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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1323.401', 'a10': [-0.2225209339563144, 0.9749279121818236], 'a2': [0.5837436722347898, -0.8119380057158565], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.31848665025168443, -0.9479273461671317], 'a5': [-0.9214762118704076, 0.38843479627469474], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.9555728057861407, -0.2947551744109042], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 142.1760955032889, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [7, [1]]], 'bad_primes': [3, 7], 'central_character': '1323.401', 'coeff_info': ['x^126 - 1', '0.998756921218922 + 0.0498458856606972*I', '\\\\zeta_{126}'], 'conductor': 1323, 'conductor_radical': 21, 'conjugate': 'dirichlet_L_1323.452', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^107', 0, 'a^88', 'a^55', 0, 0, 'a^69', 0, 'a^36', 'a^107', 0, 'a^58', 0, 0, 'a^50', 'a^45', 0, 'a^0', 'a^17', 0, 'a^88', 'a^67', 0, 'a^110', 'a^39', 0, 0, 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'187.33537069267948807972865878660', '188.184614841651073508729595810392', '188.61852304688492832551946215955', '189.55501650597554535020440128115', '190.42078061571799977677820891722', '190.68857022963691916228620846566', '191.13703861724287786227228239365', '191.95371206708623324467397231208', '192.47883144672942621577379431818', '192.7554049041575521950453059378', '193.777389067156071259612760256779', '194.21358997971672373728168740739', '194.5908711540024261543953104407', '195.40870003762937812688013005452', '195.62249511734757374029694664453', '196.22746964509291292672855022755', '197.190415926533301238884311675879', '197.56102814257255044902082234416', '198.39354854368239058870325152666', '199.09854547115567052909983801778', '199.544433833365116047634086584318'], 'prelabel': '1-1323-1323.401-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 142.1760955032889, 'root_angle': -0.15230536659108088, 'root_number': '0.576005351657970830198324340590-0.817445921673952301194838465342*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.152305366591', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(126)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.907643734658938124374103346985-0.436878590893952684608912636428*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.516461118406', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.74431182991', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.76756572551', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 142.1760955032889, 'bad_primes': [3, 7], 'central_character': '1323.401', 'conductor': 1323, 'conductor_radical': 21, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1323/401'], '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': '1-1323-1323.401-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': '1-1323-1323.401-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 142.1760955032889, 'root_angle': -0.15230536659108088, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.516461118406', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1323.401', 'Lhash_array': ['dirichlet_L_1323.401'], 'factors': ['1-1323-1323.401-r1-0-0'], 'label': '1-1323-1323.401-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1323/401'}
Lfunction data - 1-1323-1323.401-r1-0-0