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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_1287.553', 'a10': [0.5, 0.8660254037844386], 'a2': [0.9510565162951535, 0.30901699437494745], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.8090169943749475, 0.5877852522924731], 'a5': [0.7431448254773942, 0.6691306063588582], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.9945218953682733, 0.10452846326765347], 'a8': [0.5877852522924731, 0.8090169943749475], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 138.3073582106824, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [11, [1]], [13, [1]]], 'bad_primes': [3, 11, 13], 'central_character': '1287.553', 'coeff_info': ['x^60 - 1', '0.994521895368273 + 0.104528463267653*I', '\\\\zeta_{60}'], 'conductor': 1287, 'conductor_radical': 429, 'conjugate': 'dirichlet_L_1287.1159', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^3', 0, 'a^6', 'a^7', 0, 'a^1', 'a^9', 0, 'a^10', 0, 0, 0, 'a^4', 0, 'a^12', 'a^2', 0, 'a^59', 'a^13', 0, 0, 'a^50', 0, 'a^14', 0, 0, 'a^7', 'a^36', 0, 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0.38953065086414485, 'root_number': '0.340124883773689058734608444245+0.940380275972403894421784982787*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.194765325432', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(60)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '2.52633236660463079600790386686+0.998961224489020931261522333092*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.22222078594', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.23094589963', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.97739278094', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 138.3073582106824, 'bad_primes': [3, 11, 13], 'central_character': '1287.553', 'conductor': 1287, 'conductor_radical': 429, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1287/553'], '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': '1-1287-1287.553-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': '1-1287-1287.553-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 138.3073582106824, 'root_angle': 0.19476532543207242, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.22222078594', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_1287.553', 'Lhash_array': ['dirichlet_L_1287.553'], 'label': '1-1287-1287.553-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1287/553'}