Table lfunc_lfunctions
L-functions
{'Lhash': '1328033901018199049202104013237', 'a10': [-1.0, -2.0], 'a2': [0, -1.0], 'a3': [0, 0], 'a4': [-1.0, 0], 'a5': [2.0, -1.0], 'a6': [0, 0], 'a7': [0, 2.0], 'a8': [0, 1.0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 22.27826216393724, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [0, 1.0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-2.0, 1.0]]], [31, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 5, 31], 'central_character': '2790.559', 'coefficient_field': 'CDF', 'conductor': 2790, 'conductor_radical': 930, 'conjugate': '1138718108367351951925318054129', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 1.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.0, 1.0]], [[1.0, 0], [0, -2.0], [-7.0, 0]], [[1.0, 0], [-4.0, 0], [11.0, 0]], [[1.0, 0], [0, -2.0], [-13.0, 0]], [[1.0, 0], [0, 6.0], [-17.0, 0]], [[1.0, 0], [4.0, 0], [19.0, 0]], [[1.0, 0], [0, 0], [-23.0, 0]], [[1.0, 0], [-2.0, 0], [29.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 2.0], [-37.0, 0]], [[1.0, 0], [0, 0], [41.0, 0]], [[1.0, 0], [0, -4.0], [-43.0, 0]], [[1.0, 0], [0, 0], [-47.0, 0]], [[1.0, 0], [0, -2.0], [-53.0, 0]], [[1.0, 0], [-14.0, 0], [59.0, 0]], [[1.0, 0], [-10.0, 0], [61.0, 0]], [[1.0, 0], [0, 2.0], [-67.0, 0]], [[1.0, 0], [-6.0, 0], [71.0, 0]], [[1.0, 0], [0, 6.0], [-73.0, 0]], [[1.0, 0], [-4.0, 0], [79.0, 0]], [[1.0, 0], [0, -12.0], [-83.0, 0]], [[1.0, 0], [-6.0, 0], [89.0, 0]], [[1.0, 0], [0, 12.0], [-97.0, 0]], [[1.0, 0], [4.0, 0], [101.0, 0]], [[1.0, 0], [0, -2.0], [-103.0, 0]], [[1.0, 0], [0, -4.0], [-107.0, 0]], [[1.0, 0], [-2.0, 0], [109.0, 0]], [[1.0, 0], [0, 2.0], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 23536296, 'index': 49, 'label': '2-2790-5.4-c1-0-49', 'leading_term': '2.2095529663057442700025125926336464484461599684766912778', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/2790/2/d/h/559/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 24}, 'plot_values': [2.2095529663057443, 2.2491106128695764, 2.277969350931906, 2.2955709345053257, 2.3012072095440765, 2.2940363026786805, 2.2731103309491596, 2.2374132524982633, 2.1859070409547128, 2.1175841089264997, 2.0315238102331348, 1.9269508789454919, 1.8032937719693285, 1.660241030336381, 1.4977939320337574, 1.3163138578800828, 1.1165629249094704, 0.8997365610914544, 0.6674868087900725, 0.42193526259525954, 0.16567468078035552, -0.09824153195255016, -0.36632258249834665, -0.6346766737567685, -0.899060637043167, -1.1549426340660613, -1.3975774180453375, -1.6220932861561075, -1.823589481336944, -1.99724242102603, -2.1384187554551817, -2.2427929016789636, -2.3064663751483154, -2.326085962188662, -2.298957557809667, -2.223152346732469, -2.0976019430203685, -1.922179135161739, -1.6977610165828563, -1.4262715213898574, -1.1107007335941383, -0.7550987936785243, -0.3645427839472381, 0.054924375322626284, 0.49638325619727186, 0.9521549228906552, 1.4139442064041834, 1.8730070014756777, 2.320338481045228, 2.7468783044969425, 3.1437281391209617, 3.5023761485724862, 3.814922555801291, 4.0742999873613535, 4.274482074650982, 4.410673744984479, 4.479476796009872, 4.479024719571675, 4.4090813277841425, 4.271098529773438, 4.068229599689553, 3.8052954449770993, 3.4887027008634743, 3.126313907899225, 2.7272715332299824, 2.3017791269185373, 1.8608444119608987, 1.4159905381471323, 0.9789430324446386, 0.5613011001953276, 0.1742028233862936, -0.17200557896748608, -0.4680859541258017, -0.7061994363752331, -0.8801626211238175, -0.9856593697898767, -1.020400016506739, -0.9842211726531044, -0.8791210478317575, -0.7092271796490148, -0.4806956312729994, -0.20154300685433296, 0.1185850261288914, 0.4687027140421908, 0.8368225154890209, 1.2103325627848323, 1.5764014350771518, 1.922397059857819, 2.236305654150084, 2.507136189366914, 2.725295950784075, 2.8829233818241553, 2.974165553366764, 2.9953892570062974, 2.945316845797359, 2.825080473760347, 2.638191234959716, 2.3904227768489257, 2.0896121503016447, 1.7453838406114883, 1.3688059752224486, 0.9719905005327497, 0.5676515423431325, 0.16863810310949556, -0.21254139007867323, -0.564184464481524, -0.8758316802723297, -1.1386579037668674, -1.3458017157099453, -1.4926190284908465, -1.5768497433490096, -1.5986895666998573, -1.560762805178318, -1.4679959316704427, -1.3273958026217891, -1.1477404427436693, -0.9391941254078893, -0.7128618973022627, -0.4803015667168073, -0.2530133564162914, -0.041928799345150224, 0.14307905604278673, 0.2936425131459616, 0.4032829461764747, 0.467713462484053, 0.48504575662419175, 0.4558902927610551, 0.3833434233870392, 0.27285992748248306, 0.1320145264966139, -0.029839007735433527, -0.20199772920091927, -0.3729106133762313, -0.5307294458275575, -0.6638852805832632, -0.761664467268221, -0.8147575994946432, -0.8157552867347897, -0.7595664102957811, -0.6437374485568448, -0.46865544976401324, -0.23762214229926854, 0.04320769519539131, 0.36502436590504433, 0.7166923208207537, 1.0851983324338863, 1.456201058357802, 1.8146590382569214, 2.1455098470379403, 2.434369956694704, 2.668223023625954, 2.836063946047373, 2.9294671908186585, 2.9430505639342295, 2.874809715046257, 2.7263040735034454, 2.5026813948073783, 2.212535376964742, 1.8675985635040435, 1.482280628038826, 1.0730697608415591, 0.6578218775426928, 0.25496838839906993, -0.11732201595027814, -0.4419889566437321, -0.7038933487511962, -0.8905582906980014, -0.9928008031579971, -1.005221643971462, -0.9265264164716172, -0.7596586446782034, -0.5117340895579197, -0.19377493917229827, 0.17974781407430918, 0.591545959217901, 1.022292845592735, 1.4515147382438143, 1.8585537782040646, 2.2235570689030406, 2.528444026905363, 2.7578040546816744, 2.899678884502279, 2.946188558881501, 2.8939667897789607, 2.74438009844002, 2.503515300158018, 2.1819310964937775, 1.7941812388670484, 1.3581283582233976, 0.8940785287235478, 0.42377637822919983, -0.030691450571411833, -0.4480308989891014, -0.8088563345870599, -1.0967303848793535, -1.2990729646695849, -1.407889996769051, -1.4202802743155816, -1.338689179288947, -1.1708900953745496, -0.9296877656047967, -0.6323518960798145, -0.2998032958216425, 0.04441194722870337, 0.3753130190680716, 0.6677828054709708, 0.8979103757714189, 1.044309837214677, 1.0893473643681835, 1.0202111753185152, 0.8297656037659559, 0.5171399606972064, 0.08801517829937587, -0.44541428337807315, -1.0648098026487618, -1.746379078358354, -2.4618610128145364, -3.1797627126004855, -3.866792572158721, -4.489422217960348, -5.015502102583002, -5.415851229269257, -5.66574115861537, -5.746198199030964, -5.645055399822271, -5.357697328903753, -4.887455107709958, -4.245626101218725, -3.451111187278168, -2.529681722838403, -1.5129071988832294, -0.43679214327178867, 0.6598138449828346, 1.7369567994943902, 2.75538521397088, 3.6783341561718856, 4.473198149469564, 5.113009205967974, 5.577645682802951, 5.854710869580803, 5.940036746912593, 5.837787345566555, 5.5601566021268205, 5.126676477726334, 4.563171274066547, 3.9004124630668007, 3.1725439448569834, 2.4153596051287636, 1.6645226876003867, 0.9538193890676142, 0.3135370369767116, -0.23094969489870854, -0.6603124884648562, -0.9620662742362964, -1.1309909903819877, -1.1691603706380134, -1.0855813745736709], 'positive_zeros': ['1.04763402532140809353572430221284', '2.17711126895890250240907946991993', '3.57940189006391263707356431858567', '4.14589273795814278155203325110958', '5.25254825207630439003445249599169', '6.10457356830804435143921625847484', '6.59253756002942286688827595137580', '7.20362365466727305038331240103145', '8.260734868488792664472413144114470', '8.761517094717355604273970603783747'], 'prelabel': '2-2790-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.71998539869958, 'root_angle': 0.17620819117478337, 'root_number': '0.4472135954999579392818347337462552470881236719223051449 + 0.8944271909999158785636694674925104941762473438446102897*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.17620819117478337', 'prec': 57}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.04763402532140809353572430221', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.17711126895890250240907946992', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.57940189006391263707356431859', 'prec': 100}}