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 | 165.4 | ||
Character | \(\chi\) | \(=\) | 784.165 |
Dual form | 784.2.x.l.765.4 |
$q$-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 \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(687\) | \(689\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.114575 | + | 1.40956i | 0.0810165 | + | 0.996713i | ||||
\(3\) | 0.509227 | + | 1.90046i | 0.294002 | + | 1.09723i | 0.942006 | + | 0.335595i | \(0.108937\pi\) |
−0.648004 | + | 0.761637i | \(0.724396\pi\) | |||||||
\(4\) | −1.97375 | + | 0.323001i | −0.986873 | + | 0.161500i | ||||
\(5\) | 0.792364 | − | 2.95714i | 0.354356 | − | 1.32247i | −0.526937 | − | 0.849904i | \(-0.676660\pi\) |
0.881293 | − | 0.472570i | \(-0.156674\pi\) | |||||||
\(6\) | −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 | ||||
\(10\) | 4.25907 | + | 0.778075i | 1.34684 | + | 0.246049i | ||||
\(11\) | 4.22870 | − | 1.13308i | 1.27500 | − | 0.341636i | 0.443057 | − | 0.896493i | \(-0.353894\pi\) |
0.831945 | + | 0.554858i | \(0.187227\pi\) | |||||||
\(12\) | −1.61893 | − | 3.58655i | −0.467346 | − | 1.03535i | ||||
\(13\) | 1.75410 | − | 1.75410i | 0.486499 | − | 0.486499i | −0.420701 | − | 0.907200i | \(-0.638216\pi\) |
0.907200 | + | 0.420701i | \(0.138216\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 6.02343 | 1.55524 | ||||||||
\(16\) | 3.79134 | − | 1.27504i | 0.947835 | − | 0.318760i | ||||
\(17\) | 2.60235 | − | 4.50740i | 0.631163 | − | 1.09321i | −0.356152 | − | 0.934428i | \(-0.615911\pi\) |
0.987314 | − | 0.158778i | \(-0.0507553\pi\) | |||||||
\(18\) | −0.700343 | − | 1.01343i | −0.165073 | − | 0.238867i | ||||
\(19\) | 1.16333 | + | 0.311715i | 0.266887 | + | 0.0715122i | 0.389781 | − | 0.920908i | \(-0.372551\pi\) |
−0.122894 | + | 0.992420i | \(0.539217\pi\) | |||||||
\(20\) | −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 | \(-0.888438\pi\) |
−0.172254 | + | 0.985053i | \(0.555105\pi\) | |||||||
\(24\) | 4.86998 | − | 2.69292i | 0.994081 | − | 0.549690i | ||||
\(25\) | −3.78672 | − | 2.18626i | −0.757344 | − | 0.437253i | ||||
\(26\) | 2.67349 | + | 2.27154i | 0.524314 | + | 0.445485i | ||||
\(27\) | 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 | \(0.944264\pi\) | |||||||
\(30\) | 0.690132 | + | 8.49041i | 0.126000 | + | 1.55013i | ||||
\(31\) | 1.39123 | − | 2.40969i | 0.249873 | − | 0.432793i | −0.713617 | − | 0.700536i | \(-0.752944\pi\) |
0.963490 | + | 0.267743i | \(0.0862778\pi\) | |||||||
\(32\) | 2.23165 | + | 5.19805i | 0.394503 | + | 0.918895i | ||||
\(33\) | 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 | ||||
\(37\) | 1.50511 | − | 5.61713i | 0.247438 | − | 0.923450i | −0.724705 | − | 0.689060i | \(-0.758024\pi\) |
0.972142 | − | 0.234391i | \(-0.0753095\pi\) | |||||||
\(38\) | −0.306093 | + | 1.67551i | −0.0496549 | + | 0.271804i | ||||
\(39\) | 4.22683 | + | 2.44036i | 0.676834 | + | 0.390770i | ||||
\(40\) | −8.65763 | − | 0.160040i | −1.36889 | − | 0.0253045i | ||||
\(41\) | − | 6.32956i | − | 0.988511i | −0.869317 | − | 0.494255i | \(-0.835441\pi\) | ||
0.869317 | − | 0.494255i | \(-0.164559\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.05937 | + | 3.05937i | 0.466549 | + | 0.466549i | 0.900795 | − | 0.434245i | \(-0.142985\pi\) |
−0.434245 | + | 0.900795i | \(0.642985\pi\) | |||||||
\(44\) | −7.98040 | + | 3.60228i | −1.20309 | + | 0.543064i | ||||
\(45\) | 0.690201 | + | 2.57587i | 0.102889 | + | 0.383988i | ||||
\(46\) | −4.94866 | − | 7.16092i | −0.729640 | − | 1.05582i | ||||
\(47\) | −1.80192 | − | 3.12101i | −0.262836 | − | 0.455246i | 0.704158 | − | 0.710043i | \(-0.251325\pi\) |
−0.966994 | + | 0.254797i | \(0.917991\pi\) | |||||||
\(48\) | 4.35382 | + | 6.55601i | 0.628420 | + | 0.946279i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 2.64782 | − | 5.58812i | 0.374458 | − | 0.790279i | ||||
\(51\) | 9.89133 | + | 2.65037i | 1.38506 | + | 0.371127i | ||||
\(52\) | −2.89557 | + | 4.02872i | −0.401543 | + | 0.558682i | ||||
\(53\) | −7.21798 | + | 1.93405i | −0.991466 | + | 0.265662i | −0.717866 | − | 0.696181i | \(-0.754881\pi\) |
−0.273600 | + | 0.961844i | \(0.588214\pi\) | |||||||
\(54\) | −3.83556 | + | 4.51427i | −0.521954 | + | 0.614314i | ||||
\(55\) | − | 13.4027i | − | 1.80722i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.36961i | 0.313862i | ||||||||
\(58\) | −9.51209 | − | 8.08198i | −1.24900 | − | 1.06122i | ||||
\(59\) | 9.74734 | − | 2.61179i | 1.26900 | − | 0.340026i | 0.439350 | − | 0.898316i | \(-0.355209\pi\) |
0.829646 | + | 0.558290i | \(0.188542\pi\) | |||||||
\(60\) | −11.8887 | + | 1.94557i | −1.53483 | + | 0.251172i | ||||
\(61\) | −1.42056 | − | 0.380638i | −0.181884 | − | 0.0487357i | 0.166727 | − | 0.986003i | \(-0.446680\pi\) |
−0.348611 | + | 0.937267i | \(0.613347\pi\) | |||||||
\(62\) | 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 | ||||
\(66\) | −10.0212 | + | 6.92530i | −1.23352 | + | 0.852446i | ||||
\(67\) | −0.353834 | − | 1.32053i | −0.0432277 | − | 0.161328i | 0.940938 | − | 0.338579i | \(-0.109946\pi\) |
−0.984166 | + | 0.177251i | \(0.943280\pi\) | |||||||
\(68\) | −3.68048 | + | 9.73703i | −0.446324 | + | 1.18079i | ||||
\(69\) | −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 | \(0.796386\pi\) | |||||||
\(72\) | 1.70964 | + | 1.77403i | 0.201483 | + | 0.209072i | ||||
\(73\) | 13.1391 | + | 7.58585i | 1.53781 | + | 0.887857i | 0.998966 | + | 0.0454536i | \(0.0144733\pi\) |
0.538847 | + | 0.842404i | \(0.318860\pi\) | |||||||
\(74\) | 8.09016 | + | 1.47796i | 0.940461 | + | 0.171810i | ||||
\(75\) | 2.22661 | − | 8.30982i | 0.257107 | − | 0.959535i | ||||
\(76\) | −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 | 0.989879 | − | 0.141915i | \(-0.0453259\pi\) |
−0.617841 | + | 0.786303i | \(0.711993\pi\) | |||||||
\(80\) | −0.766358 | − | 12.2218i | −0.0856815 | − | 1.36644i | ||||
\(81\) | −5.42722 | + | 9.40022i | −0.603025 | + | 1.04447i | ||||
\(82\) | 8.92192 | − | 0.725206i | 0.985261 | − | 0.0800856i | ||||
\(83\) | −7.41730 | + | 7.41730i | −0.814154 | + | 0.814154i | −0.985254 | − | 0.171100i | \(-0.945268\pi\) |
0.171100 | + | 0.985254i | \(0.445268\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −11.2670 | − | 11.2670i | −1.22208 | − | 1.22208i | ||||
\(86\) | −3.96185 | + | 4.66290i | −0.427218 | + | 0.502814i | ||||
\(87\) | −15.0388 | − | 8.68264i | −1.61232 | − | 0.930876i | ||||
\(88\) | −5.99200 | − | 10.8362i | −0.638749 | − | 1.15514i | ||||
\(89\) | −2.82449 | + | 1.63072i | −0.299396 | + | 0.172856i | −0.642171 | − | 0.766561i | \(-0.721966\pi\) |
0.342776 | + | 0.939417i | \(0.388633\pi\) | |||||||
\(90\) | −3.55177 | + | 1.26801i | −0.374390 | + | 0.133660i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 9.52678 | − | 7.79591i | 0.993236 | − | 0.812780i | ||||
\(93\) | 5.28798 | + | 1.41691i | 0.548337 | + | 0.146927i | ||||
\(94\) | 4.19281 | − | 2.89750i | 0.432455 | − | 0.298855i | ||||
\(95\) | 1.84357 | − | 3.19315i | 0.189146 | − | 0.327611i | ||||
\(96\) | −8.74229 | + | 6.88815i | −0.892256 | + | 0.703018i | ||||
\(97\) | −7.66352 | −0.778112 | −0.389056 | − | 0.921214i | \(-0.627199\pi\) | ||||
−0.389056 | + | 0.921214i | \(0.627199\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.69650 | + | 2.69650i | −0.271008 | + | 0.271008i | ||||
\(100\) | 8.18018 | + | 3.09201i | 0.818018 | + | 0.309201i | ||||
\(101\) | −13.5681 | + | 3.63555i | −1.35007 | + | 0.361751i | −0.860162 | − | 0.510021i | \(-0.829638\pi\) |
−0.489912 | + | 0.871772i | \(0.662971\pi\) | |||||||
\(102\) | −2.60258 | + | 14.2461i | −0.257694 | + | 1.41058i | ||||
\(103\) | 1.39602 | − | 0.805993i | 0.137554 | − | 0.0794169i | −0.429644 | − | 0.902998i | \(-0.641361\pi\) |
0.567198 | + | 0.823582i | \(0.308028\pi\) | |||||||
\(104\) | −6.01049 | − | 3.61990i | −0.589377 | − | 0.354960i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.55317 | − | 9.95262i | −0.345114 | − | 0.966684i | ||||
\(107\) | 2.90028 | − | 10.8240i | 0.280381 | − | 1.04640i | −0.671768 | − | 0.740762i | \(-0.734465\pi\) |
0.952149 | − | 0.305634i | \(-0.0988686\pi\) | |||||||
\(108\) | −6.80261 | − | 4.88925i | −0.654581 | − | 0.470468i | ||||
\(109\) | 2.08261 | + | 7.77240i | 0.199478 | + | 0.744461i | 0.991062 | + | 0.133401i | \(0.0425899\pi\) |
−0.791584 | + | 0.611060i | \(0.790743\pi\) | |||||||
\(110\) | 18.8920 | − | 1.53561i | 1.80128 | − | 0.146414i | ||||
\(111\) | 11.4416 | 1.08599 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 15.2609 | 1.43563 | 0.717813 | − | 0.696235i | \(-0.245143\pi\) | ||||
0.717813 | + | 0.696235i | \(0.245143\pi\) | |||||||
\(114\) | −3.34011 | + | 0.271497i | −0.312830 | + | 0.0254280i | ||||
\(115\) | 4.87699 | + | 18.2012i | 0.454782 | + | 1.69727i | ||||
\(116\) | 10.3022 | − | 14.3339i | 0.956538 | − | 1.33087i | ||||
\(117\) | −0.559263 | + | 2.08720i | −0.0517039 | + | 0.192962i | ||||
\(118\) | 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 | ||||
\(122\) | 0.373774 | − | 2.04598i | 0.0338399 | − | 0.185235i | ||||
\(123\) | 12.0291 | − | 3.22318i | 1.08463 | − | 0.290624i | ||||
\(124\) | −1.96761 | + | 5.20548i | −0.176697 | + | 0.467466i | ||||
\(125\) | 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 | \(0.525523\pi\) | |||||||
\(128\) | −6.08367 | − | 9.53881i | −0.537726 | − | 0.843120i | ||||
\(129\) | −4.25630 | + | 7.37213i | −0.374746 | + | 0.649080i | ||||
\(130\) | 8.83564 | − | 6.10600i | 0.774937 | − | 0.535532i | ||||
\(131\) | −12.6845 | − | 3.39881i | −1.10825 | − | 0.296956i | −0.342132 | − | 0.939652i | \(-0.611149\pi\) |
−0.766121 | + | 0.642696i | \(0.777816\pi\) | |||||||
\(132\) | −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 | ||||
\(136\) | −14.1467 | − | 4.07226i | −1.21307 | − | 0.349194i | ||||
\(137\) | 6.87323 | + | 3.96826i | 0.587220 | + | 0.339031i | 0.763997 | − | 0.645219i | \(-0.223234\pi\) |
−0.176778 | + | 0.984251i | \(0.556567\pi\) | |||||||
\(138\) | 11.0891 | − | 13.0513i | 0.943963 | − | 1.11100i | ||||
\(139\) | −2.06915 | − | 2.06915i | −0.175503 | − | 0.175503i | 0.613889 | − | 0.789392i | \(-0.289604\pi\) |
−0.789392 | + | 0.613889i | \(0.789604\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.01377 | − | 5.01377i | 0.422236 | − | 0.422236i | ||||
\(142\) | −14.1798 | + | 1.15258i | −1.18994 | + | 0.0967227i | ||||
\(143\) | 5.43003 | − | 9.40509i | 0.454082 | − | 0.786493i | ||||
\(144\) | −2.30473 | + | 2.61310i | −0.192061 | + | 0.217759i | ||||
\(145\) | 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 | ||||
\(149\) | 3.35096 | − | 12.5060i | 0.274521 | − | 1.02453i | −0.681640 | − | 0.731688i | \(-0.738733\pi\) |
0.956161 | − | 0.292840i | \(-0.0946004\pi\) | |||||||
\(150\) | 11.9683 | + | 2.18646i | 0.977211 | + | 0.178523i | ||||
\(151\) | 2.42743 | + | 1.40148i | 0.197541 | + | 0.114051i | 0.595508 | − | 0.803349i | \(-0.296951\pi\) |
−0.397967 | + | 0.917400i | \(0.630284\pi\) | |||||||
\(152\) | 0.0629594 | − | 3.40590i | 0.00510668 | − | 0.276255i | ||||
\(153\) | 4.53364i | 0.366523i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.02343 | − | 6.02343i | −0.483813 | − | 0.483813i | ||||
\(156\) | −9.13092 | − | 3.45138i | −0.731059 | − | 0.276332i | ||||
\(157\) | 0.350944 | + | 1.30974i | 0.0280084 | + | 0.104529i | 0.978515 | − | 0.206176i | \(-0.0661018\pi\) |
−0.950507 | + | 0.310704i | \(0.899435\pi\) | |||||||
\(158\) | −7.69434 | + | 5.31729i | −0.612129 | + | 0.423021i | ||||
\(159\) | −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 | ||||
\(163\) | −17.6498 | − | 4.72925i | −1.38244 | − | 0.370423i | −0.510432 | − | 0.859918i | \(-0.670515\pi\) |
−0.872006 | + | 0.489495i | \(0.837181\pi\) | |||||||
\(164\) | 2.04445 | + | 12.4929i | 0.159645 | + | 0.975534i | ||||
\(165\) | 25.4713 | − | 6.82501i | 1.98294 | − | 0.531326i | ||||
\(166\) | −11.3050 | − | 9.60533i | −0.877438 | − | 0.745518i | ||||
\(167\) | 1.96111i | 0.151755i | 0.997117 | + | 0.0758775i | \(0.0241758\pi\) | ||||
−0.997117 | + | 0.0758775i | \(0.975824\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.84629i | 0.526637i | ||||||||
\(170\) | 14.5907 | − | 17.1725i | 1.11905 | − | 1.31707i | ||||
\(171\) | −1.01334 | + | 0.271524i | −0.0774922 | + | 0.0207640i | ||||
\(172\) | −7.02659 | − | 5.05024i | −0.535773 | − | 0.385077i | ||||
\(173\) | 5.65589 | + | 1.51549i | 0.430009 | + | 0.115221i | 0.467330 | − | 0.884083i | \(-0.345216\pi\) |
−0.0373213 | + | 0.999303i | \(0.511883\pi\) | |||||||
\(174\) | 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 | ||||
\(178\) | −2.62222 | − | 3.79447i | −0.196544 | − | 0.284407i | ||||
\(179\) | −3.48281 | − | 12.9980i | −0.260318 | − | 0.971519i | −0.965054 | − | 0.262050i | \(-0.915602\pi\) |
0.704737 | − | 0.709469i | \(-0.251065\pi\) | |||||||
\(180\) | −2.19429 | − | 4.86117i | −0.163553 | − | 0.362330i | ||||
\(181\) | 7.60424 | + | 7.60424i | 0.565219 | + | 0.565219i | 0.930785 | − | 0.365566i | \(-0.119125\pi\) |
−0.365566 | + | 0.930785i | \(0.619125\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 2.89355i | − | 0.213897i | ||||||
\(184\) | 12.0804 | + | 12.5354i | 0.890577 | + | 0.924122i | ||||
\(185\) | −15.4181 | − | 8.90162i | −1.13356 | − | 0.654460i | ||||
\(186\) | −1.39136 | + | 7.61608i | −0.102019 | + | 0.558438i | ||||
\(187\) | 5.89733 | − | 22.0091i | 0.431256 | − | 1.60947i | ||||
\(188\) | 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 | 0.951939 | + | 0.306289i | \(0.0990873\pi\) |
−0.210715 | + | 0.977547i | \(0.567579\pi\) | |||||||
\(192\) | −10.7109 | − | 11.5336i | −0.772995 | − | 0.832367i | ||||
\(193\) | −6.35776 | + | 11.0120i | −0.457642 | + | 0.792659i | −0.998836 | − | 0.0482388i | \(-0.984639\pi\) |
0.541194 | + | 0.840898i | \(0.317972\pi\) | |||||||
\(194\) | −0.878044 | − | 10.8022i | −0.0630399 | − | 0.775554i | ||||
\(195\) | 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 | \(0.974423\pi\) | |||||||
\(198\) | −4.10984 | − | 3.49194i | −0.292073 | − | 0.248161i | ||||
\(199\) | −1.27174 | − | 0.734237i | −0.0901510 | − | 0.0520487i | 0.454247 | − | 0.890876i | \(-0.349908\pi\) |
−0.544398 | + | 0.838827i | \(0.683242\pi\) | |||||||
\(200\) | −3.42115 | + | 11.8848i | −0.241912 | + | 0.840380i | ||||
\(201\) | 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 | ||||
\(205\) | −18.7174 | − | 5.01531i | −1.30728 | − | 0.350284i | ||||
\(206\) | 1.29605 | + | 1.87544i | 0.0903000 | + | 0.130668i | ||||
\(207\) | 2.68070 | − | 4.64312i | 0.186322 | − | 0.322719i | ||||
\(208\) | 4.41383 | − | 8.88693i | 0.306044 | − | 0.616198i | ||||
\(209\) | 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 | \(0.241713\pi\) | |||||||
\(212\) | 13.6218 | − | 6.14874i | 0.935546 | − | 0.422297i | ||||
\(213\) | −19.1180 | + | 5.12266i | −1.30995 | + | 0.350999i | ||||
\(214\) | 15.5894 | + | 2.84798i | 1.06567 | + | 0.194684i | ||||
\(215\) | 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 | ||||
\(219\) | −7.72585 | + | 28.8333i | −0.522064 | + | 1.94837i | ||||
\(220\) | 4.32908 | + | 26.4535i | 0.291866 | + | 1.78349i | ||||
\(221\) | −3.34165 | − | 12.4712i | −0.224784 | − | 0.838903i | ||||
\(222\) | 1.31091 | + | 16.1276i | 0.0879828 | + | 1.08242i | ||||
\(223\) | −7.83775 | −0.524855 | −0.262427 | − | 0.964952i | \(-0.584523\pi\) | ||||
−0.262427 | + | 0.964952i | \(0.584523\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.80876 | 0.253917 | ||||||||
\(226\) | 1.74851 | + | 21.5113i | 0.116309 | + | 1.43091i | ||||
\(227\) | 0.0906182 | + | 0.338192i | 0.00601454 | + | 0.0224466i | 0.968868 | − | 0.247578i | \(-0.0796347\pi\) |
−0.962853 | + | 0.270025i | \(0.912968\pi\) | |||||||
\(228\) | −0.765384 | − | 4.67700i | −0.0506888 | − | 0.309742i | ||||
\(229\) | −5.71108 | + | 21.3140i | −0.377399 | + | 1.40847i | 0.472409 | + | 0.881379i | \(0.343384\pi\) |
−0.849808 | + | 0.527092i | \(0.823282\pi\) | |||||||
\(230\) | −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 | \(-0.767556\pi\) |
0.205179 | + | 0.978724i | \(0.434222\pi\) | |||||||
\(234\) | −3.00612 | − | 0.549178i | −0.196516 | − | 0.0359009i | ||||
\(235\) | −10.6570 | + | 2.85554i | −0.695188 | + | 0.186275i | ||||
\(236\) | −18.3952 | + | 8.30341i | −1.19742 | + | 0.540506i | ||||
\(237\) | −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 | \(0.291349\pi\) | |||||||
\(240\) | 22.8369 | − | 7.68012i | 1.47411 | − | 0.495750i | ||||
\(241\) | 3.19914 | − | 5.54108i | 0.206075 | − | 0.356932i | −0.744400 | − | 0.667734i | \(-0.767264\pi\) |
0.950475 | + | 0.310802i | \(0.100598\pi\) | |||||||
\(242\) | 6.56537 | + | 9.50036i | 0.422038 | + | 0.610706i | ||||
\(243\) | −8.49058 | − | 2.27504i | −0.544671 | − | 0.145944i | ||||
\(244\) | 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 | ||||
\(248\) | −7.56290 | − | 2.17706i | −0.480245 | − | 0.138243i | ||||
\(249\) | −17.8734 | − | 10.3192i | −1.13268 | − | 0.653953i | ||||
\(250\) | 2.07030 | + | 1.75904i | 0.130937 | + | 0.111251i | ||||
\(251\) | −2.93159 | − | 2.93159i | −0.185040 | − | 0.185040i | 0.608508 | − | 0.793548i | \(-0.291768\pi\) |
−0.793548 | + | 0.608508i | \(0.791768\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −19.0536 | + | 19.0536i | −1.19789 | + | 1.19789i | ||||
\(254\) | −0.206840 | − | 2.54467i | −0.0129783 | − | 0.159667i | ||||
\(255\) | 15.6751 | − | 27.1500i | 0.981611 | − | 1.70020i | ||||
\(256\) | 12.7485 | − | 9.66824i | 0.796784 | − | 0.604265i | ||||
\(257\) | −14.4838 | − | 25.0867i | −0.903475 | − | 1.56487i | −0.822951 | − | 0.568113i | \(-0.807674\pi\) |
−0.0805246 | − | 0.996753i | \(-0.525660\pi\) | |||||||
\(258\) | −10.8792 | − | 5.15487i | −0.677306 | − | 0.320928i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 9.61914 | + | 11.7548i | 0.596554 | + | 0.729002i | ||||
\(261\) | 1.98982 | − | 7.42611i | 0.123167 | − | 0.459665i | ||||
\(262\) | 3.33752 | − | 18.2691i | 0.206193 | − | 1.12867i | ||||
\(263\) | 0.298299 | + | 0.172223i | 0.0183939 | + | 0.0106197i | 0.509169 | − | 0.860667i | \(-0.329953\pi\) |
−0.490775 | + | 0.871286i | \(0.663286\pi\) | |||||||
\(264\) | 17.5424 | − | 16.9056i | 1.07966 | − | 1.04047i | ||||
\(265\) | 22.8771i | 1.40533i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.53743 | − | 4.53743i | −0.277686 | − | 0.277686i | ||||
\(268\) | 1.12491 | + | 2.49210i | 0.0687148 | + | 0.152229i | ||||
\(269\) | −3.61587 | − | 13.4946i | −0.220463 | − | 0.822781i | −0.984171 | − | 0.177219i | \(-0.943290\pi\) |
0.763708 | − | 0.645562i | \(-0.223377\pi\) | |||||||
\(270\) | 10.3102 | + | 14.9192i | 0.627457 | + | 0.907956i | ||||
\(271\) | 6.24843 | + | 10.8226i | 0.379565 | + | 0.657426i | 0.990999 | − | 0.133869i | \(-0.0427403\pi\) |
−0.611434 | + | 0.791296i | \(0.709407\pi\) | |||||||
\(272\) | 4.11927 | − | 20.4072i | 0.249767 | − | 1.23737i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.80602 | + | 10.1429i | −0.290342 | + | 0.612756i | ||||
\(275\) | −18.4901 | − | 4.95441i | −1.11500 | − | 0.298762i | ||||
\(276\) | 19.6671 | + | 14.1354i | 1.18382 | + | 0.850851i | ||||
\(277\) | 8.19541 | − | 2.19595i | 0.492415 | − | 0.131942i | −0.00406280 | − | 0.999992i | \(-0.501293\pi\) |
0.496477 | + | 0.868050i | \(0.334627\pi\) | |||||||
\(278\) | 2.67953 | − | 3.15367i | 0.160708 | − | 0.189145i | ||||
\(279\) | 2.42372i | 0.145104i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.56494i | 0.570596i | 0.958439 | + | 0.285298i | \(0.0920926\pi\) | ||||
−0.958439 | + | 0.285298i | \(0.907907\pi\) | |||||||
\(282\) | 7.64169 | + | 6.49279i | 0.455056 | + | 0.386640i | ||||
\(283\) | −15.9658 | + | 4.27803i | −0.949070 | + | 0.254303i | −0.699968 | − | 0.714175i | \(-0.746802\pi\) |
−0.249102 | + | 0.968477i | \(0.580136\pi\) | |||||||
\(284\) | −3.24928 | − | 19.8553i | −0.192810 | − | 1.17819i | ||||
\(285\) | 7.00726 | + | 1.87759i | 0.415074 | + | 0.111219i | ||||
\(286\) | 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 | ||||
\(290\) | −31.4366 | + | 21.7247i | −1.84602 | + | 1.27572i | ||||
\(291\) | −3.90247 | − | 14.5642i | −0.228767 | − | 0.853769i | ||||
\(292\) | −28.3834 | − | 10.7286i | −1.66102 | − | 0.627845i | ||||
\(293\) | −15.2913 | − | 15.2913i | −0.893328 | − | 0.893328i | 0.101507 | − | 0.994835i | \(-0.467634\pi\) |
−0.994835 | + | 0.101507i | \(0.967634\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 30.8938i | − | 1.79870i | ||||||
\(296\) | −16.4453 | − | 0.303998i | −0.955863 | − | 0.0176695i | ||||
\(297\) | 15.8808 | + | 9.16877i | 0.921496 | + | 0.532026i | ||||
\(298\) | 18.0119 | + | 3.29053i | 1.04340 | + | 0.190615i | ||||
\(299\) | −3.95178 | + | 14.7482i | −0.228537 | + | 0.852913i | ||||
\(300\) | −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 | ||||
\(304\) | 4.80805 | − | 0.301484i | 0.275760 | − | 0.0172913i | ||||
\(305\) | −2.25120 | + | 3.89919i | −0.128903 | + | 0.223267i | ||||
\(306\) | −6.39046 | + | 0.519440i | −0.365318 | + | 0.0296944i | ||||
\(307\) | −4.16259 | + | 4.16259i | −0.237571 | + | 0.237571i | −0.815844 | − | 0.578272i | \(-0.803727\pi\) |
0.578272 | + | 0.815844i | \(0.303727\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.24265 | + | 2.24265i | 0.127580 | + | 0.127580i | ||||
\(310\) | 7.80028 | − | 9.18054i | 0.443026 | − | 0.521420i | ||||
\(311\) | 0.695092 | + | 0.401312i | 0.0394151 | + | 0.0227563i | 0.519578 | − | 0.854423i | \(-0.326089\pi\) |
−0.480163 | + | 0.877179i | \(0.659422\pi\) | |||||||
\(312\) | 3.81877 | − | 13.2661i | 0.216196 | − | 0.751043i | ||||
\(313\) | −15.3533 | + | 8.86423i | −0.867819 | + | 0.501036i | −0.866623 | − | 0.498964i | \(-0.833714\pi\) |
−0.00119626 | + | 0.999999i | \(0.500381\pi\) | |||||||
\(314\) | −1.80596 | + | 0.644742i | −0.101916 | + | 0.0363849i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.37664 | − | 10.2364i | −0.471223 | − | 0.575845i | ||||
\(317\) | −14.1644 | − | 3.79534i | −0.795552 | − | 0.213168i | −0.161922 | − | 0.986804i | \(-0.551769\pi\) |
−0.633630 | + | 0.773636i | \(0.718436\pi\) | |||||||
\(318\) | 17.1052 | − | 11.8208i | 0.959212 | − | 0.662878i | ||||
\(319\) | −19.3197 | + | 33.4627i | −1.08169 | + | 1.87355i | ||||
\(320\) | 5.46025 | + | 23.8752i | 0.305238 | + | 1.33467i | ||||
\(321\) | 22.0475 | 1.23057 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.43243 | − | 4.43243i | 0.246627 | − | 0.246627i | ||||
\(324\) | 7.67567 | − | 20.3066i | 0.426426 | − | 1.12815i | ||||
\(325\) | −10.4772 | + | 2.80735i | −0.581170 | + | 0.155724i | ||||
\(326\) | 4.64396 | − | 25.4204i | 0.257205 | − | 1.40790i | ||||
\(327\) | −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 | ||||
\(331\) | −0.0816464 | + | 0.304708i | −0.00448769 | + | 0.0167483i | −0.968133 | − | 0.250435i | \(-0.919426\pi\) |
0.963646 | + | 0.267183i | \(0.0860930\pi\) | |||||||
\(332\) | 12.2441 | − | 17.0356i | 0.671980 | − | 0.934952i | ||||
\(333\) | 1.31105 | + | 4.89289i | 0.0718449 | + | 0.268129i | ||||
\(334\) | −2.76431 | + | 0.224693i | −0.151256 | + | 0.0122947i | ||||
\(335\) | −4.18535 | −0.228670 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −26.7633 | −1.45789 | −0.728944 | − | 0.684573i | \(-0.759989\pi\) | ||||
−0.728944 | + | 0.684573i | \(0.759989\pi\) | |||||||
\(338\) | −9.65028 | + | 0.784411i | −0.524906 | + | 0.0426663i | ||||
\(339\) | 7.77128 | + | 29.0028i | 0.422078 | + | 1.57522i | ||||
\(340\) | 25.8775 | + | 18.5990i | 1.40340 | + | 1.00867i | ||||
\(341\) | 3.15275 | − | 11.7662i | 0.170731 | − | 0.637178i | ||||
\(342\) | −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 | ||||
\(346\) | −1.48816 | + | 8.14597i | −0.0800040 | + | 0.437930i | ||||
\(347\) | −33.6147 | + | 9.00704i | −1.80453 | + | 0.483523i | −0.994671 | − | 0.103098i | \(-0.967124\pi\) |
−0.809861 | + | 0.586621i | \(0.800458\pi\) | |||||||
\(348\) | 32.4872 | + | 12.2798i | 1.74150 | + | 0.658265i | ||||
\(349\) | 13.7818 | − | 13.7818i | 0.737725 | − | 0.737725i | −0.234412 | − | 0.972137i | \(-0.575317\pi\) |
0.972137 | + | 0.234412i | \(0.0753166\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 10.3907 | 0.554616 | ||||||||
\(352\) | 15.3268 | + | 19.4524i | 0.816920 | + | 1.03682i | ||||
\(353\) | 13.0221 | − | 22.5550i | 0.693099 | − | 1.20048i | −0.277718 | − | 0.960663i | \(-0.589578\pi\) |
0.970817 | − | 0.239820i | \(-0.0770884\pi\) | |||||||
\(354\) | −23.0993 | + | 15.9631i | −1.22771 | + | 0.848430i | ||||
\(355\) | 29.7479 | + | 7.97093i | 1.57886 | + | 0.423053i | ||||
\(356\) | 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 | \(-0.479318\pi\) |
0.896663 | + | 0.442714i | \(0.145984\pi\) | |||||||
\(360\) | 6.60072 | − | 3.64996i | 0.347889 | − | 0.192370i | ||||
\(361\) | −15.1983 | − | 8.77474i | −0.799911 | − | 0.461829i | ||||
\(362\) | −9.84742 | + | 11.5899i | −0.517569 | + | 0.609153i | ||||
\(363\) | 11.3606 | + | 11.3606i | 0.596274 | + | 0.596274i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 32.8434 | − | 32.8434i | 1.71910 | − | 1.71910i | ||||
\(366\) | 4.07865 | − | 0.331528i | 0.213194 | − | 0.0173292i | ||||
\(367\) | −3.70670 | + | 6.42020i | −0.193488 | + | 0.335132i | −0.946404 | − | 0.322986i | \(-0.895313\pi\) |
0.752916 | + | 0.658117i | \(0.228647\pi\) | |||||||
\(368\) | −16.2854 | + | 18.4643i | −0.848933 | + | 0.962518i | ||||
\(369\) | 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 | ||||
\(373\) | 1.37367 | − | 5.12662i | 0.0711261 | − | 0.265446i | −0.921201 | − | 0.389087i | \(-0.872790\pi\) |
0.992327 | + | 0.123641i | \(0.0394571\pi\) | |||||||
\(374\) | 31.6990 | + | 5.79098i | 1.63912 | + | 0.299445i | ||||
\(375\) | 3.27318 | + | 1.88977i | 0.169026 | + | 0.0975873i | ||||
\(376\) | −7.33964 | + | 7.07322i | −0.378513 | + | 0.364773i | ||||
\(377\) | 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 | \(0.510129\pi\) | |||||||
\(380\) | −2.60734 | + | 6.89795i | −0.133754 | + | 0.353857i | ||||
\(381\) | −0.919300 | − | 3.43087i | −0.0470972 | − | 0.175769i | ||||
\(382\) | −23.8362 | + | 16.4723i | −1.21956 | + | 0.842799i | ||||
\(383\) | 2.47310 | + | 4.28353i | 0.126369 | + | 0.218878i | 0.922267 | − | 0.386553i | \(-0.126334\pi\) |
−0.795898 | + | 0.605431i | \(0.793001\pi\) | |||||||
\(384\) | 15.0302 | − | 16.4192i | 0.767005 | − | 0.837889i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −16.2505 | − | 7.69999i | −0.827130 | − | 0.391919i | ||||
\(387\) | −3.64034 | − | 0.975426i | −0.185049 | − | 0.0495837i | ||||
\(388\) | 15.1258 | − | 2.47532i | 0.767898 | − | 0.125665i | ||||
\(389\) | −19.1608 | + | 5.13412i | −0.971491 | + | 0.260310i | −0.709457 | − | 0.704748i | \(-0.751060\pi\) |
−0.262034 | + | 0.965059i | \(0.584393\pi\) | |||||||
\(390\) | 16.1036 | + | 13.6824i | 0.815436 | + | 0.692838i | ||||
\(391\) | 32.0349i | 1.62007i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 25.8372i | − | 1.30332i | ||||||
\(394\) | 16.6585 | − | 19.6062i | 0.839244 | − | 0.987748i | ||||
\(395\) | 19.5570 | − | 5.24028i | 0.984020 | − | 0.263667i | ||||
\(396\) | 4.45123 | − | 6.19317i | 0.223683 | − | 0.311218i | ||||
\(397\) | 0.0872772 | + | 0.0233859i | 0.00438032 | + | 0.00117370i | 0.261009 | − | 0.965336i | \(-0.415945\pi\) |
−0.256628 | + | 0.966510i | \(0.582612\pi\) | |||||||
\(398\) | 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 | 0.986628 | + | 0.162988i | \(0.0521133\pi\) |
−0.352162 | + | 0.935939i | \(0.614553\pi\) | |||||||
\(402\) | 2.16261 | + | 3.12939i | 0.107861 | + | 0.156080i | ||||
\(403\) | −1.78647 | − | 6.66719i | −0.0889903 | − | 0.332116i | ||||
\(404\) | 25.6056 | − | 11.5582i | 1.27393 | − | 0.575040i | ||||
\(405\) | 23.4975 | + | 23.4975i | 1.16760 | + | 1.16760i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 25.4586i | − | 1.26194i | ||||||
\(408\) | 0.535316 | − | 28.9589i | 0.0265021 | − | 1.43368i | ||||
\(409\) | 19.4037 | + | 11.2027i | 0.959450 | + | 0.553939i | 0.896004 | − | 0.444047i | \(-0.146458\pi\) |
0.0634462 | + | 0.997985i | \(0.479791\pi\) | |||||||
\(410\) | 4.92487 | − | 26.9580i | 0.243222 | − | 1.33136i | ||||
\(411\) | −4.04149 | + | 15.0831i | −0.199352 | + | 0.743992i | ||||
\(412\) | −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 | ||||
\(416\) | 13.0324 | + | 5.20337i | 0.638967 | + | 0.255116i | ||||
\(417\) | 2.87867 | − | 4.98601i | 0.140969 | − | 0.244166i | ||||
\(418\) | 0.604106 | + | 7.43207i | 0.0295478 | + | 0.363514i | ||||
\(419\) | −24.2758 | + | 24.2758i | −1.18595 | + | 1.18595i | −0.207775 | + | 0.978177i | \(0.566622\pi\) |
−0.978177 | + | 0.207775i | \(0.933378\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.0270 | + | 16.0270i | 0.781108 | + | 0.781108i | 0.980018 | − | 0.198910i | \(-0.0637400\pi\) |
−0.198910 | + | 0.980018i | \(0.563740\pi\) | |||||||
\(422\) | 0.815059 | + | 0.692518i | 0.0396765 | + | 0.0337112i | ||||
\(423\) | 2.71861 | + | 1.56959i | 0.132183 | + | 0.0763160i | ||||
\(424\) | 10.2278 | + | 18.4963i | 0.496704 | + | 0.898258i | ||||
\(425\) | −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 | ||||
\(429\) | 20.6391 | + | 5.53024i | 0.996466 | + | 0.267002i | ||||
\(430\) | 10.6496 | + | 15.4105i | 0.513571 | + | 0.743159i | ||||
\(431\) | 15.8307 | − | 27.4196i | 0.762540 | − | 1.32076i | −0.178998 | − | 0.983849i | \(-0.557285\pi\) |
0.941538 | − | 0.336908i | \(-0.109381\pi\) | |||||||
\(432\) | 15.0058 | + | 7.45289i | 0.721969 | + | 0.358577i | ||||
\(433\) | −11.6823 | −0.561413 | −0.280707 | − | 0.959794i | \(-0.590569\pi\) | ||||
−0.280707 | + | 0.959794i | \(0.590569\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −37.5920 | + | 37.5920i | −1.80240 | + | 1.80240i | ||||
\(436\) | −6.62103 | − | 14.6681i | −0.317090 | − | 0.702473i | ||||
\(437\) | −7.16032 | + | 1.91860i | −0.342525 | + | 0.0917792i | ||||
\(438\) | −41.5275 | − | 7.58652i | −1.98426 | − | 0.362498i | ||||
\(439\) | 11.3637 | − | 6.56086i | 0.542362 | − | 0.313133i | −0.203674 | − | 0.979039i | \(-0.565288\pi\) |
0.746036 | + | 0.665906i | \(0.231955\pi\) | |||||||
\(440\) | −36.7919 | + | 9.13301i | −1.75399 | + | 0.435399i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 17.1961 | − | 6.13915i | 0.817935 | − | 0.292010i | ||||
\(443\) | −5.93692 | + | 22.1569i | −0.282071 | + | 1.05271i | 0.668881 | + | 0.743369i | \(0.266773\pi\) |
−0.950953 | + | 0.309336i | \(0.899893\pi\) | |||||||
\(444\) | −22.5828 | + | 3.69564i | −1.07173 | + | 0.175387i | ||||
\(445\) | 2.58425 | + | 9.64455i | 0.122505 | + | 0.457196i | ||||
\(446\) | −0.898007 | − | 11.0478i | −0.0425219 | − | 0.523129i | ||||
\(447\) | 25.4735 | 1.20485 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −15.6396 | −0.738077 | −0.369038 | − | 0.929414i | \(-0.620313\pi\) | ||||
−0.369038 | + | 0.929414i | \(0.620313\pi\) | |||||||
\(450\) | 0.436387 | + | 5.36870i | 0.0205715 | + | 0.253083i | ||||
\(451\) | −7.17188 | − | 26.7658i | −0.337711 | − | 1.26035i | ||||
\(452\) | −30.1212 | + | 4.92929i | −1.41678 | + | 0.231854i | ||||
\(453\) | −1.42734 | + | 5.32691i | −0.0670623 | + | 0.250280i | ||||
\(454\) | −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 | \(-0.574322\pi\) |
0.726840 | + | 0.686807i | \(0.240988\pi\) | |||||||
\(458\) | −30.6979 | − | 5.60809i | −1.43442 | − | 0.262049i | ||||
\(459\) | 21.0580 | − | 5.64247i | 0.982903 | − | 0.263368i | ||||
\(460\) | −15.5049 | − | 34.3492i | −0.722922 | − | 1.60154i | ||||
\(461\) | −13.4658 | + | 13.4658i | −0.627163 | + | 0.627163i | −0.947353 | − | 0.320191i | \(-0.896253\pi\) |
0.320191 | + | 0.947353i | \(0.396253\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −24.7807 | −1.15166 | −0.575829 | − | 0.817570i | \(-0.695321\pi\) | ||||
−0.575829 | + | 0.817570i | \(0.695321\pi\) | |||||||
\(464\) | −15.7041 | + | 31.6191i | −0.729045 | + | 1.46788i | ||||
\(465\) | 8.38000 | − | 14.5146i | 0.388613 | − | 0.673098i | ||||
\(466\) | −7.65007 | − | 11.0700i | −0.354383 | − | 0.512806i | ||||
\(467\) | −31.6485 | − | 8.48020i | −1.46452 | − | 0.392417i | −0.563472 | − | 0.826135i | \(-0.690535\pi\) |
−0.901048 | + | 0.433718i | \(0.857201\pi\) | |||||||
\(468\) | 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 | ||||
\(472\) | −13.8118 | − | 24.9778i | −0.635740 | − | 1.14970i | ||||
\(473\) | 16.4037 | + | 9.47066i | 0.754242 | + | 0.435462i | ||||
\(474\) | −14.0235 | − | 11.9151i | −0.644119 | − | 0.547278i | ||||
\(475\) | −3.72373 | − | 3.72373i | −0.170857 | − | 0.170857i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.60265 | − | 4.60265i | 0.210741 | − | 0.210741i | ||||
\(478\) | 2.15938 | + | 26.5659i | 0.0987676 | + | 1.21510i | ||||
\(479\) | −17.6824 | + | 30.6268i | −0.807930 | + | 1.39938i | 0.106365 | + | 0.994327i | \(0.466079\pi\) |
−0.914295 | + | 0.405049i | \(0.867254\pi\) | |||||||
\(480\) | 13.4422 | + | 31.3101i | 0.613548 | + | 1.42910i | ||||
\(481\) | −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 | ||||
\(485\) | −6.07229 | + | 22.6621i | −0.275729 | + | 1.02903i | ||||
\(486\) | 2.23402 | − | 12.2287i | 0.101337 | − | 0.554705i | ||||
\(487\) | 14.4850 | + | 8.36292i | 0.656378 | + | 0.378960i | 0.790896 | − | 0.611951i | \(-0.209615\pi\) |
−0.134517 | + | 0.990911i | \(0.542948\pi\) | |||||||
\(488\) | −0.0768804 | + | 4.15898i | −0.00348021 | + | 0.188268i | ||||
\(489\) | − | 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 | \(0.689374\pi\) | |||||||
\(492\) | −22.7012 | + | 10.2471i | −1.02345 | + | 0.461977i | ||||
\(493\) | 11.8894 | + | 44.3717i | 0.535470 | + | 1.99840i | ||||
\(494\) | 2.40209 | + | 3.47593i | 0.108075 | + | 0.156389i | ||||
\(495\) | 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 | ||||
\(499\) | 7.59066 | + | 2.03391i | 0.339805 | + | 0.0910504i | 0.424686 | − | 0.905341i | \(-0.360384\pi\) |
−0.0848814 | + | 0.996391i | \(0.527051\pi\) | |||||||
\(500\) | −2.24227 | + | 3.11976i | −0.100278 | + | 0.139520i | ||||
\(501\) | −3.72701 | + | 0.998649i | −0.166510 | + | 0.0446164i | ||||
\(502\) | 3.79638 | − | 4.46815i | 0.169441 | − | 0.199423i | ||||
\(503\) | 6.99765i | 0.312010i | 0.987756 | + | 0.156005i | \(0.0498616\pi\) | ||||
−0.987756 | + | 0.156005i | \(0.950138\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 43.0034i | 1.91363i | ||||||||
\(506\) | −29.0403 | − | 24.6742i | −1.29100 | − | 1.09690i | ||||
\(507\) | −13.0111 | + | 3.48631i | −0.577843 | + | 0.154833i | ||||
\(508\) | 3.56317 | − | 0.583108i | 0.158090 | − | 0.0258712i | ||||
\(509\) | −4.88676 | − | 1.30940i | −0.216602 | − | 0.0580383i | 0.148886 | − | 0.988854i | \(-0.452431\pi\) |
−0.365488 | + | 0.930816i | \(0.619098\pi\) | |||||||
\(510\) | 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 | ||||
\(514\) | 33.7018 | − | 23.2902i | 1.48652 | − | 1.02729i | ||||
\(515\) | −1.27728 | − | 4.76687i | −0.0562837 | − | 0.210053i | ||||
\(516\) | 6.01965 | − | 15.9255i | 0.265000 | − | 0.701080i | ||||
\(517\) | −11.1561 | − | 11.1561i | −0.490645 | − | 0.490645i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 11.5205i | 0.505695i | ||||||||
\(520\) | −15.4671 | + | 14.9056i | −0.678275 | + | 0.653654i | ||||
\(521\) | 15.0383 | + | 8.68234i | 0.658838 | + | 0.380380i | 0.791834 | − | 0.610736i | \(-0.209126\pi\) |
−0.132996 | + | 0.991117i | \(0.542460\pi\) | |||||||
\(522\) | 10.6956 | + | 1.95394i | 0.468132 | + | 0.0855215i | ||||
\(523\) | −9.49950 | + | 35.4526i | −0.415384 | + | 1.55023i | 0.368681 | + | 0.929556i | \(0.379810\pi\) |
−0.784065 | + | 0.620679i | \(0.786857\pi\) | |||||||
\(524\) | 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 | ||||
\(528\) | 25.8395 | + | 22.7902i | 1.12452 | + | 0.991817i | ||||
\(529\) | 7.44198 | − | 12.8899i | 0.323564 | − | 0.560430i | ||||
\(530\) | −32.2467 | + | 2.62113i | −1.40071 | + | 0.113855i | ||||
\(531\) | −6.21554 | + | 6.21554i | −0.269731 | + | 0.269731i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −11.1027 | − | 11.1027i | −0.480909 | − | 0.480909i | ||||
\(534\) | 5.87593 | − | 6.91568i | 0.254276 | − | 0.299271i | ||||
\(535\) | −29.7100 | − | 17.1531i | −1.28448 | − | 0.741593i | ||||
\(536\) | −3.38388 | + | 1.87116i | −0.146162 | + | 0.0808220i | ||||
\(537\) | 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 | ||||
\(541\) | 15.4749 | + | 4.14648i | 0.665317 | + | 0.178271i | 0.575644 | − | 0.817700i | \(-0.304751\pi\) |
0.0896726 | + | 0.995971i | \(0.471418\pi\) | |||||||
\(542\) | −14.5392 | + | 10.0476i | −0.624514 | + | 0.431580i | ||||
\(543\) | −10.5793 | + | 18.3239i | −0.454001 | + | 0.786352i | ||||
\(544\) | 29.2372 | + | 3.46823i | 1.25354 | + | 0.148699i | ||||
\(545\) | 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 | \(0.356307\pi\) | |||||||
\(548\) | −14.8478 | − | 5.61228i | −0.634265 | − | 0.239745i | ||||
\(549\) | 1.23740 | − | 0.331561i | 0.0528111 | − | 0.0141507i | ||||
\(550\) | 4.86507 | − | 26.6307i | 0.207447 | − | 1.13554i | ||||
\(551\) | −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 | ||||
\(555\) | 9.06589 | − | 33.8344i | 0.384826 | − | 1.43619i | ||||
\(556\) | 4.75231 | + | 3.41564i | 0.201543 | + | 0.144855i | ||||
\(557\) | −5.77540 | − | 21.5541i | −0.244711 | − | 0.913275i | −0.973528 | − | 0.228567i | \(-0.926596\pi\) |
0.728817 | − | 0.684709i | \(-0.240071\pi\) | |||||||
\(558\) | −3.41638 | + | 0.277696i | −0.144627 | + | 0.0117558i | ||||
\(559\) | 10.7329 | 0.453952 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 44.8306 | 1.89275 | ||||||||
\(562\) | −13.4824 | + | 1.09590i | −0.568721 | + | 0.0462277i | ||||
\(563\) | 5.40483 | + | 20.1711i | 0.227786 | + | 0.850110i | 0.981269 | + | 0.192643i | \(0.0617058\pi\) |
−0.753483 | + | 0.657468i | \(0.771628\pi\) | |||||||
\(564\) | −8.27646 | + | 11.5154i | −0.348502 | + | 0.484884i | ||||
\(565\) | 12.0922 | − | 45.1287i | 0.508723 | − | 1.89858i | ||||
\(566\) | −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 | \(-0.546274\pi\) |
0.784459 | + | 0.620181i | \(0.212941\pi\) | |||||||
\(570\) | −1.84373 | + | 10.0923i | −0.0772254 | + | 0.422720i | ||||
\(571\) | 8.29448 | − | 2.22250i | 0.347113 | − | 0.0930087i | −0.0810502 | − | 0.996710i | \(-0.525827\pi\) |
0.428164 | + | 0.903701i | \(0.359161\pi\) | |||||||
\(572\) | −7.67965 | + | 20.3171i | −0.321102 | + | 0.849503i | ||||
\(573\) | −28.5034 | + | 28.5034i | −1.19074 | + | 1.19074i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 26.9129 | 1.12234 | ||||||||
\(576\) | 3.70493 | − | 5.90203i | 0.154372 | − | 0.245918i | ||||
\(577\) | 17.6514 | − | 30.5732i | 0.734838 | − | 1.27278i | −0.219956 | − | 0.975510i | \(-0.570591\pi\) |
0.954794 | − | 0.297268i | \(-0.0960753\pi\) | |||||||
\(578\) | 11.7377 | − | 8.11155i | 0.488226 | − | 0.337396i | ||||
\(579\) | −24.1654 | − | 6.47509i | −1.00428 | − | 0.269096i | ||||
\(580\) | −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 | ||||
\(584\) | 11.8707 | − | 41.2375i | 0.491211 | − | 1.70642i | ||||
\(585\) | 5.72900 | + | 3.30764i | 0.236865 | + | 0.136754i | ||||
\(586\) | 19.8021 | − | 23.3061i | 0.818017 | − | 0.962766i | ||||
\(587\) | −2.38838 | − | 2.38838i | −0.0985791 | − | 0.0985791i | 0.656097 | − | 0.754676i | \(-0.272206\pi\) |
−0.754676 | + | 0.656097i | \(0.772206\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.36961 | − | 2.36961i | 0.0976379 | − | 0.0976379i | ||||
\(590\) | 43.5467 | − | 3.53964i | 1.79279 | − | 0.145725i | ||||
\(591\) | 17.8966 | − | 30.9978i | 0.736167 | − | 1.27508i | ||||
\(592\) | −1.45571 | − | 23.2155i | −0.0598292 | − | 0.954152i | ||||
\(593\) | −5.78207 | − | 10.0148i | −0.237441 | − | 0.411260i | 0.722538 | − | 0.691331i | \(-0.242975\pi\) |
−0.959979 | + | 0.280071i | \(0.909642\pi\) | |||||||
\(594\) | −11.1044 | + | 23.4355i | −0.455621 | + | 0.961570i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.57451 | + | 25.7659i | −0.105456 | + | 1.05541i | ||||
\(597\) | 0.747787 | − | 2.79078i | 0.0306049 | − | 0.114219i | ||||
\(598\) | −21.2414 | − | 3.88051i | −0.868624 | − | 0.158686i | ||||
\(599\) | 10.6273 | + | 6.13567i | 0.434219 | + | 0.250697i | 0.701142 | − | 0.713021i | \(-0.252674\pi\) |
−0.266923 | + | 0.963718i | \(0.586007\pi\) | |||||||
\(600\) | −24.3287 | − | 0.449725i | −0.993214 | − | 0.0183600i | ||||
\(601\) | − | 14.1538i | − | 0.577347i | −0.957428 | − | 0.288674i | \(-0.906786\pi\) | ||
0.957428 | − | 0.288674i | \(-0.0932143\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.842054 | + | 0.842054i | 0.0342911 | + | 0.0342911i | ||||
\(604\) | −5.24381 | − | 1.98210i | −0.213367 | − | 0.0806504i | ||||
\(605\) | −6.47029 | − | 24.1474i | −0.263055 | − | 0.981733i | ||||
\(606\) | 32.1537 | − | 22.2203i | 1.30615 | − | 0.902637i | ||||
\(607\) | 12.8174 | + | 22.2005i | 0.520244 | + | 0.901089i | 0.999723 | + | 0.0235358i | \(0.00749237\pi\) |
−0.479479 | + | 0.877553i | \(0.659174\pi\) | |||||||
\(608\) | 0.975842 | + | 6.74271i | 0.0395756 | + | 0.273453i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −5.75410 | − | 2.72646i | −0.232977 | − | 0.110391i | ||||
\(611\) | −8.63529 | − | 2.31382i | −0.349346 | − | 0.0936071i | ||||
\(612\) | −1.46437 | − | 8.94825i | −0.0591936 | − | 0.361712i | ||||
\(613\) | −9.30020 | + | 2.49198i | −0.375632 | + | 0.100650i | −0.441695 | − | 0.897165i | \(-0.645623\pi\) |
0.0660634 | + | 0.997815i | \(0.478956\pi\) | |||||||
\(614\) | −6.34436 | − | 5.39051i | −0.256038 | − | 0.217543i | ||||
\(615\) | − | 38.1256i | − | 1.53737i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 23.1951i | − | 0.933800i | −0.884310 | − | 0.466900i | \(-0.845371\pi\) | ||
0.884310 | − | 0.466900i | \(-0.154629\pi\) | |||||||
\(618\) | −2.90421 | + | 3.41811i | −0.116824 | + | 0.137497i | ||||
\(619\) | −32.4267 | + | 8.68871i | −1.30334 | + | 0.349229i | −0.842712 | − | 0.538365i | \(-0.819042\pi\) |
−0.460627 | + | 0.887594i | \(0.652375\pi\) | |||||||
\(620\) | 13.8343 | + | 9.94314i | 0.555598 | + | 0.399326i | ||||
\(621\) | −24.9028 | − | 6.67270i | −0.999317 | − | 0.267766i | ||||
\(622\) | −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 | ||||
\(626\) | −14.2538 | − | 20.6258i | −0.569696 | − | 0.824374i | ||||
\(627\) | 2.68495 | + | 10.0204i | 0.107227 | + | 0.400175i | ||||
\(628\) | −1.11572 | − | 2.47174i | −0.0445221 | − | 0.0986332i | ||||
\(629\) | −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 | \(-0.205735\pi\) | |||||||
\(632\) | 13.4692 | − | 12.9802i | 0.535775 | − | 0.516326i | ||||
\(633\) | 1.28862 | + | 0.743986i | 0.0512181 | + | 0.0295708i | ||||
\(634\) | 3.72690 | − | 20.4005i | 0.148014 | − | 0.810207i | ||||
\(635\) | −1.43044 | + | 5.33848i | −0.0567654 | + | 0.211851i | ||||
\(636\) | 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 | ||||
\(640\) | −33.0281 | + | 10.4321i | −1.30555 | + | 0.412364i | ||||
\(641\) | 3.34695 | − | 5.79709i | 0.132197 | − | 0.228971i | −0.792326 | − | 0.610097i | \(-0.791130\pi\) |
0.924523 | + | 0.381126i | \(0.124464\pi\) | |||||||
\(642\) | 2.52608 | + | 31.0774i | 0.0996966 | + | 1.22653i | ||||
\(643\) | 24.7491 | − | 24.7491i | 0.976007 | − | 0.976007i | −0.0237114 | − | 0.999719i | \(-0.507548\pi\) |
0.999719 | + | 0.0237114i | \(0.00754828\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 18.4279 | + | 18.4279i | 0.725597 | + | 0.725597i | ||||
\(646\) | 6.75564 | + | 5.73995i | 0.265797 | + | 0.225835i | ||||
\(647\) | 37.7857 | + | 21.8156i | 1.48551 | + | 0.857659i | 0.999864 | − | 0.0164976i | \(-0.00525159\pi\) |
0.485645 | + | 0.874156i | \(0.338585\pi\) | |||||||
\(648\) | 29.5030 | + | 8.49273i | 1.15899 | + | 0.333626i | ||||
\(649\) | 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 | ||||
\(653\) | 24.4355 | + | 6.54748i | 0.956236 | + | 0.256223i | 0.703006 | − | 0.711184i | \(-0.251841\pi\) |
0.253230 | + | 0.967406i | \(0.418507\pi\) | |||||||
\(654\) | −12.7288 | − | 18.4191i | −0.497734 | − | 0.720243i | ||||
\(655\) | −20.1015 | + | 34.8169i | −0.785432 | + | 1.36041i | ||||
\(656\) | −8.07045 | − | 23.9975i | −0.315098 | − | 0.936945i | ||||
\(657\) | −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 | \(0.395626\pi\) | |||||||
\(660\) | −48.0694 | + | 21.6981i | −1.87110 | + | 0.844597i | ||||
\(661\) | −10.5300 | + | 2.82150i | −0.409568 | + | 0.109743i | −0.457720 | − | 0.889097i | \(-0.651334\pi\) |
0.0481514 | + | 0.998840i | \(0.484667\pi\) | |||||||
\(662\) | −0.438861 | − | 0.0801740i | −0.0170568 | − | 0.00311605i | ||||
\(663\) | 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 | ||||
\(667\) | 14.0602 | − | 52.4732i | 0.544412 | − | 2.03177i | ||||
\(668\) | −0.633439 | − | 3.87073i | −0.0245085 | − | 0.149763i | ||||
\(669\) | −3.99120 | − | 14.8953i | −0.154309 | − | 0.575887i | ||||
\(670\) | −0.479535 | − | 5.89952i | −0.0185261 | − | 0.227918i | ||||
\(671\) | −6.43842 | −0.248553 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.82580 | 0.0703795 | 0.0351897 | − | 0.999381i | \(-0.488796\pi\) | ||||
0.0351897 | + | 0.999381i | \(0.488796\pi\) | |||||||
\(674\) | −3.06639 | − | 37.7246i | −0.118113 | − | 1.45310i | ||||
\(675\) | −4.74030 | − | 17.6911i | −0.182454 | − | 0.680929i | ||||
\(676\) | −2.21135 | − | 13.5128i | −0.0850521 | − | 0.519724i | ||||
\(677\) | 7.00518 | − | 26.1437i | 0.269231 | − | 1.00478i | −0.690379 | − | 0.723448i | \(-0.742556\pi\) |
0.959610 | − | 0.281335i | \(-0.0907772\pi\) | |||||||
\(678\) | −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 | ||||
\(682\) | 16.9465 | + | 3.09590i | 0.648915 | + | 0.118548i | ||||
\(683\) | 19.3386 | − | 5.18175i | 0.739970 | − | 0.198274i | 0.130905 | − | 0.991395i | \(-0.458212\pi\) |
0.609065 | + | 0.793121i | \(0.291545\pi\) | |||||||
\(684\) | 1.91238 | − | 0.863230i | 0.0731215 | − | 0.0330064i | ||||
\(685\) | 17.1808 | − | 17.1808i | 0.656445 | − | 0.656445i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −43.4148 | −1.65638 | ||||||||
\(688\) | 15.4999 | + | 7.69829i | 0.590929 | + | 0.293494i | ||||
\(689\) | −9.26852 | + | 16.0536i | −0.353103 | + | 0.611592i | ||||
\(690\) | −29.8079 | − | 43.1333i | −1.13477 | − | 1.64205i | ||||
\(691\) | 14.7787 | + | 3.95994i | 0.562208 | + | 0.150643i | 0.528720 | − | 0.848796i | \(-0.322672\pi\) |
0.0334874 | + | 0.999439i | \(0.489339\pi\) | |||||||
\(692\) | −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 | ||||
\(696\) | −13.5869 | + | 47.1997i | −0.515012 | + | 1.78910i | ||||
\(697\) | −28.5299 | − | 16.4717i | −1.08065 | − | 0.623911i | ||||
\(698\) | 21.0054 | + | 17.8473i | 0.795068 | + | 0.675532i | ||||
\(699\) | −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 | \(0.227538\pi\) | |||||||
\(702\) | 1.19051 | + | 14.6464i | 0.0449330 | + | 0.552793i | ||||
\(703\) | 3.50188 | − | 6.06544i | 0.132076 | − | 0.228762i | ||||
\(704\) | −25.6634 | + | 23.8328i | −0.967224 | + | 0.898233i | ||||
\(705\) | −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 | ||||
\(709\) | −7.42020 | + | 27.6926i | −0.278671 | + | 1.04002i | 0.674669 | + | 0.738120i | \(0.264286\pi\) |
−0.953341 | + | 0.301896i | \(0.902380\pi\) | |||||||
\(710\) | −7.82719 | + | 42.8449i | −0.293749 | + | 1.60794i | ||||
\(711\) | −4.98899 | − | 2.88039i | −0.187102 | − | 0.108023i | ||||
\(712\) | 6.40122 | + | 6.64233i | 0.239896 | + | 0.248932i | ||||
\(713\) | 17.1261i | 0.641377i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −23.5096 | − | 23.5096i | −0.879210 | − | 0.879210i | ||||
\(716\) | 11.0726 | + | 24.5299i | 0.413801 | + | 0.916724i | ||||
\(717\) | 9.59735 | + | 35.8178i | 0.358420 | + | 1.33764i | ||||
\(718\) | 16.9148 | + | 24.4765i | 0.631256 | + | 0.913453i | ||||
\(719\) | −10.0679 | − | 17.4381i | −0.375468 | − | 0.650330i | 0.614929 | − | 0.788583i | \(-0.289185\pi\) |
−0.990397 | + | 0.138253i | \(0.955851\pi\) | |||||||
\(720\) | 5.90113 | + | 8.88595i | 0.219922 | + | 0.331160i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 10.6272 | − | 22.4284i | 0.395505 | − | 0.834697i | ||||
\(723\) | 12.1597 | + | 3.25818i | 0.452224 | + | 0.121173i | ||||
\(724\) | −17.4650 | − | 12.5527i | −0.649082 | − | 0.466516i | ||||
\(725\) | 37.2771 | − | 9.98838i | 1.38444 | − | 0.370959i | ||||
\(726\) | −14.7118 | + | 17.3151i | −0.546006 | + | 0.642622i | ||||
\(727\) | − | 30.0313i | − | 1.11380i | −0.830580 | − | 0.556900i | \(-0.811991\pi\) | ||
0.830580 | − | 0.556900i | \(-0.188009\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 15.2688i | 0.565511i | ||||||||
\(730\) | 50.0579 | + | 42.5319i | 1.85273 | + | 1.57417i | ||||
\(731\) | 21.7514 | − | 5.82826i | 0.804503 | − | 0.215566i | ||||
\(732\) | 0.934619 | + | 5.71113i | 0.0345445 | + | 0.211090i | ||||
\(733\) | 12.3660 | + | 3.31347i | 0.456750 | + | 0.122386i | 0.479856 | − | 0.877347i | \(-0.340689\pi\) |
−0.0231062 | + | 0.999733i | \(0.507356\pi\) | |||||||
\(734\) | −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 | ||||
\(738\) | −6.41454 | + | 4.43286i | −0.236122 | + | 0.163176i | ||||
\(739\) | 7.39398 | + | 27.5947i | 0.271992 | + | 1.01509i | 0.957831 | + | 0.287334i | \(0.0927689\pi\) |
−0.685839 | + | 0.727754i | \(0.740564\pi\) | |||||||
\(740\) | 33.3065 | + | 12.5895i | 1.22437 | + | 0.462799i | ||||
\(741\) | 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 | \(0.794164\pi\) | |||||||
\(744\) | 0.286184 | − | 15.4816i | 0.0104920 | − | 0.567584i | ||||
\(745\) | −34.3267 | − | 19.8185i | −1.25763 | − | 0.726095i | ||||
\(746\) | 7.38369 | + | 1.34890i | 0.270336 | + | 0.0493868i | ||||
\(747\) | 2.36487 | − | 8.82583i | 0.0865262 | − | 0.322920i | ||||
\(748\) | −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 | 0.659585 | − | 0.751630i | \(-0.270732\pi\) |
−0.980723 | + | 0.195402i | \(0.937399\pi\) | |||||||
\(752\) | −10.8111 | − | 9.53529i | −0.394240 | − | 0.347716i | ||||
\(753\) | 4.07852 | − | 7.06421i | 0.148630 | − | 0.257434i | ||||
\(754\) | −30.8617 | + | 2.50855i | −1.12392 | + | 0.0913561i | ||||
\(755\) | 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 | \(0.839749\pi\) | |||||||
\(758\) | −24.3959 | + | 28.7127i | −0.886098 | + | 1.04289i | ||||
\(759\) | −45.9132 | − | 26.5080i | −1.66654 | − | 0.962179i | ||||
\(760\) | −10.0218 | − | 2.88489i | −0.363530 | − | 0.104646i | ||||
\(761\) | 1.13395 | − | 0.654687i | 0.0411057 | − | 0.0237324i | −0.479306 | − | 0.877648i | \(-0.659112\pi\) |
0.520412 | + | 0.853915i | \(0.325778\pi\) | |||||||
\(762\) | 4.73071 | − | 1.68890i | 0.171376 | − | 0.0611825i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −25.9499 | − | 31.7113i | −0.938833 | − | 1.14728i | ||||
\(765\) | 13.4066 | + | 3.59229i | 0.484717 | + | 0.129880i | ||||
\(766\) | −5.75456 | + | 3.97678i | −0.207921 | + | 0.143687i | ||||
\(767\) | 12.5164 | − | 21.6791i | 0.451943 | − | 0.782788i | ||||
\(768\) | 24.8660 | + | 19.3048i | 0.897275 | + | 0.696601i | ||||
\(769\) | 22.6761 | 0.817720 | 0.408860 | − | 0.912597i | \(-0.365926\pi\) | ||||
0.408860 | + | 0.912597i | \(0.365926\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 40.3008 | − | 40.3008i | 1.45140 | − | 1.45140i | ||||
\(772\) | 8.99173 | − | 23.7884i | 0.323620 | − | 0.856163i | ||||
\(773\) | 3.78685 | − | 1.01468i | 0.136203 | − | 0.0364956i | −0.190073 | − | 0.981770i | \(-0.560873\pi\) |
0.326277 | + | 0.945274i | \(0.394206\pi\) | |||||||
\(774\) | 0.957836 | − | 5.24305i | 0.0344287 | − | 0.188458i | ||||
\(775\) | −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 | ||||
\(779\) | 1.97301 | − | 7.36339i | 0.0706906 | − | 0.263821i | ||||
\(780\) | −17.4412 | + | 24.2667i | −0.624496 | + | 0.868886i | ||||
\(781\) | 11.3984 | + | 42.5394i | 0.407867 | + | 1.52218i | ||||
\(782\) | −45.1553 | + | 3.67039i | −1.61475 | + | 0.131253i | ||||
\(783\) | −36.9695 | −1.32118 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.15117 | 0.148161 | ||||||||
\(786\) | 36.4193 | − | 2.96029i | 1.29903 | − | 0.105590i | ||||
\(787\) | 8.04395 | + | 30.0204i | 0.286736 | + | 1.07011i | 0.947562 | + | 0.319573i | \(0.103540\pi\) |
−0.660826 | + | 0.750539i | \(0.729794\pi\) | |||||||
\(788\) | 29.5449 | + | 21.2349i | 1.05249 | + | 0.756461i | ||||
\(789\) | −0.175401 | + | 0.654607i | −0.00624445 | + | 0.0233046i | ||||
\(790\) | 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 | ||||
\(794\) | −0.0229641 | + | 0.125702i | −0.000814967 | + | 0.00446101i | ||||
\(795\) | −43.4770 | + | 11.6496i | −1.54197 | + | 0.413170i | ||||
\(796\) | 2.74724 | + | 1.03843i | 0.0973734 | + | 0.0368060i | ||||
\(797\) | 27.7986 | − | 27.7986i | 0.984679 | − | 0.984679i | −0.0152058 | − | 0.999884i | \(-0.504840\pi\) |
0.999884 | + | 0.0152058i | \(0.00484033\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18.7569 | −0.663570 | ||||||||
\(800\) | 2.91370 | − | 24.5625i | 0.103015 | − | 0.868417i | ||||
\(801\) | 1.42047 | − | 2.46032i | 0.0501897 | − | 0.0869312i | ||||
\(802\) | −29.5632 | + | 20.4301i | −1.04391 | + | 0.721412i | ||||
\(803\) | 64.1567 | + | 17.1907i | 2.26404 | + | 0.606648i | ||||
\(804\) | −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 | ||||
\(808\) | 19.2257 | + | 34.7685i | 0.676359 | + | 1.22315i | ||||
\(809\) | 42.7813 | + | 24.6998i | 1.50411 | + | 0.868398i | 0.999989 | + | 0.00476483i | \(0.00151670\pi\) |
0.504121 | + | 0.863633i | \(0.331817\pi\) | |||||||
\(810\) | −30.4290 | + | 35.8134i | −1.06917 | + | 1.25835i | ||||
\(811\) | −13.1428 | − | 13.1428i | −0.461506 | − | 0.461506i | 0.437643 | − | 0.899149i | \(-0.355813\pi\) |
−0.899149 | + | 0.437643i | \(0.855813\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −17.3861 | + | 17.3861i | −0.609756 | + | 0.609756i | ||||
\(814\) | 35.8855 | − | 2.91691i | 1.25779 | − | 0.102238i | ||||
\(815\) | −27.9701 | + | 48.4457i | −0.979750 | + | 1.69698i | ||||
\(816\) | 40.8808 | − | 2.56339i | 1.43111 | − | 0.0897366i | ||||
\(817\) | 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 | ||||
\(821\) | 0.278293 | − | 1.03860i | 0.00971248 | − | 0.0362475i | −0.960900 | − | 0.276897i | \(-0.910694\pi\) |
0.970612 | + | 0.240650i | \(0.0773605\pi\) | |||||||
\(822\) | −21.7236 | − | 3.96861i | −0.757697 | − | 0.138421i | ||||
\(823\) | −17.3926 | − | 10.0416i | −0.606268 | − | 0.350029i | 0.165235 | − | 0.986254i | \(-0.447162\pi\) |
−0.771504 | + | 0.636225i | \(0.780495\pi\) | |||||||
\(824\) | −3.16384 | − | 3.28301i | −0.110217 | − | 0.114369i | ||||
\(825\) | − | 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 | \(0.694957\pi\) | |||||||
\(828\) | −3.79130 | + | 10.0302i | −0.131757 | + | 0.348574i | ||||
\(829\) | −11.9771 | − | 44.6990i | −0.415980 | − | 1.55246i | −0.782864 | − | 0.622193i | \(-0.786242\pi\) |
0.366884 | − | 0.930267i | \(-0.380425\pi\) | |||||||
\(830\) | −37.3620 | + | 25.8196i | −1.29685 | + | 0.896210i | ||||
\(831\) | 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 | ||||
\(835\) | 5.79927 | + | 1.55391i | 0.200692 | + | 0.0537753i | ||||
\(836\) | −10.4068 | + | 1.70305i | −0.359925 | + | 0.0589013i | ||||
\(837\) | 11.2577 | − | 3.01650i | 0.389125 | − | 0.104266i | ||||
\(838\) | −36.9997 | − | 31.4369i | −1.27813 | − | 1.08597i | ||||
\(839\) | 11.1872i | 0.386225i | 0.981177 | + | 0.193113i | \(0.0618583\pi\) | ||||
−0.981177 | + | 0.193113i | \(0.938142\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 48.8991i | − | 1.68618i | ||||||
\(842\) | −20.7548 | + | 24.4274i | −0.715258 | + | 0.841823i | ||||
\(843\) | −18.1778 | + | 4.87073i | −0.626077 | + | 0.167757i | ||||
\(844\) | −0.882764 | + | 1.22822i | −0.0303860 | + | 0.0422772i | ||||
\(845\) | 20.2454 | + | 5.42475i | 0.696464 | + | 0.186617i | ||||
\(846\) | −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 | ||||
\(850\) | −18.2973 | − | 26.4770i | −0.627594 | − | 0.908154i | ||||
\(851\) | 9.26392 | + | 34.5734i | 0.317563 | + | 1.18516i | ||||
\(852\) | 36.0795 | − | 16.2860i | 1.23606 | − | 0.557948i | ||||
\(853\) | −25.4369 | − | 25.4369i | −0.870944 | − | 0.870944i | 0.121632 | − | 0.992575i | \(-0.461187\pi\) |
−0.992575 | + | 0.121632i | \(0.961187\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.21174i | 0.109839i | ||||||||
\(856\) | −31.6895 | − | 0.585792i | −1.08312 | − | 0.0200220i | ||||
\(857\) | −28.5281 | − | 16.4707i | −0.974500 | − | 0.562628i | −0.0738951 | − | 0.997266i | \(-0.523543\pi\) |
−0.900605 | + | 0.434638i | \(0.856876\pi\) | |||||||
\(858\) | −5.43051 | + | 29.7258i | −0.185394 | + | 1.01482i | ||||
\(859\) | −10.9512 | + | 40.8704i | −0.373649 | + | 1.39448i | 0.481659 | + | 0.876359i | \(0.340034\pi\) |
−0.855308 | + | 0.518120i | \(0.826632\pi\) | |||||||
\(860\) | −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 | 0.618482 | − | 0.785799i | \(-0.287748\pi\) |
−0.989763 | + | 0.142721i | \(0.954415\pi\) | |||||||
\(864\) | −8.78604 | + | 22.0056i | −0.298907 | + | 0.748646i | ||||
\(865\) | 8.96304 | − | 15.5244i | 0.304752 | − | 0.527847i | ||||
\(866\) | −1.33849 | − | 16.4669i | −0.0454837 | − | 0.559568i | ||||
\(867\) | 14.0360 | − | 14.0360i | 0.476689 | − | 0.476689i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 20.4729 | + | 20.4729i | 0.694495 | + | 0.694495i | ||||
\(870\) | −57.2954 | − | 48.6812i | −1.94250 | − | 1.65045i | ||||
\(871\) | −2.93699 | − | 1.69567i | −0.0995162 | − | 0.0574557i | ||||
\(872\) | 19.9170 | − | 11.0134i | 0.674474 | − | 0.372959i | ||||
\(873\) | 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 | ||||
\(877\) | −13.5170 | − | 3.62186i | −0.456435 | − | 0.122302i | 0.0232736 | − | 0.999729i | \(-0.492591\pi\) |
−0.479709 | + | 0.877428i | \(0.659258\pi\) | |||||||
\(878\) | 10.5500 | + | 15.2662i | 0.356044 | + | 0.515210i | ||||
\(879\) | 21.2738 | − | 36.8473i | 0.717548 | − | 1.24283i | ||||
\(880\) | −17.0890 | − | 50.8142i | −0.576070 | − | 1.71295i | ||||
\(881\) | −12.3319 | −0.415471 | −0.207735 | − | 0.978185i | \(-0.566609\pi\) | ||||
−0.207735 | + | 0.978185i | \(0.566609\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24.3508 | − | 24.3508i | 0.819469 | − | 0.819469i | −0.166562 | − | 0.986031i | \(-0.553267\pi\) |
0.986031 | + | 0.166562i | \(0.0532667\pi\) | |||||||
\(884\) | 10.6238 | + | 23.5356i | 0.357316 | + | 0.791588i | ||||
\(885\) | 58.7124 | − | 15.7319i | 1.97360 | − | 0.528823i | ||||
\(886\) | −31.9118 | − | 5.82985i | −1.07210 | − | 0.195858i | ||||
\(887\) | 3.69725 | − | 2.13461i | 0.124141 | − | 0.0716731i | −0.436643 | − | 0.899635i | \(-0.643833\pi\) |
0.560785 | + | 0.827962i | \(0.310500\pi\) | |||||||
\(888\) | −7.79665 | − | 31.4084i | −0.261638 | − | 1.05400i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −13.2985 | + | 4.74769i | −0.445768 | + | 0.159143i | ||||
\(891\) | −12.2989 | + | 45.9002i | −0.412030 | + | 1.53772i | ||||
\(892\) | 15.4697 | − | 2.53160i | 0.517965 | − | 0.0847642i | ||||
\(893\) | −1.12337 | − | 4.19246i | −0.0375920 | − | 0.140295i | ||||
\(894\) | 2.91861 | + | 35.9065i | 0.0976131 | + | 1.20089i | ||||
\(895\) | −41.1967 | −1.37705 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −30.0408 | −1.00303 | ||||||||
\(898\) | −1.79190 | − | 22.0450i | −0.0597964 | − | 0.735651i | ||||
\(899\) | 6.35613 | + | 23.7214i | 0.211989 | + | 0.791153i | ||||
\(900\) | −7.51752 | + | 1.23023i | −0.250584 | + | 0.0410077i | ||||
\(901\) | −10.0662 | + | 37.5674i | −0.335352 | + | 1.25155i | ||||
\(902\) | 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 | ||||
\(906\) | −7.67216 | − | 1.40160i | −0.254890 | − | 0.0465651i | ||||
\(907\) | 32.5246 | − | 8.71495i | 1.07996 | − | 0.289375i | 0.325382 | − | 0.945583i | \(-0.394507\pi\) |
0.754580 | + | 0.656208i | \(0.227840\pi\) | |||||||
\(908\) | −0.288093 | − | 0.638235i | −0.00956071 | − | 0.0211806i | ||||
\(909\) | 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 | \(0.477690\pi\) | |||||||
\(912\) | 3.02135 | + | 8.98399i | 0.100047 | + | 0.297490i | ||||
\(913\) | −22.9612 | + | 39.7699i | −0.759904 | + | 1.31619i | ||||
\(914\) | 9.83337 | + | 14.2293i | 0.325259 | + | 0.470663i | ||||
\(915\) | −8.55664 | − | 2.29275i | −0.282874 | − | 0.0757958i | ||||
\(916\) | 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 | \(-0.549693\pi\) |
0.777752 | + | 0.628571i | \(0.216360\pi\) | |||||||
\(920\) | 46.6410 | − | 25.7908i | 1.53771 | − | 0.850297i | ||||
\(921\) | −10.0305 | − | 5.79113i | −0.330517 | − | 0.190824i | ||||
\(922\) | −20.5237 | − | 17.4380i | −0.675911 | − | 0.574290i | ||||
\(923\) | 17.6457 | + | 17.6457i | 0.580814 | + | 0.580814i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −17.9799 | + | 17.9799i | −0.591177 | + | 0.591177i | ||||
\(926\) | −2.83924 | − | 34.9301i | −0.0933033 | − | 1.14787i | ||||
\(927\) | −0.702074 | + | 1.21603i | −0.0230591 | + | 0.0399396i | ||||
\(928\) | −46.3684 | − | 18.5132i | −1.52212 | − | 0.607726i | ||||
\(929\) | 15.6683 | + | 27.1384i | 0.514062 | + | 0.890381i | 0.999867 | + | 0.0163141i | \(0.00519316\pi\) |
−0.485805 | + | 0.874067i | \(0.661474\pi\) | |||||||
\(930\) | 21.4194 | + | 10.1491i | 0.702369 | + | 0.332804i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 14.7273 | − | 12.0516i | 0.482410 | − | 0.394763i | ||||
\(933\) | −0.408718 | + | 1.52535i | −0.0133808 | + | 0.0499379i | ||||
\(934\) | 8.32727 | − | 45.5823i | 0.272477 | − | 1.49150i | ||||
\(935\) | −60.4113 | − | 34.8785i | −1.97566 | − | 1.14065i | ||||
\(936\) | 6.11070 | + | 0.112959i | 0.199734 | + | 0.00369217i | ||||
\(937\) | 53.9341i | 1.76195i | 0.473162 | + | 0.880975i | \(0.343113\pi\) | ||||
−0.473162 | + | 0.880975i | \(0.656887\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −24.6644 | − | 24.6644i | −0.804893 | − | 0.804893i | ||||
\(940\) | 20.1119 | − | 9.07835i | 0.655979 | − | 0.296103i | ||||
\(941\) | −12.8332 | − | 47.8941i | −0.418350 | − | 1.56130i | −0.778030 | − | 0.628227i | \(-0.783781\pi\) |
0.359680 | − | 0.933076i | \(-0.382886\pi\) | |||||||
\(942\) | −2.14495 | − | 3.10383i | −0.0698862 | − | 0.101128i | ||||
\(943\) | 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 | ||||
\(947\) | −0.0877997 | − | 0.0235259i | −0.00285311 | − | 0.000764488i | 0.257392 | − | 0.966307i | \(-0.417137\pi\) |
−0.260245 | + | 0.965543i | \(0.583803\pi\) | |||||||
\(948\) | 15.1883 | − | 21.1321i | 0.493295 | − | 0.686340i | ||||
\(949\) | 36.3536 | − | 9.74091i | 1.18009 | − | 0.316203i | ||||
\(950\) | 4.82220 | − | 5.67549i | 0.156453 | − | 0.184137i | ||||
\(951\) | − | 28.8516i | − | 0.935577i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 45.4195i | 1.47128i | 0.677371 | + | 0.735641i | \(0.263119\pi\) | ||||
−0.677371 | + | 0.735641i | \(0.736881\pi\) | |||||||
\(954\) | 7.01508 | + | 5.96039i | 0.227122 | + | 0.192975i | ||||
\(955\) | 60.5854 | − | 16.2338i | 1.96050 | − | 0.525314i | ||||
\(956\) | −37.1990 | + | 6.08756i | −1.20310 | + | 0.196886i | ||||
\(957\) | −73.4326 | − | 19.6762i | −2.37374 | − | 0.636041i | ||||
\(958\) | −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 | ||||
\(962\) | 16.7834 | − | 11.5984i | 0.541119 | − | 0.373948i | ||||
\(963\) | 2.52634 | + | 9.42843i | 0.0814102 | + | 0.303827i | ||||
\(964\) | −4.52452 | + | 11.9700i | −0.145725 | + | 0.385528i | ||||
\(965\) | 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 | \(0.582242\pi\) | |||||||
\(968\) | −16.0270 | − | 16.6307i | −0.515127 | − | 0.534530i | ||||
\(969\) | 10.6808 | + | 6.16655i | 0.343116 | + | 0.198098i | ||||
\(970\) | −32.6394 | − | 5.96279i | −1.04799 | − | 0.191454i | ||||
\(971\) | 9.75682 | − | 36.4130i | 0.313111 | − | 1.16855i | −0.612624 | − | 0.790375i | \(-0.709886\pi\) |
0.925735 | − | 0.378173i | \(-0.123448\pi\) | |||||||
\(972\) | 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 | ||||
\(976\) | −5.87116 | + | 0.368145i | −0.187931 | + | 0.0117840i | ||||
\(977\) | 12.3444 | − | 21.3811i | 0.394932 | − | 0.684042i | −0.598161 | − | 0.801376i | \(-0.704102\pi\) |
0.993092 | + | 0.117334i | \(0.0374349\pi\) | |||||||
\(978\) | 50.6753 | − | 4.11907i | 1.62042 | − | 0.131713i | ||||
\(979\) | −10.0962 | + | 10.0962i | −0.322676 | + | 0.322676i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.95619 | − | 4.95619i | −0.158239 | − | 0.158239i | ||||
\(982\) | −7.68244 | + | 9.04186i | −0.245157 | + | 0.288537i | ||||
\(983\) | 4.43148 | + | 2.55852i | 0.141342 | + | 0.0816041i | 0.569004 | − | 0.822335i | \(-0.307329\pi\) |
−0.427661 | + | 0.903939i | \(0.640662\pi\) | |||||||
\(984\) | −17.0450 | − | 30.8248i | −0.543374 | − | 0.982659i | ||||
\(985\) | −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 | ||||
\(989\) | −25.7228 | − | 6.89240i | −0.817938 | − | 0.219166i | ||||
\(990\) | −13.5826 | + | 9.38648i | −0.431684 | + | 0.298322i | ||||
\(991\) | 2.71965 | − | 4.71056i | 0.0863924 | − | 0.149636i | −0.819591 | − | 0.572949i | \(-0.805799\pi\) |
0.905984 | + | 0.423313i | \(0.139133\pi\) | |||||||
\(992\) | 15.6304 | + | 1.85414i | 0.496267 | + | 0.0588690i | ||||
\(993\) | −0.620663 | −0.0196961 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.17892 | + | 3.17892i | −0.100779 | + | 0.100779i | ||||
\(996\) | 38.6106 | + | 14.5944i | 1.22342 | + | 0.462440i | ||||
\(997\) | 11.6799 | − | 3.12961i | 0.369905 | − | 0.0991157i | −0.0690777 | − | 0.997611i | \(-0.522006\pi\) |
0.438983 | + | 0.898496i | \(0.355339\pi\) | |||||||
\(998\) | −1.99723 | + | 10.9326i | −0.0632213 | + | 0.346064i | ||||
\(999\) | 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.l.165.4 | 24 | ||
7.2 | even | 3 | inner | 784.2.x.l.373.6 | 24 | ||
7.3 | odd | 6 | 784.2.m.h.197.1 | 12 | |||
7.4 | even | 3 | 112.2.m.d.85.1 | yes | 12 | ||
7.5 | odd | 6 | 784.2.x.m.373.6 | 24 | |||
7.6 | odd | 2 | 784.2.x.m.165.4 | 24 | |||
16.13 | even | 4 | inner | 784.2.x.l.557.6 | 24 | ||
28.11 | odd | 6 | 448.2.m.d.113.2 | 12 | |||
56.11 | odd | 6 | 896.2.m.h.225.5 | 12 | |||
56.53 | even | 6 | 896.2.m.g.225.2 | 12 | |||
112.11 | odd | 12 | 896.2.m.h.673.5 | 12 | |||
112.13 | odd | 4 | 784.2.x.m.557.6 | 24 | |||
112.45 | odd | 12 | 784.2.m.h.589.1 | 12 | |||
112.53 | even | 12 | 896.2.m.g.673.2 | 12 | |||
112.61 | odd | 12 | 784.2.x.m.765.4 | 24 | |||
112.67 | odd | 12 | 448.2.m.d.337.2 | 12 | |||
112.93 | even | 12 | inner | 784.2.x.l.765.4 | 24 | ||
112.109 | even | 12 | 112.2.m.d.29.1 | ✓ | 12 | ||
224.67 | odd | 24 | 7168.2.a.bi.1.3 | 12 | |||
224.109 | even | 24 | 7168.2.a.bj.1.3 | 12 | |||
224.179 | odd | 24 | 7168.2.a.bi.1.10 | 12 | |||
224.221 | even | 24 | 7168.2.a.bj.1.10 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
112.2.m.d.29.1 | ✓ | 12 | 112.109 | even | 12 | ||
112.2.m.d.85.1 | yes | 12 | 7.4 | even | 3 | ||
448.2.m.d.113.2 | 12 | 28.11 | odd | 6 | |||
448.2.m.d.337.2 | 12 | 112.67 | odd | 12 | |||
784.2.m.h.197.1 | 12 | 7.3 | odd | 6 | |||
784.2.m.h.589.1 | 12 | 112.45 | odd | 12 | |||
784.2.x.l.165.4 | 24 | 1.1 | even | 1 | trivial | ||
784.2.x.l.373.6 | 24 | 7.2 | even | 3 | inner | ||
784.2.x.l.557.6 | 24 | 16.13 | even | 4 | inner | ||
784.2.x.l.765.4 | 24 | 112.93 | even | 12 | inner | ||
784.2.x.m.165.4 | 24 | 7.6 | odd | 2 | |||
784.2.x.m.373.6 | 24 | 7.5 | odd | 6 | |||
784.2.x.m.557.6 | 24 | 112.13 | odd | 4 | |||
784.2.x.m.765.4 | 24 | 112.61 | odd | 12 | |||
896.2.m.g.225.2 | 12 | 56.53 | even | 6 | |||
896.2.m.g.673.2 | 12 | 112.53 | even | 12 | |||
896.2.m.h.225.5 | 12 | 56.11 | odd | 6 | |||
896.2.m.h.673.5 | 12 | 112.11 | odd | 12 | |||
7168.2.a.bi.1.3 | 12 | 224.67 | odd | 24 | |||
7168.2.a.bi.1.10 | 12 | 224.179 | odd | 24 | |||
7168.2.a.bj.1.3 | 12 | 224.109 | even | 24 | |||
7168.2.a.bj.1.10 | 12 | 224.221 | even | 24 |