Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3969,2,Mod(1,3969)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3969, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3969.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3969 = 3^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3969.a (trivial) |
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: | yes |
Analytic conductor: | \(31.6926245622\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.14013.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 6x^{2} + 6x + 3 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 567) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-2.37167\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3969.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.37167 | 1.67703 | 0.838513 | − | 0.544881i | \(-0.183425\pi\) | ||||
0.838513 | + | 0.544881i | \(0.183425\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.62484 | 1.81242 | ||||||||
\(5\) | −1.22875 | −0.549512 | −0.274756 | − | 0.961514i | \(-0.588597\pi\) | ||||
−0.274756 | + | 0.961514i | \(0.588597\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 3.85358 | 1.36245 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.91418 | −0.921546 | ||||||||
\(11\) | −2.66102 | −0.802328 | −0.401164 | − | 0.916006i | \(-0.631394\pi\) | ||||
−0.401164 | + | 0.916006i | \(0.631394\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.62484 | −1.00535 | −0.502674 | − | 0.864476i | \(-0.667651\pi\) | ||||
−0.502674 | + | 0.864476i | \(0.667651\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.88977 | 0.472441 | ||||||||
\(17\) | −6.73158 | −1.63265 | −0.816324 | − | 0.577594i | \(-0.803992\pi\) | ||||
−0.816324 | + | 0.577594i | \(0.803992\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.51460 | 0.576889 | 0.288445 | − | 0.957497i | \(-0.406862\pi\) | ||||
0.288445 | + | 0.957497i | \(0.406862\pi\) | |||||||
\(20\) | −4.45400 | −0.995945 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −6.31107 | −1.34553 | ||||||||
\(23\) | 7.99651 | 1.66739 | 0.833694 | − | 0.552227i | \(-0.186222\pi\) | ||||
0.833694 | + | 0.552227i | \(0.186222\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.49018 | −0.698037 | ||||||||
\(26\) | −8.59693 | −1.68600 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.24967 | −0.417754 | −0.208877 | − | 0.977942i | \(-0.566981\pi\) | ||||
−0.208877 | + | 0.977942i | \(0.566981\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.2253 | −1.83651 | −0.918255 | − | 0.395989i | \(-0.870402\pi\) | ||||
−0.918255 | + | 0.395989i | \(0.870402\pi\) | |||||||
\(32\) | −3.22526 | −0.570150 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −15.9651 | −2.73799 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.53902 | −0.581811 | −0.290906 | − | 0.956752i | \(-0.593957\pi\) | ||||
−0.290906 | + | 0.956752i | \(0.593957\pi\) | |||||||
\(38\) | 5.96382 | 0.967459 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −4.73507 | −0.748680 | ||||||||
\(41\) | −1.86535 | −0.291319 | −0.145659 | − | 0.989335i | \(-0.546530\pi\) | ||||
−0.145659 | + | 0.989335i | \(0.546530\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.13944 | 0.783757 | 0.391879 | − | 0.920017i | \(-0.371825\pi\) | ||||
0.391879 | + | 0.920017i | \(0.371825\pi\) | |||||||
\(44\) | −9.64576 | −1.45415 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 18.9651 | 2.79625 | ||||||||
\(47\) | 2.14642 | 0.313087 | 0.156544 | − | 0.987671i | \(-0.449965\pi\) | ||||
0.156544 | + | 0.987671i | \(0.449965\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −8.27758 | −1.17063 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −13.1394 | −1.82211 | ||||||||
\(53\) | −2.97209 | −0.408248 | −0.204124 | − | 0.978945i | \(-0.565435\pi\) | ||||
−0.204124 | + | 0.978945i | \(0.565435\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.26972 | 0.440888 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.33549 | −0.700584 | ||||||||
\(59\) | 8.72809 | 1.13630 | 0.568150 | − | 0.822925i | \(-0.307659\pi\) | ||||
0.568150 | + | 0.822925i | \(0.307659\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −15.0048 | −1.92117 | −0.960583 | − | 0.277993i | \(-0.910331\pi\) | ||||
−0.960583 | + | 0.277993i | \(0.910331\pi\) | |||||||
\(62\) | −24.2510 | −3.07988 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −11.4288 | −1.42860 | ||||||||
\(65\) | 4.45400 | 0.552451 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.64925 | −0.323658 | −0.161829 | − | 0.986819i | \(-0.551739\pi\) | ||||
−0.161829 | + | 0.986819i | \(0.551739\pi\) | |||||||
\(68\) | −24.4009 | −2.95904 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.1150 | 1.20043 | 0.600216 | − | 0.799838i | \(-0.295081\pi\) | ||||
0.600216 | + | 0.799838i | \(0.295081\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.29413 | 0.853714 | 0.426857 | − | 0.904319i | \(-0.359621\pi\) | ||||
0.426857 | + | 0.904319i | \(0.359621\pi\) | |||||||
\(74\) | −8.39340 | −0.975713 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 9.11502 | 1.04556 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.313764 | −0.0353012 | −0.0176506 | − | 0.999844i | \(-0.505619\pi\) | ||||
−0.0176506 | + | 0.999844i | \(0.505619\pi\) | |||||||
\(80\) | −2.32204 | −0.259612 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.42400 | −0.488549 | ||||||||
\(83\) | −7.69371 | −0.844495 | −0.422247 | − | 0.906481i | \(-0.638759\pi\) | ||||
−0.422247 | + | 0.906481i | \(0.638759\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.27140 | 0.897159 | ||||||||
\(86\) | 12.1891 | 1.31438 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −10.2545 | −1.09313 | ||||||||
\(89\) | 7.19256 | 0.762410 | 0.381205 | − | 0.924491i | \(-0.375509\pi\) | ||||
0.381205 | + | 0.924491i | \(0.375509\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 28.9860 | 3.02200 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 5.09060 | 0.525056 | ||||||||
\(95\) | −3.08981 | −0.317007 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.1839 | −1.33862 | −0.669311 | − | 0.742982i | \(-0.733411\pi\) | ||||
−0.669311 | + | 0.742982i | \(0.733411\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −12.6513 | −1.26513 | ||||||||
\(101\) | 2.78302 | 0.276921 | 0.138460 | − | 0.990368i | \(-0.455785\pi\) | ||||
0.138460 | + | 0.990368i | \(0.455785\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.00647 | 0.591835 | 0.295917 | − | 0.955214i | \(-0.404375\pi\) | ||||
0.295917 | + | 0.955214i | \(0.404375\pi\) | |||||||
\(104\) | −13.9686 | −1.36973 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.04883 | −0.684643 | ||||||||
\(107\) | 11.7364 | 1.13460 | 0.567299 | − | 0.823512i | \(-0.307988\pi\) | ||||
0.567299 | + | 0.823512i | \(0.307988\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.98474 | −0.764800 | −0.382400 | − | 0.923997i | \(-0.624902\pi\) | ||||
−0.382400 | + | 0.923997i | \(0.624902\pi\) | |||||||
\(110\) | 7.75470 | 0.739382 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.64009 | −0.436503 | −0.218252 | − | 0.975893i | \(-0.570035\pi\) | ||||
−0.218252 | + | 0.975893i | \(0.570035\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9.82567 | −0.916249 | ||||||||
\(116\) | −8.15470 | −0.757144 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 20.7002 | 1.90561 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.91897 | −0.356270 | ||||||||
\(122\) | −35.5865 | −3.22185 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −37.0649 | −3.32852 | ||||||||
\(125\) | 10.4323 | 0.933091 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.32633 | −0.295164 | −0.147582 | − | 0.989050i | \(-0.547149\pi\) | ||||
−0.147582 | + | 0.989050i | \(0.547149\pi\) | |||||||
\(128\) | −20.6548 | −1.82565 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 10.5634 | 0.926475 | ||||||||
\(131\) | 8.44702 | 0.738020 | 0.369010 | − | 0.929425i | \(-0.379697\pi\) | ||||
0.369010 | + | 0.929425i | \(0.379697\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −6.28317 | −0.542783 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −25.9407 | −2.22440 | ||||||||
\(137\) | −13.9965 | −1.19580 | −0.597901 | − | 0.801570i | \(-0.703999\pi\) | ||||
−0.597901 | + | 0.801570i | \(0.703999\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.64009 | −0.478386 | −0.239193 | − | 0.970972i | \(-0.576883\pi\) | ||||
−0.239193 | + | 0.970972i | \(0.576883\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 23.9895 | 2.01316 | ||||||||
\(143\) | 9.64576 | 0.806619 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.76427 | 0.229561 | ||||||||
\(146\) | 17.2993 | 1.43170 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −12.8284 | −1.05449 | ||||||||
\(149\) | −8.76945 | −0.718421 | −0.359211 | − | 0.933257i | \(-0.616954\pi\) | ||||
−0.359211 | + | 0.933257i | \(0.616954\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.56075 | −0.778042 | −0.389021 | − | 0.921229i | \(-0.627187\pi\) | ||||
−0.389021 | + | 0.921229i | \(0.627187\pi\) | |||||||
\(152\) | 9.69022 | 0.785981 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 12.5642 | 1.00918 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.15907 | 0.172312 | 0.0861562 | − | 0.996282i | \(-0.472542\pi\) | ||||
0.0861562 | + | 0.996282i | \(0.472542\pi\) | |||||||
\(158\) | −0.744146 | −0.0592011 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3.96302 | 0.313304 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 20.9743 | 1.64283 | 0.821416 | − | 0.570330i | \(-0.193185\pi\) | ||||
0.821416 | + | 0.570330i | \(0.193185\pi\) | |||||||
\(164\) | −6.76158 | −0.527991 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −18.2470 | −1.41624 | ||||||||
\(167\) | −4.27409 | −0.330739 | −0.165370 | − | 0.986232i | \(-0.552882\pi\) | ||||
−0.165370 | + | 0.986232i | \(0.552882\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.139438 | 0.0107260 | ||||||||
\(170\) | 19.6171 | 1.50456 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 18.6296 | 1.42050 | ||||||||
\(173\) | −1.81660 | −0.138113 | −0.0690567 | − | 0.997613i | \(-0.521999\pi\) | ||||
−0.0690567 | + | 0.997613i | \(0.521999\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −5.02871 | −0.379053 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 17.0584 | 1.27858 | ||||||||
\(179\) | −8.05013 | −0.601695 | −0.300848 | − | 0.953672i | \(-0.597270\pi\) | ||||
−0.300848 | + | 0.953672i | \(0.597270\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 25.3467 | 1.88401 | 0.942004 | − | 0.335601i | \(-0.108939\pi\) | ||||
0.942004 | + | 0.335601i | \(0.108939\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 30.8152 | 2.27173 | ||||||||
\(185\) | 4.34855 | 0.319712 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 17.9129 | 1.30992 | ||||||||
\(188\) | 7.78042 | 0.567445 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −7.32801 | −0.531630 | ||||||||
\(191\) | 7.15121 | 0.517443 | 0.258722 | − | 0.965952i | \(-0.416699\pi\) | ||||
0.258722 | + | 0.965952i | \(0.416699\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.3555 | 0.817389 | 0.408695 | − | 0.912671i | \(-0.365984\pi\) | ||||
0.408695 | + | 0.912671i | \(0.365984\pi\) | |||||||
\(194\) | −31.2679 | −2.24490 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −20.0998 | −1.43205 | −0.716024 | − | 0.698075i | \(-0.754040\pi\) | ||||
−0.716024 | + | 0.698075i | \(0.754040\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.3250 | 0.731921 | 0.365961 | − | 0.930630i | \(-0.380740\pi\) | ||||
0.365961 | + | 0.930630i | \(0.380740\pi\) | |||||||
\(200\) | −13.4497 | −0.951038 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 6.60042 | 0.464404 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.29204 | 0.160083 | ||||||||
\(206\) | 14.2454 | 0.992523 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −6.85009 | −0.474968 | ||||||||
\(209\) | −6.69141 | −0.462854 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.598737 | 0.0412188 | 0.0206094 | − | 0.999788i | \(-0.493439\pi\) | ||||
0.0206094 | + | 0.999788i | \(0.493439\pi\) | |||||||
\(212\) | −10.7734 | −0.739917 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 27.8348 | 1.90275 | ||||||||
\(215\) | −6.31506 | −0.430684 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −18.9372 | −1.28259 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 11.8522 | 0.799074 | ||||||||
\(221\) | 24.4009 | 1.64138 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.02004 | 0.202237 | 0.101119 | − | 0.994874i | \(-0.467758\pi\) | ||||
0.101119 | + | 0.994874i | \(0.467758\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −11.0048 | −0.732028 | ||||||||
\(227\) | 20.1080 | 1.33462 | 0.667309 | − | 0.744781i | \(-0.267446\pi\) | ||||
0.667309 | + | 0.744781i | \(0.267446\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −20.0065 | −1.32206 | −0.661032 | − | 0.750357i | \(-0.729881\pi\) | ||||
−0.661032 | + | 0.750357i | \(0.729881\pi\) | |||||||
\(230\) | −23.3033 | −1.53657 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −8.66930 | −0.569167 | ||||||||
\(233\) | 0.302795 | 0.0198368 | 0.00991839 | − | 0.999951i | \(-0.496843\pi\) | ||||
0.00991839 | + | 0.999951i | \(0.496843\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.63740 | −0.172045 | ||||||||
\(236\) | 31.6379 | 2.05945 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.54680 | −0.229423 | −0.114712 | − | 0.993399i | \(-0.536594\pi\) | ||||
−0.114712 | + | 0.993399i | \(0.536594\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.00647 | 0.386911 | 0.193455 | − | 0.981109i | \(-0.438031\pi\) | ||||
0.193455 | + | 0.981109i | \(0.438031\pi\) | |||||||
\(242\) | −9.29452 | −0.597474 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −54.3899 | −3.48196 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −9.11502 | −0.579975 | ||||||||
\(248\) | −39.4039 | −2.50215 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 24.7420 | 1.56482 | ||||||||
\(251\) | 21.0113 | 1.32622 | 0.663109 | − | 0.748523i | \(-0.269236\pi\) | ||||
0.663109 | + | 0.748523i | \(0.269236\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −21.2789 | −1.33779 | ||||||||
\(254\) | −7.88897 | −0.494998 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −26.1290 | −1.63306 | ||||||||
\(257\) | −20.5690 | −1.28306 | −0.641530 | − | 0.767098i | \(-0.721700\pi\) | ||||
−0.641530 | + | 0.767098i | \(0.721700\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 16.1450 | 1.00127 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 20.0336 | 1.23768 | ||||||||
\(263\) | 14.2030 | 0.875796 | 0.437898 | − | 0.899025i | \(-0.355723\pi\) | ||||
0.437898 | + | 0.899025i | \(0.355723\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.65195 | 0.224337 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −9.60311 | −0.586603 | ||||||||
\(269\) | 31.1325 | 1.89818 | 0.949090 | − | 0.315006i | \(-0.102006\pi\) | ||||
0.949090 | + | 0.315006i | \(0.102006\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.64278 | −0.0997921 | −0.0498960 | − | 0.998754i | \(-0.515889\pi\) | ||||
−0.0498960 | + | 0.998754i | \(0.515889\pi\) | |||||||
\(272\) | −12.7211 | −0.771331 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −33.1952 | −2.00539 | ||||||||
\(275\) | 9.28745 | 0.560055 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −22.0950 | −1.32756 | −0.663779 | − | 0.747929i | \(-0.731049\pi\) | ||||
−0.663779 | + | 0.747929i | \(0.731049\pi\) | |||||||
\(278\) | −13.3765 | −0.802267 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −15.4814 | −0.923543 | −0.461771 | − | 0.886999i | \(-0.652786\pi\) | ||||
−0.461771 | + | 0.886999i | \(0.652786\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −26.2348 | −1.55950 | −0.779749 | − | 0.626092i | \(-0.784654\pi\) | ||||
−0.779749 | + | 0.626092i | \(0.784654\pi\) | |||||||
\(284\) | 36.6653 | 2.17569 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 22.8766 | 1.35272 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 28.3142 | 1.66554 | ||||||||
\(290\) | 6.55596 | 0.384979 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 26.4400 | 1.54729 | ||||||||
\(293\) | 16.9085 | 0.987805 | 0.493903 | − | 0.869517i | \(-0.335570\pi\) | ||||
0.493903 | + | 0.869517i | \(0.335570\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.7246 | −0.624410 | ||||||||
\(296\) | −13.6379 | −0.792687 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −20.7983 | −1.20481 | ||||||||
\(299\) | −28.9860 | −1.67631 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −22.6750 | −1.30480 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.75201 | 0.272546 | ||||||||
\(305\) | 18.4371 | 1.05570 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −14.6835 | −0.838034 | −0.419017 | − | 0.907978i | \(-0.637625\pi\) | ||||
−0.419017 | + | 0.907978i | \(0.637625\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 29.7983 | 1.69243 | ||||||||
\(311\) | −11.8222 | −0.670375 | −0.335187 | − | 0.942152i | \(-0.608800\pi\) | ||||
−0.335187 | + | 0.942152i | \(0.608800\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.355120 | −0.0200726 | −0.0100363 | − | 0.999950i | \(-0.503195\pi\) | ||||
−0.0100363 | + | 0.999950i | \(0.503195\pi\) | |||||||
\(314\) | 5.12061 | 0.288973 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.13734 | −0.0639805 | ||||||||
\(317\) | 10.4497 | 0.586914 | 0.293457 | − | 0.955972i | \(-0.405194\pi\) | ||||
0.293457 | + | 0.955972i | \(0.405194\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.98643 | 0.335175 | ||||||||
\(320\) | 14.0431 | 0.785031 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −16.9272 | −0.941857 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12.6513 | 0.701771 | ||||||||
\(326\) | 49.7441 | 2.75507 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −7.18827 | −0.396906 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.8670 | 0.817166 | 0.408583 | − | 0.912721i | \(-0.366023\pi\) | ||||
0.408583 | + | 0.912721i | \(0.366023\pi\) | |||||||
\(332\) | −27.8885 | −1.53058 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −10.1367 | −0.554658 | ||||||||
\(335\) | 3.25526 | 0.177854 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.41353 | 0.512788 | 0.256394 | − | 0.966572i | \(-0.417466\pi\) | ||||
0.256394 | + | 0.966572i | \(0.417466\pi\) | |||||||
\(338\) | 0.330703 | 0.0179878 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 29.9825 | 1.62603 | ||||||||
\(341\) | 27.2096 | 1.47348 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 19.8052 | 1.06783 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.30838 | −0.231620 | ||||||||
\(347\) | −26.5865 | −1.42724 | −0.713618 | − | 0.700535i | \(-0.752945\pi\) | ||||
−0.713618 | + | 0.700535i | \(0.752945\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.55297 | 0.511359 | 0.255679 | − | 0.966762i | \(-0.417701\pi\) | ||||
0.255679 | + | 0.966762i | \(0.417701\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 8.58247 | 0.457447 | ||||||||
\(353\) | −17.0729 | −0.908697 | −0.454349 | − | 0.890824i | \(-0.650128\pi\) | ||||
−0.454349 | + | 0.890824i | \(0.650128\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −12.4288 | −0.659651 | ||||||||
\(356\) | 26.0719 | 1.38181 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −19.0923 | −1.00906 | ||||||||
\(359\) | −25.6667 | −1.35464 | −0.677318 | − | 0.735690i | \(-0.736858\pi\) | ||||
−0.677318 | + | 0.735690i | \(0.736858\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.6768 | −0.667199 | ||||||||
\(362\) | 60.1142 | 3.15953 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.96263 | −0.469126 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.3752 | −0.541579 | −0.270790 | − | 0.962639i | \(-0.587285\pi\) | ||||
−0.270790 | + | 0.962639i | \(0.587285\pi\) | |||||||
\(368\) | 15.1115 | 0.787743 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 10.3134 | 0.536166 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −19.8152 | −1.02599 | −0.512996 | − | 0.858391i | \(-0.671465\pi\) | ||||
−0.512996 | + | 0.858391i | \(0.671465\pi\) | |||||||
\(374\) | 42.4835 | 2.19677 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 8.27140 | 0.426565 | ||||||||
\(377\) | 8.15470 | 0.419988 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.1716 | 0.727948 | 0.363974 | − | 0.931409i | \(-0.381420\pi\) | ||||
0.363974 | + | 0.931409i | \(0.381420\pi\) | |||||||
\(380\) | −11.2000 | −0.574550 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 16.9603 | 0.867766 | ||||||||
\(383\) | 13.4487 | 0.687197 | 0.343598 | − | 0.939117i | \(-0.388354\pi\) | ||||
0.343598 | + | 0.939117i | \(0.388354\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 26.9316 | 1.37078 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −47.7895 | −2.42614 | ||||||||
\(389\) | −20.9297 | −1.06118 | −0.530590 | − | 0.847629i | \(-0.678029\pi\) | ||||
−0.530590 | + | 0.847629i | \(0.678029\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −53.8292 | −2.72226 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −47.6701 | −2.40158 | ||||||||
\(395\) | 0.385536 | 0.0193984 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −25.1415 | −1.26182 | −0.630909 | − | 0.775857i | \(-0.717318\pi\) | ||||
−0.630909 | + | 0.775857i | \(0.717318\pi\) | |||||||
\(398\) | 24.4876 | 1.22745 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −6.59563 | −0.329782 | ||||||||
\(401\) | −21.1603 | −1.05669 | −0.528347 | − | 0.849029i | \(-0.677188\pi\) | ||||
−0.528347 | + | 0.849029i | \(0.677188\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 37.0649 | 1.84633 | ||||||||
\(404\) | 10.0880 | 0.501897 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.41740 | 0.466803 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.543806 | 0.0268895 | 0.0134447 | − | 0.999910i | \(-0.495720\pi\) | ||||
0.0134447 | + | 0.999910i | \(0.495720\pi\) | |||||||
\(410\) | 5.43597 | 0.268463 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 21.7725 | 1.07265 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.45362 | 0.464060 | ||||||||
\(416\) | 11.6910 | 0.573200 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −15.8698 | −0.776219 | ||||||||
\(419\) | 23.8087 | 1.16313 | 0.581566 | − | 0.813499i | \(-0.302440\pi\) | ||||
0.581566 | + | 0.813499i | \(0.302440\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.90981 | −0.141815 | −0.0709077 | − | 0.997483i | \(-0.522590\pi\) | ||||
−0.0709077 | + | 0.997483i | \(0.522590\pi\) | |||||||
\(422\) | 1.42001 | 0.0691250 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −11.4532 | −0.556217 | ||||||||
\(425\) | 23.4945 | 1.13965 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 42.5424 | 2.05637 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −14.9773 | −0.722268 | ||||||||
\(431\) | 31.3794 | 1.51149 | 0.755747 | − | 0.654863i | \(-0.227274\pi\) | ||||
0.755747 | + | 0.654863i | \(0.227274\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −26.9281 | −1.29408 | −0.647042 | − | 0.762455i | \(-0.723994\pi\) | ||||
−0.647042 | + | 0.762455i | \(0.723994\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −28.9434 | −1.38614 | ||||||||
\(437\) | 20.1080 | 0.961898 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −25.3294 | −1.20891 | −0.604453 | − | 0.796641i | \(-0.706608\pi\) | ||||
−0.604453 | + | 0.796641i | \(0.706608\pi\) | |||||||
\(440\) | 12.6001 | 0.600687 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 57.8709 | 2.75264 | ||||||||
\(443\) | 13.0314 | 0.619140 | 0.309570 | − | 0.950877i | \(-0.399815\pi\) | ||||
0.309570 | + | 0.950877i | \(0.399815\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.83783 | −0.418953 | ||||||||
\(446\) | 7.16256 | 0.339157 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 19.4353 | 0.917206 | 0.458603 | − | 0.888641i | \(-0.348350\pi\) | ||||
0.458603 | + | 0.888641i | \(0.348350\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.96373 | 0.233733 | ||||||||
\(452\) | −16.8196 | −0.791126 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 47.6897 | 2.23819 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −28.6975 | −1.34241 | −0.671206 | − | 0.741271i | \(-0.734223\pi\) | ||||
−0.671206 | + | 0.741271i | \(0.734223\pi\) | |||||||
\(458\) | −47.4488 | −2.21714 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −35.6165 | −1.66063 | ||||||||
\(461\) | 23.0479 | 1.07345 | 0.536725 | − | 0.843757i | \(-0.319661\pi\) | ||||
0.536725 | + | 0.843757i | \(0.319661\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 29.2148 | 1.35773 | 0.678863 | − | 0.734265i | \(-0.262473\pi\) | ||||
0.678863 | + | 0.734265i | \(0.262473\pi\) | |||||||
\(464\) | −4.25135 | −0.197364 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.718132 | 0.0332668 | ||||||||
\(467\) | −4.36508 | −0.201992 | −0.100996 | − | 0.994887i | \(-0.532203\pi\) | ||||
−0.100996 | + | 0.994887i | \(0.532203\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −6.25506 | −0.288524 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 33.6344 | 1.54815 | ||||||||
\(473\) | −13.6762 | −0.628830 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.77643 | −0.402690 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −8.41185 | −0.384749 | ||||||||
\(479\) | 15.9229 | 0.727535 | 0.363767 | − | 0.931490i | \(-0.381490\pi\) | ||||
0.363767 | + | 0.931490i | \(0.381490\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12.8284 | 0.584923 | ||||||||
\(482\) | 14.2454 | 0.648859 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −14.2056 | −0.645710 | ||||||||
\(485\) | 16.1997 | 0.735588 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −38.2657 | −1.73399 | −0.866993 | − | 0.498321i | \(-0.833950\pi\) | ||||
−0.866993 | + | 0.498321i | \(0.833950\pi\) | |||||||
\(488\) | −57.8222 | −2.61749 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13.3908 | −0.604318 | −0.302159 | − | 0.953258i | \(-0.597707\pi\) | ||||
−0.302159 | + | 0.953258i | \(0.597707\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 15.1439 | 0.682045 | ||||||||
\(494\) | −21.6179 | −0.972633 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −19.3233 | −0.867643 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.40706 | 0.242053 | 0.121027 | − | 0.992649i | \(-0.461381\pi\) | ||||
0.121027 | + | 0.992649i | \(0.461381\pi\) | |||||||
\(500\) | 37.8153 | 1.69115 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 49.8318 | 2.22410 | ||||||||
\(503\) | −9.49157 | −0.423208 | −0.211604 | − | 0.977355i | \(-0.567869\pi\) | ||||
−0.211604 | + | 0.977355i | \(0.567869\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.41962 | −0.152171 | ||||||||
\(506\) | −50.4666 | −2.24351 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −12.0574 | −0.534961 | ||||||||
\(509\) | 37.2297 | 1.65018 | 0.825088 | − | 0.565005i | \(-0.191126\pi\) | ||||
0.825088 | + | 0.565005i | \(0.191126\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −20.6597 | −0.913039 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −48.7830 | −2.15173 | ||||||||
\(515\) | −7.38042 | −0.325220 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.71166 | −0.251199 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 17.1639 | 0.752685 | ||||||||
\(521\) | 15.2016 | 0.665996 | 0.332998 | − | 0.942928i | \(-0.391940\pi\) | ||||
0.332998 | + | 0.942928i | \(0.391940\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.79647 | 0.209735 | 0.104867 | − | 0.994486i | \(-0.466558\pi\) | ||||
0.104867 | + | 0.994486i | \(0.466558\pi\) | |||||||
\(524\) | 30.6191 | 1.33760 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 33.6849 | 1.46873 | ||||||||
\(527\) | 68.8321 | 2.99837 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 40.9442 | 1.78018 | ||||||||
\(530\) | 8.66122 | 0.376219 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.76158 | 0.292877 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −14.4210 | −0.623475 | ||||||||
\(536\) | −10.2091 | −0.440967 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 73.8360 | 3.18330 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.45320 | −0.277445 | −0.138722 | − | 0.990331i | \(-0.544300\pi\) | ||||
−0.138722 | + | 0.990331i | \(0.544300\pi\) | |||||||
\(542\) | −3.89615 | −0.167354 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 21.7111 | 0.930854 | ||||||||
\(545\) | 9.81122 | 0.420266 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 26.2561 | 1.12263 | 0.561316 | − | 0.827602i | \(-0.310295\pi\) | ||||
0.561316 | + | 0.827602i | \(0.310295\pi\) | |||||||
\(548\) | −50.7351 | −2.16729 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 22.0268 | 0.939226 | ||||||||
\(551\) | −5.65703 | −0.240998 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −52.4021 | −2.22635 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −20.4444 | −0.867036 | ||||||||
\(557\) | 0.0143322 | 0.000607275 0 | 0.000303638 | − | 1.00000i | \(-0.499903\pi\) | ||||
0.000303638 | 1.00000i | \(0.499903\pi\) | ||||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −18.6296 | −0.787949 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −36.7168 | −1.54881 | ||||||||
\(563\) | 17.1826 | 0.724160 | 0.362080 | − | 0.932147i | \(-0.382067\pi\) | ||||
0.362080 | + | 0.932147i | \(0.382067\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.70149 | 0.239864 | ||||||||
\(566\) | −62.2205 | −2.61532 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 38.9791 | 1.63553 | ||||||||
\(569\) | 29.4779 | 1.23578 | 0.617889 | − | 0.786265i | \(-0.287988\pi\) | ||||
0.617889 | + | 0.786265i | \(0.287988\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −32.8321 | −1.37398 | −0.686991 | − | 0.726666i | \(-0.741069\pi\) | ||||
−0.686991 | + | 0.726666i | \(0.741069\pi\) | |||||||
\(572\) | 34.9643 | 1.46193 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −27.9093 | −1.16390 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 31.9573 | 1.33040 | 0.665201 | − | 0.746665i | \(-0.268346\pi\) | ||||
0.665201 | + | 0.746665i | \(0.268346\pi\) | |||||||
\(578\) | 67.1520 | 2.79315 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 10.0200 | 0.416060 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.90880 | 0.327549 | ||||||||
\(584\) | 28.1085 | 1.16314 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 40.1014 | 1.65658 | ||||||||
\(587\) | 4.74633 | 0.195902 | 0.0979509 | − | 0.995191i | \(-0.468771\pi\) | ||||
0.0979509 | + | 0.995191i | \(0.468771\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −25.7124 | −1.05946 | ||||||||
\(590\) | −25.4353 | −1.04715 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −6.68792 | −0.274872 | ||||||||
\(593\) | 1.94079 | 0.0796988 | 0.0398494 | − | 0.999206i | \(-0.487312\pi\) | ||||
0.0398494 | + | 0.999206i | \(0.487312\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −31.7878 | −1.30208 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −68.7454 | −2.81121 | ||||||||
\(599\) | 8.80134 | 0.359613 | 0.179807 | − | 0.983702i | \(-0.442453\pi\) | ||||
0.179807 | + | 0.983702i | \(0.442453\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14.9603 | −0.610244 | −0.305122 | − | 0.952313i | \(-0.598697\pi\) | ||||
−0.305122 | + | 0.952313i | \(0.598697\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −34.6561 | −1.41014 | ||||||||
\(605\) | 4.81542 | 0.195775 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.79138 | 0.113299 | 0.0566494 | − | 0.998394i | \(-0.481958\pi\) | ||||
0.0566494 | + | 0.998394i | \(0.481958\pi\) | |||||||
\(608\) | −8.11023 | −0.328913 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 43.7267 | 1.77044 | ||||||||
\(611\) | −7.78042 | −0.314762 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 26.6436 | 1.07612 | 0.538062 | − | 0.842905i | \(-0.319157\pi\) | ||||
0.538062 | + | 0.842905i | \(0.319157\pi\) | |||||||
\(614\) | −34.8246 | −1.40541 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 38.1120 | 1.53433 | 0.767166 | − | 0.641448i | \(-0.221666\pi\) | ||||
0.767166 | + | 0.641448i | \(0.221666\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −23.9315 | −0.961890 | −0.480945 | − | 0.876751i | \(-0.659706\pi\) | ||||
−0.480945 | + | 0.876751i | \(0.659706\pi\) | |||||||
\(620\) | 45.5433 | 1.82906 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −28.0384 | −1.12424 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.63231 | 0.185293 | ||||||||
\(626\) | −0.842228 | −0.0336622 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 7.82627 | 0.312302 | ||||||||
\(629\) | 23.8232 | 0.949893 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.6748 | −0.663812 | −0.331906 | − | 0.943313i | \(-0.607692\pi\) | ||||
−0.331906 | + | 0.943313i | \(0.607692\pi\) | |||||||
\(632\) | −1.20912 | −0.0480960 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 24.7833 | 0.984271 | ||||||||
\(635\) | 4.08721 | 0.162196 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 14.1978 | 0.562098 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 25.3795 | 1.00321 | ||||||||
\(641\) | −32.0213 | −1.26477 | −0.632383 | − | 0.774656i | \(-0.717923\pi\) | ||||
−0.632383 | + | 0.774656i | \(0.717923\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.51939 | −0.138791 | −0.0693956 | − | 0.997589i | \(-0.522107\pi\) | ||||
−0.0693956 | + | 0.997589i | \(0.522107\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −40.1459 | −1.57952 | ||||||||
\(647\) | −41.5546 | −1.63368 | −0.816839 | − | 0.576865i | \(-0.804276\pi\) | ||||
−0.816839 | + | 0.576865i | \(0.804276\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −23.2256 | −0.911686 | ||||||||
\(650\) | 30.0049 | 1.17689 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 76.0283 | 2.97750 | ||||||||
\(653\) | −10.2858 | −0.402513 | −0.201257 | − | 0.979539i | \(-0.564503\pi\) | ||||
−0.201257 | + | 0.979539i | \(0.564503\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.3792 | −0.405550 | ||||||||
\(656\) | −3.52507 | −0.137631 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −20.3551 | −0.792923 | −0.396461 | − | 0.918051i | \(-0.629762\pi\) | ||||
−0.396461 | + | 0.918051i | \(0.629762\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.6527 | −0.647716 | −0.323858 | − | 0.946106i | \(-0.604980\pi\) | ||||
−0.323858 | + | 0.946106i | \(0.604980\pi\) | |||||||
\(662\) | 35.2597 | 1.37041 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −29.6484 | −1.15058 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −17.9895 | −0.696557 | ||||||||
\(668\) | −15.4929 | −0.599437 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 7.72041 | 0.298265 | ||||||||
\(671\) | 39.9280 | 1.54141 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.2188 | 0.393905 | 0.196953 | − | 0.980413i | \(-0.436895\pi\) | ||||
0.196953 | + | 0.980413i | \(0.436895\pi\) | |||||||
\(674\) | 22.3258 | 0.859958 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.505442 | 0.0194401 | ||||||||
\(677\) | −6.38685 | −0.245466 | −0.122733 | − | 0.992440i | \(-0.539166\pi\) | ||||
−0.122733 | + | 0.992440i | \(0.539166\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 31.8745 | 1.22233 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 64.5323 | 2.47107 | ||||||||
\(683\) | 30.8122 | 1.17900 | 0.589499 | − | 0.807769i | \(-0.299325\pi\) | ||||
0.589499 | + | 0.807769i | \(0.299325\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 17.1981 | 0.657107 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 9.71234 | 0.370279 | ||||||||
\(689\) | 10.7734 | 0.410432 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.86804 | −0.185189 | −0.0925945 | − | 0.995704i | \(-0.529516\pi\) | ||||
−0.0925945 | + | 0.995704i | \(0.529516\pi\) | |||||||
\(692\) | −6.58487 | −0.250319 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −63.0544 | −2.39351 | ||||||||
\(695\) | 6.93024 | 0.262879 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 12.5567 | 0.475621 | ||||||||
\(698\) | 22.6565 | 0.857562 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −44.4038 | −1.67711 | −0.838554 | − | 0.544819i | \(-0.816598\pi\) | ||||
−0.838554 | + | 0.544819i | \(0.816598\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.89923 | −0.335641 | ||||||||
\(704\) | 30.4122 | 1.14620 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −40.4913 | −1.52391 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −26.5768 | −0.998112 | −0.499056 | − | 0.866570i | \(-0.666320\pi\) | ||||
−0.499056 | + | 0.866570i | \(0.666320\pi\) | |||||||
\(710\) | −29.4770 | −1.10625 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 27.7171 | 1.03874 | ||||||||
\(713\) | −81.7664 | −3.06217 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −11.8522 | −0.443247 | ||||||||
\(716\) | −29.1804 | −1.09052 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −60.8730 | −2.27176 | ||||||||
\(719\) | 33.8924 | 1.26397 | 0.631987 | − | 0.774979i | \(-0.282239\pi\) | ||||
0.631987 | + | 0.774979i | \(0.282239\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −30.0652 | −1.11891 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 91.8778 | 3.41461 | ||||||||
\(725\) | 7.85177 | 0.291608 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −23.9417 | −0.887949 | −0.443974 | − | 0.896039i | \(-0.646432\pi\) | ||||
−0.443974 | + | 0.896039i | \(0.646432\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −21.2564 | −0.786736 | ||||||||
\(731\) | −34.5965 | −1.27960 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −37.5703 | −1.38769 | −0.693846 | − | 0.720124i | \(-0.744085\pi\) | ||||
−0.693846 | + | 0.720124i | \(0.744085\pi\) | |||||||
\(734\) | −24.6065 | −0.908243 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −25.7908 | −0.950661 | ||||||||
\(737\) | 7.04972 | 0.259680 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.64110 | −0.207511 | −0.103756 | − | 0.994603i | \(-0.533086\pi\) | ||||
−0.103756 | + | 0.994603i | \(0.533086\pi\) | |||||||
\(740\) | 15.7628 | 0.579452 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −15.1703 | −0.556545 | −0.278273 | − | 0.960502i | \(-0.589762\pi\) | ||||
−0.278273 | + | 0.960502i | \(0.589762\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10.7754 | 0.394781 | ||||||||
\(746\) | −46.9952 | −1.72062 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 64.9312 | 2.37412 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 25.8935 | 0.944869 | 0.472434 | − | 0.881366i | \(-0.343375\pi\) | ||||
0.472434 | + | 0.881366i | \(0.343375\pi\) | |||||||
\(752\) | 4.05623 | 0.147915 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 19.3403 | 0.704331 | ||||||||
\(755\) | 11.7477 | 0.427543 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 36.9054 | 1.34135 | 0.670675 | − | 0.741752i | \(-0.266005\pi\) | ||||
0.670675 | + | 0.741752i | \(0.266005\pi\) | |||||||
\(758\) | 33.6105 | 1.22079 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −11.9068 | −0.431906 | ||||||||
\(761\) | −28.4009 | −1.02953 | −0.514765 | − | 0.857331i | \(-0.672121\pi\) | ||||
−0.514765 | + | 0.857331i | \(0.672121\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 25.9219 | 0.937823 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 31.8959 | 1.15245 | ||||||||
\(767\) | −31.6379 | −1.14238 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.26152 | −0.189735 | −0.0948677 | − | 0.995490i | \(-0.530243\pi\) | ||||
−0.0948677 | + | 0.995490i | \(0.530243\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 41.1620 | 1.48145 | ||||||||
\(773\) | 41.3747 | 1.48814 | 0.744071 | − | 0.668100i | \(-0.232892\pi\) | ||||
0.744071 | + | 0.668100i | \(0.232892\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 35.6880 | 1.28195 | ||||||||
\(776\) | −50.8052 | −1.82380 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −49.6385 | −1.77963 | ||||||||
\(779\) | −4.69061 | −0.168059 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −26.9163 | −0.963140 | ||||||||
\(782\) | −127.665 | −4.56530 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.65295 | −0.0946877 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.36129 | 0.191109 | 0.0955547 | − | 0.995424i | \(-0.469538\pi\) | ||||
0.0955547 | + | 0.995424i | \(0.469538\pi\) | |||||||
\(788\) | −72.8584 | −2.59547 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0.914366 | 0.0325317 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 54.3899 | 1.93144 | ||||||||
\(794\) | −59.6275 | −2.11610 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 37.4265 | 1.32655 | ||||||||
\(797\) | −30.4204 | −1.07755 | −0.538773 | − | 0.842451i | \(-0.681112\pi\) | ||||
−0.538773 | + | 0.842451i | \(0.681112\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −14.4488 | −0.511161 | ||||||||
\(800\) | 11.2567 | 0.397986 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −50.1853 | −1.77210 | ||||||||
\(803\) | −19.4098 | −0.684958 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 87.9058 | 3.09635 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 10.7246 | 0.377290 | ||||||||
\(809\) | −43.5458 | −1.53099 | −0.765494 | − | 0.643443i | \(-0.777505\pi\) | ||||
−0.765494 | + | 0.643443i | \(0.777505\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17.4078 | 0.611272 | 0.305636 | − | 0.952148i | \(-0.401131\pi\) | ||||
0.305636 | + | 0.952148i | \(0.401131\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 22.3350 | 0.782842 | ||||||||
\(815\) | −25.7720 | −0.902755 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12.9236 | 0.452141 | ||||||||
\(818\) | 1.28973 | 0.0450944 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 8.30826 | 0.290137 | ||||||||
\(821\) | −23.0636 | −0.804925 | −0.402462 | − | 0.915437i | \(-0.631846\pi\) | ||||
−0.402462 | + | 0.915437i | \(0.631846\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10.0780 | 0.351298 | 0.175649 | − | 0.984453i | \(-0.443798\pi\) | ||||
0.175649 | + | 0.984453i | \(0.443798\pi\) | |||||||
\(824\) | 23.1464 | 0.806344 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 28.4954 | 0.990882 | 0.495441 | − | 0.868642i | \(-0.335007\pi\) | ||||
0.495441 | + | 0.868642i | \(0.335007\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.81520 | −0.0630447 | −0.0315223 | − | 0.999503i | \(-0.510036\pi\) | ||||
−0.0315223 | + | 0.999503i | \(0.510036\pi\) | |||||||
\(830\) | 22.4209 | 0.778241 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 41.4275 | 1.43624 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.25177 | 0.181745 | ||||||||
\(836\) | −24.2553 | −0.838886 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 56.4666 | 1.95060 | ||||||||
\(839\) | −6.87720 | −0.237427 | −0.118714 | − | 0.992929i | \(-0.537877\pi\) | ||||
−0.118714 | + | 0.992929i | \(0.537877\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.9390 | −0.825482 | ||||||||
\(842\) | −6.90112 | −0.237828 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 2.17032 | 0.0747057 | ||||||||
\(845\) | −0.171334 | −0.00589408 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −5.61656 | −0.192873 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 55.7212 | 1.91122 | ||||||||
\(851\) | −28.2998 | −0.970105 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.69270 | −0.0921965 | −0.0460982 | − | 0.998937i | \(-0.514679\pi\) | ||||
−0.0460982 | + | 0.998937i | \(0.514679\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 45.2271 | 1.54583 | ||||||||
\(857\) | 23.6722 | 0.808625 | 0.404313 | − | 0.914621i | \(-0.367511\pi\) | ||||
0.404313 | + | 0.914621i | \(0.367511\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −13.0275 | −0.444492 | −0.222246 | − | 0.974991i | \(-0.571339\pi\) | ||||
−0.222246 | + | 0.974991i | \(0.571339\pi\) | |||||||
\(860\) | −22.8911 | −0.780579 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 74.4218 | 2.53482 | ||||||||
\(863\) | −19.7559 | −0.672499 | −0.336250 | − | 0.941773i | \(-0.609159\pi\) | ||||
−0.336250 | + | 0.941773i | \(0.609159\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.23214 | 0.0758950 | ||||||||
\(866\) | −63.8647 | −2.17021 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.834932 | 0.0283231 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.60311 | 0.325389 | ||||||||
\(872\) | −30.7699 | −1.04200 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 47.6897 | 1.61313 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 12.6814 | 0.428222 | 0.214111 | − | 0.976809i | \(-0.431315\pi\) | ||||
0.214111 | + | 0.976809i | \(0.431315\pi\) | |||||||
\(878\) | −60.0731 | −2.02737 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 6.17900 | 0.208294 | ||||||||
\(881\) | 43.7202 | 1.47297 | 0.736485 | − | 0.676454i | \(-0.236484\pi\) | ||||
0.736485 | + | 0.676454i | \(0.236484\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.03795 | −0.0349298 | −0.0174649 | − | 0.999847i | \(-0.505560\pi\) | ||||
−0.0174649 | + | 0.999847i | \(0.505560\pi\) | |||||||
\(884\) | 88.4492 | 2.97487 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 30.9062 | 1.03831 | ||||||||
\(887\) | 6.38256 | 0.214305 | 0.107153 | − | 0.994243i | \(-0.465827\pi\) | ||||
0.107153 | + | 0.994243i | \(0.465827\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −20.9604 | −0.702596 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 10.9472 | 0.366538 | ||||||||
\(893\) | 5.39739 | 0.180617 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.89156 | 0.330638 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 46.0941 | 1.53818 | ||||||||
\(899\) | 23.0035 | 0.767209 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 20.0069 | 0.666526 | ||||||||
\(902\) | 11.7723 | 0.391976 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −17.8810 | −0.594712 | ||||||||
\(905\) | −31.1447 | −1.03528 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −45.4262 | −1.50835 | −0.754176 | − | 0.656672i | \(-0.771964\pi\) | ||||
−0.754176 | + | 0.656672i | \(0.771964\pi\) | |||||||
\(908\) | 72.8884 | 2.41889 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.48708 | −0.148664 | −0.0743318 | − | 0.997234i | \(-0.523682\pi\) | ||||
−0.0743318 | + | 0.997234i | \(0.523682\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 20.4731 | 0.677562 | ||||||||
\(914\) | −68.0611 | −2.25126 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −72.5202 | −2.39613 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −34.6378 | −1.14260 | −0.571298 | − | 0.820743i | \(-0.693560\pi\) | ||||
−0.571298 | + | 0.820743i | \(0.693560\pi\) | |||||||
\(920\) | −37.8640 | −1.24834 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 54.6622 | 1.80020 | ||||||||
\(923\) | −36.6653 | −1.20685 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 12.3518 | 0.406126 | ||||||||
\(926\) | 69.2879 | 2.27694 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 7.25577 | 0.238182 | ||||||||
\(929\) | −15.2728 | −0.501084 | −0.250542 | − | 0.968106i | \(-0.580609\pi\) | ||||
−0.250542 | + | 0.968106i | \(0.580609\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 1.09758 | 0.0359526 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −10.3525 | −0.338746 | ||||||||
\(935\) | −22.0104 | −0.719816 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 16.6920 | 0.545305 | 0.272652 | − | 0.962113i | \(-0.412099\pi\) | ||||
0.272652 | + | 0.962113i | \(0.412099\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −9.56015 | −0.311818 | ||||||||
\(941\) | −21.2479 | −0.692661 | −0.346330 | − | 0.938113i | \(-0.612572\pi\) | ||||
−0.346330 | + | 0.938113i | \(0.612572\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −14.9163 | −0.485741 | ||||||||
\(944\) | 16.4940 | 0.536836 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −32.4354 | −1.05456 | ||||||||
\(947\) | −39.3146 | −1.27755 | −0.638777 | − | 0.769392i | \(-0.720559\pi\) | ||||
−0.638777 | + | 0.769392i | \(0.720559\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −26.4400 | −0.858280 | ||||||||
\(950\) | −20.8148 | −0.675322 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 15.1311 | 0.490143 | 0.245072 | − | 0.969505i | \(-0.421189\pi\) | ||||
0.245072 | + | 0.969505i | \(0.421189\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.78701 | −0.284341 | ||||||||
\(956\) | −12.8566 | −0.415811 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 37.7639 | 1.22009 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 73.5558 | 2.37277 | ||||||||
\(962\) | 30.4247 | 0.980932 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 21.7725 | 0.701244 | ||||||||
\(965\) | −13.9531 | −0.449165 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 31.3881 | 1.00937 | 0.504687 | − | 0.863303i | \(-0.331608\pi\) | ||||
0.504687 | + | 0.863303i | \(0.331608\pi\) | |||||||
\(968\) | −15.1021 | −0.485399 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 38.4203 | 1.23360 | ||||||||
\(971\) | −34.9521 | −1.12167 | −0.560833 | − | 0.827929i | \(-0.689519\pi\) | ||||
−0.560833 | + | 0.827929i | \(0.689519\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −90.7538 | −2.90794 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −28.3555 | −0.907639 | ||||||||
\(977\) | 7.68632 | 0.245907 | 0.122954 | − | 0.992412i | \(-0.460763\pi\) | ||||
0.122954 | + | 0.992412i | \(0.460763\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −19.1396 | −0.611703 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −31.7586 | −1.01346 | ||||||||
\(983\) | −2.18071 | −0.0695538 | −0.0347769 | − | 0.999395i | \(-0.511072\pi\) | ||||
−0.0347769 | + | 0.999395i | \(0.511072\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 24.6975 | 0.786928 | ||||||||
\(986\) | 35.9163 | 1.14381 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −33.0405 | −1.05116 | ||||||||
\(989\) | 41.0976 | 1.30683 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.70317 | −0.181167 | −0.0905837 | − | 0.995889i | \(-0.528873\pi\) | ||||
−0.0905837 | + | 0.995889i | \(0.528873\pi\) | |||||||
\(992\) | 32.9791 | 1.04709 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −12.6868 | −0.402199 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 31.3797 | 0.993804 | 0.496902 | − | 0.867807i | \(-0.334471\pi\) | ||||
0.496902 | + | 0.867807i | \(0.334471\pi\) | |||||||
\(998\) | 12.8238 | 0.405930 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 3969.2.a.s.1.4 | 4 | ||
3.2 | odd | 2 | 3969.2.a.x.1.1 | 4 | |||
7.2 | even | 3 | 567.2.e.d.487.1 | yes | 8 | ||
7.4 | even | 3 | 567.2.e.d.163.1 | yes | 8 | ||
7.6 | odd | 2 | 3969.2.a.t.1.4 | 4 | |||
21.2 | odd | 6 | 567.2.e.c.487.4 | yes | 8 | ||
21.11 | odd | 6 | 567.2.e.c.163.4 | ✓ | 8 | ||
21.20 | even | 2 | 3969.2.a.w.1.1 | 4 | |||
63.2 | odd | 6 | 567.2.g.j.109.4 | 8 | |||
63.4 | even | 3 | 567.2.g.k.541.1 | 8 | |||
63.11 | odd | 6 | 567.2.h.k.352.1 | 8 | |||
63.16 | even | 3 | 567.2.g.k.109.1 | 8 | |||
63.23 | odd | 6 | 567.2.h.k.298.1 | 8 | |||
63.25 | even | 3 | 567.2.h.j.352.4 | 8 | |||
63.32 | odd | 6 | 567.2.g.j.541.4 | 8 | |||
63.58 | even | 3 | 567.2.h.j.298.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
567.2.e.c.163.4 | ✓ | 8 | 21.11 | odd | 6 | ||
567.2.e.c.487.4 | yes | 8 | 21.2 | odd | 6 | ||
567.2.e.d.163.1 | yes | 8 | 7.4 | even | 3 | ||
567.2.e.d.487.1 | yes | 8 | 7.2 | even | 3 | ||
567.2.g.j.109.4 | 8 | 63.2 | odd | 6 | |||
567.2.g.j.541.4 | 8 | 63.32 | odd | 6 | |||
567.2.g.k.109.1 | 8 | 63.16 | even | 3 | |||
567.2.g.k.541.1 | 8 | 63.4 | even | 3 | |||
567.2.h.j.298.4 | 8 | 63.58 | even | 3 | |||
567.2.h.j.352.4 | 8 | 63.25 | even | 3 | |||
567.2.h.k.298.1 | 8 | 63.23 | odd | 6 | |||
567.2.h.k.352.1 | 8 | 63.11 | odd | 6 | |||
3969.2.a.s.1.4 | 4 | 1.1 | even | 1 | trivial | ||
3969.2.a.t.1.4 | 4 | 7.6 | odd | 2 | |||
3969.2.a.w.1.1 | 4 | 21.20 | even | 2 | |||
3969.2.a.x.1.1 | 4 | 3.2 | odd | 2 |