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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_407.174', 'a10': [1.0, 0.0], 'a2': [0.9135454576426009, -0.4067366430758002], 'a3': [-0.9781476007338057, 0.20791169081775934], 'a4': [0.6691306063588582, -0.7431448254773942], 'a5': [0.9135454576426009, 0.4067366430758002], 'a6': [-0.8090169943749475, 0.5877852522924731], 'a7': [0.6691306063588582, -0.7431448254773942], 'a8': [0.30901699437494745, -0.9510565162951535], 'a9': [0.9135454576426009, -0.4067366430758002], 'algebraic': True, 'analytic_conductor': 1.8901000538530248, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]], [37, [1]]], 'bad_primes': [11, 37], 'central_character': '407.174', 'coeff_info': ['x^15 - 1', '0.913545457642601 + 0.406736643075800*I', '\\\\zeta_{15}'], 'conductor': 407, 'conductor_radical': 407, 'conjugate': 'dirichlet_L_407.269', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^14', 'a^7', 'a^13', 'a^1', 'a^6', 'a^13', 'a^12', 'a^14', 'a^0', 0, 'a^5', 'a^4', 'a^12', 'a^8', 'a^11', 'a^11', 'a^13', 'a^7', 'a^14', 'a^5', 0, 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'st_group': 'mu(15)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.59284970801119163953727315968-0.435351486878728872832845107930*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.21985448165', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.25770461876', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.7963678545', 'prec': 40}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.8901000538530248, 'bad_primes': [11, 37], 'central_character': '407.174', 'conductor': 407, 'conductor_radical': 407, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/407/174'], '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': '1-407-407.174-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': '1-407-407.174-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8901000538530248, 'root_angle': -0.13279583011224735, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.21985448165', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_407.174', 'Lhash_array': ['dirichlet_L_407.174'], 'label': '1-407-407.174-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/407/174'}