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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_1157.1004', 'a10': [0.5800569095711982, 0.8145759520503357], 'a2': [0.23575893550942723, -0.9718115683235417], 'a3': [0.8888354486549235, -0.4582265217274104], 'a4': [-0.8888354486549235, -0.4582265217274104], 'a5': [-0.6548607339452851, 0.7557495743542583], 'a6': [-0.23575893550942723, -0.9718115683235417], 'a7': [-0.9819286972627067, -0.18925124436041021], 'a8': [-0.6548607339452851, 0.7557495743542583], 'a9': [0.5800569095711982, -0.8145759520503357], 'algebraic': True, 'analytic_conductor': 5.373085411076043, 'analytic_normalization': 0, 'bad_lfactors': [[13, [1]], [89, [1]]], 'bad_primes': [13, 89], 'central_character': '1157.1004', 'coeff_info': ['x^66 - 1', '0.995471922573085 + 0.0950560433041827*I', '\\\\zeta_{66}'], 'conductor': 1157, 'conductor_radical': 1157, 'conjugate': 'dirichlet_L_1157.1036', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^52', 'a^61', 'a^38', 'a^24', 'a^47', 'a^35', 'a^24', 'a^56', 'a^10', 'a^64', 'a^33', 0, 'a^21', 'a^19', 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'199.19131992227635261328226621921', '199.873852421594410382532751674779'], 'prelabel': '1-1157-1157.1004-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.373085411076043, 'root_angle': -0.3915673541499918, 'root_number': '0.334100946630262848081316094254-0.942537297649680416113782771196*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.195783677075', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(66)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.09896466226457234778404197304-0.620569977581875072038220238673*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.917343212063', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.02276651003', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.03101528708', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.373085411076043, 'bad_primes': [13, 89], 'central_character': '1157.1004', 'conductor': 1157, 'conductor_radical': 1157, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1157/1004'], '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': '1-1157-1157.1004-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': '1-1157-1157.1004-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.373085411076043, 'root_angle': -0.1957836770749959, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.917343212063', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_1157.1004', 'Lhash_array': ['dirichlet_L_1157.1004'], 'label': '1-1157-1157.1004-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1157/1004'}