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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_4729.1031', 'a10': [-0.545307582949571, -0.8382360287995838], 'a2': [0.35116152500179476, -0.9363148954056076], 'a3': [-0.9087264778787534, 0.41739212786308705], 'a4': [-0.7533711667168278, -0.6575955331050582], 'a5': [0.5933618372070801, -0.8049358546780225], 'a6': [0.0717006907618376, 0.9974261932314968], 'a7': [-0.7392195387265885, -0.6734645302945432], 'a8': [-0.88027146059512, 0.4744703949265267], 'a9': [0.6515676231958488, -0.7585905564946828], 'algebraic': True, 'analytic_conductor': 21.961383672410207, 'analytic_normalization': 0, 'bad_lfactors': [[4729, [1]]], 'bad_primes': [4729], 'central_character': '4729.1031', 'coeff_info': ['x^1182 - 1', '0.999985871574519 + 0.00531569857584313*I', '\\\\zeta_{1182}'], 'conductor': 4729, 'conductor_radical': 4729, 'conjugate': 'dirichlet_L_4729.3408', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^954', 'a^510', 'a^726', 'a^1006', 'a^282', 'a^730', 'a^498', 'a^1020', 'a^778', 'a^75', 'a^54', 'a^118', 'a^502', 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'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(1182)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.702542315843637631091212511589-0.406263095285996352828939496027*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.00305968251', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.4876099324', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '2.52586335655', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 21.961383672410207, 'bad_primes': [4729], 'central_character': '4729.1031', 'conductor': 4729, 'conductor_radical': 4729, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4729/1031'], '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': '1-4729-4729.1031-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': '1-4729-4729.1031-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 21.961383672410207, 'root_angle': 0.09471395411259632, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.00305968251', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_4729.1031', 'Lhash_array': ['dirichlet_L_4729.1031'], 'factors': ['1-4729-4729.1031-r0-0-0'], 'label': '1-4729-4729.1031-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4729/1031'}
Lfunction data - 1-4729-4729.1031-r0-0-0