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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_287.121', 'a10': [-0.9781476007338057, -0.20791169081775934], 'a2': [-0.9135454576426009, -0.4067366430758002], 'a3': [-0.8660254037844386, -0.5], 'a4': [0.6691306063588582, 0.7431448254773942], 'a5': [0.9781476007338057, -0.20791169081775934], 'a6': [0.5877852522924731, 0.8090169943749475], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.30901699437494745, -0.9510565162951535], 'a9': [0.5, 0.8660254037844386], 'algebraic': True, 'analytic_conductor': 1.3328223966973418, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [41, [1]]], 'bad_primes': [7, 41], 'central_character': '287.121', 'coeff_info': ['x^60 - 1', '0.994521895368273 + 0.104528463267653*I', '\\\\zeta_{60}'], 'conductor': 287, 'conductor_radical': 287, 'conjugate': 'dirichlet_L_287.102', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^34', 'a^35', 'a^8', 'a^58', 'a^9', 0, 'a^42', 'a^10', 'a^32', 'a^47', 'a^43', 'a^39', 0, 'a^33', 'a^16', 'a^17', 'a^44', 'a^1', 'a^6', 0, 'a^21', 'a^4', 'a^17', 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{'__RealLiteral__': 0, 'data': '3.25615286351', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.3328223966973418, 'bad_primes': [7, 41], 'central_character': '287.121', 'conductor': 287, 'conductor_radical': 287, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/287/121'], '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': '1-287-287.121-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': '1-287-287.121-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3328223966973418, 'root_angle': -0.23195278983378084, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.850855882771', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_287.121', 'Lhash_array': ['dirichlet_L_287.121'], 'label': '1-287-287.121-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/287/121'}