-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1157249836071287574327393456449', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [10562.184773443865, 0.0], 'a6': [0.0, 0.0], 'a7': [36457.995529921514, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 110.64141800058083, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '5.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '144.1', 'coefficient_field': 'CDF', 'conductor': 144, 'conductor_radical': 6, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-10562.184773443865, 0], [48828125.0, 0]], [[1.0, 0], [-36457.995529921514, 0], [1977326743.0, 0]], [[1.0, 0], [286882.754822316, 0], [285311670611.0, 0]], [[1.0, 0], [1974717.3914031994, 0], [1792160394037.0, 0]], [[1.0, 0], [-1342981.6958841516, 0], [34271896307633.0, 0]], [[1.0, 0], [-16872632.46597349, 0], [116490258898219.0, 0]], [[1.0, 0], [-39597621.03632165, 0], [952809757913927.0, 0]], [[1.0, 0], [-170464226.10299775, 0], [12200509765705828, 0]], [[1.0, 0], [159742423.9325809, 0], [25408476896404830, 0]], [[1.0, 0], [292344862.4881098, 0], [177917621779460400, 0]], [[1.0, 0], [222596802.05839336, 0], [550329031716248450, 0]], [[1.0, 0], [-828318326.0955665, 0], [929293739471222700, 0]], [[1.0, 0], [-671759766.4486463, 0], [2472159215084012500, 0]], [[1.0, 0], [3765687122.2222705, 0], [9269035929372190000, 0]], [[1.0, 0], [1139069408.8301783, 0], [30155888444737843000, 0]], [[1.0, 0], [-9138710413.618755, 0], [43513917611435835000, 0]], [[1.0, 0], [-8393075822.869445, 0], [122130132904968010000, 0]], [[1.0, 0], [-27351203437.57982, 0], [231122292121701580000, 0]], [[1.0, 0], [16222029845.014788, 0], [313726685568359700000, 0]], [[1.0, 0], [-19590570296.259598, 0], [747993810527521000000, 0]], [[1.0, 0], [-47977123367.79103, 0], [1287831418538085800000, 0]], [[1.0, 0], [2861278068.758, 0], [2775173073766990000000, 0]], [[1.0, 0], [-64715925185.99735, 0], [7153014030880804000000, 0]], [[1.0, 0], [139682569339.00427, 0], [11156683466653166000000, 0]], [[1.0, 0], [-167404228018.62988, 0], [13842338707244455000000, 0]], [[1.0, 0], [271875033785.98822, 0], [21048519522998347000000, 0]], [[1.0, 0], [-215539261081.92615, 0], [25804264053054076000000, 0]], [[1.0, 0], [47946685050.60707, 0], [38358611506121120000000, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 10, 'label': '2-12e2-1.1-c11-0-10', 'leading_term': '3.4574301089732633970472758120812', 'load_key': 'CMFs-workshop', 'motivic_weight': 11, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [11], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/144/12/a/t/1/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [3.4574301089732633, 3.4341203926036914, 3.3646548157287683, 3.2504145416290826, 3.0936698505711115, 2.897533300470254, 2.665895437127337, 2.403344312391978, 2.1150703900432815, 1.806758712769238, 1.484470463982019, 1.154516280410838, 0.823323851103313, 0.49730247190426347, 0.18270730863021356, -0.11449384525515635, -0.3887485510871033, -0.6350397562138773, -0.8489953099164025, -1.0269845792622765, -1.1662000091918, -1.2647217468032297, -1.3215637679550876, -1.3367002999045454, -1.3110717208589149, -1.2465695293414314, -1.1460004057603197, -1.013029827510707, -0.8521061388349406, -0.6683664086735659, -0.4675258248196494, -0.2557527617832311, -0.039532013978134106, 0.17448100339504286, 0.3796120240914099, 0.569322408939304, 0.7373629345870221, 0.8779234299421682, 0.9857748064192764, 1.056400113900264, 1.0861114177534852, 1.0721495325829056, 1.0127639630642358, 0.9072707869501114, 0.7560866639793941, 0.5607376591465905, 0.323842120058077, 0.04906743488091915, -0.25893889270653964, -0.5946427956276218, -0.9517401518553374, -1.3232939833067439, -1.701889518881176, -2.079803784634799, -2.449185937517906, -2.8022441901829325, -3.131434895296848, -3.4296491790665065, -3.6903924437651128, -3.9079521040122533, -4.077549084831331, -4.1954688916230065, -4.259168460636862, -4.267355507638241, -4.220037703439409, -4.118539705896235, -3.9654868540429207, -3.764755163753997, -3.5213881358563177, -3.241481775222751, -2.932040099909267, -2.6008042688476585, -2.2560592507536494, -1.9064226719716029, -1.560621094298325, -1.2272594645779102, -0.9145898277077508, -0.6302855884599388, -0.3812276337544189, -0.17330847851880835, -0.01126027249407713, 0.10148799528468821, 0.16291942553730226, 0.17250042505386712, 0.13121132340566038, 0.041534576949914734, -0.0926000916180243, -0.2659130514750306, -0.4719128109157694, -0.7030717148613838, -0.9510350725368298, -1.2068583994317783, -1.4612664831742357, -1.704927163362965, -1.9287320810177682, -2.124076230022032, -2.283127951269356, -2.3990810644389926, -2.4663811396745605, -2.480918471656213, -2.4401811235078728, -2.3433624415860006, -2.1914186805776117, -1.9870737902364701, -1.7347699625447852, -1.4405641773560858, -1.1119726672754087, -0.7577668970156889, -0.3877262653423608, -0.012354235505830967, 0.3574340690579533, 0.7106436514087396, 1.036540800809738, 1.3249930541311377, 1.5667971488612622, 1.7539842607326896, 1.8800922719856301, 1.9403956160215785, 1.9320843758195434, 1.854385750570946, 1.7086227099392113, 1.4982065802168134, 1.2285623943500212, 0.9069880236886274, 0.542450323108896, 0.1453236891114194, -0.2729215221833002, -0.7000714168366237, -1.1235509341641365, -1.5308240120624803, -1.9097985063036287, -2.2492223596385403, -2.539057503047598, -2.770818422569402, -2.9378632392726525, -3.0356265092203567, -3.061784720523165, -3.0163475959149237, -2.9016707373534603, -2.722387796894658, -2.4852631380555805, -2.1989687690057105, -1.8737920836899091, -1.5212835388855275, -1.1538557263559164, -0.7843472781145434, -0.4255665876735151, -0.0898313725694509, 0.21147940878438642, 0.4683448732768528, 0.6724770511146272, 0.8176368280424692, 0.8998784286500777, 0.9177122401290695, 0.87217857272336, 0.7668280923119593, 0.6076080343280368, 0.40265679669131266, 0.16201298478103054, -0.10275168749871673, -0.37896317948917396, -0.653324467435505, -0.9124261780205168, -1.143269693016458, -1.3337830390285987, -1.473309739733418, -1.5530514266780993, -1.5664463746447668, -1.509468215576536, -1.3808318290117063, -1.1820967174117119, -0.9176619375229059, -0.5946507388233784, -0.22268730571781895, 0.18642775080332416, 0.6191324207811874, 1.060594354031183, 1.495260190300994, 1.9074427566036571, 2.281923830554709, 2.6045491131707887, 2.8627919035377354, 3.0462627491281715, 3.147144050610191, 3.1605311824457316, 3.0846650673551865, 2.921045196287131, 2.6744166676887544, 2.3526297569747268, 1.966375626441636, 1.5288068431247026, 1.0550561793615687, 0.5616715252115843, 0.0659884540213726, -0.4145351152181503, -0.8629957606473214, -1.2637056029914535, -1.602810457756873, -1.8688393315166758, -2.053161928674083, -2.150334282040379, -2.1583169627603636, -2.0785553990847423, -1.9159174407955428, -1.6784892208825024, -1.3772363439919828, -1.0255432193546843, -0.6386487035931602, -0.2330008882342003, 0.1744423563061065, 0.5669377647982, 0.9286751820271387, 1.245459190430756, 1.5053240081166077, 1.6990542640850077, 1.8205879502819093, 1.8672826404676994, 1.8400317666484602, 1.7432241235668267, 1.5845465639473824, 1.3746367610729688, 1.1265996481373526, 0.8554073942014986, 0.5772082576750953, 0.3085741110853505, 0.06571963661036447, -0.1362720175438463, -0.2841820626800602, -0.3673136184326518, -0.378043063495716, -0.3122385456756653, -0.1695245647481919, 0.04662185073658015, 0.3289504705153342, 0.6666919563020814, 1.0459780427157337, 1.450411436025825, 1.8617619787882433, 2.260759488595929, 2.627948781003934, 2.9445689784859432, 3.193417473957447, 3.359658970509543, 3.4315418898803314, 3.400988078712114, 3.264027008728821, 3.021052351042073, 2.6768866219938743, 2.2406482058387223, 1.7254240719136102, 1.1477605078552322, 0.5269927652139561, -0.11555774934302232, -0.7574835825562066, -1.376248509453379, -1.9501586662236259, -2.4593030419797954], 'positive_zeros': ['0.912909153250063435981704558500976', '2.01143900556977213023236143023934', '2.94789604103584933305580191471270', '5.00518225661839339093114826712186', '5.33408253897021989392462519550627', '6.81456276176915912878331360185246', '7.83448411675412657729886145820683', '9.205309321916639519767826333106215', '9.913729654100494335298439170468680', '10.84709380781366376862700380918026'], 'prelabel': '2-12e2-1.1-c11-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.518622438350985, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c11-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.912909153250063435981704558501', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.01143900556977213023236143024', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.94789604103584933305580191471', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 110.64141800058083, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 144, 'conductor_radical': 6, 'degree': 2, 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/144/12/a/t/1/3'], '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': '2-12e2-1.1-c11-0-10', 'motivic_weight': 11, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [11], 'order_of_vanishing': 0, 'prelabel': '2-12e2-1.1-c11-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.518622438350985, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c11-0', 'z1': {'__RealLiteral__': 0, 'data': '0.912909153250063435981704558501', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1157249836071287574327393456449', 'Lhash_array': ['1157249836071287574327393456449'], 'label': '2-12e2-1.1-c11-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/144/12/a/t/1/3'}