-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2114713876411569346797858417269', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, -1.0], 'a4': [0, 0], 'a5': [1.4811943040920157, -1.6751308705666461], 'a6': [0, 0], 'a7': [0, 1.0], 'a8': [0, 0], 'a9': [-1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 13.414867539575111, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 1.0]]], [5, [[1.0, 0], [-1.4811943040920157, 1.6751308705666461]]], [7, [[1.0, 0], [0, -1.0]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '1680.1009', 'coefficient_field': 'CDF', 'conductor': 1680, 'conductor_radical': 210, 'conjugate': '674044257856354092750295294397', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [-1.4811943040920157, 1.6751308705666461]], [[1.0, 0], [0, -1.0]], [[1.0, 0], [0.3878731329492609, 0], [11.0, 0]], [[1.0, 0], [0, 2.9623886081840314], [-13.0, 0]], [[1.0, 0], [0, 3.3502617411332922], [-17.0, 0]], [[1.0, 0], [2.9623886081840314, 0], [19.0, 0]], [[1.0, 0], [0, -0.9623886081840313], [-23.0, 0]], [[1.0, 0], [1.2242537341014783, 0], [29.0, 0]], [[1.0, 0], [2.9623886081840314, 0], [31.0, 0]], [[1.0, 0], [0, 5.924777216368063], [-37.0, 0]], [[1.0, 0], [-1.0376113918159688, 0], [41.0, 0]], [[1.0, 0], [0, 10.700523482266584], [-43.0, 0]], [[1.0, 0], [0, -3.2242537341014783], [-47.0, 0]], [[1.0, 0], [0, 5.662912090450615], [-53.0, 0]], [[1.0, 0], [-3.2242537341014783, 0], [59.0, 0]], [[1.0, 0], [-14.625300698634646, 0], [61.0, 0]], [[1.0, 0], [0, 0], [-67.0, 0]], [[1.0, 0], [5.5369040834188015, 0], [71.0, 0]], [[1.0, 0], [0, -6.186642342285509], [-73.0, 0]], [[1.0, 0], [13.924777216368062, 0], [79.0, 0]], [[1.0, 0], [0, 3.2242537341014783], [-83.0, 0]], [[1.0, 0], [3.738134874082553, 0], [89.0, 0]], [[1.0, 0], [0, -7.738134874082553], [-97.0, 0]], [[1.0, 0], [7.587689306818678, 0], [101.0, 0]], [[1.0, 0], [0, 14.700523482266584], [-103.0, 0]], [[1.0, 0], [0, -16.438658356349137], [-107.0, 0]], [[1.0, 0], [-2.7757462658985217, 0], [109.0, 0]], [[1.0, 0], [0, -4.261865125917447], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 30, 'label': '2-1680-5.4-c1-0-30', 'leading_term': '1.458847712455273121756421576217676000706430554741654589', '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/1680/2/t/i/1009/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.4588477124552732, 1.605248202416809, 1.7486090348761616, 1.8885699146258876, 2.024504997415528, 2.155490833581523, 2.2802932443974715, 2.397373294441571, 2.5049113682589637, 2.6008475481769078, 2.6829360262772552, 2.7488111006773766, 2.7960623049022315, 2.8223163006519987, 2.825323252559272, 2.803045453091388, 2.7537459599882705, 2.6760749529824963, 2.5691514304171643, 2.432637775995401, 2.2668046591069975, 2.0725837150311515, 1.8516055060821621, 1.6062204089085619, 1.339500318839201, 1.055219416056954, 0.7578127015713986, 0.45231157899734453, 0.144256421080568, -0.160413197532268, -0.4554891179435456, -0.7346437455930904, -0.9915945688708788, -1.2202800723916132, -1.4150423166424535, -1.5708107999379948, -1.6832816953611, -1.7490861982756392, -1.7659415594136927, -1.732778439923861, -1.6498385271344973, -1.5187369042631225, -1.3424844758708847, -1.1254668053549142, -0.8733770022237547, -0.5931017752796588, -0.29256140223562155, 0.019493894355924225, 0.3337268907495085, 0.6404895893117367, 0.9301250265816638, 1.1932854618221242, 1.4212564923071414, 1.6062757023978902, 1.741833891792189, 1.8229467968411992, 1.8463855563747784, 1.8108550022530798, 1.7171101779868825, 1.568003288544619, 1.3684555214095042, 1.125350791740292, 0.8473513708771275, 0.5446384562045661, 0.22858391433611822, -0.0886374505057587, -0.39448282158075143, -0.6765086058735928, -0.9228529602062633, -1.1227150316978118, -1.2668114730142788, -1.3477907012007835, -1.3605861030465856, -1.3026909700300744, -1.1743403554347118, -0.978588230260349, -0.7212721794730577, -0.41086229532891216, -0.05819572586582296, 0.32389666806078166, 0.7210601179113177, 1.1179660546836754, 1.4989221008684677, 1.8485179664764655, 2.152280600670805, 2.397310350058432, 2.57286947358247, 2.670895245634582, 2.6864120712489443, 2.6178205073953946, 2.467045737257976, 2.239533723035779, 1.9440897524940273, 1.5925611297008122, 1.1993730347933895, 0.7809337567634144, 0.35493223934624074, -0.060443171566549485, -0.44733105440402915, -0.7890311505476313, -1.0708075481960682, -1.280621835741728, -1.409759120471719, -1.4533135551901029, -1.4105055387714533, -1.2848098645893304, -1.083882502457691, -0.8192830554495278, -0.505999808304351, -0.16179420842834114, 0.19360890140170908, 0.5394504429306972, 0.8549436741377787, 1.1203108975313116, 1.317799909941535, 1.4326291008990064, 1.4538119641962222, 1.3748162069749057, 1.1940194969072504, 0.9149329228550632, 0.5461740753661269, 0.10118378816323854, -0.40230656061762776, -0.9430373509580078, -1.4971804456573834, -2.0394530711715695, -2.544333392169351, -2.987318560200063, -3.346162140891956, -3.6020271337771503, -3.740493438865507, -3.7523645650996356, -3.6342274090231785, -3.3887306735024607, -3.024561401421111, -2.5561144861083256, -2.002866102399198, -1.3884779281513988, -0.739673924082683, -0.08494446593828951, 0.5468569909152038, 1.1279524348505527, 1.6330374008709072, 2.0405637752681876, 2.3338372845878643, 2.501868481437243, 2.5399284505277944, 2.4497758467616495, 2.239539452782334, 1.9232592679485279, 1.5201081772264333, 1.0533344181730036, 0.5489813074365071, 0.0344540270343931, -0.46298713168242905, -0.9177224540994374, -1.307172378713061, -1.6130204175818978, -1.8221881373036437, -1.9275045115319402, -1.9280291770768654, -1.8290090336051872, -1.6414690975038282, -1.3814603064090858, -1.0690077737400672, -0.726821539459722, -0.3788469849283447, -0.04874278449576253, 0.24162019389334458, 0.47354570446339594, 0.6326971357175925, 0.7100045205947283, 0.7022336000490771, 0.6121772861155023, 0.44845302982070656, 0.2249142501407675, -0.040291383306264285, -0.32596094329579006, -0.6092966110479885, -0.8674958608161922, -1.0793697312158064, -1.2268835260352813, -1.2965170161893416, -1.2803505891501907, -1.1767993816016582, -0.990938397089034, -0.7343867496324075, -0.4247469842387827, -0.08462419221628995, 0.25972245819216455, 0.5800179321605528, 0.8478005841001225, 1.0363287392668252, 1.1224428050412159, 1.0882606890780817, 0.9225917513618468, 0.621969567126059, 0.19122565184254, -0.35644624046430895, -0.9999542219506141, -1.7112863232780482, -2.4569547011315542, -3.1998271291165157, -3.901240149172353, -4.523267678954205, -5.031005942729773, -5.394731340294167, -5.5917927688691345, -5.608113857756904, -5.43920285999823, -5.0905973008843315, -4.57770514734897, -3.925042083084136, -3.164903043613588, -2.335542973104052, -1.4789743621545914, -0.6385152916285197, 0.1437603996892788, 0.8295109159617255, 1.3863943966647028, 1.78997141847838, 2.0251187370270607, 2.0868614187692156, 1.9805675435501677, 1.721490829461887, 1.3336891533486595, 0.8483881772324945, 0.30189635272854515, -0.26679209225276374, -0.8185481170672221, -1.3166436908908095, -1.7291036811146456, -2.0307167560051025, -2.204570773160102, -2.2430100160528283, -2.147950817895062, -1.9305359586459956, -1.6101537581904566, -1.212891876275919, -0.7695353829317914, -0.31325086945058267, 0.12287910820090449, 0.5082958150945043, 0.817204055649113, 1.0304510166597245, 1.136908447258231, 1.1342572939454916, 1.0291163279795175, 0.8365032922356158, 0.5786653436211873, 0.2833616258079516, -0.018278666444771195, -0.294167367808666, -0.5137611467008727, -0.6504731643491433, -0.683812656572421, -0.60109064345495], 'positive_zeros': ['1.66821510282946547914017341764569', '2.75027625346384550231324048306648', '3.79210960496064903669336808824385', '4.57948093329126913116799050014625', '5.67487280491658869331510574775428', '6.41341815869977239177429424352830', '7.10210523485312717754006984472535', '8.152230698652909033678314632694199', '8.968803425662126432300952902476486', '9.794356389261152945571180931281840'], 'prelabel': '2-1680-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.6626312317205936, 'root_angle': 0.7304663929790445, 'root_number': '-0.66241023036704836934394295657888095753754327898659579537 + 0.74914129955908445453105880718175956359649879110032479350*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.3652331964895223', 'prec': 60}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.66821510282946547914017341765', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.75027625346384550231324048307', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.79210960496064903669336808824', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 13.414867539575111, 'bad_primes': [2, 3, 5, 7], 'central_character': '5.4', 'conductor': 1680, 'conductor_radical': 210, 'degree': 2, 'index': 30, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1680/2/t/i/1009/3'], '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': '2-1680-5.4-c1-0-30', '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': '2-1680-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.6626312317205936, 'root_angle': 0.36523319648952224, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.66821510282946547914017341765', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2114713876411569346797858417269', 'Lhash_array': ['2114713876411569346797858417269'], 'label': '2-1680-5.4-c1-0-30', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1680/2/t/i/1009/3'}