Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1080,2,Mod(541,1080)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1080, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1080.541");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1080.k (of order \(2\), degree \(1\), 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: | \(8.62384341830\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - x^{18} + 5x^{16} + 28x^{12} - 28x^{10} + 112x^{8} + 320x^{4} - 256x^{2} + 1024 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 541.2 | ||
Root | \(-1.34522 - 0.436333i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1080.541 |
Dual form | 1080.2.k.d.541.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1080\mathbb{Z}\right)^\times\).
\(n\) | \(217\) | \(271\) | \(541\) | \(1001\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.34522 | + | 0.436333i | −0.951213 | + | 0.308534i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.61923 | − | 1.17393i | 0.809613 | − | 0.586963i | ||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.61492 | −1.36631 | −0.683155 | − | 0.730273i | \(-0.739393\pi\) | ||||
−0.683155 | + | 0.730273i | \(0.739393\pi\) | |||||||
\(8\) | −1.66599 | + | 2.28571i | −0.589017 | + | 0.808121i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.436333 | − | 1.34522i | −0.137981 | − | 0.425396i | ||||
\(11\) | 0.460301i | 0.138786i | 0.997589 | + | 0.0693930i | \(0.0221063\pi\) | ||||
−0.997589 | + | 0.0693930i | \(0.977894\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 3.67457i | − | 1.01914i | −0.860429 | − | 0.509571i | \(-0.829804\pi\) | ||
0.860429 | − | 0.509571i | \(-0.170196\pi\) | |||||||
\(14\) | 4.86285 | − | 1.57731i | 1.29965 | − | 0.421553i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.24379 | − | 3.80171i | 0.310948 | − | 0.950427i | ||||
\(17\) | 6.59150 | 1.59867 | 0.799337 | − | 0.600883i | \(-0.205184\pi\) | ||||
0.799337 | + | 0.600883i | \(0.205184\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 3.13421i | − | 0.719036i | −0.933138 | − | 0.359518i | \(-0.882941\pi\) | ||
0.933138 | − | 0.359518i | \(-0.117059\pi\) | |||||||
\(20\) | 1.17393 | + | 1.61923i | 0.262498 | + | 0.362070i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.200845 | − | 0.619206i | −0.0428202 | − | 0.132015i | ||||
\(23\) | −3.60210 | −0.751090 | −0.375545 | − | 0.926804i | \(-0.622545\pi\) | ||||
−0.375545 | + | 0.926804i | \(0.622545\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 1.60333 | + | 4.94310i | 0.314440 | + | 0.969421i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −5.85337 | + | 4.24365i | −1.10618 | + | 0.801974i | ||||
\(29\) | 9.83716i | 1.82671i | 0.407159 | + | 0.913357i | \(0.366519\pi\) | ||||
−0.407159 | + | 0.913357i | \(0.633481\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.34649 | 1.67868 | 0.839340 | − | 0.543607i | \(-0.182942\pi\) | ||||
0.839340 | + | 0.543607i | \(0.182942\pi\) | |||||||
\(32\) | −0.0143608 | + | 5.65684i | −0.00253866 | + | 0.999997i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −8.86701 | + | 2.87609i | −1.52068 | + | 0.493245i | ||||
\(35\) | − | 3.61492i | − | 0.611032i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.66397i | 1.09555i | 0.836626 | + | 0.547775i | \(0.184525\pi\) | ||||
−0.836626 | + | 0.547775i | \(0.815475\pi\) | |||||||
\(38\) | 1.36756 | + | 4.21619i | 0.221847 | + | 0.683957i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.28571 | − | 1.66599i | −0.361403 | − | 0.263416i | ||||
\(41\) | 10.2939 | 1.60763 | 0.803815 | − | 0.594880i | \(-0.202800\pi\) | ||||
0.803815 | + | 0.594880i | \(0.202800\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.05114i | 0.922790i | 0.887195 | + | 0.461395i | \(0.152651\pi\) | ||||
−0.887195 | + | 0.461395i | \(0.847349\pi\) | |||||||
\(44\) | 0.540360 | + | 0.745332i | 0.0814623 | + | 0.112363i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.84562 | − | 1.57172i | 0.714447 | − | 0.231737i | ||||
\(47\) | −6.61929 | −0.965522 | −0.482761 | − | 0.875752i | \(-0.660366\pi\) | ||||
−0.482761 | + | 0.875752i | \(0.660366\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.06762 | 0.866803 | ||||||||
\(50\) | 1.34522 | − | 0.436333i | 0.190243 | − | 0.0617068i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.31367 | − | 5.94996i | −0.598199 | − | 0.825111i | ||||
\(53\) | − | 3.27127i | − | 0.449344i | −0.974434 | − | 0.224672i | \(-0.927869\pi\) | ||
0.974434 | − | 0.224672i | \(-0.0721311\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.460301 | −0.0620670 | ||||||||
\(56\) | 6.02242 | − | 8.26265i | 0.804780 | − | 1.10414i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.29228 | − | 13.2331i | −0.563604 | − | 1.73759i | ||||
\(59\) | 5.19188i | 0.675925i | 0.941160 | + | 0.337962i | \(0.109738\pi\) | ||||
−0.941160 | + | 0.337962i | \(0.890262\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 6.80877i | − | 0.871774i | −0.900001 | − | 0.435887i | \(-0.856435\pi\) | ||
0.900001 | − | 0.435887i | \(-0.143565\pi\) | |||||||
\(62\) | −12.5731 | + | 4.07818i | −1.59678 | + | 0.517930i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −2.44895 | − | 7.61595i | −0.306118 | − | 0.951993i | ||||
\(65\) | 3.67457 | 0.455774 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.0766i | 1.23105i | 0.788117 | + | 0.615525i | \(0.211056\pi\) | ||||
−0.788117 | + | 0.615525i | \(0.788944\pi\) | |||||||
\(68\) | 10.6731 | − | 7.73794i | 1.29431 | − | 0.938363i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.57731 | + | 4.86285i | 0.188524 | + | 0.581222i | ||||
\(71\) | 2.98940 | 0.354776 | 0.177388 | − | 0.984141i | \(-0.443235\pi\) | ||||
0.177388 | + | 0.984141i | \(0.443235\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.27127 | 0.265833 | 0.132916 | − | 0.991127i | \(-0.457566\pi\) | ||||
0.132916 | + | 0.991127i | \(0.457566\pi\) | |||||||
\(74\) | −2.90771 | − | 8.96449i | −0.338014 | − | 1.04210i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.67933 | − | 5.07499i | −0.422048 | − | 0.582141i | ||||
\(77\) | − | 1.66395i | − | 0.189625i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.9124 | 1.67777 | 0.838887 | − | 0.544306i | \(-0.183207\pi\) | ||||
0.838887 | + | 0.544306i | \(0.183207\pi\) | |||||||
\(80\) | 3.80171 | + | 1.24379i | 0.425044 | + | 0.139060i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −13.8475 | + | 4.49155i | −1.52920 | + | 0.496009i | ||||
\(83\) | 6.88619i | 0.755858i | 0.925835 | + | 0.377929i | \(0.123364\pi\) | ||||
−0.925835 | + | 0.377929i | \(0.876636\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.59150i | 0.714949i | ||||||||
\(86\) | −2.64031 | − | 8.14011i | −0.284712 | − | 0.877771i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.05212 | − | 0.766858i | −0.112156 | − | 0.0817473i | ||||
\(89\) | −6.05114 | −0.641420 | −0.320710 | − | 0.947177i | \(-0.603921\pi\) | ||||
−0.320710 | + | 0.947177i | \(0.603921\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13.2833i | 1.39246i | ||||||||
\(92\) | −5.83262 | + | 4.22861i | −0.608093 | + | 0.440863i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 8.90439 | − | 2.88821i | 0.918418 | − | 0.297897i | ||||
\(95\) | 3.13421 | 0.321563 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.0408 | 1.32409 | 0.662047 | − | 0.749463i | \(-0.269688\pi\) | ||||
0.662047 | + | 0.749463i | \(0.269688\pi\) | |||||||
\(98\) | −8.16228 | + | 2.64751i | −0.824515 | + | 0.267438i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.61923 | + | 1.17393i | −0.161923 | + | 0.117393i | ||||
\(101\) | 2.99241i | 0.297756i | 0.988856 | + | 0.148878i | \(0.0475661\pi\) | ||||
−0.988856 | + | 0.148878i | \(0.952434\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.0869913 | −0.00857151 | −0.00428575 | − | 0.999991i | \(-0.501364\pi\) | ||||
−0.00428575 | + | 0.999991i | \(0.501364\pi\) | |||||||
\(104\) | 8.39900 | + | 6.12180i | 0.823589 | + | 0.600291i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.42737 | + | 4.40058i | 0.138638 | + | 0.427422i | ||||
\(107\) | − | 4.14702i | − | 0.400908i | −0.979703 | − | 0.200454i | \(-0.935758\pi\) | ||
0.979703 | − | 0.200454i | \(-0.0642417\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 19.2619i | 1.84496i | 0.386047 | + | 0.922479i | \(0.373840\pi\) | ||||
−0.386047 | + | 0.922479i | \(0.626160\pi\) | |||||||
\(110\) | 0.619206 | − | 0.200845i | 0.0590390 | − | 0.0191498i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −4.49620 | + | 13.7429i | −0.424851 | + | 1.29858i | ||||
\(113\) | 14.2190 | 1.33762 | 0.668808 | − | 0.743436i | \(-0.266805\pi\) | ||||
0.668808 | + | 0.743436i | \(0.266805\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 3.60210i | − | 0.335898i | ||||||
\(116\) | 11.5481 | + | 15.9286i | 1.07221 | + | 1.47893i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.26539 | − | 6.98421i | −0.208546 | − | 0.642949i | ||||
\(119\) | −23.8277 | −2.18428 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.7881 | 0.980738 | ||||||||
\(122\) | 2.97089 | + | 9.15929i | 0.268972 | + | 0.829243i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 15.1341 | − | 10.9721i | 1.35908 | − | 0.985324i | ||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.91301 | −0.169752 | −0.0848760 | − | 0.996392i | \(-0.527049\pi\) | ||||
−0.0848760 | + | 0.996392i | \(0.527049\pi\) | |||||||
\(128\) | 6.61746 | + | 9.17656i | 0.584906 | + | 0.811101i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −4.94310 | + | 1.60333i | −0.433538 | + | 0.140622i | ||||
\(131\) | − | 8.63351i | − | 0.754313i | −0.926150 | − | 0.377157i | \(-0.876902\pi\) | ||
0.926150 | − | 0.377157i | \(-0.123098\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 11.3299i | 0.982427i | ||||||||
\(134\) | −4.39675 | − | 13.5552i | −0.379821 | − | 1.17099i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −10.9814 | + | 15.0663i | −0.941646 | + | 1.29192i | ||||
\(137\) | −9.11300 | −0.778576 | −0.389288 | − | 0.921116i | \(-0.627279\pi\) | ||||
−0.389288 | + | 0.921116i | \(0.627279\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 9.77039i | − | 0.828713i | −0.910115 | − | 0.414357i | \(-0.864007\pi\) | ||
0.910115 | − | 0.414357i | \(-0.135993\pi\) | |||||||
\(140\) | −4.24365 | − | 5.85337i | −0.358654 | − | 0.494700i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −4.02140 | + | 1.30437i | −0.337468 | + | 0.109461i | ||||
\(143\) | 1.69141 | 0.141443 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.83716 | −0.816931 | ||||||||
\(146\) | −3.05536 | + | 0.991032i | −0.252863 | + | 0.0820184i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 7.82301 | + | 10.7905i | 0.643047 | + | 0.886971i | ||||
\(149\) | 15.8372i | 1.29743i | 0.761031 | + | 0.648715i | \(0.224693\pi\) | ||||
−0.761031 | + | 0.648715i | \(0.775307\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.38445 | −0.682317 | −0.341158 | − | 0.940006i | \(-0.610819\pi\) | ||||
−0.341158 | + | 0.940006i | \(0.610819\pi\) | |||||||
\(152\) | 7.16389 | + | 5.22156i | 0.581068 | + | 0.423524i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.726037 | + | 2.23838i | 0.0585057 | + | 0.180374i | ||||
\(155\) | 9.34649i | 0.750728i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 10.8788i | − | 0.868221i | −0.900860 | − | 0.434110i | \(-0.857063\pi\) | ||
0.900860 | − | 0.434110i | \(-0.142937\pi\) | |||||||
\(158\) | −20.0604 | + | 6.50676i | −1.59592 | + | 0.517650i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −5.65684 | − | 0.0143608i | −0.447212 | − | 0.00113532i | ||||
\(161\) | 13.0213 | 1.02622 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 11.4469i | − | 0.896592i | −0.893885 | − | 0.448296i | \(-0.852031\pi\) | ||
0.893885 | − | 0.448296i | \(-0.147969\pi\) | |||||||
\(164\) | 16.6681 | − | 12.0842i | 1.30156 | − | 0.943620i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.00467 | − | 9.26343i | −0.233208 | − | 0.718982i | ||||
\(167\) | 1.88089 | 0.145548 | 0.0727740 | − | 0.997348i | \(-0.476815\pi\) | ||||
0.0727740 | + | 0.997348i | \(0.476815\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.502438 | −0.0386490 | ||||||||
\(170\) | −2.87609 | − | 8.86701i | −0.220586 | − | 0.680069i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 7.10360 | + | 9.79817i | 0.541644 | + | 0.747104i | ||||
\(173\) | − | 2.11666i | − | 0.160927i | −0.996758 | − | 0.0804633i | \(-0.974360\pi\) | ||
0.996758 | − | 0.0804633i | \(-0.0256400\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.61492 | 0.273262 | ||||||||
\(176\) | 1.74993 | + | 0.572519i | 0.131906 | + | 0.0431552i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 8.14011 | − | 2.64031i | 0.610127 | − | 0.197900i | ||||
\(179\) | 2.30923i | 0.172600i | 0.996269 | + | 0.0863000i | \(0.0275044\pi\) | ||||
−0.996269 | + | 0.0863000i | \(0.972496\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 3.60210i | − | 0.267742i | −0.990999 | − | 0.133871i | \(-0.957259\pi\) | ||
0.990999 | − | 0.133871i | \(-0.0427408\pi\) | |||||||
\(182\) | −5.79592 | − | 17.8689i | −0.429622 | − | 1.32453i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 6.00107 | − | 8.23337i | 0.442405 | − | 0.606972i | ||||
\(185\) | −6.66397 | −0.489944 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.03408i | 0.221874i | ||||||||
\(188\) | −10.7181 | + | 7.77056i | −0.781700 | + | 0.566726i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.21619 | + | 1.36756i | −0.305875 | + | 0.0992131i | ||||
\(191\) | −0.250626 | −0.0181346 | −0.00906732 | − | 0.999959i | \(-0.502886\pi\) | ||||
−0.00906732 | + | 0.999959i | \(0.502886\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.6901 | 0.985437 | 0.492719 | − | 0.870189i | \(-0.336003\pi\) | ||||
0.492719 | + | 0.870189i | \(0.336003\pi\) | |||||||
\(194\) | −17.5427 | + | 5.69014i | −1.25950 | + | 0.408528i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 9.82486 | − | 7.12295i | 0.701776 | − | 0.508782i | ||||
\(197\) | 2.11735i | 0.150855i | 0.997151 | + | 0.0754276i | \(0.0240322\pi\) | ||||
−0.997151 | + | 0.0754276i | \(0.975968\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.80338 | 0.340502 | 0.170251 | − | 0.985401i | \(-0.445542\pi\) | ||||
0.170251 | + | 0.985401i | \(0.445542\pi\) | |||||||
\(200\) | 1.66599 | − | 2.28571i | 0.117803 | − | 0.161624i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.30569 | − | 4.02544i | −0.0918677 | − | 0.283229i | ||||
\(203\) | − | 35.5605i | − | 2.49586i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 10.2939i | 0.718954i | ||||||||
\(206\) | 0.117022 | − | 0.0379572i | 0.00815333 | − | 0.00264460i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −13.9696 | − | 4.57039i | −0.968619 | − | 0.316900i | ||||
\(209\) | 1.44268 | 0.0997922 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 24.5575i | 1.69061i | 0.534288 | + | 0.845303i | \(0.320580\pi\) | ||||
−0.534288 | + | 0.845303i | \(0.679420\pi\) | |||||||
\(212\) | −3.84024 | − | 5.29693i | −0.263749 | − | 0.363795i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.80948 | + | 5.57865i | 0.123694 | + | 0.381349i | ||||
\(215\) | −6.05114 | −0.412684 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −33.7868 | −2.29360 | ||||||||
\(218\) | −8.40462 | − | 25.9115i | −0.569232 | − | 1.75495i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.745332 | + | 0.540360i | −0.0502503 | + | 0.0364311i | ||||
\(221\) | − | 24.2209i | − | 1.62927i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 22.4334 | 1.50225 | 0.751126 | − | 0.660159i | \(-0.229511\pi\) | ||||
0.751126 | + | 0.660159i | \(0.229511\pi\) | |||||||
\(224\) | 0.0519131 | − | 20.4490i | 0.00346859 | − | 1.36631i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −19.1277 | + | 6.20424i | −1.27236 | + | 0.412700i | ||||
\(227\) | − | 12.6411i | − | 0.839019i | −0.907751 | − | 0.419510i | \(-0.862202\pi\) | ||
0.907751 | − | 0.419510i | \(-0.137798\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 23.9002i | − | 1.57937i | −0.613513 | − | 0.789685i | \(-0.710244\pi\) | ||
0.613513 | − | 0.789685i | \(-0.289756\pi\) | |||||||
\(230\) | 1.57172 | + | 4.84562i | 0.103636 | + | 0.319510i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −22.4849 | − | 16.3886i | −1.47621 | − | 1.07597i | ||||
\(233\) | 12.8040 | 0.838820 | 0.419410 | − | 0.907797i | \(-0.362237\pi\) | ||||
0.419410 | + | 0.907797i | \(0.362237\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 6.61929i | − | 0.431795i | ||||||
\(236\) | 6.09488 | + | 8.40683i | 0.396743 | + | 0.547238i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 32.0535 | − | 10.3968i | 2.07772 | − | 0.673926i | ||||
\(239\) | −26.4216 | −1.70907 | −0.854535 | − | 0.519394i | \(-0.826158\pi\) | ||||
−0.854535 | + | 0.519394i | \(0.826158\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.5273 | −0.678122 | −0.339061 | − | 0.940764i | \(-0.610109\pi\) | ||||
−0.339061 | + | 0.940764i | \(0.610109\pi\) | |||||||
\(242\) | −14.5124 | + | 4.70721i | −0.932891 | + | 0.302591i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −7.99300 | − | 11.0249i | −0.511699 | − | 0.705800i | ||||
\(245\) | 6.06762i | 0.387646i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −11.5168 | −0.732800 | ||||||||
\(248\) | −15.5712 | + | 21.3634i | −0.988771 | + | 1.35658i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0.436333 | + | 1.34522i | 0.0275961 | + | 0.0850791i | ||||
\(251\) | − | 19.6743i | − | 1.24183i | −0.783877 | − | 0.620916i | \(-0.786761\pi\) | ||
0.783877 | − | 0.620916i | \(-0.213239\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 1.65805i | − | 0.104241i | ||||||
\(254\) | 2.57342 | − | 0.834709i | 0.161470 | − | 0.0523743i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −12.9060 | − | 9.45706i | −0.806623 | − | 0.591067i | ||||
\(257\) | 0.423338 | 0.0264071 | 0.0132035 | − | 0.999913i | \(-0.495797\pi\) | ||||
0.0132035 | + | 0.999913i | \(0.495797\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 24.0897i | − | 1.49686i | ||||||
\(260\) | 5.94996 | − | 4.31367i | 0.369001 | − | 0.267523i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 3.76708 | + | 11.6140i | 0.232731 | + | 0.717513i | ||||
\(263\) | −3.20667 | −0.197732 | −0.0988659 | − | 0.995101i | \(-0.531521\pi\) | ||||
−0.0988659 | + | 0.995101i | \(0.531521\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.27127 | 0.200953 | ||||||||
\(266\) | −4.94361 | − | 15.2412i | −0.303112 | − | 0.934497i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 11.8292 | + | 16.3163i | 0.722582 | + | 0.996675i | ||||
\(269\) | − | 20.4597i | − | 1.24745i | −0.781645 | − | 0.623724i | \(-0.785619\pi\) | ||
0.781645 | − | 0.623724i | \(-0.214381\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.60732 | −0.583603 | −0.291802 | − | 0.956479i | \(-0.594255\pi\) | ||||
−0.291802 | + | 0.956479i | \(0.594255\pi\) | |||||||
\(272\) | 8.19845 | − | 25.0590i | 0.497104 | − | 1.51942i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 12.2590 | − | 3.97630i | 0.740592 | − | 0.240217i | ||||
\(275\) | − | 0.460301i | − | 0.0277572i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 23.3766i | 1.40456i | 0.711899 | + | 0.702282i | \(0.247835\pi\) | ||||
−0.711899 | + | 0.702282i | \(0.752165\pi\) | |||||||
\(278\) | 4.26314 | + | 13.1433i | 0.255686 | + | 0.788283i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 8.26265 | + | 6.02242i | 0.493788 | + | 0.359908i | ||||
\(281\) | 14.4810 | 0.863864 | 0.431932 | − | 0.901906i | \(-0.357832\pi\) | ||||
0.431932 | + | 0.901906i | \(0.357832\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 8.92352i | − | 0.530448i | −0.964187 | − | 0.265224i | \(-0.914554\pi\) | ||
0.964187 | − | 0.265224i | \(-0.0854459\pi\) | |||||||
\(284\) | 4.84051 | − | 3.50934i | 0.287232 | − | 0.208241i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.27531 | + | 0.738017i | −0.134542 | + | 0.0436399i | ||||
\(287\) | −37.2114 | −2.19652 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 26.4479 | 1.55576 | ||||||||
\(290\) | 13.2331 | − | 4.29228i | 0.777076 | − | 0.252051i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3.67771 | − | 2.66631i | 0.215222 | − | 0.156034i | ||||
\(293\) | 0.117355i | 0.00685593i | 0.999994 | + | 0.00342796i | \(0.00109116\pi\) | ||||
−0.999994 | + | 0.00342796i | \(0.998909\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.19188 | −0.302283 | ||||||||
\(296\) | −15.2319 | − | 11.1021i | −0.885336 | − | 0.645297i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −6.91028 | − | 21.3044i | −0.400301 | − | 1.23413i | ||||
\(299\) | 13.2362i | 0.765467i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 21.8744i | − | 1.26082i | ||||||
\(302\) | 11.2789 | − | 3.65841i | 0.649029 | − | 0.210518i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −11.9153 | − | 3.89830i | −0.683391 | − | 0.223583i | ||||
\(305\) | 6.80877 | 0.389869 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.9667i | 1.19663i | 0.801260 | + | 0.598316i | \(0.204163\pi\) | ||||
−0.801260 | + | 0.598316i | \(0.795837\pi\) | |||||||
\(308\) | −1.95336 | − | 2.69431i | −0.111303 | − | 0.153523i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −4.07818 | − | 12.5731i | −0.231625 | − | 0.714103i | ||||
\(311\) | −23.9561 | −1.35842 | −0.679212 | − | 0.733942i | \(-0.737678\pi\) | ||||
−0.679212 | + | 0.733942i | \(0.737678\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.83089 | −0.386105 | −0.193052 | − | 0.981188i | \(-0.561839\pi\) | ||||
−0.193052 | + | 0.981188i | \(0.561839\pi\) | |||||||
\(314\) | 4.74677 | + | 14.6343i | 0.267876 | + | 0.825863i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 24.1465 | − | 17.5060i | 1.35835 | − | 0.984792i | ||||
\(317\) | 13.6557i | 0.766982i | 0.923545 | + | 0.383491i | \(0.125278\pi\) | ||||
−0.923545 | + | 0.383491i | \(0.874722\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.52806 | −0.253522 | ||||||||
\(320\) | 7.61595 | − | 2.44895i | 0.425744 | − | 0.136900i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −17.5165 | + | 5.68163i | −0.976156 | + | 0.316625i | ||||
\(323\) | − | 20.6591i | − | 1.14950i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.67457i | 0.203828i | ||||||||
\(326\) | 4.99467 | + | 15.3986i | 0.276629 | + | 0.852850i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −17.1495 | + | 23.5288i | −0.946921 | + | 1.29916i | ||||
\(329\) | 23.9282 | 1.31920 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 30.3581i | − | 1.66863i | −0.551287 | − | 0.834316i | \(-0.685863\pi\) | ||
0.551287 | − | 0.834316i | \(-0.314137\pi\) | |||||||
\(332\) | 8.08388 | + | 11.1503i | 0.443661 | + | 0.611953i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.53021 | + | 0.820696i | −0.138447 | + | 0.0449065i | ||||
\(335\) | −10.0766 | −0.550543 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.67022 | −0.472297 | −0.236148 | − | 0.971717i | \(-0.575885\pi\) | ||||
−0.236148 | + | 0.971717i | \(0.575885\pi\) | |||||||
\(338\) | 0.675889 | − | 0.219230i | 0.0367635 | − | 0.0119245i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 7.73794 | + | 10.6731i | 0.419649 | + | 0.578832i | ||||
\(341\) | 4.30220i | 0.232977i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.37046 | 0.181988 | ||||||||
\(344\) | −13.8312 | − | 10.0811i | −0.745726 | − | 0.543539i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.923568 | + | 2.84737i | 0.0496513 | + | 0.153075i | ||||
\(347\) | 30.6433i | 1.64502i | 0.568751 | + | 0.822510i | \(0.307427\pi\) | ||||
−0.568751 | + | 0.822510i | \(0.692573\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.74457i | 0.414557i | 0.978282 | + | 0.207279i | \(0.0664606\pi\) | ||||
−0.978282 | + | 0.207279i | \(0.933539\pi\) | |||||||
\(350\) | −4.86285 | + | 1.57731i | −0.259930 | + | 0.0843106i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.60385 | − | 0.00661030i | −0.138786 | − | 0.000352330i | ||||
\(353\) | 6.41334 | 0.341348 | 0.170674 | − | 0.985328i | \(-0.445406\pi\) | ||||
0.170674 | + | 0.985328i | \(0.445406\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.98940i | 0.158661i | ||||||||
\(356\) | −9.79817 | + | 7.10360i | −0.519302 | + | 0.376490i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.00759 | − | 3.10642i | −0.0532530 | − | 0.164179i | ||||
\(359\) | 27.4857 | 1.45064 | 0.725320 | − | 0.688412i | \(-0.241692\pi\) | ||||
0.725320 | + | 0.688412i | \(0.241692\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.17675 | 0.482987 | ||||||||
\(362\) | 1.57172 | + | 4.84562i | 0.0826076 | + | 0.254680i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 15.5936 | + | 21.5086i | 0.817325 | + | 1.12736i | ||||
\(365\) | 2.27127i | 0.118884i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.52793 | −0.392955 | −0.196477 | − | 0.980508i | \(-0.562950\pi\) | ||||
−0.196477 | + | 0.980508i | \(0.562950\pi\) | |||||||
\(368\) | −4.48027 | + | 13.6941i | −0.233550 | + | 0.713857i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 8.96449 | − | 2.90771i | 0.466042 | − | 0.151165i | ||||
\(371\) | 11.8254i | 0.613943i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 12.4978i | − | 0.647113i | −0.946209 | − | 0.323557i | \(-0.895121\pi\) | ||
0.946209 | − | 0.323557i | \(-0.104879\pi\) | |||||||
\(374\) | −1.32387 | − | 4.08150i | −0.0684556 | − | 0.211049i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 11.0277 | − | 15.1298i | 0.568709 | − | 0.780259i | ||||
\(377\) | 36.1473 | 1.86168 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.59150i | 0.338583i | 0.985566 | + | 0.169291i | \(0.0541479\pi\) | ||||
−0.985566 | + | 0.169291i | \(0.945852\pi\) | |||||||
\(380\) | 5.07499 | − | 3.67933i | 0.260342 | − | 0.188746i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0.337147 | − | 0.109356i | 0.0172499 | − | 0.00559516i | ||||
\(383\) | 6.51916 | 0.333113 | 0.166557 | − | 0.986032i | \(-0.446735\pi\) | ||||
0.166557 | + | 0.986032i | \(0.446735\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.66395 | 0.0848028 | ||||||||
\(386\) | −18.4162 | + | 5.97346i | −0.937361 | + | 0.304041i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 21.1160 | − | 15.3090i | 1.07200 | − | 0.777194i | ||||
\(389\) | 14.6791i | 0.744261i | 0.928180 | + | 0.372131i | \(0.121373\pi\) | ||||
−0.928180 | + | 0.372131i | \(0.878627\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −23.7433 | −1.20075 | ||||||||
\(392\) | −10.1086 | + | 13.8688i | −0.510562 | + | 0.700482i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −0.923872 | − | 2.84830i | −0.0465440 | − | 0.143496i | ||||
\(395\) | 14.9124i | 0.750323i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 28.9764i | − | 1.45429i | −0.686486 | − | 0.727143i | \(-0.740848\pi\) | ||
0.686486 | − | 0.727143i | \(-0.259152\pi\) | |||||||
\(398\) | −6.46160 | + | 2.09587i | −0.323890 | + | 0.105057i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.24379 | + | 3.80171i | −0.0621896 | + | 0.190085i | ||||
\(401\) | −23.8391 | −1.19047 | −0.595233 | − | 0.803553i | \(-0.702940\pi\) | ||||
−0.595233 | + | 0.803553i | \(0.702940\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 34.3443i | − | 1.71081i | ||||||
\(404\) | 3.51287 | + | 4.84538i | 0.174772 | + | 0.241067i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 15.5162 | + | 47.8367i | 0.770057 | + | 2.37409i | ||||
\(407\) | −3.06743 | −0.152047 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −25.7793 | −1.27470 | −0.637352 | − | 0.770573i | \(-0.719970\pi\) | ||||
−0.637352 | + | 0.770573i | \(0.719970\pi\) | |||||||
\(410\) | −4.49155 | − | 13.8475i | −0.221822 | − | 0.683878i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −0.140859 | + | 0.102121i | −0.00693961 | + | 0.00503116i | ||||
\(413\) | − | 18.7682i | − | 0.923523i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.88619 | −0.338030 | ||||||||
\(416\) | 20.7864 | + | 0.0527697i | 1.01914 | + | 0.00258725i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.94072 | + | 0.629489i | −0.0949237 | + | 0.0307893i | ||||
\(419\) | 25.8254i | 1.26165i | 0.775924 | + | 0.630826i | \(0.217284\pi\) | ||||
−0.775924 | + | 0.630826i | \(0.782716\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 20.6935i | − | 1.00854i | −0.863546 | − | 0.504270i | \(-0.831762\pi\) | ||
0.863546 | − | 0.504270i | \(-0.168238\pi\) | |||||||
\(422\) | −10.7152 | − | 33.0352i | −0.521609 | − | 1.60813i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 7.47719 | + | 5.44991i | 0.363124 | + | 0.264671i | ||||
\(425\) | −6.59150 | −0.319735 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 24.6131i | 1.19111i | ||||||||
\(428\) | −4.86830 | − | 6.71497i | −0.235318 | − | 0.324580i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 8.14011 | − | 2.64031i | 0.392551 | − | 0.127327i | ||||
\(431\) | 14.4065 | 0.693937 | 0.346969 | − | 0.937877i | \(-0.387211\pi\) | ||||
0.346969 | + | 0.937877i | \(0.387211\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.24912 | −0.204200 | −0.102100 | − | 0.994774i | \(-0.532556\pi\) | ||||
−0.102100 | + | 0.994774i | \(0.532556\pi\) | |||||||
\(434\) | 45.4506 | − | 14.7423i | 2.18170 | − | 0.707653i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 22.6121 | + | 31.1894i | 1.08292 | + | 1.49370i | ||||
\(437\) | 11.2897i | 0.540061i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.77643 | −0.227967 | −0.113983 | − | 0.993483i | \(-0.536361\pi\) | ||||
−0.113983 | + | 0.993483i | \(0.536361\pi\) | |||||||
\(440\) | 0.766858 | − | 1.05212i | 0.0365585 | − | 0.0501576i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 10.5684 | + | 32.5824i | 0.502687 | + | 1.54979i | ||||
\(443\) | − | 15.5792i | − | 0.740189i | −0.928994 | − | 0.370094i | \(-0.879325\pi\) | ||
0.928994 | − | 0.370094i | \(-0.120675\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 6.05114i | − | 0.286852i | ||||||
\(446\) | −30.1778 | + | 9.78844i | −1.42896 | + | 0.463496i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 8.85274 | + | 27.5310i | 0.418253 | + | 1.30072i | ||||
\(449\) | −39.8219 | −1.87931 | −0.939655 | − | 0.342124i | \(-0.888854\pi\) | ||||
−0.939655 | + | 0.342124i | \(0.888854\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.73827i | 0.223117i | ||||||||
\(452\) | 23.0239 | − | 16.6921i | 1.08295 | − | 0.785131i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 5.51573 | + | 17.0050i | 0.258866 | + | 0.798086i | ||||
\(455\) | −13.2833 | −0.622728 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −37.4853 | −1.75349 | −0.876744 | − | 0.480958i | \(-0.840289\pi\) | ||||
−0.876744 | + | 0.480958i | \(0.840289\pi\) | |||||||
\(458\) | 10.4284 | + | 32.1510i | 0.487289 | + | 1.50232i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −4.22861 | − | 5.83262i | −0.197160 | − | 0.271947i | ||||
\(461\) | 41.2161i | 1.91963i | 0.280642 | + | 0.959813i | \(0.409453\pi\) | ||||
−0.280642 | + | 0.959813i | \(0.590547\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9.97645 | −0.463645 | −0.231823 | − | 0.972758i | \(-0.574469\pi\) | ||||
−0.231823 | + | 0.972758i | \(0.574469\pi\) | |||||||
\(464\) | 37.3980 | + | 12.2354i | 1.73616 | + | 0.568013i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −17.2242 | + | 5.58682i | −0.797897 | + | 0.258805i | ||||
\(467\) | − | 30.9987i | − | 1.43445i | −0.696842 | − | 0.717225i | \(-0.745412\pi\) | ||
0.696842 | − | 0.717225i | \(-0.254588\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 36.4260i | − | 1.68200i | ||||||
\(470\) | 2.88821 | + | 8.90439i | 0.133223 | + | 0.410729i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −11.8671 | − | 8.64962i | −0.546229 | − | 0.398131i | ||||
\(473\) | −2.78535 | −0.128070 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.13421i | 0.143807i | ||||||||
\(476\) | −38.5825 | + | 27.9720i | −1.76843 | + | 1.28210i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 35.5428 | − | 11.5286i | 1.62569 | − | 0.527306i | ||||
\(479\) | −15.7934 | −0.721620 | −0.360810 | − | 0.932639i | \(-0.617500\pi\) | ||||
−0.360810 | + | 0.932639i | \(0.617500\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 24.4872 | 1.11652 | ||||||||
\(482\) | 14.1615 | − | 4.59341i | 0.645039 | − | 0.209224i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 17.4684 | − | 12.6645i | 0.794019 | − | 0.575658i | ||||
\(485\) | 13.0408i | 0.592153i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −31.5225 | −1.42842 | −0.714211 | − | 0.699930i | \(-0.753215\pi\) | ||||
−0.714211 | + | 0.699930i | \(0.753215\pi\) | |||||||
\(488\) | 15.5629 | + | 11.3434i | 0.704499 | + | 0.513490i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.64751 | − | 8.16228i | −0.119602 | − | 0.368734i | ||||
\(491\) | − | 22.5728i | − | 1.01870i | −0.860561 | − | 0.509348i | \(-0.829887\pi\) | ||
0.860561 | − | 0.509348i | \(-0.170113\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 64.8416i | 2.92032i | ||||||||
\(494\) | 15.4927 | − | 5.02518i | 0.697049 | − | 0.226094i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 11.6251 | − | 35.5326i | 0.521982 | − | 1.59546i | ||||
\(497\) | −10.8064 | −0.484735 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 39.6903i | 1.77678i | 0.459089 | + | 0.888390i | \(0.348176\pi\) | ||||
−0.459089 | + | 0.888390i | \(0.651824\pi\) | |||||||
\(500\) | −1.17393 | − | 1.61923i | −0.0524996 | − | 0.0724140i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 8.58455 | + | 26.4663i | 0.383147 | + | 1.18125i | ||||
\(503\) | 15.5597 | 0.693773 | 0.346886 | − | 0.937907i | \(-0.387239\pi\) | ||||
0.346886 | + | 0.937907i | \(0.387239\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.99241 | −0.133160 | ||||||||
\(506\) | 0.723463 | + | 2.23044i | 0.0321619 | + | 0.0991553i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3.09760 | + | 2.24573i | −0.137434 | + | 0.0996383i | ||||
\(509\) | 22.0581i | 0.977707i | 0.872366 | + | 0.488853i | \(0.162585\pi\) | ||||
−0.872366 | + | 0.488853i | \(0.837415\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.21047 | −0.363210 | ||||||||
\(512\) | 21.4878 | + | 7.09052i | 0.949635 | + | 0.313360i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −0.569482 | + | 0.184716i | −0.0251188 | + | 0.00814749i | ||||
\(515\) | − | 0.0869913i | − | 0.00383329i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 3.04687i | − | 0.134001i | ||||||
\(518\) | 10.5111 | + | 32.4059i | 0.461832 | + | 1.42383i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −6.12180 | + | 8.39900i | −0.268458 | + | 0.368320i | ||||
\(521\) | 11.3190 | 0.495895 | 0.247947 | − | 0.968774i | \(-0.420244\pi\) | ||||
0.247947 | + | 0.968774i | \(0.420244\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 31.9623i | − | 1.39761i | −0.715311 | − | 0.698806i | \(-0.753715\pi\) | ||
0.715311 | − | 0.698806i | \(-0.246285\pi\) | |||||||
\(524\) | −10.1351 | − | 13.9796i | −0.442754 | − | 0.610702i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.31367 | − | 1.39918i | 0.188085 | − | 0.0610070i | ||||
\(527\) | 61.6074 | 2.68366 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.0249 | −0.435863 | ||||||||
\(530\) | −4.40058 | + | 1.42737i | −0.191149 | + | 0.0620008i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 13.3005 | + | 18.3457i | 0.576648 | + | 0.795386i | ||||
\(533\) | − | 37.8254i | − | 1.63840i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.14702 | 0.179291 | ||||||||
\(536\) | −23.0322 | − | 16.7875i | −0.994837 | − | 0.725109i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 8.92723 | + | 27.5227i | 0.384880 | + | 1.18659i | ||||
\(539\) | 2.79294i | 0.120300i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.47508i | 0.407366i | 0.979037 | + | 0.203683i | \(0.0652911\pi\) | ||||
−0.979037 | + | 0.203683i | \(0.934709\pi\) | |||||||
\(542\) | 12.9240 | − | 4.19199i | 0.555131 | − | 0.180062i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −0.0946593 | + | 37.2870i | −0.00405848 | + | 1.59867i | ||||
\(545\) | −19.2619 | −0.825090 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 23.6218i | − | 1.00999i | −0.863121 | − | 0.504997i | \(-0.831493\pi\) | ||
0.863121 | − | 0.504997i | \(-0.168507\pi\) | |||||||
\(548\) | −14.7560 | + | 10.6980i | −0.630346 | + | 0.456996i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.200845 | + | 0.619206i | 0.00856405 | + | 0.0264030i | ||||
\(551\) | 30.8317 | 1.31347 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −53.9070 | −2.29236 | ||||||||
\(554\) | −10.2000 | − | 31.4467i | −0.433356 | − | 1.33604i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −11.4697 | − | 15.8205i | −0.486424 | − | 0.670937i | ||||
\(557\) | − | 21.2630i | − | 0.900944i | −0.892791 | − | 0.450472i | \(-0.851256\pi\) | ||
0.892791 | − | 0.450472i | \(-0.148744\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 22.2353 | 0.940454 | ||||||||
\(560\) | −13.7429 | − | 4.49620i | −0.580742 | − | 0.189999i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −19.4801 | + | 6.31854i | −0.821719 | + | 0.266531i | ||||
\(563\) | 35.1684i | 1.48217i | 0.671411 | + | 0.741086i | \(0.265689\pi\) | ||||
−0.671411 | + | 0.741086i | \(0.734311\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 14.2190i | 0.598200i | ||||||||
\(566\) | 3.89363 | + | 12.0041i | 0.163661 | + | 0.504569i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.98031 | + | 6.83290i | −0.208969 | + | 0.286702i | ||||
\(569\) | −4.53588 | −0.190154 | −0.0950770 | − | 0.995470i | \(-0.530310\pi\) | ||||
−0.0950770 | + | 0.995470i | \(0.530310\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 43.9496i | 1.83923i | 0.392819 | + | 0.919616i | \(0.371500\pi\) | ||||
−0.392819 | + | 0.919616i | \(0.628500\pi\) | |||||||
\(572\) | 2.73877 | − | 1.98559i | 0.114514 | − | 0.0830216i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 50.0575 | − | 16.2366i | 2.08936 | − | 0.677702i | ||||
\(575\) | 3.60210 | 0.150218 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 32.8371 | 1.36703 | 0.683513 | − | 0.729938i | \(-0.260451\pi\) | ||||
0.683513 | + | 0.729938i | \(0.260451\pi\) | |||||||
\(578\) | −35.5782 | + | 11.5401i | −1.47986 | + | 0.480005i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −15.9286 | + | 11.5481i | −0.661399 | + | 0.479509i | ||||
\(581\) | − | 24.8930i | − | 1.03274i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.50577 | 0.0623627 | ||||||||
\(584\) | −3.78392 | + | 5.19148i | −0.156580 | + | 0.214825i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.0512057 | − | 0.157868i | −0.00211529 | − | 0.00652145i | ||||
\(587\) | 26.1919i | 1.08106i | 0.841326 | + | 0.540529i | \(0.181776\pi\) | ||||
−0.841326 | + | 0.540529i | \(0.818224\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 29.2938i | − | 1.20703i | ||||||
\(590\) | 6.98421 | − | 2.26539i | 0.287535 | − | 0.0932645i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 25.3344 | + | 8.28858i | 1.04124 | + | 0.340659i | ||||
\(593\) | 35.2748 | 1.44856 | 0.724281 | − | 0.689505i | \(-0.242172\pi\) | ||||
0.724281 | + | 0.689505i | \(0.242172\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 23.8277i | − | 0.976842i | ||||||
\(596\) | 18.5917 | + | 25.6440i | 0.761544 | + | 1.05042i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −5.77538 | − | 17.8055i | −0.236173 | − | 0.728123i | ||||
\(599\) | 4.41530 | 0.180404 | 0.0902022 | − | 0.995923i | \(-0.471249\pi\) | ||||
0.0902022 | + | 0.995923i | \(0.471249\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.09117 | −0.330046 | −0.165023 | − | 0.986290i | \(-0.552770\pi\) | ||||
−0.165023 | + | 0.986290i | \(0.552770\pi\) | |||||||
\(602\) | 9.54451 | + | 29.4258i | 0.389005 | + | 1.19931i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −13.5763 | + | 9.84273i | −0.552413 | + | 0.400495i | ||||
\(605\) | 10.7881i | 0.438600i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15.0891 | 0.612449 | 0.306225 | − | 0.951959i | \(-0.400934\pi\) | ||||
0.306225 | + | 0.951959i | \(0.400934\pi\) | |||||||
\(608\) | 17.7297 | + | 0.0450097i | 0.719034 | + | 0.00182539i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −9.15929 | + | 2.97089i | −0.370849 | + | 0.120288i | ||||
\(611\) | 24.3230i | 0.984004i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 39.7493i | 1.60546i | 0.596344 | + | 0.802729i | \(0.296619\pi\) | ||||
−0.596344 | + | 0.802729i | \(0.703381\pi\) | |||||||
\(614\) | −9.14845 | − | 28.2048i | −0.369202 | − | 1.13825i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.80331 | + | 2.77213i | 0.153240 | + | 0.111692i | ||||
\(617\) | −5.32118 | −0.214223 | −0.107111 | − | 0.994247i | \(-0.534160\pi\) | ||||
−0.107111 | + | 0.994247i | \(0.534160\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 13.7069i | 0.550927i | 0.961312 | + | 0.275463i | \(0.0888313\pi\) | ||||
−0.961312 | + | 0.275463i | \(0.911169\pi\) | |||||||
\(620\) | 10.9721 | + | 15.1341i | 0.440650 | + | 0.607800i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 32.2262 | − | 10.4528i | 1.29215 | − | 0.419120i | ||||
\(623\) | 21.8744 | 0.876378 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 9.18904 | − | 2.98054i | 0.367268 | − | 0.119127i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −12.7709 | − | 17.6152i | −0.509614 | − | 0.702923i | ||||
\(629\) | 43.9255i | 1.75143i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.8516 | 0.909710 | 0.454855 | − | 0.890566i | \(-0.349691\pi\) | ||||
0.454855 | + | 0.890566i | \(0.349691\pi\) | |||||||
\(632\) | −24.8439 | + | 34.0854i | −0.988237 | + | 1.35584i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −5.95844 | − | 18.3699i | −0.236640 | − | 0.729563i | ||||
\(635\) | − | 1.91301i | − | 0.0759154i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 22.2959i | − | 0.883395i | ||||||
\(638\) | 6.09123 | − | 1.97574i | 0.241154 | − | 0.0782203i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −9.17656 | + | 6.61746i | −0.362735 | + | 0.261578i | ||||
\(641\) | −22.8938 | −0.904252 | −0.452126 | − | 0.891954i | \(-0.649334\pi\) | ||||
−0.452126 | + | 0.891954i | \(0.649334\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 29.0899i | − | 1.14719i | −0.819138 | − | 0.573597i | \(-0.805548\pi\) | ||
0.819138 | − | 0.573597i | \(-0.194452\pi\) | |||||||
\(644\) | 21.0844 | − | 15.2861i | 0.830843 | − | 0.602355i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 9.01426 | + | 27.7910i | 0.354661 | + | 1.09342i | ||||
\(647\) | 23.5493 | 0.925819 | 0.462910 | − | 0.886405i | \(-0.346805\pi\) | ||||
0.462910 | + | 0.886405i | \(0.346805\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.38983 | −0.0938089 | ||||||||
\(650\) | −1.60333 | − | 4.94310i | −0.0628880 | − | 0.193884i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −13.4378 | − | 18.5352i | −0.526267 | − | 0.725893i | ||||
\(653\) | − | 0.995952i | − | 0.0389746i | −0.999810 | − | 0.0194873i | \(-0.993797\pi\) | ||
0.999810 | − | 0.0194873i | \(-0.00620339\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.63351 | 0.337339 | ||||||||
\(656\) | 12.8034 | − | 39.1342i | 0.499889 | − | 1.52793i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −32.1886 | + | 10.4407i | −1.25484 | + | 0.407019i | ||||
\(659\) | 5.16847i | 0.201335i | 0.994920 | + | 0.100668i | \(0.0320979\pi\) | ||||
−0.994920 | + | 0.100668i | \(0.967902\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 42.6961i | − | 1.66069i | −0.557252 | − | 0.830343i | \(-0.688144\pi\) | ||
0.557252 | − | 0.830343i | \(-0.311856\pi\) | |||||||
\(662\) | 13.2462 | + | 40.8383i | 0.514830 | + | 1.58722i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −15.7398 | − | 11.4723i | −0.610824 | − | 0.445213i | ||||
\(665\) | −11.3299 | −0.439354 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 35.4345i | − | 1.37203i | ||||||
\(668\) | 3.04559 | − | 2.20803i | 0.117838 | − | 0.0854313i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 13.5552 | − | 4.39675i | 0.523683 | − | 0.169861i | ||||
\(671\) | 3.13409 | 0.120990 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.845304 | −0.0325841 | −0.0162920 | − | 0.999867i | \(-0.505186\pi\) | ||||
−0.0162920 | + | 0.999867i | \(0.505186\pi\) | |||||||
\(674\) | 11.6633 | − | 3.78310i | 0.449255 | − | 0.145720i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −0.813561 | + | 0.589825i | −0.0312908 | + | 0.0226856i | ||||
\(677\) | − | 46.3596i | − | 1.78175i | −0.454253 | − | 0.890873i | \(-0.650094\pi\) | ||
0.454253 | − | 0.890873i | \(-0.349906\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −47.1414 | −1.80912 | ||||||||
\(680\) | −15.0663 | − | 10.9814i | −0.577765 | − | 0.421117i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.87719 | − | 5.78740i | −0.0718814 | − | 0.221611i | ||||
\(683\) | 9.34244i | 0.357479i | 0.983896 | + | 0.178739i | \(0.0572019\pi\) | ||||
−0.983896 | + | 0.178739i | \(0.942798\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 9.11300i | − | 0.348190i | ||||||
\(686\) | −4.53401 | + | 1.47064i | −0.173109 | + | 0.0561494i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 23.0047 | + | 7.52636i | 0.877045 | + | 0.286940i | ||||
\(689\) | −12.0205 | −0.457945 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 24.7917i | 0.943122i | 0.881833 | + | 0.471561i | \(0.156309\pi\) | ||||
−0.881833 | + | 0.471561i | \(0.843691\pi\) | |||||||
\(692\) | −2.48480 | − | 3.42735i | −0.0944580 | − | 0.130288i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −13.3707 | − | 41.2220i | −0.507545 | − | 1.56476i | ||||
\(695\) | 9.77039 | 0.370612 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 67.8520 | 2.57008 | ||||||||
\(698\) | −3.37921 | − | 10.4181i | −0.127905 | − | 0.394332i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 5.85337 | − | 4.24365i | 0.221237 | − | 0.160395i | ||||
\(701\) | − | 30.1602i | − | 1.13914i | −0.821944 | − | 0.569568i | \(-0.807110\pi\) | ||
0.821944 | − | 0.569568i | \(-0.192890\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 20.8862 | 0.787739 | ||||||||
\(704\) | 3.50563 | − | 1.12725i | 0.132123 | − | 0.0424850i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −8.62734 | + | 2.79835i | −0.324694 | + | 0.105317i | ||||
\(707\) | − | 10.8173i | − | 0.406826i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 1.78076i | − | 0.0668780i | −0.999441 | − | 0.0334390i | \(-0.989354\pi\) | ||
0.999441 | − | 0.0334390i | \(-0.0106459\pi\) | |||||||
\(710\) | −1.30437 | − | 4.02140i | −0.0489523 | − | 0.150920i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 10.0811 | − | 13.8312i | 0.377807 | − | 0.518345i | ||||
\(713\) | −33.6670 | −1.26084 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.69141i | 0.0632551i | ||||||||
\(716\) | 2.71087 | + | 3.73917i | 0.101310 | + | 0.139739i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −36.9743 | + | 11.9929i | −1.37987 | + | 0.447572i | ||||
\(719\) | 14.4640 | 0.539416 | 0.269708 | − | 0.962942i | \(-0.413073\pi\) | ||||
0.269708 | + | 0.962942i | \(0.413073\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.314466 | 0.0117113 | ||||||||
\(722\) | −12.3447 | + | 4.00412i | −0.459424 | + | 0.149018i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −4.22861 | − | 5.83262i | −0.157155 | − | 0.216768i | ||||
\(725\) | − | 9.83716i | − | 0.365343i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 35.6743 | 1.32309 | 0.661544 | − | 0.749907i | \(-0.269902\pi\) | ||||
0.661544 | + | 0.749907i | \(0.269902\pi\) | |||||||
\(728\) | −30.3617 | − | 22.1298i | −1.12528 | − | 0.820184i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −0.991032 | − | 3.05536i | −0.0366797 | − | 0.113084i | ||||
\(731\) | 39.8861i | 1.47524i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 40.6687i | 1.50213i | 0.660226 | + | 0.751067i | \(0.270460\pi\) | ||||
−0.660226 | + | 0.751067i | \(0.729540\pi\) | |||||||
\(734\) | 10.1267 | − | 3.28468i | 0.373784 | − | 0.121240i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.0517291 | − | 20.3765i | 0.00190676 | − | 0.751088i | ||||
\(737\) | −4.63826 | −0.170853 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 24.2936i | 0.893655i | 0.894620 | + | 0.446827i | \(0.147446\pi\) | ||||
−0.894620 | + | 0.446827i | \(0.852554\pi\) | |||||||
\(740\) | −10.7905 | + | 7.82301i | −0.396666 | + | 0.287579i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −5.15981 | − | 15.9077i | −0.189422 | − | 0.583991i | ||||
\(743\) | 22.4851 | 0.824897 | 0.412448 | − | 0.910981i | \(-0.364674\pi\) | ||||
0.412448 | + | 0.910981i | \(0.364674\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15.8372 | −0.580229 | ||||||||
\(746\) | 5.45322 | + | 16.8123i | 0.199657 | + | 0.615543i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3.56178 | + | 4.91286i | 0.130232 | + | 0.179632i | ||||
\(749\) | 14.9911i | 0.547764i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −26.0441 | −0.950364 | −0.475182 | − | 0.879887i | \(-0.657618\pi\) | ||||
−0.475182 | + | 0.879887i | \(0.657618\pi\) | |||||||
\(752\) | −8.23301 | + | 25.1646i | −0.300227 | + | 0.917658i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −48.6260 | + | 15.7723i | −1.77085 | + | 0.574392i | ||||
\(755\) | − | 8.38445i | − | 0.305141i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 12.4087i | − | 0.451003i | −0.974243 | − | 0.225501i | \(-0.927598\pi\) | ||
0.974243 | − | 0.225501i | \(-0.0724020\pi\) | |||||||
\(758\) | −2.87609 | − | 8.86701i | −0.104464 | − | 0.322064i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −5.22156 | + | 7.16389i | −0.189406 | + | 0.259862i | ||||
\(761\) | −14.4810 | −0.524936 | −0.262468 | − | 0.964941i | \(-0.584536\pi\) | ||||
−0.262468 | + | 0.964941i | \(0.584536\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 69.6303i | − | 2.52079i | ||||||
\(764\) | −0.405820 | + | 0.294216i | −0.0146821 | + | 0.0106444i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −8.76969 | + | 2.84452i | −0.316862 | + | 0.102777i | ||||
\(767\) | 19.0779 | 0.688863 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 31.4714 | 1.13489 | 0.567445 | − | 0.823412i | \(-0.307932\pi\) | ||||
0.567445 | + | 0.823412i | \(0.307932\pi\) | |||||||
\(770\) | −2.23838 | + | 0.726037i | −0.0806655 | + | 0.0261646i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 22.1674 | − | 16.0712i | 0.797823 | − | 0.578416i | ||||
\(773\) | 6.49345i | 0.233553i | 0.993158 | + | 0.116777i | \(0.0372561\pi\) | ||||
−0.993158 | + | 0.116777i | \(0.962744\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.34649 | −0.335736 | ||||||||
\(776\) | −21.7259 | + | 29.8075i | −0.779913 | + | 1.07003i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −6.40499 | − | 19.7466i | −0.229630 | − | 0.707951i | ||||
\(779\) | − | 32.2631i | − | 1.15594i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.37602i | 0.0492380i | ||||||||
\(782\) | 31.9399 | − | 10.3600i | 1.14217 | − | 0.370472i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 7.54686 | − | 23.0673i | 0.269531 | − | 0.823833i | ||||
\(785\) | 10.8788 | 0.388280 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 38.2974i | 1.36515i | 0.730813 | + | 0.682577i | \(0.239141\pi\) | ||||
−0.730813 | + | 0.682577i | \(0.760859\pi\) | |||||||
\(788\) | 2.48562 | + | 3.42848i | 0.0885465 | + | 0.122134i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −6.50676 | − | 20.0604i | −0.231500 | − | 0.713717i | ||||
\(791\) | −51.4007 | −1.82760 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −25.0193 | −0.888461 | ||||||||
\(794\) | 12.6434 | + | 38.9796i | 0.448697 | + | 1.38334i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 7.77776 | − | 5.63882i | 0.275675 | − | 0.199863i | ||||
\(797\) | − | 3.86049i | − | 0.136746i | −0.997660 | − | 0.0683728i | \(-0.978219\pi\) | ||
0.997660 | − | 0.0683728i | \(-0.0217807\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −43.6310 | −1.54356 | ||||||||
\(800\) | 0.0143608 | − | 5.65684i | 0.000507731 | − | 0.199999i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 32.0687 | − | 10.4018i | 1.13239 | − | 0.367299i | ||||
\(803\) | 1.04547i | 0.0368939i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 13.0213i | 0.458941i | ||||||||
\(806\) | 14.9856 | + | 46.2006i | 0.527844 | + | 1.62735i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −6.83977 | − | 4.98532i | −0.240622 | − | 0.175383i | ||||
\(809\) | −52.9957 | −1.86323 | −0.931614 | − | 0.363449i | \(-0.881599\pi\) | ||||
−0.931614 | + | 0.363449i | \(0.881599\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14.3640i | 0.504387i | 0.967677 | + | 0.252194i | \(0.0811520\pi\) | ||||
−0.967677 | + | 0.252194i | \(0.918848\pi\) | |||||||
\(812\) | −41.7454 | − | 57.5805i | −1.46498 | − | 2.02068i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 4.12637 | − | 1.33842i | 0.144629 | − | 0.0469117i | ||||
\(815\) | 11.4469 | 0.400968 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 18.9655 | 0.663520 | ||||||||
\(818\) | 34.6788 | − | 11.2484i | 1.21251 | − | 0.393289i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 12.0842 | + | 16.6681i | 0.422000 | + | 0.582075i | ||||
\(821\) | − | 28.6033i | − | 0.998261i | −0.866527 | − | 0.499131i | \(-0.833653\pi\) | ||
0.866527 | − | 0.499131i | \(-0.166347\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.30220 | 0.289397 | 0.144698 | − | 0.989476i | \(-0.453779\pi\) | ||||
0.144698 | + | 0.989476i | \(0.453779\pi\) | |||||||
\(824\) | 0.144927 | − | 0.198837i | 0.00504876 | − | 0.00692681i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 8.18919 | + | 25.2473i | 0.284938 | + | 0.878467i | ||||
\(827\) | 2.35542i | 0.0819058i | 0.999161 | + | 0.0409529i | \(0.0130394\pi\) | ||||
−0.999161 | + | 0.0409529i | \(0.986961\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14.5848i | 0.506551i | 0.967394 | + | 0.253275i | \(0.0815079\pi\) | ||||
−0.967394 | + | 0.253275i | \(0.918492\pi\) | |||||||
\(830\) | 9.26343 | − | 3.00467i | 0.321538 | − | 0.104294i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −27.9853 | + | 8.99882i | −0.970216 | + | 0.311978i | ||||
\(833\) | 39.9948 | 1.38574 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.88089i | 0.0650910i | ||||||||
\(836\) | 2.33603 | − | 1.69360i | 0.0807931 | − | 0.0585744i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −11.2685 | − | 34.7408i | −0.389263 | − | 1.20010i | ||||
\(839\) | −46.9537 | −1.62102 | −0.810511 | − | 0.585723i | \(-0.800811\pi\) | ||||
−0.810511 | + | 0.585723i | \(0.800811\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −67.7697 | −2.33688 | ||||||||
\(842\) | 9.02927 | + | 27.8373i | 0.311169 | + | 0.959337i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 28.8287 | + | 39.7641i | 0.992323 | + | 1.36874i | ||||
\(845\) | − | 0.502438i | − | 0.0172844i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −38.9982 | −1.33999 | ||||||||
\(848\) | −12.4364 | − | 4.06878i | −0.427069 | − | 0.139723i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 8.86701 | − | 2.87609i | 0.304136 | − | 0.0986491i | ||||
\(851\) | − | 24.0043i | − | 0.822856i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15.9013i | 0.544449i | 0.962234 | + | 0.272224i | \(0.0877593\pi\) | ||||
−0.962234 | + | 0.272224i | \(0.912241\pi\) | |||||||
\(854\) | −10.7395 | − | 33.1101i | −0.367499 | − | 1.13300i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 9.47889 | + | 6.90890i | 0.323982 | + | 0.236141i | ||||
\(857\) | −1.31445 | −0.0449009 | −0.0224504 | − | 0.999748i | \(-0.507147\pi\) | ||||
−0.0224504 | + | 0.999748i | \(0.507147\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 7.87272i | − | 0.268614i | −0.990940 | − | 0.134307i | \(-0.957119\pi\) | ||
0.990940 | − | 0.134307i | \(-0.0428808\pi\) | |||||||
\(860\) | −9.79817 | + | 7.10360i | −0.334115 | + | 0.242231i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −19.3799 | + | 6.28604i | −0.660082 | + | 0.214103i | ||||
\(863\) | −15.7044 | −0.534584 | −0.267292 | − | 0.963616i | \(-0.586129\pi\) | ||||
−0.267292 | + | 0.963616i | \(0.586129\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.11666 | 0.0719685 | ||||||||
\(866\) | 5.71600 | − | 1.85403i | 0.194237 | − | 0.0630026i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −54.7085 | + | 39.6632i | −1.85693 | + | 1.34626i | ||||
\(869\) | 6.86419i | 0.232852i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 37.0271 | 1.25461 | ||||||||
\(872\) | −44.0272 | − | 32.0902i | −1.49095 | − | 1.08671i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −4.92608 | − | 15.1872i | −0.166627 | − | 0.513713i | ||||
\(875\) | 3.61492i | 0.122206i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.74255i | 0.261447i | 0.991419 | + | 0.130724i | \(0.0417301\pi\) | ||||
−0.991419 | + | 0.130724i | \(0.958270\pi\) | |||||||
\(878\) | 6.42534 | − | 2.08411i | 0.216845 | − | 0.0703355i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.572519 | + | 1.74993i | −0.0192996 | + | 0.0589902i | ||||
\(881\) | −24.8472 | −0.837123 | −0.418562 | − | 0.908188i | \(-0.637466\pi\) | ||||
−0.418562 | + | 0.908188i | \(0.637466\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 36.9495i | − | 1.24345i | −0.783236 | − | 0.621724i | \(-0.786432\pi\) | ||
0.783236 | − | 0.621724i | \(-0.213568\pi\) | |||||||
\(884\) | −28.4336 | − | 39.2191i | −0.956325 | − | 1.31908i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6.79771 | + | 20.9574i | 0.228374 | + | 0.704078i | ||||
\(887\) | 14.4532 | 0.485291 | 0.242646 | − | 0.970115i | \(-0.421985\pi\) | ||||
0.242646 | + | 0.970115i | \(0.421985\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.91537 | 0.231934 | ||||||||
\(890\) | 2.64031 | + | 8.14011i | 0.0885035 | + | 0.272857i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 36.3248 | − | 26.3352i | 1.21624 | − | 0.881767i | ||||
\(893\) | 20.7462i | 0.694245i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.30923 | −0.0771891 | ||||||||
\(896\) | −23.9216 | − | 33.1725i | −0.799163 | − | 1.10822i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 53.5691 | − | 17.3756i | 1.78762 | − | 0.579831i | ||||
\(899\) | 91.9429i | 3.06647i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 21.5626i | − | 0.718355i | ||||||
\(902\) | −2.06747 | − | 6.37402i | −0.0688391 | − | 0.212231i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −23.6888 | + | 32.5006i | −0.787878 | + | 1.08095i | ||||
\(905\) | 3.60210 | 0.119738 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 22.2344i | 0.738282i | 0.929373 | + | 0.369141i | \(0.120348\pi\) | ||||
−0.929373 | + | 0.369141i | \(0.879652\pi\) | |||||||
\(908\) | −14.8397 | − | 20.4688i | −0.492474 | − | 0.679281i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 17.8689 | − | 5.79592i | 0.592348 | − | 0.192133i | ||||
\(911\) | 5.74665 | 0.190395 | 0.0951975 | − | 0.995458i | \(-0.469652\pi\) | ||||
0.0951975 | + | 0.995458i | \(0.469652\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.16972 | −0.104903 | ||||||||
\(914\) | 50.4259 | − | 16.3561i | 1.66794 | − | 0.541011i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −28.0571 | − | 38.6998i | −0.927032 | − | 1.27868i | ||||
\(917\) | 31.2094i | 1.03063i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 56.8021 | 1.87373 | 0.936864 | − | 0.349693i | \(-0.113714\pi\) | ||||
0.936864 | + | 0.349693i | \(0.113714\pi\) | |||||||
\(920\) | 8.23337 | + | 6.00107i | 0.271446 | + | 0.197849i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −17.9839 | − | 55.4447i | −0.592270 | − | 1.82597i | ||||
\(923\) | − | 10.9847i | − | 0.361567i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 6.66397i | − | 0.219110i | ||||||
\(926\) | 13.4205 | − | 4.35306i | 0.441025 | − | 0.143050i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −55.6472 | − | 0.141270i | −1.82671 | − | 0.00463740i | ||||
\(929\) | 35.4250 | 1.16226 | 0.581129 | − | 0.813812i | \(-0.302611\pi\) | ||||
0.581129 | + | 0.813812i | \(0.302611\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 19.0172i | − | 0.623263i | ||||||
\(932\) | 20.7326 | − | 15.0310i | 0.679120 | − | 0.492357i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 13.5258 | + | 41.7001i | 0.442577 | + | 1.36447i | ||||
\(935\) | −3.03408 | −0.0992249 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −29.4633 | −0.962524 | −0.481262 | − | 0.876577i | \(-0.659821\pi\) | ||||
−0.481262 | + | 0.876577i | \(0.659821\pi\) | |||||||
\(938\) | 15.8939 | + | 49.0009i | 0.518953 | + | 1.59994i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −7.77056 | − | 10.7181i | −0.253448 | − | 0.349587i | ||||
\(941\) | 21.8705i | 0.712956i | 0.934304 | + | 0.356478i | \(0.116023\pi\) | ||||
−0.934304 | + | 0.356478i | \(0.883977\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −37.0795 | −1.20748 | ||||||||
\(944\) | 19.7380 | + | 6.45761i | 0.642417 | + | 0.210177i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.74690 | − | 1.21534i | 0.121822 | − | 0.0395141i | ||||
\(947\) | − | 60.9594i | − | 1.98092i | −0.137816 | − | 0.990458i | \(-0.544008\pi\) | ||
0.137816 | − | 0.990458i | \(-0.455992\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 8.34595i | − | 0.270921i | ||||||
\(950\) | −1.36756 | − | 4.21619i | −0.0443694 | − | 0.136791i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 39.6968 | − | 54.4633i | 1.28658 | − | 1.76517i | ||||
\(953\) | −42.1708 | −1.36604 | −0.683022 | − | 0.730397i | \(-0.739335\pi\) | ||||
−0.683022 | + | 0.730397i | \(0.739335\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 0.250626i | − | 0.00811006i | ||||||
\(956\) | −42.7825 | + | 31.0170i | −1.38369 | + | 1.00316i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 21.2456 | − | 6.89120i | 0.686415 | − | 0.222644i | ||||
\(959\) | 32.9428 | 1.06378 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 56.3569 | 1.81797 | ||||||||
\(962\) | −32.9406 | + | 10.6846i | −1.06205 | + | 0.344484i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −17.0461 | + | 12.3583i | −0.549017 | + | 0.398033i | ||||
\(965\) | 13.6901i | 0.440701i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 34.5812 | 1.11206 | 0.556028 | − | 0.831164i | \(-0.312325\pi\) | ||||
0.556028 | + | 0.831164i | \(0.312325\pi\) | |||||||
\(968\) | −17.9729 | + | 24.6585i | −0.577671 | + | 0.792555i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −5.69014 | − | 17.5427i | −0.182699 | − | 0.563263i | ||||
\(971\) | − | 11.7129i | − | 0.375885i | −0.982180 | − | 0.187942i | \(-0.939818\pi\) | ||
0.982180 | − | 0.187942i | \(-0.0601819\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 35.3191i | 1.13228i | ||||||||
\(974\) | 42.4047 | − | 13.7543i | 1.35873 | − | 0.440717i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −25.8850 | − | 8.46869i | −0.828558 | − | 0.271076i | ||||
\(977\) | 4.75315 | 0.152067 | 0.0760334 | − | 0.997105i | \(-0.475774\pi\) | ||||
0.0760334 | + | 0.997105i | \(0.475774\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 2.78535i | − | 0.0890201i | ||||||
\(980\) | 7.12295 | + | 9.82486i | 0.227534 | + | 0.313844i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 9.84925 | + | 30.3653i | 0.314302 | + | 0.968997i | ||||
\(983\) | 54.1689 | 1.72772 | 0.863860 | − | 0.503731i | \(-0.168040\pi\) | ||||
0.863860 | + | 0.503731i | \(0.168040\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.11735 | −0.0674645 | ||||||||
\(986\) | −28.2926 | − | 87.2262i | −0.901018 | − | 2.77785i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −18.6484 | + | 13.5199i | −0.593284 | + | 0.430127i | ||||
\(989\) | − | 21.7968i | − | 0.693099i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 15.8470 | 0.503398 | 0.251699 | − | 0.967806i | \(-0.419011\pi\) | ||||
0.251699 | + | 0.967806i | \(0.419011\pi\) | |||||||
\(992\) | −0.134223 | + | 52.8716i | −0.00426159 | + | 1.67867i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 14.5370 | − | 4.71520i | 0.461086 | − | 0.149557i | ||||
\(995\) | 4.80338i | 0.152277i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 18.0274i | − | 0.570934i | −0.958389 | − | 0.285467i | \(-0.907851\pi\) | ||
0.958389 | − | 0.285467i | \(-0.0921487\pi\) | |||||||
\(998\) | −17.3182 | − | 53.3921i | −0.548197 | − | 1.69010i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1080.2.k.d.541.2 | yes | 20 | |
3.2 | odd | 2 | inner | 1080.2.k.d.541.19 | yes | 20 | |
4.3 | odd | 2 | 4320.2.k.d.2161.19 | 20 | |||
8.3 | odd | 2 | 4320.2.k.d.2161.10 | 20 | |||
8.5 | even | 2 | inner | 1080.2.k.d.541.1 | ✓ | 20 | |
12.11 | even | 2 | 4320.2.k.d.2161.9 | 20 | |||
24.5 | odd | 2 | inner | 1080.2.k.d.541.20 | yes | 20 | |
24.11 | even | 2 | 4320.2.k.d.2161.20 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1080.2.k.d.541.1 | ✓ | 20 | 8.5 | even | 2 | inner | |
1080.2.k.d.541.2 | yes | 20 | 1.1 | even | 1 | trivial | |
1080.2.k.d.541.19 | yes | 20 | 3.2 | odd | 2 | inner | |
1080.2.k.d.541.20 | yes | 20 | 24.5 | odd | 2 | inner | |
4320.2.k.d.2161.9 | 20 | 12.11 | even | 2 | |||
4320.2.k.d.2161.10 | 20 | 8.3 | odd | 2 | |||
4320.2.k.d.2161.19 | 20 | 4.3 | odd | 2 | |||
4320.2.k.d.2161.20 | 20 | 24.11 | even | 2 |