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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_1157.687', 'a10': [-0.5800569095711982, -0.8145759520503357], 'a2': [0.9718115683235417, 0.23575893550942723], 'a3': [-0.8888354486549235, 0.4582265217274104], 'a4': [0.8888354486549235, 0.4582265217274104], 'a5': [-0.7557495743542583, -0.6548607339452851], 'a6': [-0.9718115683235417, 0.23575893550942723], 'a7': [0.18925124436041021, -0.9819286972627067], 'a8': [0.7557495743542583, 0.6548607339452851], 'a9': [0.5800569095711982, -0.8145759520503357], 'algebraic': True, 'analytic_conductor': 124.33691798738116, 'analytic_normalization': 0, 'bad_lfactors': [[13, [1]], [89, [1]]], 'bad_primes': [13, 89], 'central_character': '1157.687', 'coeff_info': ['x^132 - 1', '0.998867339183008 + 0.0475819158237423*I', '\\\\zeta_{132}'], 'conductor': 1157, 'conductor_radical': 1157, 'conjugate': 'dirichlet_L_1157.32', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^5', 'a^56', 'a^10', 'a^81', 'a^61', 'a^103', 'a^15', 'a^112', 'a^86', 'a^95', 'a^66', 0, 'a^108', 'a^5', 'a^20', 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'199.10772711099833222087900772722', '199.46378922315099988374981437734'], 'prelabel': '1-1157-1157.687-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 124.33691798738116, 'root_angle': -0.5161760715975768, 'root_number': '-0.0507967570559944622842895227511-0.998709011410528065036318115488*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.258088035799', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(132)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.35524014802021251676749860277-0.147170800027989313631508359787*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.416171268818', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.24482588664', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.11175627523', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 124.33691798738116, 'bad_primes': [13, 89], 'central_character': '1157.687', 'conductor': 1157, 'conductor_radical': 1157, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1157/687'], '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': '1-1157-1157.687-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-1157-1157.687-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 124.33691798738116, 'root_angle': -0.2580880357987884, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.416171268818', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_1157.687', 'Lhash_array': ['dirichlet_L_1157.687'], 'label': '1-1157-1157.687-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1157/687'}