Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1792,2,Mod(895,1792)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1792, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1792.895");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1792 = 2^{8} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1792.e (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(14.3091920422\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.40960000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 7x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 896) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 895.1 | ||
Root | \(-0.437016 - 0.437016i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1792.895 |
Dual form | 1792.2.e.h.895.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1792\mathbb{Z}\right)^\times\).
\(n\) | \(1023\) | \(1025\) | \(1541\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 2.28825i | − | 1.32112i | −0.750774 | − | 0.660560i | \(-0.770319\pi\) | ||
0.750774 | − | 0.660560i | \(-0.229681\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.540182 | −0.241577 | −0.120788 | − | 0.992678i | \(-0.538542\pi\) | ||||
−0.120788 | + | 0.992678i | \(0.538542\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.41421 | − | 2.23607i | −0.534522 | − | 0.845154i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.23607 | −0.745356 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.23607 | 0.372689 | 0.186344 | − | 0.982485i | \(-0.440336\pi\) | ||||
0.186344 | + | 0.982485i | \(0.440336\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.28825 | 0.634645 | 0.317323 | − | 0.948318i | \(-0.397216\pi\) | ||||
0.317323 | + | 0.948318i | \(0.397216\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.23607i | 0.319151i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 1.74806i | − | 0.423968i | −0.977273 | − | 0.211984i | \(-0.932008\pi\) | ||
0.977273 | − | 0.211984i | \(-0.0679924\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 5.11667i | − | 1.17385i | −0.809643 | − | 0.586923i | \(-0.800339\pi\) | ||
0.809643 | − | 0.586923i | \(-0.199661\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.11667 | + | 3.23607i | −1.11655 | + | 0.706168i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 3.23607i | − | 0.674767i | −0.941367 | − | 0.337383i | \(-0.890458\pi\) | ||
0.941367 | − | 0.337383i | \(-0.109542\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.70820 | −0.941641 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 1.74806i | − | 0.336415i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.00000i | 0.371391i | 0.982607 | + | 0.185695i | \(0.0594537\pi\) | ||||
−0.982607 | + | 0.185695i | \(0.940546\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.90879 | −0.702039 | −0.351020 | − | 0.936368i | \(-0.614165\pi\) | ||||
−0.351020 | + | 0.936368i | \(0.614165\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 2.82843i | − | 0.492366i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.763932 | + | 1.20788i | 0.129128 | + | 0.204169i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.94427i | 1.14163i | 0.821078 | + | 0.570816i | \(0.193373\pi\) | ||||
−0.821078 | + | 0.570816i | \(0.806627\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 5.23607i | − | 0.838442i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 10.2333i | − | 1.59818i | −0.601211 | − | 0.799090i | \(-0.705315\pi\) | ||
0.601211 | − | 0.799090i | \(-0.294685\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.7082 | 1.78548 | 0.892742 | − | 0.450568i | \(-0.148778\pi\) | ||||
0.892742 | + | 0.450568i | \(0.148778\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.20788 | 0.180061 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10.9010 | −1.59008 | −0.795041 | − | 0.606556i | \(-0.792550\pi\) | ||||
−0.795041 | + | 0.606556i | \(0.792550\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.00000 | + | 6.32456i | −0.428571 | + | 0.903508i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.00000 | −0.560112 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.47214i | 1.16374i | 0.813283 | + | 0.581869i | \(0.197678\pi\) | ||||
−0.813283 | + | 0.581869i | \(0.802322\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.667701 | −0.0900328 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −11.7082 | −1.55079 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 1.62054i | − | 0.210977i | −0.994421 | − | 0.105488i | \(-0.966359\pi\) | ||
0.994421 | − | 0.105488i | \(-0.0336406\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.1893 | −1.68872 | −0.844358 | − | 0.535780i | \(-0.820018\pi\) | ||||
−0.844358 | + | 0.535780i | \(0.820018\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.16228 | + | 5.00000i | 0.398410 | + | 0.629941i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.23607 | −0.153315 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.70820 | −0.453029 | −0.226515 | − | 0.974008i | \(-0.572733\pi\) | ||||
−0.226515 | + | 0.974008i | \(0.572733\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −7.40492 | −0.891447 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.0000i | 1.18678i | 0.804914 | + | 0.593391i | \(0.202211\pi\) | ||||
−0.804914 | + | 0.593391i | \(0.797789\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 14.1421i | − | 1.65521i | −0.561310 | − | 0.827606i | \(-0.689702\pi\) | ||
0.561310 | − | 0.827606i | \(-0.310298\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 10.7735i | 1.24402i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.74806 | − | 2.76393i | −0.199210 | − | 0.314979i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 3.52786i | − | 0.396916i | −0.980109 | − | 0.198458i | \(-0.936407\pi\) | ||
0.980109 | − | 0.198458i | \(-0.0635933\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.7082 | −1.18980 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.02546i | 0.990673i | 0.868701 | + | 0.495337i | \(0.164955\pi\) | ||||
−0.868701 | + | 0.495337i | \(0.835045\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.944272i | 0.102421i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.57649 | 0.490651 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.4775i | 1.64062i | 0.571922 | + | 0.820308i | \(0.306198\pi\) | ||||
−0.571922 | + | 0.820308i | \(0.693802\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.23607 | − | 5.11667i | −0.339232 | − | 0.536373i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.94427i | 0.927478i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.76393i | 0.283573i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.74806i | 0.177489i | 0.996054 | + | 0.0887445i | \(0.0282855\pi\) | ||||
−0.996054 | + | 0.0887445i | \(0.971715\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.76393 | −0.277786 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.4412 | 1.13844 | 0.569222 | − | 0.822184i | \(-0.307244\pi\) | ||||
0.569222 | + | 0.822184i | \(0.307244\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.7295 | 1.35281 | 0.676403 | − | 0.736532i | \(-0.263538\pi\) | ||||
0.676403 | + | 0.736532i | \(0.263538\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.76393 | − | 1.74806i | 0.269732 | − | 0.170594i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.291796 | −0.0282090 | −0.0141045 | − | 0.999901i | \(-0.504490\pi\) | ||||
−0.0141045 | + | 0.999901i | \(0.504490\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 3.52786i | − | 0.337908i | −0.985624 | − | 0.168954i | \(-0.945961\pi\) | ||
0.985624 | − | 0.168954i | \(-0.0540389\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 15.8902 | 1.50823 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.29180 | 0.215594 | 0.107797 | − | 0.994173i | \(-0.465620\pi\) | ||||
0.107797 | + | 0.994173i | \(0.465620\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.74806i | 0.163008i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.11667 | −0.473037 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.90879 | + | 2.47214i | −0.358318 | + | 0.226620i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.47214 | −0.861103 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −23.4164 | −2.11139 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.24419 | 0.469055 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 0.763932i | − | 0.0677880i | −0.999425 | − | 0.0338940i | \(-0.989209\pi\) | ||
0.999425 | − | 0.0338940i | \(-0.0107909\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 26.7912i | − | 2.35884i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 5.78437i | − | 0.505383i | −0.967547 | − | 0.252692i | \(-0.918684\pi\) | ||
0.967547 | − | 0.252692i | \(-0.0813158\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −11.4412 | + | 7.23607i | −0.992080 | + | 0.627447i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.944272i | 0.0812700i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.4721 | 1.06557 | 0.532783 | − | 0.846252i | \(-0.321146\pi\) | ||||
0.532783 | + | 0.846252i | \(0.321146\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.70091i | 0.229088i | 0.993418 | + | 0.114544i | \(0.0365407\pi\) | ||||
−0.993418 | + | 0.114544i | \(0.963459\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 24.9443i | 2.10069i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.82843 | 0.236525 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 1.08036i | − | 0.0897193i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 14.4721 | + | 6.86474i | 1.19364 | + | 0.566194i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 13.4164i | − | 1.09911i | −0.835456 | − | 0.549557i | \(-0.814796\pi\) | ||
0.835456 | − | 0.549557i | \(-0.185204\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 11.2361i | − | 0.914378i | −0.889369 | − | 0.457189i | \(-0.848856\pi\) | ||
0.889369 | − | 0.457189i | \(-0.151144\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.90879i | 0.316007i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.11146 | 0.169596 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.4412 | 0.913109 | 0.456555 | − | 0.889695i | \(-0.349083\pi\) | ||||
0.456555 | + | 0.889695i | \(0.349083\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 19.3863 | 1.53744 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.23607 | + | 4.57649i | −0.570282 | + | 0.360678i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −17.2361 | −1.35003 | −0.675017 | − | 0.737803i | \(-0.735864\pi\) | ||||
−0.675017 | + | 0.737803i | \(0.735864\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.52786i | 0.118944i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.07262 | −0.624678 | −0.312339 | − | 0.949971i | \(-0.601112\pi\) | ||||
−0.312339 | + | 0.949971i | \(0.601112\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.76393 | −0.597226 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 11.4412i | 0.874933i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −18.1784 | −1.38208 | −0.691041 | − | 0.722816i | \(-0.742848\pi\) | ||||
−0.691041 | + | 0.722816i | \(0.742848\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.65841 | + | 10.5279i | 0.503328 | + | 0.795832i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.70820 | −0.278726 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 20.6525 | 1.54364 | 0.771819 | − | 0.635842i | \(-0.219347\pi\) | ||||
0.771819 | + | 0.635842i | \(0.219347\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.540182 | −0.0401514 | −0.0200757 | − | 0.999798i | \(-0.506391\pi\) | ||||
−0.0200757 | + | 0.999798i | \(0.506391\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 30.1803i | 2.23099i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 3.75117i | − | 0.275791i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 2.16073i | − | 0.158008i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.90879 | + | 2.47214i | −0.284323 | + | 0.179821i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 22.9443i | − | 1.66019i | −0.557623 | − | 0.830095i | \(-0.688286\pi\) | ||
0.557623 | − | 0.830095i | \(-0.311714\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.2361 | −0.808790 | −0.404395 | − | 0.914584i | \(-0.632518\pi\) | ||||
−0.404395 | + | 0.914584i | \(0.632518\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.82843i | 0.202548i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 18.9443i | − | 1.34972i | −0.737944 | − | 0.674862i | \(-0.764203\pi\) | ||
0.737944 | − | 0.674862i | \(-0.235797\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.73722 | −0.477589 | −0.238794 | − | 0.971070i | \(-0.576752\pi\) | ||||
−0.238794 | + | 0.971070i | \(0.576752\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.48528i | 0.598506i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.47214 | − | 2.82843i | 0.313882 | − | 0.198517i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.52786i | 0.386083i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.23607i | 0.502941i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 6.32456i | − | 0.437479i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.23607 | 0.0850944 | 0.0425472 | − | 0.999094i | \(-0.486453\pi\) | ||||
0.0425472 | + | 0.999094i | \(0.486453\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 22.8825 | 1.56788 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6.32456 | −0.431331 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.52786 | + | 8.74032i | 0.375256 | + | 0.593332i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −32.3607 | −2.18673 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 4.00000i | − | 0.269069i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −16.1452 | −1.08117 | −0.540583 | − | 0.841291i | \(-0.681796\pi\) | ||||
−0.540583 | + | 0.841291i | \(0.681796\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 10.5279 | 0.701858 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.87558i | 0.124487i | 0.998061 | + | 0.0622434i | \(0.0198255\pi\) | ||||
−0.998061 | + | 0.0622434i | \(0.980174\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.20788 | −0.0798191 | −0.0399096 | − | 0.999203i | \(-0.512707\pi\) | ||||
−0.0399096 | + | 0.999203i | \(0.512707\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.32456 | + | 4.00000i | −0.416125 | + | 0.263181i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 13.4164 | 0.878938 | 0.439469 | − | 0.898258i | \(-0.355167\pi\) | ||||
0.439469 | + | 0.898258i | \(0.355167\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.88854 | 0.384126 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.07262 | −0.524373 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 18.6525i | − | 1.20653i | −0.797541 | − | 0.603264i | \(-0.793866\pi\) | ||
0.797541 | − | 0.603264i | \(-0.206134\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 1.74806i | − | 0.112603i | −0.998414 | − | 0.0563014i | \(-0.982069\pi\) | ||
0.998414 | − | 0.0563014i | \(-0.0179308\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 19.2588i | 1.23545i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.62054 | − | 3.41641i | 0.103533 | − | 0.218266i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 11.7082i | − | 0.744975i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 20.6525 | 1.30880 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 19.2588i | − | 1.21561i | −0.794088 | − | 0.607803i | \(-0.792051\pi\) | ||
0.794088 | − | 0.607803i | \(-0.207949\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 4.00000i | − | 0.251478i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.16073 | 0.135310 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 16.9706i | 1.05859i | 0.848436 | + | 0.529297i | \(0.177544\pi\) | ||||
−0.848436 | + | 0.529297i | \(0.822456\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 15.5279 | − | 9.82068i | 0.964855 | − | 0.610228i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 4.47214i | − | 0.276818i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.88854i | 0.239778i | 0.992787 | + | 0.119889i | \(0.0382539\pi\) | ||||
−0.992787 | + | 0.119889i | \(0.961746\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 4.57649i | − | 0.281132i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 35.4164 | 2.16745 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 19.2588 | 1.17423 | 0.587115 | − | 0.809503i | \(-0.300264\pi\) | ||||
0.587115 | + | 0.809503i | \(0.300264\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −26.1235 | −1.58689 | −0.793446 | − | 0.608640i | \(-0.791715\pi\) | ||||
−0.793446 | + | 0.608640i | \(0.791715\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −11.7082 | + | 7.40492i | −0.708613 | + | 0.448166i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.81966 | −0.350939 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 18.9443i | 1.13825i | 0.822251 | + | 0.569125i | \(0.192718\pi\) | ||||
−0.822251 | + | 0.569125i | \(0.807282\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.74032 | 0.523269 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.88854 | 0.231971 | 0.115986 | − | 0.993251i | \(-0.462997\pi\) | ||||
0.115986 | + | 0.993251i | \(0.462997\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 20.5942i | − | 1.22420i | −0.790781 | − | 0.612099i | \(-0.790325\pi\) | ||
0.790781 | − | 0.612099i | \(-0.209675\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6.32456 | 0.374634 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −22.8825 | + | 14.4721i | −1.35071 | + | 0.854263i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.9443 | 0.820251 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.00000 | 0.234484 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 28.4118 | 1.65983 | 0.829917 | − | 0.557886i | \(-0.188388\pi\) | ||||
0.829917 | + | 0.557886i | \(0.188388\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.875388i | 0.0509671i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 2.16073i | − | 0.125378i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 7.40492i | − | 0.428237i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −16.5579 | − | 26.1803i | −0.954382 | − | 1.50901i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 26.1803i | − | 1.50402i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7.12461 | 0.407954 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 13.6020i | − | 0.776305i | −0.921595 | − | 0.388152i | \(-0.873113\pi\) | ||
0.921595 | − | 0.388152i | \(-0.126887\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 31.4164i | − | 1.78722i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −14.1421 | −0.801927 | −0.400963 | − | 0.916094i | \(-0.631325\pi\) | ||||
−0.400963 | + | 0.916094i | \(0.631325\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 8.89794i | − | 0.502941i | −0.967865 | − | 0.251471i | \(-0.919086\pi\) | ||
0.967865 | − | 0.251471i | \(-0.0809142\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.70820 | − | 2.70091i | −0.0962464 | − | 0.152179i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 19.8885i | − | 1.11705i | −0.829487 | − | 0.558526i | \(-0.811367\pi\) | ||
0.829487 | − | 0.558526i | \(-0.188633\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.47214i | 0.138413i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.667701i | 0.0372674i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.94427 | −0.497673 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −10.7735 | −0.597608 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −8.07262 | −0.446417 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 15.4164 | + | 24.3755i | 0.849934 | + | 1.34386i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.1246 | 0.831324 | 0.415662 | − | 0.909519i | \(-0.363550\pi\) | ||||
0.415662 | + | 0.909519i | \(0.363550\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 15.5279i | − | 0.850922i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.00310 | 0.109441 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 25.1246 | 1.36862 | 0.684312 | − | 0.729189i | \(-0.260102\pi\) | ||||
0.684312 | + | 0.729189i | \(0.260102\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 5.24419i | − | 0.284825i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.83153 | −0.261642 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.3848 | − | 2.23607i | 0.992685 | − | 0.120736i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.00000 | 0.215353 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −9.23607 | −0.495818 | −0.247909 | − | 0.968783i | \(-0.579743\pi\) | ||||
−0.247909 | + | 0.968783i | \(0.579743\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.9343 | 0.692355 | 0.346177 | − | 0.938169i | \(-0.387480\pi\) | ||||
0.346177 | + | 0.938169i | \(0.387480\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 4.00000i | − | 0.213504i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 16.1452i | 0.859324i | 0.902990 | + | 0.429662i | \(0.141367\pi\) | ||||
−0.902990 | + | 0.429662i | \(0.858633\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 5.40182i | − | 0.286699i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5.65685 | + | 8.94427i | 0.299392 | + | 0.473381i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 27.2361i | − | 1.43746i | −0.695287 | − | 0.718732i | \(-0.744723\pi\) | ||
0.695287 | − | 0.718732i | \(-0.255277\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.18034 | −0.377913 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 21.6746i | 1.13762i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.63932i | 0.399860i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.65685 | −0.295285 | −0.147643 | − | 0.989041i | \(-0.547169\pi\) | ||||
−0.147643 | + | 0.989041i | \(0.547169\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 22.8825i | 1.19121i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 18.9443 | − | 11.9814i | 0.983538 | − | 0.622044i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 5.05573i | − | 0.261776i | −0.991397 | − | 0.130888i | \(-0.958217\pi\) | ||
0.991397 | − | 0.130888i | \(-0.0417828\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 12.0000i | − | 0.619677i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.57649i | 0.235701i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.29180 | 0.425921 | 0.212960 | − | 0.977061i | \(-0.431689\pi\) | ||||
0.212960 | + | 0.977061i | \(0.431689\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.74806 | −0.0895560 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 29.2070 | 1.49241 | 0.746204 | − | 0.665717i | \(-0.231874\pi\) | ||||
0.746204 | + | 0.665717i | \(0.231874\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.944272 | + | 1.49302i | 0.0481246 | + | 0.0760916i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −26.1803 | −1.33082 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 28.8328i | − | 1.46188i | −0.682441 | − | 0.730941i | \(-0.739081\pi\) | ||
0.682441 | − | 0.730941i | \(-0.260919\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.65685 | −0.286079 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −13.2361 | −0.667671 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.90569i | 0.0958855i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 31.2402 | 1.56790 | 0.783951 | − | 0.620823i | \(-0.213201\pi\) | ||||
0.783951 | + | 0.620823i | \(0.213201\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 16.5579 | + | 26.1803i | 0.828932 | + | 1.31066i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14.6525 | 0.731710 | 0.365855 | − | 0.930672i | \(-0.380777\pi\) | ||||
0.365855 | + | 0.930672i | \(0.380777\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.94427 | −0.445546 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 5.78437 | 0.287428 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.58359i | 0.425473i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 5.91189i | − | 0.292324i | −0.989261 | − | 0.146162i | \(-0.953308\pi\) | ||
0.989261 | − | 0.146162i | \(-0.0466921\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 28.5393i | − | 1.40774i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.62365 | + | 2.29180i | −0.178308 | + | 0.112772i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 4.87539i | − | 0.239323i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.18034 | 0.302653 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 22.7549i | − | 1.11165i | −0.831299 | − | 0.555826i | \(-0.812402\pi\) | ||
0.831299 | − | 0.555826i | \(-0.187598\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.4164i | 0.848824i | 0.905469 | + | 0.424412i | \(0.139519\pi\) | ||||
−0.905469 | + | 0.424412i | \(0.860481\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 24.3755 | 1.18518 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 8.23024i | 0.399225i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 18.6525 | + | 29.4922i | 0.902657 | + | 1.42723i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 6.47214i | − | 0.312478i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.29180i | 0.110392i | 0.998476 | + | 0.0551960i | \(0.0175784\pi\) | ||||
−0.998476 | + | 0.0551960i | \(0.982422\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 14.3972i | − | 0.691884i | −0.938256 | − | 0.345942i | \(-0.887559\pi\) | ||
0.938256 | − | 0.345942i | \(-0.112441\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.47214 | −0.118530 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −16.5579 | −0.792072 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −26.7912 | −1.27868 | −0.639338 | − | 0.768926i | \(-0.720792\pi\) | ||||
−0.639338 | + | 0.768926i | \(0.720792\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.70820 | − | 14.1421i | 0.319438 | − | 0.673435i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −31.7082 | −1.50650 | −0.753251 | − | 0.657733i | \(-0.771515\pi\) | ||||
−0.753251 | + | 0.657733i | \(0.771515\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 8.36068i | − | 0.396334i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −30.7000 | −1.45206 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 30.3607 | 1.43281 | 0.716405 | − | 0.697685i | \(-0.245787\pi\) | ||||
0.716405 | + | 0.697685i | \(0.245787\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 12.6491i | − | 0.595623i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −25.7109 | −1.20800 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.74806 | + | 2.76393i | 0.0819505 | + | 0.129575i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −30.6525 | −1.43386 | −0.716931 | − | 0.697144i | \(-0.754454\pi\) | ||||
−0.716931 | + | 0.697144i | \(0.754454\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.05573 | −0.142629 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17.7658 | 0.827435 | 0.413718 | − | 0.910405i | \(-0.364230\pi\) | ||||
0.413718 | + | 0.910405i | \(0.364230\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 31.8885i | 1.48199i | 0.671513 | + | 0.740993i | \(0.265645\pi\) | ||||
−0.671513 | + | 0.740993i | \(0.734355\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 4.83153i | − | 0.224057i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0.540182i | 0.0249966i | 0.999922 | + | 0.0124983i | \(0.00397844\pi\) | ||||
−0.999922 | + | 0.0124983i | \(0.996022\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.24419 | + | 8.29180i | 0.242154 | + | 0.382880i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 26.1803i | − | 1.20633i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 14.4721 | 0.665430 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 24.0903i | 1.10534i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 18.9443i | − | 0.867399i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 27.8716 | 1.27349 | 0.636743 | − | 0.771076i | \(-0.280281\pi\) | ||||
0.636743 | + | 0.771076i | \(0.280281\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 15.8902i | 0.724531i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 10.4721 | + | 16.5579i | 0.476499 | + | 0.753411i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 0.944272i | − | 0.0428772i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 34.0689i | − | 1.54381i | −0.635739 | − | 0.771904i | \(-0.719304\pi\) | ||
0.635739 | − | 0.771904i | \(-0.280696\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 39.4404i | 1.78355i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 27.7082 | 1.25045 | 0.625227 | − | 0.780443i | \(-0.285006\pi\) | ||||
0.625227 | + | 0.780443i | \(0.285006\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.49613 | 0.157458 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.49302 | 0.0671065 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 22.3607 | − | 14.1421i | 1.00301 | − | 0.634361i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −25.2361 | −1.12972 | −0.564861 | − | 0.825186i | \(-0.691070\pi\) | ||||
−0.564861 | + | 0.825186i | \(0.691070\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 18.4721i | 0.825274i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 28.1266 | 1.25411 | 0.627053 | − | 0.778977i | \(-0.284261\pi\) | ||||
0.627053 | + | 0.778977i | \(0.284261\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.18034 | −0.275022 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 17.7658i | 0.789006i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 25.5834 | 1.13396 | 0.566981 | − | 0.823731i | \(-0.308111\pi\) | ||||
0.566981 | + | 0.823731i | \(0.308111\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −31.6228 | + | 20.0000i | −1.39891 | + | 0.884748i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −8.94427 | −0.394899 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7.41641 | −0.326806 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −13.4744 | −0.592605 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 41.5967i | 1.82589i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15.0649i | 0.660004i | 0.943980 | + | 0.330002i | \(0.107049\pi\) | ||||
−0.943980 | + | 0.330002i | \(0.892951\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.3500i | 0.671209i | 0.942003 | + | 0.335605i | \(0.108941\pi\) | ||||
−0.942003 | + | 0.335605i | \(0.891059\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 24.0903 | − | 15.2361i | 1.05139 | − | 0.664957i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.83282i | 0.297642i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12.5279 | 0.544690 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.62365i | 0.157253i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 23.4164i | − | 1.01428i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.157623 | 0.00681463 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 47.2579i | − | 2.03933i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.70820 | + | 7.81758i | −0.159724 | + | 0.336727i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.47214i | 0.364246i | 0.983276 | + | 0.182123i | \(0.0582968\pi\) | ||||
−0.983276 | + | 0.182123i | \(0.941703\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.23607i | 0.0530448i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.90569i | 0.0816307i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.12461 | −0.133599 | −0.0667994 | − | 0.997766i | \(-0.521279\pi\) | ||||
−0.0667994 | + | 0.997766i | \(0.521279\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 29.4922 | 1.25869 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10.2333 | 0.435955 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.88854 | + | 4.98915i | −0.335455 | + | 0.212160i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −8.58359 | −0.364353 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 42.3607i | − | 1.79488i | −0.441137 | − | 0.897440i | \(-0.645425\pi\) | ||
0.441137 | − | 0.897440i | \(-0.354575\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 26.7912 | 1.13315 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.94427 | −0.208747 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 35.8167i | 1.50949i | 0.656016 | + | 0.754747i | \(0.272240\pi\) | ||||
−0.656016 | + | 0.754747i | \(0.727760\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.23799 | −0.0520825 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 15.1437 | + | 23.9443i | 0.635975 | + | 1.00556i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 34.0689 | 1.42824 | 0.714121 | − | 0.700022i | \(-0.246827\pi\) | ||||
0.714121 | + | 0.700022i | \(0.246827\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.1803 | −0.593429 | −0.296714 | − | 0.954966i | \(-0.595891\pi\) | ||||
−0.296714 | + | 0.954966i | \(0.595891\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −52.5021 | −2.19331 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 15.2361i | 0.635388i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 35.2765i | 1.46858i | 0.678835 | + | 0.734291i | \(0.262485\pi\) | ||||
−0.678835 | + | 0.734291i | \(0.737515\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 25.7109i | 1.06851i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 20.1815 | − | 12.7639i | 0.837272 | − | 0.529537i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.4721i | 0.433712i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.76393 | 0.114275 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8.86784i | 0.366015i | 0.983112 | + | 0.183007i | \(0.0585833\pi\) | ||||
−0.983112 | + | 0.183007i | \(0.941417\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 20.0000i | 0.824086i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −43.3491 | −1.78315 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 11.3137i | − | 0.464598i | −0.972644 | − | 0.232299i | \(-0.925375\pi\) | ||
0.972644 | − | 0.232299i | \(-0.0746248\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.11146 | − | 1.33540i | 0.0865613 | − | 0.0547462i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 15.4164i | 0.630952i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.52786i | 0.144145i | 0.997399 | + | 0.0720723i | \(0.0229612\pi\) | ||||
−0.997399 | + | 0.0720723i | \(0.977039\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 24.6305i | − | 1.00470i | −0.864664 | − | 0.502350i | \(-0.832469\pi\) | ||
0.864664 | − | 0.502350i | \(-0.167531\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.29180 | 0.337668 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.11667 | 0.208022 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 23.1375 | 0.939122 | 0.469561 | − | 0.882900i | \(-0.344412\pi\) | ||||
0.469561 | + | 0.882900i | \(0.344412\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6.47214 | − | 10.2333i | −0.262264 | − | 0.414676i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −24.9443 | −1.00914 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.41641i | 0.380325i | 0.981753 | + | 0.190163i | \(0.0609015\pi\) | ||||
−0.981753 | + | 0.190163i | \(0.939098\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 12.6491 | 0.510061 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7.23607 | −0.291313 | −0.145657 | − | 0.989335i | \(-0.546529\pi\) | ||||
−0.145657 | + | 0.989335i | \(0.546529\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.70401i | 0.189070i | 0.995522 | + | 0.0945351i | \(0.0301365\pi\) | ||||
−0.995522 | + | 0.0945351i | \(0.969864\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.65685 | −0.227002 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 34.6088 | − | 21.8885i | 1.38657 | − | 0.876946i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 20.7082 | 0.828328 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −14.4721 | −0.577961 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 12.1390 | 0.484015 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.472136i | 0.0187954i | 0.999956 | + | 0.00939772i | \(0.00299143\pi\) | ||||
−0.999956 | + | 0.00939772i | \(0.997009\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 2.82843i | − | 0.112420i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.412662i | 0.0163760i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.86474 | + | 14.4721i | −0.271991 | + | 0.573407i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 22.3607i | − | 0.884575i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −16.1803 | −0.639085 | −0.319543 | − | 0.947572i | \(-0.603529\pi\) | ||||
−0.319543 | + | 0.947572i | \(0.603529\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 16.6854i | 0.658009i | 0.944328 | + | 0.329004i | \(0.106713\pi\) | ||||
−0.944328 | + | 0.329004i | \(0.893287\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 14.4721i | 0.569840i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.41577 | −0.0949735 | −0.0474868 | − | 0.998872i | \(-0.515121\pi\) | ||||
−0.0474868 | + | 0.998872i | \(0.515121\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 2.00310i | − | 0.0786287i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 20.0000 | − | 12.6491i | 0.783862 | − | 0.495758i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 13.4164i | 0.525025i | 0.964929 | + | 0.262512i | \(0.0845510\pi\) | ||||
−0.964929 | + | 0.262512i | \(0.915449\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.12461i | 0.122089i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 31.6228i | 1.23372i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 41.0132 | 1.59765 | 0.798823 | − | 0.601566i | \(-0.205456\pi\) | ||||
0.798823 | + | 0.601566i | \(0.205456\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −26.5061 | −1.03097 | −0.515484 | − | 0.856899i | \(-0.672388\pi\) | ||||
−0.515484 | + | 0.856899i | \(0.672388\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −9.15298 | −0.355472 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 6.18034 | − | 3.90879i | 0.239663 | − | 0.151576i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.47214 | 0.250602 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 36.9443i | 1.42835i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −16.3029 | −0.629365 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −40.8328 | −1.57399 | −0.786995 | − | 0.616960i | \(-0.788364\pi\) | ||||
−0.786995 | + | 0.616960i | \(0.788364\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 8.23024i | 0.316782i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 32.5756 | 1.25198 | 0.625991 | − | 0.779830i | \(-0.284694\pi\) | ||||
0.625991 | + | 0.779830i | \(0.284694\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.90879 | − | 2.47214i | 0.150006 | − | 0.0948719i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.29180 | 0.164462 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −10.1803 | −0.389540 | −0.194770 | − | 0.980849i | \(-0.562396\pi\) | ||||
−0.194770 | + | 0.980849i | \(0.562396\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.73722 | −0.257416 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.76393i | 0.105451i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 19.3863i | 0.738560i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 6.60970i | − | 0.251445i | −0.992065 | − | 0.125722i | \(-0.959875\pi\) | ||
0.992065 | − | 0.125722i | \(-0.0401249\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.90879 | + | 6.18034i | 0.148483 | + | 0.234772i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 1.45898i | − | 0.0553423i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −17.8885 | −0.677577 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 30.7000i | − | 1.16118i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 31.5279i | − | 1.19079i | −0.803433 | − | 0.595395i | \(-0.796995\pi\) | ||
0.803433 | − | 0.595395i | \(-0.203005\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 35.5316 | 1.34010 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 13.4744i | − | 0.507477i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −16.1803 | − | 25.5834i | −0.608524 | − | 0.962161i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 12.4721i | − | 0.468401i | −0.972188 | − | 0.234200i | \(-0.924753\pi\) | ||
0.972188 | − | 0.234200i | \(-0.0752472\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.88854i | 0.295844i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 12.6491i | 0.473713i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.52786 | −0.0571389 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −42.6814 | −1.59397 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −45.3523 | −1.69135 | −0.845677 | − | 0.533695i | \(-0.820803\pi\) | ||||
−0.845677 | + | 0.533695i | \(0.820803\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −19.4164 | − | 30.7000i | −0.723105 | − | 1.14333i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −4.00000 | −0.148762 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 9.41641i | − | 0.349717i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.41577 | −0.0895958 | −0.0447979 | − | 0.998996i | \(-0.514264\pi\) | ||||
−0.0447979 | + | 0.998996i | \(0.514264\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 11.9443 | 0.442380 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 20.4667i | − | 0.756988i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.02236 | −0.259377 | −0.129688 | − | 0.991555i | \(-0.541398\pi\) | ||||
−0.129688 | + | 0.991555i | \(0.541398\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −7.81758 | − | 3.70820i | −0.288356 | − | 0.136779i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.58359 | −0.168839 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.40325 | −0.0884051 | −0.0442025 | − | 0.999023i | \(-0.514075\pi\) | ||||
−0.0442025 | + | 0.999023i | \(0.514075\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −26.7912 | −0.984201 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 17.7082i | 0.649651i | 0.945774 | + | 0.324825i | \(0.105306\pi\) | ||||
−0.945774 | + | 0.324825i | \(0.894694\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.24730i | 0.265520i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 20.1815i | − | 0.738404i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.412662 | + | 0.652476i | 0.0150783 | + | 0.0238409i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 52.5410i | − | 1.91725i | −0.284674 | − | 0.958625i | \(-0.591885\pi\) | ||
0.284674 | − | 0.958625i | \(-0.408115\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −44.0689 | −1.60596 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6.06952i | 0.220892i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 22.3607i | 0.812713i | 0.913715 | + | 0.406356i | \(0.133201\pi\) | ||||
−0.913715 | + | 0.406356i | \(0.866799\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −9.15298 | −0.332232 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 8.07262i | 0.292632i | 0.989238 | + | 0.146316i | \(0.0467417\pi\) | ||||
−0.989238 | + | 0.146316i | \(0.953258\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.88854 | + | 4.98915i | −0.285584 | + | 0.180619i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − | 2.11146i | − | 0.0763399i | ||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 3.70820i | − | 0.133895i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 8.23024i | − | 0.296790i | −0.988928 | − | 0.148395i | \(-0.952589\pi\) | ||
0.988928 | − | 0.148395i | \(-0.0474107\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 38.8328 | 1.39853 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −49.8012 | −1.79123 | −0.895613 | − | 0.444835i | \(-0.853262\pi\) | ||||
−0.895613 | + | 0.444835i | \(0.853262\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 18.4034 | 0.661069 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −22.4721 | − | 35.5316i | −0.806183 | − | 1.27469i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −52.3607 | −1.87602 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12.3607i | 0.442300i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.49613 | 0.124941 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.18034 | −0.220586 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 10.7735i | − | 0.384035i | −0.981392 | − | 0.192017i | \(-0.938497\pi\) | ||
0.981392 | − | 0.192017i | \(-0.0615030\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 8.89794 | 0.316775 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.24109 | − | 5.12461i | −0.115240 | − | 0.182210i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −30.1803 | −1.07174 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −10.4721 | −0.371408 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 13.6020 | 0.481806 | 0.240903 | − | 0.970549i | \(-0.422556\pi\) | ||||
0.240903 | + | 0.970549i | \(0.422556\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 19.0557i | 0.674143i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 34.6088i | − | 1.22284i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 17.4806i | − | 0.616878i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.90879 | − | 2.47214i | 0.137767 | − | 0.0871313i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 44.0689i | − | 1.55130i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.06888 | 0.0727381 | 0.0363690 | − | 0.999338i | \(-0.488421\pi\) | ||||
0.0363690 | + | 0.999338i | \(0.488421\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 36.7394i | − | 1.29010i | −0.764142 | − | 0.645048i | \(-0.776837\pi\) | ||
0.764142 | − | 0.645048i | \(-0.223163\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 59.7771i | 2.09647i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 9.31061 | 0.326136 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 59.9070i | − | 2.09588i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 7.23607 | + | 11.4412i | 0.252849 | + | 0.399789i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 11.8885i | − | 0.414913i | −0.978244 | − | 0.207457i | \(-0.933481\pi\) | ||
0.978244 | − | 0.207457i | \(-0.0665186\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16.8328i | 0.586755i | 0.955997 | + | 0.293378i | \(0.0947793\pi\) | ||||
−0.955997 | + | 0.293378i | \(0.905221\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 13.3168i | 0.463632i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 24.0689 | 0.836957 | 0.418479 | − | 0.908227i | \(-0.362564\pi\) | ||||
0.418479 | + | 0.908227i | \(0.362564\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −35.8167 | −1.24397 | −0.621983 | − | 0.783031i | \(-0.713673\pi\) | ||||
−0.621983 | + | 0.783031i | \(0.713673\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 43.3491 | 1.50377 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 11.0557 | + | 5.24419i | 0.383058 | + | 0.181700i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.36068 | 0.150908 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.83282i | 0.236177i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −54.6629 | −1.88717 | −0.943586 | − | 0.331128i | \(-0.892571\pi\) | ||||
−0.943586 | + | 0.331128i | \(0.892571\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25.0000 | 0.862069 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 8.89794i | − | 0.306461i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.19393 | 0.144276 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 13.3956 | + | 21.1803i | 0.460279 | + | 0.727765i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −47.1246 | −1.61731 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 22.4721 | 0.770335 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.19393 | −0.143598 | −0.0717988 | − | 0.997419i | \(-0.522874\pi\) | ||||
−0.0717988 | + | 0.997419i | \(0.522874\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 6.18034i | − | 0.211363i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 43.3491i | 1.48078i | 0.672178 | + | 0.740389i | \(0.265359\pi\) | ||||
−0.672178 | + | 0.740389i | \(0.734641\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 18.6885i | 0.637644i | 0.947815 | + | 0.318822i | \(0.103287\pi\) | ||||
−0.947815 | + | 0.318822i | \(0.896713\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 33.1158 | + | 52.3607i | 1.12858 | + | 1.78445i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 10.0000i | − | 0.340404i | −0.985409 | − | 0.170202i | \(-0.945558\pi\) | ||
0.985409 | − | 0.170202i | \(-0.0544420\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.81966 | 0.333878 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 31.9079i | − | 1.08365i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 4.36068i | − | 0.147926i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.48528 | −0.287513 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 3.90879i | − | 0.132293i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −7.41641 | − | 11.7264i | −0.250720 | − | 0.396424i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 30.0000i | 1.01303i | 0.862232 | + | 0.506514i | \(0.169066\pi\) | ||||
−0.862232 | + | 0.506514i | \(0.830934\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 65.0132i | − | 2.19284i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 32.2918 | 1.08671 | 0.543353 | − | 0.839505i | \(-0.317155\pi\) | ||||
0.543353 | + | 0.839505i | \(0.317155\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.00310 | 0.0673336 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.41577 | −0.0811135 | −0.0405567 | − | 0.999177i | \(-0.512913\pi\) | ||||
−0.0405567 | + | 0.999177i | \(0.512913\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.70820 | + | 1.08036i | −0.0572913 | + | 0.0362342i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −13.2361 | −0.443425 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 55.7771i | 1.86651i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −11.1561 | −0.372907 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −16.9443 | −0.565753 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 7.81758i | − | 0.260731i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 14.8098 | 0.493387 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −59.9070 | + | 37.8885i | −1.99358 | + | 1.26085i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.291796 | 0.00969963 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.291796 | 0.00968893 | 0.00484446 | − | 0.999988i | \(-0.498458\pi\) | ||||
0.00484446 | + | 0.999988i | \(0.498458\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −25.5834 | −0.848547 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 25.1246i | 0.832416i | 0.909270 | + | 0.416208i | \(0.136641\pi\) | ||||
−0.909270 | + | 0.416208i | \(0.863359\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 11.1561i | 0.369213i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 16.3029i | − | 0.538956i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −12.9343 | + | 8.18034i | −0.427127 | + | 0.270139i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.94427i | 0.229070i | 0.993419 | + | 0.114535i | \(0.0365379\pi\) | ||||
−0.993419 | + | 0.114535i | \(0.963462\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −31.1246 | −1.02559 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 22.8825i | 0.753185i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 32.6950i | − | 1.07501i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −30.7000 | −1.00832 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 45.3523i | − | 1.48796i | −0.668202 | − | 0.743980i | \(-0.732936\pi\) | ||
0.668202 | − | 0.743980i | \(-0.267064\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 32.3607 | + | 15.3500i | 1.06058 | + | 0.503077i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 32.3607i | 1.05944i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.16718i | 0.0381710i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 45.0972i | − | 1.47326i | −0.676295 | − | 0.736631i | \(-0.736416\pi\) | ||
0.676295 | − | 0.736631i | \(-0.263584\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −20.3607 | −0.664446 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −39.9805 | −1.30333 | −0.651664 | − | 0.758508i | \(-0.725929\pi\) | ||||
−0.651664 | + | 0.758508i | \(0.725929\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −33.1158 | −1.07840 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.11146 | − | 1.33540i | 0.0686857 | − | 0.0434406i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 15.1246 | 0.491484 | 0.245742 | − | 0.969335i | \(-0.420968\pi\) | ||||
0.245742 | + | 0.969335i | \(0.420968\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 32.3607i | − | 1.05047i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −45.5099 | −1.47576 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.05573 | 0.0341984 | 0.0170992 | − | 0.999854i | \(-0.494557\pi\) | ||||
0.0170992 | + | 0.999854i | \(0.494557\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 12.3941i | 0.401063i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5.65685 | 0.182860 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −17.6383 | − | 27.8885i | −0.569569 | − | 0.900568i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.7214 | −0.507141 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.652476 | 0.0210257 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.06952 | 0.195385 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 17.3475i | − | 0.557859i | −0.960312 | − | 0.278929i | \(-0.910020\pi\) | ||
0.960312 | − | 0.278929i | \(-0.0899795\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 20.4667i | 0.657485i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 20.1815i | 0.647657i | 0.946116 | + | 0.323828i | \(0.104970\pi\) | ||||
−0.946116 | + | 0.323828i | \(0.895030\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.03941 | − | 3.81966i | 0.193615 | − | 0.122453i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 24.6525i | 0.789511i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 33.4164 | 1.06909 | 0.534543 | − | 0.845141i | \(-0.320484\pi\) | ||||
0.534543 | + | 0.845141i | \(0.320484\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 19.1313i | 0.611439i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.88854i | 0.251862i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.90569 | −0.0607820 | −0.0303910 | − | 0.999538i | \(-0.509675\pi\) | ||||
−0.0303910 | + | 0.999538i | \(0.509675\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10.2333i | 0.326061i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 55.7771 | − | 35.2765i | 1.77540 | − | 1.12286i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 37.8885i | − | 1.20479i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 34.3607i | − | 1.09150i | −0.837947 | − | 0.545751i | \(-0.816244\pi\) | ||
0.837947 | − | 0.545751i | \(-0.183756\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 34.6088i | − | 1.09828i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.63932 | 0.115374 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −37.9774 | −1.20276 | −0.601379 | − | 0.798964i | \(-0.705382\pi\) | ||||
−0.601379 | + | 0.798964i | \(0.705382\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 12.1390 | 0.384062 |
(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 | 1792.2.e.h.895.1 | 8 | ||
4.3 | odd | 2 | 1792.2.e.i.895.7 | 8 | |||
7.6 | odd | 2 | inner | 1792.2.e.h.895.8 | 8 | ||
8.3 | odd | 2 | inner | 1792.2.e.h.895.2 | 8 | ||
8.5 | even | 2 | 1792.2.e.i.895.8 | 8 | |||
16.3 | odd | 4 | 896.2.f.b.895.2 | yes | 8 | ||
16.5 | even | 4 | 896.2.f.a.895.1 | ✓ | 8 | ||
16.11 | odd | 4 | 896.2.f.a.895.7 | yes | 8 | ||
16.13 | even | 4 | 896.2.f.b.895.8 | yes | 8 | ||
28.27 | even | 2 | 1792.2.e.i.895.2 | 8 | |||
56.13 | odd | 2 | 1792.2.e.i.895.1 | 8 | |||
56.27 | even | 2 | inner | 1792.2.e.h.895.7 | 8 | ||
112.13 | odd | 4 | 896.2.f.b.895.1 | yes | 8 | ||
112.27 | even | 4 | 896.2.f.a.895.2 | yes | 8 | ||
112.69 | odd | 4 | 896.2.f.a.895.8 | yes | 8 | ||
112.83 | even | 4 | 896.2.f.b.895.7 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
896.2.f.a.895.1 | ✓ | 8 | 16.5 | even | 4 | ||
896.2.f.a.895.2 | yes | 8 | 112.27 | even | 4 | ||
896.2.f.a.895.7 | yes | 8 | 16.11 | odd | 4 | ||
896.2.f.a.895.8 | yes | 8 | 112.69 | odd | 4 | ||
896.2.f.b.895.1 | yes | 8 | 112.13 | odd | 4 | ||
896.2.f.b.895.2 | yes | 8 | 16.3 | odd | 4 | ||
896.2.f.b.895.7 | yes | 8 | 112.83 | even | 4 | ||
896.2.f.b.895.8 | yes | 8 | 16.13 | even | 4 | ||
1792.2.e.h.895.1 | 8 | 1.1 | even | 1 | trivial | ||
1792.2.e.h.895.2 | 8 | 8.3 | odd | 2 | inner | ||
1792.2.e.h.895.7 | 8 | 56.27 | even | 2 | inner | ||
1792.2.e.h.895.8 | 8 | 7.6 | odd | 2 | inner | ||
1792.2.e.i.895.1 | 8 | 56.13 | odd | 2 | |||
1792.2.e.i.895.2 | 8 | 28.27 | even | 2 | |||
1792.2.e.i.895.7 | 8 | 4.3 | odd | 2 | |||
1792.2.e.i.895.8 | 8 | 8.5 | even | 2 |