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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1001.20', 'a10': [-0.5, -0.8660254037844386], 'a2': [-0.9945218953682733, -0.10452846326765347], 'a3': [0.9781476007338057, -0.20791169081775934], 'a4': [0.9781476007338057, 0.20791169081775934], 'a5': [0.5877852522924731, 0.8090169943749475], 'a6': [-0.9945218953682733, 0.10452846326765347], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.9510565162951535, -0.30901699437494745], 'a9': [0.9135454576426009, -0.4067366430758002], 'algebraic': True, 'analytic_conductor': 4.648624456773655, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [11, [1]], [13, [1]]], 'bad_primes': [7, 11, 13], 'central_character': '1001.20', 'coeff_info': ['x^60 - 1', '0.994521895368273 + 0.104528463267653*I', '\\\\zeta_{60}'], 'conductor': 1001, 'conductor_radical': 1001, 'conjugate': 'dirichlet_L_1001.951', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^31', 'a^58', 'a^2', 'a^9', 'a^29', 0, 'a^33', 'a^56', 'a^40', 0, 'a^0', 0, 0, 'a^7', 'a^4', 'a^44', 'a^27', 'a^53', 'a^11', 0, 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'190.039502264975023049898729553752', '190.52684929319537041821509266016', '191.0949557704192923975529503699', '191.5495662282396428508564940759', '192.212370426666932672445152414', '192.91310068692691139300442830940', '193.35059090399202886972960994126', '193.818780183136831048326024927397', '194.80554038610598846703693086512', '195.516650708991175791539552160417', '196.27229133404044104511328657974', '196.850732484735714605656567066327', '197.38055384466377984219542456486', '197.849900748190747031203513031943', '198.23245475047354326955373207613', '198.95292430994210782133471012554', '199.486928853944950963886579790999'], 'prelabel': '1-1001-1001.20-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.648624456773655, 'root_angle': -0.01055835729294752, 'root_number': '0.999449924073893124589039613139-0.0331639754656957326193700482161*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.00527917864647', 'prec': 57}, 'spectral_label': 'r0-0', 'st_group': 'mu(60)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.15247432171727099441141581455+0.0158826058706643197636039622007*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.07321477232', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.15739719336', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.84622488996', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 4.648624456773655, 'bad_primes': [7, 11, 13], 'central_character': '1001.20', 'conductor': 1001, 'conductor_radical': 1001, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1001/20'], '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': '1-1001-1001.20-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': '1-1001-1001.20-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.648624456773655, 'root_angle': -0.00527917864647376, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.07321477232', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1001.20', 'Lhash_array': ['dirichlet_L_1001.20'], 'label': '1-1001-1001.20-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1001/20'}
Lfunction data - 1-1001-1001.20-r0-0-0