Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [784,2,Mod(165,784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(784, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 3, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("784.165");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.x (of order \(12\), degree \(4\), not 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: | \(6.26027151847\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 112) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 373.6 | ||
Character | \(\chi\) | \(=\) | 784.373 |
Dual form | 784.2.x.m.557.6 |
$q$-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 \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(687\) | \(689\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.16343 | − | 0.804007i | 0.822670 | − | 0.568519i | ||||
\(3\) | 1.90046 | + | 0.509227i | 1.09723 | + | 0.294002i | 0.761637 | − | 0.648004i | \(-0.224396\pi\) |
0.335595 | + | 0.942006i | \(0.391063\pi\) | |||||||
\(4\) | 0.707146 | − | 1.87081i | 0.353573 | − | 0.935407i | ||||
\(5\) | 2.95714 | − | 0.792364i | 1.32247 | − | 0.354356i | 0.472570 | − | 0.881293i | \(-0.343326\pi\) |
0.849904 | + | 0.526937i | \(0.176660\pi\) | |||||||
\(6\) | 2.62048 | − | 0.935533i | 1.06981 | − | 0.381930i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −0.681431 | − | 2.74511i | −0.240922 | − | 0.970544i | ||||
\(9\) | 0.754366 | + | 0.435533i | 0.251455 | + | 0.145178i | ||||
\(10\) | 2.80337 | − | 3.29942i | 0.886502 | − | 1.04337i | ||||
\(11\) | −1.13308 | + | 4.22870i | −0.341636 | + | 1.27500i | 0.554858 | + | 0.831945i | \(0.312773\pi\) |
−0.896493 | + | 0.443057i | \(0.853894\pi\) | |||||||
\(12\) | 2.29657 | − | 3.19531i | 0.662963 | − | 0.922407i | ||||
\(13\) | −1.75410 | + | 1.75410i | −0.486499 | + | 0.486499i | −0.907200 | − | 0.420701i | \(-0.861784\pi\) |
0.420701 | + | 0.907200i | \(0.361784\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 6.02343 | 1.55524 | ||||||||
\(16\) | −2.99989 | − | 2.64588i | −0.749972 | − | 0.661469i | ||||
\(17\) | −2.60235 | − | 4.50740i | −0.631163 | − | 1.09321i | −0.987314 | − | 0.158778i | \(-0.949245\pi\) |
0.356152 | − | 0.934428i | \(-0.384089\pi\) | |||||||
\(18\) | 1.22782 | − | 0.0998021i | 0.289401 | − | 0.0235236i | ||||
\(19\) | 0.311715 | + | 1.16333i | 0.0715122 | + | 0.266887i | 0.992420 | − | 0.122894i | \(-0.0392174\pi\) |
−0.920908 | + | 0.389781i | \(0.872551\pi\) | |||||||
\(20\) | 0.608766 | − | 6.09258i | 0.136124 | − | 1.36234i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.08165 | + | 5.83081i | 0.443809 | + | 1.24313i | ||||
\(23\) | 5.33038 | + | 3.07750i | 1.11146 | + | 0.641703i | 0.939208 | − | 0.343350i | \(-0.111562\pi\) |
0.172254 | + | 0.985053i | \(0.444895\pi\) | |||||||
\(24\) | 0.102853 | − | 5.56399i | 0.0209947 | − | 1.13574i | ||||
\(25\) | 3.78672 | − | 2.18626i | 0.757344 | − | 0.437253i | ||||
\(26\) | −0.630466 | + | 3.45108i | −0.123645 | + | 0.676812i | ||||
\(27\) | −2.96185 | − | 2.96185i | −0.570007 | − | 0.570007i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.24096 | + | 6.24096i | −1.15892 | + | 1.15892i | −0.174208 | + | 0.984709i | \(0.555736\pi\) |
−0.984709 | + | 0.174208i | \(0.944264\pi\) | |||||||
\(30\) | 7.00784 | − | 4.84288i | 1.27945 | − | 0.884184i | ||||
\(31\) | −1.39123 | − | 2.40969i | −0.249873 | − | 0.432793i | 0.713617 | − | 0.700536i | \(-0.247056\pi\) |
−0.963490 | + | 0.267743i | \(0.913722\pi\) | |||||||
\(32\) | −5.61747 | − | 0.666365i | −0.993038 | − | 0.117798i | ||||
\(33\) | −4.30674 | + | 7.45950i | −0.749708 | + | 1.29853i | ||||
\(34\) | −6.65164 | − | 3.15175i | −1.14075 | − | 0.540520i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.34825 | − | 1.10329i | 0.224708 | − | 0.183882i | ||||
\(37\) | −5.61713 | + | 1.50511i | −0.923450 | + | 0.247438i | −0.689060 | − | 0.724705i | \(-0.741976\pi\) |
−0.234391 | + | 0.972142i | \(0.575310\pi\) | |||||||
\(38\) | 1.29799 | + | 1.10284i | 0.210561 | + | 0.178904i | ||||
\(39\) | −4.22683 | + | 2.44036i | −0.676834 | + | 0.390770i | ||||
\(40\) | −4.19022 | − | 7.57775i | −0.662532 | − | 1.19815i | ||||
\(41\) | 6.32956i | 0.988511i | 0.869317 | + | 0.494255i | \(0.164559\pi\) | ||||
−0.869317 | + | 0.494255i | \(0.835441\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.05937 | + | 3.05937i | 0.466549 | + | 0.466549i | 0.900795 | − | 0.434245i | \(-0.142985\pi\) |
−0.434245 | + | 0.900795i | \(0.642985\pi\) | |||||||
\(44\) | 7.10987 | + | 5.11009i | 1.07185 | + | 0.770375i | ||||
\(45\) | 2.57587 | + | 0.690201i | 0.383988 | + | 0.102889i | ||||
\(46\) | 8.67586 | − | 0.705206i | 1.27919 | − | 0.103977i | ||||
\(47\) | 1.80192 | − | 3.12101i | 0.262836 | − | 0.455246i | −0.704158 | − | 0.710043i | \(-0.748675\pi\) |
0.966994 | + | 0.254797i | \(0.0820087\pi\) | |||||||
\(48\) | −4.35382 | − | 6.55601i | −0.628420 | − | 0.946279i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 2.64782 | − | 5.58812i | 0.374458 | − | 0.790279i | ||||
\(51\) | −2.65037 | − | 9.89133i | −0.371127 | − | 1.38506i | ||||
\(52\) | 2.04119 | + | 4.52199i | 0.283062 | + | 0.627087i | ||||
\(53\) | 1.93405 | − | 7.21798i | 0.265662 | − | 0.991466i | −0.696181 | − | 0.717866i | \(-0.745119\pi\) |
0.961844 | − | 0.273600i | \(-0.0882144\pi\) | |||||||
\(54\) | −5.82725 | − | 1.06456i | −0.792988 | − | 0.144868i | ||||
\(55\) | 13.4027i | 1.80722i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.36961i | 0.313862i | ||||||||
\(58\) | −2.24315 | + | 12.2787i | −0.294541 | + | 1.61227i | ||||
\(59\) | 2.61179 | − | 9.74734i | 0.340026 | − | 1.26900i | −0.558290 | − | 0.829646i | \(-0.688542\pi\) |
0.898316 | − | 0.439350i | \(-0.144791\pi\) | |||||||
\(60\) | 4.25944 | − | 11.2687i | 0.549892 | − | 1.45478i | ||||
\(61\) | −0.380638 | − | 1.42056i | −0.0487357 | − | 0.181884i | 0.937267 | − | 0.348611i | \(-0.113347\pi\) |
−0.986003 | + | 0.166727i | \(0.946680\pi\) | |||||||
\(62\) | −3.55601 | − | 1.68495i | −0.451614 | − | 0.213988i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.07130 | + | 3.74121i | −0.883913 | + | 0.467652i | ||||
\(65\) | −3.79723 | + | 6.57700i | −0.470988 | + | 0.815776i | ||||
\(66\) | 0.986887 | + | 12.1413i | 0.121477 | + | 1.49449i | ||||
\(67\) | 1.32053 | + | 0.353834i | 0.161328 | + | 0.0432277i | 0.338579 | − | 0.940938i | \(-0.390054\pi\) |
−0.177251 | + | 0.984166i | \(0.556720\pi\) | |||||||
\(68\) | −10.2728 | + | 1.68112i | −1.24575 | + | 0.203866i | ||||
\(69\) | 8.56304 | + | 8.56304i | 1.03087 | + | 1.03087i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.0597i | 1.19386i | 0.802291 | + | 0.596932i | \(0.203614\pi\) | ||||
−0.802291 | + | 0.596932i | \(0.796386\pi\) | |||||||
\(72\) | 0.681540 | − | 2.36761i | 0.0803203 | − | 0.279025i | ||||
\(73\) | 13.1391 | − | 7.58585i | 1.53781 | − | 0.887857i | 0.538847 | − | 0.842404i | \(-0.318860\pi\) |
0.998966 | − | 0.0454536i | \(-0.0144733\pi\) | |||||||
\(74\) | −5.32503 | + | 6.26730i | −0.619022 | + | 0.728559i | ||||
\(75\) | 8.30982 | − | 2.22661i | 0.959535 | − | 0.257107i | ||||
\(76\) | 2.39681 | + | 0.239487i | 0.274933 | + | 0.0274711i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −2.95556 | + | 6.23759i | −0.334651 | + | 0.706268i | ||||
\(79\) | 3.30674 | − | 5.72745i | 0.372038 | − | 0.644388i | −0.617841 | − | 0.786303i | \(-0.711993\pi\) |
0.989879 | + | 0.141915i | \(0.0453259\pi\) | |||||||
\(80\) | −10.9676 | − | 5.44723i | −1.22621 | − | 0.609019i | ||||
\(81\) | −5.42722 | − | 9.40022i | −0.603025 | − | 1.04447i | ||||
\(82\) | 5.08901 | + | 7.36400i | 0.561987 | + | 0.813218i | ||||
\(83\) | 7.41730 | − | 7.41730i | 0.814154 | − | 0.814154i | −0.171100 | − | 0.985254i | \(-0.554732\pi\) |
0.985254 | + | 0.171100i | \(0.0547320\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −11.2670 | − | 11.2670i | −1.22208 | − | 1.22208i | ||||
\(86\) | 6.01912 | + | 1.09961i | 0.649058 | + | 0.118574i | ||||
\(87\) | −15.0388 | + | 8.68264i | −1.61232 | + | 0.930876i | ||||
\(88\) | 12.3804 | + | 0.228856i | 1.31975 | + | 0.0243962i | ||||
\(89\) | −2.82449 | − | 1.63072i | −0.299396 | − | 0.172856i | 0.342776 | − | 0.939417i | \(-0.388633\pi\) |
−0.642171 | + | 0.766561i | \(0.721966\pi\) | |||||||
\(90\) | 3.55177 | − | 1.26801i | 0.374390 | − | 0.133660i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 9.52678 | − | 7.79591i | 0.993236 | − | 0.812780i | ||||
\(93\) | −1.41691 | − | 5.28798i | −0.146927 | − | 0.548337i | ||||
\(94\) | −0.412907 | − | 5.07983i | −0.0425881 | − | 0.523945i | ||||
\(95\) | 1.84357 | + | 3.19315i | 0.189146 | + | 0.327611i | ||||
\(96\) | −10.3365 | − | 4.12697i | −1.05496 | − | 0.421207i | ||||
\(97\) | 7.66352 | 0.778112 | 0.389056 | − | 0.921214i | \(-0.372801\pi\) | ||||
0.389056 | + | 0.921214i | \(0.372801\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.69650 | + | 2.69650i | −0.271008 | + | 0.271008i | ||||
\(100\) | −1.41233 | − | 8.63025i | −0.141233 | − | 0.863025i | ||||
\(101\) | −3.63555 | + | 13.5681i | −0.361751 | + | 1.35007i | 0.510021 | + | 0.860162i | \(0.329638\pi\) |
−0.871772 | + | 0.489912i | \(0.837029\pi\) | |||||||
\(102\) | −11.0362 | − | 9.37697i | −1.09275 | − | 0.928458i | ||||
\(103\) | 1.39602 | + | 0.805993i | 0.137554 | + | 0.0794169i | 0.567198 | − | 0.823582i | \(-0.308028\pi\) |
−0.429644 | + | 0.902998i | \(0.641361\pi\) | |||||||
\(104\) | 6.01049 | + | 3.61990i | 0.589377 | + | 0.354960i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.55317 | − | 9.95262i | −0.345114 | − | 0.966684i | ||||
\(107\) | −10.8240 | + | 2.90028i | −1.04640 | + | 0.280381i | −0.740762 | − | 0.671768i | \(-0.765535\pi\) |
−0.305634 | + | 0.952149i | \(0.598869\pi\) | |||||||
\(108\) | −7.63552 | + | 3.44660i | −0.734728 | + | 0.331650i | ||||
\(109\) | −7.77240 | − | 2.08261i | −0.744461 | − | 0.199478i | −0.133401 | − | 0.991062i | \(-0.542590\pi\) |
−0.611060 | + | 0.791584i | \(0.709257\pi\) | |||||||
\(110\) | 10.7759 | + | 15.5931i | 1.02744 | + | 1.48674i | ||||
\(111\) | −11.4416 | −1.08599 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 15.2609 | 1.43563 | 0.717813 | − | 0.696235i | \(-0.245143\pi\) | ||||
0.717813 | + | 0.696235i | \(0.245143\pi\) | |||||||
\(114\) | 1.90518 | + | 2.75688i | 0.178436 | + | 0.258205i | ||||
\(115\) | 18.2012 | + | 4.87699i | 1.69727 | + | 0.454782i | ||||
\(116\) | 7.26240 | + | 16.0889i | 0.674297 | + | 1.49382i | ||||
\(117\) | −2.08720 | + | 0.559263i | −0.192962 | + | 0.0517039i | ||||
\(118\) | −4.79829 | − | 13.4403i | −0.441718 | − | 1.23728i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −4.10455 | − | 16.5350i | −0.374693 | − | 1.50943i | ||||
\(121\) | −7.07180 | − | 4.08290i | −0.642891 | − | 0.371173i | ||||
\(122\) | −1.58499 | − | 1.34669i | −0.143498 | − | 0.121924i | ||||
\(123\) | −3.22318 | + | 12.0291i | −0.290624 | + | 1.08463i | ||||
\(124\) | −5.49188 | + | 0.898739i | −0.493186 | + | 0.0807092i | ||||
\(125\) | −1.35834 | + | 1.35834i | −0.121494 | + | 0.121494i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.80529 | −0.160193 | −0.0800966 | − | 0.996787i | \(-0.525523\pi\) | ||||
−0.0800966 | + | 0.996787i | \(0.525523\pi\) | |||||||
\(128\) | −5.21902 | + | 10.0380i | −0.461300 | + | 0.887244i | ||||
\(129\) | 4.25630 | + | 7.37213i | 0.374746 | + | 0.649080i | ||||
\(130\) | 0.870132 | + | 10.7049i | 0.0763157 | + | 0.938880i | ||||
\(131\) | −3.39881 | − | 12.6845i | −0.296956 | − | 1.10825i | −0.939652 | − | 0.342132i | \(-0.888851\pi\) |
0.642696 | − | 0.766121i | \(-0.277816\pi\) | |||||||
\(132\) | 10.9098 | + | 13.3321i | 0.949579 | + | 1.16041i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1.82083 | − | 0.650051i | 0.157296 | − | 0.0561559i | ||||
\(135\) | −11.1055 | − | 6.41174i | −0.955805 | − | 0.551835i | ||||
\(136\) | −10.6000 | + | 10.2152i | −0.908943 | + | 0.875949i | ||||
\(137\) | −6.87323 | + | 3.96826i | −0.587220 | + | 0.339031i | −0.763997 | − | 0.645219i | \(-0.776766\pi\) |
0.176778 | + | 0.984251i | \(0.443433\pi\) | |||||||
\(138\) | 16.8473 | + | 3.07777i | 1.43413 | + | 0.261997i | ||||
\(139\) | 2.06915 | + | 2.06915i | 0.175503 | + | 0.175503i | 0.789392 | − | 0.613889i | \(-0.210396\pi\) |
−0.613889 | + | 0.789392i | \(0.710396\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.01377 | − | 5.01377i | 0.422236 | − | 0.422236i | ||||
\(142\) | 8.08806 | + | 11.7038i | 0.678735 | + | 0.982157i | ||||
\(143\) | −5.43003 | − | 9.40509i | −0.454082 | − | 0.786493i | ||||
\(144\) | −1.11065 | − | 3.30251i | −0.0925539 | − | 0.275209i | ||||
\(145\) | −13.5103 | + | 23.4005i | −1.12197 | + | 1.94331i | ||||
\(146\) | 9.18735 | − | 19.3895i | 0.760350 | − | 1.60469i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.15636 | + | 11.5729i | −0.0950521 | + | 0.951289i | ||||
\(149\) | −12.5060 | + | 3.35096i | −1.02453 | + | 0.274521i | −0.731688 | − | 0.681640i | \(-0.761267\pi\) |
−0.292840 | + | 0.956161i | \(0.594600\pi\) | |||||||
\(150\) | 7.87770 | − | 9.27166i | 0.643211 | − | 0.757028i | ||||
\(151\) | −2.42743 | + | 1.40148i | −0.197541 | + | 0.114051i | −0.595508 | − | 0.803349i | \(-0.703049\pi\) |
0.397967 | + | 0.917400i | \(0.369716\pi\) | |||||||
\(152\) | 2.98107 | − | 1.64842i | 0.241797 | − | 0.133705i | ||||
\(153\) | − | 4.53364i | − | 0.366523i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.02343 | − | 6.02343i | −0.483813 | − | 0.483813i | ||||
\(156\) | 1.57648 | + | 9.63330i | 0.126219 | + | 0.771281i | ||||
\(157\) | 1.30974 | + | 0.350944i | 0.104529 | + | 0.0280084i | 0.310704 | − | 0.950507i | \(-0.399435\pi\) |
−0.206176 | + | 0.978515i | \(0.566102\pi\) | |||||||
\(158\) | −0.757737 | − | 9.32213i | −0.0602823 | − | 0.741629i | ||||
\(159\) | 7.35118 | − | 12.7326i | 0.582987 | − | 1.00976i | ||||
\(160\) | −17.1397 | + | 2.48054i | −1.35501 | + | 0.196104i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −13.8720 | − | 6.57299i | −1.08989 | − | 0.516423i | ||||
\(163\) | 4.72925 | + | 17.6498i | 0.370423 | + | 1.38244i | 0.859918 | + | 0.510432i | \(0.170515\pi\) |
−0.489495 | + | 0.872006i | \(0.662819\pi\) | |||||||
\(164\) | 11.8414 | + | 4.47592i | 0.924660 | + | 0.349511i | ||||
\(165\) | −6.82501 | + | 25.4713i | −0.531326 | + | 1.98294i | ||||
\(166\) | 2.66596 | − | 14.5931i | 0.206919 | − | 1.13264i | ||||
\(167\) | − | 1.96111i | − | 0.151755i | −0.997117 | − | 0.0758775i | \(-0.975824\pi\) | ||
0.997117 | − | 0.0758775i | \(-0.0241758\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.84629i | 0.526637i | ||||||||
\(170\) | −22.1672 | − | 4.04964i | −1.70014 | − | 0.310594i | ||||
\(171\) | −0.271524 | + | 1.01334i | −0.0207640 | + | 0.0774922i | ||||
\(172\) | 7.88693 | − | 3.56009i | 0.601373 | − | 0.271454i | ||||
\(173\) | 1.51549 | + | 5.65589i | 0.115221 | + | 0.430009i | 0.999303 | − | 0.0373213i | \(-0.0118825\pi\) |
−0.884083 | + | 0.467330i | \(0.845216\pi\) | |||||||
\(174\) | −10.5157 | + | 22.1929i | −0.797191 | + | 1.68244i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 14.5877 | − | 9.68766i | 1.09959 | − | 0.730235i | ||||
\(177\) | 9.92722 | − | 17.1945i | 0.746176 | − | 1.29241i | ||||
\(178\) | −4.59722 | + | 0.373679i | −0.344576 | + | 0.0280084i | ||||
\(179\) | 12.9980 | + | 3.48281i | 0.971519 | + | 0.260318i | 0.709469 | − | 0.704737i | \(-0.248935\pi\) |
0.262050 | + | 0.965054i | \(0.415602\pi\) | |||||||
\(180\) | 3.11275 | − | 4.33089i | 0.232011 | − | 0.322806i | ||||
\(181\) | −7.60424 | − | 7.60424i | −0.565219 | − | 0.565219i | 0.365566 | − | 0.930785i | \(-0.380875\pi\) |
−0.930785 | + | 0.365566i | \(0.880875\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 2.89355i | − | 0.213897i | ||||||
\(184\) | 4.81579 | − | 16.7296i | 0.355025 | − | 1.23332i | ||||
\(185\) | −15.4181 | + | 8.90162i | −1.13356 | + | 0.654460i | ||||
\(186\) | −5.90004 | − | 5.01299i | −0.432612 | − | 0.367570i | ||||
\(187\) | 22.0091 | − | 5.89733i | 1.60947 | − | 0.431256i | ||||
\(188\) | −4.56461 | − | 5.57806i | −0.332908 | − | 0.406822i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.71218 | + | 2.23277i | 0.341858 | + | 0.161982i | ||||
\(191\) | 10.2439 | − | 17.7430i | 0.741223 | − | 1.28384i | −0.210715 | − | 0.977547i | \(-0.567579\pi\) |
0.951939 | − | 0.306289i | \(-0.0990873\pi\) | |||||||
\(192\) | −15.3439 | + | 3.50913i | −1.10735 | + | 0.253250i | ||||
\(193\) | −6.35776 | − | 11.0120i | −0.457642 | − | 0.792659i | 0.541194 | − | 0.840898i | \(-0.317972\pi\) |
−0.998836 | + | 0.0482388i | \(0.984639\pi\) | |||||||
\(194\) | 8.91598 | − | 6.16152i | 0.640130 | − | 0.442371i | ||||
\(195\) | −10.5657 | + | 10.5657i | −0.756624 | + | 0.756624i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −12.8638 | − | 12.8638i | −0.916509 | − | 0.916509i | 0.0802649 | − | 0.996774i | \(-0.474423\pi\) |
−0.996774 | + | 0.0802649i | \(0.974423\pi\) | |||||||
\(198\) | −0.969187 | + | 5.30519i | −0.0688771 | + | 0.377023i | ||||
\(199\) | −1.27174 | + | 0.734237i | −0.0901510 | + | 0.0520487i | −0.544398 | − | 0.838827i | \(-0.683242\pi\) |
0.454247 | + | 0.890876i | \(0.349908\pi\) | |||||||
\(200\) | −8.58193 | − | 8.90519i | −0.606834 | − | 0.629692i | ||||
\(201\) | 2.32943 | + | 1.34490i | 0.164305 | + | 0.0948617i | ||||
\(202\) | 6.67911 | + | 18.7085i | 0.469940 | + | 1.31633i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −20.3790 | − | 2.03626i | −1.42682 | − | 0.142567i | ||||
\(205\) | 5.01531 | + | 18.7174i | 0.350284 | + | 1.30728i | ||||
\(206\) | 2.27220 | − | 0.184693i | 0.158312 | − | 0.0128681i | ||||
\(207\) | 2.68070 | + | 4.64312i | 0.186322 | + | 0.322719i | ||||
\(208\) | 9.90322 | − | 0.620972i | 0.686665 | − | 0.0430567i | ||||
\(209\) | −5.27260 | −0.364713 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.534767 | − | 0.534767i | 0.0368149 | − | 0.0368149i | −0.688460 | − | 0.725275i | \(-0.741713\pi\) |
0.725275 | + | 0.688460i | \(0.241713\pi\) | |||||||
\(212\) | −12.1358 | − | 8.72242i | −0.833493 | − | 0.599058i | ||||
\(213\) | −5.12266 | + | 19.1180i | −0.350999 | + | 1.30995i | ||||
\(214\) | −10.2611 | + | 12.0769i | −0.701437 | + | 0.825557i | ||||
\(215\) | 11.4711 | + | 6.62285i | 0.782324 | + | 0.451675i | ||||
\(216\) | −6.11231 | + | 10.1489i | −0.415890 | + | 0.690545i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −10.7171 | + | 3.82609i | −0.725853 | + | 0.259136i | ||||
\(219\) | 28.8333 | − | 7.72585i | 1.94837 | − | 0.522064i | ||||
\(220\) | 25.0739 | + | 9.47766i | 1.69048 | + | 0.638983i | ||||
\(221\) | 12.4712 | + | 3.34165i | 0.838903 | + | 0.224784i | ||||
\(222\) | −13.3115 | + | 9.19911i | −0.893409 | + | 0.617404i | ||||
\(223\) | 7.83775 | 0.524855 | 0.262427 | − | 0.964952i | \(-0.415477\pi\) | ||||
0.262427 | + | 0.964952i | \(0.415477\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.80876 | 0.253917 | ||||||||
\(226\) | 17.7550 | − | 12.2699i | 1.18105 | − | 0.816181i | ||||
\(227\) | 0.338192 | + | 0.0906182i | 0.0224466 | + | 0.00601454i | 0.270025 | − | 0.962853i | \(-0.412968\pi\) |
−0.247578 | + | 0.968868i | \(0.579635\pi\) | |||||||
\(228\) | 4.43309 | + | 1.67566i | 0.293589 | + | 0.110973i | ||||
\(229\) | −21.3140 | + | 5.71108i | −1.40847 | + | 0.377399i | −0.881379 | − | 0.472409i | \(-0.843384\pi\) |
−0.527092 | + | 0.849808i | \(0.676718\pi\) | |||||||
\(230\) | 25.0970 | − | 8.95983i | 1.65485 | − | 0.590794i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 21.3849 | + | 12.8794i | 1.40399 | + | 0.845571i | ||||
\(233\) | 8.24017 | + | 4.75746i | 0.539831 | + | 0.311672i | 0.745011 | − | 0.667053i | \(-0.232444\pi\) |
−0.205179 | + | 0.978724i | \(0.565778\pi\) | |||||||
\(234\) | −1.97866 | + | 2.32879i | −0.129349 | + | 0.152238i | ||||
\(235\) | 2.85554 | − | 10.6570i | 0.186275 | − | 0.695188i | ||||
\(236\) | −16.3885 | − | 11.7790i | −1.06680 | − | 0.766746i | ||||
\(237\) | 9.20091 | − | 9.20091i | 0.597663 | − | 0.597663i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.8469 | 1.21910 | 0.609552 | − | 0.792746i | \(-0.291349\pi\) | ||||
0.609552 | + | 0.792746i | \(0.291349\pi\) | |||||||
\(240\) | −18.0696 | − | 15.9372i | −1.16639 | − | 1.02874i | ||||
\(241\) | −3.19914 | − | 5.54108i | −0.206075 | − | 0.356932i | 0.744400 | − | 0.667734i | \(-0.232736\pi\) |
−0.950475 | + | 0.310802i | \(0.899402\pi\) | |||||||
\(242\) | −11.5102 | + | 0.935594i | −0.739906 | + | 0.0601423i | ||||
\(243\) | −2.27504 | − | 8.49058i | −0.145944 | − | 0.544671i | ||||
\(244\) | −2.92677 | − | 0.292441i | −0.187367 | − | 0.0187216i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 5.92151 | + | 16.5865i | 0.377542 | + | 1.05751i | ||||
\(247\) | −2.58738 | − | 1.49382i | −0.164631 | − | 0.0950498i | ||||
\(248\) | −5.66684 | + | 5.46113i | −0.359845 | + | 0.346782i | ||||
\(249\) | 17.8734 | − | 10.3192i | 1.13268 | − | 0.653953i | ||||
\(250\) | −0.488221 | + | 2.67245i | −0.0308778 | + | 0.169021i | ||||
\(251\) | 2.93159 | + | 2.93159i | 0.185040 | + | 0.185040i | 0.793548 | − | 0.608508i | \(-0.208232\pi\) |
−0.608508 | + | 0.793548i | \(0.708232\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −19.0536 | + | 19.0536i | −1.19789 | + | 1.19789i | ||||
\(254\) | −2.10033 | + | 1.45146i | −0.131786 | + | 0.0910728i | ||||
\(255\) | −15.6751 | − | 27.1500i | −0.981611 | − | 1.70020i | ||||
\(256\) | 1.99867 | + | 15.8747i | 0.124917 | + | 0.992167i | ||||
\(257\) | 14.4838 | − | 25.0867i | 0.903475 | − | 1.56487i | 0.0805246 | − | 0.996753i | \(-0.474340\pi\) |
0.822951 | − | 0.568113i | \(-0.192326\pi\) | |||||||
\(258\) | 10.8792 | + | 5.15487i | 0.677306 | + | 0.320928i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 9.61914 | + | 11.7548i | 0.596554 | + | 0.729002i | ||||
\(261\) | −7.42611 | + | 1.98982i | −0.459665 | + | 0.123167i | ||||
\(262\) | −14.1527 | − | 12.0249i | −0.874359 | − | 0.742902i | ||||
\(263\) | −0.298299 | + | 0.172223i | −0.0183939 | + | 0.0106197i | −0.509169 | − | 0.860667i | \(-0.670047\pi\) |
0.490775 | + | 0.871286i | \(0.336714\pi\) | |||||||
\(264\) | 23.4119 | + | 6.73936i | 1.44090 | + | 0.414779i | ||||
\(265\) | − | 22.8771i | − | 1.40533i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.53743 | − | 4.53743i | −0.277686 | − | 0.277686i | ||||
\(268\) | 1.59576 | − | 2.22025i | 0.0974768 | − | 0.135623i | ||||
\(269\) | −13.4946 | − | 3.61587i | −0.822781 | − | 0.220463i | −0.177219 | − | 0.984171i | \(-0.556710\pi\) |
−0.645562 | + | 0.763708i | \(0.723377\pi\) | |||||||
\(270\) | −18.0755 | + | 1.46924i | −1.10004 | + | 0.0894154i | ||||
\(271\) | −6.24843 | + | 10.8226i | −0.379565 | + | 0.657426i | −0.990999 | − | 0.133869i | \(-0.957260\pi\) |
0.611434 | + | 0.791296i | \(0.290593\pi\) | |||||||
\(272\) | −4.11927 | + | 20.4072i | −0.249767 | + | 1.23737i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.80602 | + | 10.1429i | −0.290342 | + | 0.612756i | ||||
\(275\) | 4.95441 | + | 18.4901i | 0.298762 | + | 1.11500i | ||||
\(276\) | 22.0752 | − | 9.96454i | 1.32877 | − | 0.599795i | ||||
\(277\) | −2.19595 | + | 8.19541i | −0.131942 | + | 0.492415i | −0.999992 | − | 0.00406280i | \(-0.998707\pi\) |
0.868050 | + | 0.496477i | \(0.165373\pi\) | |||||||
\(278\) | 4.07093 | + | 0.743704i | 0.244158 | + | 0.0446044i | ||||
\(279\) | − | 2.42372i | − | 0.145104i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.56494i | 0.570596i | 0.958439 | + | 0.285298i | \(0.0920926\pi\) | ||||
−0.958439 | + | 0.285298i | \(0.907907\pi\) | |||||||
\(282\) | 1.80207 | − | 9.86429i | 0.107312 | − | 0.587410i | ||||
\(283\) | −4.27803 | + | 15.9658i | −0.254303 | + | 0.949070i | 0.714175 | + | 0.699968i | \(0.246802\pi\) |
−0.968477 | + | 0.249102i | \(0.919864\pi\) | |||||||
\(284\) | 18.8198 | + | 7.11367i | 1.11675 | + | 0.422118i | ||||
\(285\) | 1.87759 | + | 7.00726i | 0.111219 | + | 0.415074i | ||||
\(286\) | −13.8792 | − | 6.57639i | −0.820696 | − | 0.388870i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −3.94740 | − | 2.94928i | −0.232603 | − | 0.173788i | ||||
\(289\) | −5.04445 | + | 8.73725i | −0.296732 | + | 0.513956i | ||||
\(290\) | 3.09587 | + | 38.0873i | 0.181796 | + | 2.23656i | ||||
\(291\) | 14.5642 | + | 3.90247i | 0.853769 | + | 0.228767i | ||||
\(292\) | −4.90047 | − | 29.9451i | −0.286778 | − | 1.75240i | ||||
\(293\) | 15.2913 | + | 15.2913i | 0.893328 | + | 0.893328i | 0.994835 | − | 0.101507i | \(-0.0323664\pi\) |
−0.101507 | + | 0.994835i | \(0.532366\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 30.8938i | − | 1.79870i | ||||||
\(296\) | 7.95937 | + | 14.3940i | 0.462629 | + | 0.836636i | ||||
\(297\) | 15.8808 | − | 9.16877i | 0.921496 | − | 0.532026i | ||||
\(298\) | −11.8556 | + | 13.9535i | −0.686778 | + | 0.808304i | ||||
\(299\) | −14.7482 | + | 3.95178i | −0.852913 | + | 0.228537i | ||||
\(300\) | 1.71068 | − | 17.1207i | 0.0987663 | − | 0.988462i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −1.69735 | + | 3.58219i | −0.0976716 | + | 0.206132i | ||||
\(303\) | −13.8185 | + | 23.9343i | −0.793850 | + | 1.37499i | ||||
\(304\) | 2.14293 | − | 4.31463i | 0.122906 | − | 0.247461i | ||||
\(305\) | −2.25120 | − | 3.89919i | −0.128903 | − | 0.223267i | ||||
\(306\) | −3.64508 | − | 5.27458i | −0.208375 | − | 0.301528i | ||||
\(307\) | 4.16259 | − | 4.16259i | 0.237571 | − | 0.237571i | −0.578272 | − | 0.815844i | \(-0.696273\pi\) |
0.815844 | + | 0.578272i | \(0.196273\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.24265 | + | 2.24265i | 0.127580 | + | 0.127580i | ||||
\(310\) | −11.8507 | − | 2.16497i | −0.673076 | − | 0.122962i | ||||
\(311\) | 0.695092 | − | 0.401312i | 0.0394151 | − | 0.0227563i | −0.480163 | − | 0.877179i | \(-0.659422\pi\) |
0.519578 | + | 0.854423i | \(0.326089\pi\) | |||||||
\(312\) | 9.57936 | + | 9.94019i | 0.542325 | + | 0.562752i | ||||
\(313\) | −15.3533 | − | 8.86423i | −0.867819 | − | 0.501036i | −0.00119626 | − | 0.999999i | \(-0.500381\pi\) |
−0.866623 | + | 0.498964i | \(0.833714\pi\) | |||||||
\(314\) | 1.80596 | − | 0.644742i | 0.101916 | − | 0.0363849i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.37664 | − | 10.2364i | −0.471223 | − | 0.575845i | ||||
\(317\) | 3.79534 | + | 14.1644i | 0.213168 | + | 0.795552i | 0.986804 | + | 0.161922i | \(0.0517693\pi\) |
−0.773636 | + | 0.633630i | \(0.781564\pi\) | |||||||
\(318\) | −1.68452 | − | 20.7239i | −0.0944631 | − | 1.16214i | ||||
\(319\) | −19.3197 | − | 33.4627i | −1.08169 | − | 1.87355i | ||||
\(320\) | −17.9464 | + | 16.6663i | −1.00324 | + | 0.931677i | ||||
\(321\) | −22.0475 | −1.23057 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.43243 | − | 4.43243i | 0.246627 | − | 0.246627i | ||||
\(324\) | −21.4239 | + | 3.50599i | −1.19022 | + | 0.194777i | ||||
\(325\) | −2.80735 | + | 10.4772i | −0.155724 | + | 0.581170i | ||||
\(326\) | 19.6927 | + | 16.7320i | 1.09068 | + | 0.926699i | ||||
\(327\) | −13.7106 | − | 7.91584i | −0.758200 | − | 0.437747i | ||||
\(328\) | 17.3754 | − | 4.31316i | 0.959393 | − | 0.238154i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 12.5387 | + | 35.1215i | 0.690230 | + | 1.93337i | ||||
\(331\) | 0.304708 | − | 0.0816464i | 0.0167483 | − | 0.00448769i | −0.250435 | − | 0.968133i | \(-0.580574\pi\) |
0.267183 | + | 0.963646i | \(0.413907\pi\) | |||||||
\(332\) | −8.63127 | − | 19.1215i | −0.473702 | − | 1.04943i | ||||
\(333\) | −4.89289 | − | 1.31105i | −0.268129 | − | 0.0718449i | ||||
\(334\) | −1.57674 | − | 2.28161i | −0.0862756 | − | 0.124844i | ||||
\(335\) | 4.18535 | 0.228670 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −26.7633 | −1.45789 | −0.728944 | − | 0.684573i | \(-0.759989\pi\) | ||||
−0.728944 | + | 0.684573i | \(0.759989\pi\) | |||||||
\(338\) | 5.50446 | + | 7.96519i | 0.299403 | + | 0.433249i | ||||
\(339\) | 29.0028 | + | 7.77128i | 1.57522 | + | 0.422078i | ||||
\(340\) | −29.0459 | + | 13.1111i | −1.57524 | + | 0.711048i | ||||
\(341\) | 11.7662 | − | 3.15275i | 0.637178 | − | 0.170731i | ||||
\(342\) | 0.498834 | + | 1.39726i | 0.0269739 | + | 0.0755552i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 6.31357 | − | 10.4831i | 0.340405 | − | 0.565209i | ||||
\(345\) | 32.1072 | + | 18.5371i | 1.72859 | + | 0.998003i | ||||
\(346\) | 6.31054 | + | 5.36177i | 0.339257 | + | 0.288251i | ||||
\(347\) | 9.00704 | − | 33.6147i | 0.483523 | − | 1.80453i | −0.103098 | − | 0.994671i | \(-0.532876\pi\) |
0.586621 | − | 0.809861i | \(-0.300458\pi\) | |||||||
\(348\) | 5.60899 | + | 34.2746i | 0.300674 | + | 1.83731i | ||||
\(349\) | −13.7818 | + | 13.7818i | −0.737725 | + | 0.737725i | −0.972137 | − | 0.234412i | \(-0.924683\pi\) |
0.234412 | + | 0.972137i | \(0.424683\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 10.3907 | 0.554616 | ||||||||
\(352\) | 9.18289 | − | 22.9996i | 0.489450 | − | 1.22588i | ||||
\(353\) | −13.0221 | − | 22.5550i | −0.693099 | − | 1.20048i | −0.970817 | − | 0.239820i | \(-0.922912\pi\) |
0.277718 | − | 0.960663i | \(-0.410422\pi\) | |||||||
\(354\) | −2.27481 | − | 27.9861i | −0.120905 | − | 1.48745i | ||||
\(355\) | 7.97093 | + | 29.7479i | 0.423053 | + | 1.57886i | ||||
\(356\) | −5.04811 | + | 4.13094i | −0.267549 | + | 0.218940i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 17.9225 | − | 6.39850i | 0.947235 | − | 0.338171i | ||||
\(359\) | −18.2196 | − | 10.5191i | −0.961593 | − | 0.555176i | −0.0649297 | − | 0.997890i | \(-0.520682\pi\) |
−0.896663 | + | 0.442714i | \(0.854016\pi\) | |||||||
\(360\) | 0.139405 | − | 7.54137i | 0.00734730 | − | 0.397465i | ||||
\(361\) | 15.1983 | − | 8.77474i | 0.799911 | − | 0.461829i | ||||
\(362\) | −14.9609 | − | 2.73315i | −0.786326 | − | 0.143651i | ||||
\(363\) | −11.3606 | − | 11.3606i | −0.596274 | − | 0.596274i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 32.8434 | − | 32.8434i | 1.71910 | − | 1.71910i | ||||
\(366\) | −2.32644 | − | 3.36645i | −0.121605 | − | 0.175967i | ||||
\(367\) | 3.70670 | + | 6.42020i | 0.193488 | + | 0.335132i | 0.946404 | − | 0.322986i | \(-0.104687\pi\) |
−0.752916 | + | 0.658117i | \(0.771353\pi\) | |||||||
\(368\) | −7.84788 | − | 23.3357i | −0.409099 | − | 1.21646i | ||||
\(369\) | −2.75673 | + | 4.77480i | −0.143510 | + | 0.248566i | ||||
\(370\) | −10.7809 | + | 22.7526i | −0.560472 | + | 1.18285i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −10.8948 | − | 1.08860i | −0.564868 | − | 0.0564412i | ||||
\(373\) | −5.12662 | + | 1.37367i | −0.265446 | + | 0.0711261i | −0.389087 | − | 0.921201i | \(-0.627210\pi\) |
0.123641 | + | 0.992327i | \(0.460543\pi\) | |||||||
\(374\) | 20.8646 | − | 24.5566i | 1.07888 | − | 1.26979i | ||||
\(375\) | −3.27318 | + | 1.88977i | −0.169026 | + | 0.0975873i | ||||
\(376\) | −9.79541 | − | 2.81971i | −0.505160 | − | 0.145415i | ||||
\(377\) | − | 21.8945i | − | 1.12762i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.8387 | + | 18.8387i | 0.967677 | + | 0.967677i | 0.999494 | − | 0.0318167i | \(-0.0101293\pi\) |
−0.0318167 | + | 0.999494i | \(0.510129\pi\) | |||||||
\(380\) | 7.27747 | − | 1.19095i | 0.373326 | − | 0.0610943i | ||||
\(381\) | −3.43087 | − | 0.919300i | −0.175769 | − | 0.0470972i | ||||
\(382\) | −2.34738 | − | 28.8789i | −0.120103 | − | 1.47757i | ||||
\(383\) | −2.47310 | + | 4.28353i | −0.126369 | + | 0.218878i | −0.922267 | − | 0.386553i | \(-0.873666\pi\) |
0.795898 | + | 0.605431i | \(0.206999\pi\) | |||||||
\(384\) | −15.0302 | + | 16.4192i | −0.767005 | + | 0.837889i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −16.2505 | − | 7.69999i | −0.827130 | − | 0.391919i | ||||
\(387\) | 0.975426 | + | 3.64034i | 0.0495837 | + | 0.185049i | ||||
\(388\) | 5.41922 | − | 14.3370i | 0.275119 | − | 0.727851i | ||||
\(389\) | 5.13412 | − | 19.1608i | 0.260310 | − | 0.971491i | −0.704748 | − | 0.709457i | \(-0.748940\pi\) |
0.965059 | − | 0.262034i | \(-0.0843932\pi\) | |||||||
\(390\) | −3.79756 | + | 20.7873i | −0.192297 | + | 1.05261i | ||||
\(391\) | − | 32.0349i | − | 1.62007i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 25.8372i | − | 1.30332i | ||||||
\(394\) | −25.3088 | − | 4.62357i | −1.27504 | − | 0.232932i | ||||
\(395\) | 5.24028 | − | 19.5570i | 0.263667 | − | 0.984020i | ||||
\(396\) | 3.13783 | + | 6.95146i | 0.157682 | + | 0.349324i | ||||
\(397\) | 0.0233859 | + | 0.0872772i | 0.00117370 | + | 0.00438032i | 0.966510 | − | 0.256628i | \(-0.0826116\pi\) |
−0.965336 | + | 0.261009i | \(0.915945\pi\) | |||||||
\(398\) | −0.889246 | + | 1.87672i | −0.0445739 | + | 0.0940714i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −17.1443 | − | 3.46064i | −0.857216 | − | 0.173032i | ||||
\(401\) | 12.7052 | − | 22.0060i | 0.634466 | − | 1.09893i | −0.352162 | − | 0.935939i | \(-0.614553\pi\) |
0.986628 | − | 0.162988i | \(-0.0521133\pi\) | |||||||
\(402\) | 3.79144 | − | 0.308182i | 0.189100 | − | 0.0153707i | ||||
\(403\) | 6.66719 | + | 1.78647i | 0.332116 | + | 0.0889903i | ||||
\(404\) | 22.8125 | + | 16.3961i | 1.13496 | + | 0.815734i | ||||
\(405\) | −23.4975 | − | 23.4975i | −1.16760 | − | 1.16760i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 25.4586i | − | 1.26194i | ||||||
\(408\) | −25.3468 | + | 14.0158i | −1.25485 | + | 0.693888i | ||||
\(409\) | 19.4037 | − | 11.2027i | 0.959450 | − | 0.553939i | 0.0634462 | − | 0.997985i | \(-0.479791\pi\) |
0.896004 | + | 0.444047i | \(0.146458\pi\) | |||||||
\(410\) | 20.8839 | + | 17.7441i | 1.03138 | + | 0.876317i | ||||
\(411\) | −15.0831 | + | 4.04149i | −0.743992 | + | 0.199352i | ||||
\(412\) | 2.49505 | − | 2.04174i | 0.122922 | − | 0.100589i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 6.85191 | + | 3.24664i | 0.336753 | + | 0.159564i | ||||
\(415\) | 16.0568 | − | 27.8112i | 0.788197 | − | 1.36520i | ||||
\(416\) | 11.0225 | − | 8.68472i | 0.540420 | − | 0.425803i | ||||
\(417\) | 2.87867 | + | 4.98601i | 0.140969 | + | 0.244166i | ||||
\(418\) | −6.13430 | + | 4.23920i | −0.300039 | + | 0.207346i | ||||
\(419\) | 24.2758 | − | 24.2758i | 1.18595 | − | 1.18595i | 0.207775 | − | 0.978177i | \(-0.433378\pi\) |
0.978177 | − | 0.207775i | \(-0.0666220\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.0270 | + | 16.0270i | 0.781108 | + | 0.781108i | 0.980018 | − | 0.198910i | \(-0.0637400\pi\) |
−0.198910 | + | 0.980018i | \(0.563740\pi\) | |||||||
\(422\) | 0.192208 | − | 1.05212i | 0.00935656 | − | 0.0512164i | ||||
\(423\) | 2.71861 | − | 1.56959i | 0.132183 | − | 0.0763160i | ||||
\(424\) | −21.1321 | − | 0.390635i | −1.02627 | − | 0.0189709i | ||||
\(425\) | −19.7087 | − | 11.3788i | −0.956014 | − | 0.551955i | ||||
\(426\) | 9.41117 | + | 26.3612i | 0.455973 | + | 1.27720i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −2.22826 | + | 22.3006i | −0.107707 | + | 1.07794i | ||||
\(429\) | −5.53024 | − | 20.6391i | −0.267002 | − | 0.996466i | ||||
\(430\) | 18.6707 | − | 1.51762i | 0.900380 | − | 0.0731862i | ||||
\(431\) | 15.8307 | + | 27.4196i | 0.762540 | + | 1.32076i | 0.941538 | + | 0.336908i | \(0.109381\pi\) |
−0.178998 | + | 0.983849i | \(0.557285\pi\) | |||||||
\(432\) | 1.04853 | + | 16.7219i | 0.0504474 | + | 0.804532i | ||||
\(433\) | 11.6823 | 0.561413 | 0.280707 | − | 0.959794i | \(-0.409431\pi\) | ||||
0.280707 | + | 0.959794i | \(0.409431\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −37.5920 | + | 37.5920i | −1.80240 | + | 1.80240i | ||||
\(436\) | −9.39240 | + | 13.0680i | −0.449814 | + | 0.625844i | ||||
\(437\) | −1.91860 | + | 7.16032i | −0.0917792 | + | 0.342525i | ||||
\(438\) | 27.3339 | − | 32.1706i | 1.30606 | − | 1.53717i | ||||
\(439\) | 11.3637 | + | 6.56086i | 0.542362 | + | 0.313133i | 0.746036 | − | 0.665906i | \(-0.231955\pi\) |
−0.203674 | + | 0.979039i | \(0.565288\pi\) | |||||||
\(440\) | 36.7919 | − | 9.13301i | 1.75399 | − | 0.435399i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 17.1961 | − | 6.13915i | 0.817935 | − | 0.292010i | ||||
\(443\) | 22.1569 | − | 5.93692i | 1.05271 | − | 0.282071i | 0.309336 | − | 0.950953i | \(-0.399893\pi\) |
0.743369 | + | 0.668881i | \(0.233227\pi\) | |||||||
\(444\) | −8.09087 | + | 21.4051i | −0.383976 | + | 1.01584i | ||||
\(445\) | −9.64455 | − | 2.58425i | −0.457196 | − | 0.122505i | ||||
\(446\) | 9.11869 | − | 6.30160i | 0.431782 | − | 0.298390i | ||||
\(447\) | −25.4735 | −1.20485 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −15.6396 | −0.738077 | −0.369038 | − | 0.929414i | \(-0.620313\pi\) | ||||
−0.369038 | + | 0.929414i | \(0.620313\pi\) | |||||||
\(450\) | 4.43123 | − | 3.06227i | 0.208890 | − | 0.144357i | ||||
\(451\) | −26.7658 | − | 7.17188i | −1.26035 | − | 0.337711i | ||||
\(452\) | 10.7917 | − | 28.5503i | 0.507599 | − | 1.34290i | ||||
\(453\) | −5.32691 | + | 1.42734i | −0.250280 | + | 0.0670623i | ||||
\(454\) | 0.466321 | − | 0.166480i | 0.0218855 | − | 0.00781331i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6.50484 | − | 1.61472i | 0.304617 | − | 0.0756164i | ||||
\(457\) | −10.5919 | − | 6.11523i | −0.495468 | − | 0.286058i | 0.231372 | − | 0.972865i | \(-0.425678\pi\) |
−0.726840 | + | 0.686807i | \(0.759012\pi\) | |||||||
\(458\) | −20.2057 | + | 23.7811i | −0.944150 | + | 1.11122i | ||||
\(459\) | −5.64247 | + | 21.0580i | −0.263368 | + | 0.982903i | ||||
\(460\) | 21.9948 | − | 30.6023i | 1.02552 | − | 1.42684i | ||||
\(461\) | 13.4658 | − | 13.4658i | 0.627163 | − | 0.627163i | −0.320191 | − | 0.947353i | \(-0.603747\pi\) |
0.947353 | + | 0.320191i | \(0.103747\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −24.7807 | −1.15166 | −0.575829 | − | 0.817570i | \(-0.695321\pi\) | ||||
−0.575829 | + | 0.817570i | \(0.695321\pi\) | |||||||
\(464\) | 35.2350 | − | 2.20938i | 1.63574 | − | 0.102568i | ||||
\(465\) | −8.38000 | − | 14.5146i | −0.388613 | − | 0.673098i | ||||
\(466\) | 13.4119 | − | 1.09017i | 0.621295 | − | 0.0505011i | ||||
\(467\) | −8.48020 | − | 31.6485i | −0.392417 | − | 1.46452i | −0.826135 | − | 0.563472i | \(-0.809465\pi\) |
0.433718 | − | 0.901048i | \(-0.357201\pi\) | |||||||
\(468\) | −0.429677 | + | 4.30024i | −0.0198618 | + | 0.198779i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −5.24610 | − | 14.6946i | −0.241985 | − | 0.677812i | ||||
\(471\) | 2.31040 | + | 1.33391i | 0.106458 | + | 0.0614634i | ||||
\(472\) | −28.5373 | − | 0.527524i | −1.31354 | − | 0.0242812i | ||||
\(473\) | −16.4037 | + | 9.47066i | −0.754242 | + | 0.435462i | ||||
\(474\) | 3.30703 | − | 18.1022i | 0.151897 | − | 0.831462i | ||||
\(475\) | 3.72373 | + | 3.72373i | 0.170857 | + | 0.170857i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.60265 | − | 4.60265i | 0.210741 | − | 0.210741i | ||||
\(478\) | 21.9271 | − | 15.1530i | 1.00292 | − | 0.693084i | ||||
\(479\) | 17.6824 | + | 30.6268i | 0.807930 | + | 1.39938i | 0.914295 | + | 0.405049i | \(0.132746\pi\) |
−0.106365 | + | 0.994327i | \(0.533921\pi\) | |||||||
\(480\) | −33.8364 | − | 4.01380i | −1.54441 | − | 0.183204i | ||||
\(481\) | 7.21289 | − | 12.4931i | 0.328879 | − | 0.569636i | ||||
\(482\) | −8.17705 | − | 3.87453i | −0.372454 | − | 0.176480i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −12.6391 | + | 10.3428i | −0.574507 | + | 0.470128i | ||||
\(485\) | 22.6621 | − | 6.07229i | 1.02903 | − | 0.275729i | ||||
\(486\) | −9.47334 | − | 8.04906i | −0.429720 | − | 0.365113i | ||||
\(487\) | −14.4850 | + | 8.36292i | −0.656378 | + | 0.378960i | −0.790896 | − | 0.611951i | \(-0.790385\pi\) |
0.134517 | + | 0.990911i | \(0.457052\pi\) | |||||||
\(488\) | −3.64022 | + | 2.01291i | −0.164785 | + | 0.0911201i | ||||
\(489\) | 35.9510i | 1.62576i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.93243 | + | 5.93243i | 0.267727 | + | 0.267727i | 0.828184 | − | 0.560457i | \(-0.189374\pi\) |
−0.560457 | + | 0.828184i | \(0.689374\pi\) | |||||||
\(492\) | 20.2249 | + | 14.5363i | 0.911809 | + | 0.655346i | ||||
\(493\) | 44.3717 | + | 11.8894i | 1.99840 | + | 0.535470i | ||||
\(494\) | −4.21128 | + | 0.342309i | −0.189475 | + | 0.0154012i | ||||
\(495\) | −5.83732 | + | 10.1105i | −0.262368 | + | 0.454434i | ||||
\(496\) | −2.20219 | + | 10.9098i | −0.0988813 | + | 0.489866i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 12.4977 | − | 26.3760i | 0.560037 | − | 1.18194i | ||||
\(499\) | −2.03391 | − | 7.59066i | −0.0910504 | − | 0.339805i | 0.905341 | − | 0.424686i | \(-0.139616\pi\) |
−0.996391 | + | 0.0848814i | \(0.972949\pi\) | |||||||
\(500\) | 1.58066 | + | 3.50175i | 0.0706892 | + | 0.156603i | ||||
\(501\) | 0.998649 | − | 3.72701i | 0.0446164 | − | 0.166510i | ||||
\(502\) | 5.76772 | + | 1.05368i | 0.257426 | + | 0.0470282i | ||||
\(503\) | − | 6.99765i | − | 0.312010i | −0.987756 | − | 0.156005i | \(-0.950138\pi\) | ||
0.987756 | − | 0.156005i | \(-0.0498616\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 43.0034i | 1.91363i | ||||||||
\(506\) | −6.84832 | + | 37.4867i | −0.304445 | + | 1.66649i | ||||
\(507\) | −3.48631 | + | 13.0111i | −0.154833 | + | 0.577843i | ||||
\(508\) | −1.27660 | + | 3.37735i | −0.0566400 | + | 0.149846i | ||||
\(509\) | −1.30940 | − | 4.88676i | −0.0580383 | − | 0.216602i | 0.930816 | − | 0.365488i | \(-0.119098\pi\) |
−0.988854 | + | 0.148886i | \(0.952431\pi\) | |||||||
\(510\) | −40.0657 | − | 18.9843i | −1.77414 | − | 0.840640i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 15.0887 | + | 16.8622i | 0.666831 | + | 0.745209i | ||||
\(513\) | 2.52237 | − | 4.36887i | 0.111365 | − | 0.192890i | ||||
\(514\) | −3.31895 | − | 40.8317i | −0.146393 | − | 1.80101i | ||||
\(515\) | 4.76687 | + | 1.27728i | 0.210053 | + | 0.0562837i | ||||
\(516\) | 16.8017 | − | 2.74957i | 0.739654 | − | 0.121043i | ||||
\(517\) | 11.1561 | + | 11.1561i | 0.490645 | + | 0.490645i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 11.5205i | 0.505695i | ||||||||
\(520\) | 20.6422 | + | 5.94206i | 0.905218 | + | 0.260577i | ||||
\(521\) | 15.0383 | − | 8.68234i | 0.658838 | − | 0.380380i | −0.132996 | − | 0.991117i | \(-0.542460\pi\) |
0.791834 | + | 0.610736i | \(0.209126\pi\) | |||||||
\(522\) | −7.03994 | + | 8.28566i | −0.308130 | + | 0.362654i | ||||
\(523\) | −35.4526 | + | 9.49950i | −1.55023 | + | 0.415384i | −0.929556 | − | 0.368681i | \(-0.879810\pi\) |
−0.620679 | + | 0.784065i | \(0.713143\pi\) | |||||||
\(524\) | −26.1339 | − | 2.61128i | −1.14166 | − | 0.114074i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.208582 | + | 0.440204i | −0.00909461 | + | 0.0191938i | ||||
\(527\) | −7.24096 | + | 12.5417i | −0.315421 | + | 0.546325i | ||||
\(528\) | 32.6567 | − | 10.9826i | 1.42120 | − | 0.477954i | ||||
\(529\) | 7.44198 | + | 12.8899i | 0.323564 | + | 0.560430i | ||||
\(530\) | −18.3933 | − | 26.6159i | −0.798955 | − | 1.15612i | ||||
\(531\) | 6.21554 | − | 6.21554i | 0.269731 | − | 0.269731i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −11.1027 | − | 11.1027i | −0.480909 | − | 0.480909i | ||||
\(534\) | −8.92712 | − | 1.63087i | −0.386314 | − | 0.0705744i | ||||
\(535\) | −29.7100 | + | 17.1531i | −1.28448 | + | 0.741593i | ||||
\(536\) | 0.0714666 | − | 3.86611i | 0.00308689 | − | 0.166991i | ||||
\(537\) | 22.9287 | + | 13.2379i | 0.989448 | + | 0.571258i | ||||
\(538\) | −18.6072 | + | 6.64294i | −0.802215 | + | 0.286397i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −19.8483 | + | 16.2422i | −0.854137 | + | 0.698953i | ||||
\(541\) | −4.14648 | − | 15.4749i | −0.178271 | − | 0.665317i | −0.995971 | − | 0.0896726i | \(-0.971418\pi\) |
0.817700 | − | 0.575644i | \(-0.195249\pi\) | |||||||
\(542\) | 1.43182 | + | 17.6151i | 0.0615021 | + | 0.756635i | ||||
\(543\) | −10.5793 | − | 18.3239i | −0.454001 | − | 0.786352i | ||||
\(544\) | 11.6150 | + | 27.0543i | 0.497991 | + | 1.15994i | ||||
\(545\) | −24.6343 | −1.05522 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.8422 | + | 10.8422i | −0.463578 | + | 0.463578i | −0.899826 | − | 0.436248i | \(-0.856307\pi\) |
0.436248 | + | 0.899826i | \(0.356307\pi\) | |||||||
\(548\) | 2.56350 | + | 15.6647i | 0.109507 | + | 0.669162i | ||||
\(549\) | 0.331561 | − | 1.23740i | 0.0141507 | − | 0.0528111i | ||||
\(550\) | 20.6303 | + | 17.5286i | 0.879679 | + | 0.747422i | ||||
\(551\) | −9.20572 | − | 5.31493i | −0.392177 | − | 0.226423i | ||||
\(552\) | 17.6714 | − | 29.3416i | 0.752145 | − | 1.24886i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 4.03433 | + | 11.3004i | 0.171402 | + | 0.480106i | ||||
\(555\) | −33.8344 | + | 9.06589i | −1.43619 | + | 0.384826i | ||||
\(556\) | 5.33419 | − | 2.40781i | 0.226220 | − | 0.102114i | ||||
\(557\) | 21.5541 | + | 5.77540i | 0.913275 | + | 0.244711i | 0.684709 | − | 0.728817i | \(-0.259929\pi\) |
0.228567 | + | 0.973528i | \(0.426596\pi\) | |||||||
\(558\) | −1.94868 | − | 2.81983i | −0.0824944 | − | 0.119373i | ||||
\(559\) | −10.7329 | −0.453952 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 44.8306 | 1.89275 | ||||||||
\(562\) | 7.69028 | + | 11.1282i | 0.324395 | + | 0.469413i | ||||
\(563\) | 20.1711 | + | 5.40483i | 0.850110 | + | 0.227786i | 0.657468 | − | 0.753483i | \(-0.271628\pi\) |
0.192643 | + | 0.981269i | \(0.438294\pi\) | |||||||
\(564\) | −5.83437 | − | 12.9253i | −0.245671 | − | 0.544254i | ||||
\(565\) | 45.1287 | − | 12.0922i | 1.89858 | − | 0.508723i | ||||
\(566\) | 7.85944 | + | 22.0147i | 0.330357 | + | 0.925348i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 27.6150 | − | 6.85498i | 1.15870 | − | 0.287629i | ||||
\(569\) | −15.2567 | − | 8.80848i | −0.639596 | − | 0.369271i | 0.144863 | − | 0.989452i | \(-0.453726\pi\) |
−0.784459 | + | 0.620181i | \(0.787059\pi\) | |||||||
\(570\) | 7.81833 | + | 6.64287i | 0.327474 | + | 0.278239i | ||||
\(571\) | −2.22250 | + | 8.29448i | −0.0930087 | + | 0.347113i | −0.996710 | − | 0.0810502i | \(-0.974173\pi\) |
0.903701 | + | 0.428164i | \(0.140839\pi\) | |||||||
\(572\) | −21.4350 | + | 3.50781i | −0.896242 | + | 0.146669i | ||||
\(573\) | 28.5034 | − | 28.5034i | 1.19074 | − | 1.19074i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 26.9129 | 1.12234 | ||||||||
\(576\) | −6.96377 | − | 0.257544i | −0.290157 | − | 0.0107310i | ||||
\(577\) | −17.6514 | − | 30.5732i | −0.734838 | − | 1.27278i | −0.954794 | − | 0.297268i | \(-0.903925\pi\) |
0.219956 | − | 0.975510i | \(-0.429409\pi\) | |||||||
\(578\) | 1.15593 | + | 14.2210i | 0.0480804 | + | 0.591514i | ||||
\(579\) | −6.47509 | − | 24.1654i | −0.269096 | − | 1.00428i | ||||
\(580\) | 34.2242 | + | 41.8228i | 1.42108 | + | 1.73660i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 20.0821 | − | 7.16947i | 0.832429 | − | 0.297184i | ||||
\(583\) | 28.3313 | + | 16.3571i | 1.17336 | + | 0.677441i | ||||
\(584\) | −29.7774 | − | 30.8991i | −1.23220 | − | 1.27861i | ||||
\(585\) | −5.72900 | + | 3.30764i | −0.236865 | + | 0.136754i | ||||
\(586\) | 30.0847 | + | 5.49608i | 1.24279 | + | 0.227041i | ||||
\(587\) | 2.38838 | + | 2.38838i | 0.0985791 | + | 0.0985791i | 0.754676 | − | 0.656097i | \(-0.227794\pi\) |
−0.656097 | + | 0.754676i | \(0.727794\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.36961 | − | 2.36961i | 0.0976379 | − | 0.0976379i | ||||
\(590\) | −24.8388 | − | 35.9428i | −1.02260 | − | 1.47974i | ||||
\(591\) | −17.8966 | − | 30.9978i | −0.736167 | − | 1.27508i | ||||
\(592\) | 20.8331 | + | 10.3471i | 0.856235 | + | 0.425263i | ||||
\(593\) | 5.78207 | − | 10.0148i | 0.237441 | − | 0.411260i | −0.722538 | − | 0.691331i | \(-0.757025\pi\) |
0.959979 | + | 0.280071i | \(0.0903580\pi\) | |||||||
\(594\) | 11.1044 | − | 23.4355i | 0.455621 | − | 0.961570i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.57451 | + | 25.7659i | −0.105456 | + | 1.05541i | ||||
\(597\) | −2.79078 | + | 0.747787i | −0.114219 | + | 0.0306049i | ||||
\(598\) | −13.9813 | + | 16.4553i | −0.571738 | + | 0.672908i | ||||
\(599\) | −10.6273 | + | 6.13567i | −0.434219 | + | 0.250697i | −0.701142 | − | 0.713021i | \(-0.747326\pi\) |
0.266923 | + | 0.963718i | \(0.413993\pi\) | |||||||
\(600\) | −11.7749 | − | 21.2941i | −0.480707 | − | 0.869329i | ||||
\(601\) | 14.1538i | 0.577347i | 0.957428 | + | 0.288674i | \(0.0932143\pi\) | ||||
−0.957428 | + | 0.288674i | \(0.906786\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.842054 | + | 0.842054i | 0.0342911 | + | 0.0342911i | ||||
\(604\) | 0.905356 | + | 5.53232i | 0.0368384 | + | 0.225107i | ||||
\(605\) | −24.1474 | − | 6.47029i | −0.981733 | − | 0.263055i | ||||
\(606\) | 3.16649 | + | 38.9560i | 0.128630 | + | 1.58248i | ||||
\(607\) | −12.8174 | + | 22.2005i | −0.520244 | + | 0.901089i | 0.479479 | + | 0.877553i | \(0.340826\pi\) |
−0.999723 | + | 0.0235358i | \(0.992508\pi\) | |||||||
\(608\) | −0.975842 | − | 6.74271i | −0.0395756 | − | 0.273453i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −5.75410 | − | 2.72646i | −0.232977 | − | 0.110391i | ||||
\(611\) | 2.31382 | + | 8.63529i | 0.0936071 | + | 0.349346i | ||||
\(612\) | −8.48160 | − | 3.20594i | −0.342848 | − | 0.129593i | ||||
\(613\) | 2.49198 | − | 9.30020i | 0.100650 | − | 0.375632i | −0.897165 | − | 0.441695i | \(-0.854377\pi\) |
0.997815 | + | 0.0660634i | \(0.0210440\pi\) | |||||||
\(614\) | 1.49614 | − | 8.18963i | 0.0603792 | − | 0.330507i | ||||
\(615\) | 38.1256i | 1.53737i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 23.1951i | − | 0.933800i | −0.884310 | − | 0.466900i | \(-0.845371\pi\) | ||
0.884310 | − | 0.466900i | \(-0.154629\pi\) | |||||||
\(618\) | 4.41228 | + | 0.806064i | 0.177488 | + | 0.0324247i | ||||
\(619\) | −8.68871 | + | 32.4267i | −0.349229 | + | 1.30334i | 0.538365 | + | 0.842712i | \(0.319042\pi\) |
−0.887594 | + | 0.460627i | \(0.847625\pi\) | |||||||
\(620\) | −15.5282 | + | 7.00927i | −0.623626 | + | 0.281499i | ||||
\(621\) | −6.67270 | − | 24.9028i | −0.267766 | − | 0.999317i | ||||
\(622\) | 0.486035 | − | 1.02576i | 0.0194882 | − | 0.0411291i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 19.1369 | + | 3.86286i | 0.766089 | + | 0.154638i | ||||
\(625\) | −13.8718 | + | 24.0267i | −0.554873 | + | 0.961068i | ||||
\(626\) | −24.9894 | + | 2.03123i | −0.998777 | + | 0.0811843i | ||||
\(627\) | −10.0204 | − | 2.68495i | −0.400175 | − | 0.107227i | ||||
\(628\) | 1.58273 | − | 2.20211i | 0.0631578 | − | 0.0878739i | ||||
\(629\) | 21.4019 | + | 21.4019i | 0.853348 | + | 0.853348i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 30.2574i | − | 1.20453i | −0.798296 | − | 0.602265i | \(-0.794265\pi\) | ||
0.798296 | − | 0.602265i | \(-0.205735\pi\) | |||||||
\(632\) | −17.9758 | − | 5.17452i | −0.715039 | − | 0.205832i | ||||
\(633\) | 1.28862 | − | 0.743986i | 0.0512181 | − | 0.0295708i | ||||
\(634\) | 15.8039 | + | 13.4278i | 0.627653 | + | 0.533287i | ||||
\(635\) | −5.33848 | + | 1.43044i | −0.211851 | + | 0.0567654i | ||||
\(636\) | −18.6220 | − | 22.7565i | −0.738411 | − | 0.902355i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −49.3813 | − | 23.3984i | −1.95503 | − | 0.926350i | ||||
\(639\) | −4.38133 | + | 7.58868i | −0.173323 | + | 0.300204i | ||||
\(640\) | −7.47960 | + | 33.8192i | −0.295657 | + | 1.33682i | ||||
\(641\) | 3.34695 | + | 5.79709i | 0.132197 | + | 0.228971i | 0.924523 | − | 0.381126i | \(-0.124464\pi\) |
−0.792326 | + | 0.610097i | \(0.791130\pi\) | |||||||
\(642\) | −25.6508 | + | 17.7263i | −1.01236 | + | 0.699603i | ||||
\(643\) | −24.7491 | + | 24.7491i | −0.976007 | + | 0.976007i | −0.999719 | − | 0.0237114i | \(-0.992452\pi\) |
0.0237114 | + | 0.999719i | \(0.492452\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 18.4279 | + | 18.4279i | 0.725597 | + | 0.725597i | ||||
\(646\) | 1.59312 | − | 8.72053i | 0.0626806 | − | 0.343105i | ||||
\(647\) | 37.7857 | − | 21.8156i | 1.48551 | − | 0.857659i | 0.485645 | − | 0.874156i | \(-0.338585\pi\) |
0.999864 | + | 0.0164976i | \(0.00525159\pi\) | |||||||
\(648\) | −22.1064 | + | 21.3039i | −0.868422 | + | 0.836898i | ||||
\(649\) | 38.2593 | + | 22.0890i | 1.50181 | + | 0.867069i | ||||
\(650\) | 5.15757 | + | 14.4466i | 0.202296 | + | 0.566643i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 36.3637 | + | 3.63344i | 1.42411 | + | 0.142296i | ||||
\(653\) | −6.54748 | − | 24.4355i | −0.256223 | − | 0.956236i | −0.967406 | − | 0.253230i | \(-0.918507\pi\) |
0.711184 | − | 0.703006i | \(-0.248159\pi\) | |||||||
\(654\) | −22.3158 | + | 1.81391i | −0.872616 | + | 0.0709294i | ||||
\(655\) | −20.1015 | − | 34.8169i | −0.785432 | − | 1.36041i | ||||
\(656\) | 16.7472 | − | 18.9880i | 0.653869 | − | 0.741356i | ||||
\(657\) | 13.2156 | 0.515588 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −16.0357 | + | 16.0357i | −0.624662 | + | 0.624662i | −0.946720 | − | 0.322058i | \(-0.895626\pi\) |
0.322058 | + | 0.946720i | \(0.395626\pi\) | |||||||
\(660\) | 42.8258 | + | 30.7802i | 1.66699 | + | 1.19812i | ||||
\(661\) | −2.82150 | + | 10.5300i | −0.109743 | + | 0.409568i | −0.998840 | − | 0.0481514i | \(-0.984667\pi\) |
0.889097 | + | 0.457720i | \(0.151334\pi\) | |||||||
\(662\) | 0.288863 | − | 0.339978i | 0.0112270 | − | 0.0132136i | ||||
\(663\) | 21.9994 | + | 12.7013i | 0.854385 | + | 0.493279i | ||||
\(664\) | −25.4157 | − | 15.3069i | −0.986321 | − | 0.594025i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −6.74664 | + | 2.40861i | −0.261427 | + | 0.0933316i | ||||
\(667\) | −52.4732 | + | 14.0602i | −2.03177 | + | 0.544412i | ||||
\(668\) | −3.66887 | − | 1.38679i | −0.141953 | − | 0.0536565i | ||||
\(669\) | 14.8953 | + | 3.99120i | 0.575887 | + | 0.154309i | ||||
\(670\) | 4.86937 | − | 3.36505i | 0.188120 | − | 0.130003i | ||||
\(671\) | 6.43842 | 0.248553 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.82580 | 0.0703795 | 0.0351897 | − | 0.999381i | \(-0.488796\pi\) | ||||
0.0351897 | + | 0.999381i | \(0.488796\pi\) | |||||||
\(674\) | −31.1372 | + | 21.5178i | −1.19936 | + | 0.828837i | ||||
\(675\) | −17.6911 | − | 4.74030i | −0.680929 | − | 0.182454i | ||||
\(676\) | 12.8081 | + | 4.84132i | 0.492620 | + | 0.186205i | ||||
\(677\) | 26.1437 | − | 7.00518i | 1.00478 | − | 0.269231i | 0.281335 | − | 0.959610i | \(-0.409223\pi\) |
0.723448 | + | 0.690379i | \(0.242556\pi\) | |||||||
\(678\) | 39.9909 | − | 14.2771i | 1.53584 | − | 0.548309i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −23.2516 | + | 38.6070i | −0.891656 | + | 1.48051i | ||||
\(681\) | 0.596575 | + | 0.344433i | 0.0228608 | + | 0.0131987i | ||||
\(682\) | 11.1544 | − | 13.1282i | 0.427123 | − | 0.502703i | ||||
\(683\) | −5.18175 | + | 19.3386i | −0.198274 | + | 0.739970i | 0.793121 | + | 0.609065i | \(0.208455\pi\) |
−0.991395 | + | 0.130905i | \(0.958212\pi\) | |||||||
\(684\) | 1.70377 | + | 1.22455i | 0.0651452 | + | 0.0468219i | ||||
\(685\) | −17.1808 | + | 17.1808i | −0.656445 | + | 0.656445i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −43.4148 | −1.65638 | ||||||||
\(688\) | −1.08305 | − | 17.2725i | −0.0412911 | − | 0.658507i | ||||
\(689\) | 9.26852 | + | 16.0536i | 0.353103 | + | 0.611592i | ||||
\(690\) | 52.2584 | − | 4.24776i | 1.98944 | − | 0.161709i | ||||
\(691\) | 3.95994 | + | 14.7787i | 0.150643 | + | 0.562208i | 0.999439 | + | 0.0334874i | \(0.0106614\pi\) |
−0.848796 | + | 0.528720i | \(0.822672\pi\) | |||||||
\(692\) | 11.6528 | + | 1.16434i | 0.442972 | + | 0.0442614i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −16.5474 | − | 46.3501i | −0.628130 | − | 1.75943i | ||||
\(695\) | 7.75829 | + | 4.47925i | 0.294289 | + | 0.169908i | ||||
\(696\) | 34.0827 | + | 35.3665i | 1.29190 | + | 1.34056i | ||||
\(697\) | 28.5299 | − | 16.4717i | 1.08065 | − | 0.623911i | ||||
\(698\) | −4.95353 | + | 27.1149i | −0.187494 | + | 1.02631i | ||||
\(699\) | 13.2375 | + | 13.2375i | 0.500688 | + | 0.500688i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.64009 | − | 2.64009i | 0.0997148 | − | 0.0997148i | −0.655490 | − | 0.755204i | \(-0.727538\pi\) |
0.755204 | + | 0.655490i | \(0.227538\pi\) | |||||||
\(702\) | 12.0889 | − | 8.35422i | 0.456266 | − | 0.315310i | ||||
\(703\) | −3.50188 | − | 6.06544i | −0.132076 | − | 0.228762i | ||||
\(704\) | −7.80815 | − | 34.1415i | −0.294281 | − | 1.28676i | ||||
\(705\) | 10.8537 | − | 18.7992i | 0.408774 | − | 0.708018i | ||||
\(706\) | −33.2848 | − | 15.7713i | −1.25269 | − | 0.593562i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −25.1476 | − | 30.7310i | −0.945106 | − | 1.15494i | ||||
\(709\) | 27.6926 | − | 7.42020i | 1.04002 | − | 0.278671i | 0.301896 | − | 0.953341i | \(-0.402380\pi\) |
0.738120 | + | 0.674669i | \(0.235714\pi\) | |||||||
\(710\) | 33.1912 | + | 28.2010i | 1.24564 | + | 1.05836i | ||||
\(711\) | 4.98899 | − | 2.88039i | 0.187102 | − | 0.108023i | ||||
\(712\) | −2.55182 | + | 8.86478i | −0.0956335 | + | 0.332222i | ||||
\(713\) | − | 17.1261i | − | 0.641377i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −23.5096 | − | 23.5096i | −0.879210 | − | 0.879210i | ||||
\(716\) | 15.7072 | − | 21.8541i | 0.587006 | − | 0.816724i | ||||
\(717\) | 35.8178 | + | 9.59735i | 1.33764 | + | 0.358420i | ||||
\(718\) | −29.6546 | + | 2.41044i | −1.10670 | + | 0.0899568i | ||||
\(719\) | 10.0679 | − | 17.4381i | 0.375468 | − | 0.650330i | −0.614929 | − | 0.788583i | \(-0.710815\pi\) |
0.990397 | + | 0.138253i | \(0.0441486\pi\) | |||||||
\(720\) | −5.90113 | − | 8.88595i | −0.219922 | − | 0.331160i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 10.6272 | − | 22.4284i | 0.395505 | − | 0.834697i | ||||
\(723\) | −3.25818 | − | 12.1597i | −0.121173 | − | 0.452224i | ||||
\(724\) | −19.6034 | + | 8.84882i | −0.728556 | + | 0.328864i | ||||
\(725\) | −9.98838 | + | 37.2771i | −0.370959 | + | 1.38444i | ||||
\(726\) | −22.3512 | − | 4.08326i | −0.829530 | − | 0.151544i | ||||
\(727\) | 30.0313i | 1.11380i | 0.830580 | + | 0.556900i | \(0.188009\pi\) | ||||
−0.830580 | + | 0.556900i | \(0.811991\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 15.2688i | 0.565511i | ||||||||
\(730\) | 11.8047 | − | 64.6173i | 0.436912 | − | 2.39159i | ||||
\(731\) | 5.82826 | − | 21.7514i | 0.215566 | − | 0.804503i | ||||
\(732\) | −5.41330 | − | 2.04616i | −0.200081 | − | 0.0756284i | ||||
\(733\) | 3.31347 | + | 12.3660i | 0.122386 | + | 0.456750i | 0.999733 | − | 0.0231062i | \(-0.00735557\pi\) |
−0.877347 | + | 0.479856i | \(0.840689\pi\) | |||||||
\(734\) | 9.47438 | + | 4.48925i | 0.349706 | + | 0.165701i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −27.8925 | − | 20.8397i | −1.02813 | − | 0.768163i | ||||
\(737\) | −2.99252 | + | 5.18320i | −0.110231 | + | 0.190926i | ||||
\(738\) | 0.631703 | + | 7.77158i | 0.0232533 | + | 0.286076i | ||||
\(739\) | −27.5947 | − | 7.39398i | −1.01509 | − | 0.271992i | −0.287334 | − | 0.957831i | \(-0.592769\pi\) |
−0.727754 | + | 0.685839i | \(0.759436\pi\) | |||||||
\(740\) | 5.75046 | + | 35.1391i | 0.211391 | + | 1.29174i | ||||
\(741\) | −4.15652 | − | 4.15652i | −0.152694 | − | 0.152694i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 32.8469i | 1.20504i | 0.798106 | + | 0.602518i | \(0.205836\pi\) | ||||
−0.798106 | + | 0.602518i | \(0.794164\pi\) | |||||||
\(744\) | −13.5506 | + | 7.49297i | −0.496788 | + | 0.274706i | ||||
\(745\) | −34.3267 | + | 19.8185i | −1.25763 | + | 0.726095i | ||||
\(746\) | −4.86003 | + | 5.72001i | −0.177938 | + | 0.209424i | ||||
\(747\) | 8.82583 | − | 2.36487i | 0.322920 | − | 0.0865262i | ||||
\(748\) | 4.53086 | − | 45.3453i | 0.165665 | − | 1.65799i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −2.28873 | + | 4.83028i | −0.0835726 | + | 0.176377i | ||||
\(751\) | −8.80060 | + | 15.2431i | −0.321138 | + | 0.556228i | −0.980723 | − | 0.195402i | \(-0.937399\pi\) |
0.659585 | + | 0.751630i | \(0.270732\pi\) | |||||||
\(752\) | −13.6634 | + | 4.59503i | −0.498251 | + | 0.167564i | ||||
\(753\) | 4.07852 | + | 7.06421i | 0.148630 | + | 0.257434i | ||||
\(754\) | −17.6033 | − | 25.4727i | −0.641075 | − | 0.927663i | ||||
\(755\) | −6.06777 | + | 6.06777i | −0.220829 | + | 0.220829i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10.8261 | − | 10.8261i | −0.393480 | − | 0.393480i | 0.482446 | − | 0.875926i | \(-0.339749\pi\) |
−0.875926 | + | 0.482446i | \(0.839749\pi\) | |||||||
\(758\) | 37.0639 | + | 6.77108i | 1.34622 | + | 0.245937i | ||||
\(759\) | −45.9132 | + | 26.5080i | −1.66654 | + | 0.962179i | ||||
\(760\) | 7.50931 | − | 7.23672i | 0.272391 | − | 0.262503i | ||||
\(761\) | 1.13395 | + | 0.654687i | 0.0411057 | + | 0.0237324i | 0.520412 | − | 0.853915i | \(-0.325778\pi\) |
−0.479306 | + | 0.877648i | \(0.659112\pi\) | |||||||
\(762\) | −4.73071 | + | 1.68890i | −0.171376 | + | 0.0611825i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −25.9499 | − | 31.7113i | −0.938833 | − | 1.14728i | ||||
\(765\) | −3.59229 | − | 13.4066i | −0.129880 | − | 0.484717i | ||||
\(766\) | 0.566708 | + | 6.97198i | 0.0204760 | + | 0.251908i | ||||
\(767\) | 12.5164 | + | 21.6791i | 0.451943 | + | 0.782788i | ||||
\(768\) | −4.28542 | + | 31.1870i | −0.154637 | + | 1.12536i | ||||
\(769\) | −22.6761 | −0.817720 | −0.408860 | − | 0.912597i | \(-0.634074\pi\) | ||||
−0.408860 | + | 0.912597i | \(0.634074\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 40.3008 | − | 40.3008i | 1.45140 | − | 1.45140i | ||||
\(772\) | −25.0972 | + | 4.10712i | −0.903269 | + | 0.147819i | ||||
\(773\) | 1.01468 | − | 3.78685i | 0.0364956 | − | 0.136203i | −0.945274 | − | 0.326277i | \(-0.894206\pi\) |
0.981770 | + | 0.190073i | \(0.0608725\pi\) | |||||||
\(774\) | 4.06170 | + | 3.45104i | 0.145995 | + | 0.124045i | ||||
\(775\) | −10.5364 | − | 6.08321i | −0.378480 | − | 0.218515i | ||||
\(776\) | −5.22216 | − | 21.0372i | −0.187465 | − | 0.755192i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −9.43222 | − | 26.4201i | −0.338161 | − | 0.947208i | ||||
\(779\) | −7.36339 | + | 1.97301i | −0.263821 | + | 0.0706906i | ||||
\(780\) | 12.2949 | + | 27.2379i | 0.440229 | + | 0.975273i | ||||
\(781\) | −42.5394 | − | 11.3984i | −1.52218 | − | 0.407867i | ||||
\(782\) | −25.7563 | − | 37.2704i | −0.921043 | − | 1.33279i | ||||
\(783\) | 36.9695 | 1.32118 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.15117 | 0.148161 | ||||||||
\(786\) | −20.7733 | − | 30.0599i | −0.740960 | − | 1.07220i | ||||
\(787\) | 30.0204 | + | 8.04395i | 1.07011 | + | 0.286736i | 0.750539 | − | 0.660826i | \(-0.229794\pi\) |
0.319573 | + | 0.947562i | \(0.396460\pi\) | |||||||
\(788\) | −33.1624 | + | 14.9692i | −1.18136 | + | 0.533256i | ||||
\(789\) | −0.654607 | + | 0.175401i | −0.0233046 | + | 0.00624445i | ||||
\(790\) | −9.62726 | − | 26.9665i | −0.342522 | − | 0.959424i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 9.23967 | + | 5.56471i | 0.328317 | + | 0.197733i | ||||
\(793\) | 3.15948 | + | 1.82412i | 0.112196 | + | 0.0647766i | ||||
\(794\) | 0.0973794 | + | 0.0827387i | 0.00345586 | + | 0.00293629i | ||||
\(795\) | 11.6496 | − | 43.4770i | 0.413170 | − | 1.54197i | ||||
\(796\) | 0.474318 | + | 2.89839i | 0.0168118 | + | 0.102731i | ||||
\(797\) | −27.7986 | + | 27.7986i | −0.984679 | + | 0.984679i | −0.999884 | − | 0.0152058i | \(-0.995160\pi\) |
0.0152058 | + | 0.999884i | \(0.495160\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18.7569 | −0.663570 | ||||||||
\(800\) | −22.7286 | + | 9.75793i | −0.803578 | + | 0.344995i | ||||
\(801\) | −1.42047 | − | 2.46032i | −0.0501897 | − | 0.0869312i | ||||
\(802\) | −2.91138 | − | 35.8175i | −0.102804 | − | 1.26476i | ||||
\(803\) | 17.1907 | + | 64.1567i | 0.606648 | + | 2.26404i | ||||
\(804\) | 4.16330 | − | 3.40689i | 0.146828 | − | 0.120152i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 9.19315 | − | 3.28203i | 0.323815 | − | 0.115605i | ||||
\(807\) | −23.8047 | − | 13.7436i | −0.837964 | − | 0.483799i | ||||
\(808\) | 39.7233 | + | 0.734301i | 1.39746 | + | 0.0258326i | ||||
\(809\) | −42.7813 | + | 24.6998i | −1.50411 | + | 0.868398i | −0.504121 | + | 0.863633i | \(0.668183\pi\) |
−0.999989 | + | 0.00476483i | \(0.998483\pi\) | |||||||
\(810\) | −46.2298 | − | 8.44557i | −1.62435 | − | 0.296747i | ||||
\(811\) | 13.1428 | + | 13.1428i | 0.461506 | + | 0.461506i | 0.899149 | − | 0.437643i | \(-0.144187\pi\) |
−0.437643 | + | 0.899149i | \(0.644187\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −17.3861 | + | 17.3861i | −0.609756 | + | 0.609756i | ||||
\(814\) | −20.4689 | − | 29.6193i | −0.717434 | − | 1.03816i | ||||
\(815\) | 27.9701 | + | 48.4457i | 0.979750 | + | 1.69698i | ||||
\(816\) | −18.2204 | + | 36.6855i | −0.637842 | + | 1.28425i | ||||
\(817\) | −2.60542 | + | 4.51272i | −0.0911521 | + | 0.157880i | ||||
\(818\) | 13.5678 | − | 28.6343i | 0.474386 | − | 1.00117i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 38.5633 | + | 3.85322i | 1.34669 | + | 0.134560i | ||||
\(821\) | −1.03860 | + | 0.278293i | −0.0362475 | + | 0.00971248i | −0.276897 | − | 0.960900i | \(-0.589306\pi\) |
0.240650 | + | 0.970612i | \(0.422639\pi\) | |||||||
\(822\) | −14.2987 | + | 16.8289i | −0.498725 | + | 0.586975i | ||||
\(823\) | 17.3926 | − | 10.0416i | 0.606268 | − | 0.350029i | −0.165235 | − | 0.986254i | \(-0.552838\pi\) |
0.771504 | + | 0.636225i | \(0.219505\pi\) | |||||||
\(824\) | 1.26125 | − | 4.38147i | 0.0439377 | − | 0.152636i | ||||
\(825\) | 37.6627i | 1.31125i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6.99770 | + | 6.99770i | 0.243334 | + | 0.243334i | 0.818228 | − | 0.574894i | \(-0.194957\pi\) |
−0.574894 | + | 0.818228i | \(0.694957\pi\) | |||||||
\(828\) | 10.5821 | − | 1.73174i | 0.367752 | − | 0.0601821i | ||||
\(829\) | −44.6990 | − | 11.9771i | −1.55246 | − | 0.415980i | −0.622193 | − | 0.782864i | \(-0.713758\pi\) |
−0.930267 | + | 0.366884i | \(0.880425\pi\) | |||||||
\(830\) | −3.67940 | − | 45.2662i | −0.127714 | − | 1.57121i | ||||
\(831\) | −8.34665 | + | 14.4568i | −0.289542 | + | 0.501502i | ||||
\(832\) | 5.84130 | − | 18.9662i | 0.202511 | − | 0.657535i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 7.35793 | + | 3.48641i | 0.254784 | + | 0.120724i | ||||
\(835\) | −1.55391 | − | 5.79927i | −0.0537753 | − | 0.200692i | ||||
\(836\) | −3.72849 | + | 9.86405i | −0.128953 | + | 0.341155i | ||||
\(837\) | −3.01650 | + | 11.2577i | −0.104266 | + | 0.389125i | ||||
\(838\) | 8.72533 | − | 47.7612i | 0.301411 | − | 1.64988i | ||||
\(839\) | − | 11.1872i | − | 0.386225i | −0.981177 | − | 0.193113i | \(-0.938142\pi\) | ||
0.981177 | − | 0.193113i | \(-0.0618583\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 48.8991i | − | 1.68618i | ||||||
\(842\) | 31.5321 | + | 5.76050i | 1.08667 | + | 0.198520i | ||||
\(843\) | −4.87073 | + | 18.1778i | −0.167757 | + | 0.626077i | ||||
\(844\) | −0.622291 | − | 1.37861i | −0.0214201 | − | 0.0474536i | ||||
\(845\) | 5.42475 | + | 20.2454i | 0.186617 | + | 0.696464i | ||||
\(846\) | 1.90095 | − | 4.01189i | 0.0653561 | − | 0.137931i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −24.8998 | + | 16.5359i | −0.855064 | + | 0.567844i | ||||
\(849\) | −16.2605 | + | 28.1640i | −0.558058 | + | 0.966585i | ||||
\(850\) | −32.0784 | + | 2.60745i | −1.10028 | + | 0.0894349i | ||||
\(851\) | −34.5734 | − | 9.26392i | −1.18516 | − | 0.317563i | ||||
\(852\) | 32.1438 | + | 23.1028i | 1.10123 | + | 0.791489i | ||||
\(853\) | 25.4369 | + | 25.4369i | 0.870944 | + | 0.870944i | 0.992575 | − | 0.121632i | \(-0.0388127\pi\) |
−0.121632 | + | 0.992575i | \(0.538813\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.21174i | 0.109839i | ||||||||
\(856\) | 15.3374 | + | 27.7368i | 0.524222 | + | 0.948024i | ||||
\(857\) | −28.5281 | + | 16.4707i | −0.974500 | + | 0.562628i | −0.900605 | − | 0.434638i | \(-0.856876\pi\) |
−0.0738951 | + | 0.997266i | \(0.523543\pi\) | |||||||
\(858\) | −23.0281 | − | 19.5659i | −0.786165 | − | 0.667967i | ||||
\(859\) | −40.8704 | + | 10.9512i | −1.39448 | + | 0.373649i | −0.876359 | − | 0.481659i | \(-0.840034\pi\) |
−0.518120 | + | 0.855308i | \(0.673368\pi\) | |||||||
\(860\) | 20.5019 | − | 16.7770i | 0.699108 | − | 0.572091i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 40.4636 | + | 19.1729i | 1.37819 | + | 0.653030i | ||||
\(863\) | −10.9071 | + | 18.8916i | −0.371281 | + | 0.643078i | −0.989763 | − | 0.142721i | \(-0.954415\pi\) |
0.618482 | + | 0.785799i | \(0.287748\pi\) | |||||||
\(864\) | 14.6644 | + | 18.6117i | 0.498893 | + | 0.633184i | ||||
\(865\) | 8.96304 | + | 15.5244i | 0.304752 | + | 0.527847i | ||||
\(866\) | 13.5915 | − | 9.39261i | 0.461858 | − | 0.319174i | ||||
\(867\) | −14.0360 | + | 14.0360i | −0.476689 | + | 0.476689i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 20.4729 | + | 20.4729i | 0.694495 | + | 0.694495i | ||||
\(870\) | −13.5115 | + | 73.9599i | −0.458082 | + | 2.50747i | ||||
\(871\) | −2.93699 | + | 1.69567i | −0.0995162 | + | 0.0574557i | ||||
\(872\) | −0.420640 | + | 22.7553i | −0.0142447 | + | 0.770591i | ||||
\(873\) | 5.78109 | + | 3.33772i | 0.195660 | + | 0.112965i | ||||
\(874\) | 3.52478 | + | 9.87311i | 0.119228 | + | 0.333963i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 5.93570 | − | 59.4049i | 0.200549 | − | 2.00711i | ||||
\(877\) | 3.62186 | + | 13.5170i | 0.122302 | + | 0.456435i | 0.999729 | − | 0.0232736i | \(-0.00740889\pi\) |
−0.877428 | + | 0.479709i | \(0.840742\pi\) | |||||||
\(878\) | 18.4959 | − | 1.50342i | 0.624207 | − | 0.0507378i | ||||
\(879\) | 21.2738 | + | 36.8473i | 0.717548 | + | 1.24283i | ||||
\(880\) | 35.4619 | − | 40.2066i | 1.19542 | − | 1.35536i | ||||
\(881\) | 12.3319 | 0.415471 | 0.207735 | − | 0.978185i | \(-0.433391\pi\) | ||||
0.207735 | + | 0.978185i | \(0.433391\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24.3508 | − | 24.3508i | 0.819469 | − | 0.819469i | −0.166562 | − | 0.986031i | \(-0.553267\pi\) |
0.986031 | + | 0.166562i | \(0.0532667\pi\) | |||||||
\(884\) | 15.0706 | − | 20.9683i | 0.506878 | − | 0.705239i | ||||
\(885\) | 15.7319 | − | 58.7124i | 0.528823 | − | 1.97360i | ||||
\(886\) | 21.0047 | − | 24.7215i | 0.705666 | − | 0.830534i | ||||
\(887\) | 3.69725 | + | 2.13461i | 0.124141 | + | 0.0716731i | 0.560785 | − | 0.827962i | \(-0.310500\pi\) |
−0.436643 | + | 0.899635i | \(0.643833\pi\) | |||||||
\(888\) | 7.79665 | + | 31.4084i | 0.261638 | + | 1.05400i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −13.2985 | + | 4.74769i | −0.445768 | + | 0.159143i | ||||
\(891\) | 45.9002 | − | 12.2989i | 1.53772 | − | 0.412030i | ||||
\(892\) | 5.54243 | − | 14.6630i | 0.185574 | − | 0.490953i | ||||
\(893\) | 4.19246 | + | 1.12337i | 0.140295 | + | 0.0375920i | ||||
\(894\) | −29.6367 | + | 20.4809i | −0.991198 | + | 0.684982i | ||||
\(895\) | 41.1967 | 1.37705 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −30.0408 | −1.00303 | ||||||||
\(898\) | −18.1956 | + | 12.5743i | −0.607194 | + | 0.419610i | ||||
\(899\) | 23.7214 | + | 6.35613i | 0.791153 | + | 0.211989i | ||||
\(900\) | 2.69335 | − | 7.12548i | 0.0897783 | − | 0.237516i | ||||
\(901\) | −37.5674 | + | 10.0662i | −1.25155 | + | 0.335352i | ||||
\(902\) | −36.9064 | + | 13.1759i | −1.22885 | + | 0.438710i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −10.3993 | − | 41.8930i | −0.345875 | − | 1.39334i | ||||
\(905\) | −28.5122 | − | 16.4615i | −0.947776 | − | 0.547199i | ||||
\(906\) | −5.04990 | + | 5.94348i | −0.167772 | + | 0.197459i | ||||
\(907\) | −8.71495 | + | 32.5246i | −0.289375 | + | 1.07996i | 0.656208 | + | 0.754580i | \(0.272160\pi\) |
−0.945583 | + | 0.325382i | \(0.894507\pi\) | |||||||
\(908\) | 0.408681 | − | 0.568613i | 0.0135625 | − | 0.0188701i | ||||
\(909\) | −8.65188 | + | 8.65188i | −0.286965 | + | 0.286965i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.22749 | 0.140063 | 0.0700315 | − | 0.997545i | \(-0.477690\pi\) | ||||
0.0700315 | + | 0.997545i | \(0.477690\pi\) | |||||||
\(912\) | 6.26969 | − | 7.10856i | 0.207610 | − | 0.235388i | ||||
\(913\) | 22.9612 | + | 39.7699i | 0.759904 | + | 1.31619i | ||||
\(914\) | −17.2396 | + | 1.40130i | −0.570236 | + | 0.0463509i | ||||
\(915\) | −2.29275 | − | 8.55664i | −0.0757958 | − | 0.282874i | ||||
\(916\) | −4.38777 | + | 43.9132i | −0.144976 | + | 1.45093i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 10.3661 | + | 29.0361i | 0.342134 | + | 0.958335i | ||||
\(919\) | −18.8641 | − | 10.8912i | −0.622270 | − | 0.359268i | 0.155482 | − | 0.987839i | \(-0.450307\pi\) |
−0.777752 | + | 0.628571i | \(0.783640\pi\) | |||||||
\(920\) | 0.985044 | − | 53.2877i | 0.0324759 | − | 1.75684i | ||||
\(921\) | 10.0305 | − | 5.79113i | 0.330517 | − | 0.190824i | ||||
\(922\) | 4.83992 | − | 26.4930i | 0.159394 | − | 0.872502i | ||||
\(923\) | −17.6457 | − | 17.6457i | −0.580814 | − | 0.580814i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −17.9799 | + | 17.9799i | −0.591177 | + | 0.591177i | ||||
\(926\) | −28.8307 | + | 19.9239i | −0.947435 | + | 0.654739i | ||||
\(927\) | 0.702074 | + | 1.21603i | 0.0230591 | + | 0.0399396i | ||||
\(928\) | 39.2171 | − | 30.8996i | 1.28737 | − | 1.01433i | ||||
\(929\) | −15.6683 | + | 27.1384i | −0.514062 | + | 0.890381i | 0.485805 | + | 0.874067i | \(0.338526\pi\) |
−0.999867 | + | 0.0163141i | \(0.994807\pi\) | |||||||
\(930\) | −21.4194 | − | 10.1491i | −0.702369 | − | 0.332804i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 14.7273 | − | 12.0516i | 0.482410 | − | 0.394763i | ||||
\(933\) | 1.52535 | − | 0.408718i | 0.0499379 | − | 0.0133808i | ||||
\(934\) | −35.3118 | − | 30.0028i | −1.15544 | − | 0.981721i | ||||
\(935\) | 60.4113 | − | 34.8785i | 1.97566 | − | 1.14065i | ||||
\(936\) | 2.95752 | + | 5.34850i | 0.0966697 | + | 0.174821i | ||||
\(937\) | − | 53.9341i | − | 1.76195i | −0.473162 | − | 0.880975i | \(-0.656887\pi\) | ||
0.473162 | − | 0.880975i | \(-0.343113\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −24.6644 | − | 24.6644i | −0.804893 | − | 0.804893i | ||||
\(940\) | −17.9180 | − | 12.8783i | −0.584422 | − | 0.420043i | ||||
\(941\) | −47.8941 | − | 12.8332i | −1.56130 | − | 0.418350i | −0.628227 | − | 0.778030i | \(-0.716219\pi\) |
−0.933076 | + | 0.359680i | \(0.882886\pi\) | |||||||
\(942\) | 3.76047 | − | 0.305665i | 0.122523 | − | 0.00995910i | ||||
\(943\) | −19.4792 | + | 33.7390i | −0.634330 | + | 1.09869i | ||||
\(944\) | −33.6254 | + | 22.3305i | −1.09441 | + | 0.726795i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −11.4701 | + | 24.2071i | −0.372924 | + | 0.787042i | ||||
\(947\) | 0.0235259 | + | 0.0877997i | 0.000764488 | + | 0.00285311i | 0.966307 | − | 0.257392i | \(-0.0828632\pi\) |
−0.965543 | + | 0.260245i | \(0.916197\pi\) | |||||||
\(948\) | −10.7068 | − | 23.7196i | −0.347741 | − | 0.770376i | ||||
\(949\) | −9.74091 | + | 36.3536i | −0.316203 | + | 1.18009i | ||||
\(950\) | 7.32621 | + | 1.33840i | 0.237694 | + | 0.0434235i | ||||
\(951\) | 28.8516i | 0.935577i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 45.4195i | 1.47128i | 0.677371 | + | 0.735641i | \(0.263119\pi\) | ||||
−0.677371 | + | 0.735641i | \(0.736881\pi\) | |||||||
\(954\) | 1.65431 | − | 9.05544i | 0.0535602 | − | 0.293181i | ||||
\(955\) | 16.2338 | − | 60.5854i | 0.525314 | − | 1.96050i | ||||
\(956\) | 13.3275 | − | 35.2590i | 0.431042 | − | 1.14036i | ||||
\(957\) | −19.6762 | − | 73.4326i | −0.636041 | − | 2.37374i | ||||
\(958\) | 45.1965 | + | 21.4155i | 1.46023 | + | 0.691902i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −42.5935 | + | 22.5349i | −1.37470 | + | 0.727312i | ||||
\(961\) | 11.6289 | − | 20.1419i | 0.375127 | − | 0.649739i | ||||
\(962\) | −1.65283 | − | 20.3341i | −0.0532893 | − | 0.655597i | ||||
\(963\) | −9.42843 | − | 2.52634i | −0.303827 | − | 0.0814102i | ||||
\(964\) | −12.6286 | + | 2.06665i | −0.406739 | + | 0.0665623i | ||||
\(965\) | −27.5263 | − | 27.5263i | −0.886103 | − | 0.886103i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 60.1289i | 1.93362i | 0.255506 | + | 0.966808i | \(0.417758\pi\) | ||||
−0.255506 | + | 0.966808i | \(0.582242\pi\) | |||||||
\(968\) | −6.38909 | + | 22.1951i | −0.205353 | + | 0.713378i | ||||
\(969\) | 10.6808 | − | 6.16655i | 0.343116 | − | 0.198098i | ||||
\(970\) | 21.4836 | − | 25.2852i | 0.689798 | − | 0.811858i | ||||
\(971\) | 36.4130 | − | 9.75682i | 1.16855 | − | 0.313111i | 0.378173 | − | 0.925735i | \(-0.376552\pi\) |
0.790375 | + | 0.612624i | \(0.209886\pi\) | |||||||
\(972\) | −17.4931 | − | 1.74790i | −0.561091 | − | 0.0560638i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −10.1285 | + | 21.3757i | −0.324537 | + | 0.684923i | ||||
\(975\) | −10.6705 | + | 18.4819i | −0.341731 | + | 0.591895i | ||||
\(976\) | −2.61676 | + | 5.26865i | −0.0837603 | + | 0.168645i | ||||
\(977\) | 12.3444 | + | 21.3811i | 0.394932 | + | 0.684042i | 0.993092 | − | 0.117334i | \(-0.0374349\pi\) |
−0.598161 | + | 0.801376i | \(0.704102\pi\) | |||||||
\(978\) | 28.9049 | + | 41.8265i | 0.924276 | + | 1.33747i | ||||
\(979\) | 10.0962 | − | 10.0962i | 0.322676 | − | 0.322676i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.95619 | − | 4.95619i | −0.158239 | − | 0.158239i | ||||
\(982\) | 11.6717 | + | 2.13226i | 0.372459 | + | 0.0680433i | ||||
\(983\) | 4.43148 | − | 2.55852i | 0.141342 | − | 0.0816041i | −0.427661 | − | 0.903939i | \(-0.640662\pi\) |
0.569004 | + | 0.822335i | \(0.307329\pi\) | |||||||
\(984\) | 35.2176 | + | 0.651011i | 1.12270 | + | 0.0207535i | ||||
\(985\) | −48.2329 | − | 27.8473i | −1.53683 | − | 0.887289i | ||||
\(986\) | 61.1825 | − | 21.8427i | 1.94845 | − | 0.695613i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −4.62432 | + | 3.78415i | −0.147119 | + | 0.120390i | ||||
\(989\) | 6.89240 | + | 25.7228i | 0.219166 | + | 0.817938i | ||||
\(990\) | 1.33762 | + | 16.4561i | 0.0425122 | + | 0.523011i | ||||
\(991\) | 2.71965 | + | 4.71056i | 0.0863924 | + | 0.149636i | 0.905984 | − | 0.423313i | \(-0.139133\pi\) |
−0.819591 | + | 0.572949i | \(0.805799\pi\) | |||||||
\(992\) | 6.20948 | + | 14.4634i | 0.197151 | + | 0.459214i | ||||
\(993\) | 0.620663 | 0.0196961 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.17892 | + | 3.17892i | −0.100779 | + | 0.100779i | ||||
\(996\) | −6.66621 | − | 40.7349i | −0.211227 | − | 1.29074i | ||||
\(997\) | 3.12961 | − | 11.6799i | 0.0991157 | − | 0.369905i | −0.898496 | − | 0.438983i | \(-0.855339\pi\) |
0.997611 | + | 0.0690777i | \(0.0220057\pi\) | |||||||
\(998\) | −8.46926 | − | 7.19594i | −0.268090 | − | 0.227783i | ||||
\(999\) | 21.0950 | + | 12.1792i | 0.667415 | + | 0.385332i |
(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 | 784.2.x.m.373.6 | 24 | ||
7.2 | even | 3 | 784.2.m.h.197.1 | 12 | |||
7.3 | odd | 6 | 784.2.x.l.165.4 | 24 | |||
7.4 | even | 3 | inner | 784.2.x.m.165.4 | 24 | ||
7.5 | odd | 6 | 112.2.m.d.85.1 | yes | 12 | ||
7.6 | odd | 2 | 784.2.x.l.373.6 | 24 | |||
16.13 | even | 4 | inner | 784.2.x.m.765.4 | 24 | ||
28.19 | even | 6 | 448.2.m.d.113.2 | 12 | |||
56.5 | odd | 6 | 896.2.m.g.225.2 | 12 | |||
56.19 | even | 6 | 896.2.m.h.225.5 | 12 | |||
112.5 | odd | 12 | 896.2.m.g.673.2 | 12 | |||
112.13 | odd | 4 | 784.2.x.l.765.4 | 24 | |||
112.19 | even | 12 | 448.2.m.d.337.2 | 12 | |||
112.45 | odd | 12 | 784.2.x.l.557.6 | 24 | |||
112.61 | odd | 12 | 112.2.m.d.29.1 | ✓ | 12 | ||
112.75 | even | 12 | 896.2.m.h.673.5 | 12 | |||
112.93 | even | 12 | 784.2.m.h.589.1 | 12 | |||
112.109 | even | 12 | inner | 784.2.x.m.557.6 | 24 | ||
224.19 | even | 24 | 7168.2.a.bi.1.10 | 12 | |||
224.61 | odd | 24 | 7168.2.a.bj.1.10 | 12 | |||
224.131 | even | 24 | 7168.2.a.bi.1.3 | 12 | |||
224.173 | odd | 24 | 7168.2.a.bj.1.3 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
112.2.m.d.29.1 | ✓ | 12 | 112.61 | odd | 12 | ||
112.2.m.d.85.1 | yes | 12 | 7.5 | odd | 6 | ||
448.2.m.d.113.2 | 12 | 28.19 | even | 6 | |||
448.2.m.d.337.2 | 12 | 112.19 | even | 12 | |||
784.2.m.h.197.1 | 12 | 7.2 | even | 3 | |||
784.2.m.h.589.1 | 12 | 112.93 | even | 12 | |||
784.2.x.l.165.4 | 24 | 7.3 | odd | 6 | |||
784.2.x.l.373.6 | 24 | 7.6 | odd | 2 | |||
784.2.x.l.557.6 | 24 | 112.45 | odd | 12 | |||
784.2.x.l.765.4 | 24 | 112.13 | odd | 4 | |||
784.2.x.m.165.4 | 24 | 7.4 | even | 3 | inner | ||
784.2.x.m.373.6 | 24 | 1.1 | even | 1 | trivial | ||
784.2.x.m.557.6 | 24 | 112.109 | even | 12 | inner | ||
784.2.x.m.765.4 | 24 | 16.13 | even | 4 | inner | ||
896.2.m.g.225.2 | 12 | 56.5 | odd | 6 | |||
896.2.m.g.673.2 | 12 | 112.5 | odd | 12 | |||
896.2.m.h.225.5 | 12 | 56.19 | even | 6 | |||
896.2.m.h.673.5 | 12 | 112.75 | even | 12 | |||
7168.2.a.bi.1.3 | 12 | 224.131 | even | 24 | |||
7168.2.a.bi.1.10 | 12 | 224.19 | even | 24 | |||
7168.2.a.bj.1.3 | 12 | 224.173 | odd | 24 | |||
7168.2.a.bj.1.10 | 12 | 224.61 | odd | 24 |