-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '897265217114550678567956042365', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [-5.0, 0.0], 'a6': [0.0, 0.0], 'a7': [9.465485281243435, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 63.722062806199894, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [5.0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '1080.1', 'coefficient_field': 'CDF', 'conductor': 1080, 'conductor_radical': 30, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [5.0, 0]], [[1.0, 0], [-9.465485281243435, 0], [343.0, 0]], [[1.0, 0], [49.04737504948102, 0], [1331.0, 0]], [[1.0, 0], [-55.44383089321132, 0], [2197.0, 0]], [[1.0, 0], [-27.97834561196789, 0], [4913.0, 0]], [[1.0, 0], [-26.396455843730305, 0], [6859.0, 0]], [[1.0, 0], [9.534514718756565, 0], [12167.0, 0]], [[1.0, 0], [218.378867729115, 0], [24389.0, 0]], [[1.0, 0], [158.96075749735257, 0], [29791.0, 0]], [[1.0, 0], [-189.65498547916752, 0], [50653.0, 0]], [[1.0, 0], [-246.14619142185984, 0], [68921.0, 0]], [[1.0, 0], [-40.23267630725514, 0], [79507.0, 0]], [[1.0, 0], [-213.9646911040362, 0], [103823.0, 0]], [[1.0, 0], [-283.30997095833504, 0], [148877.0, 0]], [[1.0, 0], [-92.0, 0], [205379.0, 0]], [[1.0, 0], [-370.1717794165756, 0], [226981.0, 0]], [[1.0, 0], [-1087.5253244844412, 0], [300763.0, 0]], [[1.0, 0], [333.68057347388327, 0], [357911.0, 0]], [[1.0, 0], [606.7914559997793, 0], [389017.0, 0]], [[1.0, 0], [44.375066789164514, 0], [493039.0, 0]], [[1.0, 0], [-107.73174946331474, 0], [571787.0, 0]], [[1.0, 0], [257.81889768237585, 0], [704969.0, 0]], [[1.0, 0], [-1312.0499856352164, 0], [912673.0, 0]], [[1.0, 0], [-63.32928009409795, 0], [1030301.0, 0]], [[1.0, 0], [-1219.8523528904589, 0], [1092727.0, 0]], [[1.0, 0], [-42.394734822582684, 0], [1225043.0, 0]], [[1.0, 0], [-266.7414703645628, 0], [1295029.0, 0]], [[1.0, 0], [-1871.596433840757, 0], [1442897.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 11, 'label': '2-1080-1.1-c3-0-11', 'leading_term': '1.8217392466376013365923611192742', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1080/4/a/h/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.8217392466376012, 1.8070822274298433, 1.7632922819158785, 1.6909127640700428, 1.5908492059015487, 1.4643688279579679, 1.3130990706126762, 1.1390244123700208, 0.9444806000714807, 0.7321453213632259, 0.5050243080073621, 0.2664318732991177, 0.01996495945497775, -0.23053009937064334, -0.4809987086092014, -0.7272274156755941, -0.9649016825135696, -1.1896718152436507, -1.3972264995827564, -1.5833730368866672, -1.744123017695505, -1.8757818196589768, -1.9750399873165456, -2.039064255296368, -2.0655857269195588, -2.0529825294097175, -2.0003541465972483, -1.9075845906680509, -1.7753916249945862, -1.6053593971709355, -1.3999520892817618, -1.1625065424445165, -0.8972022627350772, -0.6090077600969142, -0.3036028013099658, 0.012723140733388318, 0.33319520341110126, 0.650698388622755, 0.957941127224744, 1.2476337424016894, 1.5126776618976043, 1.7463605644166313, 1.9425520846777204, 2.0958942731447054, 2.2019807367648476, 2.2575182991883653, 2.260465131419042, 2.2101396295055205, 2.1072948608913045, 1.9541541640429958, 1.754404457462662, 1.5131449761327527, 1.2367904792270652, 0.9329294276195813, 0.6101391707146075, 0.27776176008365433, -0.054354432355037924, -0.3761406297026234, -0.6776130890506027, -0.949188901801613, -1.1820020931684965, -1.3682093624904748, -1.5012745570610369, -1.5762211038265066, -1.5898421566725085, -1.540859159082082, -1.4300208643077594, -1.2601365731708494, -1.036039402014897, -0.7644777229765923, -0.45393545346613373, -0.11438452638062735, 0.2430244486029328, 0.6063247223565217, 0.9631381175680657, 1.3011087666279237, 1.6083509991733982, 1.8738952574382945, 2.0881152352266463, 2.243119376243463, 2.333090467508195, 2.3545583366178935, 2.3065925936522658, 2.1909049072774205, 2.0118533996818715, 1.7763452889800886, 1.4936377787779096, 1.1750412500770648, 0.8335328920720445, 0.48329284711716164, 0.13917856936036874, -0.18384376163497584, -0.4712894278918222, -0.709743889266982, -0.8874261178042435, -0.9947027650972148, -1.0245305101124869, -0.9728060728519196, -0.8386064773357316, -0.6243061159663511, -0.3355618737913837, 0.018837156321419676, 0.4272532034922399, 0.875608667339659, 1.3479067160980938, 1.8268447967297552, 2.2944975753112575, 2.7330420398497326, 3.125494774993822, 3.4564299252973667, 3.7126462185670532, 3.88375268467153, 3.9626453771886205, 3.9458514195327092, 3.83372192276718, 3.630461566199823, 3.3439896453208684, 2.985634879308445, 2.569673902115133, 2.1127307864194504, 1.6330618131120562, 1.1497556572390788, 0.6818839003726389, 0.24764003078101576, -0.13649335128115705, -0.45650967979710183, -0.7015386325947306, -0.8643681149621613, -0.9418004413708091, -0.9348223502412287, -0.8485768960280674, -0.6921345018035627, -0.4780701003981652, -0.22186288365204201, 0.058855756194332004, 0.3451724362487268, 0.6178398384015223, 0.8582574567630499, 1.0494371353854894, 1.1769050513774086, 1.2294937557837824, 1.1999822197424406, 1.0855484023964466, 0.8880073971201625, 0.6138183514658201, 0.27385462701687197, -0.11705647265622501, -0.5408062137464931, -0.9768597344248892, -1.4032546357699212, -1.797695066342464, -2.1386874523002697, -2.406660591892339, -2.5850122748444844, -2.6610270155432465, -2.6266148624464782, -2.4788293665462224, -2.2201333093103828, -1.8583932177861167, -1.4065974274994877, -0.8823068005797335, -0.30686142172423647, 0.2956200824171689, 0.8994002593054171, 1.4783838418448119, 2.007415776840895, 2.4635487415354986, 2.8272129151101466, 3.0832246890018884, 3.2215784165764245, 3.2379759031025417, 3.134061621709667, 2.917346949456507, 2.60082325964185, 2.202280602394173, 1.743365032554136, 1.2484224861478674, 0.7431896070908288, 0.25340133521880237, -0.19660921008468088, -0.5852413833996066, -0.8948136779541068, -1.112538738815993, -1.2312298548503013, -1.2496962597557781, -1.1728014504928352, -1.0111773875155807, -0.7806068518401377, -0.501105307269976, -0.19575125299374857, 0.11067079072880394, 0.3931387680423789, 0.6278895501503837, 0.7938569650920262, 0.8739670184521147, 0.8562128983966711, 0.7344439610076575, 0.5088185465526585, 0.1858893519699329, -0.2216888611934846, -0.6958174039595707, -1.2139440750696897, -1.7503321223896489, -2.277536663577973, -2.768004020062503, -3.195700735218665, -3.537675754550751, -3.7754616482920764, -3.896228826292474, -3.8936200615590413, -3.7682106056810807, -3.527560757261042, -3.1858517042677583, -2.7631204028704985, -2.284133688858851, -1.7769642519935416, -1.271350137053755, -0.7969338439121497, -0.38148591522265457, -0.049220478672205345, 0.180693725377541, 0.29533363280586017, 0.28885647859047064, 0.16291298178900324, -0.0733916870692024, -0.40399263525417306, -0.8067911893445646, -1.2549606581101536, -1.718556364993825, -2.166334533853943, -2.5676703564668104, -2.8944579123548833, -3.122874144348711, -3.234895970435752, -3.2194735284247242, -3.0732827499581767, -2.8010057787180247, -2.4151166730620233, -1.9351805979675545, -1.3867053978657549, -0.7996131034145549, -0.20642370782521913, 0.35973718747897526, 0.8671828282929546, 1.287633140615781, 1.5979806803767915, 1.7817409620982725, 1.8300923945635472, 1.7424363516571695, 1.5264380034259906, 1.197541551448953, 0.7779873575127487, 0.29539093984237563, -0.21902719702444082, -0.732448375640445, -1.2125701754172509, -1.629691184086395], 'positive_zeros': ['0.70781745139631214253111536533527', '2.04844775726154793262508172963993', '3.27158258157935411961709577307119', '4.17913637251256716492393273132969', '5.29806262730187595240166070136710', '5.91508107824151688638658826859555', '7.24376618121188601251448817184745', '7.83950516558325037752876989356742', '8.537774972035303840631030684562336', '9.463610380468137059124679827827133'], 'prelabel': '2-1080-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.982610024684902, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.70781745139631214253111536534', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.04844775726154793262508172964', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.27158258157935411961709577307', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 63.722062806199894, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 1080, 'conductor_radical': 30, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1080/4/a/h/1/2'], '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': '2-1080-1.1-c3-0-11', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-1080-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.982610024684902, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.70781745139631214253111536534', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '897265217114550678567956042365', 'Lhash_array': ['897265217114550678567956042365'], 'label': '2-1080-1.1-c3-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1080/4/a/h/1/2'}