-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '460249858548355056722645353577', 'a10': [2.9097718244007145, -2.8379156304025255], 'a2': [-1.3031830900850958, 0.5492848384183391], 'a3': [-0.9888308262251285, -0.14904226617617444], 'a4': [1.3965723325674781, -1.4316374261338076], 'a5': [-2.6753947330278, 1.0500150571142868], 'a6': [1.3704942687855446, -0.3489204196173901], 'a7': [-0.927901979066279, -2.4777001265780494], 'a8': [-1.033612715595081, 2.6328016929043785], 'a9': [0.9555728057861407, 0.2947551744109042], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.6952036388512886, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.3031830900850958, -0.5492848384183391]]], [3, [[1.0, 0], [0.9888308262251285, 0.14904226617617444]]], [7, [[1.0, 0], [0.927901979066279, 2.4777001265780494]]]], 'bad_primes': [2, 3, 7], 'central_character': '588.187', 'coefficient_field': 'CDF', 'conductor': 588, 'conductor_radical': 42, 'conjugate': '1365376378537011668161043564246', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.3031830900850958, -0.5492848384183391]], [[1.0, 0], [0.9888308262251285, 0.14904226617617444]], [[1.0, 0], [2.6753947330278, -1.0500150571142868], [3.6652593591491316, -3.400863688854597]], [[1.0, 0], [0.927901979066279, 2.4777001265780494]], [[1.0, 0], [1.2131881327898149, 3.9330593273327983], [-9.088626517475944, 6.196520638699842]], [[1.0, 0], [-4.154326577579526, -0.9481979318180916], [11.71259528273145, 5.640488608528256]], [[1.0, 0], [1.4127400398747014, -2.0721090652897916], [-6.210797414228716, -15.824853726951472]], [[1.0, 0], [1.7771713800346927, -3.0781511239773858], [-9.5, -16.454482671904334]], [[1.0, 0], [0.08064650999135653, 0.11828670506988305], [-8.402843560427085, 21.410096218816697]], [[1.0, 0], [1.8806662852488785, -0.9056811494228996], [18.081204253903273, -22.673112991572864]], [[1.0, 0], [-2.0924920790232857, -3.624302595303761], [-15.5, 26.846787517317598]], [[1.0, 0], [0.2130321426337861, -2.8427163858743816], [-36.58674057032976, -5.5145638485184545]], [[1.0, 0], [-5.749317988778605, -4.584928100273841], [9.123358292208891, 39.97204439945477]], [[1.0, 0], [-0.5301898396704081, 0.4228122881929787], [9.56840016012152, -41.92190022381841]], [[1.0, 0], [-4.033809824205507, -3.7428285462642155], [3.51231439856194, 46.86857846751547]], [[1.0, 0], [-0.9877139218863134, -13.180126320792903], [-52.408033789931814, 7.899240107337246]], [[1.0, 0], [0.2594867872821443, -0.6611615512380142], [-43.25006043795975, -40.13019152848425]], [[1.0, 0], [8.242728425183298, 0.617707100958332], [60.31868039973284, 9.091578236746642]], [[1.0, 0], [13.269099545322275, -7.660918194395757], [33.5, -58.023702053557386]], [[1.0, 0], [-6.003572272601016, 12.466546279924417], [-44.26777593197008, -55.510035255230115]], [[1.0, 0], [-8.638061674421273, -9.309616407396573], [-5.455296831808971, 72.79587719422615]], [[1.0, 0], [-0.8030993070542193, -0.46366960111375544], [39.5, 68.41600689897065]], [[1.0, 0], [-3.425704023579794, -15.008989995148942], [-74.78041603590079, 36.01235034675732]], [[1.0, 0], [-4.14664425934729, 13.443090515444728], [-73.53525091412354, -50.13548516766236]], [[1.0, 0], [0, 1.939281035437233], [-97.0, 0]], [[1.0, 0], [-0.392702742770847, 2.6054124615628402], [-96.51285338440022, -29.770272615501327]], [[1.0, 0], [-4.208448957887355, -10.72295306611272], [-75.50434279847211, 70.0577919904047]], [[1.0, 0], [2.6840832582635454, -8.70158420522581], [-88.40754885181146, -60.27524621280756]], [[1.0, 0], [-17.33965981621823, 5.348576709600288], [90.06002640044345, -61.4018863289348]], [[1.0, 0], [0.6097919894519732, 2.67167326943867], [-101.80948207297337, 49.028862520284065]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 4, 'label': '2-588-196.187-c1-0-4', '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/588/2/ba/b/187/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.3643987833511737, 0.25797084028858924, 0.13210054359229564, -0.01499404510038488, -0.18450936233711873, -0.37578087738762644, -0.5852840705257693, -0.806000565288578, -1.0271846998456724, -1.2345538852908318, -1.4109270411346504, -1.5373257843984653, -1.5945233869855204, -1.564977718332876, -1.4350229189861257, -1.197129632976965, -0.8519859671847737, -0.41011223767808885, 0.10728720384832309, 0.6685033500757549, 1.232729564799448, 1.7527774171510275, 2.1790302528505556, 2.4643877762881754, 2.5697759764807797, 2.469639651942477, 2.1567269352922147, 1.6454423610186486, 0.9731069410964158, 0.19862980404147854, -0.601638437858896, -1.3407561138523902, -1.9302440840132504, -2.290464030193828, -2.3611313660037845, -2.1105850271779647, -1.542420945902636, -0.6982819550876961, 0.34401365978533127, 1.477259582693109, 2.5761447673120856, 3.51191555277016, 4.168686180085596, 4.459244805423944, 4.338061302713168, 3.8094007223496233, 2.928990369285998, 1.7985306521267206, 0.5533759186628872, -0.655207786464875, -1.680849676991811, -2.4029366552063967, -2.744309748320097, -2.6828760397020317, -2.2550300808279946, -1.5500048924924392, -0.6957338807682063, 0.16173594895008206, 0.8820405862073459, 1.3535623627066757, 1.511770397495264, 1.349514691592798, 0.9172562228106975, 0.31296142313602443, -0.3367226857943324, -0.9007148309215777, -1.2687283290811242, -1.3726961113349356, -1.2001674633796253, -0.7968665116525757, -0.2576388076485391, 0.29270131045216474, 0.7250211829883951, 0.9329625062689008, 0.8559355001966552, 0.4931125700254984, -0.09478898915799402, -0.796699466581345, -1.47340562440486, -1.9863852199866932, -2.227276154846849, -2.141614725623703, -1.7414786437304193, -1.1039030138956303, -0.35497389366258253, 0.3572903035655238, 0.895497977676413, 1.1636315695451978, 1.128837743404151, 0.8288810344161032, 0.36299660709140125, -0.13230066099924823, -0.5172176004820711, -0.6846081047231514, -0.589002571317206, -0.26104870938727587, 0.19726586711553376, 0.6368342556657715, 0.9005319397839936, 0.8685898126360295, 0.4993505565088784, -0.14530486214010413, -0.8977982571972002, -1.5089882375496964, -1.6955839988517225, -1.2020156662101835, 0.13624440641019805, 2.342358649042503, 5.2734178093537505, 8.629070342582475, 11.994190052538311, 14.908662011346598, 16.95088657367821, 17.817840218846335, 17.384507617159315, 15.729394508604226, 13.11990607030295, 9.960101278375049, 6.711724639838152, 3.805491795464872, 1.5618710020796969, 0.1384348380741943, -0.4853134899140804, -0.48349255997914126, -0.12689353470876685, 0.29182202250573697, 0.5321931955704435, 0.46136326807122413, 0.0779633385387194, -0.5001276555484973, -1.0794292627895166, -1.4531921568207442, -1.465084514852988, -1.0568834288710292, -0.28740998875195395, 0.682077259034408, 1.6315842463644605, 2.342739449817193, 2.658799957111132, 2.5274286368735974, 2.014195920118176, 1.2829868514398062, 0.5488493505411751, 0.01668144013215642, -0.17672260699182027, -0.0005926535535941139, 0.4629548873064909, 1.0452244937670436, 1.5428706376417791, 1.780283276349261, 1.66395716547679, 1.2124444130280143, 0.5524648635392185, -0.1183042158495041, -0.5911865324455066, -0.711475530492589, -0.4286300006809809, 0.18422739531423726, 0.9486174020643937, 1.632625452316068, 2.0217732736046687, 1.9877340117303437, 1.5334912330734898, 0.7997583875191318, 0.02861050471304512, -0.5068139637535785, -0.5868347749244948, -0.11886411272794462, 0.8230162528194371, 2.0066439715173003, 3.0988474064663274, 3.756719086954115, 3.7277704721269767, 2.929655819128552, 1.4847460417076737, -0.3029655332649989, -2.0246424382415578, -3.2770314852379294, -3.7757085080666473, -3.4382329928071287, -2.4118981909551587, -1.036148756264622, 0.25138666624401884, 1.0394385205900156, 1.0626521687358996, 0.28108489099705114, -1.1045263469211712, -2.7075401535962147, -4.06551097130236, -4.774269911666176, -4.606985611677573, -3.5830065318408417, -1.9656365728274532, -0.1887814843403387, 1.2665152119926502, 2.009590632852496, 1.8512955887566989, 0.8560137536796444, -0.680578052274592, -2.320956708041665, -3.615265382514024, -4.231896038561719, -4.050162481936609, -3.187965820311757, -1.9574256313885288, -0.7634907620641826, 0.02228102683764521, 0.17358038440680265, -0.3270881854605396, -1.2912999215388759, -2.3910575174459967, -3.2657788531835523, -3.6349516231345484, -3.380749896040076, -2.5756539880030744, -1.448659872223804, -0.30381468656850436, 0.5800877312465773, 1.0346896787736317, 1.044552243696201, 0.7349084681195656, 0.3119388877546923, -0.020843347868405342, -0.13876013079884522, -0.03684004203842099, 0.17899574871090196, 0.34617968136117694, 0.3237621763603986, 0.06383221657779829, -0.35292465760488606, -0.7338154214288932, -0.8398718813858593, -0.4787188579538653, 0.4091728334893836, 1.704462799016329, 3.124218944066478, 4.2985440008098355, 4.88624550708761, 4.69154118505855, 3.740734171191216, 2.289173557857907, 0.7513934918128824, -0.42626925224277395, -0.910134165474575, -0.5920794315966421, 0.3694413337751614, 1.5978599868168368, 2.624041336403557, 3.049340784938868, 2.6917403181957518, 1.6637966388208936, 0.35203925477077797, -0.7003036758818623, -0.9723537656429823, -0.14894052243836298, 1.753230829387685, 4.361563513592857], 'positive_zeros': ['0.36307312004229800848581699241567', '2.22519980550406112752422249530339', '3.65589336390072172935826807409277', '4.71058691516972008006198003227919', '6.05582749977515526943765820777098', '7.10044872518084991265908427539391', '7.934716198921215129390536365509567', '8.807016443026779739591183887680587', '9.481987805937519517897178661723670', '10.55989931959110970942866460477758'], 'prelabel': '2-588-196.187-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.166841858293145, 'root_angle': -0.5398915696795531, 'root_number': '-0.1249952684798546 - 0.9921573377532663*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.26994578484', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.36307312004229800848581699242', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.22519980550406112752422249530', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.65589336390072172935826807409', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 4.6952036388512886, 'bad_primes': [2, 3, 7], 'central_character': '196.187', 'conductor': 588, 'conductor_radical': 42, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/588/2/ba/b/187/4'], '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': '2-588-196.187-c1-0-4', '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': '2-588-196.187-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.166841858293145, 'root_angle': -0.26994578483977655, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.36307312004229800848581699242', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '460249858548355056722645353577', 'Lhash_array': ['460249858548355056722645353577'], 'label': '2-588-196.187-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/588/2/ba/b/187/4'}