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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_127.84', 'a10': [0.8262387743159949, 0.5633200580636221], 'a2': [-0.9009688679024191, -0.4338837391175581], 'a3': [0.9214762118704076, 0.38843479627469474], 'a4': [0.6234898018587335, 0.7818314824680298], 'a5': [-0.9888308262251285, -0.14904226617617444], 'a6': [-0.6616858375968594, -0.7497812029677342], 'a7': [-0.31848665025168443, 0.9479273461671317], 'a8': [-0.2225209339563144, -0.9749279121818236], 'a9': [0.6982368180860729, 0.7158668492597184], 'algebraic': True, 'analytic_conductor': 0.5897855204897645, 'analytic_normalization': 0, 'bad_lfactors': [[127, [1]]], 'bad_primes': [127], 'central_character': '127.84', 'coeff_info': ['x^63 - 1', '0.995030775365401 + 0.0995678465958167*I', '\\\\zeta_{63}'], 'conductor': 127, 'conductor_radical': 127, 'conjugate': 'dirichlet_L_127.62', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^36', 'a^4', 'a^9', 'a^33', 'a^40', 'a^19', 'a^45', 'a^8', 'a^6', 'a^20', 'a^13', 'a^61', 'a^55', 'a^37', 'a^18', 'a^26', 'a^44', 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'3.22089795653', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.38866776803', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.5897855204897645, 'bad_primes': [127], 'central_character': '127.84', 'conductor': 127, 'conductor_radical': 127, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/127/84'], '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': '1-127-127.84-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': '1-127-127.84-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5897855204897645, 'root_angle': 0.18186967026640674, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.99452227633', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_127.84', 'Lhash_array': ['dirichlet_L_127.84'], 'label': '1-127-127.84-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/127/84'}