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{'Lhash': 'dirichlet_L_195.134', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.5, 0.8660254037844386], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.5, 0.8660254037844386], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.5, 0.8660254037844386], 'a8': [-1.0, -1.4081532572346456e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 20.95566033495188, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [5, [1]], [13, [1]]], 'bad_primes': [3, 5, 13], 'central_character': '195.134', 'coeff_info': ['x^6 - 1', '0.500000000000000 + 0.866025403784439*I', '\\\\zeta_{6}'], 'conductor': 195, 'conductor_radical': 195, 'conjugate': 'dirichlet_L_195.179', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^1', 0, 'a^2', 0, 0, 'a^2', 'a^3', 0, 0, 'a^4', 0, 0, 'a^3', 0, 'a^4', 'a^2', 0, 'a^5', 0, 0, 'a^5', 'a^4', 0, 0, 0, 0, 'a^4', 'a^1', 0, 'a^3', 'a^5', 0, 'a^3', 0, 0, 'a^4', 'a^0', 0, 0, 'a^4', 0, 'a^5', 'a^0', 0, 'a^5', 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'190.41386434914095617976876488957', '191.04501316616031612360909820356', '192.26165527123178805127605084433', '192.88027946280858544265499593185', '193.642399918955750057302602240', '194.349108945355340770929455796117', '194.9736428707496394719184286537', '195.69432349193997014062370029731', '196.56478934159378882099454944142', '197.01246566314918637214310195029', '197.44119280277050234399142731839', '198.662397458018542281990483495543', '199.15097623318324489550186267205', '199.64338548130227831674818451220'], 'prelabel': '1-195-195.134-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 20.95566033495188, 'root_angle': -0.4959180972148666, 'root_number': '0.0128233243368878929083906585448-0.999917777796230092950753187392*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.247959048607', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(6)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.773499311169228405791353032417+0.459904892416993971112554142322*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.015990153178', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.56131871148', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.71397524789', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 20.95566033495188, 'bad_primes': [3, 5, 13], 'central_character': '195.134', 'conductor': 195, 'conductor_radical': 195, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/195/134'], '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': '1-195-195.134-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': '1-195-195.134-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 20.95566033495188, 'root_angle': -0.2479590486074333, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.015990153178', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_195.134', 'Lhash_array': ['dirichlet_L_195.134'], 'label': '1-195-195.134-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/195/134'}