Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [912,2,Mod(79,912)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(912, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([9, 0, 0, 13]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("912.79");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 912 = 2^{4} \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 912.ci (of order \(18\), degree \(6\), 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: | \(7.28235666434\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{18})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 6 x^{17} - 3 x^{16} + 100 x^{15} - 171 x^{14} - 471 x^{13} + 1537 x^{12} + 321 x^{11} - 3936 x^{10} - 1317 x^{9} + 4941 x^{8} + 21078 x^{7} - 14829 x^{6} + \cdots + 1367631 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 751.3 | ||
Root | \(-2.15607 - 0.0639189i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 912.751 |
Dual form | 912.2.ci.f.895.3 |
$q$-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 \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(229\) | \(305\) | \(799\) |
\(\chi(n)\) | \(e\left(\frac{17}{18}\right)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 0.766044 | − | 0.642788i | 0.442276 | − | 0.371114i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.02685 | + | 1.10168i | 1.35365 | + | 0.492688i | 0.914085 | − | 0.405522i | \(-0.132910\pi\) |
0.439565 | + | 0.898211i | \(0.355133\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.81645 | + | 1.04873i | 0.686553 | + | 0.396381i | 0.802319 | − | 0.596895i | \(-0.203599\pi\) |
−0.115767 | + | 0.993276i | \(0.536932\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.173648 | − | 0.984808i | 0.0578827 | − | 0.328269i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.32141 | + | 0.762916i | −0.398420 | + | 0.230028i | −0.685802 | − | 0.727788i | \(-0.740548\pi\) |
0.287382 | + | 0.957816i | \(0.407215\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.47269 | − | 4.13859i | 0.963151 | − | 1.14784i | −0.0258107 | − | 0.999667i | \(-0.508217\pi\) |
0.988962 | − | 0.148172i | \(-0.0473388\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.02685 | − | 1.10168i | 0.781530 | − | 0.284454i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.0697157 | − | 0.395377i | −0.0169085 | − | 0.0958931i | 0.975186 | − | 0.221389i | \(-0.0710590\pi\) |
−0.992094 | + | 0.125496i | \(0.959948\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.70519 | + | 4.01152i | −0.391199 | + | 0.920306i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.06559 | − | 0.364219i | 0.450748 | − | 0.0794791i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.994583 | − | 2.73259i | −0.207385 | − | 0.569785i | 0.791773 | − | 0.610815i | \(-0.209158\pi\) |
−0.999158 | + | 0.0410302i | \(0.986936\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.11792 | + | 3.45534i | 0.823583 | + | 0.691068i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.500000 | − | 0.866025i | −0.0962250 | − | 0.166667i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.725223 | − | 0.127876i | −0.134671 | − | 0.0237460i | 0.105907 | − | 0.994376i | \(-0.466226\pi\) |
−0.240577 | + | 0.970630i | \(0.577337\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.72904 | + | 4.72684i | −0.490150 | + | 0.848965i | −0.999936 | − | 0.0113364i | \(-0.996391\pi\) |
0.509786 | + | 0.860302i | \(0.329725\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.521865 | + | 1.43381i | −0.0908451 | + | 0.249595i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.34276 | + | 5.17550i | 0.734060 | + | 0.874819i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.91535i | 0.643679i | 0.946794 | + | 0.321839i | \(0.104301\pi\) | ||||
−0.946794 | + | 0.321839i | \(0.895699\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 5.40255i | − | 0.865100i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.82246 | + | 4.55543i | 0.596967 | + | 0.711438i | 0.976929 | − | 0.213564i | \(-0.0685073\pi\) |
−0.379962 | + | 0.925002i | \(0.624063\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.67537 | − | 7.35052i | 0.407990 | − | 1.12094i | −0.550255 | − | 0.834996i | \(-0.685470\pi\) |
0.958245 | − | 0.285947i | \(-0.0923082\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.61056 | − | 2.78956i | 0.240087 | − | 0.415844i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.18147 | − | 1.61894i | −1.33925 | − | 0.236147i | −0.542299 | − | 0.840185i | \(-0.682446\pi\) |
−0.796955 | + | 0.604039i | \(0.793557\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.30035 | − | 2.25226i | −0.185764 | − | 0.321752i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.307549 | − | 0.258064i | −0.0430655 | − | 0.0361362i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.116137 | − | 0.319084i | −0.0159527 | − | 0.0438296i | 0.931461 | − | 0.363842i | \(-0.118535\pi\) |
−0.947413 | + | 0.320012i | \(0.896313\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.84021 | + | 0.853459i | −0.652653 | + | 0.115080i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.27230 | + | 4.16908i | 0.168520 | + | 0.552208i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.81685 | + | 10.3039i | 0.236534 | + | 1.34145i | 0.839359 | + | 0.543578i | \(0.182931\pi\) |
−0.602825 | + | 0.797874i | \(0.705958\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.45154 | + | 0.892288i | −0.313888 | + | 0.114246i | −0.494160 | − | 0.869371i | \(-0.664524\pi\) |
0.180272 | + | 0.983617i | \(0.442302\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.34822 | − | 1.60674i | 0.169859 | − | 0.202431i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 15.0708 | − | 8.70110i | 1.86930 | − | 1.07924i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.74510 | − | 9.89698i | 0.213198 | − | 1.20911i | −0.670807 | − | 0.741632i | \(-0.734052\pi\) |
0.884006 | − | 0.467476i | \(-0.154837\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.51837 | − | 1.45398i | −0.303176 | − | 0.175039i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.09275 | − | 0.397729i | −0.129686 | − | 0.0472017i | 0.276362 | − | 0.961054i | \(-0.410871\pi\) |
−0.406048 | + | 0.913852i | \(0.633093\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.32157 | − | 3.62623i | 0.505801 | − | 0.424418i | −0.353848 | − | 0.935303i | \(-0.615127\pi\) |
0.859649 | + | 0.510886i | \(0.170682\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.37556 | 0.620716 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.20036 | −0.364715 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.16316 | − | 6.84971i | 0.918428 | − | 0.770652i | −0.0552759 | − | 0.998471i | \(-0.517604\pi\) |
0.973704 | + | 0.227819i | \(0.0731594\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.939693 | − | 0.342020i | −0.104410 | − | 0.0380022i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −11.4897 | − | 6.63357i | −1.26116 | − | 0.728129i | −0.287858 | − | 0.957673i | \(-0.592943\pi\) |
−0.973298 | + | 0.229544i | \(0.926276\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.224562 | − | 1.27355i | 0.0243572 | − | 0.138136i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.637750 | + | 0.368205i | −0.0683740 | + | 0.0394758i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.157877 | + | 0.188151i | −0.0167350 | + | 0.0199439i | −0.774347 | − | 0.632761i | \(-0.781921\pi\) |
0.757612 | + | 0.652705i | \(0.226366\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.6482 | − | 3.87563i | 1.11624 | − | 0.406277i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.947786 | + | 5.37516i | 0.0982808 | + | 0.557378i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −9.58081 | + | 10.2637i | −0.982970 | + | 1.05303i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15.3071 | − | 2.69906i | 1.55421 | − | 0.274048i | 0.670435 | − | 0.741969i | \(-0.266108\pi\) |
0.883771 | + | 0.467920i | \(0.154997\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.521865 | + | 1.43381i | 0.0524494 | + | 0.144104i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.78201 | + | 3.17348i | 0.376324 | + | 0.315773i | 0.811257 | − | 0.584689i | \(-0.198784\pi\) |
−0.434933 | + | 0.900463i | \(0.643228\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.11152 | + | 8.85342i | 0.503654 | + | 0.872353i | 0.999991 | + | 0.00422386i | \(0.00134450\pi\) |
−0.496338 | + | 0.868130i | \(0.665322\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 6.65349 | + | 1.17319i | 0.649314 | + | 0.114492i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.32768 | + | 14.4240i | −0.805067 | + | 1.39442i | 0.111178 | + | 0.993800i | \(0.464537\pi\) |
−0.916246 | + | 0.400617i | \(0.868796\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.95854 | + | 5.38104i | −0.187594 | + | 0.515410i | −0.997462 | − | 0.0712020i | \(-0.977317\pi\) |
0.809868 | + | 0.586612i | \(0.199539\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.51674 | + | 2.99933i | 0.238878 | + | 0.284684i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 16.6565i | − | 1.56692i | −0.621445 | − | 0.783458i | \(-0.713454\pi\) | ||
0.621445 | − | 0.783458i | \(-0.286546\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 9.36688i | − | 0.873466i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.47269 | − | 4.13859i | −0.321050 | − | 0.382613i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.288008 | − | 0.791295i | 0.0264016 | − | 0.0725379i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.33592 | + | 7.51003i | −0.394174 | + | 0.682730i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.85634 | + | 1.03263i | 0.528049 | + | 0.0931092i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.604858 | + | 1.04764i | 0.0541001 | + | 0.0937041i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.69721 | − | 6.45873i | −0.683017 | − | 0.573120i | 0.233869 | − | 0.972268i | \(-0.424861\pi\) |
−0.916886 | + | 0.399149i | \(0.869306\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.67537 | − | 7.35052i | −0.235553 | − | 0.647177i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −15.1931 | + | 2.67895i | −1.32742 | + | 0.234061i | −0.791999 | − | 0.610522i | \(-0.790960\pi\) |
−0.535425 | + | 0.844583i | \(0.679848\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.30439 | + | 5.49844i | −0.633371 | + | 0.476775i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.559340 | − | 3.17218i | −0.0481403 | − | 0.273017i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −13.7733 | + | 5.01306i | −1.17673 | + | 0.428295i | −0.855046 | − | 0.518552i | \(-0.826471\pi\) |
−0.321685 | + | 0.946847i | \(0.604249\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.24652 | − | 11.0196i | 0.784280 | − | 0.934669i | −0.214838 | − | 0.976650i | \(-0.568922\pi\) |
0.999118 | + | 0.0419811i | \(0.0133669\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.07404 | + | 4.66155i | −0.679957 | + | 0.392573i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.43145 | + | 8.11814i | −0.119704 | + | 0.678873i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.05426 | − | 1.18603i | −0.170597 | − | 0.0984945i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.44385 | − | 0.889488i | −0.201565 | − | 0.0733638i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −15.5901 | + | 13.0817i | −1.27719 | + | 1.07169i | −0.283569 | + | 0.958952i | \(0.591518\pi\) |
−0.993625 | + | 0.112740i | \(0.964037\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.81477 | 0.473199 | 0.236600 | − | 0.971607i | \(-0.423967\pi\) | ||||
0.236600 | + | 0.971607i | \(0.423967\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.401477 | −0.0324575 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −13.4679 | + | 11.3009i | −1.08177 | + | 0.907711i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −20.7381 | − | 7.54804i | −1.65508 | − | 0.602400i | −0.665501 | − | 0.746397i | \(-0.731782\pi\) |
−0.989578 | + | 0.143997i | \(0.954004\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.294070 | − | 0.169781i | −0.0233212 | − | 0.0134645i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.05914 | − | 6.00666i | 0.0834716 | − | 0.473391i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.5945 | − | 7.27141i | 0.986474 | − | 0.569541i | 0.0822556 | − | 0.996611i | \(-0.473788\pi\) |
0.904218 | + | 0.427070i | \(0.140454\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.15922 | + | 3.76501i | −0.245945 | + | 0.293106i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 19.7550 | − | 7.19023i | 1.52869 | − | 0.556397i | 0.565388 | − | 0.824825i | \(-0.308727\pi\) |
0.963300 | + | 0.268429i | \(0.0865044\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.81093 | − | 15.9416i | −0.216226 | − | 1.22628i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.65447 | + | 2.37588i | 0.279465 | + | 0.181688i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −24.5257 | + | 4.32455i | −1.86466 | + | 0.328789i | −0.988258 | − | 0.152795i | \(-0.951173\pi\) |
−0.876400 | + | 0.481584i | \(0.840062\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.85627 | + | 10.5950i | 0.291507 | + | 0.800908i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.01500 | + | 6.72538i | 0.602444 | + | 0.505511i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.0720 | + | 20.9094i | 0.902307 | + | 1.56284i | 0.824491 | + | 0.565874i | \(0.191461\pi\) |
0.0778159 | + | 0.996968i | \(0.475205\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.0659 | − | 1.95121i | −0.822520 | − | 0.145033i | −0.253478 | − | 0.967341i | \(-0.581575\pi\) |
−0.569042 | + | 0.822308i | \(0.692686\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.30444 | + | 2.25935i | −0.0964268 | + | 0.167016i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.31348 | + | 11.8512i | −0.317133 | + | 0.871316i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.393763 | + | 0.469268i | 0.0287948 | + | 0.0343163i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 2.09745i | − | 0.152567i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 0.336347i | − | 0.0243372i | −0.999926 | − | 0.0121686i | \(-0.996127\pi\) | ||
0.999926 | − | 0.0121686i | \(-0.00387349\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.535482 | + | 0.638163i | 0.0385449 | + | 0.0459360i | 0.784972 | − | 0.619531i | \(-0.212677\pi\) |
−0.746428 | + | 0.665467i | \(0.768233\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.95190 | − | 16.3527i | 0.426225 | − | 1.17104i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.01903 | + | 8.69322i | −0.357591 | + | 0.619366i | −0.987558 | − | 0.157256i | \(-0.949735\pi\) |
0.629967 | + | 0.776622i | \(0.283069\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.64607 | − | 0.819227i | −0.329351 | − | 0.0580735i | 0.00652776 | − | 0.999979i | \(-0.497922\pi\) |
−0.335879 | + | 0.941905i | \(0.609033\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.02483 | − | 8.70325i | −0.354424 | − | 0.613880i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.18322 | − | 0.992841i | −0.0830459 | − | 0.0696838i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.55137 | + | 17.9998i | 0.457568 | + | 1.25716i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.86379 | + | 0.504963i | −0.199047 | + | 0.0350973i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.807194 | − | 6.60178i | −0.0558348 | − | 0.456655i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.37181 | + | 13.4512i | 0.163282 | + | 0.926020i | 0.950818 | + | 0.309751i | \(0.100246\pi\) |
−0.787536 | + | 0.616269i | \(0.788643\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.09275 | + | 0.397729i | −0.0748740 | + | 0.0272519i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 16.1959 | − | 19.3015i | 1.10455 | − | 1.31635i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.91432 | + | 5.72404i | −0.673028 | + | 0.388573i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.979620 | − | 5.55570i | 0.0661966 | − | 0.375419i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.87841 | − | 1.08450i | −0.126355 | − | 0.0729513i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −14.4781 | − | 5.26960i | −0.969526 | − | 0.352878i | −0.191766 | − | 0.981441i | \(-0.561422\pi\) |
−0.777759 | + | 0.628562i | \(0.783644\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.11792 | − | 3.45534i | 0.274528 | − | 0.230356i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.5959 | −0.769648 | −0.384824 | − | 0.922990i | \(-0.625738\pi\) | ||||
−0.384824 | + | 0.922990i | \(0.625738\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −21.6883 | −1.43320 | −0.716600 | − | 0.697484i | \(-0.754303\pi\) | ||||
−0.716600 | + | 0.697484i | \(0.754303\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.45162 | + | 2.05715i | −0.161305 | + | 0.135351i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 17.5176 | + | 6.37589i | 1.14762 | + | 0.417698i | 0.844658 | − | 0.535306i | \(-0.179804\pi\) |
0.302958 | + | 0.953004i | \(0.402026\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −26.0074 | − | 15.0154i | −1.69654 | − | 0.979495i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.85044 | − | 10.4944i | 0.120199 | − | 0.681682i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.148903 | + | 0.0859691i | −0.00963173 | + | 0.00556088i | −0.504808 | − | 0.863232i | \(-0.668437\pi\) |
0.495176 | + | 0.868792i | \(0.335103\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.11891 | − | 9.67573i | 0.522985 | − | 0.623269i | −0.438299 | − | 0.898829i | \(-0.644419\pi\) |
0.961284 | + | 0.275560i | \(0.0888634\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.939693 | + | 0.342020i | −0.0602813 | + | 0.0219406i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.45467 | − | 8.24985i | −0.0929355 | − | 0.527063i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 10.6804 | + | 20.9879i | 0.679580 | + | 1.33543i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −13.0656 | + | 2.30381i | −0.827998 | + | 0.145998i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.00146 | + | 2.75149i | 0.0632117 | + | 0.173673i | 0.967278 | − | 0.253720i | \(-0.0816543\pi\) |
−0.904066 | + | 0.427393i | \(0.859432\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.39899 | + | 2.85209i | 0.213693 | + | 0.179309i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.646601 | − | 1.11995i | −0.0404917 | − | 0.0701337i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 13.2464 | + | 2.33571i | 0.826290 | + | 0.145697i | 0.570774 | − | 0.821107i | \(-0.306643\pi\) |
0.255517 | + | 0.966805i | \(0.417754\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.10613 | + | 7.11202i | −0.255142 | + | 0.441920i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.251867 | + | 0.692000i | −0.0155902 | + | 0.0428337i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −19.8129 | − | 23.6121i | −1.22172 | − | 1.45599i | −0.849292 | − | 0.527924i | \(-0.822971\pi\) |
−0.372426 | − | 0.928062i | \(-0.621474\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 1.09377i | − | 0.0671896i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.245613i | 0.0150313i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −11.5225 | − | 13.7320i | −0.702539 | − | 0.837253i | 0.290272 | − | 0.956944i | \(-0.406254\pi\) |
−0.992811 | + | 0.119691i | \(0.961810\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.98801 | − | 13.7044i | 0.303000 | − | 0.832486i | −0.690975 | − | 0.722879i | \(-0.742819\pi\) |
0.993975 | − | 0.109607i | \(-0.0349593\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.66579 | − | 9.81344i | 0.342909 | − | 0.593937i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −8.07759 | − | 1.42430i | −0.487097 | − | 0.0858883i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.0315 | − | 17.3750i | −0.602732 | − | 1.04396i | −0.992406 | − | 0.123009i | \(-0.960746\pi\) |
0.389674 | − | 0.920953i | \(-0.372588\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.18113 | + | 3.50839i | 0.250318 | + | 0.210042i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.48132 | + | 4.06990i | 0.0883682 | + | 0.242790i | 0.976003 | − | 0.217759i | \(-0.0698748\pi\) |
−0.887634 | + | 0.460549i | \(0.847653\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.82206 | − | 0.850259i | 0.286642 | − | 0.0505426i | −0.0284787 | − | 0.999594i | \(-0.509066\pi\) |
0.315120 | + | 0.949052i | \(0.397955\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.741943 | + | 14.0209i | −0.0439489 | + | 0.830525i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.16590 | + | 12.2834i | 0.127849 | + | 0.725066i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.8233 | − | 5.75921i | 0.930783 | − | 0.338777i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.99103 | − | 11.9068i | 0.585685 | − | 0.697992i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.64527 | − | 3.25930i | 0.329800 | − | 0.190410i | −0.325952 | − | 0.945386i | \(-0.605685\pi\) |
0.655752 | + | 0.754976i | \(0.272352\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.85229 | + | 33.1900i | −0.340733 | + | 1.93239i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.32141 | + | 0.762916i | 0.0766759 | + | 0.0442689i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −14.7630 | − | 5.37328i | −0.853764 | − | 0.310745i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.5684 | − | 10.5461i | 0.724428 | − | 0.607867i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.93706 | 0.283627 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −8.40348 | −0.481182 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −17.8847 | + | 15.0071i | −1.02074 | + | 0.856499i | −0.989720 | − | 0.143020i | \(-0.954319\pi\) |
−0.0310157 | + | 0.999519i | \(0.509874\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 9.60652 | + | 3.49649i | 0.546496 | + | 0.198908i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.0195 | + | 5.78478i | 0.568155 | + | 0.328025i | 0.756412 | − | 0.654095i | \(-0.226950\pi\) |
−0.188257 | + | 0.982120i | \(0.560284\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.04399 | + | 28.6059i | −0.285103 | + | 1.61690i | 0.419815 | + | 0.907610i | \(0.362095\pi\) |
−0.704918 | + | 0.709289i | \(0.749016\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5.85098 | − | 3.37807i | 0.329665 | − | 0.190332i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −0.836331 | + | 0.996701i | −0.0469730 | + | 0.0559803i | −0.789019 | − | 0.614368i | \(-0.789411\pi\) |
0.742046 | + | 0.670349i | \(0.233855\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.05587 | − | 0.384307i | 0.0591176 | − | 0.0215171i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.89217 | + | 16.4023i | 0.161425 | + | 0.915489i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.70494 | + | 0.394529i | 0.0948656 | + | 0.0219522i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 28.6005 | − | 5.04304i | 1.58647 | − | 0.279737i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.95854 | + | 5.38104i | 0.108307 | + | 0.297572i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −14.9798 | − | 12.5696i | −0.825865 | − | 0.692983i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.43410 | + | 4.21599i | 0.133790 | + | 0.231732i | 0.925135 | − | 0.379639i | \(-0.123952\pi\) |
−0.791344 | + | 0.611371i | \(0.790618\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.85586 | + | 0.679893i | 0.211300 | + | 0.0372579i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 16.1855 | − | 28.0342i | 0.884310 | − | 1.53167i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.15510 | + | 5.92109i | −0.117396 | + | 0.322542i | −0.984448 | − | 0.175675i | \(-0.943789\pi\) |
0.867053 | + | 0.498217i | \(0.166012\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −10.7066 | − | 12.7597i | −0.581504 | − | 0.693009i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 8.32811i | − | 0.450993i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 20.1370i | − | 1.08730i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −6.02091 | − | 7.17545i | −0.324155 | − | 0.386313i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.14064 | + | 3.13389i | −0.0612329 | + | 0.168236i | −0.966537 | − | 0.256529i | \(-0.917421\pi\) |
0.905304 | + | 0.424765i | \(0.139643\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12.4520 | + | 21.5674i | −0.666539 | + | 1.15448i | 0.312327 | + | 0.949975i | \(0.398891\pi\) |
−0.978866 | + | 0.204504i | \(0.934442\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.32047 | − | 0.938142i | −0.283986 | − | 0.0500743i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 14.5254 | + | 25.1587i | 0.773109 | + | 1.33906i | 0.935851 | + | 0.352396i | \(0.114633\pi\) |
−0.162742 | + | 0.986669i | \(0.552034\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.86942 | − | 2.40773i | −0.152293 | − | 0.127789i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.288008 | − | 0.791295i | −0.0152430 | − | 0.0418798i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −12.5139 | + | 2.20653i | −0.660456 | + | 0.116456i | −0.493822 | − | 0.869563i | \(-0.664401\pi\) |
−0.166633 | + | 0.986019i | \(0.553290\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.1846 | − | 13.6809i | −0.693927 | − | 0.720045i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.50585 | + | 8.54009i | 0.0790366 | + | 0.448239i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 17.0757 | − | 6.21505i | 0.893784 | − | 0.325311i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.130303 | + | 0.155289i | −0.00680174 | + | 0.00810600i | −0.769435 | − | 0.638726i | \(-0.779462\pi\) |
0.762633 | + | 0.646832i | \(0.223906\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.14998 | − | 2.97334i | 0.268097 | − | 0.154786i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.123675 | − | 0.701396i | 0.00642089 | − | 0.0364147i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 29.8215 | + | 17.2174i | 1.54410 | + | 0.891485i | 0.998574 | + | 0.0533902i | \(0.0170027\pi\) |
0.545524 | + | 0.838095i | \(0.316331\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.13676 | + | 0.413747i | 0.0587021 | + | 0.0213658i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.04770 | + | 2.55733i | −0.156965 | + | 0.131709i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.0115 | 0.925190 | 0.462595 | − | 0.886570i | \(-0.346918\pi\) | ||||
0.462595 | + | 0.886570i | \(0.346918\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −10.0480 | −0.514775 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.54762 | − | 6.33320i | 0.385665 | − | 0.323612i | −0.429256 | − | 0.903183i | \(-0.641224\pi\) |
0.814922 | + | 0.579571i | \(0.196780\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9.68702 | − | 3.52579i | −0.493697 | − | 0.179691i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.77428 | − | 3.91113i | −0.344356 | − | 0.198814i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.56302 | − | 25.8782i | 0.231354 | − | 1.31208i | −0.618802 | − | 0.785547i | \(-0.712382\pi\) |
0.850157 | − | 0.526530i | \(-0.176507\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.01107 | + | 0.583740i | −0.0511319 | + | 0.0295210i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −9.91656 | + | 11.8181i | −0.500225 | + | 0.596144i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 32.2549 | − | 11.7398i | 1.62292 | − | 0.590695i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.55629 | − | 8.82617i | −0.0781081 | − | 0.442973i | −0.998632 | − | 0.0522869i | \(-0.983349\pi\) |
0.920524 | − | 0.390686i | \(-0.127762\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.06116 | + | 8.90722i | −0.103187 | + | 0.445919i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14.2316 | − | 2.50941i | 0.710692 | − | 0.125314i | 0.193396 | − | 0.981121i | \(-0.438050\pi\) |
0.517296 | + | 0.855807i | \(0.326939\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.0853 | + | 27.7092i | 0.502386 | + | 1.38029i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.46751 | − | 2.07049i | −0.122612 | − | 0.102883i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.98708 | − | 5.17377i | −0.148064 | − | 0.256454i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −17.0972 | − | 3.01469i | −0.845401 | − | 0.149067i | −0.265862 | − | 0.964011i | \(-0.585656\pi\) |
−0.579539 | + | 0.814944i | \(0.696768\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.32861 | + | 12.6935i | −0.361494 | + | 0.626125i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7.50574 | + | 20.6219i | −0.369333 | + | 1.01474i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −27.4695 | − | 32.7369i | −1.34842 | − | 1.60699i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 14.3850i | − | 0.704438i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8.21138i | 0.401152i | 0.979678 | + | 0.200576i | \(0.0642814\pi\) | ||||
−0.979678 | + | 0.200576i | \(0.935719\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.67005 | + | 4.37379i | 0.178867 | + | 0.213166i | 0.848027 | − | 0.529953i | \(-0.177790\pi\) |
−0.669160 | + | 0.743118i | \(0.733346\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.18869 | + | 8.76085i | −0.155039 | + | 0.425967i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.07908 | − | 1.86902i | 0.0523431 | − | 0.0906609i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.38886 | − | 0.950202i | −0.260785 | − | 0.0459835i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.12169 | + | 7.13897i | 0.198997 | + | 0.344673i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13.8723 | + | 11.6402i | 0.668205 | + | 0.560690i | 0.912533 | − | 0.409002i | \(-0.134123\pi\) |
−0.244329 | + | 0.969692i | \(0.578568\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.75295 | − | 10.3112i | −0.180355 | − | 0.495522i | 0.816264 | − | 0.577679i | \(-0.196041\pi\) |
−0.996619 | + | 0.0821567i | \(0.973819\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.33602 | + | 0.411904i | −0.112004 | + | 0.0197493i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 12.6578 | + | 0.669814i | 0.605505 | + | 0.0320415i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.64492 | + | 9.32880i | 0.0785077 | + | 0.445239i | 0.998570 | + | 0.0534665i | \(0.0170270\pi\) |
−0.920062 | + | 0.391773i | \(0.871862\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.44385 | + | 0.889488i | −0.116374 | + | 0.0423566i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.19553 | − | 10.9588i | 0.436893 | − | 0.520668i | −0.502005 | − | 0.864865i | \(-0.667404\pi\) |
0.938898 | + | 0.344196i | \(0.111849\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.685154 | + | 0.395574i | −0.0324794 | + | 0.0187520i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.53399 | + | 20.0423i | −0.167152 | + | 0.947967i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −24.3612 | − | 14.0650i | −1.14968 | − | 0.663767i | −0.200869 | − | 0.979618i | \(-0.564377\pi\) |
−0.948809 | + | 0.315851i | \(0.897710\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.52643 | − | 3.10337i | −0.401494 | − | 0.146132i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.45437 | − | 3.73766i | 0.209285 | − | 0.175611i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 36.5003 | 1.71116 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 31.3287 | 1.46549 | 0.732747 | − | 0.680501i | \(-0.238238\pi\) | ||||
0.732747 | + | 0.680501i | \(0.238238\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.307549 | + | 0.258064i | −0.0143552 | + | 0.0120454i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 22.9582 | + | 8.35612i | 1.06927 | + | 0.389183i | 0.815904 | − | 0.578187i | \(-0.196240\pi\) |
0.253368 | + | 0.967370i | \(0.418462\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 28.1155 | + | 16.2325i | 1.30664 | + | 0.754388i | 0.981534 | − | 0.191290i | \(-0.0612670\pi\) |
0.325105 | + | 0.945678i | \(0.394600\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.05292 | + | 17.3140i | −0.141576 | + | 0.802917i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 30.6095 | − | 17.6724i | 1.41644 | − | 0.817782i | 0.420455 | − | 0.907313i | \(-0.361870\pi\) |
0.995984 | + | 0.0895318i | \(0.0285371\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.5491 | − | 16.1472i | 0.625640 | − | 0.745609i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −20.7381 | + | 7.54804i | −0.955560 | + | 0.347796i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.07257 | + | 11.7541i | 0.0952968 | + | 0.540455i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −20.8830 | + | 10.6271i | −0.958179 | + | 0.487604i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.334404 | + | 0.0589644i | −0.0153113 | + | 0.00269979i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.88844 | + | 18.9258i | 0.314741 | + | 0.864743i | 0.991683 | + | 0.128707i | \(0.0410825\pi\) |
−0.676942 | + | 0.736036i | \(0.736695\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.2040 | + | 13.5968i | 0.738840 | + | 0.619960i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.04966 | − | 5.28217i | −0.138764 | − | 0.240347i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 49.3060 | + | 8.69398i | 2.23887 | + | 0.394773i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.5623 | − | 20.0265i | 0.523938 | − | 0.907488i | −0.475673 | − | 0.879622i | \(-0.657796\pi\) |
0.999612 | − | 0.0278660i | \(-0.00887117\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.97394 | − | 13.6658i | 0.224929 | − | 0.617988i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10.8736 | − | 12.9587i | −0.490719 | − | 0.584816i | 0.462681 | − | 0.886525i | \(-0.346887\pi\) |
−0.953400 | + | 0.301709i | \(0.902443\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.295652i | 0.0133155i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.91487i | 0.220907i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.56782 | − | 1.86845i | −0.0703261 | − | 0.0838114i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.04525 | − | 11.1142i | 0.181090 | − | 0.497541i | −0.815620 | − | 0.578588i | \(-0.803604\pi\) |
0.996710 | + | 0.0810466i | \(0.0258263\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10.5114 | − | 18.2063i | 0.469615 | − | 0.813397i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −40.7110 | − | 7.17845i | −1.81521 | − | 0.320071i | −0.840210 | − | 0.542261i | \(-0.817568\pi\) |
−0.975003 | + | 0.222190i | \(0.928679\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.95141 | + | 13.7723i | 0.353833 | + | 0.612857i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.4004 | − | 10.4051i | −0.550719 | − | 0.462108i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7.07846 | − | 19.4479i | −0.313747 | − | 0.862013i | −0.991892 | − | 0.127085i | \(-0.959438\pi\) |
0.678145 | − | 0.734928i | \(-0.262784\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.6528 | − | 2.05471i | 0.515490 | − | 0.0908949i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.32668 | − | 0.529019i | 0.191027 | − | 0.0233568i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.71816 | + | 32.4293i | 0.251972 | + | 1.42901i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13.3676 | − | 4.86540i | 0.587906 | − | 0.213980i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −16.0080 | + | 19.0776i | −0.702675 | + | 0.837416i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10.7254 | − | 6.19234i | 0.469890 | − | 0.271291i | −0.246304 | − | 0.969193i | \(-0.579216\pi\) |
0.716194 | + | 0.697902i | \(0.245883\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.64093 | − | 31.9913i | 0.246661 | − | 1.39888i | −0.569943 | − | 0.821684i | \(-0.693035\pi\) |
0.816604 | − | 0.577199i | \(-0.195854\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 9.76442 | + | 5.63749i | 0.426154 | + | 0.246040i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.05914 | + | 0.749466i | 0.0896976 | + | 0.0326473i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.1411 | − | 9.34853i | 0.484398 | − | 0.406458i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10.4628 | 0.454049 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 32.1273 | 1.39159 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −41.0973 | + | 34.4848i | −1.77679 | + | 1.49091i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 22.6880 | + | 8.25777i | 0.979061 | + | 0.356349i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.43657 | + | 1.98411i | 0.148024 | + | 0.0854616i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.72312 | + | 38.1287i | −0.289049 | + | 1.63928i | 0.401402 | + | 0.915902i | \(0.368523\pi\) |
−0.690452 | + | 0.723378i | \(0.742588\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −9.73117 | + | 5.61830i | −0.417605 | + | 0.241104i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −11.8564 | + | 14.1299i | −0.507873 | + | 0.605260i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13.9476 | − | 5.07652i | 0.596358 | − | 0.217056i | −0.0261658 | − | 0.999658i | \(-0.508330\pi\) |
0.622523 | + | 0.782601i | \(0.286108\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.453026 | + | 2.56924i | 0.0193347 | + | 0.109652i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.74963 | − | 2.69119i | 0.0745365 | − | 0.114649i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 22.0114 | − | 3.88121i | 0.936021 | − | 0.165046i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.31348 | + | 11.8512i | 0.183097 | + | 0.503055i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.53033 | + | 1.28410i | 0.0648423 | + | 0.0544092i | 0.674633 | − | 0.738153i | \(-0.264302\pi\) |
−0.609790 | + | 0.792563i | \(0.708746\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −21.1301 | − | 36.5983i | −0.893706 | − | 1.54794i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.603279 | + | 0.106374i | 0.0254705 | + | 0.00449113i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.52511 | + | 4.37363i | −0.106421 | + | 0.184326i | −0.914318 | − | 0.404997i | \(-0.867272\pi\) |
0.807897 | + | 0.589324i | \(0.200606\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 18.3503 | − | 50.4170i | 0.772002 | − | 2.12106i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.34822 | − | 1.60674i | −0.0566198 | − | 0.0674768i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 30.0760i | 1.26085i | 0.776250 | + | 0.630425i | \(0.217119\pi\) | ||||
−0.776250 | + | 0.630425i | \(0.782881\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 30.2742i | 1.26694i | 0.773769 | + | 0.633468i | \(0.218369\pi\) | ||||
−0.773769 | + | 0.633468i | \(0.781631\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −0.216200 | − | 0.257657i | −0.00903188 | − | 0.0107638i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.34644 | − | 14.6892i | 0.222962 | − | 0.612583i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.10084 | + | 14.0311i | −0.337242 | + | 0.584121i | −0.983913 | − | 0.178648i | \(-0.942828\pi\) |
0.646671 | + | 0.762769i | \(0.276161\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.820406 | + | 0.144660i | 0.0340949 | + | 0.00601186i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −13.9136 | − | 24.0991i | −0.577233 | − | 0.999798i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.396899 | + | 0.333038i | 0.0164379 | + | 0.0137930i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5.95190 | − | 16.3527i | −0.246081 | − | 0.676102i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 44.5886 | − | 7.86217i | 1.84037 | − | 0.324507i | 0.858317 | − | 0.513120i | \(-0.171510\pi\) |
0.982051 | + | 0.188613i | \(0.0603992\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −14.3083 | − | 19.0078i | −0.589562 | − | 0.783202i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.74309 | + | 9.88556i | 0.0717012 | + | 0.406638i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 11.8547 | − | 4.31475i | 0.486814 | − | 0.177186i | −0.0869401 | − | 0.996214i | \(-0.527709\pi\) |
0.573754 | + | 0.819028i | \(0.305487\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.74352 | − | 2.07784i | 0.0714772 | − | 0.0851832i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4.08568 | + | 2.35887i | −0.167216 | + | 0.0965421i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7.32116 | − | 41.5203i | 0.299134 | − | 1.69647i | −0.350772 | − | 0.936461i | \(-0.614081\pi\) |
0.649907 | − | 0.760014i | \(-0.274808\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.65341 | − | 3.26400i | −0.230607 | − | 0.133141i | 0.380245 | − | 0.924886i | \(-0.375840\pi\) |
−0.610852 | + | 0.791745i | \(0.709173\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −9.44358 | − | 3.43718i | −0.384572 | − | 0.139973i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −21.3979 | + | 17.9550i | −0.869948 | + | 0.729973i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 20.5432 | 0.833823 | 0.416911 | − | 0.908947i | \(-0.363113\pi\) | ||||
0.416911 | + | 0.908947i | \(0.363113\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.54459 | −0.0625898 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −38.5845 | + | 32.3763i | −1.56096 | + | 1.30980i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.5887 | + | 5.30984i | 0.589230 | + | 0.214462i | 0.619391 | − | 0.785083i | \(-0.287380\pi\) |
−0.0301606 | + | 0.999545i | \(0.509602\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 16.5887 | + | 9.57747i | 0.668919 | + | 0.386201i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.31200 | − | 13.1120i | 0.0930777 | − | 0.527870i | −0.902242 | − | 0.431231i | \(-0.858080\pi\) |
0.995319 | − | 0.0966394i | \(-0.0308094\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14.8667 | − | 8.58327i | 0.597542 | − | 0.344991i | −0.170532 | − | 0.985352i | \(-0.554549\pi\) |
0.768074 | + | 0.640361i | \(0.221215\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.86920 | + | 2.22763i | −0.0750086 | + | 0.0893917i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.484094 | + | 0.176196i | −0.0193948 | + | 0.00705914i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3.99064 | − | 22.6320i | −0.159625 | − | 0.905281i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4.86189 | − | 4.53840i | −0.194165 | − | 0.181246i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.54804 | − | 0.272961i | 0.0617244 | − | 0.0108837i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.13920 | + | 11.3724i | 0.164779 | + | 0.452726i | 0.994410 | − | 0.105585i | \(-0.0336716\pi\) |
−0.829631 | + | 0.558312i | \(0.811449\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 10.4632 | + | 8.77966i | 0.415874 | + | 0.348960i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −16.1829 | − | 28.0295i | −0.642197 | − | 1.11232i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −13.8369 | − | 2.43982i | −0.548238 | − | 0.0966691i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.581440 | + | 1.00708i | −0.0230014 | + | 0.0398396i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.12178 | − | 14.0720i | 0.202298 | − | 0.555809i | −0.796510 | − | 0.604626i | \(-0.793323\pi\) |
0.998808 | + | 0.0488164i | \(0.0155449\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.47730 | − | 7.71935i | −0.255440 | − | 0.304421i | 0.623050 | − | 0.782182i | \(-0.285893\pi\) |
−0.878490 | + | 0.477760i | \(0.841449\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 25.1964i | − | 0.992106i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 34.3782i | − | 1.35155i | −0.737110 | − | 0.675773i | \(-0.763810\pi\) | ||
0.737110 | − | 0.675773i | \(-0.236190\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.2618 | − | 12.2295i | −0.402811 | − | 0.480051i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.91547 | + | 10.7577i | −0.153459 | + | 0.421626i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −8.12795 | + | 14.0780i | −0.318071 | + | 0.550916i | −0.980086 | − | 0.198576i | \(-0.936368\pi\) |
0.662014 | + | 0.749491i | \(0.269702\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −48.9385 | − | 8.62918i | −1.91219 | − | 0.337170i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.82070 | − | 4.88560i | −0.110046 | − | 0.190605i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −24.1316 | − | 20.2488i | −0.940034 | − | 0.788783i | 0.0375568 | − | 0.999294i | \(-0.488042\pi\) |
−0.977591 | + | 0.210512i | \(0.932487\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.6013 | + | 40.1168i | 0.567925 | + | 1.56036i | 0.807737 | + | 0.589542i | \(0.200692\pi\) |
−0.239812 | + | 0.970819i | \(0.577086\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.13604 | + | 0.376642i | −0.0829571 | + | 0.0146276i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −28.1669 | + | 8.59584i | −1.09226 | + | 0.333332i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.371860 | + | 2.10892i | 0.0143985 | + | 0.0816578i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −14.4781 | + | 5.26960i | −0.559756 | + | 0.203734i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.55875 | − | 3.04940i | 0.0987793 | − | 0.117721i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.57314 | + | 3.79500i | −0.253376 | + | 0.146287i | −0.621309 | − | 0.783566i | \(-0.713399\pi\) |
0.367933 | + | 0.929852i | \(0.380066\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.933456 | − | 5.29389i | 0.0359287 | − | 0.203762i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −19.8392 | − | 11.4542i | −0.762482 | − | 0.440219i | 0.0677044 | − | 0.997705i | \(-0.478433\pi\) |
−0.830186 | + | 0.557486i | \(0.811766\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 30.6352 | + | 11.1503i | 1.17567 | + | 0.427909i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.88299 | + | 7.45371i | −0.340397 | + | 0.285627i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 36.2226 | 1.38602 | 0.693010 | − | 0.720928i | \(-0.256284\pi\) | ||||
0.693010 | + | 0.720928i | \(0.256284\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −47.2125 | −1.80390 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −16.6142 | + | 13.9409i | −0.633870 | + | 0.531880i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.72387 | − | 0.627436i | −0.0656741 | − | 0.0239034i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 23.9484 | + | 13.8266i | 0.911042 | + | 0.525990i | 0.880766 | − | 0.473551i | \(-0.157028\pi\) |
0.0302754 | + | 0.999542i | \(0.490362\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.555737 | + | 3.15174i | −0.0211107 | + | 0.119725i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 40.1280 | − | 23.1679i | 1.52214 | − | 0.878809i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.53463 | − | 1.82890i | 0.0581281 | − | 0.0692744i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 17.5176 | − | 6.37589i | 0.662577 | − | 0.241158i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.63438 | + | 31.9542i | 0.212808 | + | 1.20689i | 0.884671 | + | 0.466217i | \(0.154383\pi\) |
−0.671863 | + | 0.740675i | \(0.734506\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −15.7065 | − | 6.67643i | −0.592382 | − | 0.251806i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −29.5745 | + | 5.21479i | −1.11384 | + | 0.196400i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.54171 | + | 9.73076i | 0.133200 | + | 0.365963i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −19.9454 | − | 16.7362i | −0.749064 | − | 0.628539i | 0.186191 | − | 0.982514i | \(-0.440386\pi\) |
−0.935255 | + | 0.353974i | \(0.884830\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.32813 | − | 9.22859i | −0.199820 | − | 0.346099i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 15.6308 | + | 2.75613i | 0.585377 | + | 0.103218i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −13.2764 | + | 22.9954i | −0.496510 | + | 0.859980i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −0.0588064 | + | 0.161569i | −0.00219616 | + | 0.00603391i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −31.5963 | − | 37.6550i | −1.17834 | − | 1.40429i | −0.895462 | − | 0.445138i | \(-0.853155\pi\) |
−0.282880 | − | 0.959155i | \(-0.591290\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 21.4424i | 0.798556i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 12.6308i | − | 0.469744i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.54455 | − | 3.03248i | −0.0945023 | − | 0.112623i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −11.4331 | + | 31.4123i | −0.424031 | + | 1.16502i | 0.525349 | + | 0.850887i | \(0.323935\pi\) |
−0.949380 | + | 0.314130i | \(0.898287\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.500000 | + | 0.866025i | −0.0185185 | + | 0.0320750i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.09274 | − | 0.545334i | −0.114389 | − | 0.0201699i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12.0527 | + | 20.8759i | 0.445177 | + | 0.771069i | 0.998065 | − | 0.0621867i | \(-0.0198074\pi\) |
−0.552888 | + | 0.833256i | \(0.686474\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −6.41724 | − | 5.38470i | −0.236703 | − | 0.198618i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.24456 | + | 14.4093i | 0.193186 | + | 0.530774i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −46.7284 | + | 8.23949i | −1.71893 | + | 0.303094i | −0.944244 | − | 0.329247i | \(-0.893205\pi\) |
−0.774690 | + | 0.632341i | \(0.782094\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 21.6724 | + | 9.21239i | 0.796157 | + | 0.338426i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.99639 | + | 22.6646i | 0.146613 | + | 0.831485i | 0.966058 | + | 0.258326i | \(0.0831710\pi\) |
−0.819445 | + | 0.573158i | \(0.805718\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −61.6009 | + | 22.4209i | −2.25688 | + | 0.821438i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −8.52795 | + | 10.1632i | −0.312021 | + | 0.371853i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −30.2536 | + | 17.4669i | −1.10544 | + | 0.638227i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.09632 | + | 6.21756i | −0.0400054 | + | 0.226882i | −0.998255 | − | 0.0590513i | \(-0.981192\pi\) |
0.958250 | + | 0.285933i | \(0.0923035\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.53579 | + | 1.46404i | 0.0924093 | + | 0.0533525i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 17.6005 | + | 6.40604i | 0.640546 | + | 0.233140i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18.1562 | − | 15.2348i | 0.659897 | − | 0.553719i | −0.250159 | − | 0.968205i | \(-0.580483\pi\) |
0.910056 | + | 0.414485i | \(0.136038\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.43706 | 0.161055 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.15456 | −0.150603 | −0.0753013 | − | 0.997161i | \(-0.523992\pi\) | ||||
−0.0753013 | + | 0.997161i | \(0.523992\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.20082 | + | 7.72041i | −0.333092 | + | 0.279498i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.21521 | − | 0.442301i | −0.0439361 | − | 0.0159914i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 48.9529 | + | 28.2630i | 1.76759 | + | 1.02052i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.811565 | − | 4.60261i | 0.0292658 | − | 0.165974i | −0.966672 | − | 0.256018i | \(-0.917589\pi\) |
0.995938 | + | 0.0900433i | \(0.0287005\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11.6487 | − | 6.72540i | 0.419519 | − | 0.242209i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0.966318 | − | 1.15161i | 0.0347561 | − | 0.0414207i | −0.748386 | − | 0.663263i | \(-0.769171\pi\) |
0.783142 | + | 0.621842i | \(0.213616\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −27.5708 | + | 10.0350i | −0.990373 | + | 0.360466i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.42604 | + | 8.08749i | 0.0511590 | + | 0.290137i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −24.7922 | + | 7.56598i | −0.888274 | + | 0.271079i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.74740 | − | 0.308114i | 0.0625270 | − | 0.0110252i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.251867 | + | 0.692000i | 0.00900100 | + | 0.0247301i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −54.4556 | − | 45.6937i | −1.94360 | − | 1.63088i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.80025 | − | 6.58223i | −0.135464 | − | 0.234631i | 0.790310 | − | 0.612707i | \(-0.209919\pi\) |
−0.925775 | + | 0.378075i | \(0.876586\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −30.3552 | − | 5.35243i | −1.08067 | − | 0.190552i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 17.4682 | − | 30.2558i | 0.621096 | − | 1.07577i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.82063 | + | 13.2446i | −0.171185 | + | 0.470328i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.703060 | − | 0.837875i | −0.0249350 | − | 0.0297164i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 35.7008i | 1.26459i | 0.774728 | + | 0.632294i | \(0.217887\pi\) | ||||
−0.774728 | + | 0.632294i | \(0.782113\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.74301i | 0.132418i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.157877 | + | 0.188151i | 0.00557832 | + | 0.00664798i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.94405 | + | 8.08872i | −0.103893 | + | 0.285445i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.82330 | − | 17.0144i | 0.346226 | − | 0.599680i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −17.6535 | − | 3.11279i | −0.621432 | − | 0.109575i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −24.6049 | − | 42.6170i | −0.865063 | − | 1.49833i | −0.866985 | − | 0.498334i | \(-0.833945\pi\) |
0.00192213 | − | 0.999998i | \(-0.499388\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −21.7575 | − | 18.2567i | −0.764010 | − | 0.641080i | 0.175158 | − | 0.984540i | \(-0.443957\pi\) |
−0.939167 | + | 0.343460i | \(0.888401\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.98801 | − | 13.7044i | −0.174937 | − | 0.480636i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 46.1324 | − | 8.13439i | 1.61595 | − | 0.284935i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 24.9247 | + | 23.2664i | 0.872006 | + | 0.813987i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.96771 | − | 11.1594i | −0.0687573 | − | 0.389942i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 20.6181 | − | 7.50437i | 0.719576 | − | 0.261904i | 0.0438304 | − | 0.999039i | \(-0.486044\pi\) |
0.675746 | + | 0.737135i | \(0.263822\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.31110 | + | 7.52128i | −0.219991 | + | 0.262175i | −0.864741 | − | 0.502219i | \(-0.832517\pi\) |
0.644750 | + | 0.764394i | \(0.276962\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −7.10331 | + | 4.10110i | −0.247306 | + | 0.142782i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.74234 | + | 9.88131i | −0.0605871 | + | 0.343607i | 0.939413 | + | 0.342789i | \(0.111371\pi\) |
−1.00000 | 0.000817979i | \(0.999740\pi\) | ||||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13.5109 | + | 7.80055i | 0.469254 | + | 0.270924i | 0.715928 | − | 0.698175i | \(-0.246004\pi\) |
−0.246673 | + | 0.969099i | \(0.579337\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −18.8530 | − | 6.86192i | −0.654002 | − | 0.238037i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.799840 | + | 0.671145i | −0.0277128 | + | 0.0232538i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 67.7169 | 2.34344 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.45808 | 0.188659 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −11.7747 | + | 9.88011i | −0.406506 | + | 0.341099i | −0.823002 | − | 0.568038i | \(-0.807703\pi\) |
0.416496 | + | 0.909138i | \(0.363258\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.7415 | − | 9.73311i | −0.922120 | − | 0.335624i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.75084 | + | 2.16555i | 0.129186 | + | 0.0745854i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9.05432 | − | 51.3496i | 0.311478 | − | 1.76648i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −15.7519 | + | 9.09439i | −0.541243 | + | 0.312487i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3.14737 | − | 3.75089i | 0.108018 | − | 0.128730i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10.6990 | − | 3.89414i | 0.366759 | − | 0.133489i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.62836 | − | 26.2487i | −0.158472 | − | 0.898740i | −0.955543 | − | 0.294853i | \(-0.904729\pi\) |
0.797070 | − | 0.603886i | \(-0.206382\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8.44409 | + | 11.2175i | 0.288782 | + | 0.383631i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −10.7571 | + | 1.89677i | −0.367456 | + | 0.0647925i | −0.354328 | − | 0.935121i | \(-0.615290\pi\) |
−0.0131287 | + | 0.999914i | \(0.504179\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.6810 | + | 45.8306i | 0.569147 | + | 1.56372i | 0.805839 | + | 0.592134i | \(0.201714\pi\) |
−0.236692 | + | 0.971585i | \(0.576063\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 9.55479 | + | 8.01742i | 0.325626 | + | 0.273233i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −15.3261 | − | 26.5455i | −0.521706 | − | 0.903621i | −0.999681 | − | 0.0252475i | \(-0.991963\pi\) |
0.477976 | − | 0.878373i | \(-0.341371\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −79.0002 | − | 13.9299i | −2.68609 | − | 0.473629i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 8.41941 | − | 14.5828i | 0.285938 | − | 0.495259i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.56113 | + | 15.2791i | −0.188648 | + | 0.518307i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −34.8993 | − | 41.5914i | −1.18252 | − | 1.40927i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 15.5433i | − | 0.526061i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.53732i | 0.0857771i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15.7467 | + | 18.7662i | 0.531727 | + | 0.633688i | 0.963312 | − | 0.268385i | \(-0.0864898\pi\) |
−0.431585 | + | 0.902072i | \(0.642045\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.22949 | − | 6.12548i | 0.0751989 | − | 0.206607i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.09864 | + | 7.09906i | −0.138087 | + | 0.239173i | −0.926772 | − | 0.375623i | \(-0.877429\pi\) |
0.788686 | + | 0.614797i | \(0.210762\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −13.6696 | − | 2.41031i | −0.460018 | − | 0.0811136i | −0.0611633 | − | 0.998128i | \(-0.519481\pi\) |
−0.398855 | + | 0.917014i | \(0.630592\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 16.8510 | + | 29.1868i | 0.566440 | + | 0.981102i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 7.29985 | + | 6.12530i | 0.245105 | + | 0.205668i | 0.757061 | − | 0.653344i | \(-0.226634\pi\) |
−0.511956 | + | 0.859012i | \(0.671079\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.20815 | − | 19.8042i | −0.241753 | − | 0.664212i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.50265 | − | 0.264958i | 0.0503407 | − | 0.00887642i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 22.1506 | − | 34.0710i | 0.741242 | − | 1.14014i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 13.5048 | + | 76.5893i | 0.451414 | + | 2.56010i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −14.7630 | + | 5.37328i | −0.492921 | + | 0.179409i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.58361 | − | 3.07903i | 0.0861684 | − | 0.102691i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.118062 | + | 0.0681632i | −0.00393322 | + | 0.00227084i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.84901 | − | 16.1576i | 0.0948093 | − | 0.537690i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −31.3452 | − | 18.0972i | −1.04195 | − | 0.601570i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −35.9397 | − | 13.0810i | −1.19336 | − | 0.434347i | −0.332457 | − | 0.943118i | \(-0.607878\pi\) |
−0.860902 | + | 0.508771i | \(0.830100\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.78201 | − | 3.17348i | 0.125441 | − | 0.105258i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 30.9861 | 1.02662 | 0.513308 | − | 0.858204i | \(-0.328420\pi\) | ||||
0.513308 | + | 0.858204i | \(0.328420\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 20.2434 | 0.669959 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −6.43744 | + | 5.40165i | −0.212815 | + | 0.178573i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −30.4069 | − | 11.0672i | −1.00412 | − | 0.365471i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 22.6165 | + | 13.0576i | 0.746048 | + | 0.430731i | 0.824264 | − | 0.566205i | \(-0.191589\pi\) |
−0.0782160 | + | 0.996936i | \(0.524922\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.05414 | + | 22.9922i | −0.133588 | + | 0.757618i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5.44082 | + | 3.14126i | −0.179087 | + | 0.103396i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −13.5289 | + | 16.1231i | −0.444826 | + | 0.530123i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 9.60652 | − | 3.49649i | 0.315520 | − | 0.114840i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5.88318 | + | 33.3652i | 0.193021 | + | 1.09468i | 0.915209 | + | 0.402979i | \(0.132025\pi\) |
−0.722188 | + | 0.691696i | \(0.756864\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11.2523 | − | 1.37581i | 0.368781 | − | 0.0450905i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 11.3938 | − | 2.00903i | 0.373016 | − | 0.0657728i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.674877 | + | 1.85421i | 0.0220708 | + | 0.0606391i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.57998 | + | 6.36036i | 0.247627 | + | 0.207784i | 0.758150 | − | 0.652081i | \(-0.226104\pi\) |
−0.510523 | + | 0.859864i | \(0.670548\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 14.5236 | + | 25.1556i | 0.473959 | + | 0.820921i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 46.2398 | + | 8.15333i | 1.50738 | + | 0.265791i | 0.865458 | − | 0.500982i | \(-0.167028\pi\) |
0.641918 | + | 0.766773i | \(0.278139\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.64638 | − | 14.9760i | 0.281565 | − | 0.487685i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.31073 | − | 6.34869i | 0.0751681 | − | 0.206523i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −0.876606 | − | 1.04470i | −0.0284859 | − | 0.0339481i | 0.751613 | − | 0.659604i | \(-0.229276\pi\) |
−0.780099 | + | 0.625656i | \(0.784831\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 30.4780i | − | 0.989356i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.30110i | 0.0421911i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 15.4953 | + | 18.4666i | 0.501943 | + | 0.598192i | 0.956213 | − | 0.292672i | \(-0.0945443\pi\) |
−0.454270 | + | 0.890864i | \(0.650100\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.370549 | − | 1.01807i | 0.0119907 | − | 0.0329441i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.561819 | − | 0.973100i | 0.0181610 | − | 0.0314558i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −30.2758 | − | 5.33844i | −0.977656 | − | 0.172387i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.604671 | + | 1.04732i | 0.0195055 | + | 0.0337845i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 12.7587 | + | 10.7059i | 0.411145 | + | 0.344991i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.917772 | + | 2.52156i | 0.0295441 | + | 0.0811719i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 39.7633 | − | 7.01134i | 1.27870 | − | 0.225470i | 0.507273 | − | 0.861785i | \(-0.330654\pi\) |
0.771429 | + | 0.636316i | \(0.219542\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.55966 | − | 0.793690i | 0.0501035 | − | 0.0254970i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.00455 | − | 5.69711i | −0.0322377 | − | 0.182829i | 0.964437 | − | 0.264313i | \(-0.0851452\pi\) |
−0.996675 | + | 0.0814840i | \(0.974034\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 28.3524 | − | 10.3194i | 0.908935 | − | 0.330825i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 18.6676 | − | 22.2472i | 0.597843 | − | 0.712482i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 30.7077 | − | 17.7291i | 0.982426 | − | 0.567204i | 0.0794240 | − | 0.996841i | \(-0.474692\pi\) |
0.903002 | + | 0.429637i | \(0.141359\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.0650772 | − | 0.369071i | 0.00207988 | − | 0.0117956i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.95919 | + | 2.86319i | 0.158335 | + | 0.0914147i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 6.74093 | + | 2.45350i | 0.215002 | + | 0.0782544i | 0.447276 | − | 0.894396i | \(-0.352394\pi\) |
−0.232274 | + | 0.972650i | \(0.574616\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −24.7691 | + | 20.7837i | −0.789208 | + | 0.662224i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −19.5548 | −0.622435 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −22.7469 | −0.723308 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.95401 | + | 5.83510i | −0.220901 | + | 0.185358i | −0.746522 | − | 0.665361i | \(-0.768278\pi\) |
0.525621 | + | 0.850719i | \(0.323833\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4.57462 | + | 1.66502i | 0.145171 | + | 0.0528380i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −13.1604 | − | 7.59818i | −0.417214 | − | 0.240879i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.88088 | + | 22.0096i | −0.122909 | + | 0.697050i | 0.859619 | + | 0.510935i | \(0.170701\pi\) |
−0.982528 | + | 0.186115i | \(0.940410\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.39079 | − | 1.95767i | 0.107280 | − | 0.0619380i |
(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 | 912.2.ci.f.751.3 | yes | 18 | |
4.3 | odd | 2 | 912.2.ci.e.751.3 | ✓ | 18 | ||
19.2 | odd | 18 | 912.2.ci.e.895.3 | yes | 18 | ||
76.59 | even | 18 | inner | 912.2.ci.f.895.3 | yes | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
912.2.ci.e.751.3 | ✓ | 18 | 4.3 | odd | 2 | ||
912.2.ci.e.895.3 | yes | 18 | 19.2 | odd | 18 | ||
912.2.ci.f.751.3 | yes | 18 | 1.1 | even | 1 | trivial | |
912.2.ci.f.895.3 | yes | 18 | 76.59 | even | 18 | inner |