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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_147.110', 'a10': [-0.8262387743159949, 0.5633200580636221], 'a2': [-0.36534102436639504, 0.9308737486442042], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.7330518718298263, -0.6801727377709194], 'a5': [0.8262387743159949, 0.5633200580636221], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.9009688679024191, -0.4338837391175581], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 0.6826651300157116, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [7, [1]]], 'bad_primes': [3, 7], 'central_character': '147.110', 'coeff_info': ['x^42 - 1', '0.988830826225129 + 0.149042266176174*I', '\\\\zeta_{42}'], 'conductor': 147, 'conductor_radical': 21, 'conjugate': 'dirichlet_L_147.143', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^13', 0, 'a^26', 'a^4', 0, 0, 'a^39', 0, 'a^17', 'a^41', 0, 'a^27', 0, 0, 'a^10', 'a^2', 0, 'a^7', 'a^30', 0, 'a^12', 'a^19', 0, 'a^8', 'a^40', 0, 0, 'a^9', 0, 'a^35', 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'196.29873504056407568835246409765', '196.7281448674202337440176205756', '197.79366085921776561505810651888', '198.008226063209829194484731247505', '198.785397821306327931713810009105', '199.68917762319525975853305980010'], 'prelabel': '1-147-147.110-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6826651300157116, 'root_angle': 0.21258503401360546, 'root_number': '0.232925808418378593274720164517+0.972494507836751123339749511660*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.212585034014', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(42)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.867830647728912158878424470602+0.448074660324056160021023844660*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.54594098501', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.51685405121', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '5.27585578126', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.6826651300157116, 'bad_primes': [3, 7], 'central_character': '147.110', 'conductor': 147, 'conductor_radical': 21, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/147/110'], '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': '1-147-147.110-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': '1-147-147.110-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6826651300157116, 'root_angle': 0.21258503401360546, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.54594098501', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_147.110', 'Lhash_array': ['dirichlet_L_147.110'], 'factors': ['1-147-147.110-r0-0-0'], 'label': '1-147-147.110-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/147/110'}
Lfunction data - 1-147-147.110-r0-0-0