-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '3665406339760983222343592608176', 'a10': [1.603627345569151, 1.345603114212875], 'a2': [-0.9730448705798238, 0.23061587074244017], 'a3': [-0.5982384014813555, -1.625457109551966], 'a4': [0.8936326403234123, -0.44879918020046217], 'a5': [-1.2500839290696595, -1.6791541247658928], 'a6': [0.9569690146191229, 1.443679432927859], 'a7': [-0.7257418451144687, 0.4773279205326034], 'a8': [-0.766044443118978, 0.6427876096865394], 'a9': [-2.284221629986065, 1.9448217257897455], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.293576512744743, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.9730448705798238, -0.23061587074244017]]], [3, [[1.0, 0], [0.5982384014813555, 1.625457109551966]]]], 'bad_primes': [2, 3], 'central_character': '162.157', 'coefficient_field': 'CDF', 'conductor': 162, 'conductor_radical': 6, 'conjugate': '627243130295608978009889314797', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.9730448705798238, -0.23061587074244017]], [[1.0, 0], [0.5982384014813555, 1.625457109551966]], [[1.0, 0], [1.2500839290696595, 1.6791541247658928], [-1.4340161635554514, 4.789947561577445]], [[1.0, 0], [0.7257418451144687, -0.4773279205326034], [2.772558362274098, -6.427512748161918]], [[1.0, 0], [4.158870387865508, 0.4861022321913543], [10.703493576378062, 2.536774578166842]], [[1.0, 0], [0.6449155892790203, 2.15416808596584], [-10.861341548368173, 7.143616714920478]], [[1.0, 0], [-0.7666327206402015, 4.347790210890837], [-15.974774553360442, -5.814342436536369]], [[1.0, 0], [-0.162474013562232, -0.9214359192758076], [-17.854159794932258, 6.498382723187706]], [[1.0, 0], [1.333127991961216, 0.8768120737288959], [9.109834618900607, 21.118970458246302]], [[1.0, 0], [1.000763679199939, 1.060747529040117], [-1.686200038403799, 28.950936589866778]], [[1.0, 0], [-0.025975650581316945, 0.44598469679322517], [-30.790389090000232, -3.5988803378821372]], [[1.0, 0], [-6.437791356187058, 2.343164428068336], [28.343644395402187, -23.783141558401955]], [[1.0, 0], [-12.17452411624602, -2.8854152206463826], [36.6389382532599, 18.400766388218948]], [[1.0, 0], [4.1022229015248195, 9.51002162988765], [-29.508390428355543, 31.277066587641094]], [[1.0, 0], [-0.6036508537060715, -10.364284895051304], [-46.68220281387132, 5.456366963885821]], [[1.0, 0], [-6.723112886905705, 11.644773105141752], [-26.5, -45.89934640057525]], [[1.0, 0], [3.4811897127758713, -0.4068927213984276], [57.409647364209604, -13.60633637380397]], [[1.0, 0], [9.529306414800319, 4.785797556917351], [36.426674093869956, 48.92951475805767]], [[1.0, 0], [-8.97123499012983, 9.508953558172893], [-3.8957035370018804, -66.88664660417497]], [[1.0, 0], [5.721485493262669, 4.8008963671828635], [12.329020614352055, 69.92135046386677]], [[1.0, 0], [-0.29851092384373873, 0.2504804060996703], [12.676316969685915, -71.89096596989118]], [[1.0, 0], [12.588771776986095, -2.983593719781438], [70.59697858554956, -35.455135235836515]], [[1.0, 0], [-1.5641506501368845, 0.37071051403695776], [74.17150914684322, -37.25033195663836]], [[1.0, 0], [-8.4871540061751, 7.121567796326301], [15.4546878123568, -87.64789001808651]], [[1.0, 0], [-2.0731546167486044, 2.784729924959214], [-27.819913572975754, -92.92498269460242]], [[1.0, 0], [-7.644915576026991, -3.839420907881052], [60.3130177619814, 81.01444246825942]], [[1.0, 0], [6.278632188917167, -0.7338668526545634], [100.22362166972185, -23.753434686471337]], [[1.0, 0], [-3.6096615410240753, -6.252117187181067], [-53.5, 92.66471820493493]], [[1.0, 0], [10.128407393454754, -17.542916205219896], [-54.5, -94.39676901250381]], [[1.0, 0], [6.772280580667473, -15.699911085249958], [-77.5453050791669, -82.19322149775451]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 7, 'label': '2-162-81.76-c1-0-7', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/162/2/g/a/157/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.41877807157660196, 0.5256350818652573, 0.6411075810247753, 0.7681042997591185, 0.908205246648967, 1.061487896664191, 1.2264690651642314, 1.4001120760137706, 1.577871219159661, 1.7537727035740946, 1.9205490203040663, 2.069849678164093, 2.1925487517090194, 2.2791619509613597, 2.3203751498809946, 2.3076737038438018, 2.2340482644706148, 2.0947389957358764, 1.8879671415428028, 1.6155920568270576, 1.283624521156054, 0.9025248688321776, 0.4872185171873527, 0.056772844957201175, -0.3663014799892851, -0.7571349630169226, -1.0899467202724975, -1.3397946772482843, -1.4845295218342809, -1.506816939070791, -1.3960627442081717, -1.1500565420392073, -0.7761455069853034, -0.29176397107081653, 0.2758215010899471, 0.8906380813631276, 1.5100189577088594, 2.0874331427996107, 2.5759741465391746, 2.9322619254686213, 3.120438499525869, 3.1158866036793325, 2.908281807558737, 2.503608512538534, 1.9248324866315765, 1.211026065711922, 0.41488078697726916, -0.4012950461347335, -1.1708250420461421, -1.8287295765929132, -2.318045608658646, -2.5957581931298237, -2.637682999299342, -2.4416958911278908, -2.0288381478136066, -1.442026574192378, -0.7423495108969528, -0.003207118903085685, 0.6971743578147578, 1.2840937521098386, 1.694673439890104, 1.885129803388952, 1.8361001577852551, 1.5552902898232053, 1.0769936533032538, 0.45839908024086545, -0.22699308209652488, -0.8981369086077452, -1.4763568579201851, -1.8951754103362008, -2.108761432799637, -2.097828578638015, -1.8721024898114227, -1.468906088628341, -0.9479329678289014, -0.3828215780570344, 0.14936956375856733, 0.5793284232916118, 0.8556761816622358, 0.9526191766235106, 0.8738151503937195, 0.6517153812814731, 0.34230182672281634, 0.015850244282252086, -0.25499008488950364, -0.40800874462032966, -0.40309607829262495, -0.23076813329171963, 0.08405428325749913, 0.48395881376543076, 0.8867307414243799, 1.1979630592900214, 1.3268634016371492, 1.2028810693842942, 0.7904633134185284, 0.09935141042039528, -0.8116414941671092, -1.8385221939460088, -2.843669390068094, -3.6737930541887787, -4.181921086699318, -4.250215356422996, -3.810066965908261, -2.85612346106192, -1.4516618131629242, 0.276049651238825, 2.150233984649952, 3.967184452065337, 5.523809210143688, 6.646071651881634, 7.2139386417783085, 7.178838648611865, 6.57069801513121, 5.493217939638182, 4.107930523353225, 2.6094221197472334, 1.1956188352524408, 0.03792037021980786, -0.7439317228604408, -1.0981011301243258, -1.0453386973641043, -0.6713857409918296, -0.10851521454556202, 0.49045619175351074, 0.9809994084133362, 1.2533336633481278, 1.2517150915597417, 0.983052962610193, 0.513322525824116, -0.04747132716899903, -0.5688474050801489, -0.9273316764671433, -1.0324815876715676, -0.8462874046531692, -0.39202202779531686, 0.24935924204758403, 0.954720345072291, 1.583206503998621, 2.0048645573968944, 2.127676110381746, 1.9174482400063446, 1.406325656335726, 0.6879036874890254, -0.1003891607737955, -0.8043406537112814, -1.2841082011076344, -1.4431548780817487, -1.248928861678382, -0.740788265733769, -0.023196019444911366, 0.7547785105769156, 1.4297253149295954, 1.85784408340203, 1.9455493242145077, 1.6702045653165747, 1.086358208949431, 0.3157916858043974, -0.4769202005067248, -1.1185032531373535, -1.4636993452905949, -1.4268090708304688, -1.0011570474628648, -0.2619815502628479, 0.6482949368854543, 1.5496667840111389, 2.262956152203987, 2.648873670728077, 2.639187573881646, 2.252940094538927, 1.5937317121072092, 0.8281552508007424, 0.14964074447093226, -0.2646525665362675, -0.2944668528705691, 0.09458711083779427, 0.8406095135078481, 1.7964978789467245, 2.7607731884718842, 3.521875903948477, 3.906400991786379, 3.820499792554705, 3.2748094604458906, 2.3866120326387037, 1.357806413871921, 0.4326576593777204, -0.15602192401982676, -0.24068447956708933, 0.23915790012689203, 1.2169269650962733, 2.5060423055113623, 3.8335234648805065, 4.893726855244937, 5.4111983141367155, 5.199329378547302, 4.202107461973869, 2.5096789806570814, 0.34399069436051755, -1.9827664621158556, -4.128250608437548, -5.785867884187911, -6.742478973666546, -6.91576319114432, -6.363653858204621, -5.264509491112584, -3.8731960869074267, -2.4635293385221515, -1.2703452897744105, -0.4441877282083468, -0.028303819466018506, 0.03787451499975569, -0.10901272322698237, -0.30029066510343855, -0.3839104719397986, -0.26529353140682765, 0.06975233980519827, 0.5553251201617605, 1.068101051840769, 1.465722650417257, 1.6301630828446212, 1.5040680590656839, 1.1099734422368617, 0.5468834332309923, -0.035199863624215115, -0.47616463473778115, -0.6510889588116194, -0.5074319163882718, -0.08341910854955051, 0.4983070443046079, 1.0611696418660885, 1.4220555450859735, 1.4434768833651488, 1.0764636053945926, 0.3819523374056003, -0.4764152718675808, -1.2678962187123792, -1.7508925456673727, -1.7361984446322638, -1.1410322310278118, -0.019192335962821536, 1.4418666946540553, 2.9581384974447857, 4.212694433019271, 4.93101992046521, 4.949584852687757, 4.260110333446683, 3.0174502307981164, 1.5077448470389223, 0.08339694516301026, -0.9200285148329943, -1.2648990320382625, -0.8704879846957958, 0.1652333135167977, 1.5870631887374413, 3.0426687163619306, 4.166954121852135, 4.670078746744152, 4.407382270683683], 'positive_zeros': ['2.89149576318668478118595334983012', '4.19107606501831344389353880077973', '5.81328812919611735813494082591070', '7.12554713709543517743583494986900', '8.209044634741029786383589077128186', '9.463087988255789681815788952428554', '10.38141551581282488342283116618265', '10.97069018707506946764561071830569', '11.88999690254385834027291881693695', '13.10605610190429940022964979306315'], 'prelabel': '2-162-81.76-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1373550513119213, 'root_angle': 0.8225872933117659, 'root_number': '-0.8486553051359689 + 0.5289462856137432*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.411293646656', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.89149576318668478118595334983', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.19107606501831344389353880078', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.81328812919611735813494082591', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1.293576512744743, 'bad_primes': [2, 3], 'central_character': '81.76', 'conductor': 162, 'conductor_radical': 6, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/162/2/g/a/157/2'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, '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': '2-162-81.76-c1-0-7', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-162-81.76-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1373550513119213, 'root_angle': 0.41129364665588297, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.89149576318668478118595334983', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '3665406339760983222343592608176', 'Lhash_array': ['3665406339760983222343592608176'], 'label': '2-162-81.76-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/162/2/g/a/157/2'}