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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_2888.115', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.6772815716257411, -0.7357239106731316], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [0.8794737512064891, -0.47594739303707356], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.24548548714079915, 0.9694002659393304], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-0.08257934547233232, 0.9965844930066698], 'algebraic': True, 'analytic_conductor': 310.3587028068771, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [19, [1]]], 'bad_primes': [2, 19], 'central_character': '2888.115', 'coeff_info': ['x^38 - 1', '0.986361303402722 + 0.164594590280734*I', '\\\\zeta_{38}'], 'conductor': 2888, 'conductor_radical': 38, 'conjugate': 'dirichlet_L_2888.1331', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^24', 0, 'a^35', 0, 'a^49', 0, 'a^10', 0, 'a^28', 0, 'a^43', 0, 'a^21', 0, 'a^30', 0, 0, 0, 'a^35', 0, 'a^33', 0, 'a^32', 0, 'a^34', 0, 'a^49', 0, 'a^53', 0, 'a^14', 0, 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'spectral_label': 'r1-0', 'st_group': 'mu(38)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.986804973557393860347777178977-0.131297209839451952097539216603*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.868792391635', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.49308300958', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.47730681812', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 310.3587028068771, 'bad_primes': [2, 19], 'central_character': '2888.115', 'conductor': 2888, 'conductor_radical': 38, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/2888/115'], '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': '1-2888-2888.115-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': '1-2888-2888.115-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 310.3587028068771, 'root_angle': 0.12465373961218837, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.868792391635', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_2888.115', 'Lhash_array': ['dirichlet_L_2888.115'], 'label': '1-2888-2888.115-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/2888/115'}