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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_441.236', 'a10': [0.7330518718298263, 0.6801727377709194], 'a2': [-0.8262387743159949, 0.5633200580636221], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.36534102436639504, -0.9308737486442042], 'a5': [-0.2225209339563144, -0.9749279121818236], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.2225209339563144, 0.9749279121818236], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 2.047995390047135, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [7, [1]]], 'bad_primes': [3, 7], 'central_character': '441.236', 'coeff_info': ['x^42 - 1', '0.988830826225129 + 0.149042266176174*I', '\\\\zeta_{42}'], 'conductor': 441, 'conductor_radical': 21, 'conjugate': 'dirichlet_L_441.185', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^17', 0, 'a^34', 'a^30', 0, 0, 'a^9', 0, 'a^5', 'a^3', 0, 'a^17', 0, 0, 'a^26', 'a^8', 0, 'a^7', 'a^22', 0, 'a^20', 'a^27', 0, 'a^18', 'a^34', 0, 0, 'a^1', 0, 'a^7', 'a^1', 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'191.23004097802500933972137001080', '191.57309623554894665517898403248', '192.44294832566990998588930305605', '192.92589853105410106204124630170', '193.459749933559220759695058389048', '194.91415551136509152219845856104', '195.17067538593706742583665167120', '195.9972783334241599627704674258', '196.40385027129503277416619922844', '197.14169439601720603320157200131', '197.76209244670807835798241387901', '198.66221721004099547031762065805', '198.814444745532514824572020023768', '199.796755491477971575298682623934'], 'prelabel': '1-21e2-441.236-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.047995390047135, 'root_angle': 0.19274376417233557, 'root_number': '0.822204867777949273858731779834+0.569191668423076052234369057625*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0963718820862', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(42)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.737740626159341149617639660134+0.121688945331377281927479633901*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.06285790282', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.07026893879', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.99643779732', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 2.047995390047135, 'bad_primes': [3, 7], 'central_character': '441.236', 'conductor': 441, 'conductor_radical': 21, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/441/236'], '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': '1-21e2-441.236-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': '1-21e2-441.236-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.047995390047135, 'root_angle': 0.09637188208616779, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.06285790282', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_441.236', 'Lhash_array': ['dirichlet_L_441.236'], 'label': '1-21e2-441.236-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/441/236'}
Lfunction data - 1-21e2-441.236-r0-0-0