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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_2552.1341', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.6234898018587335, -0.7818314824680298], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [0.9009688679024191, -0.4338837391175581], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.6234898018587335, -0.7818314824680298], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-0.2225209339563144, 0.9749279121818236], 'algebraic': True, 'analytic_conductor': 274.2504880758831, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [11, [1]], [29, [1]]], 'bad_primes': [2, 11, 29], 'central_character': '2552.1341', 'coeff_info': ['x^14 - 1', '0.900968867902419 + 0.433883739117558*I', '\\\\zeta_{14}'], 'conductor': 2552, 'conductor_radical': 638, 'conjugate': 'dirichlet_L_2552.373', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^9', 0, 'a^13', 0, 'a^9', 0, 'a^4', 0, 0, 0, 'a^10', 0, 'a^8', 0, 'a^7', 0, 'a^12', 0, 'a^18', 0, 'a^8', 0, 'a^12', 0, 'a^13', 0, 0, 0, 'a^6', 0, 0, 0, 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'190.72121288293027669169684515346', '191.25962535767139491176939642028', '191.94332996136764617069431834395', '192.55361644996396498750570546161', '193.263294577401295107637138283119', '193.6890799111313886860331817579', '194.2295139575927176961586456643', '194.69501789855352172527196526544', '195.26275057868665415956435362897', '195.93482924597426474632103351233', '196.45416304766952576577508095717', '197.036750669083904091225490745449', '197.23903379476533304571799018764', '197.89116648740018431027938562195', '198.82141259659954726816495779488', '199.31306906673837650931381609907', '199.94758566622168090757836057665'], 'prelabel': '1-2552-2552.1341-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 274.2504880758831, 'root_angle': 0.2136681182021348, 'root_number': '0.226302428235437063117110655777+0.974057088149737175298377063989*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.213668118202', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(14)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.632420440712628141511820965263-0.460182838672423054637250324022*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.138158230172', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '0.635275414838', 'prec': 47}, 'z3': {'__RealLiteral__': 0, 'data': '1.72595040802', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 274.2504880758831, 'bad_primes': [2, 11, 29], 'central_character': '2552.1341', 'conductor': 2552, 'conductor_radical': 638, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/2552/1341'], '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': '1-2552-2552.1341-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': '1-2552-2552.1341-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 274.2504880758831, 'root_angle': 0.2136681182021348, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.138158230172', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_2552.1341', 'Lhash_array': ['dirichlet_L_2552.1341'], 'factors': ['1-2552-2552.1341-r1-0-0'], 'label': '1-2552-2552.1341-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/2552/1341'}