196.608057763380490186119061272025', '197.32301773314398915801598939041', '198.13195774117590017396068365603', '198.420340686681240217725539221391', '199.602390298223334189902942214666'], 'prelabel': '1-14e2-196.183-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 21.063125259746503, 'root_angle': 0.2448979591836735, 'root_number': '0.0320515775716551742335505253458+0.999486216200687867697489397011*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.244897959184', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(14)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.945881404978327228194207380479+0.0251180074732983801411320337895*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.5150283099', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '2.77758250891', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.94965800687', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 21.063125259746503, 'bad_primes': [2, 7], 'central_character': '196.183', 'conductor': 196, 'conductor_radical': 14, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/196/183'], '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': '1-14e2-196.183-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-14e2-196.183-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 21.063125259746503, 'root_angle': 0.2448979591836735, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.5150283099', 'prec': 40}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_196.183', 'Lhash_array': ['dirichlet_L_196.183'], 'factors': ['1-14e2-196.183-r1-0-0'], 'label': '1-14e2-196.183-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/196/183'}
Lfunction data - 1-14e2-196.183-r1-0-0