Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2100,2,Mod(157,2100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2100, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2100.157");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2100.ce (of order \(12\), degree \(4\), 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: | \(16.7685844245\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{12})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 493.1 | ||
Character | \(\chi\) | \(=\) | 2100.493 |
Dual form | 2100.2.ce.d.1657.1 |
$q$-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 \(\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times\).
\(n\) | \(701\) | \(1051\) | \(1177\) | \(1501\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{1}{6}\right)\) |
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 | ||||||||
\(3\) | −0.258819 | − | 0.965926i | −0.149429 | − | 0.557678i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.38886 | − | 2.25190i | 0.524940 | − | 0.851139i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.866025 | + | 0.500000i | −0.288675 | + | 0.166667i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.42437 | + | 4.19914i | −0.730976 | + | 1.26609i | 0.225491 | + | 0.974245i | \(0.427601\pi\) |
−0.956467 | + | 0.291842i | \(0.905732\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.27726 | + | 2.27726i | −0.631597 | + | 0.631597i | −0.948468 | − | 0.316872i | \(-0.897368\pi\) |
0.316872 | + | 0.948468i | \(0.397368\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.14486 | − | 0.574714i | 0.520206 | − | 0.139389i | 0.0108439 | − | 0.999941i | \(-0.496548\pi\) |
0.509362 | + | 0.860553i | \(0.329882\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.107324 | + | 0.185890i | 0.0246218 | + | 0.0426462i | 0.878074 | − | 0.478525i | \(-0.158829\pi\) |
−0.853452 | + | 0.521172i | \(0.825495\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.53463 | − | 0.758702i | −0.553103 | − | 0.165562i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.78090 | − | 6.64641i | 0.371343 | − | 1.38587i | −0.487272 | − | 0.873251i | \(-0.662008\pi\) |
0.858615 | − | 0.512621i | \(-0.171326\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.707107 | + | 0.707107i | 0.136083 | + | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 9.28979i | − | 1.72507i | −0.505996 | − | 0.862536i | \(-0.668875\pi\) | ||
0.505996 | − | 0.862536i | \(-0.331125\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.78979 | − | 4.49744i | −1.39909 | − | 0.807764i | −0.404791 | − | 0.914409i | \(-0.632656\pi\) |
−0.994297 | + | 0.106645i | \(0.965989\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.68353 | + | 1.25495i | 0.815297 | + | 0.218458i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.78514 | − | 2.62192i | −1.60867 | − | 0.431041i | −0.661022 | − | 0.750367i | \(-0.729877\pi\) |
−0.947645 | + | 0.319326i | \(0.896544\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.78906 | + | 1.61026i | 0.446606 | + | 0.257848i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 2.32866i | − | 0.363675i | −0.983329 | − | 0.181838i | \(-0.941795\pi\) | ||
0.983329 | − | 0.181838i | \(-0.0582046\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.01729 | + | 5.01729i | 0.765129 | + | 0.765129i | 0.977245 | − | 0.212115i | \(-0.0680353\pi\) |
−0.212115 | + | 0.977245i | \(0.568035\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.50989 | − | 9.36705i | 0.366106 | − | 1.36633i | −0.499810 | − | 0.866135i | \(-0.666597\pi\) |
0.865916 | − | 0.500190i | \(-0.166737\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.14213 | − | 6.25516i | −0.448876 | − | 0.893594i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.11026 | − | 1.92303i | −0.155468 | − | 0.269278i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.93140 | + | 0.785466i | −0.402658 | + | 0.107892i | −0.454464 | − | 0.890765i | \(-0.650169\pi\) |
0.0518054 | + | 0.998657i | \(0.483502\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.151779 | − | 0.151779i | 0.0201036 | − | 0.0201036i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.68173 | − | 4.64490i | 0.349132 | − | 0.604714i | −0.636964 | − | 0.770894i | \(-0.719810\pi\) |
0.986095 | + | 0.166180i | \(0.0531432\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.2321 | + | 7.63957i | −1.69420 | + | 0.978147i | −0.743142 | + | 0.669134i | \(0.766665\pi\) |
−0.951058 | + | 0.309013i | \(0.900001\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.0768377 | + | 2.64464i | −0.00968064 | + | 0.333193i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.33261 | + | 4.97338i | 0.162804 | + | 0.607595i | 0.998310 | + | 0.0581126i | \(0.0185082\pi\) |
−0.835506 | + | 0.549482i | \(0.814825\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.88087 | −0.828359 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.9873 | −1.54131 | −0.770653 | − | 0.637255i | \(-0.780070\pi\) | ||||
−0.770653 | + | 0.637255i | \(0.780070\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.0391479 | − | 0.146102i | −0.00458192 | − | 0.0170999i | 0.963597 | − | 0.267359i | \(-0.0861509\pi\) |
−0.968179 | + | 0.250259i | \(0.919484\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.08893 | + | 11.2915i | 0.693898 | + | 1.28678i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.0599887 | − | 0.0346345i | 0.00674926 | − | 0.00389669i | −0.496622 | − | 0.867967i | \(-0.665426\pi\) |
0.503371 | + | 0.864070i | \(0.332093\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.500000 | − | 0.866025i | 0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.467804 | − | 0.467804i | 0.0513482 | − | 0.0513482i | −0.680966 | − | 0.732315i | \(-0.738440\pi\) |
0.732315 | + | 0.680966i | \(0.238440\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −8.97325 | + | 2.40438i | −0.962034 | + | 0.257776i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.997017 | + | 1.72688i | 0.105684 | + | 0.183049i | 0.914017 | − | 0.405675i | \(-0.132964\pi\) |
−0.808334 | + | 0.588725i | \(0.799630\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.96537 | + | 8.29095i | 0.206026 | + | 0.869127i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.32805 | + | 8.68839i | −0.241407 | + | 0.900944i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.51529 | + | 7.51529i | 0.763062 | + | 0.763062i | 0.976875 | − | 0.213813i | \(-0.0685883\pi\) |
−0.213813 | + | 0.976875i | \(0.568588\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 4.84874i | − | 0.487317i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.35510 | + | 2.51442i | 0.433349 | + | 0.250194i | 0.700772 | − | 0.713385i | \(-0.252839\pi\) |
−0.267423 | + | 0.963579i | \(0.586172\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.64945 | + | 1.51377i | 0.556657 | + | 0.149156i | 0.526170 | − | 0.850379i | \(-0.323628\pi\) |
0.0304870 | + | 0.999535i | \(0.490294\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.39179 | − | 0.908827i | −0.327896 | − | 0.0878596i | 0.0911154 | − | 0.995840i | \(-0.470957\pi\) |
−0.419012 | + | 0.907981i | \(0.637623\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.1903 | − | 5.88338i | −0.976055 | − | 0.563525i | −0.0749780 | − | 0.997185i | \(-0.523889\pi\) |
−0.901077 | + | 0.433660i | \(0.857222\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.1303i | 0.961528i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.96763 | − | 9.96763i | −0.937676 | − | 0.937676i | 0.0604926 | − | 0.998169i | \(-0.480733\pi\) |
−0.998169 | + | 0.0604926i | \(0.980733\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.833533 | − | 3.11079i | 0.0770602 | − | 0.287592i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.68472 | − | 5.62822i | 0.154438 | − | 0.515938i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.25516 | − | 10.8343i | −0.568651 | − | 0.984932i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.24931 | + | 0.602701i | −0.202814 | + | 0.0543437i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.70771 | − | 3.70771i | 0.329006 | − | 0.329006i | −0.523203 | − | 0.852208i | \(-0.675263\pi\) |
0.852208 | + | 0.523203i | \(0.175263\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.54776 | − | 6.14490i | 0.312363 | − | 0.541028i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.28979 | + | 5.36347i | −0.811653 | + | 0.468608i | −0.847530 | − | 0.530748i | \(-0.821911\pi\) |
0.0358765 | + | 0.999356i | \(0.488578\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.567665 | + | 0.0164930i | 0.0492228 | + | 0.00143013i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.68516 | − | 13.7532i | −0.314845 | − | 1.17502i | −0.924134 | − | 0.382068i | \(-0.875212\pi\) |
0.609290 | − | 0.792948i | \(-0.291455\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.9764 | 1.18546 | 0.592731 | − | 0.805401i | \(-0.298050\pi\) | ||||
0.592731 | + | 0.805401i | \(0.298050\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.69749 | −0.816676 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.04159 | − | 15.0834i | −0.337975 | − | 1.26134i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5.22878 | + | 4.65402i | −0.431262 | + | 0.383857i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −9.74836 | + | 5.62822i | −0.798617 | + | 0.461082i | −0.842987 | − | 0.537933i | \(-0.819205\pi\) |
0.0443704 | + | 0.999015i | \(0.485872\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.16285 | + | 7.21027i | −0.338768 | + | 0.586764i | −0.984201 | − | 0.177053i | \(-0.943344\pi\) |
0.645433 | + | 0.763817i | \(0.276677\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.57015 | + | 1.57015i | −0.126939 | + | 0.126939i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.22158 | + | 1.66707i | −0.496536 | + | 0.133046i | −0.498392 | − | 0.866952i | \(-0.666076\pi\) |
0.00185597 | + | 0.999998i | \(0.499409\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.51740 | + | 2.62822i | 0.120338 | + | 0.208431i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −12.4936 | − | 13.2413i | −0.984637 | − | 1.04356i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.68973 | − | 10.0382i | 0.210676 | − | 0.786252i | −0.776969 | − | 0.629539i | \(-0.783244\pi\) |
0.987644 | − | 0.156713i | \(-0.0500897\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 13.1957 | + | 13.1957i | 1.02112 | + | 1.02112i | 0.999772 | + | 0.0213437i | \(0.00679444\pi\) |
0.0213437 | + | 0.999772i | \(0.493206\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.62822i | 0.202171i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.185890 | − | 0.107324i | −0.0142154 | − | 0.00820726i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −12.9386 | − | 3.46687i | −0.983700 | − | 0.263582i | −0.269098 | − | 0.963113i | \(-0.586726\pi\) |
−0.714602 | + | 0.699531i | \(0.753392\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.18071 | − | 1.38817i | −0.389406 | − | 0.104341i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.19615 | − | 3.00000i | −0.388379 | − | 0.224231i | 0.293079 | − | 0.956088i | \(-0.405320\pi\) |
−0.681457 | + | 0.731858i | \(0.738654\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 6.61889i | − | 0.491978i | −0.969273 | − | 0.245989i | \(-0.920887\pi\) | ||
0.969273 | − | 0.245989i | \(-0.0791127\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 10.8040 | + | 10.8040i | 0.798653 | + | 0.798653i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.78664 | + | 10.3999i | −0.203779 | + | 0.760515i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.57441 | − | 0.610262i | 0.187261 | − | 0.0443901i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.22052 | − | 9.04221i | −0.377744 | − | 0.654272i | 0.612990 | − | 0.790091i | \(-0.289967\pi\) |
−0.990734 | + | 0.135819i | \(0.956633\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.576279 | + | 0.154414i | −0.0414815 | + | 0.0111149i | −0.279500 | − | 0.960146i | \(-0.590169\pi\) |
0.238019 | + | 0.971261i | \(0.423502\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.5058 | − | 16.5058i | 1.17599 | − | 1.17599i | 0.195236 | − | 0.980756i | \(-0.437453\pi\) |
0.980756 | − | 0.195236i | \(-0.0625474\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.8357 | − | 22.2321i | 0.909900 | − | 1.57599i | 0.0956992 | − | 0.995410i | \(-0.469491\pi\) |
0.814201 | − | 0.580583i | \(-0.197175\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.45901 | − | 2.57441i | 0.314514 | − | 0.181585i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −20.9197 | − | 12.9022i | −1.46828 | − | 0.905559i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.78090 | + | 6.64641i | 0.123781 | + | 0.461957i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.04077 | −0.0719917 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.8847 | 0.818174 | 0.409087 | − | 0.912495i | \(-0.365847\pi\) | ||||
0.409087 | + | 0.912495i | \(0.365847\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.36136 | + | 12.5448i | 0.230316 | + | 0.859552i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −20.9467 | + | 11.2955i | −1.42196 | + | 0.766791i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.130991 | + | 0.0756280i | −0.00885158 | + | 0.00511046i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.57563 | + | 6.19317i | −0.240523 | + | 0.416598i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −18.7946 | + | 18.7946i | −1.25858 | + | 1.25858i | −0.306809 | + | 0.951771i | \(0.599261\pi\) |
−0.951771 | + | 0.306809i | \(0.900739\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 17.8673 | − | 4.78753i | 1.18590 | − | 0.317760i | 0.388633 | − | 0.921393i | \(-0.372947\pi\) |
0.797262 | + | 0.603633i | \(0.206281\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.39680 | − | 11.0796i | −0.422713 | − | 0.732160i | 0.573491 | − | 0.819212i | \(-0.305589\pi\) |
−0.996204 | + | 0.0870520i | \(0.972255\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 9.33079 | − | 8.80390i | 0.613921 | − | 0.579254i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.98174 | − | 14.8600i | 0.260852 | − | 0.973514i | −0.703888 | − | 0.710311i | \(-0.748554\pi\) |
0.964740 | − | 0.263203i | \(-0.0847789\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.0489806 | − | 0.0489806i | −0.00318163 | − | 0.00318163i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.3231i | 0.861803i | 0.902399 | + | 0.430901i | \(0.141804\pi\) | ||||
−0.902399 | + | 0.430901i | \(0.858196\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.71925 | + | 1.56996i | 0.175162 | + | 0.101130i | 0.585018 | − | 0.811021i | \(-0.301088\pi\) |
−0.409856 | + | 0.912150i | \(0.634421\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.965926 | − | 0.258819i | −0.0619642 | − | 0.0166032i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.667724 | − | 0.178916i | −0.0424863 | − | 0.0113842i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.572941 | − | 0.330787i | −0.0363086 | − | 0.0209628i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 16.4250i | 1.03674i | 0.855157 | + | 0.518369i | \(0.173461\pi\) | ||||
−0.855157 | + | 0.518369i | \(0.826539\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 23.5916 | + | 23.5916i | 1.48319 | + | 1.48319i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.23404 | + | 15.8016i | −0.264112 | + | 0.985679i | 0.698680 | + | 0.715435i | \(0.253771\pi\) |
−0.962792 | + | 0.270245i | \(0.912895\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −19.4945 | + | 18.3937i | −1.21133 | + | 1.14293i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.64490 | + | 8.04520i | 0.287512 | + | 0.497985i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 27.8296 | − | 7.45693i | 1.71605 | − | 0.459814i | 0.739154 | − | 0.673536i | \(-0.235225\pi\) |
0.976894 | + | 0.213722i | \(0.0685587\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.40999 | − | 1.40999i | 0.0862903 | − | 0.0862903i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.88087 | + | 11.9180i | −0.419534 | + | 0.726654i | −0.995893 | − | 0.0905428i | \(-0.971140\pi\) |
0.576359 | + | 0.817197i | \(0.304473\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.3141 | + | 5.95485i | −0.626538 | + | 0.361732i | −0.779410 | − | 0.626514i | \(-0.784481\pi\) |
0.152872 | + | 0.988246i | \(0.451148\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 7.49977 | − | 4.04425i | 0.453906 | − | 0.244769i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.20054 | − | 19.4087i | −0.312470 | − | 1.16615i | −0.926322 | − | 0.376733i | \(-0.877048\pi\) |
0.613852 | − | 0.789421i | \(-0.289619\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.99488 | 0.538509 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.5796 | 0.750435 | 0.375218 | − | 0.926937i | \(-0.377568\pi\) | ||||
0.375218 | + | 0.926937i | \(0.377568\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.65545 | + | 17.3744i | 0.276738 | + | 1.03280i | 0.954668 | + | 0.297673i | \(0.0962106\pi\) |
−0.677930 | + | 0.735126i | \(0.737123\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.24391 | − | 3.23418i | −0.309538 | − | 0.190908i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.4523 | + | 6.03463i | −0.614841 | + | 0.354978i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.31411 | − | 9.20431i | 0.311519 | − | 0.539566i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.409831 | − | 0.409831i | 0.0239426 | − | 0.0239426i | −0.695034 | − | 0.718977i | \(-0.744611\pi\) |
0.718977 | + | 0.695034i | \(0.244611\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.68353 | + | 1.25495i | −0.271766 | + | 0.0728194i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 11.0800 | + | 19.1911i | 0.640773 | + | 1.10985i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 18.2668 | − | 4.33013i | 1.05288 | − | 0.249584i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.30156 | − | 4.85749i | 0.0747726 | − | 0.279055i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −0.747094 | − | 0.747094i | −0.0426389 | − | 0.0426389i | 0.685466 | − | 0.728105i | \(-0.259599\pi\) |
−0.728105 | + | 0.685466i | \(0.759599\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 5.84874i | − | 0.332723i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 16.2731 | + | 9.39529i | 0.922764 | + | 0.532758i | 0.884516 | − | 0.466510i | \(-0.154489\pi\) |
0.0382480 | + | 0.999268i | \(0.487822\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.71760 | + | 0.996128i | 0.210131 | + | 0.0563045i | 0.362349 | − | 0.932042i | \(-0.381975\pi\) |
−0.152218 | + | 0.988347i | \(0.548642\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.06856 | − | 0.822219i | −0.172348 | − | 0.0461804i | 0.171613 | − | 0.985164i | \(-0.445102\pi\) |
−0.343961 | + | 0.938984i | \(0.611769\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 39.0091 | + | 22.5219i | 2.18409 | + | 1.26099i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.51144i | 0.195989i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.337029 | + | 0.337029i | 0.0187528 | + | 0.0187528i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.04546 | + | 11.3658i | −0.168414 | + | 0.628531i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −17.6078 | − | 18.6616i | −0.970749 | − | 1.02885i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.01032 | + | 13.8743i | 0.440287 | + | 0.762599i | 0.997711 | − | 0.0676289i | \(-0.0215434\pi\) |
−0.557424 | + | 0.830228i | \(0.688210\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 9.78514 | − | 2.62192i | 0.536222 | − | 0.143680i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 18.6413 | − | 18.6413i | 1.01545 | − | 1.01545i | 0.0155754 | − | 0.999879i | \(-0.495042\pi\) |
0.999879 | − | 0.0155754i | \(-0.00495802\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7.04818 | + | 12.2078i | −0.382805 | + | 0.663037i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 37.7707 | − | 21.8069i | 2.04540 | − | 1.18091i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.4500 | − | 1.61178i | −0.996206 | − | 0.0870278i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.91820 | − | 22.0870i | −0.317705 | − | 1.18569i | −0.921444 | − | 0.388511i | \(-0.872990\pi\) |
0.603739 | − | 0.797182i | \(-0.293677\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.69212 | −0.411750 | −0.205875 | − | 0.978578i | \(-0.566004\pi\) | ||||
−0.205875 | + | 0.978578i | \(0.566004\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.22052 | −0.171899 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7.89336 | − | 29.4584i | −0.420121 | − | 1.56791i | −0.774352 | − | 0.632755i | \(-0.781924\pi\) |
0.354231 | − | 0.935158i | \(-0.384743\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −5.87248 | − | 0.170620i | −0.310805 | − | 0.00903017i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 17.1496 | − | 9.90134i | 0.905122 | − | 0.522572i | 0.0262636 | − | 0.999655i | \(-0.491639\pi\) |
0.878858 | + | 0.477083i | \(0.158306\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.47696 | − | 16.4146i | 0.498788 | − | 0.863925i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −8.84613 | + | 8.84613i | −0.464301 | + | 0.464301i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −31.5042 | + | 8.44151i | −1.64450 | + | 0.440643i | −0.958067 | − | 0.286546i | \(-0.907493\pi\) |
−0.686437 | + | 0.727189i | \(0.740826\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.16433 | + | 2.01668i | 0.0606126 | + | 0.104984i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.30251 | + | 7.69212i | −0.119540 | + | 0.399355i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.97189 | + | 26.0194i | −0.360991 | + | 1.34724i | 0.511785 | + | 0.859114i | \(0.328984\pi\) |
−0.872776 | + | 0.488122i | \(0.837682\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 21.1552 | + | 21.1552i | 1.08955 | + | 1.08955i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.13854i | 0.366682i | 0.983049 | + | 0.183341i | \(0.0586913\pi\) | ||||
−0.983049 | + | 0.183341i | \(0.941309\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.54099 | − | 2.62174i | −0.232642 | − | 0.134316i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9.36705 | − | 2.50989i | −0.478634 | − | 0.128250i | 0.0114324 | − | 0.999935i | \(-0.496361\pi\) |
−0.490067 | + | 0.871685i | \(0.663028\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.85374 | − | 1.83645i | −0.348395 | − | 0.0933522i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4.84308 | − | 2.79615i | −0.245554 | − | 0.141771i | 0.372173 | − | 0.928163i | \(-0.378613\pi\) |
−0.617727 | + | 0.786393i | \(0.711946\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 15.2791i | − | 0.772699i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.58508 | + | 7.58508i | 0.382617 | + | 0.382617i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.47195 | − | 27.8857i | 0.375006 | − | 1.39954i | −0.478330 | − | 0.878180i | \(-0.658758\pi\) |
0.853336 | − | 0.521362i | \(-0.174576\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.130991 | − | 0.552591i | −0.00655778 | − | 0.0276642i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.40769 | − | 11.0985i | −0.319985 | − | 0.554230i | 0.660500 | − | 0.750826i | \(-0.270345\pi\) |
−0.980485 | + | 0.196596i | \(0.937011\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 27.9812 | − | 7.49753i | 1.39384 | − | 0.373479i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 34.7326 | − | 34.7326i | 1.72163 | − | 1.72163i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.58555 | + | 9.67445i | −0.276188 | + | 0.478371i | −0.970434 | − | 0.241366i | \(-0.922404\pi\) |
0.694247 | + | 0.719737i | \(0.255738\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −12.3308 | + | 7.11918i | −0.608233 | + | 0.351163i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.73530 | − | 12.4901i | −0.331423 | − | 0.614598i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.61735 | − | 13.5002i | −0.177143 | − | 0.661105i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 33.2585 | 1.62478 | 0.812391 | − | 0.583113i | \(-0.198166\pi\) | ||||
0.812391 | + | 0.583113i | \(0.198166\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.64886 | 0.421519 | 0.210760 | − | 0.977538i | \(-0.432406\pi\) | ||||
0.210760 | + | 0.977538i | \(0.432406\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.50989 | + | 9.36705i | 0.122035 | + | 0.455442i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.17401 | + | 40.4078i | −0.0568145 | + | 1.95547i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −13.5234 | + | 7.80775i | −0.652917 | + | 0.376962i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.0819870 | + | 0.142006i | −0.00394917 | + | 0.00684017i | −0.867993 | − | 0.496576i | \(-0.834590\pi\) |
0.864044 | + | 0.503416i | \(0.167924\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13.2611 | − | 13.2611i | 0.637288 | − | 0.637288i | −0.312597 | − | 0.949886i | \(-0.601199\pi\) |
0.949886 | + | 0.312597i | \(0.101199\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.42664 | − | 0.382266i | 0.0682453 | − | 0.0182863i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.1355 | + | 17.5553i | 0.483743 | + | 0.837867i | 0.999826 | − | 0.0186713i | \(-0.00594362\pi\) |
−0.516083 | + | 0.856539i | \(0.672610\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.84874 | + | 3.84606i | 0.278512 | + | 0.183146i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.82246 | − | 29.1938i | 0.371656 | − | 1.38704i | −0.486513 | − | 0.873673i | \(-0.661731\pi\) |
0.858169 | − | 0.513366i | \(-0.171602\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 7.95950 | + | 7.95950i | 0.376472 | + | 0.376472i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 5.18461i | − | 0.244677i | −0.992488 | − | 0.122338i | \(-0.960961\pi\) | ||
0.992488 | − | 0.122338i | \(-0.0390393\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.77835 | + | 5.64554i | 0.460445 | + | 0.265838i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.04202 | + | 2.15485i | 0.377847 | + | 0.101244i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.7570 | − | 3.15027i | −0.549967 | − | 0.147363i | −0.0268740 | − | 0.999639i | \(-0.508555\pi\) |
−0.523093 | + | 0.852276i | \(0.675222\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.92303 | + | 1.11026i | 0.0897594 | + | 0.0518226i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 21.8254i | − | 1.01651i | −0.861207 | − | 0.508255i | \(-0.830291\pi\) | ||
0.861207 | − | 0.508255i | \(-0.169709\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.2272 | − | 10.2272i | −0.475299 | − | 0.475299i | 0.428326 | − | 0.903624i | \(-0.359104\pi\) |
−0.903624 | + | 0.428326i | \(0.859104\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10.0210 | − | 37.3988i | 0.463716 | − | 1.73061i | −0.197395 | − | 0.980324i | \(-0.563248\pi\) |
0.661111 | − | 0.750288i | \(-0.270085\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.0504 | + | 3.90642i | 0.602610 | + | 0.180382i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.22052 | + | 5.57811i | 0.148394 | + | 0.257026i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −33.2320 | + | 8.90450i | −1.52801 | + | 0.409429i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.14593 | − | 2.14593i | 0.0982555 | − | 0.0982555i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.04221 | + | 15.6616i | −0.413149 | + | 0.715596i | −0.995232 | − | 0.0975338i | \(-0.968905\pi\) |
0.582083 | + | 0.813129i | \(0.302238\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 28.2540 | − | 16.3125i | 1.28827 | − | 0.743785i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −9.55657 | + | 15.4950i | −0.434839 | + | 0.705049i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.86366 | − | 6.95527i | −0.0844504 | − | 0.315173i | 0.910759 | − | 0.412938i | \(-0.135497\pi\) |
−0.995210 | + | 0.0977647i | \(0.968831\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −10.3923 | −0.469956 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 43.9746 | 1.98454 | 0.992272 | − | 0.124081i | \(-0.0395981\pi\) | ||||
0.992272 | + | 0.124081i | \(0.0395981\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.33898 | − | 19.9253i | −0.240455 | − | 0.897392i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −18.0375 | + | 29.2461i | −0.809094 | + | 1.31187i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −19.0704 | + | 11.0103i | −0.853710 | + | 0.492890i | −0.861901 | − | 0.507077i | \(-0.830726\pi\) |
0.00819105 | + | 0.999966i | \(0.497393\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9.33079 | − | 16.1614i | 0.416869 | − | 0.722038i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −12.7279 | + | 12.7279i | −0.567510 | + | 0.567510i | −0.931430 | − | 0.363920i | \(-0.881438\pi\) |
0.363920 | + | 0.931430i | \(0.381438\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.53866 | − | 0.680233i | 0.112746 | − | 0.0302102i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9.74836 | + | 16.8847i | 0.432089 | + | 0.748399i | 0.997053 | − | 0.0767160i | \(-0.0244435\pi\) |
−0.564964 | + | 0.825115i | \(0.691110\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.383379 | − | 0.114758i | −0.0169597 | − | 0.00507660i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.0555549 | + | 0.207334i | −0.00245281 | + | 0.00915401i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 33.2486 | + | 33.2486i | 1.46227 | + | 1.46227i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 13.3950i | 0.587974i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 33.9514 | + | 19.6018i | 1.48744 | + | 0.858772i | 0.999897 | − | 0.0143293i | \(-0.00456131\pi\) |
0.487539 | + | 0.873101i | \(0.337895\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12.4778 | + | 3.34343i | 0.545618 | + | 0.146198i | 0.521091 | − | 0.853501i | \(-0.325525\pi\) |
0.0245272 | + | 0.999699i | \(0.492192\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −19.2928 | − | 5.16948i | −0.840407 | − | 0.225186i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.0846 | − | 12.1732i | −0.916720 | − | 0.529268i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.36347i | 0.232755i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.30295 | + | 5.30295i | 0.229696 | + | 0.229696i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.55291 | + | 5.79555i | −0.0670132 | + | 0.250097i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 33.8840 | + | 1.97060i | 1.45949 | + | 0.0848799i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.09231 | + | 5.35603i | 0.132949 | + | 0.230274i | 0.924812 | − | 0.380425i | \(-0.124222\pi\) |
−0.791863 | + | 0.610698i | \(0.790889\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −6.39335 | + | 1.71309i | −0.274365 | + | 0.0735159i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.87524 | − | 6.87524i | 0.293964 | − | 0.293964i | −0.544680 | − | 0.838644i | \(-0.683349\pi\) |
0.838644 | + | 0.544680i | \(0.183349\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7.63957 | − | 13.2321i | 0.326049 | − | 0.564733i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.72688 | − | 0.997017i | 0.0735677 | − | 0.0424743i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.00532247 | − | 0.183191i | 0.000226334 | − | 0.00779008i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.29681 | + | 27.2321i | 0.309176 | + | 1.15386i | 0.929291 | + | 0.369349i | \(0.120419\pi\) |
−0.620115 | + | 0.784511i | \(0.712914\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −22.8513 | −0.966506 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 10.7668 | 0.454573 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6.57270 | + | 24.5297i | 0.277006 | + | 1.03380i | 0.954485 | + | 0.298259i | \(0.0964061\pi\) |
−0.677478 | + | 0.735543i | \(0.736927\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.25577 | − | 2.32874i | −0.0527376 | − | 0.0977979i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −15.7373 | + | 9.08595i | −0.659743 | + | 0.380903i | −0.792179 | − | 0.610289i | \(-0.791053\pi\) |
0.132436 | + | 0.991192i | \(0.457720\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.37306 | − | 5.84231i | 0.141158 | − | 0.244493i | −0.786775 | − | 0.617240i | \(-0.788251\pi\) |
0.927933 | + | 0.372747i | \(0.121584\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7.38294 | + | 7.38294i | −0.308427 | + | 0.308427i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.39256 | + | 0.641085i | −0.0996037 | + | 0.0266887i | −0.308277 | − | 0.951297i | \(-0.599752\pi\) |
0.208673 | + | 0.977985i | \(0.433086\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.298304 | + | 0.516678i | 0.0123971 | + | 0.0214724i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.403734 | − | 1.70316i | −0.0167497 | − | 0.0706591i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.80852 | − | 14.2136i | 0.157733 | − | 0.588667i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5.92874 | + | 5.92874i | 0.244705 | + | 0.244705i | 0.818793 | − | 0.574088i | \(-0.194643\pi\) |
−0.574088 | + | 0.818793i | \(0.694643\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 1.93073i | − | 0.0795544i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −20.2154 | − | 11.6714i | −0.831552 | − | 0.480097i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.65864 | + | 2.32008i | 0.355568 | + | 0.0952741i | 0.432181 | − | 0.901787i | \(-0.357744\pi\) |
−0.0766134 | + | 0.997061i | \(0.524411\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −24.7967 | − | 6.64426i | −1.01486 | − | 0.271931i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.89633 | − | 4.55895i | −0.322635 | − | 0.186274i | 0.329931 | − | 0.944005i | \(-0.392974\pi\) |
−0.652567 | + | 0.757731i | \(0.726308\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 45.0586i | 1.83798i | 0.394281 | + | 0.918990i | \(0.370994\pi\) | ||||
−0.394281 | + | 0.918990i | \(0.629006\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.64076 | − | 3.64076i | −0.148263 | − | 0.148263i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.658351 | + | 2.45700i | −0.0267217 | + | 0.0997266i | −0.977999 | − | 0.208611i | \(-0.933106\pi\) |
0.951277 | + | 0.308337i | \(0.0997725\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −7.04818 | + | 23.5462i | −0.285607 | + | 0.954141i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 15.6155 | + | 27.0468i | 0.631736 | + | 1.09420i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.14248 | + | 0.306125i | −0.0461442 | + | 0.0123643i | −0.281817 | − | 0.959468i | \(-0.590937\pi\) |
0.235673 | + | 0.971832i | \(0.424271\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.58337 | − | 2.58337i | 0.104003 | − | 0.104003i | −0.653191 | − | 0.757193i | \(-0.726570\pi\) |
0.757193 | + | 0.653191i | \(0.226570\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.51887 | − | 6.09486i | 0.141435 | − | 0.244973i | −0.786602 | − | 0.617460i | \(-0.788162\pi\) |
0.928037 | + | 0.372487i | \(0.121495\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.95901 | − | 3.44043i | 0.239127 | − | 0.138060i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.27349 | + | 0.153217i | 0.211278 | + | 0.00613851i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.269372 | + | 1.00531i | 0.0107577 | + | 0.0401482i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −22.4946 | −0.896920 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.92817 | 0.0767594 | 0.0383797 | − | 0.999263i | \(-0.487780\pi\) | ||||
0.0383797 | + | 0.999263i | \(0.487780\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.07598 | − | 11.4797i | −0.122259 | − | 0.456277i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 21.4000 | + | 7.08916i | 0.847900 | + | 0.280883i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 11.2473 | − | 6.49364i | 0.444937 | − | 0.256884i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −14.7962 | + | 25.6277i | −0.584413 | + | 1.01223i | 0.410535 | + | 0.911845i | \(0.365342\pi\) |
−0.994948 | + | 0.100388i | \(0.967992\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −16.2563 | + | 16.2563i | −0.641085 | + | 0.641085i | −0.950822 | − | 0.309737i | \(-0.899759\pi\) |
0.309737 | + | 0.950822i | \(0.399759\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −38.9839 | + | 10.4457i | −1.53261 | + | 0.410663i | −0.923871 | − | 0.382705i | \(-0.874993\pi\) |
−0.608743 | + | 0.793367i | \(0.708326\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13.0030 | + | 22.5219i | 0.510414 | + | 0.884063i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 16.3321 | + | 17.3095i | 0.640104 | + | 0.678413i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10.0233 | − | 37.4074i | 0.392242 | − | 1.46387i | −0.434186 | − | 0.900823i | \(-0.642964\pi\) |
0.826428 | − | 0.563043i | \(-0.190369\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.106954 | + | 0.106954i | 0.00417268 | + | 0.00417268i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 17.2564i | 0.672215i | 0.941824 | + | 0.336108i | \(0.109111\pi\) | ||||
−0.941824 | + | 0.336108i | \(0.890889\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21.8475 | − | 12.6136i | −0.849768 | − | 0.490614i | 0.0108046 | − | 0.999942i | \(-0.496561\pi\) |
−0.860573 | + | 0.509328i | \(0.829894\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6.90758 | + | 1.85088i | 0.268268 | + | 0.0718823i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −61.7438 | − | 16.5442i | −2.39073 | − | 0.640594i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 23.0186 | + | 13.2898i | 0.889950 | + | 0.513813i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 74.0846i | − | 2.86001i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 21.3943 | + | 21.3943i | 0.824690 | + | 0.824690i | 0.986777 | − | 0.162087i | \(-0.0518224\pi\) |
−0.162087 | + | 0.986777i | \(0.551822\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.06660 | + | 7.71265i | −0.0794258 | + | 0.296421i | −0.994200 | − | 0.107544i | \(-0.965702\pi\) |
0.914775 | + | 0.403965i | \(0.132368\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 27.3614 | − | 6.48600i | 1.05003 | − | 0.248910i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.24880 | − | 16.0194i | −0.354415 | − | 0.613864i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9.25458 | − | 2.47976i | 0.354117 | − | 0.0948853i | −0.0773753 | − | 0.997002i | \(-0.524654\pi\) |
0.431492 | + | 0.902117i | \(0.357987\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −9.04645 | + | 9.04645i | −0.345143 | + | 0.345143i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.88683 | − | 8.46425i | 0.186174 | − | 0.322462i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.01288 | − | 1.73949i | 0.114615 | − | 0.0661731i | −0.441596 | − | 0.897214i | \(-0.645588\pi\) |
0.556212 | + | 0.831041i | \(0.312254\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −10.9189 | − | 6.73423i | −0.414775 | − | 0.255812i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.33831 | − | 4.99465i | −0.0506922 | − | 0.189186i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −15.3842 | −0.581886 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −28.6129 | −1.08070 | −0.540348 | − | 0.841442i | \(-0.681707\pi\) | ||||
−0.540348 | + | 0.841442i | \(0.681707\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.562789 | − | 2.10036i | −0.0212260 | − | 0.0792165i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 11.7109 | − | 6.31509i | 0.440432 | − | 0.237503i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 29.7847 | − | 17.1962i | 1.11859 | − | 0.645817i | 0.177548 | − | 0.984112i | \(-0.443183\pi\) |
0.941040 | + | 0.338295i | \(0.109850\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.0346345 | + | 0.0599887i | −0.00129890 | + | 0.00224975i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −43.7647 | + | 43.7647i | −1.63900 | + | 1.63900i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 12.8692 | − | 3.44828i | 0.480608 | − | 0.128779i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −16.4619 | − | 28.5129i | −0.613926 | − | 1.06335i | −0.990572 | − | 0.136994i | \(-0.956256\pi\) |
0.376646 | − | 0.926357i | \(-0.377077\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.2552 | − | 10.6196i | 0.419164 | − | 0.395495i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.812670 | − | 3.03292i | 0.0302235 | − | 0.112796i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 34.2948 | + | 34.2948i | 1.27192 | + | 1.27192i | 0.945078 | + | 0.326846i | \(0.105986\pi\) |
0.326846 | + | 0.945078i | \(0.394014\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 13.6449 | + | 7.87788i | 0.504675 | + | 0.291374i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.26793 | + | 2.48333i | 0.342319 | + | 0.0917240i | 0.425883 | − | 0.904778i | \(-0.359964\pi\) |
−0.0835640 | + | 0.996502i | \(0.526630\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −24.1146 | − | 6.46149i | −0.888274 | − | 0.238012i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 10.5145 | + | 6.07055i | 0.386782 | + | 0.223309i | 0.680765 | − | 0.732502i | \(-0.261648\pi\) |
−0.293983 | + | 0.955811i | \(0.594981\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.691279i | 0.0253948i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 35.2058 | + | 35.2058i | 1.29158 | + | 1.29158i | 0.933811 | + | 0.357766i | \(0.116461\pi\) |
0.357766 | + | 0.933811i | \(0.383539\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.171228 | + | 0.639032i | −0.00626491 | + | 0.0233810i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.75731 | + | 6.37574i | −0.246907 | + | 0.232964i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.23084 | − | 12.5242i | −0.263857 | − | 0.457014i | 0.703406 | − | 0.710788i | \(-0.251661\pi\) |
−0.967264 | + | 0.253774i | \(0.918328\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 15.8654 | − | 4.25111i | 0.578166 | − | 0.154919i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.14729 | − | 1.14729i | 0.0416989 | − | 0.0416989i | −0.685950 | − | 0.727649i | \(-0.740613\pi\) |
0.727649 | + | 0.685950i | \(0.240613\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 16.6818 | − | 28.8937i | 0.605510 | − | 1.04877i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −31.6887 | + | 18.2955i | −1.14872 | + | 0.663211i | −0.948574 | − | 0.316556i | \(-0.897474\pi\) |
−0.200142 | + | 0.979767i | \(0.564140\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −27.4017 | + | 14.7764i | −0.992009 | + | 0.534941i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.47063 | + | 16.6846i | 0.161425 | + | 0.602446i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9.84303 | −0.354949 | −0.177474 | − | 0.984125i | \(-0.556793\pi\) | ||||
−0.177474 | + | 0.984125i | \(0.556793\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 16.3591 | 0.589157 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −9.48871 | − | 35.4124i | −0.341285 | − | 1.27369i | −0.896892 | − | 0.442249i | \(-0.854181\pi\) |
0.555607 | − | 0.831445i | \(-0.312486\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 22.8125 | + | 14.0696i | 0.818394 | + | 0.504744i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.432875 | − | 0.249921i | 0.0155094 | − | 0.00895434i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 31.4860 | − | 54.5354i | 1.12666 | − | 1.95143i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6.56888 | − | 6.56888i | 0.234752 | − | 0.234752i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 22.0134 | − | 5.89847i | 0.784693 | − | 0.210258i | 0.155840 | − | 0.987782i | \(-0.450191\pi\) |
0.628853 | + | 0.777524i | \(0.283525\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −14.4057 | − | 24.9514i | −0.512856 | − | 0.888292i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −36.2898 | + | 8.60248i | −1.29032 | + | 0.305869i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12.7357 | − | 47.5302i | 0.452257 | − | 1.68785i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 31.7293 | + | 31.7293i | 1.12391 | + | 1.12391i | 0.991148 | + | 0.132760i | \(0.0423838\pi\) |
0.132760 | + | 0.991148i | \(0.457616\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 21.5335i | − | 0.761801i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.72688 | − | 0.997017i | −0.0610164 | − | 0.0352279i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.708411 | + | 0.189818i | 0.0249993 | + | 0.00669854i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 13.2928 | + | 3.56180i | 0.467929 | + | 0.125381i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −14.9445 | − | 8.62822i | −0.525421 | − | 0.303352i | 0.213729 | − | 0.976893i | \(-0.431439\pi\) |
−0.739150 | + | 0.673541i | \(0.764772\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 46.1720i | 1.62132i | 0.585517 | + | 0.810660i | \(0.300891\pi\) | ||||
−0.585517 | + | 0.810660i | \(0.699109\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 8.42144 | + | 8.42144i | 0.295353 | + | 0.295353i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.394191 | + | 1.47114i | −0.0137910 | + | 0.0514687i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −5.84753 | − | 6.19749i | −0.204329 | − | 0.216558i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9.49364 | − | 16.4435i | −0.331330 | − | 0.573881i | 0.651443 | − | 0.758698i | \(-0.274164\pi\) |
−0.982773 | + | 0.184817i | \(0.940831\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −28.6978 | + | 7.68955i | −1.00034 | + | 0.268041i | −0.721589 | − | 0.692322i | \(-0.756588\pi\) |
−0.278753 | + | 0.960363i | \(0.589921\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 20.1361 | − | 20.1361i | 0.700201 | − | 0.700201i | −0.264253 | − | 0.964453i | \(-0.585125\pi\) |
0.964453 | + | 0.264253i | \(0.0851254\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −23.6174 | + | 40.9066i | −0.820267 | + | 1.42074i | 0.0852165 | + | 0.996362i | \(0.472842\pi\) |
−0.905483 | + | 0.424382i | \(0.860492\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −17.4013 | + | 10.0467i | −0.603646 | + | 0.348515i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −10.3344 | − | 11.6106i | −0.358065 | − | 0.402284i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.32805 | − | 8.68839i | −0.0804690 | − | 0.300315i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 40.5791 | 1.40094 | 0.700472 | − | 0.713680i | \(-0.252973\pi\) | ||||
0.700472 | + | 0.713680i | \(0.252973\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −57.3003 | −1.97587 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.25584 | − | 12.1509i | −0.112137 | − | 0.418501i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −33.0852 | − | 0.961264i | −1.13682 | − | 0.0330294i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 15.5774 | − | 8.99364i | 0.534616 | − | 0.308661i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −34.8527 | + | 60.3667i | −1.19474 | + | 2.06934i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −34.2440 | + | 34.2440i | −1.17249 | + | 1.17249i | −0.190879 | + | 0.981614i | \(0.561134\pi\) |
−0.981614 | + | 0.190879i | \(0.938866\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −20.6512 | + | 5.53347i | −0.705432 | + | 0.189020i | −0.593662 | − | 0.804714i | \(-0.702318\pi\) |
−0.111769 | + | 0.993734i | \(0.535652\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −19.0104 | − | 32.9271i | −0.648628 | − | 1.12346i | −0.983451 | − | 0.181175i | \(-0.942010\pi\) |
0.334823 | − | 0.942281i | \(-0.391324\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.76676 | + | 5.90230i | −0.0602109 | + | 0.201150i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −5.72588 | + | 21.3693i | −0.194911 | + | 0.727419i | 0.797378 | + | 0.603480i | \(0.206219\pi\) |
−0.992290 | + | 0.123939i | \(0.960447\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 8.53426 | + | 8.53426i | 0.289839 | + | 0.289839i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.335868i | 0.0113935i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14.3603 | − | 8.29095i | −0.486582 | − | 0.280928i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −10.2661 | − | 2.75079i | −0.347454 | − | 0.0931000i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −23.9286 | − | 6.41164i | −0.808010 | − | 0.216506i | −0.168912 | − | 0.985631i | \(-0.554025\pi\) |
−0.639098 | + | 0.769125i | \(0.720692\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −0.501938 | − | 0.289794i | −0.0169299 | − | 0.00977451i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 30.2237i | − | 1.01826i | −0.860689 | − | 0.509130i | \(-0.829967\pi\) | ||
0.860689 | − | 0.509130i | \(-0.170033\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −15.9836 | − | 15.9836i | −0.537890 | − | 0.537890i | 0.385019 | − | 0.922909i | \(-0.374195\pi\) |
−0.922909 | + | 0.385019i | \(0.874195\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 11.3416 | − | 42.3276i | 0.380815 | − | 1.42122i | −0.463844 | − | 0.885917i | \(-0.653530\pi\) |
0.844659 | − | 0.535305i | \(-0.179803\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.19990 | − | 13.4989i | −0.107321 | − | 0.452738i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.42437 | + | 4.19914i | 0.0812195 | + | 0.140676i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.01062 | − | 0.538743i | 0.0672828 | − | 0.0180284i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 15.6695 | − | 15.6695i | 0.523189 | − | 0.523189i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −41.7803 | + | 72.3656i | −1.39345 | + | 2.41353i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.83603 | + | 3.36943i | −0.194426 | + | 0.112252i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8.91037 | − | 16.5236i | −0.296518 | − | 0.549871i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.63874 | − | 6.11585i | −0.0544134 | − | 0.203074i | 0.933368 | − | 0.358922i | \(-0.116856\pi\) |
−0.987781 | + | 0.155848i | \(0.950189\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −5.02884 | −0.166796 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.12582 | −0.103563 | −0.0517815 | − | 0.998658i | \(-0.516490\pi\) | ||||
−0.0517815 | + | 0.998658i | \(0.516490\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.830242 | + | 3.09850i | 0.0274770 | + | 0.102546i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −0.824233 | + | 28.3688i | −0.0272186 | + | 0.936821i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 22.2726 | − | 12.8591i | 0.734704 | − | 0.424181i | −0.0854368 | − | 0.996344i | \(-0.527229\pi\) |
0.820140 | + | 0.572162i | \(0.193895\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.528276 | + | 0.915000i | −0.0174073 | + | 0.0301503i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 29.5754 | − | 29.5754i | 0.973485 | − | 0.973485i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −5.64945 | + | 1.51377i | −0.185552 | + | 0.0497186i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −12.9320 | − | 22.3989i | −0.424286 | − | 0.734885i | 0.572067 | − | 0.820207i | \(-0.306142\pi\) |
−0.996353 | + | 0.0853214i | \(0.972808\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.825549 | − | 1.25542i | 0.0270563 | − | 0.0411447i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4.86336 | − | 18.1503i | 0.159219 | − | 0.594214i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −37.7290 | − | 37.7290i | −1.23255 | − | 1.23255i | −0.962980 | − | 0.269571i | \(-0.913118\pi\) |
−0.269571 | − | 0.962980i | \(-0.586882\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 3.84874i | − | 0.125599i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 12.7755 | + | 7.37595i | 0.416470 | + | 0.240449i | 0.693566 | − | 0.720393i | \(-0.256039\pi\) |
−0.277096 | + | 0.960842i | \(0.589372\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −15.4772 | − | 4.14711i | −0.504008 | − | 0.135048i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −10.9420 | − | 2.93189i | −0.355566 | − | 0.0952737i | 0.0766141 | − | 0.997061i | \(-0.475589\pi\) |
−0.432181 | + | 0.901787i | \(0.642256\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.421861 | + | 0.243562i | 0.0136942 | + | 0.00790635i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.17681i | 0.103015i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 25.4266 | + | 25.4266i | 0.823648 | + | 0.823648i | 0.986629 | − | 0.162981i | \(-0.0521109\pi\) |
−0.162981 | + | 0.986629i | \(0.552111\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 11.6582 | − | 43.5090i | 0.376856 | − | 1.40645i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −36.0891 | − | 10.8027i | −1.16538 | − | 0.348836i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 24.9539 | + | 43.2215i | 0.804965 | + | 1.39424i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.39179 | − | 0.908827i | 0.109299 | − | 0.0292865i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 42.9279 | − | 42.9279i | 1.38047 | − | 1.38047i | 0.536691 | − | 0.843779i | \(-0.319674\pi\) |
0.843779 | − | 0.536691i | \(-0.180326\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.238315 | − | 0.412774i | 0.00765579 | − | 0.0132602i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 38.9180 | − | 22.4693i | 1.24894 | − | 0.721075i | 0.278041 | − | 0.960569i | \(-0.410315\pi\) |
0.970898 | + | 0.239494i | \(0.0769817\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 19.4113 | − | 31.4735i | 0.622296 | − | 1.00899i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −11.0555 | − | 41.2596i | −0.353696 | − | 1.32001i | −0.882117 | − | 0.471030i | \(-0.843882\pi\) |
0.528421 | − | 0.848982i | \(-0.322784\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.66856 | −0.309009 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11.7668 | 0.375684 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.32066 | + | 4.92876i | 0.0421224 | + | 0.157203i | 0.983784 | − | 0.179359i | \(-0.0574024\pi\) |
−0.941661 | + | 0.336562i | \(0.890736\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −13.4685 | + | 21.8378i | −0.428706 | + | 0.695105i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 42.2822 | − | 24.4117i | 1.34450 | − | 0.776245i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.44233 | + | 7.69434i | −0.141115 | + | 0.244419i | −0.927917 | − | 0.372787i | \(-0.878402\pi\) |
0.786802 | + | 0.617206i | \(0.211735\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 11.3283 | − | 11.3283i | 0.359493 | − | 0.359493i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 32.1754 | − | 8.62137i | 1.01901 | − | 0.273042i | 0.289618 | − | 0.957142i | \(-0.406472\pi\) |
0.729388 | + | 0.684101i | \(0.239805\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.06516 | − | 8.77312i | −0.160255 | − | 0.277569i |
(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 | 2100.2.ce.d.493.1 | yes | 24 | |
5.2 | odd | 4 | inner | 2100.2.ce.d.157.1 | ✓ | 24 | |
5.3 | odd | 4 | inner | 2100.2.ce.d.157.6 | yes | 24 | |
5.4 | even | 2 | inner | 2100.2.ce.d.493.5 | yes | 24 | |
7.5 | odd | 6 | inner | 2100.2.ce.d.1993.1 | yes | 24 | |
35.12 | even | 12 | inner | 2100.2.ce.d.1657.1 | yes | 24 | |
35.19 | odd | 6 | inner | 2100.2.ce.d.1993.5 | yes | 24 | |
35.33 | even | 12 | inner | 2100.2.ce.d.1657.5 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2100.2.ce.d.157.1 | ✓ | 24 | 5.2 | odd | 4 | inner | |
2100.2.ce.d.157.6 | yes | 24 | 5.3 | odd | 4 | inner | |
2100.2.ce.d.493.1 | yes | 24 | 1.1 | even | 1 | trivial | |
2100.2.ce.d.493.5 | yes | 24 | 5.4 | even | 2 | inner | |
2100.2.ce.d.1657.1 | yes | 24 | 35.12 | even | 12 | inner | |
2100.2.ce.d.1657.5 | yes | 24 | 35.33 | even | 12 | inner | |
2100.2.ce.d.1993.1 | yes | 24 | 7.5 | odd | 6 | inner | |
2100.2.ce.d.1993.5 | yes | 24 | 35.19 | odd | 6 | inner |