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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1001.201', 'a10': [1.0, 0.0], 'a2': [0.7431448254773942, -0.6691306063588582], 'a3': [0.8090169943749475, -0.5877852522924731], 'a4': [0.10452846326765347, -0.9945218953682733], 'a5': [0.7431448254773942, 0.6691306063588582], 'a6': [0.20791169081775934, -0.9781476007338057], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.5877852522924731, -0.8090169943749475], 'a9': [0.30901699437494745, -0.9510565162951535], 'algebraic': True, 'analytic_conductor': 4.648624456773655, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [11, [1]], [13, [1]]], 'bad_primes': [7, 11, 13], 'central_character': '1001.201', 'coeff_info': ['x^60 - 1', '0.994521895368273 + 0.104528463267653*I', '\\\\zeta_{60}'], 'conductor': 1001, 'conductor_radical': 1001, 'conjugate': 'dirichlet_L_1001.752', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^53', 'a^54', 'a^46', 'a^7', 'a^47', 0, 'a^39', 'a^48', 'a^0', 0, 'a^40', 0, 0, 'a^1', 'a^32', 'a^52', 'a^41', 'a^39', 'a^53', 0, 0, 'a^50', 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'190.49350474292115055872018106837', '191.03987244794950026041762403055', '191.527313816642384511247838605246', '192.30218635195959323068330873562', '192.70995886403634123958990316019', '193.37732206662536255648000785107', '193.96744871342797176262009525265', '194.57084182071034548004635774764', '195.12005400990070572464324590355', '195.94032102486404712421551814180', '196.23240861126822217913141974229', '196.97961877987358222637125441320', '197.478693979695557204235277172981', '197.91518611017289685975008619956', '198.83102580102268838481174360641', '199.45134016215840627417158702993'], 'prelabel': '1-1001-1001.201-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.648624456773655, 'root_angle': -0.6268711859436352, 'root_number': '-0.388107818485461099971874837292-0.921613976256033336907016502246*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.313435592972', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(60)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.77848965825265972019447339762-1.30670080565471005786580211503*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.0443918756', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '2.0699007339', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '2.81415440365', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 4.648624456773655, 'bad_primes': [7, 11, 13], 'central_character': '1001.201', 'conductor': 1001, 'conductor_radical': 1001, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1001/201'], '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': '1-1001-1001.201-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': '1-1001-1001.201-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.648624456773655, 'root_angle': -0.3134355929718176, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.0443918756', 'prec': 40}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1001.201', 'Lhash_array': ['dirichlet_L_1001.201'], 'label': '1-1001-1001.201-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1001/201'}
Lfunction data - 1-1001-1001.201-r0-0-0