Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [891,2,Mod(161,891)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(891, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([5, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("891.161");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 891 = 3^{4} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 891.k (of order \(10\), 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: | \(7.11467082010\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(20\) over \(\Q(\zeta_{10})\) |
Twist minimal: | no (minimal twist has level 99) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 161.7 | ||
Character | \(\chi\) | \(=\) | 891.161 |
Dual form | 891.2.k.a.404.7 |
$q$-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 \(\left(\mathbb{Z}/891\mathbb{Z}\right)^\times\).
\(n\) | \(244\) | \(650\) |
\(\chi(n)\) | \(e\left(\frac{7}{10}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.931921 | − | 0.677080i | −0.658967 | − | 0.478768i | 0.207347 | − | 0.978268i | \(-0.433517\pi\) |
−0.866314 | + | 0.499500i | \(0.833517\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.207995 | − | 0.640143i | −0.103998 | − | 0.320072i | ||||
\(5\) | −0.551104 | − | 0.758530i | −0.246461 | − | 0.339225i | 0.667807 | − | 0.744335i | \(-0.267233\pi\) |
−0.914268 | + | 0.405110i | \(0.867233\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.824408 | + | 0.267866i | −0.311597 | + | 0.101244i | −0.460641 | − | 0.887587i | \(-0.652380\pi\) |
0.149044 | + | 0.988831i | \(0.452380\pi\) | |||||||
\(8\) | −0.951517 | + | 2.92847i | −0.336412 | + | 1.03537i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.08003i | 0.341536i | ||||||||
\(11\) | 1.59130 | + | 2.90994i | 0.479794 | + | 0.877381i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.693143 | − | 0.954029i | 0.192243 | − | 0.264600i | −0.702004 | − | 0.712173i | \(-0.747711\pi\) |
0.894248 | + | 0.447572i | \(0.147711\pi\) | |||||||
\(14\) | 0.949650 | + | 0.308560i | 0.253805 | + | 0.0824661i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.78047 | − | 1.29359i | 0.445117 | − | 0.323397i | ||||
\(17\) | −2.52191 | + | 1.83228i | −0.611653 | + | 0.444392i | −0.849996 | − | 0.526789i | \(-0.823396\pi\) |
0.238343 | + | 0.971181i | \(0.423396\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.59786 | + | 2.14377i | 1.51365 | + | 0.491816i | 0.943965 | − | 0.330046i | \(-0.107064\pi\) |
0.569688 | + | 0.821861i | \(0.307064\pi\) | |||||||
\(20\) | −0.370941 | + | 0.510556i | −0.0829449 | + | 0.114164i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.487302 | − | 3.78927i | 0.103893 | − | 0.807876i | ||||
\(23\) | 2.36655i | 0.493459i | 0.969084 | + | 0.246730i | \(0.0793559\pi\) | ||||
−0.969084 | + | 0.246730i | \(0.920644\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.27343 | − | 3.91922i | 0.254687 | − | 0.783845i | ||||
\(26\) | −1.29191 | + | 0.419767i | −0.253364 | + | 0.0823230i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.342946 | + | 0.472024i | 0.0648106 | + | 0.0892042i | ||||
\(29\) | 1.11875 | + | 3.44315i | 0.207746 | + | 0.639376i | 0.999589 | + | 0.0286522i | \(0.00912152\pi\) |
−0.791844 | + | 0.610724i | \(0.790878\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.13662 | + | 3.73198i | 0.922565 | + | 0.670283i | 0.944161 | − | 0.329484i | \(-0.106875\pi\) |
−0.0215963 | + | 0.999767i | \(0.506875\pi\) | |||||||
\(32\) | 3.62323 | 0.640503 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.59082 | 0.615820 | ||||||||
\(35\) | 0.657520 | + | 0.477716i | 0.111141 | + | 0.0807487i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.46847 | − | 7.59716i | −0.405813 | − | 1.24897i | −0.920214 | − | 0.391415i | \(-0.871986\pi\) |
0.514401 | − | 0.857550i | \(-0.328014\pi\) | |||||||
\(38\) | −4.69717 | − | 6.46511i | −0.761982 | − | 1.04878i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.74572 | − | 0.892138i | 0.434136 | − | 0.141059i | ||||
\(41\) | 1.11348 | − | 3.42695i | 0.173897 | − | 0.535199i | −0.825685 | − | 0.564132i | \(-0.809211\pi\) |
0.999581 | + | 0.0289327i | \(0.00921085\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 3.83119i | − | 0.584251i | −0.956380 | − | 0.292126i | \(-0.905637\pi\) | ||
0.956380 | − | 0.292126i | \(-0.0943625\pi\) | |||||||
\(44\) | 1.53180 | − | 1.62391i | 0.230927 | − | 0.244814i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.60234 | − | 2.20543i | 0.236252 | − | 0.325174i | ||||
\(47\) | 0.152329 | + | 0.0494946i | 0.0222194 | + | 0.00721952i | 0.320106 | − | 0.947382i | \(-0.396282\pi\) |
−0.297886 | + | 0.954601i | \(0.596282\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.05522 | + | 3.67283i | −0.722175 | + | 0.524691i | ||||
\(50\) | −3.84037 | + | 2.79019i | −0.543110 | + | 0.394592i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.754886 | − | 0.245277i | −0.104684 | − | 0.0340138i | ||||
\(53\) | 5.71174 | − | 7.86153i | 0.784567 | − | 1.07986i | −0.210196 | − | 0.977659i | \(-0.567410\pi\) |
0.994763 | − | 0.102205i | \(-0.0325898\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.33031 | − | 2.81073i | 0.179379 | − | 0.378999i | ||||
\(56\) | − | 2.66913i | − | 0.356678i | ||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.28870 | − | 3.96622i | 0.169215 | − | 0.520790i | ||||
\(59\) | −8.27039 | + | 2.68721i | −1.07671 | + | 0.349845i | −0.793099 | − | 0.609093i | \(-0.791534\pi\) |
−0.283614 | + | 0.958938i | \(0.591534\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.97576 | + | 10.9777i | 1.02119 | + | 1.40555i | 0.911365 | + | 0.411598i | \(0.135029\pi\) |
0.109826 | + | 0.993951i | \(0.464971\pi\) | |||||||
\(62\) | −2.26008 | − | 6.95581i | −0.287030 | − | 0.883389i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −6.93750 | − | 5.04039i | −0.867188 | − | 0.630049i | ||||
\(65\) | −1.10565 | −0.137140 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.64298 | 0.811569 | 0.405785 | − | 0.913969i | \(-0.366998\pi\) | ||||
0.405785 | + | 0.913969i | \(0.366998\pi\) | |||||||
\(68\) | 1.69746 | + | 1.23328i | 0.205848 | + | 0.149557i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.289304 | − | 0.890387i | −0.0345785 | − | 0.106422i | ||||
\(71\) | 6.53958 | + | 9.00097i | 0.776106 | + | 1.06822i | 0.995701 | + | 0.0926270i | \(0.0295264\pi\) |
−0.219595 | + | 0.975591i | \(0.570474\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.29787 | − | 1.07154i | 0.385987 | − | 0.125415i | −0.109594 | − | 0.993976i | \(-0.534955\pi\) |
0.495581 | + | 0.868562i | \(0.334955\pi\) | |||||||
\(74\) | −2.84347 | + | 8.75130i | −0.330547 | + | 1.01732i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 4.66947i | − | 0.535625i | ||||||
\(77\) | −2.09135 | − | 1.97273i | −0.238332 | − | 0.224813i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.43649 | − | 6.10630i | 0.499144 | − | 0.687012i | −0.482898 | − | 0.875677i | \(-0.660416\pi\) |
0.982042 | + | 0.188664i | \(0.0604158\pi\) | |||||||
\(80\) | −1.96245 | − | 0.637639i | −0.219409 | − | 0.0712902i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.35800 | + | 2.43973i | −0.370829 | + | 0.269423i | ||||
\(83\) | 11.6734 | − | 8.48120i | 1.28132 | − | 0.930933i | 0.281727 | − | 0.959495i | \(-0.409093\pi\) |
0.999592 | + | 0.0285622i | \(0.00909286\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.77967 | + | 0.903171i | 0.301498 | + | 0.0979626i | ||||
\(86\) | −2.59402 | + | 3.57037i | −0.279721 | + | 0.385003i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −10.0358 | + | 1.89120i | −1.06982 | + | 0.201603i | ||||
\(89\) | − | 9.28531i | − | 0.984241i | −0.870527 | − | 0.492120i | \(-0.836222\pi\) | ||
0.870527 | − | 0.492120i | \(-0.163778\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.315880 | + | 0.972179i | −0.0331132 | + | 0.101912i | ||||
\(92\) | 1.51493 | − | 0.492230i | 0.157942 | − | 0.0513186i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.108446 | − | 0.149264i | −0.0111854 | − | 0.0153954i | ||||
\(95\) | −2.00999 | − | 6.18612i | −0.206221 | − | 0.634682i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.85618 | + | 7.16093i | 1.00074 | + | 0.727082i | 0.962247 | − | 0.272176i | \(-0.0877434\pi\) |
0.0384957 | + | 0.999259i | \(0.487743\pi\) | |||||||
\(98\) | 7.19787 | 0.727095 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.77373 | −0.277373 | ||||||||
\(101\) | 4.90121 | + | 3.56094i | 0.487689 | + | 0.354327i | 0.804295 | − | 0.594230i | \(-0.202543\pi\) |
−0.316606 | + | 0.948557i | \(0.602543\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.23254 | − | 3.79337i | −0.121446 | − | 0.373772i | 0.871791 | − | 0.489878i | \(-0.162959\pi\) |
−0.993237 | + | 0.116106i | \(0.962959\pi\) | |||||||
\(104\) | 2.13431 | + | 2.93762i | 0.209286 | + | 0.288058i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −10.6458 | + | 3.45902i | −1.03401 | + | 0.335970i | ||||
\(107\) | −1.90097 | + | 5.85057i | −0.183773 | + | 0.565596i | −0.999925 | − | 0.0122414i | \(-0.996103\pi\) |
0.816152 | + | 0.577838i | \(0.196103\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 16.9364i | 1.62221i | 0.584897 | + | 0.811107i | \(0.301135\pi\) | ||||
−0.584897 | + | 0.811107i | \(0.698865\pi\) | |||||||
\(110\) | −3.14283 | + | 1.71865i | −0.299657 | + | 0.163867i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.12132 | + | 1.54337i | −0.105955 | + | 0.145835i | ||||
\(113\) | 7.61414 | + | 2.47398i | 0.716278 | + | 0.232733i | 0.644409 | − | 0.764681i | \(-0.277104\pi\) |
0.0718692 | + | 0.997414i | \(0.477104\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.79510 | − | 1.30421i | 0.167394 | − | 0.121619i | ||||
\(116\) | 1.97141 | − | 1.43232i | 0.183041 | − | 0.132987i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 9.52681 | + | 3.09545i | 0.877014 | + | 0.284959i | ||||
\(119\) | 1.58828 | − | 2.18608i | 0.145597 | − | 0.200397i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.93555 | + | 9.26117i | −0.539595 | + | 0.841925i | ||||
\(122\) | − | 15.6306i | − | 1.41512i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.32061 | − | 4.06441i | 0.118594 | − | 0.364995i | ||||
\(125\) | −8.13317 | + | 2.64263i | −0.727453 | + | 0.236364i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.73492 | − | 5.14068i | −0.331421 | − | 0.456161i | 0.610490 | − | 0.792024i | \(-0.290972\pi\) |
−0.941911 | + | 0.335862i | \(0.890972\pi\) | |||||||
\(128\) | 0.813175 | + | 2.50270i | 0.0718752 | + | 0.221209i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.03038 | + | 0.748616i | 0.0903705 | + | 0.0656580i | ||||
\(131\) | 17.3740 | 1.51797 | 0.758985 | − | 0.651109i | \(-0.225696\pi\) | ||||
0.758985 | + | 0.651109i | \(0.225696\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.01357 | −0.521443 | ||||||||
\(134\) | −6.19073 | − | 4.49783i | −0.534798 | − | 0.388553i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.96612 | − | 9.12878i | −0.254343 | − | 0.782787i | ||||
\(137\) | −10.4042 | − | 14.3201i | −0.888890 | − | 1.22345i | −0.973878 | − | 0.227070i | \(-0.927085\pi\) |
0.0849882 | − | 0.996382i | \(-0.472915\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.87651 | + | 1.90939i | −0.498439 | + | 0.161953i | −0.547438 | − | 0.836846i | \(-0.684397\pi\) |
0.0489992 | + | 0.998799i | \(0.484397\pi\) | |||||||
\(140\) | 0.169046 | − | 0.520269i | 0.0142870 | − | 0.0439708i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 12.8160i | − | 1.07550i | ||||||
\(143\) | 3.87917 | + | 0.498862i | 0.324392 | + | 0.0417170i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.99518 | − | 2.74614i | 0.165691 | − | 0.228054i | ||||
\(146\) | −3.79887 | − | 1.23433i | −0.314397 | − | 0.102154i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.34984 | + | 3.16034i | −0.357555 | + | 0.259779i | ||||
\(149\) | 5.97193 | − | 4.33886i | 0.489239 | − | 0.355453i | −0.315652 | − | 0.948875i | \(-0.602223\pi\) |
0.804892 | + | 0.593422i | \(0.202223\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.8241 | − | 4.16680i | −1.04361 | − | 0.339090i | −0.263453 | − | 0.964672i | \(-0.584861\pi\) |
−0.780158 | + | 0.625583i | \(0.784861\pi\) | |||||||
\(152\) | −12.5560 | + | 17.2818i | −1.01842 | + | 1.40174i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.613283 | + | 3.25444i | 0.0494198 | + | 0.262250i | ||||
\(155\) | − | 5.95299i | − | 0.478156i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.906116 | + | 2.78874i | −0.0723160 | + | 0.222566i | −0.980681 | − | 0.195611i | \(-0.937331\pi\) |
0.908366 | + | 0.418177i | \(0.137331\pi\) | |||||||
\(158\) | −8.26891 | + | 2.68673i | −0.657839 | + | 0.213745i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.99678 | − | 2.74833i | −0.157859 | − | 0.217275i | ||||
\(161\) | −0.633918 | − | 1.95100i | −0.0499598 | − | 0.153760i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.8134 | + | 12.9422i | 1.39525 | + | 1.01371i | 0.995266 | + | 0.0971873i | \(0.0309846\pi\) |
0.399985 | + | 0.916522i | \(0.369015\pi\) | |||||||
\(164\) | −2.42534 | −0.189387 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −16.6211 | −1.29005 | ||||||||
\(167\) | −0.521597 | − | 0.378963i | −0.0403624 | − | 0.0293250i | 0.567421 | − | 0.823428i | \(-0.307941\pi\) |
−0.607784 | + | 0.794103i | \(0.707941\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.58750 | + | 11.0412i | 0.275961 | + | 0.849321i | ||||
\(170\) | −1.97892 | − | 2.72374i | −0.151776 | − | 0.208902i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.45251 | + | 0.796869i | −0.187002 | + | 0.0607607i | ||||
\(173\) | −4.16978 | + | 12.8333i | −0.317023 | + | 0.975695i | 0.657891 | + | 0.753113i | \(0.271449\pi\) |
−0.974914 | + | 0.222582i | \(0.928551\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.57215i | 0.270029i | ||||||||
\(176\) | 6.59752 | + | 3.12259i | 0.497307 | + | 0.235374i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −6.28690 | + | 8.65317i | −0.471223 | + | 0.648583i | ||||
\(179\) | −1.06341 | − | 0.345524i | −0.0794832 | − | 0.0258256i | 0.269005 | − | 0.963139i | \(-0.413305\pi\) |
−0.348489 | + | 0.937313i | \(0.613305\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −18.7897 | + | 13.6515i | −1.39663 | + | 1.01471i | −0.401530 | + | 0.915846i | \(0.631521\pi\) |
−0.995101 | + | 0.0988656i | \(0.968479\pi\) | |||||||
\(182\) | 0.952618 | − | 0.692118i | 0.0706128 | − | 0.0513032i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −6.93036 | − | 2.25181i | −0.510913 | − | 0.166006i | ||||
\(185\) | −4.40229 | + | 6.05923i | −0.323663 | + | 0.445484i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.34493 | − | 4.42293i | −0.683369 | − | 0.323436i | ||||
\(188\) | − | 0.107807i | − | 0.00786262i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.31534 | + | 7.12590i | −0.167973 | + | 0.516967i | ||||
\(191\) | −2.84491 | + | 0.924368i | −0.205851 | + | 0.0668849i | −0.410127 | − | 0.912028i | \(-0.634516\pi\) |
0.204277 | + | 0.978913i | \(0.434516\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.81321 | + | 8.00120i | 0.418444 | + | 0.575939i | 0.965253 | − | 0.261319i | \(-0.0841573\pi\) |
−0.546808 | + | 0.837258i | \(0.684157\pi\) | |||||||
\(194\) | −4.33665 | − | 13.3468i | −0.311353 | − | 0.958247i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.40260 | + | 2.47214i | 0.243043 | + | 0.176581i | ||||
\(197\) | 4.94568 | 0.352365 | 0.176183 | − | 0.984357i | \(-0.443625\pi\) | ||||
0.176183 | + | 0.984357i | \(0.443625\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.64868 | −0.542200 | −0.271100 | − | 0.962551i | \(-0.587387\pi\) | ||||
−0.271100 | + | 0.962551i | \(0.587387\pi\) | |||||||
\(200\) | 10.2656 | + | 7.45842i | 0.725890 | + | 0.527390i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2.15650 | − | 6.63703i | −0.151731 | − | 0.466980i | ||||
\(203\) | −1.84461 | − | 2.53888i | −0.129466 | − | 0.178195i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.21309 | + | 1.04400i | −0.224412 | + | 0.0729158i | ||||
\(206\) | −1.41978 | + | 4.36965i | −0.0989211 | + | 0.304448i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 2.59526i | − | 0.179949i | ||||||
\(209\) | 4.26089 | + | 22.6108i | 0.294732 | + | 1.56402i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.8159 | − | 19.0160i | 0.951128 | − | 1.30912i | 0.000104069 | − | 1.00000i | \(-0.499967\pi\) |
0.951024 | − | 0.309116i | \(-0.100033\pi\) | |||||||
\(212\) | −6.22052 | − | 2.02117i | −0.427227 | − | 0.138814i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 5.73286 | − | 4.16516i | 0.391890 | − | 0.284725i | ||||
\(215\) | −2.90607 | + | 2.11139i | −0.198193 | + | 0.143995i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.23434 | − | 1.70074i | −0.355330 | − | 0.115454i | ||||
\(218\) | 11.4673 | − | 15.7834i | 0.776664 | − | 1.06899i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.07597 | − | 0.266970i | −0.139962 | − | 0.0179991i | ||||
\(221\) | 3.67601i | 0.247275i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.45815 | + | 19.8761i | −0.432470 | + | 1.33100i | 0.463188 | + | 0.886260i | \(0.346705\pi\) |
−0.895658 | + | 0.444744i | \(0.853295\pi\) | |||||||
\(224\) | −2.98702 | + | 0.970542i | −0.199579 | + | 0.0648470i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −5.42069 | − | 7.46094i | −0.360579 | − | 0.496294i | ||||
\(227\) | −3.67034 | − | 11.2961i | −0.243609 | − | 0.749752i | −0.995862 | − | 0.0908773i | \(-0.971033\pi\) |
0.752253 | − | 0.658874i | \(-0.228967\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.92914 | − | 5.76086i | −0.523972 | − | 0.380688i | 0.294126 | − | 0.955767i | \(-0.404972\pi\) |
−0.818098 | + | 0.575078i | \(0.804972\pi\) | |||||||
\(230\) | −2.55595 | −0.168534 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −11.1477 | −0.731879 | ||||||||
\(233\) | 12.6222 | + | 9.17056i | 0.826907 | + | 0.600783i | 0.918683 | − | 0.394997i | \(-0.129254\pi\) |
−0.0917755 | + | 0.995780i | \(0.529254\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.0464058 | − | 0.142823i | −0.00302718 | − | 0.00931671i | ||||
\(236\) | 3.44040 | + | 4.73531i | 0.223951 | + | 0.308242i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.96030 | + | 0.961860i | −0.191888 | + | 0.0623481i | ||||
\(239\) | −9.26252 | + | 28.5071i | −0.599143 | + | 1.84397i | −0.0662251 | + | 0.997805i | \(0.521096\pi\) |
−0.532918 | + | 0.846167i | \(0.678904\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.89778i | 0.122247i | 0.998130 | + | 0.0611235i | \(0.0194684\pi\) | ||||
−0.998130 | + | 0.0611235i | \(0.980532\pi\) | |||||||
\(242\) | 11.8020 | − | 4.61184i | 0.758662 | − | 0.296460i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 5.36837 | − | 7.38893i | 0.343675 | − | 0.473028i | ||||
\(245\) | 5.57191 | + | 1.81042i | 0.355976 | + | 0.115664i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.61848 | − | 4.80861i | 0.421124 | − | 0.305964i | ||||
\(248\) | −15.8166 | + | 11.4914i | −1.00435 | + | 0.729705i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 9.36874 | + | 3.04409i | 0.592531 | + | 0.192525i | ||||
\(251\) | −1.59530 | + | 2.19574i | −0.100694 | + | 0.138594i | −0.856391 | − | 0.516328i | \(-0.827299\pi\) |
0.755696 | + | 0.654922i | \(0.227299\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.88652 | + | 3.76588i | −0.432952 | + | 0.236759i | ||||
\(254\) | 7.31955i | 0.459269i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4.36307 | + | 13.4281i | −0.272692 | + | 0.839259i | ||||
\(257\) | −8.10484 | + | 2.63342i | −0.505566 | + | 0.164268i | −0.550685 | − | 0.834713i | \(-0.685633\pi\) |
0.0451186 | + | 0.998982i | \(0.485633\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.07005 | + | 5.60194i | 0.252900 | + | 0.348088i | ||||
\(260\) | 0.229971 | + | 0.707777i | 0.0142622 | + | 0.0438945i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −16.1911 | − | 11.7636i | −1.00029 | − | 0.726755i | ||||
\(263\) | −23.8526 | −1.47081 | −0.735407 | − | 0.677626i | \(-0.763009\pi\) | ||||
−0.735407 | + | 0.677626i | \(0.763009\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.11097 | −0.559682 | ||||||||
\(266\) | 5.60417 | + | 4.07167i | 0.343614 | + | 0.249650i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.38171 | − | 4.25246i | −0.0844012 | − | 0.259760i | ||||
\(269\) | −14.1414 | − | 19.4640i | −0.862219 | − | 1.18674i | −0.981036 | − | 0.193826i | \(-0.937910\pi\) |
0.118817 | − | 0.992916i | \(-0.462090\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.2868 | − | 3.99222i | 0.746370 | − | 0.242510i | 0.0889514 | − | 0.996036i | \(-0.471648\pi\) |
0.657418 | + | 0.753526i | \(0.271648\pi\) | |||||||
\(272\) | −2.11998 | + | 6.52463i | −0.128543 | + | 0.395614i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 20.3897i | 1.23179i | ||||||||
\(275\) | 13.4311 | − | 2.53103i | 0.809928 | − | 0.152627i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.92290 | − | 5.39940i | 0.235704 | − | 0.324419i | −0.674737 | − | 0.738059i | \(-0.735743\pi\) |
0.910441 | + | 0.413640i | \(0.135743\pi\) | |||||||
\(278\) | 6.76925 | + | 2.19946i | 0.405993 | + | 0.131915i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2.02462 | + | 1.47097i | −0.120994 | + | 0.0879073i | ||||
\(281\) | 0.496529 | − | 0.360749i | 0.0296204 | − | 0.0215205i | −0.572877 | − | 0.819642i | \(-0.694173\pi\) |
0.602497 | + | 0.798121i | \(0.294173\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 17.9806 | + | 5.84225i | 1.06883 | + | 0.347286i | 0.790034 | − | 0.613063i | \(-0.210063\pi\) |
0.278801 | + | 0.960349i | \(0.410063\pi\) | |||||||
\(284\) | 4.40171 | − | 6.05843i | 0.261193 | − | 0.359502i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.27731 | − | 3.09141i | −0.193791 | − | 0.182799i | ||||
\(287\) | 3.12347i | 0.184372i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.25049 | + | 6.92628i | −0.132381 | + | 0.407428i | ||||
\(290\) | −3.71871 | + | 1.20828i | −0.218370 | + | 0.0709527i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.37188 | − | 1.88823i | −0.0802833 | − | 0.110501i | ||||
\(293\) | −0.649796 | − | 1.99987i | −0.0379615 | − | 0.116833i | 0.930280 | − | 0.366850i | \(-0.119564\pi\) |
−0.968242 | + | 0.250017i | \(0.919564\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.59618 | + | 4.79241i | 0.384044 | + | 0.279025i | ||||
\(296\) | 24.5968 | 1.42966 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −8.50312 | −0.492572 | ||||||||
\(299\) | 2.25776 | + | 1.64036i | 0.130569 | + | 0.0948642i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.02625 | + | 3.15846i | 0.0591519 | + | 0.182051i | ||||
\(302\) | 9.12979 | + | 12.5661i | 0.525360 | + | 0.723096i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 14.5204 | − | 4.71798i | 0.832805 | − | 0.270595i | ||||
\(305\) | 3.93143 | − | 12.0997i | 0.225113 | − | 0.692827i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 17.6110i | − | 1.00511i | −0.864545 | − | 0.502556i | \(-0.832393\pi\) | ||
0.864545 | − | 0.502556i | \(-0.167607\pi\) | |||||||
\(308\) | −0.827835 | + | 1.74908i | −0.0471703 | + | 0.0996633i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −4.03065 | + | 5.54772i | −0.228926 | + | 0.315089i | ||||
\(311\) | −10.4661 | − | 3.40065i | −0.593480 | − | 0.192833i | −0.00314963 | − | 0.999995i | \(-0.501003\pi\) |
−0.590330 | + | 0.807162i | \(0.701003\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.15636 | − | 2.29323i | 0.178408 | − | 0.129621i | −0.494997 | − | 0.868895i | \(-0.664831\pi\) |
0.673405 | + | 0.739274i | \(0.264831\pi\) | |||||||
\(314\) | 2.73263 | − | 1.98537i | 0.154211 | − | 0.112041i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.83167 | − | 1.56991i | −0.271803 | − | 0.0883141i | ||||
\(317\) | −12.6974 | + | 17.4765i | −0.713156 | + | 0.981576i | 0.286567 | + | 0.958060i | \(0.407486\pi\) |
−0.999723 | + | 0.0235153i | \(0.992514\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.23910 | + | 8.73456i | −0.461301 | + | 0.489041i | ||||
\(320\) | 8.04009i | 0.449455i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −0.730222 | + | 2.24739i | −0.0406937 | + | 0.125242i | ||||
\(323\) | −20.5672 | + | 6.68269i | −1.14439 | + | 0.371835i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.85638 | − | 3.93148i | −0.158444 | − | 0.218079i | ||||
\(326\) | −7.83776 | − | 24.1222i | −0.434094 | − | 1.33600i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 8.97621 | + | 6.52160i | 0.495629 | + | 0.360095i | ||||
\(329\) | −0.138839 | −0.00765443 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.85205 | −0.376623 | −0.188311 | − | 0.982109i | \(-0.560301\pi\) | ||||
−0.188311 | + | 0.982109i | \(0.560301\pi\) | |||||||
\(332\) | −7.85719 | − | 5.70858i | −0.431219 | − | 0.313299i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0.229499 | + | 0.706326i | 0.0125576 | + | 0.0386485i | ||||
\(335\) | −3.66098 | − | 5.03890i | −0.200020 | − | 0.275305i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.702984 | − | 0.228413i | 0.0382940 | − | 0.0124425i | −0.289807 | − | 0.957085i | \(-0.593591\pi\) |
0.328101 | + | 0.944643i | \(0.393591\pi\) | |||||||
\(338\) | 4.13250 | − | 12.7185i | 0.224778 | − | 0.691796i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | − | 1.96724i | − | 0.106689i | ||||||
\(341\) | −2.68594 | + | 20.8860i | −0.145452 | + | 1.13104i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.75032 | − | 9.29102i | 0.364483 | − | 0.501668i | ||||
\(344\) | 11.2195 | + | 3.64544i | 0.604916 | + | 0.196549i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 12.5751 | − | 9.13631i | 0.676039 | − | 0.491171i | ||||
\(347\) | 9.63095 | − | 6.99730i | 0.517017 | − | 0.375635i | −0.298462 | − | 0.954421i | \(-0.596474\pi\) |
0.815479 | + | 0.578787i | \(0.196474\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.68842 | + | 3.14796i | 0.518609 | + | 0.168506i | 0.556614 | − | 0.830771i | \(-0.312100\pi\) |
−0.0380047 | + | 0.999278i | \(0.512100\pi\) | |||||||
\(350\) | 2.41863 | − | 3.32896i | 0.129281 | − | 0.177940i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.76564 | + | 10.5434i | 0.307310 | + | 0.561965i | ||||
\(353\) | − | 31.4901i | − | 1.67605i | −0.545632 | − | 0.838025i | \(-0.683710\pi\) | ||
0.545632 | − | 0.838025i | \(-0.316290\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.22351 | − | 9.92094i | 0.171086 | − | 0.526549i | ||||
\(356\) | −5.94393 | + | 1.93130i | −0.315028 | + | 0.102359i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.757069 | + | 1.04202i | 0.0400123 | + | 0.0550722i | ||||
\(359\) | −8.57599 | − | 26.3942i | −0.452624 | − | 1.39303i | −0.873903 | − | 0.486101i | \(-0.838419\pi\) |
0.421279 | − | 0.906931i | \(-0.361581\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 23.5646 | + | 17.1207i | 1.24024 | + | 0.901090i | ||||
\(362\) | 26.7537 | 1.40615 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.688035 | 0.0360629 | ||||||||
\(365\) | −2.63027 | − | 1.91100i | −0.137675 | − | 0.100026i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.21807 | − | 16.0596i | −0.272381 | − | 0.838302i | −0.989901 | − | 0.141764i | \(-0.954723\pi\) |
0.717520 | − | 0.696538i | \(-0.245277\pi\) | |||||||
\(368\) | 3.06133 | + | 4.21357i | 0.159583 | + | 0.219647i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 8.20517 | − | 2.66602i | 0.426567 | − | 0.138600i | ||||
\(371\) | −2.60296 | + | 8.01109i | −0.135139 | + | 0.415915i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 6.00920i | − | 0.311145i | −0.987824 | − | 0.155572i | \(-0.950278\pi\) | ||
0.987824 | − | 0.155572i | \(-0.0497222\pi\) | |||||||
\(374\) | 5.71406 | + | 10.4491i | 0.295467 | + | 0.540309i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.289887 | + | 0.398995i | −0.0149498 | + | 0.0205766i | ||||
\(377\) | 4.06031 | + | 1.31928i | 0.209117 | + | 0.0679462i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.88315 | + | 5.00090i | −0.353563 | + | 0.256879i | −0.750362 | − | 0.661027i | \(-0.770121\pi\) |
0.396799 | + | 0.917906i | \(0.370121\pi\) | |||||||
\(380\) | −3.54193 | + | 2.57336i | −0.181697 | + | 0.132011i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3.27710 | + | 1.06480i | 0.167671 | + | 0.0544797i | ||||
\(383\) | 5.95093 | − | 8.19075i | 0.304078 | − | 0.418528i | −0.629445 | − | 0.777045i | \(-0.716718\pi\) |
0.933523 | + | 0.358517i | \(0.116718\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.343817 | + | 2.67353i | −0.0175226 | + | 0.136256i | ||||
\(386\) | − | 11.3925i | − | 0.579863i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2.53398 | − | 7.79880i | 0.128644 | − | 0.395924i | ||||
\(389\) | −8.87507 | + | 2.88369i | −0.449984 | + | 0.146209i | −0.525237 | − | 0.850956i | \(-0.676023\pi\) |
0.0752534 | + | 0.997164i | \(0.476023\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.33617 | − | 5.96822i | −0.219289 | − | 0.301826i | ||||
\(392\) | −5.94565 | − | 18.2988i | −0.300301 | − | 0.924230i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −4.60898 | − | 3.34862i | −0.232197 | − | 0.168701i | ||||
\(395\) | −7.07678 | −0.356071 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.3328 | 0.518587 | 0.259294 | − | 0.965799i | \(-0.416510\pi\) | ||||
0.259294 | + | 0.965799i | \(0.416510\pi\) | |||||||
\(398\) | 7.12796 | + | 5.17877i | 0.357292 | + | 0.259588i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.80255 | − | 8.62536i | −0.140127 | − | 0.431268i | ||||
\(401\) | −8.71867 | − | 12.0002i | −0.435390 | − | 0.599262i | 0.533790 | − | 0.845617i | \(-0.320767\pi\) |
−0.969180 | + | 0.246355i | \(0.920767\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.12083 | − | 2.31370i | 0.354714 | − | 0.115253i | ||||
\(404\) | 1.26008 | − | 3.87814i | 0.0626915 | − | 0.192944i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.61498i | 0.179409i | ||||||||
\(407\) | 18.1792 | − | 19.2724i | 0.901111 | − | 0.955299i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.13485 | − | 7.06751i | 0.253902 | − | 0.349466i | −0.662971 | − | 0.748645i | \(-0.730705\pi\) |
0.916873 | + | 0.399179i | \(0.130705\pi\) | |||||||
\(410\) | 3.70121 | + | 1.20260i | 0.182790 | + | 0.0593920i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2.17194 | + | 1.57800i | −0.107004 | + | 0.0777427i | ||||
\(413\) | 6.09836 | − | 4.43072i | 0.300081 | − | 0.218021i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.8665 | − | 4.18058i | −0.631591 | − | 0.205216i | ||||
\(416\) | 2.51142 | − | 3.45667i | 0.123132 | − | 0.169477i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 11.3385 | − | 23.9564i | 0.554584 | − | 1.17175i | ||||
\(419\) | − | 35.1723i | − | 1.71828i | −0.511743 | − | 0.859139i | \(-0.671000\pi\) | ||
0.511743 | − | 0.859139i | \(-0.329000\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.493004 | + | 1.51731i | −0.0240276 | + | 0.0739492i | −0.962351 | − | 0.271809i | \(-0.912378\pi\) |
0.938324 | + | 0.345758i | \(0.112378\pi\) | |||||||
\(422\) | −25.7507 | + | 8.36692i | −1.25353 | + | 0.407295i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 17.5874 | + | 24.2070i | 0.854121 | + | 1.17560i | ||||
\(425\) | 3.96962 | + | 12.2172i | 0.192555 | + | 0.592622i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9.51583 | − | 6.91366i | −0.460503 | − | 0.334575i | ||||
\(428\) | 4.14060 | 0.200143 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.13781 | 0.199543 | ||||||||
\(431\) | 23.8660 | + | 17.3397i | 1.14959 | + | 0.835223i | 0.988426 | − | 0.151706i | \(-0.0484766\pi\) |
0.161160 | + | 0.986928i | \(0.448477\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.54190 | + | 10.9008i | 0.170213 | + | 0.523861i | 0.999383 | − | 0.0351356i | \(-0.0111863\pi\) |
−0.829170 | + | 0.558997i | \(0.811186\pi\) | |||||||
\(434\) | 3.72645 | + | 5.12903i | 0.178876 | + | 0.246201i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 10.8417 | − | 3.52269i | 0.519225 | − | 0.168706i | ||||
\(437\) | −5.07334 | + | 15.6141i | −0.242691 | + | 0.746926i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.03783i | 0.144988i | 0.997369 | + | 0.0724938i | \(0.0230957\pi\) | ||||
−0.997369 | + | 0.0724938i | \(0.976904\pi\) | |||||||
\(440\) | 6.96532 | + | 6.57023i | 0.332059 | + | 0.313223i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.48895 | − | 3.42575i | 0.118387 | − | 0.162946i | ||||
\(443\) | −15.7419 | − | 5.11484i | −0.747918 | − | 0.243013i | −0.0898330 | − | 0.995957i | \(-0.528633\pi\) |
−0.658085 | + | 0.752943i | \(0.728633\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.04319 | + | 5.11717i | −0.333879 | + | 0.242577i | ||||
\(446\) | 19.4762 | − | 14.1503i | 0.922225 | − | 0.670036i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 7.06948 | + | 2.29701i | 0.334002 | + | 0.108524i | ||||
\(449\) | 0.152765 | − | 0.210263i | 0.00720943 | − | 0.00992293i | −0.805397 | − | 0.592736i | \(-0.798048\pi\) |
0.812606 | + | 0.582813i | \(0.198048\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.7441 | − | 2.21312i | 0.553009 | − | 0.104212i | ||||
\(452\) | − | 5.38872i | − | 0.253464i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −4.22793 | + | 13.0122i | −0.198427 | + | 0.610694i | ||||
\(455\) | 0.911510 | − | 0.296168i | 0.0427323 | − | 0.0138845i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.19749 | − | 4.40097i | −0.149572 | − | 0.205869i | 0.727656 | − | 0.685943i | \(-0.240610\pi\) |
−0.877228 | + | 0.480074i | \(0.840610\pi\) | |||||||
\(458\) | 3.48877 | + | 10.7373i | 0.163019 | + | 0.501722i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.20826 | − | 0.877849i | −0.0563352 | − | 0.0409299i | ||||
\(461\) | 29.3632 | 1.36758 | 0.683789 | − | 0.729679i | \(-0.260331\pi\) | ||||
0.683789 | + | 0.729679i | \(0.260331\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.3827 | 0.947264 | 0.473632 | − | 0.880723i | \(-0.342943\pi\) | ||||
0.473632 | + | 0.880723i | \(0.342943\pi\) | |||||||
\(464\) | 6.44590 | + | 4.68322i | 0.299244 | + | 0.217413i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5.55368 | − | 17.0925i | −0.257269 | − | 0.791793i | ||||
\(467\) | −0.293731 | − | 0.404285i | −0.0135922 | − | 0.0187081i | 0.802167 | − | 0.597100i | \(-0.203680\pi\) |
−0.815759 | + | 0.578392i | \(0.803680\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.47653 | + | 1.77943i | −0.252882 | + | 0.0821665i | ||||
\(470\) | −0.0534557 | + | 0.164520i | −0.00246573 | + | 0.00758873i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 26.7765i | − | 1.23249i | ||||||
\(473\) | 11.1486 | − | 6.09657i | 0.512611 | − | 0.280320i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 16.8039 | − | 23.1285i | 0.771014 | − | 1.06121i | ||||
\(476\) | −1.72976 | − | 0.562032i | −0.0792833 | − | 0.0257607i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 27.9335 | − | 20.2949i | 1.27765 | − | 0.928267i | ||||
\(479\) | 8.69444 | − | 6.31688i | 0.397259 | − | 0.288625i | −0.371165 | − | 0.928567i | \(-0.621041\pi\) |
0.768424 | + | 0.639942i | \(0.221041\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.95891 | − | 2.91093i | −0.408491 | − | 0.132727i | ||||
\(482\) | 1.28495 | − | 1.76858i | 0.0585279 | − | 0.0805568i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 7.16304 | + | 1.87332i | 0.325593 | + | 0.0851509i | ||||
\(485\) | − | 11.4226i | − | 0.518675i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.43244 | − | 29.0301i | 0.427425 | − | 1.31548i | −0.473228 | − | 0.880940i | \(-0.656911\pi\) |
0.900653 | − | 0.434539i | \(-0.143089\pi\) | |||||||
\(488\) | −39.7369 | + | 12.9113i | −1.79880 | + | 0.584467i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −3.96678 | − | 5.45980i | −0.179201 | − | 0.246649i | ||||
\(491\) | 7.74766 | + | 23.8448i | 0.349647 | + | 1.07610i | 0.959049 | + | 0.283241i | \(0.0914097\pi\) |
−0.609402 | + | 0.792862i | \(0.708590\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.13017 | − | 6.63346i | −0.411202 | − | 0.298756i | ||||
\(494\) | −9.42371 | −0.423993 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 13.9732 | 0.627417 | ||||||||
\(497\) | −7.80234 | − | 5.66873i | −0.349983 | − | 0.254277i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.53591 | + | 4.72705i | 0.0687568 | + | 0.211612i | 0.979531 | − | 0.201293i | \(-0.0645143\pi\) |
−0.910774 | + | 0.412905i | \(0.864514\pi\) | |||||||
\(500\) | 3.38332 | + | 4.65674i | 0.151307 | + | 0.208256i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2.97339 | − | 0.966111i | 0.132709 | − | 0.0431197i | ||||
\(503\) | −11.3085 | + | 34.8039i | −0.504219 | + | 1.55183i | 0.297860 | + | 0.954610i | \(0.403727\pi\) |
−0.802079 | + | 0.597218i | \(0.796273\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 5.68017i | − | 0.252764i | ||||||
\(506\) | 8.96749 | + | 1.15322i | 0.398654 | + | 0.0512670i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2.51392 | + | 3.46012i | −0.111537 | + | 0.153518i | ||||
\(509\) | −13.2688 | − | 4.31130i | −0.588131 | − | 0.191095i | −0.000190870 | − | 1.00000i | \(-0.500061\pi\) |
−0.587940 | + | 0.808905i | \(0.700061\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.43176 | + | 1.76678i | −0.107575 | + | 0.0781576i | ||||
\(512\) | 17.4158 | − | 12.6533i | 0.769677 | − | 0.559203i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 9.33611 | + | 3.03349i | 0.411798 | + | 0.133801i | ||||
\(515\) | −2.19813 | + | 3.02546i | −0.0968610 | + | 0.133318i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.0983737 | + | 0.522028i | 0.00432647 | + | 0.0229588i | ||||
\(518\) | − | 7.97631i | − | 0.350459i | ||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.05205 | − | 3.23787i | 0.0461354 | − | 0.141990i | ||||
\(521\) | 6.74242 | − | 2.19075i | 0.295391 | − | 0.0959783i | −0.157573 | − | 0.987507i | \(-0.550367\pi\) |
0.452963 | + | 0.891529i | \(0.350367\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.47929 | + | 10.2944i | 0.327047 | + | 0.450141i | 0.940602 | − | 0.339510i | \(-0.110261\pi\) |
−0.613556 | + | 0.789651i | \(0.710261\pi\) | |||||||
\(524\) | −3.61370 | − | 11.1218i | −0.157865 | − | 0.485859i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 22.2287 | + | 16.1501i | 0.969218 | + | 0.704178i | ||||
\(527\) | −19.7921 | −0.862158 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17.3995 | 0.756498 | ||||||||
\(530\) | 8.49070 | + | 6.16886i | 0.368813 | + | 0.267958i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.25079 | + | 3.84955i | 0.0542288 | + | 0.166899i | ||||
\(533\) | −2.49761 | − | 3.43766i | −0.108183 | − | 0.148902i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.48547 | − | 1.78234i | 0.237157 | − | 0.0770571i | ||||
\(536\) | −6.32091 | + | 19.4538i | −0.273022 | + | 0.840275i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 27.7138i | 1.19483i | ||||||||
\(539\) | −18.7321 | − | 8.86584i | −0.806849 | − | 0.381879i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.30481 | − | 3.17230i | 0.0990915 | − | 0.136388i | −0.756592 | − | 0.653887i | \(-0.773137\pi\) |
0.855684 | + | 0.517499i | \(0.173137\pi\) | |||||||
\(542\) | −14.1534 | − | 4.59871i | −0.607940 | − | 0.197532i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −9.13747 | + | 6.63876i | −0.391766 | + | 0.284634i | ||||
\(545\) | 12.8468 | − | 9.33374i | 0.550296 | − | 0.399813i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.2734 | − | 3.33803i | −0.439259 | − | 0.142724i | 0.0810349 | − | 0.996711i | \(-0.474177\pi\) |
−0.520294 | + | 0.853987i | \(0.674177\pi\) | |||||||
\(548\) | −7.00292 | + | 9.63869i | −0.299150 | + | 0.411745i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −14.2305 | − | 6.73523i | −0.606789 | − | 0.287191i | ||||
\(551\) | 25.1157i | 1.06997i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.02180 | + | 6.22247i | −0.0859758 | + | 0.264606i | ||||
\(554\) | −7.31166 | + | 2.37570i | −0.310643 | + | 0.100934i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.44457 | + | 3.36466i | 0.103673 | + | 0.142693i | ||||
\(557\) | −7.06108 | − | 21.7318i | −0.299188 | − | 0.920805i | −0.981783 | − | 0.190008i | \(-0.939149\pi\) |
0.682595 | − | 0.730797i | \(-0.260851\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.65507 | − | 2.65556i | −0.154593 | − | 0.112318i | ||||
\(560\) | 1.78866 | 0.0755847 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −0.706982 | −0.0298222 | ||||||||
\(563\) | 8.77304 | + | 6.37399i | 0.369740 | + | 0.268632i | 0.757103 | − | 0.653296i | \(-0.226614\pi\) |
−0.387363 | + | 0.921927i | \(0.626614\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.31959 | − | 7.13898i | −0.0975861 | − | 0.300339i | ||||
\(566\) | −12.8008 | − | 17.6188i | −0.538058 | − | 0.740574i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −32.5816 | + | 10.5864i | −1.36709 | + | 0.444195i | ||||
\(569\) | 5.19794 | − | 15.9976i | 0.217909 | − | 0.670655i | −0.781025 | − | 0.624499i | \(-0.785303\pi\) |
0.998934 | − | 0.0461553i | \(-0.0146969\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 16.3097i | − | 0.682541i | −0.939965 | − | 0.341271i | \(-0.889143\pi\) | ||
0.939965 | − | 0.341271i | \(-0.110857\pi\) | |||||||
\(572\) | −0.487505 | − | 2.58698i | −0.0203836 | − | 0.108167i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2.11484 | − | 2.91082i | 0.0882716 | − | 0.121495i | ||||
\(575\) | 9.27503 | + | 3.01364i | 0.386795 | + | 0.125677i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.51886 | − | 4.73623i | 0.271384 | − | 0.197172i | −0.443767 | − | 0.896142i | \(-0.646358\pi\) |
0.715150 | + | 0.698971i | \(0.246358\pi\) | |||||||
\(578\) | 6.78692 | − | 4.93099i | 0.282299 | − | 0.205102i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −2.17291 | − | 0.706021i | −0.0902251 | − | 0.0293159i | ||||
\(581\) | −7.35179 | + | 10.1189i | −0.305004 | + | 0.419801i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 31.9657 | + | 4.11080i | 1.32388 | + | 0.170252i | ||||
\(584\) | 10.6773i | 0.441830i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.748511 | + | 2.30368i | −0.0309207 | + | 0.0951642i | ||||
\(587\) | −14.9678 | + | 4.86334i | −0.617789 | + | 0.200732i | −0.601158 | − | 0.799130i | \(-0.705294\pi\) |
−0.0166304 | + | 0.999862i | \(0.505294\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 25.8902 | + | 35.6348i | 1.06679 | + | 1.46831i | ||||
\(590\) | −2.90228 | − | 8.93228i | −0.119485 | − | 0.367736i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −14.2226 | − | 10.3333i | −0.584546 | − | 0.424697i | ||||
\(593\) | −22.2880 | −0.915258 | −0.457629 | − | 0.889143i | \(-0.651301\pi\) | ||||
−0.457629 | + | 0.889143i | \(0.651301\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.53351 | −0.103864 | ||||||||
\(596\) | −4.01962 | − | 2.92043i | −0.164650 | − | 0.119625i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −0.993397 | − | 3.05736i | −0.0406230 | − | 0.125025i | ||||
\(599\) | −16.8142 | − | 23.1428i | −0.687010 | − | 0.945588i | 0.312981 | − | 0.949759i | \(-0.398672\pi\) |
−0.999991 | + | 0.00417130i | \(0.998672\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.78070 | + | 2.20318i | −0.276591 | + | 0.0898697i | −0.444028 | − | 0.896013i | \(-0.646451\pi\) |
0.167437 | + | 0.985883i | \(0.446451\pi\) | |||||||
\(602\) | 1.18215 | − | 3.63829i | 0.0481809 | − | 0.148286i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 9.07594i | 0.369295i | ||||||||
\(605\) | 10.2960 | − | 0.601583i | 0.418591 | − | 0.0244578i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.68531 | + | 3.69601i | −0.108993 | + | 0.150017i | −0.860029 | − | 0.510245i | \(-0.829555\pi\) |
0.751036 | + | 0.660262i | \(0.229555\pi\) | |||||||
\(608\) | 23.9056 | + | 7.76739i | 0.969499 | + | 0.315009i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −11.8563 | + | 8.61407i | −0.480046 | + | 0.348774i | ||||
\(611\) | 0.152805 | − | 0.111019i | 0.00618182 | − | 0.00449135i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −37.1400 | − | 12.0675i | −1.50007 | − | 0.487402i | −0.560032 | − | 0.828471i | \(-0.689211\pi\) |
−0.940038 | + | 0.341069i | \(0.889211\pi\) | |||||||
\(614\) | −11.9240 | + | 16.4120i | −0.481215 | + | 0.662336i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 7.76703 | − | 4.24738i | 0.312942 | − | 0.171132i | ||||
\(617\) | 31.1970i | 1.25594i | 0.778236 | + | 0.627972i | \(0.216115\pi\) | ||||
−0.778236 | + | 0.627972i | \(0.783885\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.95813 | − | 30.6480i | 0.400251 | − | 1.23185i | −0.524545 | − | 0.851383i | \(-0.675765\pi\) |
0.924796 | − | 0.380463i | \(-0.124235\pi\) | |||||||
\(620\) | −3.81077 | + | 1.23819i | −0.153044 | + | 0.0497270i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 7.45109 | + | 10.2556i | 0.298762 | + | 0.411210i | ||||
\(623\) | 2.48722 | + | 7.65488i | 0.0996484 | + | 0.306686i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −10.1827 | − | 7.39818i | −0.407309 | − | 0.295927i | ||||
\(626\) | −4.49418 | −0.179623 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.97366 | 0.0787576 | ||||||||
\(629\) | 20.1453 | + | 14.6365i | 0.803248 | + | 0.583594i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.555911 | − | 1.71092i | −0.0221305 | − | 0.0681105i | 0.939381 | − | 0.342874i | \(-0.111400\pi\) |
−0.961512 | + | 0.274764i | \(0.911400\pi\) | |||||||
\(632\) | 13.6607 | + | 18.8024i | 0.543394 | + | 0.747918i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 23.6659 | − | 7.68952i | 0.939894 | − | 0.305390i | ||||
\(635\) | −1.84103 | + | 5.66610i | −0.0730590 | + | 0.224852i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7.36863i | 0.291956i | ||||||||
\(638\) | 13.5922 | − | 2.56138i | 0.538120 | − | 0.101406i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.45023 | − | 1.99606i | 0.0573252 | − | 0.0789014i | ||||
\(641\) | 7.32843 | + | 2.38115i | 0.289456 | + | 0.0940499i | 0.450146 | − | 0.892955i | \(-0.351372\pi\) |
−0.160690 | + | 0.987005i | \(0.551372\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −17.1627 | + | 12.4695i | −0.676832 | + | 0.491747i | −0.872305 | − | 0.488962i | \(-0.837376\pi\) |
0.195473 | + | 0.980709i | \(0.437376\pi\) | |||||||
\(644\) | −1.11707 | + | 0.811597i | −0.0440186 | + | 0.0319814i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 23.6917 | + | 7.69791i | 0.932138 | + | 0.302870i | ||||
\(647\) | 29.4465 | − | 40.5296i | 1.15766 | − | 1.59338i | 0.438150 | − | 0.898902i | \(-0.355634\pi\) |
0.719511 | − | 0.694482i | \(-0.244366\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −20.9803 | − | 19.7902i | −0.823548 | − | 0.776834i | ||||
\(650\) | 5.59782i | 0.219565i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 4.57975 | − | 14.0950i | 0.179357 | − | 0.552004i | ||||
\(653\) | −16.7546 | + | 5.44390i | −0.655659 | + | 0.213036i | −0.617908 | − | 0.786251i | \(-0.712019\pi\) |
−0.0377511 | + | 0.999287i | \(0.512019\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.57486 | − | 13.1787i | −0.374121 | − | 0.514933i | ||||
\(656\) | −2.45053 | − | 7.54197i | −0.0956772 | − | 0.294464i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0.129387 | + | 0.0940050i | 0.00504402 | + | 0.00366470i | ||||
\(659\) | 21.1328 | 0.823218 | 0.411609 | − | 0.911360i | \(-0.364967\pi\) | ||||
0.411609 | + | 0.911360i | \(0.364967\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11.0329 | −0.429131 | −0.214566 | − | 0.976710i | \(-0.568834\pi\) | ||||
−0.214566 | + | 0.976710i | \(0.568834\pi\) | |||||||
\(662\) | 6.38557 | + | 4.63939i | 0.248182 | + | 0.180315i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 13.7295 | + | 42.2551i | 0.532809 | + | 1.63982i | ||||
\(665\) | 3.31411 | + | 4.56147i | 0.128515 | + | 0.176886i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.14837 | + | 2.64757i | −0.315506 | + | 0.102514i | ||||
\(668\) | −0.134101 | + | 0.412719i | −0.00518851 | + | 0.0159686i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 7.17463i | 0.277180i | ||||||||
\(671\) | −19.2527 | + | 40.6778i | −0.743240 | + | 1.57035i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −18.2818 | + | 25.1627i | −0.704712 | + | 0.969952i | 0.295183 | + | 0.955441i | \(0.404619\pi\) |
−0.999895 | + | 0.0145116i | \(0.995381\pi\) | |||||||
\(674\) | −0.809780 | − | 0.263113i | −0.0311915 | − | 0.0101347i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.32175 | − | 4.59302i | 0.243144 | − | 0.176655i | ||||
\(677\) | −17.2782 | + | 12.5533i | −0.664053 | + | 0.482463i | −0.868029 | − | 0.496513i | \(-0.834614\pi\) |
0.203976 | + | 0.978976i | \(0.434614\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.0437 | − | 3.26339i | −0.385441 | − | 0.125237i | ||||
\(680\) | −5.28981 | + | 7.28081i | −0.202855 | + | 0.279206i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 16.6446 | − | 17.6455i | 0.637353 | − | 0.675680i | ||||
\(683\) | − | 17.2570i | − | 0.660321i | −0.943925 | − | 0.330161i | \(-0.892897\pi\) | ||
0.943925 | − | 0.330161i | \(-0.107103\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.12846 | + | 15.7838i | −0.195949 | + | 0.603068i | ||||
\(686\) | −12.5815 | + | 4.08799i | −0.480365 | + | 0.156080i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −4.95598 | − | 6.82132i | −0.188945 | − | 0.260060i | ||||
\(689\) | −3.54108 | − | 10.8983i | −0.134904 | − | 0.415193i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16.9524 | − | 12.3166i | −0.644898 | − | 0.468546i | 0.216631 | − | 0.976253i | \(-0.430493\pi\) |
−0.861529 | + | 0.507708i | \(0.830493\pi\) | |||||||
\(692\) | 9.08243 | 0.345262 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −13.7130 | −0.520539 | ||||||||
\(695\) | 4.68690 | + | 3.40523i | 0.177784 | + | 0.129168i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.47101 | + | 10.6827i | 0.131474 | + | 0.404635i | ||||
\(698\) | −6.89742 | − | 9.49349i | −0.261071 | − | 0.359334i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2.28669 | − | 0.742990i | 0.0864286 | − | 0.0280824i | ||||
\(701\) | −15.1348 | + | 46.5802i | −0.571634 | + | 1.75931i | 0.0757293 | + | 0.997128i | \(0.475872\pi\) |
−0.647364 | + | 0.762181i | \(0.724128\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 55.4168i | − | 2.09008i | ||||||
\(704\) | 3.62762 | − | 28.2085i | 0.136721 | − | 1.06315i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −21.3213 | + | 29.3463i | −0.802439 | + | 1.10446i | ||||
\(707\) | −4.99445 | − | 1.62280i | −0.187836 | − | 0.0610315i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −33.6162 | + | 24.4236i | −1.26248 | + | 0.917248i | −0.998877 | − | 0.0473823i | \(-0.984912\pi\) |
−0.263607 | + | 0.964630i | \(0.584912\pi\) | |||||||
\(710\) | −9.72133 | + | 7.06296i | −0.364835 | + | 0.265068i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 27.1917 | + | 8.83513i | 1.01905 | + | 0.331111i | ||||
\(713\) | −8.83189 | + | 12.1561i | −0.330757 | + | 0.455248i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.75942 | − | 3.21739i | −0.0657988 | − | 0.120324i | ||||
\(716\) | 0.752603i | 0.0281261i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −9.87884 | + | 30.4039i | −0.368675 | + | 1.13466i | ||||
\(719\) | 27.4285 | − | 8.91207i | 1.02291 | − | 0.332364i | 0.250927 | − | 0.968006i | \(-0.419264\pi\) |
0.771984 | + | 0.635642i | \(0.219264\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.03223 | + | 2.79713i | 0.0756843 | + | 0.104170i | ||||
\(722\) | −10.3683 | − | 31.9103i | −0.385868 | − | 1.18758i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 12.6471 | + | 9.18867i | 0.470027 | + | 0.341494i | ||||
\(725\) | 14.9191 | 0.554082 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 18.3843 | 0.681838 | 0.340919 | − | 0.940093i | \(-0.389262\pi\) | ||||
0.340919 | + | 0.940093i | \(0.389262\pi\) | |||||||
\(728\) | −2.54643 | − | 1.85009i | −0.0943770 | − | 0.0685689i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.15730 | + | 3.56181i | 0.0428336 | + | 0.131828i | ||||
\(731\) | 7.01980 | + | 9.66193i | 0.259637 | + | 0.357359i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −30.0104 | + | 9.75096i | −1.10846 | + | 0.360160i | −0.805352 | − | 0.592797i | \(-0.798024\pi\) |
−0.303106 | + | 0.952957i | \(0.598024\pi\) | |||||||
\(734\) | −6.01078 | + | 18.4993i | −0.221862 | + | 0.682821i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 8.57455i | 0.316062i | ||||||||
\(737\) | 10.5710 | + | 19.3307i | 0.389386 | + | 0.712055i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −26.9990 | + | 37.1609i | −0.993173 | + | 1.36698i | −0.0637507 | + | 0.997966i | \(0.520306\pi\) |
−0.929422 | + | 0.369019i | \(0.879694\pi\) | |||||||
\(740\) | 4.79443 | + | 1.55781i | 0.176247 | + | 0.0572661i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 7.84990 | − | 5.70329i | 0.288179 | − | 0.209374i | ||||
\(743\) | −17.5692 | + | 12.7648i | −0.644551 | + | 0.468294i | −0.861411 | − | 0.507909i | \(-0.830419\pi\) |
0.216860 | + | 0.976203i | \(0.430419\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.58231 | − | 2.13872i | −0.241157 | − | 0.0783567i | ||||
\(746\) | −4.06871 | + | 5.60010i | −0.148966 | + | 0.205034i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −0.887605 | + | 6.90204i | −0.0324541 | + | 0.252364i | ||||
\(749\) | − | 5.33246i | − | 0.194844i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.25583 | − | 16.1758i | 0.191788 | − | 0.590262i | −0.808211 | − | 0.588893i | \(-0.799564\pi\) |
0.999999 | − | 0.00136956i | \(-0.000435943\pi\) | |||||||
\(752\) | 0.335242 | − | 0.108927i | 0.0122250 | − | 0.00397215i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2.89064 | − | 3.97862i | −0.105271 | − | 0.144893i | ||||
\(755\) | 3.90677 | + | 12.0238i | 0.142182 | + | 0.437591i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −18.8951 | − | 13.7281i | −0.686756 | − | 0.498957i | 0.188836 | − | 0.982009i | \(-0.439528\pi\) |
−0.875592 | + | 0.483051i | \(0.839528\pi\) | |||||||
\(758\) | 9.80055 | 0.355972 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 20.0284 | 0.726506 | ||||||||
\(761\) | 16.4210 | + | 11.9305i | 0.595259 | + | 0.432481i | 0.844193 | − | 0.536039i | \(-0.180080\pi\) |
−0.248934 | + | 0.968521i | \(0.580080\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.53670 | − | 13.9625i | −0.164239 | − | 0.505477i | ||||
\(764\) | 1.18346 | + | 1.62889i | 0.0428159 | + | 0.0589310i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −11.0916 | + | 3.60388i | −0.400755 | + | 0.130213i | ||||
\(767\) | −3.16888 | + | 9.75282i | −0.114422 | + | 0.352154i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 23.5119i | 0.847859i | 0.905695 | + | 0.423930i | \(0.139350\pi\) | ||||
−0.905695 | + | 0.423930i | \(0.860650\pi\) | |||||||
\(770\) | 2.13061 | − | 2.25873i | 0.0767817 | − | 0.0813989i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 3.91280 | − | 5.38550i | 0.140825 | − | 0.193828i | ||||
\(773\) | −12.8627 | − | 4.17933i | −0.462638 | − | 0.150320i | 0.0684183 | − | 0.997657i | \(-0.478205\pi\) |
−0.531056 | + | 0.847337i | \(0.678205\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 21.1676 | − | 15.3792i | 0.760362 | − | 0.552436i | ||||
\(776\) | −30.3489 | + | 22.0498i | −1.08946 | + | 0.791540i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 10.2233 | + | 3.32177i | 0.366525 | + | 0.119091i | ||||
\(779\) | 14.6932 | − | 20.2235i | 0.526439 | − | 0.724581i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −15.7859 | + | 33.3530i | −0.564863 | + | 1.19347i | ||||
\(782\) | 8.49784i | 0.303882i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4.24954 | + | 13.0787i | −0.151769 | + | 0.467098i | ||||
\(785\) | 2.61471 | − | 0.849570i | 0.0933229 | − | 0.0303225i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −27.2391 | − | 37.4914i | −0.970968 | − | 1.33642i | −0.941557 | − | 0.336855i | \(-0.890637\pi\) |
−0.0294111 | − | 0.999567i | \(-0.509363\pi\) | |||||||
\(788\) | −1.02868 | − | 3.16595i | −0.0366451 | − | 0.112782i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 6.59500 | + | 4.79155i | 0.234639 | + | 0.170476i | ||||
\(791\) | −6.93985 | −0.246753 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16.0014 | 0.568226 | ||||||||
\(794\) | −9.62933 | − | 6.99612i | −0.341732 | − | 0.248283i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.59089 | + | 4.89625i | 0.0563875 | + | 0.173543i | ||||
\(797\) | −28.6496 | − | 39.4328i | −1.01482 | − | 1.39678i | −0.915772 | − | 0.401699i | \(-0.868420\pi\) |
−0.0990490 | − | 0.995083i | \(-0.531580\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.474847 | + | 0.154287i | −0.0167989 | + | 0.00545829i | ||||
\(800\) | 4.61394 | − | 14.2003i | 0.163127 | − | 0.502055i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 17.0865i | 0.603345i | ||||||||
\(803\) | 8.36602 | + | 7.89147i | 0.295231 | + | 0.278484i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.13054 | + | 1.55605i | −0.0398462 | + | 0.0548436i | ||||
\(806\) | −8.20261 | − | 2.66519i | −0.288924 | − | 0.0938773i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −15.0917 | + | 10.9648i | −0.530924 | + | 0.385739i | ||||
\(809\) | −4.11235 | + | 2.98780i | −0.144583 | + | 0.105045i | −0.657725 | − | 0.753258i | \(-0.728481\pi\) |
0.513143 | + | 0.858303i | \(0.328481\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.95516 | + | 1.93495i | 0.209114 | + | 0.0679453i | 0.411701 | − | 0.911319i | \(-0.364935\pi\) |
−0.202587 | + | 0.979264i | \(0.564935\pi\) | |||||||
\(812\) | −1.24158 | + | 1.70889i | −0.0435709 | + | 0.0599702i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −29.9906 | + | 5.65158i | −1.05117 | + | 0.198088i | ||||
\(815\) | − | 20.6445i | − | 0.723144i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.21321 | − | 25.2777i | 0.287344 | − | 0.884353i | ||||
\(818\) | −9.57054 | + | 3.10966i | −0.334626 | + | 0.108727i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.33661 | + | 1.83969i | 0.0466766 | + | 0.0642448i | ||||
\(821\) | −10.6233 | − | 32.6953i | −0.370757 | − | 1.14107i | −0.946297 | − | 0.323299i | \(-0.895208\pi\) |
0.575540 | − | 0.817774i | \(-0.304792\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.54662 | − | 6.20948i | −0.297916 | − | 0.216449i | 0.428778 | − | 0.903410i | \(-0.358944\pi\) |
−0.726694 | + | 0.686961i | \(0.758944\pi\) | |||||||
\(824\) | 12.2815 | 0.427848 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.68314 | −0.302125 | ||||||||
\(827\) | −22.4299 | − | 16.2963i | −0.779965 | − | 0.566678i | 0.125004 | − | 0.992156i | \(-0.460106\pi\) |
−0.904969 | + | 0.425479i | \(0.860106\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.49749 | + | 23.0749i | 0.260399 | + | 0.801425i | 0.992718 | + | 0.120463i | \(0.0384379\pi\) |
−0.732319 | + | 0.680962i | \(0.761562\pi\) | |||||||
\(830\) | 9.15996 | + | 12.6076i | 0.317947 | + | 0.437616i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −9.61736 | + | 3.12487i | −0.333422 | + | 0.108335i | ||||
\(833\) | 6.01918 | − | 18.5251i | 0.208552 | − | 0.641858i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.604495i | 0.0209194i | ||||||||
\(836\) | 13.5879 | − | 7.43051i | 0.469947 | − | 0.256990i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −23.8144 | + | 32.7778i | −0.822656 | + | 1.13229i | ||||
\(839\) | 20.6658 | + | 6.71473i | 0.713463 | + | 0.231818i | 0.643187 | − | 0.765709i | \(-0.277612\pi\) |
0.0702762 | + | 0.997528i | \(0.477612\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.8578 | − | 9.34176i | 0.443373 | − | 0.322130i | ||||
\(842\) | 1.48678 | − | 1.08021i | 0.0512379 | − | 0.0372265i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −15.0466 | − | 4.88894i | −0.517926 | − | 0.168284i | ||||
\(845\) | 6.39798 | − | 8.80607i | 0.220097 | − | 0.302938i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.41255 | − | 9.22492i | 0.0828963 | − | 0.316972i | ||||
\(848\) | − | 21.3858i | − | 0.734393i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 4.57267 | − | 14.0732i | 0.156841 | − | 0.482708i | ||||
\(851\) | 17.9790 | − | 5.84174i | 0.616313 | − | 0.200252i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −24.1254 | − | 33.2058i | −0.826039 | − | 1.13695i | −0.988647 | − | 0.150255i | \(-0.951991\pi\) |
0.162608 | − | 0.986691i | \(-0.448009\pi\) | |||||||
\(854\) | 4.18690 | + | 12.8860i | 0.143273 | + | 0.440948i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −15.3244 | − | 11.1338i | −0.523778 | − | 0.380547i | ||||
\(857\) | 7.49320 | 0.255963 | 0.127981 | − | 0.991777i | \(-0.459150\pi\) | ||||
0.127981 | + | 0.991777i | \(0.459150\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.63002 | 0.0556156 | 0.0278078 | − | 0.999613i | \(-0.491147\pi\) | ||||
0.0278078 | + | 0.999613i | \(0.491147\pi\) | |||||||
\(860\) | 1.95604 | + | 1.42115i | 0.0667004 | + | 0.0484607i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −10.5009 | − | 32.3184i | −0.357662 | − | 1.10077i | ||||
\(863\) | −11.2828 | − | 15.5294i | −0.384070 | − | 0.528626i | 0.572587 | − | 0.819844i | \(-0.305940\pi\) |
−0.956657 | + | 0.291217i | \(0.905940\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.0324 | − | 3.90957i | 0.409114 | − | 0.132929i | ||||
\(866\) | 4.07998 | − | 12.5569i | 0.138643 | − | 0.426700i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 3.70448i | 0.125738i | ||||||||
\(869\) | 24.8288 | + | 3.19299i | 0.842258 | + | 0.108315i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.60454 | − | 6.33760i | 0.156019 | − | 0.214741i | ||||
\(872\) | −49.5978 | − | 16.1153i | −1.67959 | − | 0.545733i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 15.3000 | − | 11.1161i | 0.517529 | − | 0.376007i | ||||
\(875\) | 5.99718 | − | 4.35721i | 0.202742 | − | 0.147300i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −53.4401 | − | 17.3637i | −1.80454 | − | 0.586332i | −0.804573 | − | 0.593854i | \(-0.797606\pi\) |
−0.999972 | + | 0.00752149i | \(0.997606\pi\) | |||||||
\(878\) | 2.05685 | − | 2.83101i | 0.0694154 | − | 0.0955421i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.26735 | − | 6.72529i | −0.0427223 | − | 0.226709i | ||||
\(881\) | 16.2929i | 0.548922i | 0.961598 | + | 0.274461i | \(0.0884994\pi\) | ||||
−0.961598 | + | 0.274461i | \(0.911501\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −9.20073 | + | 28.3169i | −0.309629 | + | 0.952941i | 0.668280 | + | 0.743910i | \(0.267031\pi\) |
−0.977909 | + | 0.209031i | \(0.932969\pi\) | |||||||
\(884\) | 2.35317 | − | 0.764592i | 0.0791457 | − | 0.0257160i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 11.2070 | + | 15.4251i | 0.376507 | + | 0.518217i | ||||
\(887\) | −0.349006 | − | 1.07413i | −0.0117185 | − | 0.0360657i | 0.945026 | − | 0.326994i | \(-0.106036\pi\) |
−0.956745 | + | 0.290929i | \(0.906036\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.45611 | + | 3.23756i | 0.149453 | + | 0.108584i | ||||
\(890\) | 10.0284 | 0.336154 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 14.0668 | 0.470992 | ||||||||
\(893\) | 0.898937 | + | 0.653116i | 0.0300818 | + | 0.0218557i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.323961 | + | 0.997050i | 0.0108288 | + | 0.0333277i | ||||
\(896\) | −1.34078 | − | 1.84542i | −0.0447922 | − | 0.0616511i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −0.284730 | + | 0.0925143i | −0.00950156 | + | 0.00308724i | ||||
\(899\) | −7.10316 | + | 21.8613i | −0.236904 | + | 0.729114i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 30.2916i | 1.00916i | ||||||||
\(902\) | −12.4430 | − | 5.88925i | −0.414308 | − | 0.196091i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −14.4900 | + | 19.9437i | −0.481929 | + | 0.663319i | ||||
\(905\) | 20.7102 | + | 6.72916i | 0.688431 | + | 0.223685i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −21.5733 | + | 15.6739i | −0.716330 | + | 0.520444i | −0.885209 | − | 0.465193i | \(-0.845985\pi\) |
0.168880 | + | 0.985637i | \(0.445985\pi\) | |||||||
\(908\) | −6.46774 | + | 4.69909i | −0.214639 | + | 0.155945i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.04998 | − | 0.341161i | −0.0348066 | − | 0.0113094i | ||||
\(911\) | 2.30320 | − | 3.17008i | 0.0763084 | − | 0.105029i | −0.769157 | − | 0.639060i | \(-0.779323\pi\) |
0.845465 | + | 0.534031i | \(0.179323\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 43.2556 | + | 20.4727i | 1.43155 | + | 0.677549i | ||||
\(914\) | 6.26632i | 0.207271i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.03855 | + | 6.27402i | −0.0673556 | + | 0.207299i | ||||
\(917\) | −14.3232 | + | 4.65390i | −0.472994 | + | 0.153685i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −7.16542 | − | 9.86236i | −0.236365 | − | 0.325329i | 0.674313 | − | 0.738446i | \(-0.264440\pi\) |
−0.910678 | + | 0.413117i | \(0.864440\pi\) | |||||||
\(920\) | 2.11129 | + | 6.49787i | 0.0696070 | + | 0.214228i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −27.3641 | − | 19.8812i | −0.901190 | − | 0.654753i | ||||
\(923\) | 13.1201 | 0.431852 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −32.9184 | −1.08235 | ||||||||
\(926\) | −18.9950 | − | 13.8007i | −0.624216 | − | 0.453519i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4.05348 | + | 12.4753i | 0.133062 | + | 0.409522i | ||||
\(929\) | 2.77455 | + | 3.81885i | 0.0910302 | + | 0.125292i | 0.852103 | − | 0.523374i | \(-0.175327\pi\) |
−0.761073 | + | 0.648667i | \(0.775327\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −41.2274 | + | 13.3956i | −1.35117 | + | 0.439023i | ||||
\(932\) | 3.24512 | − | 9.98744i | 0.106297 | − | 0.327149i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0.575641i | 0.0188356i | ||||||||
\(935\) | 1.79511 | + | 9.52591i | 0.0587064 | + | 0.311530i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −17.0091 | + | 23.4110i | −0.555662 | + | 0.764803i | −0.990767 | − | 0.135577i | \(-0.956711\pi\) |
0.435105 | + | 0.900380i | \(0.356711\pi\) | |||||||
\(938\) | 6.30850 | + | 2.04976i | 0.205980 | + | 0.0669270i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −0.0817747 | + | 0.0594128i | −0.00266720 | + | 0.00193783i | ||||
\(941\) | 46.0903 | − | 33.4866i | 1.50250 | − | 1.09163i | 0.533129 | − | 0.846034i | \(-0.321016\pi\) |
0.969372 | − | 0.245597i | \(-0.0789841\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.11003 | + | 2.63511i | 0.264099 | + | 0.0858110i | ||||
\(944\) | −11.2490 | + | 15.4830i | −0.366125 | + | 0.503928i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −14.5174 | − | 1.86695i | −0.472002 | − | 0.0606997i | ||||
\(947\) | − | 0.938732i | − | 0.0305047i | −0.999884 | − | 0.0152524i | \(-0.995145\pi\) | ||
0.999884 | − | 0.0152524i | \(-0.00485516\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.26361 | − | 3.88900i | 0.0410186 | − | 0.126242i | ||||
\(950\) | −31.3197 | + | 10.1764i | −1.01615 | + | 0.330166i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 4.89059 | + | 6.73132i | 0.158505 | + | 0.218163i | ||||
\(953\) | 3.50554 | + | 10.7889i | 0.113556 | + | 0.349488i | 0.991643 | − | 0.129012i | \(-0.0411806\pi\) |
−0.878087 | + | 0.478500i | \(0.841181\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.26900 | + | 1.64853i | 0.0734232 | + | 0.0533451i | ||||
\(956\) | 20.1752 | 0.652512 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −12.3796 | −0.399965 | ||||||||
\(959\) | 12.4132 | + | 9.01870i | 0.400843 | + | 0.291229i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.87773 | + | 8.85675i | 0.0928301 | + | 0.285702i | ||||
\(962\) | 6.37807 | + | 8.77866i | 0.205637 | + | 0.283035i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.21485 | − | 0.394730i | 0.0391278 | − | 0.0127134i | ||||
\(965\) | 2.86547 | − | 8.81900i | 0.0922426 | − | 0.283894i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17.3054i | 0.556505i | 0.960508 | + | 0.278253i | \(0.0897553\pi\) | ||||
−0.960508 | + | 0.278253i | \(0.910245\pi\) | |||||||
\(968\) | −21.4733 | − | 26.1942i | −0.690177 | − | 0.841914i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −7.73403 | + | 10.6450i | −0.248325 | + | 0.341790i | ||||
\(971\) | 23.6890 | + | 7.69701i | 0.760215 | + | 0.247009i | 0.663371 | − | 0.748291i | \(-0.269125\pi\) |
0.0968441 | + | 0.995300i | \(0.469125\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.33318 | − | 3.14824i | 0.138915 | − | 0.100928i | ||||
\(974\) | −28.4460 | + | 20.6672i | −0.911468 | + | 0.662220i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 28.4012 | + | 9.22811i | 0.909100 | + | 0.295384i | ||||
\(977\) | −4.40208 | + | 6.05894i | −0.140835 | + | 0.193843i | −0.873608 | − | 0.486631i | \(-0.838226\pi\) |
0.732773 | + | 0.680473i | \(0.238226\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 27.0197 | − | 14.7757i | 0.863554 | − | 0.472233i | ||||
\(980\) | − | 3.94338i | − | 0.125967i | ||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 8.92466 | − | 27.4673i | 0.284797 | − | 0.876516i | ||||
\(983\) | 5.06942 | − | 1.64715i | 0.161689 | − | 0.0525361i | −0.227054 | − | 0.973882i | \(-0.572909\pi\) |
0.388743 | + | 0.921346i | \(0.372909\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.72559 | − | 3.75145i | −0.0868445 | − | 0.119531i | ||||
\(986\) | 4.01722 | + | 12.3637i | 0.127934 | + | 0.393741i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −4.45481 | − | 3.23661i | −0.141726 | − | 0.102970i | ||||
\(989\) | 9.06669 | 0.288304 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −23.5423 | −0.747846 | −0.373923 | − | 0.927460i | \(-0.621988\pi\) | ||||
−0.373923 | + | 0.927460i | \(0.621988\pi\) | |||||||
\(992\) | 18.6112 | + | 13.5218i | 0.590905 | + | 0.429318i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 3.43298 | + | 10.5656i | 0.108887 | + | 0.335121i | ||||
\(995\) | 4.21522 | + | 5.80175i | 0.133631 | + | 0.183928i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −13.5097 | + | 4.38958i | −0.427857 | + | 0.139019i | −0.515026 | − | 0.857174i | \(-0.672218\pi\) |
0.0871692 | + | 0.996194i | \(0.472218\pi\) | |||||||
\(998\) | 1.76924 | − | 5.44517i | 0.0560044 | − | 0.172364i | ||||
\(999\) | 0 | 0 |
(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 | 891.2.k.a.161.7 | 80 | ||
3.2 | odd | 2 | inner | 891.2.k.a.161.14 | 80 | ||
9.2 | odd | 6 | 99.2.p.a.95.8 | yes | 80 | ||
9.4 | even | 3 | 99.2.p.a.29.8 | ✓ | 80 | ||
9.5 | odd | 6 | 297.2.t.a.62.3 | 80 | |||
9.7 | even | 3 | 297.2.t.a.260.3 | 80 | |||
11.8 | odd | 10 | inner | 891.2.k.a.404.14 | 80 | ||
33.8 | even | 10 | inner | 891.2.k.a.404.7 | 80 | ||
99.41 | even | 30 | 297.2.t.a.8.3 | 80 | |||
99.52 | odd | 30 | 297.2.t.a.206.3 | 80 | |||
99.74 | even | 30 | 99.2.p.a.41.8 | yes | 80 | ||
99.85 | odd | 30 | 99.2.p.a.74.8 | yes | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
99.2.p.a.29.8 | ✓ | 80 | 9.4 | even | 3 | ||
99.2.p.a.41.8 | yes | 80 | 99.74 | even | 30 | ||
99.2.p.a.74.8 | yes | 80 | 99.85 | odd | 30 | ||
99.2.p.a.95.8 | yes | 80 | 9.2 | odd | 6 | ||
297.2.t.a.8.3 | 80 | 99.41 | even | 30 | |||
297.2.t.a.62.3 | 80 | 9.5 | odd | 6 | |||
297.2.t.a.206.3 | 80 | 99.52 | odd | 30 | |||
297.2.t.a.260.3 | 80 | 9.7 | even | 3 | |||
891.2.k.a.161.7 | 80 | 1.1 | even | 1 | trivial | ||
891.2.k.a.161.14 | 80 | 3.2 | odd | 2 | inner | ||
891.2.k.a.404.7 | 80 | 33.8 | even | 10 | inner | ||
891.2.k.a.404.14 | 80 | 11.8 | odd | 10 | inner |