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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_3024.1069', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [0.984807753012208, 0.17364817766693036], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 324.97393257894606, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [3, [1]], [7, [1]]], 'bad_primes': [2, 3, 7], 'central_character': '3024.1069', 'coeff_info': ['x^36 - 1', '0.984807753012208 + 0.173648177666930*I', '\\\\zeta_{36}'], 'conductor': 3024, 'conductor_radical': 42, 'conjugate': 'dirichlet_L_3024.1669', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 0, 0, 'a^37', 0, 0, 0, 0, 0, 'a^35', 0, 'a^19', 0, 0, 0, 'a^6', 0, 'a^39', 0, 0, 0, 'a^22', 0, 'a^38', 0, 0, 0, 'a^17', 0, 'a^10', 0, 0, 0, 0, 0, 'a^27', 0, 0, 0, 'a^28', 0, 'a^59', 0, 0, 0, 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'spectral_label': 'r1-0', 'st_group': 'mu(36)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.35561658391020915852562627460+0.00487501736473861654031114252232*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.576994524948', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.6669954076', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '2.19542175455', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 324.97393257894606, 'bad_primes': [2, 3, 7], 'central_character': '3024.1069', 'conductor': 3024, 'conductor_radical': 42, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/3024/1069'], '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': '1-3024-3024.1069-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': '1-3024-3024.1069-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 324.97393257894606, 'root_angle': -0.05026554564653872, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.576994524948', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_3024.1069', 'Lhash_array': ['dirichlet_L_3024.1069'], 'label': '1-3024-3024.1069-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/3024/1069'}