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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_6003.1201', 'a10': [0.7557495743542583, -0.6548607339452851], 'a2': [-0.4582265217274104, -0.8888354486549235], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.5800569095711982, 0.8145759520503357], 'a5': [0.23575893550942723, 0.9718115683235417], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.32706796331742166, 0.9450008187146685], 'a8': [0.9898214418809327, 0.14231483827328514], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 27.87781479921304, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [23, [1]], [29, [1]]], 'bad_primes': [3, 23, 29], 'central_character': '6003.1201', 'coeff_info': ['x^132 - 1', '0.998867339183008 + 0.0475819158237423*I', '\\\\zeta_{132}'], 'conductor': 6003, 'conductor_radical': 2001, 'conjugate': 'dirichlet_L_6003.3004', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^89', 0, 'a^46', 'a^28', 0, 'a^26', 'a^3', 0, 'a^117', 'a^131', 0, 'a^106', 'a^115', 0, 'a^92', 'a^75', 0, 'a^123', 'a^74', 0, 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False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(132)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.978428592783997020953337418796-0.156070161353128842466587128661*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.692735832901', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.68055900536', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.42005210982', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 27.87781479921304, 'bad_primes': [3, 23, 29], 'central_character': '6003.1201', 'conductor': 6003, 'conductor_radical': 2001, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/6003/1201'], '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': '1-6003-6003.1201-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': '1-6003-6003.1201-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 27.87781479921304, 'root_angle': -0.060383169460120165, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.692735832901', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_6003.1201', 'Lhash_array': ['dirichlet_L_6003.1201'], 'label': '1-6003-6003.1201-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/6003/1201'}