Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [804,2,Mod(5,804)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(804, base_ring=CyclotomicField(22))
chi = DirichletCharacter(H, H._module([0, 11, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("804.5");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 804 = 2^{2} \cdot 3 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 804.s (of order \(22\), degree \(10\), 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: | \(6.41997232251\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{22})\) |
Coefficient field: | \(\Q(\zeta_{33})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - x^{19} + x^{17} - x^{16} + x^{14} - x^{13} + x^{11} - x^{10} + x^{9} - x^{7} + x^{6} - x^{4} + x^{3} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{22}]$ |
Embedding invariants
Embedding label | 5.2 | ||
Root | \(0.928368 + 0.371662i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 804.5 |
Dual form | 804.2.s.a.161.2 |
$q$-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 \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).
\(n\) | \(269\) | \(337\) | \(403\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{22}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.57553 | − | 0.719520i | 0.909632 | − | 0.415415i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | −0.281733 | − | 0.959493i | \(-0.590909\pi\) | ||||
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.61965 | − | 2.26994i | −0.990134 | − | 0.857956i | −0.000273951 | − | 1.00000i | \(-0.500087\pi\) |
−0.989860 | + | 0.142044i | \(0.954633\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.96458 | − | 2.26725i | 0.654861 | − | 0.755750i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | −0.281733 | − | 0.959493i | \(-0.590909\pi\) | ||||
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.27007 | − | 5.08833i | −0.906954 | − | 1.41125i | −0.911519 | − | 0.411259i | \(-0.865089\pi\) |
0.00456441 | − | 0.999990i | \(-0.498547\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.112808 | + | 0.130187i | 0.0258799 | + | 0.0298670i | 0.768542 | − | 0.639799i | \(-0.220983\pi\) |
−0.742662 | + | 0.669666i | \(0.766437\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.76060 | − | 1.69146i | −1.25707 | − | 0.369108i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.20627 | + | 2.70320i | −0.841254 | + | 0.540641i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.46393 | − | 4.98567i | 0.281733 | − | 0.959493i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.78165 | − | 7.44039i | 0.858810 | − | 1.33633i | −0.0817313 | − | 0.996654i | \(-0.526045\pi\) |
0.940541 | − | 0.339680i | \(-0.110319\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.66687 | 0.767228 | 0.383614 | − | 0.923494i | \(-0.374679\pi\) | ||||
0.383614 | + | 0.923494i | \(0.374679\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −8.81324 | − | 5.66393i | −1.41125 | − | 0.906954i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||||
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.37247 | + | 0.628667i | 0.666796 | + | 0.0958708i | 0.467397 | − | 0.884048i | \(-0.345192\pi\) |
0.199399 | + | 0.979918i | \(0.436101\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.713735 | + | 4.96414i | 0.101962 | + | 0.709163i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.271404 | + | 0.123946i | 0.0359484 | + | 0.0164171i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.77697 | + | 9.45750i | −0.355555 | + | 1.21091i | 0.566569 | + | 0.824014i | \(0.308270\pi\) |
−0.922124 | + | 0.386895i | \(0.873548\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −10.2930 | + | 1.47991i | −1.29680 | + | 0.186452i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.66645 | − | 2.86803i | 0.936605 | − | 0.350386i | ||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.9519 | + | 3.80303i | 1.51591 | + | 0.445111i | 0.930704 | − | 0.365774i | \(-0.119196\pi\) |
0.585206 | + | 0.810885i | \(0.301014\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.68209 | + | 7.28547i | −0.540641 | + | 0.841254i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.70847 | − | 10.4386i | −0.754762 | − | 1.17443i | −0.979780 | − | 0.200078i | \(-0.935880\pi\) |
0.225018 | − | 0.974355i | \(-0.427756\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.28083 | − | 8.90839i | −0.142315 | − | 0.989821i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.98376 | + | 20.7525i | −0.312783 | + | 2.17545i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.18012 | − | 15.1630i | 0.226068 | − | 1.57233i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 18.4910i | 1.87748i | 0.344630 | + | 0.938739i | \(0.388004\pi\) | ||||
−0.344630 | + | 0.938739i | \(0.611996\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | 0.755750 | − | 0.654861i | \(-0.227273\pi\) | ||||
−0.755750 | + | 0.654861i | \(0.772727\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.2205 | + | 8.49628i | 1.30265 | + | 0.837164i | 0.993498 | − | 0.113848i | \(-0.0363178\pi\) |
0.309154 | + | 0.951012i | \(0.399954\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.0865 | − | 17.2509i | −1.06189 | − | 1.65233i | −0.689551 | − | 0.724238i | \(-0.742192\pi\) |
−0.372340 | − | 0.928096i | \(-0.621444\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.35278 | − | 3.35790i | 0.697895 | − | 0.318718i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | 0.281733 | − | 0.959493i | \(-0.409091\pi\) | ||||
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −17.9608 | − | 2.58238i | −1.66048 | − | 0.238741i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.25379 | + | 5.94705i | −0.841254 | + | 0.540641i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.6974 | − | 16.9617i | 1.30418 | − | 1.50511i | 0.582675 | − | 0.812705i | \(-0.302006\pi\) |
0.721510 | − | 0.692404i | \(-0.243448\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.34130 | − | 2.15560i | 0.646365 | − | 0.189790i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 0.597112i | − | 0.0517762i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 0.909632 | − | 0.415415i | \(-0.136364\pi\) | ||||
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.07325 | − | 7.06083i | −0.175850 | − | 0.598891i | −0.999495 | − | 0.0317847i | \(-0.989881\pi\) |
0.823644 | − | 0.567107i | \(-0.191937\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.69631 | + | 7.30760i | 0.387345 | + | 0.602720i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.51845 | + | 10.5610i | −0.123569 | + | 0.859444i | 0.829891 | + | 0.557926i | \(0.188403\pi\) |
−0.953460 | + | 0.301518i | \(0.902507\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.71678 | + | 5.94891i | 0.216822 | + | 0.474775i | 0.986521 | − | 0.163632i | \(-0.0523210\pi\) |
−0.769699 | + | 0.638407i | \(0.779594\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 22.8634 | 1.79080 | 0.895399 | − | 0.445265i | \(-0.146890\pi\) | ||||
0.895399 | + | 0.445265i | \(0.146890\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.79733 | + | 21.4532i | −0.753641 | + | 1.65024i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.516787 | 0.0395197 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 17.1551 | + | 2.46652i | 1.29680 | + | 0.186452i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | −0.909632 | − | 0.415415i | \(-0.863636\pi\) | ||||
0.909632 | + | 0.415415i | \(0.136364\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.10480 | + | 15.5574i | 0.528096 | + | 1.15637i | 0.966282 | + | 0.257485i | \(0.0828937\pi\) |
−0.438186 | + | 0.898884i | \(0.644379\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.42966 | + | 16.8987i | 0.179606 | + | 1.24918i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −15.1521 | + | 9.73769i | −1.10216 | + | 0.708313i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.909632 | − | 0.415415i | \(-0.863636\pi\) | ||||
0.909632 | + | 0.415415i | \(0.136364\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.5174 | + | 10.6151i | 1.18895 | + | 0.764089i | 0.977010 | − | 0.213195i | \(-0.0683868\pi\) |
0.211936 | + | 0.977284i | \(0.432023\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.85491 | − | 5.60287i | 0.344156 | − | 0.397177i | −0.557114 | − | 0.830436i | \(-0.688091\pi\) |
0.901269 | + | 0.433260i | \(0.142637\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10.0151 | − | 10.0348i | 0.706411 | − | 0.707802i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.53943 | + | 7.75028i | −0.243665 | + | 0.533551i | −0.991465 | − | 0.130372i | \(-0.958383\pi\) |
0.747800 | + | 0.663924i | \(0.231110\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −29.4155 | + | 8.63717i | −1.99685 | + | 0.586329i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 23.1425 | − | 3.32739i | 1.56383 | − | 0.224844i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.904960 | + | 1.98159i | −0.0606006 | + | 0.132697i | −0.937509 | − | 0.347960i | \(-0.886874\pi\) |
0.876909 | + | 0.480657i | \(0.159602\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.13472 | + | 14.8473i | −0.142315 | + | 0.989821i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −15.8836 | + | 24.7154i | −1.04962 | + | 1.63324i | −0.322718 | + | 0.946495i | \(0.604597\pi\) |
−0.726900 | + | 0.686743i | \(0.759040\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | −0.909632 | − | 0.415415i | \(-0.863636\pi\) | ||||
0.909632 | + | 0.415415i | \(0.136364\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −18.0802 | − | 11.6194i | −1.17443 | − | 0.754762i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −25.6763 | − | 7.53923i | −1.65395 | − | 0.485644i | −0.684111 | − | 0.729378i | \(-0.739809\pi\) |
−0.969842 | + | 0.243734i | \(0.921628\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −8.42776 | − | 13.1138i | −0.540641 | − | 0.841254i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.293546 | − | 0.999725i | 0.0186779 | − | 0.0636110i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||||
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −12.2256 | − | 10.5935i | −0.759659 | − | 0.658248i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 29.5662 | − | 13.5024i | 1.79602 | − | 0.820215i | 0.831818 | − | 0.555048i | \(-0.187300\pi\) |
0.964203 | − | 0.265167i | \(-0.0854270\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 10.2308 | + | 34.8430i | 0.619198 | + | 2.10880i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.0494 | − | 12.7517i | 0.663893 | − | 0.766173i | −0.319515 | − | 0.947581i | \(-0.603520\pi\) |
0.983408 | + | 0.181408i | \(0.0580655\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −7.47528 | − | 25.4585i | −0.447533 | − | 1.52416i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | −0.540641 | − | 0.841254i | \(-0.681818\pi\) | ||||
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 22.0240 | + | 25.4171i | 1.30919 | + | 1.51089i | 0.676068 | + | 0.736839i | \(0.263682\pi\) |
0.633125 | + | 0.774050i | \(0.281772\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.3114 | − | 4.78945i | −0.959493 | − | 0.281733i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 13.3046 | + | 29.1331i | 0.779932 | + | 1.70781i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.0273 | − | 11.5721i | −0.577965 | − | 0.667007i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −24.0452 | − | 15.4529i | −1.37233 | − | 0.881943i | −0.373376 | − | 0.927680i | \(-0.621800\pi\) |
−0.998954 | + | 0.0457370i | \(0.985436\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 26.9425 | + | 3.87374i | 1.53270 | + | 0.220370i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||||
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.38404 | + | 0.632072i | 0.0782308 | + | 0.0357268i | 0.454146 | − | 0.890927i | \(-0.349944\pi\) |
−0.375915 | + | 0.926654i | \(0.622672\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 27.5096 | + | 12.5632i | 1.52596 | + | 0.696881i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −29.8794 | − | 19.2023i | −1.65233 | − | 1.06189i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 35.9339 | − | 5.16652i | 1.97511 | − | 0.283977i | 0.977924 | − | 0.208962i | \(-0.0670085\pi\) |
0.997182 | − | 0.0750153i | \(-0.0239006\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 9.16844 | − | 10.5809i | 0.502428 | − | 0.579832i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −22.7016 | − | 19.6711i | −1.23664 | − | 1.07155i | −0.994864 | − | 0.101218i | \(-0.967726\pi\) |
−0.241771 | − | 0.970333i | \(-0.577728\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.71958 | + | 5.78778i | −0.200839 | + | 0.312511i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | −0.540641 | − | 0.841254i | \(-0.681818\pi\) | ||||
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.42104 | + | 16.8387i | 0.129595 | + | 0.901356i | 0.946067 | + | 0.323971i | \(0.105018\pi\) |
−0.816472 | + | 0.577386i | \(0.804073\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −30.1559 | + | 8.85456i | −1.60960 | + | 0.472622i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.69976 | − | 18.7772i | 0.142093 | − | 0.988276i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −10.3006 | + | 16.0280i | −0.540641 | + | 0.841254i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −34.2827 | − | 15.6564i | −1.78954 | − | 0.817256i | −0.969555 | − | 0.244874i | \(-0.921254\pi\) |
−0.819987 | − | 0.572383i | \(-0.806019\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 33.2555i | − | 1.72190i | −0.508686 | − | 0.860952i | \(-0.669869\pi\) | ||
0.508686 | − | 0.860952i | \(-0.330131\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 28.1982 | − | 12.8777i | 1.44844 | − | 0.661482i | 0.472865 | − | 0.881135i | \(-0.343220\pi\) |
0.975578 | + | 0.219653i | \(0.0704926\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 10.9519 | − | 37.2988i | 0.561083 | − | 1.91087i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 0.755750 | − | 0.654861i | \(-0.227273\pi\) | ||||
−0.755750 | + | 0.654861i | \(0.772727\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 10.0154 | − | 8.67842i | 0.509113 | − | 0.441149i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 24.3824 | − | 7.15932i | 1.22372 | − | 0.359316i | 0.394842 | − | 0.918749i | \(-0.370799\pi\) |
0.828876 | + | 0.559433i | \(0.188981\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.429634 | − | 0.940767i | −0.0215086 | − | 0.0470973i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −53.4955 | −2.66480 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −18.1387 | − | 15.7173i | −0.896902 | − | 0.777170i | 0.0786585 | − | 0.996902i | \(-0.474936\pi\) |
−0.975560 | + | 0.219732i | \(0.929482\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8.34686 | − | 9.63279i | −0.408748 | − | 0.471720i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −24.3843 | − | 28.1410i | −1.18842 | − | 1.37151i | −0.911854 | − | 0.410515i | \(-0.865349\pi\) |
−0.276567 | − | 0.960995i | \(-0.589197\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 28.7426 | − | 18.4718i | 1.39095 | − | 0.893912i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.3218 | − | 28.5092i | 0.880488 | − | 1.37007i | −0.0480569 | − | 0.998845i | \(-0.515303\pi\) |
0.928545 | − | 0.371221i | \(-0.121061\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −34.8444 | −1.66303 | −0.831516 | − | 0.555501i | \(-0.812527\pi\) | ||||
−0.831516 | + | 0.555501i | \(0.812527\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 12.6571 | + | 8.13424i | 0.602720 | + | 0.387345i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||||
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.20651 | + | 17.7317i | 0.244623 | + | 0.833110i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 31.9378 | − | 20.5252i | 1.49399 | − | 0.960127i | 0.498334 | − | 0.866985i | \(-0.333945\pi\) |
0.995653 | − | 0.0931420i | \(-0.0296911\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.2886 | − | 38.4455i | 0.524626 | − | 1.78671i | −0.0877454 | − | 0.996143i | \(-0.527966\pi\) |
0.612372 | − | 0.790570i | \(-0.290216\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −26.5937 | − | 9.88912i | −1.22798 | − | 0.456637i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.56072 | + | 7.41791i | 0.394457 | + | 0.341799i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.826423 | − | 0.242660i | −0.0379189 | − | 0.0111340i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15.2610 | − | 23.7465i | −0.695841 | − | 1.08275i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −42.6209 | + | 6.12796i | −1.93134 | + | 0.277684i | −0.996915 | − | 0.0784867i | \(-0.974991\pi\) |
−0.934421 | + | 0.356171i | \(0.884082\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 36.0219 | − | 16.4507i | 1.62897 | − | 0.743924i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 43.5282i | 1.94859i | 0.225277 | + | 0.974295i | \(0.427671\pi\) | ||||
−0.225277 | + | 0.974295i | \(0.572329\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 0.755750 | − | 0.654861i | \(-0.227273\pi\) | ||||
−0.755750 | + | 0.654861i | \(0.772727\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 40.8495i | 1.81419i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −25.2969 | − | 39.3627i | −1.11907 | − | 1.74130i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.814213 | − | 0.371839i | 0.0359484 | − | 0.0164171i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 0.755750 | − | 0.654861i | \(-0.227273\pi\) | ||||
−0.755750 | + | 0.654861i | \(0.772727\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −24.2239 | + | 15.5678i | −1.05924 | + | 0.680731i | −0.949671 | − | 0.313249i | \(-0.898583\pi\) |
−0.109567 | + | 0.993979i | \(0.534946\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 28.8030 | − | 8.45732i | 1.25707 | − | 0.369108i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.0618 | + | 17.3822i | −0.654861 | + | 0.755750i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.1056 | + | 44.6335i | 0.563453 | + | 1.91894i | 0.288145 | + | 0.957587i | \(0.406961\pi\) |
0.275307 | + | 0.961356i | \(0.411220\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 22.3876 | + | 19.3990i | 0.960746 | + | 0.832491i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.1824 | − | 34.6779i | −0.435366 | − | 1.48272i | −0.826791 | − | 0.562510i | \(-0.809836\pi\) |
0.391425 | − | 0.920210i | \(-0.371982\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 15.9869 | + | 24.8761i | 0.682305 | + | 1.06169i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.12111 | + | 42.5733i | −0.260296 | + | 1.81040i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −11.0994 | − | 24.3044i | −0.469456 | − | 1.02797i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | 0.281733 | − | 0.959493i | \(-0.409091\pi\) | ||||
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −16.8662 | + | 26.2443i | −0.708313 | + | 1.10216i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.7781 | + | 43.3079i | −0.827686 | + | 1.81238i | −0.334790 | + | 0.942293i | \(0.608665\pi\) |
−0.492897 | + | 0.870088i | \(0.664062\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 25.9876 | + | 3.73645i | 1.08188 | + | 0.155550i | 0.660121 | − | 0.751159i | \(-0.270505\pi\) |
0.421756 | + | 0.906709i | \(0.361414\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 33.6613 | + | 4.83977i | 1.39892 | + | 0.201134i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | −0.281733 | − | 0.959493i | \(-0.590909\pi\) | ||||
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.50805 | − | 0.216825i | 0.0621382 | − | 0.00893413i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | −0.909632 | − | 0.415415i | \(-0.863636\pi\) | ||||
0.909632 | + | 0.415415i | \(0.136364\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.61768 | − | 12.3207i | 0.148062 | − | 0.504252i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −24.0060 | + | 27.7044i | −0.979226 | + | 1.13009i | 0.0122663 | + | 0.999925i | \(0.496095\pi\) |
−0.991493 | + | 0.130163i | \(0.958450\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.55882 | − | 23.0162i | 0.348542 | − | 0.937293i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.97960 | − | 20.7236i | −0.120938 | − | 0.841145i | −0.956497 | − | 0.291743i | \(-0.905765\pi\) |
0.835558 | − | 0.549402i | \(-0.185144\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −19.3503 | + | 42.3712i | −0.781551 | + | 1.71136i | −0.0821600 | + | 0.996619i | \(0.526182\pi\) |
−0.699391 | + | 0.714739i | \(0.746545\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 19.1595 | − | 5.62573i | 0.770084 | − | 0.226117i | 0.126990 | − | 0.991904i | \(-0.459469\pi\) |
0.643094 | + | 0.765787i | \(0.277650\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 10.3854 | − | 22.7408i | 0.415415 | − | 0.909632i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.1925 | + | 25.1960i | −0.644612 | + | 1.00304i | 0.353110 | + | 0.935582i | \(0.385124\pi\) |
−0.997722 | + | 0.0674546i | \(0.978512\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 14.7575i | 0.586557i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 22.9252 | − | 19.8648i | 0.908329 | − | 0.787072i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 35.0716 | + | 10.2979i | 1.38309 | + | 0.406111i | 0.886843 | − | 0.462072i | \(-0.152894\pi\) |
0.496245 | + | 0.868183i | \(0.334712\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 0.909632 | − | 0.415415i | \(-0.136364\pi\) | ||||
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −40.1303 | + | 34.7731i | −1.57283 | + | 1.36287i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||||
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 34.0676 | − | 21.8939i | 1.32910 | − | 0.854162i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24.7004 | + | 21.4030i | 0.960733 | + | 0.832480i | 0.985923 | − | 0.167203i | \(-0.0534734\pi\) |
−0.0251892 | + | 0.999683i | \(0.508019\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3.77318i | 0.145880i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.719977 | − | 0.328802i | 0.0277531 | − | 0.0126744i | −0.401490 | − | 0.915863i | \(-0.631508\pi\) |
0.429243 | + | 0.903189i | \(0.358780\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 7.31963 | + | 24.9284i | 0.281733 | + | 0.959493i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0 | 0 | −0.755750 | − | 0.654861i | \(-0.772727\pi\) | ||||
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 41.9735 | − | 48.4400i | 1.61079 | − | 1.85895i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | −0.540641 | − | 0.841254i | \(-0.681818\pi\) | ||||
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.24188 | + | 50.3684i | −0.276295 | + | 1.92167i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20.4972 | − | 6.01851i | −0.779749 | − | 0.228955i | −0.132448 | − | 0.991190i | \(-0.542284\pi\) |
−0.647300 | + | 0.762235i | \(0.724102\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.526459 | + | 0.607567i | 0.0198558 | + | 0.0229148i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 44.8001 | + | 28.7913i | 1.68250 | + | 1.08128i | 0.842618 | + | 0.538512i | \(0.181013\pi\) |
0.839884 | + | 0.542766i | \(0.182623\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −36.8462 | − | 5.29769i | −1.38184 | − | 0.198679i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −15.3470 | − | 52.2670i | −0.571551 | − | 1.94652i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −45.8783 | + | 6.59630i | −1.70623 | + | 0.245319i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −35.5804 | − | 16.2490i | −1.31961 | − | 0.602644i | −0.373840 | − | 0.927493i | \(-0.621959\pi\) |
−0.945766 | + | 0.324850i | \(0.894686\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −22.7138 | − | 14.5973i | −0.841254 | − | 0.540641i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23.9304 | − | 3.44067i | 0.883888 | − | 0.127084i | 0.314602 | − | 0.949224i | \(-0.398129\pi\) |
0.569286 | + | 0.822140i | \(0.307220\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −17.5576 | − | 15.2138i | −0.645867 | − | 0.559647i | 0.269132 | − | 0.963103i | \(-0.413263\pi\) |
−0.914999 | + | 0.403456i | \(0.867809\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.256832 | − | 1.78631i | −0.00943497 | − | 0.0656217i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.49306 | − | 24.2948i | −0.127464 | − | 0.886528i | −0.948753 | − | 0.316017i | \(-0.897654\pi\) |
0.821290 | − | 0.570511i | \(-0.193255\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −48.9909 | + | 22.3734i | −1.78061 | + | 0.813176i | −0.805121 | + | 0.593111i | \(0.797900\pi\) |
−0.975485 | + | 0.220065i | \(0.929373\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.1158 | + | 70.3568i | −0.366216 | + | 2.54709i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 43.3970 | + | 19.8187i | 1.56494 | + | 0.714682i | 0.994310 | − | 0.106528i | \(-0.0339735\pi\) |
0.570626 | + | 0.821210i | \(0.306701\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 44.2221i | 1.58850i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −26.8839 | − | 7.89384i | −0.964456 | − | 0.283190i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 27.0832 | + | 3.89398i | 0.965412 | + | 0.138805i | 0.606951 | − | 0.794739i | \(-0.292393\pi\) |
0.358461 | + | 0.933545i | \(0.383302\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 57.2038 | − | 16.7965i | 2.03137 | − | 0.596463i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | −0.281733 | − | 0.959493i | \(-0.590909\pi\) | ||||
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16.2738 | − | 14.1013i | −0.571450 | − | 0.495165i | 0.320530 | − | 0.947238i | \(-0.396139\pi\) |
−0.891981 | + | 0.452074i | \(0.850684\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 36.8672 | − | 42.5470i | 1.29299 | − | 1.49219i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.411405 | + | 0.640159i | 0.0143932 | + | 0.0223963i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 41.1892 | + | 47.5349i | 1.43927 | + | 1.66100i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10.2989 | + | 11.8855i | 0.358996 | + | 0.414303i | 0.906303 | − | 0.422628i | \(-0.138892\pi\) |
−0.547307 | + | 0.836932i | \(0.684347\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −34.3525 | + | 22.0770i | −1.19311 | + | 0.766766i | −0.977751 | − | 0.209768i | \(-0.932729\pi\) |
−0.215361 | + | 0.976535i | \(0.569093\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.23354 | − | 28.0409i | 0.285618 | − | 0.972727i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −30.0954 | − | 34.7319i | −1.04025 | − | 1.20051i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 29.0000 | 1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 37.7411 | + | 5.42635i | 1.29680 | + | 0.186452i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 52.9876 | + | 24.1986i | 1.81853 | + | 0.830495i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.47699 | + | 52.0036i | 0.256007 | + | 1.78057i | 0.560600 | + | 0.828087i | \(0.310571\pi\) |
−0.304592 | + | 0.952483i | \(0.598520\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 31.7540 | − | 20.4070i | 1.08343 | − | 0.696279i | 0.128084 | − | 0.991763i | \(-0.459117\pi\) |
0.955348 | + | 0.295484i | \(0.0954809\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −29.1452 | + | 4.19044i | −0.989821 | + | 0.142315i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −39.6633 | − | 29.6307i | −1.34394 | − | 1.00400i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 41.9237 | + | 36.3271i | 1.41890 | + | 1.22949i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 56.5306 | + | 16.5989i | 1.90890 | + | 0.560505i | 0.983294 | + | 0.182023i | \(0.0582646\pi\) |
0.925609 | + | 0.378481i | \(0.123554\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17.1603 | + | 26.7020i | 0.577491 | + | 0.898594i | 0.999970 | − | 0.00777899i | \(-0.00247616\pi\) |
−0.422478 | + | 0.906373i | \(0.638840\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −77.0041 | + | 11.0715i | −2.58264 | + | 0.371327i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −24.1247 | − | 11.0174i | −0.802820 | − | 0.366635i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 21.6138 | + | 13.8903i | 0.717674 | + | 0.461221i | 0.847827 | − | 0.530273i | \(-0.177910\pi\) |
−0.130153 | + | 0.991494i | \(0.541547\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 33.6793 | − | 29.1833i | 1.11098 | − | 0.962668i | 0.111462 | − | 0.993769i | \(-0.464447\pi\) |
0.999516 | + | 0.0311006i | \(0.00990124\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −49.0025 | − | 7.04550i | −1.61469 | − | 0.232157i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −19.6301 | + | 12.6155i | −0.645433 | + | 0.414795i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 45.2359 | − | 13.2825i | 1.48574 | − | 0.436253i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | −0.755750 | − | 0.654861i | \(-0.772727\pi\) | ||||
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.565753 | + | 0.652913i | −0.0185418 | + | 0.0213984i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 33.6232i | 1.09842i | 0.835683 | + | 0.549212i | \(0.185072\pi\) | ||||
−0.835683 | + | 0.549212i | \(0.814928\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.63539 | 0.0860027 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.909632 | − | 0.415415i | \(-0.136364\pi\) | ||||
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −23.0027 | − | 78.3399i | −0.746698 | − | 2.54302i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.6174 | − | 42.9561i | −0.632820 | − | 1.38568i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −61.8763 | −1.98981 | −0.994904 | − | 0.100831i | \(-0.967850\pi\) | ||||
−0.994904 | + | 0.100831i | \(0.967850\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10.5965 | + | 23.2030i | −0.339707 | + | 0.743855i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 52.3816 | 1.67755 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −60.8923 | − | 8.75499i | −1.94414 | − | 0.279525i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | −0.909632 | − | 0.415415i | \(-0.863636\pi\) | ||||
0.909632 | + | 0.415415i | \(0.136364\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −30.4993 | + | 4.38514i | −0.968842 | + | 0.139298i | −0.608528 | − | 0.793533i | \(-0.708240\pi\) |
−0.360314 | + | 0.932831i | \(0.617331\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 52.8975 | − | 33.9952i | 1.67865 | − | 1.07880i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −44.2204 | − | 28.4187i | −1.40047 | − | 0.900030i | −0.400606 | − | 0.916251i | \(-0.631200\pi\) |
−0.999868 | + | 0.0162206i | \(0.994837\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 6.83194 | − | 23.2675i | 0.216153 | − | 0.736150i |
(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 | 804.2.s.a.5.2 | ✓ | 20 | |
3.2 | odd | 2 | CM | 804.2.s.a.5.2 | ✓ | 20 | |
67.27 | odd | 22 | inner | 804.2.s.a.161.2 | yes | 20 | |
201.161 | even | 22 | inner | 804.2.s.a.161.2 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
804.2.s.a.5.2 | ✓ | 20 | 1.1 | even | 1 | trivial | |
804.2.s.a.5.2 | ✓ | 20 | 3.2 | odd | 2 | CM | |
804.2.s.a.161.2 | yes | 20 | 67.27 | odd | 22 | inner | |
804.2.s.a.161.2 | yes | 20 | 201.161 | even | 22 | inner |