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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_4011.3695', 'a10': [-0.24548548714079915, -0.9694002659393304], 'a2': [0.08257934547233232, 0.9965844930066698], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.9863613034027223, 0.1645945902807339], 'a5': [-0.9863613034027223, 0.1645945902807339], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.24548548714079915, -0.9694002659393304], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 431.041813351241, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [7, [1]], [191, [1]]], 'bad_primes': [3, 7, 191], 'central_character': '4011.3695', 'coeff_info': ['x^38 - 1', '0.986361303402722 + 0.164594590280734*I', '\\\\zeta_{38}'], 'conductor': 4011, 'conductor_radical': 4011, 'conjugate': 'dirichlet_L_4011.2729', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^9', 0, 'a^18', 'a^18', 0, 0, 'a^27', 0, 'a^27', 'a^4', 0, 'a^35', 0, 0, 'a^36', 'a^14', 0, 'a^30', 'a^36', 0, 'a^13', 'a^11', 0, 'a^36', 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'198.0182924514347233571650834822', '198.69601214665126426499175222053', '198.906243346052520320730945235866', '199.44218233236244255766670005394'], 'prelabel': '1-4011-4011.3695-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 431.041813351241, 'root_angle': 0.7240241005943195, 'root_number': '-0.647113687477653239340683156829+0.762393517469209685001298221309*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.25', 'prec': 17}, 'spectral_label': 'r1-0', 'st_group': 'mu(38)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.763734698190034783926273479002+0.525641785999738923448749993680*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.643994503422', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.53087490102', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.066396381', 'prec': 37}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 431.041813351241, 'bad_primes': [3, 7, 191], 'central_character': '4011.3695', 'conductor': 4011, 'conductor_radical': 4011, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4011/3695'], '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': '1-4011-4011.3695-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': '1-4011-4011.3695-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 431.041813351241, 'root_angle': 0.36201205029715977, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.643994503422', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_4011.3695', 'Lhash_array': ['dirichlet_L_4011.3695'], 'label': '1-4011-4011.3695-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4011/3695'}