Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3344,2,Mod(1519,3344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3344, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3344.1519");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3344 = 2^{4} \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3344.o (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(26.7019744359\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1519.11 | ||
Character | \(\chi\) | \(=\) | 3344.1519 |
Dual form | 3344.2.o.a.1519.12 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3344\mathbb{Z}\right)^\times\).
\(n\) | \(705\) | \(837\) | \(2433\) | \(2927\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.31411 | −0.758701 | −0.379350 | − | 0.925253i | \(-0.623853\pi\) | ||||
−0.379350 | + | 0.925253i | \(0.623853\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.36581 | 0.610808 | 0.305404 | − | 0.952223i | \(-0.401208\pi\) | ||||
0.305404 | + | 0.952223i | \(0.401208\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.52438i | 1.71005i | 0.518584 | + | 0.855027i | \(0.326459\pi\) | ||||
−0.518584 | + | 0.855027i | \(0.673541\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.27312 | −0.424373 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000i | 0.301511i | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.15181i | 1.70621i | 0.521742 | + | 0.853103i | \(0.325282\pi\) | ||||
−0.521742 | + | 0.853103i | \(0.674718\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.79482 | −0.463421 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.08674 | −1.71879 | −0.859394 | − | 0.511315i | \(-0.829159\pi\) | ||||
−0.859394 | + | 0.511315i | \(0.829159\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.02768 | + | 3.85856i | 0.465183 | + | 0.885215i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 5.94552i | − | 1.29742i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.57220i | 0.327826i | 0.986475 | + | 0.163913i | \(0.0524117\pi\) | ||||
−0.986475 | + | 0.163913i | \(0.947588\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.13457 | −0.626913 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.61534 | 1.08067 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.00931i | 1.11590i | 0.829874 | + | 0.557951i | \(0.188412\pi\) | ||||
−0.829874 | + | 0.557951i | \(0.811588\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.17161 | −0.210427 | −0.105213 | − | 0.994450i | \(-0.533553\pi\) | ||||
−0.105213 | + | 0.994450i | \(0.533553\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 1.31411i | − | 0.228757i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.17943i | 1.04451i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 10.6012i | − | 1.74282i | −0.490557 | − | 0.871409i | \(-0.663207\pi\) | ||
0.490557 | − | 0.871409i | \(-0.336793\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 8.08415i | − | 1.29450i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 6.26175i | − | 0.977922i | −0.872306 | − | 0.488961i | \(-0.837376\pi\) | ||
0.872306 | − | 0.488961i | \(-0.162624\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.714490i | 0.108959i | 0.998515 | + | 0.0544794i | \(0.0173499\pi\) | ||||
−0.998515 | + | 0.0544794i | \(0.982650\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.73884 | −0.259211 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.81799i | 0.265181i | 0.991171 | + | 0.132591i | \(0.0423295\pi\) | ||||
−0.991171 | + | 0.132591i | \(0.957670\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −13.4700 | −1.92428 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 9.31275 | 1.30405 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 10.0904i | − | 1.38602i | −0.720928 | − | 0.693010i | \(-0.756284\pi\) | ||
0.720928 | − | 0.693010i | \(-0.243716\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.36581i | 0.184166i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.66460 | − | 5.07057i | −0.352934 | − | 0.671613i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.62345 | −0.732111 | −0.366055 | − | 0.930593i | \(-0.619292\pi\) | ||||
−0.366055 | + | 0.930593i | \(0.619292\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.63038 | −0.336786 | −0.168393 | − | 0.985720i | \(-0.553858\pi\) | ||||
−0.168393 | + | 0.985720i | \(0.553858\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 5.76007i | − | 0.725701i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 8.40220i | 1.04216i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.8075 | −1.56469 | −0.782345 | − | 0.622845i | \(-0.785977\pi\) | ||||
−0.782345 | + | 0.622845i | \(0.785977\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 2.06604i | − | 0.248722i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.4751 | 1.36185 | 0.680924 | − | 0.732354i | \(-0.261578\pi\) | ||||
0.680924 | + | 0.732354i | \(0.261578\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.28533 | 0.852683 | 0.426342 | − | 0.904562i | \(-0.359802\pi\) | ||||
0.426342 | + | 0.904562i | \(0.359802\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.11916 | 0.475640 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.52438 | −0.515600 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 16.1356 | 1.81540 | 0.907698 | − | 0.419625i | \(-0.137838\pi\) | ||||
0.907698 | + | 0.419625i | \(0.137838\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.55981 | −0.395534 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 4.65498i | − | 0.510951i | −0.966816 | − | 0.255475i | \(-0.917768\pi\) | ||
0.966816 | − | 0.255475i | \(-0.0822320\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.67913 | −1.04985 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 7.89689i | − | 0.846635i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 7.01151i | − | 0.743219i | −0.928389 | − | 0.371609i | \(-0.878806\pi\) | ||
0.928389 | − | 0.371609i | \(-0.121194\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −27.8331 | −2.91770 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.53962 | 0.159651 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.76943 | + | 5.27006i | 0.284137 | + | 0.540696i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.74462i | 0.380209i | 0.981764 | + | 0.190104i | \(0.0608826\pi\) | ||||
−0.981764 | + | 0.190104i | \(0.939117\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 1.27312i | − | 0.127953i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 17.2823 | 1.71966 | 0.859828 | − | 0.510584i | \(-0.170571\pi\) | ||||
0.859828 | + | 0.510584i | \(0.170571\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17.4647 | 1.72084 | 0.860422 | − | 0.509583i | \(-0.170200\pi\) | ||||
0.860422 | + | 0.509583i | \(0.170200\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 8.12044i | − | 0.792474i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10.4639 | 1.01158 | 0.505791 | − | 0.862656i | \(-0.331201\pi\) | ||||
0.505791 | + | 0.862656i | \(0.331201\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.48940i | 0.238441i | 0.992868 | + | 0.119220i | \(0.0380395\pi\) | ||||
−0.992868 | + | 0.119220i | \(0.961960\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 13.9311i | 1.32228i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.7800i | 1.01410i | 0.861917 | + | 0.507050i | \(0.169264\pi\) | ||||
−0.861917 | + | 0.507050i | \(0.830736\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.14733i | 0.200239i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 7.83199i | − | 0.724068i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 32.0631i | − | 2.93922i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 8.22862i | 0.741950i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.1103 | −0.993732 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.41764 | −0.303267 | −0.151633 | − | 0.988437i | \(-0.548453\pi\) | ||||
−0.151633 | + | 0.988437i | \(0.548453\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 0.938917i | − | 0.0826671i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 18.4803i | − | 1.61463i | −0.590122 | − | 0.807314i | \(-0.700920\pi\) | ||
0.590122 | − | 0.807314i | \(-0.299080\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −17.4576 | + | 9.17400i | −1.51376 | + | 0.795487i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 7.66948 | 0.660084 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.18594 | 0.186757 | 0.0933786 | − | 0.995631i | \(-0.470233\pi\) | ||||
0.0933786 | + | 0.995631i | \(0.470233\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.120434i | 0.0102151i | 0.999987 | + | 0.00510756i | \(0.00162579\pi\) | ||||
−0.999987 | + | 0.00510756i | \(0.998374\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 2.38904i | − | 0.201193i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.15181 | −0.514441 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.20757i | 0.681602i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 17.7010 | 1.45995 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −17.0025 | −1.39290 | −0.696448 | − | 0.717608i | \(-0.745237\pi\) | ||||
−0.696448 | + | 0.717608i | \(0.745237\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.1987 | −1.48099 | −0.740496 | − | 0.672061i | \(-0.765409\pi\) | ||||
−0.740496 | + | 0.672061i | \(0.765409\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 9.02227 | 0.729407 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.60019 | −0.128530 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −17.2570 | −1.37725 | −0.688627 | − | 0.725115i | \(-0.741786\pi\) | ||||
−0.688627 | + | 0.725115i | \(0.741786\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 13.2599i | 1.05158i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.11323 | −0.560601 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 21.8774i | 1.71357i | 0.515674 | + | 0.856785i | \(0.327542\pi\) | ||||
−0.515674 | + | 0.856785i | \(0.672458\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − | 1.79482i | − | 0.139727i | ||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.56662 | 0.198611 | 0.0993055 | − | 0.995057i | \(-0.468338\pi\) | ||||
0.0993055 | + | 0.995057i | \(0.468338\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −24.8448 | −1.91114 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.58148 | − | 4.91241i | −0.197411 | − | 0.375661i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.19048i | 0.546682i | 0.961917 | + | 0.273341i | \(0.0881288\pi\) | ||||
−0.961917 | + | 0.273341i | \(0.911871\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 14.1820i | − | 1.07206i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.38982 | 0.555453 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.17814 | −0.536519 | −0.268260 | − | 0.963347i | \(-0.586448\pi\) | ||||
−0.268260 | + | 0.963347i | \(0.586448\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 11.4286i | − | 0.849481i | −0.905315 | − | 0.424740i | \(-0.860365\pi\) | ||
0.905315 | − | 0.424740i | \(-0.139635\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.45661 | 0.255520 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 14.4791i | − | 1.06453i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 7.08674i | − | 0.518234i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 25.4059i | 1.84801i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.60966i | 0.188829i | 0.995533 | + | 0.0944144i | \(0.0300979\pi\) | ||||
−0.995533 | + | 0.0944144i | \(0.969902\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.51514i | 0.468970i | 0.972120 | + | 0.234485i | \(0.0753404\pi\) | ||||
−0.972120 | + | 0.234485i | \(0.924660\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 11.0414i | − | 0.790691i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 20.8746 | 1.48725 | 0.743626 | − | 0.668596i | \(-0.233104\pi\) | ||||
0.743626 | + | 0.668596i | \(0.233104\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.1308i | 1.07260i | 0.844029 | + | 0.536298i | \(0.180178\pi\) | ||||
−0.844029 | + | 0.536298i | \(0.819822\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 16.8305 | 1.18713 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −27.1884 | −1.90825 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 8.55236i | − | 0.597323i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 2.00160i | − | 0.139121i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.85856 | + | 2.02768i | −0.266902 | + | 0.140258i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −17.9753 | −1.23747 | −0.618736 | − | 0.785599i | \(-0.712355\pi\) | ||||
−0.618736 | + | 0.785599i | \(0.712355\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −15.0796 | −1.03324 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.975857i | 0.0665529i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 5.30079i | − | 0.359841i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −9.57371 | −0.646932 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 43.5963i | − | 2.93261i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −15.7739 | −1.05630 | −0.528151 | − | 0.849151i | \(-0.677114\pi\) | ||||
−0.528151 | + | 0.849151i | \(0.677114\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.99068 | 0.266045 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −10.6481 | −0.706742 | −0.353371 | − | 0.935483i | \(-0.614965\pi\) | ||||
−0.353371 | + | 0.935483i | \(0.614965\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.6593 | 0.704384 | 0.352192 | − | 0.935928i | \(-0.385436\pi\) | ||||
0.352192 | + | 0.935928i | \(0.385436\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.94552 | 0.391186 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.53532 | 0.297119 | 0.148559 | − | 0.988903i | \(-0.452536\pi\) | ||||
0.148559 | + | 0.988903i | \(0.452536\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.48303i | 0.161975i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −21.2039 | −1.37734 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 16.1688i | 1.04587i | 0.852372 | + | 0.522935i | \(0.175163\pi\) | ||||
−0.852372 | + | 0.522935i | \(0.824837\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 6.96214i | − | 0.448471i | −0.974535 | − | 0.224236i | \(-0.928012\pi\) | ||
0.974535 | − | 0.224236i | \(-0.0719885\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −12.1680 | −0.780581 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −18.3974 | −1.17537 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −23.7372 | + | 12.4739i | −1.51036 | + | 0.793697i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.11715i | 0.387659i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 7.65949i | − | 0.483463i | −0.970343 | − | 0.241731i | \(-0.922285\pi\) | ||
0.970343 | − | 0.241731i | \(-0.0777153\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.57220 | −0.0988434 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 12.7194 | 0.796522 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 19.9033i | − | 1.24153i | −0.783996 | − | 0.620766i | \(-0.786822\pi\) | ||
0.783996 | − | 0.620766i | \(-0.213178\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 47.9636 | 2.98031 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 7.65057i | − | 0.473558i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.84632i | 0.422162i | 0.977469 | + | 0.211081i | \(0.0676984\pi\) | ||||
−0.977469 | + | 0.211081i | \(0.932302\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 13.7815i | − | 0.846593i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.21389i | 0.563881i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 24.0554i | − | 1.46668i | −0.679860 | − | 0.733342i | \(-0.737959\pi\) | ||
0.679860 | − | 0.733342i | \(-0.262041\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 10.5993i | − | 0.643863i | −0.946763 | − | 0.321931i | \(-0.895668\pi\) | ||
0.946763 | − | 0.321931i | \(-0.104332\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 36.5757 | 2.21366 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 3.13457i | − | 0.189021i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.85391 | −0.471896 | −0.235948 | − | 0.971766i | \(-0.575820\pi\) | ||||
−0.235948 | + | 0.971766i | \(0.575820\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.49160 | 0.0892995 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.22570i | 0.252084i | 0.992025 | + | 0.126042i | \(0.0402274\pi\) | ||||
−0.992025 | + | 0.126042i | \(0.959773\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 31.4215i | 1.86781i | 0.357519 | + | 0.933906i | \(0.383623\pi\) | ||||
−0.357519 | + | 0.933906i | \(0.616377\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.63933 | − | 6.92543i | −0.215575 | − | 0.410227i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 28.3305 | 1.67230 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 33.2219 | 1.95423 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 4.92084i | − | 0.288465i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 21.5099i | 1.25662i | 0.777962 | + | 0.628312i | \(0.216254\pi\) | ||||
−0.777962 | + | 0.628312i | \(0.783746\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.68056 | −0.447179 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.61534i | 0.325835i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −9.67189 | −0.559340 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.23262 | −0.186325 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −22.7109 | −1.30470 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.59260 | −0.205712 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −16.7379 | −0.955281 | −0.477640 | − | 0.878555i | \(-0.658508\pi\) | ||||
−0.477640 | + | 0.878555i | \(0.658508\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −22.9504 | −1.30561 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 18.9708i | 1.07574i | 0.843029 | + | 0.537869i | \(0.180770\pi\) | ||||
−0.843029 | + | 0.537869i | \(0.819230\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.64777 | −0.375754 | −0.187877 | − | 0.982193i | \(-0.560161\pi\) | ||||
−0.187877 | + | 0.982193i | \(0.560161\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − | 7.86715i | − | 0.443264i | ||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 32.4401i | 1.82202i | 0.412389 | + | 0.911008i | \(0.364694\pi\) | ||||
−0.412389 | + | 0.911008i | \(0.635306\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.00931 | −0.336457 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −13.7507 | −0.767488 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −14.3697 | − | 27.3446i | −0.799550 | − | 1.52150i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 19.2833i | − | 1.06964i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 3.27134i | − | 0.180905i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8.22527 | −0.453474 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.4186 | −0.902446 | −0.451223 | − | 0.892411i | \(-0.649012\pi\) | ||||
−0.451223 | + | 0.892411i | \(0.649012\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 13.4965i | 0.739605i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −17.4926 | −0.955725 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.7459i | 0.748787i | 0.927270 | + | 0.374393i | \(0.122149\pi\) | ||||
−0.927270 | + | 0.374393i | \(0.877851\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 14.1661i | − | 0.769398i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 1.17161i | − | 0.0634461i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 29.2726i | − | 1.58057i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 2.82182i | − | 0.151922i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.55648i | 0.244605i | 0.992493 | + | 0.122302i | \(0.0390278\pi\) | ||||
−0.992493 | + | 0.122302i | \(0.960972\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.0704 | −0.860229 | −0.430114 | − | 0.902774i | \(-0.641527\pi\) | ||||
−0.430114 | + | 0.902774i | \(0.641527\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 34.5445i | 1.84385i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.00621 | −0.319679 | −0.159839 | − | 0.987143i | \(-0.551098\pi\) | ||||
−0.159839 | + | 0.987143i | \(0.551098\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 15.6728 | 0.831828 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 42.1344i | 2.22999i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 25.6100i | − | 1.35164i | −0.737065 | − | 0.675822i | \(-0.763789\pi\) | ||
0.737065 | − | 0.675822i | \(-0.236211\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.7770 | + | 15.6479i | −0.567210 | + | 0.823573i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.31411 | 0.0689728 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.95037 | 0.520826 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 18.2903i | 0.954745i | 0.878701 | + | 0.477372i | \(0.158411\pi\) | ||||
−0.878701 | + | 0.477372i | \(0.841589\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 7.97196i | 0.415004i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 45.6527 | 2.37017 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.86117i | 0.510592i | 0.966863 | + | 0.255296i | \(0.0821729\pi\) | ||||
−0.966863 | + | 0.255296i | \(0.917827\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 14.6001 | 0.753945 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −36.9682 | −1.90396 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.1325 | 1.08550 | 0.542752 | − | 0.839893i | \(-0.317382\pi\) | ||||
0.542752 | + | 0.839893i | \(0.317382\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.49115 | 0.230089 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.62725 | −0.134246 | −0.0671230 | − | 0.997745i | \(-0.521382\pi\) | ||||
−0.0671230 | + | 0.997745i | \(0.521382\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.17943 | −0.314933 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 0.909631i | − | 0.0462391i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −16.1936 | −0.821048 | −0.410524 | − | 0.911850i | \(-0.634654\pi\) | ||||
−0.410524 | + | 0.911850i | \(0.634654\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 11.1418i | − | 0.563464i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 24.2851i | 1.22502i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 22.0381 | 1.10886 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.2529 | 0.916085 | 0.458042 | − | 0.888930i | \(-0.348551\pi\) | ||||
0.458042 | + | 0.888930i | \(0.348551\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 22.9412 | − | 12.0556i | 1.14849 | − | 0.603537i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 23.1837i | − | 1.15774i | −0.815420 | − | 0.578870i | \(-0.803494\pi\) | ||
0.815420 | − | 0.578870i | \(-0.196506\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 7.20751i | − | 0.359032i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4.86202 | −0.241596 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.6012 | 0.525480 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 5.30810i | − | 0.262469i | −0.991351 | − | 0.131234i | \(-0.958106\pi\) | ||
0.991351 | − | 0.131234i | \(-0.0418940\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.87256 | −0.141693 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 25.4426i | − | 1.25195i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 6.35782i | − | 0.312093i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 0.158264i | − | 0.00775021i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 27.9520i | − | 1.36555i | −0.730630 | − | 0.682773i | \(-0.760774\pi\) | ||
0.730630 | − | 0.682773i | \(-0.239226\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 11.6942i | − | 0.569939i | −0.958537 | − | 0.284970i | \(-0.908017\pi\) | ||
0.958537 | − | 0.284970i | \(-0.0919835\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 2.31452i | − | 0.112536i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 22.2139 | 1.07753 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 11.9008i | − | 0.575922i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 8.08415 | 0.390306 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −32.6237 | −1.57143 | −0.785713 | − | 0.618591i | \(-0.787704\pi\) | ||||
−0.785713 | + | 0.618591i | \(0.787704\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 22.5834i | − | 1.08529i | −0.839963 | − | 0.542644i | \(-0.817423\pi\) | ||
0.839963 | − | 0.542644i | \(-0.182577\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 10.7856i | − | 0.517132i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.06643 | + | 3.18793i | −0.290197 | + | 0.152499i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.91705 | −0.186951 | −0.0934754 | − | 0.995622i | \(-0.529798\pi\) | ||||
−0.0934754 | + | 0.995622i | \(0.529798\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 17.1489 | 0.816613 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 21.0543i | 1.00032i | 0.865933 | + | 0.500160i | \(0.166725\pi\) | ||||
−0.865933 | + | 0.500160i | \(0.833275\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 9.57638i | − | 0.453964i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 22.3431 | 1.05679 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.02038i | 0.425698i | 0.977085 | + | 0.212849i | \(0.0682742\pi\) | ||||
−0.977085 | + | 0.212849i | \(0.931726\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.26175 | 0.294854 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 23.9151 | 1.12363 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −38.0147 | −1.78216 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.9244 | −0.557798 | −0.278899 | − | 0.960320i | \(-0.589969\pi\) | ||||
−0.278899 | + | 0.960320i | \(0.589969\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −39.7945 | −1.85745 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −35.7802 | −1.66645 | −0.833226 | − | 0.552933i | \(-0.813509\pi\) | ||||
−0.833226 | + | 0.552933i | \(0.813509\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 6.29863i | − | 0.292722i | −0.989231 | − | 0.146361i | \(-0.953244\pi\) | ||
0.989231 | − | 0.146361i | \(-0.0467562\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.10283 | 0.0975162 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10.9998i | 0.509008i | 0.967072 | + | 0.254504i | \(0.0819122\pi\) | ||||
−0.967072 | + | 0.254504i | \(0.918088\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 57.9461i | − | 2.67570i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 22.6775 | 1.04492 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.714490 | −0.0328523 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.35591 | − | 12.0949i | −0.291629 | − | 0.554953i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 12.8463i | 0.588190i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 26.8446i | 1.22656i | 0.789866 | + | 0.613280i | \(0.210150\pi\) | ||||
−0.789866 | + | 0.613280i | \(0.789850\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 65.2163 | 2.97361 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 9.34755 | 0.425328 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.11444i | 0.232235i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.6553 | 0.528151 | 0.264075 | − | 0.964502i | \(-0.414933\pi\) | ||||
0.264075 | + | 0.964502i | \(0.414933\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 28.7493i | − | 1.30009i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 11.7621i | − | 0.530815i | −0.964136 | − | 0.265407i | \(-0.914494\pi\) | ||
0.964136 | − | 0.265407i | \(-0.0855064\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 42.5864i | − | 1.91800i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 1.73884i | − | 0.0781549i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 51.9179i | 2.32883i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 17.2939i | − | 0.774180i | −0.922042 | − | 0.387090i | \(-0.873480\pi\) | ||
0.922042 | − | 0.387090i | \(-0.126520\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.37282 | −0.150686 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 29.9943i | 1.33738i | 0.743542 | + | 0.668689i | \(0.233144\pi\) | ||||
−0.743542 | + | 0.668689i | \(0.766856\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 23.6044 | 1.05038 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 32.6488 | 1.44998 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.12809i | 0.182974i | 0.995806 | + | 0.0914872i | \(0.0291620\pi\) | ||||
−0.995806 | + | 0.0914872i | \(0.970838\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 32.9616i | 1.45813i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 11.3861 | + | 21.6671i | 0.502710 | + | 0.956628i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 23.8534 | 1.05111 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.81799 | −0.0799551 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 9.44907i | − | 0.414768i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21.3573i | 0.935680i | 0.883813 | + | 0.467840i | \(0.154968\pi\) | ||||
−0.883813 | + | 0.467840i | \(0.845032\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.35716 | 0.409160 | 0.204580 | − | 0.978850i | \(-0.434417\pi\) | ||||
0.204580 | + | 0.978850i | \(0.434417\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 18.6366i | 0.813369i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.30288 | 0.361679 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 20.5282 | 0.892530 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.15932 | 0.310688 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 38.5211 | 1.66854 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 14.2917 | 0.617883 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9.43285 | 0.407057 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 13.4700i | − | 0.580193i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −26.2569 | −1.12887 | −0.564436 | − | 0.825477i | \(-0.690906\pi\) | ||||
−0.564436 | + | 0.825477i | \(0.690906\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 15.0184i | 0.644502i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.40004i | 0.145642i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.81380 | −0.419608 | −0.209804 | − | 0.977744i | \(-0.567283\pi\) | ||||
−0.209804 | + | 0.977744i | \(0.567283\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.34879 | 0.142923 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −23.1873 | + | 12.1850i | −0.987812 | + | 0.519098i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 73.0035i | 3.10442i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 19.0272i | 0.807658i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 33.8288 | 1.43337 | 0.716685 | − | 0.697397i | \(-0.245658\pi\) | ||||
0.716685 | + | 0.697397i | \(0.245658\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.39541 | −0.185906 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.31275i | 0.393184i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −10.5530 | −0.444755 | −0.222377 | − | 0.974961i | \(-0.571382\pi\) | ||||
−0.222377 | + | 0.974961i | \(0.571382\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 14.7235i | 0.619420i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 16.1059i | − | 0.676385i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 2.27960i | − | 0.0955657i | −0.998858 | − | 0.0477829i | \(-0.984784\pi\) | ||
0.998858 | − | 0.0477829i | \(-0.0152156\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.45694i | 0.186517i | 0.995642 | + | 0.0932585i | \(0.0297283\pi\) | ||||
−0.995642 | + | 0.0932585i | \(0.970272\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 3.42938i | − | 0.143264i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 4.92817i | − | 0.205519i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.7707 | 0.490022 | 0.245011 | − | 0.969520i | \(-0.421208\pi\) | ||||
0.245011 | + | 0.969520i | \(0.421208\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 8.56160i | − | 0.355808i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 21.0609 | 0.873753 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.0904 | 0.417901 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 10.6970i | − | 0.442267i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 2.49167i | − | 0.102842i | −0.998677 | − | 0.0514211i | \(-0.983625\pi\) | ||
0.998677 | − | 0.0514211i | \(-0.0163751\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.37565 | − | 4.52072i | −0.0978869 | − | 0.186273i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −27.4315 | −1.12838 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 32.5858 | 1.33814 | 0.669068 | − | 0.743201i | \(-0.266693\pi\) | ||||
0.669068 | + | 0.743201i | \(0.266693\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 43.7920i | − | 1.79530i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 19.8836i | − | 0.813780i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −20.9674 | −0.856704 | −0.428352 | − | 0.903612i | \(-0.640906\pi\) | ||||
−0.428352 | + | 0.903612i | \(0.640906\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.88018i | 0.280648i | 0.990106 | + | 0.140324i | \(0.0448145\pi\) | ||||
−0.990106 | + | 0.140324i | \(0.955186\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 16.3055 | 0.664012 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.36581 | −0.0555280 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 36.6400 | 1.48717 | 0.743585 | − | 0.668641i | \(-0.233124\pi\) | ||||
0.743585 | + | 0.668641i | \(0.233124\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 35.7285 | 1.44779 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −11.1839 | −0.452454 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −25.7969 | −1.04193 | −0.520964 | − | 0.853579i | \(-0.674427\pi\) | ||||
−0.520964 | + | 0.853579i | \(0.674427\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 11.2387i | 0.453189i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 14.3504 | 0.577727 | 0.288864 | − | 0.957370i | \(-0.406723\pi\) | ||||
0.288864 | + | 0.957370i | \(0.406723\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.61957i | 0.266063i | 0.991112 | + | 0.133031i | \(0.0424711\pi\) | ||||
−0.991112 | + | 0.133031i | \(0.957529\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.82844i | 0.354273i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 31.7227 | 1.27094 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.498343 | 0.0199337 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.07057 | − | 2.66460i | 0.202499 | − | 0.106414i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 75.1276i | 2.99553i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.8663i | 0.671436i | 0.941963 | + | 0.335718i | \(0.108979\pi\) | ||||
−0.941963 | + | 0.335718i | \(0.891021\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 23.6215 | 0.938871 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.66784 | −0.185238 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 82.8648i | − | 3.28322i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −14.6092 | −0.577932 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14.7897i | 0.584157i | 0.956394 | + | 0.292078i | \(0.0943468\pi\) | ||||
−0.956394 | + | 0.292078i | \(0.905653\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 44.0804i | 1.73836i | 0.494496 | + | 0.869180i | \(0.335353\pi\) | ||||
−0.494496 | + | 0.869180i | \(0.664647\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 1.28238i | − | 0.0504937i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 25.4850i | − | 1.00192i | −0.865471 | − | 0.500960i | \(-0.832980\pi\) | ||
0.865471 | − | 0.500960i | \(-0.167020\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 5.62345i | − | 0.220740i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.96582i | 0.273012i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 28.9603 | 1.13330 | 0.566651 | − | 0.823958i | \(-0.308239\pi\) | ||||
0.566651 | + | 0.823958i | \(0.308239\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 25.2405i | − | 0.986228i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −9.27509 | −0.361856 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 48.6991 | 1.89705 | 0.948523 | − | 0.316709i | \(-0.102578\pi\) | ||||
0.948523 | + | 0.316709i | \(0.102578\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 21.3401i | − | 0.830034i | −0.909814 | − | 0.415017i | \(-0.863776\pi\) | ||
0.909814 | − | 0.415017i | \(-0.136224\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 57.2903i | 2.22497i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −23.8437 | + | 12.5299i | −0.924620 | + | 0.485890i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9.44785 | −0.365822 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 20.7287 | 0.801417 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 2.63038i | − | 0.101545i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 17.6568i | − | 0.680621i | −0.940313 | − | 0.340310i | \(-0.889468\pi\) | ||
0.940313 | − | 0.340310i | \(-0.110532\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −17.6017 | −0.677488 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 36.7772i | 1.41346i | 0.707482 | + | 0.706732i | \(0.249831\pi\) | ||||
−0.707482 | + | 0.706732i | \(0.750169\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −16.9421 | −0.650177 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 13.9928 | 0.536206 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.20194 | 0.0459911 | 0.0229955 | − | 0.999736i | \(-0.492680\pi\) | ||||
0.0229955 | + | 0.999736i | \(0.492680\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.98557 | 0.114073 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −14.0074 | −0.534417 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 62.0742 | 2.36484 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.4619i | 0.512116i | 0.966661 | + | 0.256058i | \(0.0824239\pi\) | ||||
−0.966661 | + | 0.256058i | \(0.917576\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.76007 | 0.218807 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.164490i | 0.00623947i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 44.3754i | 1.68084i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5.95990 | −0.225424 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −13.1083 | −0.495094 | −0.247547 | − | 0.968876i | \(-0.579624\pi\) | ||||
−0.247547 | + | 0.968876i | \(0.579624\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 40.9052 | − | 21.4958i | 1.54277 | − | 0.810729i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 3.26297i | − | 0.122890i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 78.1917i | 2.94070i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.7076 | 0.477243 | 0.238621 | − | 0.971113i | \(-0.423305\pi\) | ||||
0.238621 | + | 0.971113i | \(0.423305\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −20.5425 | −0.770405 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 1.84200i | − | 0.0689835i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.40220 | −0.314224 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 21.2475i | − | 0.793503i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 24.0774i | − | 0.897934i | −0.893548 | − | 0.448967i | \(-0.851792\pi\) | ||
0.893548 | − | 0.448967i | \(-0.148208\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 79.0166i | 2.94273i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 9.14901i | 0.340255i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 18.8366i | − | 0.699573i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 23.5200i | − | 0.872310i | −0.899871 | − | 0.436155i | \(-0.856340\pi\) | ||
0.899871 | − | 0.436155i | \(-0.143660\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 26.6696 | 0.987762 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 5.06341i | − | 0.187277i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −45.1693 | −1.66837 | −0.834183 | − | 0.551487i | \(-0.814060\pi\) | ||||
−0.834183 | + | 0.551487i | \(0.814060\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 24.1762 | 0.891752 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 12.8075i | − | 0.471772i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 45.3574i | 1.66850i | 0.551387 | + | 0.834249i | \(0.314099\pi\) | ||||
−0.551387 | + | 0.834249i | \(0.685901\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 31.1932 | − | 16.3921i | 1.14591 | − | 0.602179i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 28.2802 | 1.03750 | 0.518750 | − | 0.854926i | \(-0.326398\pi\) | ||||
0.518750 | + | 0.854926i | \(0.326398\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −23.2221 | −0.850792 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.92635i | 0.216834i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 47.3426i | 1.72986i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −36.0025 | −1.31375 | −0.656875 | − | 0.753999i | \(-0.728122\pi\) | ||||
−0.656875 | + | 0.753999i | \(0.728122\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 10.0654i | 0.366804i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −24.8560 | −0.904602 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −31.0167 | −1.12732 | −0.563661 | − | 0.826006i | \(-0.690608\pi\) | ||||
−0.563661 | + | 0.826006i | \(0.690608\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.06604 | 0.0749926 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −10.7742 | −0.390563 | −0.195282 | − | 0.980747i | \(-0.562562\pi\) | ||||
−0.195282 | + | 0.980747i | \(0.562562\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −11.2630 | −0.407747 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 12.3227 | 0.445528 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 34.5944i | − | 1.24913i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10.0744 | 0.363293 | 0.181647 | − | 0.983364i | \(-0.441857\pi\) | ||||
0.181647 | + | 0.983364i | \(0.441857\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 26.1551i | 0.941952i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 26.1367i | − | 0.940073i | −0.882647 | − | 0.470037i | \(-0.844241\pi\) | ||
0.882647 | − | 0.470037i | \(-0.155759\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.67248 | 0.131919 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −63.0294 | −2.26117 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 24.1614 | − | 12.6969i | 0.865671 | − | 0.454912i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.4751i | 0.410613i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 33.7443i | 1.20592i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −23.5697 | −0.841239 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.63186 | −0.129462 | −0.0647310 | − | 0.997903i | \(-0.520619\pi\) | ||||
−0.0647310 | + | 0.997903i | \(0.520619\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 8.99680i | − | 0.320295i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −48.7729 | −1.73416 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 16.1816i | − | 0.574626i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 18.1104i | 0.642311i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 31.0651i | 1.10038i | 0.835039 | + | 0.550190i | \(0.185445\pi\) | ||||
−0.835039 | + | 0.550190i | \(0.814555\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 12.8836i | − | 0.455790i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.92649i | 0.315402i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7.28533i | 0.257094i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9.71531 | −0.342420 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 31.6114i | 1.11277i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 16.4773 | 0.579311 | 0.289656 | − | 0.957131i | \(-0.406459\pi\) | ||||
0.289656 | + | 0.957131i | \(0.406459\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −21.3659 | −0.750260 | −0.375130 | − | 0.926972i | \(-0.622402\pi\) | ||||
−0.375130 | + | 0.926972i | \(0.622402\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 13.9287i | 0.488499i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 29.8803i | 1.04666i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.75690 | + | 1.44876i | −0.0964519 | + | 0.0506857i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 35.4349 | 1.23819 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −10.8172 | −0.377524 | −0.188762 | − | 0.982023i | \(-0.560447\pi\) | ||||
−0.188762 | + | 0.982023i | \(0.560447\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.350273i | 0.0122097i | 0.999981 | + | 0.00610487i | \(0.00194325\pi\) | ||||
−0.999981 | + | 0.00610487i | \(0.998057\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4.11916i | 0.143411i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7.69486 | 0.267577 | 0.133788 | − | 0.991010i | \(-0.457286\pi\) | ||||
0.133788 | + | 0.991010i | \(0.457286\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 17.4792i | − | 0.607077i | −0.952819 | − | 0.303539i | \(-0.901832\pi\) | ||
0.952819 | − | 0.303539i | \(-0.0981682\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 10.3209 | 0.358028 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 95.4582 | 3.30743 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.50551 | 0.121313 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6.57898 | −0.227403 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 21.0651 | 0.727246 | 0.363623 | − | 0.931546i | \(-0.381540\pi\) | ||||
0.363623 | + | 0.931546i | \(0.381540\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.11184 | −0.245236 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 5.55303i | − | 0.191257i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −33.9333 | −1.16734 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 4.52438i | − | 0.155459i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 41.2912i | − | 1.41711i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 16.6671 | 0.571342 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.49147 | 0.0853064 | 0.0426532 | − | 0.999090i | \(-0.486419\pi\) | ||||
0.0426532 | + | 0.999090i | \(0.486419\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.52581 | − | 6.70941i | −0.120580 | − | 0.229457i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 29.7866i | − | 1.01749i | −0.860917 | − | 0.508746i | \(-0.830109\pi\) | ||
0.860917 | − | 0.508746i | \(-0.169891\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.98869i | 0.306690i | 0.988173 | + | 0.153345i | \(0.0490046\pi\) | ||||
−0.988173 | + | 0.153345i | \(0.950995\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −37.2294 | −1.26877 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −41.5449 | −1.41421 | −0.707103 | − | 0.707111i | \(-0.749998\pi\) | ||||
−0.707103 | + | 0.707111i | \(0.749998\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.82082i | 0.333918i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −43.6572 | −1.48268 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 16.1356i | 0.547362i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 78.7896i | − | 2.66968i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 4.76735i | − | 0.161350i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 50.2670i | − | 1.69933i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 22.5568i | − | 0.761691i | −0.924639 | − | 0.380845i | \(-0.875633\pi\) | ||
0.924639 | − | 0.380845i | \(-0.124367\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 28.2664i | − | 0.953402i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −0.586038 | −0.0197441 | −0.00987205 | − | 0.999951i | \(-0.503142\pi\) | ||||
−0.00987205 | + | 0.999951i | \(0.503142\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 1.51276i | − | 0.0509085i | −0.999676 | − | 0.0254543i | \(-0.991897\pi\) | ||
0.999676 | − | 0.0254543i | \(-0.00810321\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 10.0931 | 0.339275 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −47.2354 | −1.58601 | −0.793004 | − | 0.609216i | \(-0.791484\pi\) | ||||
−0.793004 | + | 0.609216i | \(0.791484\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 15.4627i | − | 0.518602i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 3.55981i | − | 0.119258i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7.01483 | + | 3.68631i | −0.234742 | + | 0.123358i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9.80396 | −0.327710 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 12.7099 | 0.424371 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 7.04056i | − | 0.234816i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 71.5079i | 2.38227i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.24802 | 0.141365 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 15.6093i | − | 0.518870i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −20.9163 | −0.694513 | −0.347256 | − | 0.937770i | \(-0.612887\pi\) | ||||
−0.347256 | + | 0.937770i | \(0.612887\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −22.0025 | −0.729776 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 32.4340 | 1.07459 | 0.537294 | − | 0.843395i | \(-0.319447\pi\) | ||||
0.537294 | + | 0.843395i | \(0.319447\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.65498 | 0.154057 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 4.72106 | 0.156074 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 83.6116 | 2.76110 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 52.8102i | − | 1.74205i | −0.491240 | − | 0.871024i | \(-0.663456\pi\) | ||
0.491240 | − | 0.871024i | \(-0.336544\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 21.9954 | 0.724772 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 70.5929i | 2.32359i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 33.2300i | 1.09260i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −22.2346 | −0.730280 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 36.2554 | 1.18950 | 0.594750 | − | 0.803911i | \(-0.297251\pi\) | ||||
0.594750 | + | 0.803911i | \(0.297251\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −27.3128 | − | 51.9747i | −0.895142 | − | 1.70340i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 24.9297i | − | 0.816163i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 9.67913i | − | 0.316541i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.79474 | 0.156637 | 0.0783186 | − | 0.996928i | \(-0.475045\pi\) | ||||
0.0783186 | + | 0.996928i | \(0.475045\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 8.73589 | 0.285085 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 18.7297i | − | 0.610570i | −0.952261 | − | 0.305285i | \(-0.901248\pi\) | ||
0.952261 | − | 0.305285i | \(-0.0987517\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.84473 | 0.320589 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 34.6996i | 1.12878i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6.58259i | 0.213906i | 0.994264 | + | 0.106953i | \(0.0341094\pi\) | ||||
−0.994264 | + | 0.106953i | \(0.965891\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 44.8180i | 1.45485i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 42.6298i | − | 1.38236i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 48.3939i | − | 1.56763i | −0.620993 | − | 0.783816i | \(-0.713270\pi\) | ||
0.620993 | − | 0.783816i | \(-0.286730\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.56430i | 0.115338i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 7.89689 | 0.255270 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9.89000i | 0.319365i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.6273 | −0.955721 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −13.3218 | −0.429288 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 8.89844i | 0.286451i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 19.5354i | 0.628217i | 0.949387 | + | 0.314108i | \(0.101706\pi\) | ||||
−0.949387 | + | 0.314108i | \(0.898294\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 18.8833 | + | 35.9338i | 0.606619 | + | 1.15436i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −39.0656 | −1.25368 | −0.626838 | − | 0.779150i | \(-0.715651\pi\) | ||||
−0.626838 | + | 0.779150i | \(0.715651\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.544890 | −0.0174684 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 25.3403i | 0.811539i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 4.11027i | − | 0.131499i | −0.997836 | − | 0.0657496i | \(-0.979056\pi\) | ||
0.997836 | − | 0.0657496i | \(-0.0209439\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.01151 | 0.224089 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 3.16930i | − | 0.101188i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −19.5833 | −0.624609 | −0.312305 | − | 0.949982i | \(-0.601101\pi\) | ||||
−0.312305 | + | 0.949982i | \(0.601101\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 28.5107 | 0.908426 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 10.8089 | 0.344051 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.12332 | −0.0357196 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 38.3122 | 1.21703 | 0.608514 | − | 0.793543i | \(-0.291766\pi\) | ||||
0.608514 | + | 0.793543i | \(0.291766\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 21.5758 | 0.684687 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 20.6658i | 0.655151i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −39.7062 | −1.25751 | −0.628753 | − | 0.777605i | \(-0.716434\pi\) | ||||
−0.628753 | + | 0.777605i | \(0.716434\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 59.5291i | − | 1.88342i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 3344.2.o.a.1519.11 | ✓ | 36 | |
4.3 | odd | 2 | inner | 3344.2.o.a.1519.26 | yes | 36 | |
19.18 | odd | 2 | inner | 3344.2.o.a.1519.25 | yes | 36 | |
76.75 | even | 2 | inner | 3344.2.o.a.1519.12 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3344.2.o.a.1519.11 | ✓ | 36 | 1.1 | even | 1 | trivial | |
3344.2.o.a.1519.12 | yes | 36 | 76.75 | even | 2 | inner | |
3344.2.o.a.1519.25 | yes | 36 | 19.18 | odd | 2 | inner | |
3344.2.o.a.1519.26 | yes | 36 | 4.3 | odd | 2 | inner |