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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_4729.1089', 'a10': [-0.9334851442746663, -0.35861606966016646], 'a2': [0.11931882848395176, 0.9928559901462132], 'a3': [0.9897180218885506, 0.14303229407729687], 'a4': [-0.9715260343384347, 0.2369328271950402], 'a5': [-0.46743646674681383, 0.8840266678982341], 'a6': [-0.023918475057802948, 0.9997139123523836], 'a7': [-0.0717006907618376, -0.9974261932314968], 'a8': [-0.35116152500179476, -0.9363148954056076], 'a9': [0.9590835257019713, 0.2831232783207275], 'algebraic': True, 'analytic_conductor': 21.961383672410207, 'analytic_normalization': 0, 'bad_lfactors': [[4729, [1]]], 'bad_primes': [4729], 'central_character': '4729.1089', 'coeff_info': ['x^788 - 1', '0.999968211136237 + 0.00797350092461664*I', '\\\\zeta_{788}'], 'conductor': 4729, 'conductor_radical': 4729, 'conjugate': 'dirichlet_L_4729.1103', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^182', 'a^18', 'a^364', 'a^258', 'a^200', 'a^582', 'a^546', 'a^36', 'a^440', 'a^49', 'a^382', 'a^324', 'a^764', 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'-0.999933442402378623123589535968+0.0115373638812751599764254565966*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(788)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.910421122054506994315414484194+0.811522876151046584537212193273*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.08302523823', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.30832609489', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.14149299113', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 21.961383672410207, 'bad_primes': [4729], 'central_character': '4729.1089', 'conductor': 4729, 'conductor_radical': 4729, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4729/1089'], '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': '1-4729-4729.1089-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': '1-4729-4729.1089-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 21.961383672410207, 'root_angle': 0.4981637307686415, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.08302523823', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_4729.1089', 'Lhash_array': ['dirichlet_L_4729.1089'], 'label': '1-4729-4729.1089-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4729/1089'}
Lfunction data - 1-4729-4729.1089-r0-0-0