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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_1225.36', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.1342332658176555, 0.9909497617679347], 'a3': [0.753071466003611, -0.6579387259397126], 'a4': [-0.9639628606958532, 0.2660368455666751], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [0.753071466003611, 0.6579387259397126], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.3930250316539236, -0.9195277725514507], 'a9': [0.1342332658176555, -0.9909497617679347], 'algebraic': True, 'analytic_conductor': 5.6888760834642635, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [7, [1]]], 'bad_primes': [5, 7], 'central_character': '1225.36', 'coeff_info': ['x^35 - 1', '0.983929588598630 + 0.178556894798637*I', '\\\\zeta_{35}'], 'conductor': 1225, 'conductor_radical': 35, 'conjugate': 'dirichlet_L_1225.1191', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^8', 'a^31', 'a^16', 0, 'a^4', 0, 'a^24', 'a^27', 0, 'a^8', 'a^12', 'a^22', 0, 0, 'a^32', 'a^19', 'a^0', 'a^14', 0, 0, 'a^16', 'a^23', 'a^20', 0, 'a^30', 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'1-35e2-1225.36-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.6888760834642635, 'root_angle': -0.6416326530612245, 'root_number': '-0.430414646891471276555205657231-0.902631282274933176587124324072*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.320816326531', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(35)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.925680111255472947239228513138+0.165151319086034241663703329261*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.139312795876', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.76728131623', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.7296765393', 'prec': 40}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.6888760834642635, 'bad_primes': [5, 7], 'central_character': '1225.36', 'conductor': 1225, 'conductor_radical': 35, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1225/36'], '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': '1-35e2-1225.36-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': '1-35e2-1225.36-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.6888760834642635, 'root_angle': -0.32081632653061226, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.139312795876', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_1225.36', 'Lhash_array': ['dirichlet_L_1225.36'], 'label': '1-35e2-1225.36-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1225/36'}