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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_361.324', 'a10': [0.5469481581224269, 0.8371664782625285], 'a2': [-0.6772815716257411, -0.7357239106731316], 'a3': [0.24548548714079915, -0.9694002659393304], 'a4': [-0.08257934547233232, 0.9965844930066698], 'a5': [-0.9863613034027223, -0.1645945902807339], 'a6': [-0.8794737512064891, 0.47594739303707356], 'a7': [-0.08257934547233232, -0.9965844930066698], 'a8': [0.7891405093963936, -0.6142127126896678], 'a9': [-0.8794737512064891, -0.47594739303707356], 'algebraic': True, 'analytic_conductor': 1.6764769519433462, 'analytic_normalization': 0, 'bad_lfactors': [[19, [1]]], 'bad_primes': [19], 'central_character': '361.324', 'coeff_info': ['x^19 - 1', '0.945817241700635 + 0.324699469204683*I', '\\\\zeta_{19}'], 'conductor': 361, 'conductor_radical': 19, 'conjugate': 'dirichlet_L_361.39', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^12', 'a^15', 'a^5', 'a^10', 'a^8', 'a^14', 'a^17', 'a^11', 'a^3', 'a^8', 'a^1', 'a^15', 'a^7', 'a^6', 'a^10', 'a^14', 'a^4', 0, 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[[1, '0.345003176126865402081003463968-0.394523881827204906900650251341*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.205137970737', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.3386169468', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '2.83155013704', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.6764769519433462, 'bad_primes': [19], 'central_character': '361.324', 'conductor': 361, 'conductor_radical': 19, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/361/324'], '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': '1-19e2-361.324-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': '1-19e2-361.324-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6764769519433462, 'root_angle': 0.2742382271468144, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.205137970737', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_361.324', 'Lhash_array': ['dirichlet_L_361.324'], 'label': '1-19e2-361.324-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/361/324'}