-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1360009245683880768969473216863', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-38.43869881969987, 66.57777933255802], 'a4': [0, 0], 'a5': [10.622602360600252, 18.39888699716073], 'a6': [0, 0], 'a7': [642.2835669515964, 641.1043749842408], 'a8': [0, 0], 'a9': [-1861.5671339031928, -3224.3288576207055], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 34.98712285422165, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-642.2835669515964, -641.1043749842408]]]], 'bad_primes': [2, 7], 'central_character': '112.81', 'coefficient_field': 'CDF', 'conductor': 112, 'conductor_radical': 14, 'conjugate': '970622818705687956356636378894', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [38.43869881969987, -66.57777933255802], [-1093.5, -1893.9975580765674]], [[1.0, 0], [-10.622602360600252, -18.39888699716073], [-39062.5, 67658.23467065927]], [[1.0, 0], [-642.2835669515964, -641.1043749842408]], [[1.0, 0], [-1633.070891737899, 2828.5617568518546], [-9743585.5, -16876385.133891404]], [[1.0, 0], [-10237.96993732235, 0], [62748517.0, 0]], [[1.0, 0], [-18264.561693121967, 31635.148830463484], [-205169336.5, -355363714.97319573]], [[1.0, 0], [16200.60381318707, 28060.268917734098], [-446935869.5, 774115633.6989733]], [[1.0, 0], [-8370.577900285793, -14498.266212008206], [-1702412723.5, 2948665332.5537066]], [[1.0, 0], [-43984.41884900102, 0], [17249876309.0, 0]], [[1.0, 0], [-66921.58181970246, 115911.57983460235], [-13756307055.5, -23826622744.64422]], [[1.0, 0], [-289938.51646155, -502188.24158254993], [-47465938566.5, 82213417226.12105]], [[1.0, 0], [532967.2845811946, 0], [194754273881.0, 0]], [[1.0, 0], [-365375.3345641196, 0], [271818611107.0, 0]], [[1.0, 0], [103431.69155676579, 179148.9448891112], [-253311560231.5, 438748492465.5019]], [[1.0, 0], [-544104.3592307672, 942416.3948073969], [-587355569918.5, -1017329689207.4161]], [[1.0, 0], [-80826.18164304426, 139995.05318754358], [-1244325742409.5, -2155235407019.1172]], [[1.0, 0], [-422154.0091778912, -731192.1925150056], [-1571371418010.5, 2721695133555.7383]], [[1.0, 0], [-613923.1948348072, 1063346.165398893], [-3030355802661.5, -5248730215220.885]], [[1.0, 0], [1107585.0302449844, 0], [9095120158391.0, 0]], [[1.0, 0], [819422.9930875581, -1419282.2569178115], [-5523699259548.5, -9567327763268.59]], [[1.0, 0], [2497106.4470911766, 4325115.238269722], [-9601954493079.5, 16631073033977.957]], [[1.0, 0], [-3383552.283669661, 0], [27136050989627.0, 0]], [[1.0, 0], [3268480.988844977, 5661175.136252466], [-22115667447764.5, 38305459662825.234]], [[1.0, 0], [-1359144.0946096187, 0], [80798284478113.0, 0]], [[1.0, 0], [5846175.765173022, -10125873.455257531], [-53606767605350.5, -92849645122004.47]], [[1.0, 0], [1086584.4376082812, 1882019.4526511976], [-61493693271243.5, 106510201090850.14]], [[1.0, 0], [-5382897.707615554, -9323452.32153618], [-80289073823921.5, 139064755155680.44]], [[1.0, 0], [-6187677.559550192, 10717371.913994731], [-91401956040834.5, -158312831773902.4]], [[1.0, 0], [19390942.13636563, 0], [235260548044817.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 16, 'label': '2-112-7.4-c7-0-16', 'leading_term': '1.749882719062563743690580049991718677032212240668902343', 'load_key': 'CMFs-workshop', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [7], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/112/8/i/a/81/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.07421875', 'prec': 34}, 'plot_values': [1.7498827190625637, 1.7404807323999956, 1.7010693143450164, 1.6338397981023944, 1.541452317253234, 1.42699400213029, 1.2939310771480566, 1.1460552222053526, 0.9874246128953995, 0.8223001162574112, 0.6550771914380308, 0.4902141274852572, 0.3321573424607436, 0.1852645673152891, 0.05372684202711382, -0.058509642795398525, -0.14782072203158494, -0.2109792157880285, -0.245226352344188, -0.24833826344909882, -0.21868611158582793, -0.15528838519842086, -0.05785390493870205, 0.07318587388961656, 0.23665659656147617, 0.4306339929490088, 0.6524511548835922, 0.8987209402347701, 1.1653740817755138, 1.4477132814446676, 1.7404832345392471, 2.0379561588393047, 2.3340320075043652, 2.6223521302163024, 2.8964247244349677, 3.149759999104379, 3.3760125691741947, 3.5691282242287246, 3.723491882216316, 3.8340732637467188, 3.89656661735452, 3.9075207043881712, 3.864455225332126, 3.7659599471161145, 3.611772980661512, 3.402834964058257, 3.141316330557901, 2.830615379535792, 2.4753255162837235, 2.0811707723699486, 1.6549095475844295, 1.2042074083179042, 0.7374807129050587, 0.2637137858669381, -0.2077466988620698, -0.6674155718293492, -1.1059058880293886, -1.5141724338833047, -1.8837553749006426, -2.2070170005830776, -2.4773643222528294, -2.6894502962997744, -2.839346695510852, -2.9246821434861885, -2.9447395626990676, -2.9005082580841313, -2.794687048774671, -2.631636245309701, -2.4172778139480675, -2.1589447309481202, -1.8651822576232504, -1.5455056052991525, -1.2101201470366532, -0.8696119065633579, -0.5346174502587223, -0.2154834632069735, 0.07807285228955757, 0.33729090826460556, 0.5546696254199469, 0.7242346214954765, 0.8417589570758336, 0.9049278676603609, 0.9134394925862721, 0.8690355753242366, 0.7754584044784125, 0.6383328229258348, 0.4649748715507813, 0.26413145907283414, 0.045658256056241554, -0.17985431117522757, -0.40149465475418983, -0.6084688107438058, -0.7905483881628562, -0.9385105679273995, -1.0445525714225103, -1.1026632247526518, -1.108935153490578, -1.0618027563088983, -0.9621933976311282, -0.8135821730600561, -0.6219440512680415, -0.39560106923234645, -0.14496641674604077, 0.11780846642687073, 0.3792734135289598, 0.6251912863935959, 0.8411039600178821, 1.0129314941653058, 1.1275811478715485, 1.1735414621973432, 1.1414361828734336, 1.0245133861160194, 0.8190468344948679, 0.5246293064811717, 0.14434134712311322, -0.3152165348373263, -0.8440349037530996, -1.4289505347992069, -2.054040418094534, -2.7011432601152, -3.3504912153148307, -3.9814291917610323, -4.573194457060304, -5.105725665371378, -5.560468038927646, -5.92114042842606, -6.1744304505019265, -6.310585898574238, -6.323874118428691, -6.212885934207936, -5.980666836705593, -5.634665271727448, -5.186495702392101, -4.651522330133312, -4.048277577171016, -3.3977372746063526, -2.7224815830215796, -2.0457766347345148, -1.3906164056332286, -0.7787671330382386, -0.22985749941448216, 0.239443310248491, 0.6161207133349296, 0.8913491258490702, 1.060838640154251, 1.1249753277446326, 1.0887459961945325, 0.9614484171699154, 0.7561984509576622, 0.4892556120688539, 0.17919793553487248, -0.15401497821375634, -0.49004558532282544, -0.8091993697444516, -1.0934120738463702, -1.3271528810500361, -1.498196618373702, -1.598223919455458, -1.6232164301632939, -1.5736241939858915, -1.4542938549056037, -1.274158700783689, -1.0457042135701367, -0.7842350316177729, -0.506980400436988, -0.23208466202925465, 0.022463450393638312, 0.23990444346468756, 0.4057248906821941, 0.5085594783125345, 0.5409252631154868, 0.49974315016472626, 0.38661231494342485, 0.2078162054100438, -0.025946776447621164, -0.3000995490813504, -0.5969659725791954, -0.8967558309810036, -1.1787045112603989, -1.4223064956581863, -1.6085746759814232, -1.7212539996145275, -1.7479183796698108, -1.6808842477999033, -1.5178824757002805, -1.262442293236318, -0.9239557270978156, -0.5174082245943342, -0.06277961047507222, 0.4158616582755051, 0.8915298850307801, 1.335701810952555, 1.7198336751391838, 2.0169348436026424, 2.2031115874542486, 2.2589937425216546, 2.1709610830015924, 1.9320952012430244, 1.5427961304621496, 1.011020231287472, 0.35211609775468283, -0.41174266362934636, -1.2525061951444434, -2.137535036107023, -3.031160903954681, -3.896440940059061, -4.697012092574819, -5.398944749269346, -5.972492841331156, -6.393641661043435, -6.645364473470538, -6.718514207579168, -6.6122963062512, -6.334292123998436, -5.900027775006785, -5.332109577160692, -4.658972655543309, -3.913312320745476, -3.130287090468852, -2.3455964435455137, -1.5935446296698152, -0.9052034977901994, -0.3067821354506231, 0.181700669888421, 0.5473629152842865, 0.7849693581199679, 0.8969759753379951, 0.8931084259230526, 0.7895028955276455, 0.6074650863752727, 0.37192727592889163, 0.10970272489068308, -0.15235003606091482, -0.38913431137178245, -0.5789763642159222, -0.7050321286706791, -0.7563471532279498, -0.7284996914087339, -0.6237839779622956, -0.45092100750826103, -0.22431563168802643, 0.03709054353058137, 0.31129318868925065, 0.5749259180128142, 0.8050706693275003, 0.9810518580925481, 1.0860877162599387, 1.1086801458865376, 1.0436405429999613, 0.8926724571700347, 0.6644612142157773, 0.3742538844473906, 0.04294805564757975, -0.30425757599608827, -0.6395661166490477, -0.9345276506527249, -1.1620959291303323], 'positive_zeros': ['1.07285812465913162608659216287929', '1.66792146921959299221710171536516', '3.97496804500164084641777848235819', '5.62010687581688194441933080990418', '6.54634827366561084924101940238601', '7.61144447498558929901340757068263', '8.485600288181441565317525714809623', '10.42526976507782221858042501806116', '11.17307671120388037049521930874747', '12.31337598722485002999978428125926'], 'prelabel': '2-112-7.4-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.914991365523846, 'root_angle': -0.11505975686942567, 'root_number': '0.749862718306704033882349681139060841882898823308516537 - 0.661593458019107558170868346592918081227384954181201601*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.11505975686942568', 'prec': 67}, 'spectral_label': 'c7-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.07285812465913162608659216288', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.66792146921959299221710171537', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.97496804500164084641777848236', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 34.98712285422165, 'bad_primes': [2, 7], 'central_character': '7.4', 'conductor': 112, 'conductor_radical': 14, 'degree': 2, 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/112/8/i/a/81/1'], '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': '2-112-7.4-c7-0-16', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [7], 'order_of_vanishing': 0, 'prelabel': '2-112-7.4-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.914991365523846, 'root_angle': -0.11505975686942567, 'self_dual': False, 'spectral_label': 'c7-0', 'z1': {'__RealLiteral__': 0, 'data': '1.07285812465913162608659216288', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1360009245683880768969473216863', 'Lhash_array': ['1360009245683880768969473216863'], 'factors': ['2-112-7.4-c7-0-16'], 'label': '2-112-7.4-c7-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/112/8/i/a/81/1'}