Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8046,2,Mod(1,8046)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8046, 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("8046.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8046 = 2 \cdot 3^{3} \cdot 149 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8046.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: | \(64.2476334663\) |
Analytic rank: | \(1\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 3x^{8} - 9x^{7} + 25x^{6} + 29x^{5} - 58x^{4} - 43x^{3} + 34x^{2} + 25x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.58022\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8046.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.72526 | −1.21877 | −0.609386 | − | 0.792874i | \(-0.708584\pi\) | ||||
−0.609386 | + | 0.792874i | \(0.708584\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.79628 | −1.05690 | −0.528448 | − | 0.848966i | \(-0.677226\pi\) | ||||
−0.528448 | + | 0.848966i | \(0.677226\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.72526 | −0.861802 | ||||||||
\(11\) | 3.26105 | 0.983243 | 0.491622 | − | 0.870809i | \(-0.336404\pi\) | ||||
0.491622 | + | 0.870809i | \(0.336404\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.91542 | −0.808591 | −0.404296 | − | 0.914628i | \(-0.632483\pi\) | ||||
−0.404296 | + | 0.914628i | \(0.632483\pi\) | |||||||
\(14\) | −2.79628 | −0.747338 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.639779 | 0.155169 | 0.0775846 | − | 0.996986i | \(-0.475279\pi\) | ||||
0.0775846 | + | 0.996986i | \(0.475279\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.70570 | 1.30898 | 0.654489 | − | 0.756072i | \(-0.272884\pi\) | ||||
0.654489 | + | 0.756072i | \(0.272884\pi\) | |||||||
\(20\) | −2.72526 | −0.609386 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.26105 | 0.695258 | ||||||||
\(23\) | −1.32811 | −0.276930 | −0.138465 | − | 0.990367i | \(-0.544217\pi\) | ||||
−0.138465 | + | 0.990367i | \(0.544217\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.42702 | 0.485404 | ||||||||
\(26\) | −2.91542 | −0.571761 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.79628 | −0.528448 | ||||||||
\(29\) | −3.22092 | −0.598110 | −0.299055 | − | 0.954236i | \(-0.596671\pi\) | ||||
−0.299055 | + | 0.954236i | \(0.596671\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.53396 | −0.814323 | −0.407162 | − | 0.913356i | \(-0.633481\pi\) | ||||
−0.407162 | + | 0.913356i | \(0.633481\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.639779 | 0.109721 | ||||||||
\(35\) | 7.62059 | 1.28811 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.32382 | 0.546433 | 0.273217 | − | 0.961953i | \(-0.411912\pi\) | ||||
0.273217 | + | 0.961953i | \(0.411912\pi\) | |||||||
\(38\) | 5.70570 | 0.925587 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.72526 | −0.430901 | ||||||||
\(41\) | 8.09895 | 1.26484 | 0.632422 | − | 0.774624i | \(-0.282061\pi\) | ||||
0.632422 | + | 0.774624i | \(0.282061\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.8813 | 1.81188 | 0.905940 | − | 0.423406i | \(-0.139166\pi\) | ||||
0.905940 | + | 0.423406i | \(0.139166\pi\) | |||||||
\(44\) | 3.26105 | 0.491622 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.32811 | −0.195819 | ||||||||
\(47\) | 5.42908 | 0.791913 | 0.395957 | − | 0.918269i | \(-0.370413\pi\) | ||||
0.395957 | + | 0.918269i | \(0.370413\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.819203 | 0.117029 | ||||||||
\(50\) | 2.42702 | 0.343232 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.91542 | −0.404296 | ||||||||
\(53\) | −8.89160 | −1.22135 | −0.610677 | − | 0.791879i | \(-0.709103\pi\) | ||||
−0.610677 | + | 0.791879i | \(0.709103\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.88719 | −1.19835 | ||||||||
\(56\) | −2.79628 | −0.373669 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.22092 | −0.422927 | ||||||||
\(59\) | 0.723299 | 0.0941655 | 0.0470827 | − | 0.998891i | \(-0.485008\pi\) | ||||
0.0470827 | + | 0.998891i | \(0.485008\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.58006 | 0.458380 | 0.229190 | − | 0.973382i | \(-0.426392\pi\) | ||||
0.229190 | + | 0.973382i | \(0.426392\pi\) | |||||||
\(62\) | −4.53396 | −0.575813 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 7.94526 | 0.985488 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.3440 | 1.38588 | 0.692942 | − | 0.720993i | \(-0.256314\pi\) | ||||
0.692942 | + | 0.720993i | \(0.256314\pi\) | |||||||
\(68\) | 0.639779 | 0.0775846 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 7.62059 | 0.910835 | ||||||||
\(71\) | −16.6286 | −1.97345 | −0.986727 | − | 0.162387i | \(-0.948081\pi\) | ||||
−0.986727 | + | 0.162387i | \(0.948081\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −14.5294 | −1.70054 | −0.850270 | − | 0.526346i | \(-0.823562\pi\) | ||||
−0.850270 | + | 0.526346i | \(0.823562\pi\) | |||||||
\(74\) | 3.32382 | 0.386387 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.70570 | 0.654489 | ||||||||
\(77\) | −9.11882 | −1.03919 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −14.8665 | −1.67261 | −0.836304 | − | 0.548266i | \(-0.815288\pi\) | ||||
−0.836304 | + | 0.548266i | \(0.815288\pi\) | |||||||
\(80\) | −2.72526 | −0.304693 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 8.09895 | 0.894379 | ||||||||
\(83\) | 5.26159 | 0.577534 | 0.288767 | − | 0.957399i | \(-0.406755\pi\) | ||||
0.288767 | + | 0.957399i | \(0.406755\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.74356 | −0.189116 | ||||||||
\(86\) | 11.8813 | 1.28119 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.26105 | 0.347629 | ||||||||
\(89\) | −16.2962 | −1.72739 | −0.863697 | − | 0.504011i | \(-0.831857\pi\) | ||||
−0.863697 | + | 0.504011i | \(0.831857\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.15234 | 0.854597 | ||||||||
\(92\) | −1.32811 | −0.138465 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 5.42908 | 0.559967 | ||||||||
\(95\) | −15.5495 | −1.59534 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −16.0563 | −1.63027 | −0.815137 | − | 0.579268i | \(-0.803338\pi\) | ||||
−0.815137 | + | 0.579268i | \(0.803338\pi\) | |||||||
\(98\) | 0.819203 | 0.0827520 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.42702 | 0.242702 | ||||||||
\(101\) | 10.8277 | 1.07739 | 0.538697 | − | 0.842500i | \(-0.318917\pi\) | ||||
0.538697 | + | 0.842500i | \(0.318917\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.1784 | 1.00291 | 0.501454 | − | 0.865184i | \(-0.332799\pi\) | ||||
0.501454 | + | 0.865184i | \(0.332799\pi\) | |||||||
\(104\) | −2.91542 | −0.285880 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.89160 | −0.863628 | ||||||||
\(107\) | −4.43299 | −0.428553 | −0.214277 | − | 0.976773i | \(-0.568739\pi\) | ||||
−0.214277 | + | 0.976773i | \(0.568739\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −19.8234 | −1.89874 | −0.949368 | − | 0.314166i | \(-0.898275\pi\) | ||||
−0.949368 | + | 0.314166i | \(0.898275\pi\) | |||||||
\(110\) | −8.88719 | −0.847360 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.79628 | −0.264224 | ||||||||
\(113\) | −11.3336 | −1.06618 | −0.533088 | − | 0.846060i | \(-0.678969\pi\) | ||||
−0.533088 | + | 0.846060i | \(0.678969\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.61944 | 0.337514 | ||||||||
\(116\) | −3.22092 | −0.299055 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.723299 | 0.0665851 | ||||||||
\(119\) | −1.78900 | −0.163998 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.365561 | −0.0332328 | ||||||||
\(122\) | 3.58006 | 0.324124 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −4.53396 | −0.407162 | ||||||||
\(125\) | 7.01203 | 0.627175 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.89207 | −0.345365 | −0.172683 | − | 0.984978i | \(-0.555243\pi\) | ||||
−0.172683 | + | 0.984978i | \(0.555243\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 7.94526 | 0.696845 | ||||||||
\(131\) | 1.37955 | 0.120532 | 0.0602660 | − | 0.998182i | \(-0.480805\pi\) | ||||
0.0602660 | + | 0.998182i | \(0.480805\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −15.9548 | −1.38345 | ||||||||
\(134\) | 11.3440 | 0.979968 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.639779 | 0.0548606 | ||||||||
\(137\) | 15.5769 | 1.33082 | 0.665411 | − | 0.746478i | \(-0.268256\pi\) | ||||
0.665411 | + | 0.746478i | \(0.268256\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.71888 | −0.315432 | −0.157716 | − | 0.987485i | \(-0.550413\pi\) | ||||
−0.157716 | + | 0.987485i | \(0.550413\pi\) | |||||||
\(140\) | 7.62059 | 0.644057 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −16.6286 | −1.39544 | ||||||||
\(143\) | −9.50732 | −0.795042 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.77783 | 0.728959 | ||||||||
\(146\) | −14.5294 | −1.20246 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.32382 | 0.273217 | ||||||||
\(149\) | −1.00000 | −0.0819232 | ||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.55019 | −0.288910 | −0.144455 | − | 0.989511i | \(-0.546143\pi\) | ||||
−0.144455 | + | 0.989511i | \(0.546143\pi\) | |||||||
\(152\) | 5.70570 | 0.462794 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −9.11882 | −0.734815 | ||||||||
\(155\) | 12.3562 | 0.992474 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −22.1681 | −1.76921 | −0.884603 | − | 0.466345i | \(-0.845571\pi\) | ||||
−0.884603 | + | 0.466345i | \(0.845571\pi\) | |||||||
\(158\) | −14.8665 | −1.18271 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.72526 | −0.215450 | ||||||||
\(161\) | 3.71377 | 0.292686 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −16.1548 | −1.26534 | −0.632670 | − | 0.774422i | \(-0.718041\pi\) | ||||
−0.632670 | + | 0.774422i | \(0.718041\pi\) | |||||||
\(164\) | 8.09895 | 0.632422 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.26159 | 0.408379 | ||||||||
\(167\) | −16.0147 | −1.23926 | −0.619628 | − | 0.784896i | \(-0.712716\pi\) | ||||
−0.619628 | + | 0.784896i | \(0.712716\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.50034 | −0.346180 | ||||||||
\(170\) | −1.74356 | −0.133725 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 11.8813 | 0.905940 | ||||||||
\(173\) | 25.3904 | 1.93039 | 0.965197 | − | 0.261523i | \(-0.0842246\pi\) | ||||
0.965197 | + | 0.261523i | \(0.0842246\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.78663 | −0.513021 | ||||||||
\(176\) | 3.26105 | 0.245811 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −16.2962 | −1.22145 | ||||||||
\(179\) | 7.95101 | 0.594286 | 0.297143 | − | 0.954833i | \(-0.403966\pi\) | ||||
0.297143 | + | 0.954833i | \(0.403966\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.41497 | 0.402492 | 0.201246 | − | 0.979541i | \(-0.435501\pi\) | ||||
0.201246 | + | 0.979541i | \(0.435501\pi\) | |||||||
\(182\) | 8.15234 | 0.604291 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.32811 | −0.0979095 | ||||||||
\(185\) | −9.05827 | −0.665977 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.08635 | 0.152569 | ||||||||
\(188\) | 5.42908 | 0.395957 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −15.5495 | −1.12808 | ||||||||
\(191\) | 8.24768 | 0.596781 | 0.298391 | − | 0.954444i | \(-0.403550\pi\) | ||||
0.298391 | + | 0.954444i | \(0.403550\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.95012 | 0.284336 | 0.142168 | − | 0.989843i | \(-0.454593\pi\) | ||||
0.142168 | + | 0.989843i | \(0.454593\pi\) | |||||||
\(194\) | −16.0563 | −1.15278 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.819203 | 0.0585145 | ||||||||
\(197\) | 18.1572 | 1.29364 | 0.646822 | − | 0.762641i | \(-0.276097\pi\) | ||||
0.646822 | + | 0.762641i | \(0.276097\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.03230 | −0.569395 | −0.284697 | − | 0.958617i | \(-0.591893\pi\) | ||||
−0.284697 | + | 0.958617i | \(0.591893\pi\) | |||||||
\(200\) | 2.42702 | 0.171616 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 10.8277 | 0.761833 | ||||||||
\(203\) | 9.00661 | 0.632140 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −22.0717 | −1.54155 | ||||||||
\(206\) | 10.1784 | 0.709163 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.91542 | −0.202148 | ||||||||
\(209\) | 18.6066 | 1.28704 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −26.9038 | −1.85213 | −0.926065 | − | 0.377363i | \(-0.876831\pi\) | ||||
−0.926065 | + | 0.377363i | \(0.876831\pi\) | |||||||
\(212\) | −8.89160 | −0.610677 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −4.43299 | −0.303033 | ||||||||
\(215\) | −32.3796 | −2.20827 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 12.6782 | 0.860655 | ||||||||
\(218\) | −19.8234 | −1.34261 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −8.88719 | −0.599174 | ||||||||
\(221\) | −1.86522 | −0.125469 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 23.1746 | 1.55189 | 0.775945 | − | 0.630801i | \(-0.217274\pi\) | ||||
0.775945 | + | 0.630801i | \(0.217274\pi\) | |||||||
\(224\) | −2.79628 | −0.186835 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −11.3336 | −0.753901 | ||||||||
\(227\) | 11.7427 | 0.779388 | 0.389694 | − | 0.920944i | \(-0.372581\pi\) | ||||
0.389694 | + | 0.920944i | \(0.372581\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −13.1092 | −0.866279 | −0.433140 | − | 0.901327i | \(-0.642594\pi\) | ||||
−0.433140 | + | 0.901327i | \(0.642594\pi\) | |||||||
\(230\) | 3.61944 | 0.238659 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.22092 | −0.211464 | ||||||||
\(233\) | −4.00233 | −0.262201 | −0.131101 | − | 0.991369i | \(-0.541851\pi\) | ||||
−0.131101 | + | 0.991369i | \(0.541851\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −14.7956 | −0.965161 | ||||||||
\(236\) | 0.723299 | 0.0470827 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.78900 | −0.115964 | ||||||||
\(239\) | 22.3878 | 1.44815 | 0.724074 | − | 0.689722i | \(-0.242267\pi\) | ||||
0.724074 | + | 0.689722i | \(0.242267\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −22.8159 | −1.46970 | −0.734852 | − | 0.678228i | \(-0.762748\pi\) | ||||
−0.734852 | + | 0.678228i | \(0.762748\pi\) | |||||||
\(242\) | −0.365561 | −0.0234992 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3.58006 | 0.229190 | ||||||||
\(245\) | −2.23254 | −0.142632 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −16.6345 | −1.05843 | ||||||||
\(248\) | −4.53396 | −0.287907 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 7.01203 | 0.443480 | ||||||||
\(251\) | 12.2272 | 0.771771 | 0.385885 | − | 0.922547i | \(-0.373896\pi\) | ||||
0.385885 | + | 0.922547i | \(0.373896\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.33103 | −0.272289 | ||||||||
\(254\) | −3.89207 | −0.244210 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −7.64557 | −0.476918 | −0.238459 | − | 0.971153i | \(-0.576642\pi\) | ||||
−0.238459 | + | 0.971153i | \(0.576642\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.29435 | −0.577523 | ||||||||
\(260\) | 7.94526 | 0.492744 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.37955 | 0.0852290 | ||||||||
\(263\) | −23.0025 | −1.41839 | −0.709196 | − | 0.705011i | \(-0.750942\pi\) | ||||
−0.709196 | + | 0.705011i | \(0.750942\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 24.2319 | 1.48855 | ||||||||
\(266\) | −15.9548 | −0.978249 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 11.3440 | 0.692942 | ||||||||
\(269\) | −23.1234 | −1.40986 | −0.704929 | − | 0.709278i | \(-0.749021\pi\) | ||||
−0.704929 | + | 0.709278i | \(0.749021\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.10401 | −0.431538 | −0.215769 | − | 0.976444i | \(-0.569226\pi\) | ||||
−0.215769 | + | 0.976444i | \(0.569226\pi\) | |||||||
\(272\) | 0.639779 | 0.0387923 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 15.5769 | 0.941033 | ||||||||
\(275\) | 7.91463 | 0.477270 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.2288 | −0.975096 | −0.487548 | − | 0.873096i | \(-0.662109\pi\) | ||||
−0.487548 | + | 0.873096i | \(0.662109\pi\) | |||||||
\(278\) | −3.71888 | −0.223044 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 7.62059 | 0.455417 | ||||||||
\(281\) | −23.2687 | −1.38809 | −0.694047 | − | 0.719930i | \(-0.744174\pi\) | ||||
−0.694047 | + | 0.719930i | \(0.744174\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.13901 | 0.246038 | 0.123019 | − | 0.992404i | \(-0.460742\pi\) | ||||
0.123019 | + | 0.992404i | \(0.460742\pi\) | |||||||
\(284\) | −16.6286 | −0.986727 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −9.50732 | −0.562180 | ||||||||
\(287\) | −22.6470 | −1.33681 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.5907 | −0.975923 | ||||||||
\(290\) | 8.77783 | 0.515452 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −14.5294 | −0.850270 | ||||||||
\(293\) | −11.8774 | −0.693888 | −0.346944 | − | 0.937886i | \(-0.612781\pi\) | ||||
−0.346944 | + | 0.937886i | \(0.612781\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.97117 | −0.114766 | ||||||||
\(296\) | 3.32382 | 0.193193 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.00000 | −0.0579284 | ||||||||
\(299\) | 3.87199 | 0.223923 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −33.2235 | −1.91497 | ||||||||
\(302\) | −3.55019 | −0.204290 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 5.70570 | 0.327244 | ||||||||
\(305\) | −9.75659 | −0.558661 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.07771 | 0.461019 | 0.230510 | − | 0.973070i | \(-0.425961\pi\) | ||||
0.230510 | + | 0.973070i | \(0.425961\pi\) | |||||||
\(308\) | −9.11882 | −0.519593 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 12.3562 | 0.701785 | ||||||||
\(311\) | 22.4413 | 1.27253 | 0.636266 | − | 0.771470i | \(-0.280478\pi\) | ||||
0.636266 | + | 0.771470i | \(0.280478\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.79049 | 0.101204 | 0.0506022 | − | 0.998719i | \(-0.483886\pi\) | ||||
0.0506022 | + | 0.998719i | \(0.483886\pi\) | |||||||
\(314\) | −22.1681 | −1.25102 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −14.8665 | −0.836304 | ||||||||
\(317\) | −11.1489 | −0.626185 | −0.313092 | − | 0.949723i | \(-0.601365\pi\) | ||||
−0.313092 | + | 0.949723i | \(0.601365\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −10.5036 | −0.588087 | ||||||||
\(320\) | −2.72526 | −0.152346 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3.71377 | 0.206960 | ||||||||
\(323\) | 3.65039 | 0.203113 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.07577 | −0.392493 | ||||||||
\(326\) | −16.1548 | −0.894730 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 8.09895 | 0.447190 | ||||||||
\(329\) | −15.1813 | −0.836970 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.96274 | 0.217812 | 0.108906 | − | 0.994052i | \(-0.465265\pi\) | ||||
0.108906 | + | 0.994052i | \(0.465265\pi\) | |||||||
\(332\) | 5.26159 | 0.288767 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −16.0147 | −0.876286 | ||||||||
\(335\) | −30.9152 | −1.68908 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −23.3207 | −1.27036 | −0.635179 | − | 0.772365i | \(-0.719074\pi\) | ||||
−0.635179 | + | 0.772365i | \(0.719074\pi\) | |||||||
\(338\) | −4.50034 | −0.244786 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.74356 | −0.0945579 | ||||||||
\(341\) | −14.7855 | −0.800678 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.2833 | 0.933208 | ||||||||
\(344\) | 11.8813 | 0.640596 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 25.3904 | 1.36500 | ||||||||
\(347\) | 3.89827 | 0.209270 | 0.104635 | − | 0.994511i | \(-0.466633\pi\) | ||||
0.104635 | + | 0.994511i | \(0.466633\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.7995 | 1.11337 | 0.556686 | − | 0.830723i | \(-0.312073\pi\) | ||||
0.556686 | + | 0.830723i | \(0.312073\pi\) | |||||||
\(350\) | −6.78663 | −0.362761 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.26105 | 0.173814 | ||||||||
\(353\) | 9.98456 | 0.531424 | 0.265712 | − | 0.964052i | \(-0.414393\pi\) | ||||
0.265712 | + | 0.964052i | \(0.414393\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 45.3172 | 2.40519 | ||||||||
\(356\) | −16.2962 | −0.863697 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 7.95101 | 0.420224 | ||||||||
\(359\) | −30.8076 | −1.62596 | −0.812982 | − | 0.582288i | \(-0.802157\pi\) | ||||
−0.812982 | + | 0.582288i | \(0.802157\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.5550 | 0.713423 | ||||||||
\(362\) | 5.41497 | 0.284605 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 8.15234 | 0.427299 | ||||||||
\(365\) | 39.5964 | 2.07257 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −32.2179 | −1.68176 | −0.840880 | − | 0.541221i | \(-0.817962\pi\) | ||||
−0.840880 | + | 0.541221i | \(0.817962\pi\) | |||||||
\(368\) | −1.32811 | −0.0692325 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −9.05827 | −0.470917 | ||||||||
\(371\) | 24.8634 | 1.29084 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.5090 | −0.647691 | −0.323845 | − | 0.946110i | \(-0.604976\pi\) | ||||
−0.323845 | + | 0.946110i | \(0.604976\pi\) | |||||||
\(374\) | 2.08635 | 0.107883 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.42908 | 0.279984 | ||||||||
\(377\) | 9.39033 | 0.483626 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.8180 | 1.06935 | 0.534675 | − | 0.845058i | \(-0.320434\pi\) | ||||
0.534675 | + | 0.845058i | \(0.320434\pi\) | |||||||
\(380\) | −15.5495 | −0.797672 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 8.24768 | 0.421988 | ||||||||
\(383\) | −38.2768 | −1.95585 | −0.977926 | − | 0.208952i | \(-0.932995\pi\) | ||||
−0.977926 | + | 0.208952i | \(0.932995\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 24.8511 | 1.26653 | ||||||||
\(386\) | 3.95012 | 0.201056 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −16.0563 | −0.815137 | ||||||||
\(389\) | 20.5628 | 1.04257 | 0.521287 | − | 0.853382i | \(-0.325452\pi\) | ||||
0.521287 | + | 0.853382i | \(0.325452\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.849696 | −0.0429710 | ||||||||
\(392\) | 0.819203 | 0.0413760 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 18.1572 | 0.914745 | ||||||||
\(395\) | 40.5149 | 2.03853 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −29.0661 | −1.45879 | −0.729394 | − | 0.684094i | \(-0.760198\pi\) | ||||
−0.729394 | + | 0.684094i | \(0.760198\pi\) | |||||||
\(398\) | −8.03230 | −0.402623 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.42702 | 0.121351 | ||||||||
\(401\) | 3.25582 | 0.162588 | 0.0812940 | − | 0.996690i | \(-0.474095\pi\) | ||||
0.0812940 | + | 0.996690i | \(0.474095\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 13.2184 | 0.658455 | ||||||||
\(404\) | 10.8277 | 0.538697 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 9.00661 | 0.446990 | ||||||||
\(407\) | 10.8391 | 0.537277 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 39.5930 | 1.95775 | 0.978873 | − | 0.204471i | \(-0.0655473\pi\) | ||||
0.978873 | + | 0.204471i | \(0.0655473\pi\) | |||||||
\(410\) | −22.0717 | −1.09004 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 10.1784 | 0.501454 | ||||||||
\(413\) | −2.02255 | −0.0995231 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −14.3392 | −0.703882 | ||||||||
\(416\) | −2.91542 | −0.142940 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 18.6066 | 0.910077 | ||||||||
\(419\) | 7.77544 | 0.379855 | 0.189927 | − | 0.981798i | \(-0.439175\pi\) | ||||
0.189927 | + | 0.981798i | \(0.439175\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −25.7009 | −1.25259 | −0.626293 | − | 0.779587i | \(-0.715429\pi\) | ||||
−0.626293 | + | 0.779587i | \(0.715429\pi\) | |||||||
\(422\) | −26.9038 | −1.30965 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −8.89160 | −0.431814 | ||||||||
\(425\) | 1.55276 | 0.0753197 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.0109 | −0.484460 | ||||||||
\(428\) | −4.43299 | −0.214277 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −32.3796 | −1.56148 | ||||||||
\(431\) | 19.0736 | 0.918744 | 0.459372 | − | 0.888244i | \(-0.348075\pi\) | ||||
0.459372 | + | 0.888244i | \(0.348075\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.1129 | 0.870451 | 0.435225 | − | 0.900321i | \(-0.356669\pi\) | ||||
0.435225 | + | 0.900321i | \(0.356669\pi\) | |||||||
\(434\) | 12.6782 | 0.608575 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −19.8234 | −0.949368 | ||||||||
\(437\) | −7.57779 | −0.362495 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.42989 | 0.211427 | 0.105714 | − | 0.994397i | \(-0.466287\pi\) | ||||
0.105714 | + | 0.994397i | \(0.466287\pi\) | |||||||
\(440\) | −8.88719 | −0.423680 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.86522 | −0.0887196 | ||||||||
\(443\) | 22.6132 | 1.07438 | 0.537192 | − | 0.843460i | \(-0.319485\pi\) | ||||
0.537192 | + | 0.843460i | \(0.319485\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 44.4113 | 2.10530 | ||||||||
\(446\) | 23.1746 | 1.09735 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.79628 | −0.132112 | ||||||||
\(449\) | −23.4810 | −1.10814 | −0.554069 | − | 0.832470i | \(-0.686926\pi\) | ||||
−0.554069 | + | 0.832470i | \(0.686926\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 26.4111 | 1.24365 | ||||||||
\(452\) | −11.3336 | −0.533088 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 11.7427 | 0.551110 | ||||||||
\(455\) | −22.2172 | −1.04156 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.3125 | −0.482400 | −0.241200 | − | 0.970475i | \(-0.577541\pi\) | ||||
−0.241200 | + | 0.970475i | \(0.577541\pi\) | |||||||
\(458\) | −13.1092 | −0.612552 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.61944 | 0.168757 | ||||||||
\(461\) | −28.1519 | −1.31116 | −0.655582 | − | 0.755124i | \(-0.727576\pi\) | ||||
−0.655582 | + | 0.755124i | \(0.727576\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 23.6846 | 1.10072 | 0.550358 | − | 0.834929i | \(-0.314491\pi\) | ||||
0.550358 | + | 0.834929i | \(0.314491\pi\) | |||||||
\(464\) | −3.22092 | −0.149527 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.00233 | −0.185404 | ||||||||
\(467\) | −17.9826 | −0.832133 | −0.416067 | − | 0.909334i | \(-0.636592\pi\) | ||||
−0.416067 | + | 0.909334i | \(0.636592\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −31.7209 | −1.46474 | ||||||||
\(470\) | −14.7956 | −0.682472 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0.723299 | 0.0332925 | ||||||||
\(473\) | 38.7455 | 1.78152 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 13.8478 | 0.635383 | ||||||||
\(476\) | −1.78900 | −0.0819989 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 22.3878 | 1.02400 | ||||||||
\(479\) | −8.58630 | −0.392318 | −0.196159 | − | 0.980572i | \(-0.562847\pi\) | ||||
−0.196159 | + | 0.980572i | \(0.562847\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.69033 | −0.441841 | ||||||||
\(482\) | −22.8159 | −1.03924 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.365561 | −0.0166164 | ||||||||
\(485\) | 43.7576 | 1.98693 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.72199 | −0.213974 | −0.106987 | − | 0.994260i | \(-0.534120\pi\) | ||||
−0.106987 | + | 0.994260i | \(0.534120\pi\) | |||||||
\(488\) | 3.58006 | 0.162062 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.23254 | −0.100856 | ||||||||
\(491\) | −2.83154 | −0.127786 | −0.0638929 | − | 0.997957i | \(-0.520352\pi\) | ||||
−0.0638929 | + | 0.997957i | \(0.520352\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.06068 | −0.0928082 | ||||||||
\(494\) | −16.6345 | −0.748422 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.53396 | −0.203581 | ||||||||
\(497\) | 46.4983 | 2.08574 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −35.6782 | −1.59718 | −0.798588 | − | 0.601878i | \(-0.794419\pi\) | ||||
−0.798588 | + | 0.601878i | \(0.794419\pi\) | |||||||
\(500\) | 7.01203 | 0.313588 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 12.2272 | 0.545724 | ||||||||
\(503\) | 27.2478 | 1.21492 | 0.607461 | − | 0.794350i | \(-0.292188\pi\) | ||||
0.607461 | + | 0.794350i | \(0.292188\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −29.5082 | −1.31310 | ||||||||
\(506\) | −4.33103 | −0.192538 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3.89207 | −0.172683 | ||||||||
\(509\) | −1.94505 | −0.0862129 | −0.0431064 | − | 0.999070i | \(-0.513725\pi\) | ||||
−0.0431064 | + | 0.999070i | \(0.513725\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 40.6284 | 1.79729 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −7.64557 | −0.337232 | ||||||||
\(515\) | −27.7387 | −1.22232 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 17.7045 | 0.778643 | ||||||||
\(518\) | −9.29435 | −0.408370 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 7.94526 | 0.348423 | ||||||||
\(521\) | 30.2679 | 1.32606 | 0.663031 | − | 0.748592i | \(-0.269270\pi\) | ||||
0.663031 | + | 0.748592i | \(0.269270\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.47550 | 0.195700 | 0.0978501 | − | 0.995201i | \(-0.468803\pi\) | ||||
0.0978501 | + | 0.995201i | \(0.468803\pi\) | |||||||
\(524\) | 1.37955 | 0.0602660 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −23.0025 | −1.00295 | ||||||||
\(527\) | −2.90073 | −0.126358 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.2361 | −0.923310 | ||||||||
\(530\) | 24.2319 | 1.05257 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −15.9548 | −0.691727 | ||||||||
\(533\) | −23.6118 | −1.02274 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.0810 | 0.522308 | ||||||||
\(536\) | 11.3440 | 0.489984 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −23.1234 | −0.996920 | ||||||||
\(539\) | 2.67146 | 0.115068 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.13187 | 0.0486630 | 0.0243315 | − | 0.999704i | \(-0.492254\pi\) | ||||
0.0243315 | + | 0.999704i | \(0.492254\pi\) | |||||||
\(542\) | −7.10401 | −0.305143 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.639779 | 0.0274303 | ||||||||
\(545\) | 54.0238 | 2.31413 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −20.4555 | −0.874616 | −0.437308 | − | 0.899312i | \(-0.644068\pi\) | ||||
−0.437308 | + | 0.899312i | \(0.644068\pi\) | |||||||
\(548\) | 15.5769 | 0.665411 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 7.91463 | 0.337481 | ||||||||
\(551\) | −18.3776 | −0.782913 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 41.5709 | 1.76777 | ||||||||
\(554\) | −16.2288 | −0.689497 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.71888 | −0.157716 | ||||||||
\(557\) | 44.2761 | 1.87604 | 0.938020 | − | 0.346581i | \(-0.112657\pi\) | ||||
0.938020 | + | 0.346581i | \(0.112657\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −34.6389 | −1.46507 | ||||||||
\(560\) | 7.62059 | 0.322029 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −23.2687 | −0.981530 | ||||||||
\(563\) | −30.8672 | −1.30090 | −0.650449 | − | 0.759550i | \(-0.725419\pi\) | ||||
−0.650449 | + | 0.759550i | \(0.725419\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 30.8870 | 1.29943 | ||||||||
\(566\) | 4.13901 | 0.173975 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −16.6286 | −0.697721 | ||||||||
\(569\) | 4.86745 | 0.204054 | 0.102027 | − | 0.994782i | \(-0.467467\pi\) | ||||
0.102027 | + | 0.994782i | \(0.467467\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −27.5505 | −1.15295 | −0.576477 | − | 0.817113i | \(-0.695573\pi\) | ||||
−0.576477 | + | 0.817113i | \(0.695573\pi\) | |||||||
\(572\) | −9.50732 | −0.397521 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −22.6470 | −0.945266 | ||||||||
\(575\) | −3.22335 | −0.134423 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 27.4508 | 1.14279 | 0.571397 | − | 0.820674i | \(-0.306402\pi\) | ||||
0.571397 | + | 0.820674i | \(0.306402\pi\) | |||||||
\(578\) | −16.5907 | −0.690081 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 8.77783 | 0.364480 | ||||||||
\(581\) | −14.7129 | −0.610394 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −28.9959 | −1.20089 | ||||||||
\(584\) | −14.5294 | −0.601232 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −11.8774 | −0.490653 | ||||||||
\(587\) | −8.74701 | −0.361028 | −0.180514 | − | 0.983572i | \(-0.557776\pi\) | ||||
−0.180514 | + | 0.983572i | \(0.557776\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −25.8694 | −1.06593 | ||||||||
\(590\) | −1.97117 | −0.0811520 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.32382 | 0.136608 | ||||||||
\(593\) | −46.3617 | −1.90385 | −0.951924 | − | 0.306334i | \(-0.900898\pi\) | ||||
−0.951924 | + | 0.306334i | \(0.900898\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.87549 | 0.199876 | ||||||||
\(596\) | −1.00000 | −0.0409616 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 3.87199 | 0.158338 | ||||||||
\(599\) | 6.12967 | 0.250451 | 0.125226 | − | 0.992128i | \(-0.460035\pi\) | ||||
0.125226 | + | 0.992128i | \(0.460035\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.43528 | 0.0585463 | 0.0292732 | − | 0.999571i | \(-0.490681\pi\) | ||||
0.0292732 | + | 0.999571i | \(0.490681\pi\) | |||||||
\(602\) | −33.2235 | −1.35409 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3.55019 | −0.144455 | ||||||||
\(605\) | 0.996248 | 0.0405032 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 20.8849 | 0.847693 | 0.423847 | − | 0.905734i | \(-0.360680\pi\) | ||||
0.423847 | + | 0.905734i | \(0.360680\pi\) | |||||||
\(608\) | 5.70570 | 0.231397 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −9.75659 | −0.395033 | ||||||||
\(611\) | −15.8280 | −0.640334 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −37.5686 | −1.51738 | −0.758691 | − | 0.651451i | \(-0.774161\pi\) | ||||
−0.758691 | + | 0.651451i | \(0.774161\pi\) | |||||||
\(614\) | 8.07771 | 0.325990 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −9.11882 | −0.367408 | ||||||||
\(617\) | −4.84106 | −0.194894 | −0.0974468 | − | 0.995241i | \(-0.531068\pi\) | ||||
−0.0974468 | + | 0.995241i | \(0.531068\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.70576 | −0.309721 | −0.154860 | − | 0.987936i | \(-0.549493\pi\) | ||||
−0.154860 | + | 0.987936i | \(0.549493\pi\) | |||||||
\(620\) | 12.3562 | 0.496237 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 22.4413 | 0.899815 | ||||||||
\(623\) | 45.5688 | 1.82568 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.2447 | −1.24979 | ||||||||
\(626\) | 1.79049 | 0.0715624 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −22.1681 | −0.884603 | ||||||||
\(629\) | 2.12651 | 0.0847896 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.62695 | −0.104577 | −0.0522887 | − | 0.998632i | \(-0.516652\pi\) | ||||
−0.0522887 | + | 0.998632i | \(0.516652\pi\) | |||||||
\(632\) | −14.8665 | −0.591356 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −11.1489 | −0.442779 | ||||||||
\(635\) | 10.6069 | 0.420921 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.38832 | −0.0946287 | ||||||||
\(638\) | −10.5036 | −0.415841 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2.72526 | −0.107725 | ||||||||
\(641\) | 22.1313 | 0.874132 | 0.437066 | − | 0.899429i | \(-0.356018\pi\) | ||||
0.437066 | + | 0.899429i | \(0.356018\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.528582 | 0.0208452 | 0.0104226 | − | 0.999946i | \(-0.496682\pi\) | ||||
0.0104226 | + | 0.999946i | \(0.496682\pi\) | |||||||
\(644\) | 3.71377 | 0.146343 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.65039 | 0.143623 | ||||||||
\(647\) | −1.05402 | −0.0414377 | −0.0207189 | − | 0.999785i | \(-0.506595\pi\) | ||||
−0.0207189 | + | 0.999785i | \(0.506595\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.35871 | 0.0925876 | ||||||||
\(650\) | −7.07577 | −0.277535 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −16.1548 | −0.632670 | ||||||||
\(653\) | −12.8500 | −0.502860 | −0.251430 | − | 0.967876i | \(-0.580901\pi\) | ||||
−0.251430 | + | 0.967876i | \(0.580901\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.75963 | −0.146901 | ||||||||
\(656\) | 8.09895 | 0.316211 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −15.1813 | −0.591827 | ||||||||
\(659\) | −3.36625 | −0.131130 | −0.0655652 | − | 0.997848i | \(-0.520885\pi\) | ||||
−0.0655652 | + | 0.997848i | \(0.520885\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −29.1141 | −1.13241 | −0.566203 | − | 0.824266i | \(-0.691588\pi\) | ||||
−0.566203 | + | 0.824266i | \(0.691588\pi\) | |||||||
\(662\) | 3.96274 | 0.154016 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5.26159 | 0.204189 | ||||||||
\(665\) | 43.4808 | 1.68611 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.27773 | 0.165634 | ||||||||
\(668\) | −16.0147 | −0.619628 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −30.9152 | −1.19436 | ||||||||
\(671\) | 11.6748 | 0.450699 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14.9029 | 0.574463 | 0.287232 | − | 0.957861i | \(-0.407265\pi\) | ||||
0.287232 | + | 0.957861i | \(0.407265\pi\) | |||||||
\(674\) | −23.3207 | −0.898279 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.50034 | −0.173090 | ||||||||
\(677\) | 21.7641 | 0.836462 | 0.418231 | − | 0.908341i | \(-0.362650\pi\) | ||||
0.418231 | + | 0.908341i | \(0.362650\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 44.8981 | 1.72303 | ||||||||
\(680\) | −1.74356 | −0.0668625 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −14.7855 | −0.566165 | ||||||||
\(683\) | −22.9350 | −0.877582 | −0.438791 | − | 0.898589i | \(-0.644593\pi\) | ||||
−0.438791 | + | 0.898589i | \(0.644593\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −42.4509 | −1.62197 | ||||||||
\(686\) | 17.2833 | 0.659878 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 11.8813 | 0.452970 | ||||||||
\(689\) | 25.9227 | 0.987577 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 27.1459 | 1.03268 | 0.516339 | − | 0.856384i | \(-0.327294\pi\) | ||||
0.516339 | + | 0.856384i | \(0.327294\pi\) | |||||||
\(692\) | 25.3904 | 0.965197 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3.89827 | 0.147976 | ||||||||
\(695\) | 10.1349 | 0.384439 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.18154 | 0.196265 | ||||||||
\(698\) | 20.7995 | 0.787273 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −6.78663 | −0.256511 | ||||||||
\(701\) | −11.2381 | −0.424459 | −0.212229 | − | 0.977220i | \(-0.568072\pi\) | ||||
−0.212229 | + | 0.977220i | \(0.568072\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 18.9647 | 0.715269 | ||||||||
\(704\) | 3.26105 | 0.122905 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 9.98456 | 0.375774 | ||||||||
\(707\) | −30.2773 | −1.13869 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 32.9160 | 1.23619 | 0.618094 | − | 0.786105i | \(-0.287905\pi\) | ||||
0.618094 | + | 0.786105i | \(0.287905\pi\) | |||||||
\(710\) | 45.3172 | 1.70073 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −16.2962 | −0.610726 | ||||||||
\(713\) | 6.02159 | 0.225510 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 25.9099 | 0.968975 | ||||||||
\(716\) | 7.95101 | 0.297143 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −30.8076 | −1.14973 | ||||||||
\(719\) | 18.7416 | 0.698942 | 0.349471 | − | 0.936947i | \(-0.386361\pi\) | ||||
0.349471 | + | 0.936947i | \(0.386361\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −28.4617 | −1.05997 | ||||||||
\(722\) | 13.5550 | 0.504466 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 5.41497 | 0.201246 | ||||||||
\(725\) | −7.81723 | −0.290325 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 45.3511 | 1.68198 | 0.840990 | − | 0.541051i | \(-0.181973\pi\) | ||||
0.840990 | + | 0.541051i | \(0.181973\pi\) | |||||||
\(728\) | 8.15234 | 0.302146 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 39.5964 | 1.46553 | ||||||||
\(731\) | 7.60140 | 0.281148 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 52.6932 | 1.94627 | 0.973133 | − | 0.230243i | \(-0.0739523\pi\) | ||||
0.973133 | + | 0.230243i | \(0.0739523\pi\) | |||||||
\(734\) | −32.2179 | −1.18918 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.32811 | −0.0489547 | ||||||||
\(737\) | 36.9932 | 1.36266 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −22.6834 | −0.834421 | −0.417211 | − | 0.908810i | \(-0.636992\pi\) | ||||
−0.417211 | + | 0.908810i | \(0.636992\pi\) | |||||||
\(740\) | −9.05827 | −0.332989 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 24.8634 | 0.912765 | ||||||||
\(743\) | −17.9688 | −0.659211 | −0.329606 | − | 0.944119i | \(-0.606916\pi\) | ||||
−0.329606 | + | 0.944119i | \(0.606916\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.72526 | 0.0998456 | ||||||||
\(746\) | −12.5090 | −0.457986 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 2.08635 | 0.0762845 | ||||||||
\(749\) | 12.3959 | 0.452936 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.566495 | 0.0206717 | 0.0103359 | − | 0.999947i | \(-0.496710\pi\) | ||||
0.0103359 | + | 0.999947i | \(0.496710\pi\) | |||||||
\(752\) | 5.42908 | 0.197978 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 9.39033 | 0.341976 | ||||||||
\(755\) | 9.67518 | 0.352116 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26.4143 | 0.960042 | 0.480021 | − | 0.877257i | \(-0.340629\pi\) | ||||
0.480021 | + | 0.877257i | \(0.340629\pi\) | |||||||
\(758\) | 20.8180 | 0.756144 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −15.5495 | −0.564040 | ||||||||
\(761\) | −2.85181 | −0.103378 | −0.0516890 | − | 0.998663i | \(-0.516460\pi\) | ||||
−0.0516890 | + | 0.998663i | \(0.516460\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 55.4318 | 2.00677 | ||||||||
\(764\) | 8.24768 | 0.298391 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −38.2768 | −1.38300 | ||||||||
\(767\) | −2.10872 | −0.0761414 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10.3071 | 0.371683 | 0.185842 | − | 0.982580i | \(-0.440499\pi\) | ||||
0.185842 | + | 0.982580i | \(0.440499\pi\) | |||||||
\(770\) | 24.8511 | 0.895572 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 3.95012 | 0.142168 | ||||||||
\(773\) | 7.81989 | 0.281262 | 0.140631 | − | 0.990062i | \(-0.455087\pi\) | ||||
0.140631 | + | 0.990062i | \(0.455087\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −11.0040 | −0.395276 | ||||||||
\(776\) | −16.0563 | −0.576389 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 20.5628 | 0.737210 | ||||||||
\(779\) | 46.2102 | 1.65565 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −54.2267 | −1.94039 | ||||||||
\(782\) | −0.849696 | −0.0303851 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.819203 | 0.0292573 | ||||||||
\(785\) | 60.4137 | 2.15626 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.48811 | 0.0886915 | 0.0443458 | − | 0.999016i | \(-0.485880\pi\) | ||||
0.0443458 | + | 0.999016i | \(0.485880\pi\) | |||||||
\(788\) | 18.1572 | 0.646822 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 40.5149 | 1.44146 | ||||||||
\(791\) | 31.6920 | 1.12684 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.4374 | −0.370642 | ||||||||
\(794\) | −29.0661 | −1.03152 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −8.03230 | −0.284697 | ||||||||
\(797\) | 2.20148 | 0.0779805 | 0.0389902 | − | 0.999240i | \(-0.487586\pi\) | ||||
0.0389902 | + | 0.999240i | \(0.487586\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.47341 | 0.122881 | ||||||||
\(800\) | 2.42702 | 0.0858081 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 3.25582 | 0.114967 | ||||||||
\(803\) | −47.3812 | −1.67205 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −10.1210 | −0.356717 | ||||||||
\(806\) | 13.2184 | 0.465598 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 10.8277 | 0.380916 | ||||||||
\(809\) | 31.9340 | 1.12274 | 0.561369 | − | 0.827565i | \(-0.310275\pi\) | ||||
0.561369 | + | 0.827565i | \(0.310275\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −24.9375 | −0.875675 | −0.437837 | − | 0.899054i | \(-0.644255\pi\) | ||||
−0.437837 | + | 0.899054i | \(0.644255\pi\) | |||||||
\(812\) | 9.00661 | 0.316070 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 10.8391 | 0.379912 | ||||||||
\(815\) | 44.0259 | 1.54216 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 67.7911 | 2.37171 | ||||||||
\(818\) | 39.5930 | 1.38434 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −22.0717 | −0.770777 | ||||||||
\(821\) | 53.9606 | 1.88324 | 0.941619 | − | 0.336681i | \(-0.109304\pi\) | ||||
0.941619 | + | 0.336681i | \(0.109304\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.62304 | −0.161149 | −0.0805745 | − | 0.996749i | \(-0.525675\pi\) | ||||
−0.0805745 | + | 0.996749i | \(0.525675\pi\) | |||||||
\(824\) | 10.1784 | 0.354581 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.02255 | −0.0703735 | ||||||||
\(827\) | −23.5970 | −0.820549 | −0.410274 | − | 0.911962i | \(-0.634567\pi\) | ||||
−0.410274 | + | 0.911962i | \(0.634567\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −41.9815 | −1.45808 | −0.729039 | − | 0.684472i | \(-0.760033\pi\) | ||||
−0.729039 | + | 0.684472i | \(0.760033\pi\) | |||||||
\(830\) | −14.3392 | −0.497720 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2.91542 | −0.101074 | ||||||||
\(833\) | 0.524109 | 0.0181593 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 43.6442 | 1.51037 | ||||||||
\(836\) | 18.6066 | 0.643522 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 7.77544 | 0.268598 | ||||||||
\(839\) | −10.7147 | −0.369912 | −0.184956 | − | 0.982747i | \(-0.559214\pi\) | ||||
−0.184956 | + | 0.982747i | \(0.559214\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.6257 | −0.642265 | ||||||||
\(842\) | −25.7009 | −0.885713 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −26.9038 | −0.926065 | ||||||||
\(845\) | 12.2646 | 0.421914 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.02221 | 0.0351237 | ||||||||
\(848\) | −8.89160 | −0.305339 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.55276 | 0.0532591 | ||||||||
\(851\) | −4.41440 | −0.151324 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 33.7916 | 1.15700 | 0.578500 | − | 0.815682i | \(-0.303638\pi\) | ||||
0.578500 | + | 0.815682i | \(0.303638\pi\) | |||||||
\(854\) | −10.0109 | −0.342565 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.43299 | −0.151516 | ||||||||
\(857\) | 30.3647 | 1.03724 | 0.518619 | − | 0.855005i | \(-0.326446\pi\) | ||||
0.518619 | + | 0.855005i | \(0.326446\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10.3030 | −0.351533 | −0.175767 | − | 0.984432i | \(-0.556240\pi\) | ||||
−0.175767 | + | 0.984432i | \(0.556240\pi\) | |||||||
\(860\) | −32.3796 | −1.10413 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 19.0736 | 0.649650 | ||||||||
\(863\) | −16.8673 | −0.574168 | −0.287084 | − | 0.957905i | \(-0.592686\pi\) | ||||
−0.287084 | + | 0.957905i | \(0.592686\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −69.1953 | −2.35271 | ||||||||
\(866\) | 18.1129 | 0.615502 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 12.6782 | 0.430327 | ||||||||
\(869\) | −48.4803 | −1.64458 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −33.0724 | −1.12061 | ||||||||
\(872\) | −19.8234 | −0.671305 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −7.57779 | −0.256323 | ||||||||
\(875\) | −19.6076 | −0.662859 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 27.9275 | 0.943044 | 0.471522 | − | 0.881854i | \(-0.343705\pi\) | ||||
0.471522 | + | 0.881854i | \(0.343705\pi\) | |||||||
\(878\) | 4.42989 | 0.149502 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −8.88719 | −0.299587 | ||||||||
\(881\) | −37.2411 | −1.25468 | −0.627342 | − | 0.778744i | \(-0.715857\pi\) | ||||
−0.627342 | + | 0.778744i | \(0.715857\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19.0955 | 0.642616 | 0.321308 | − | 0.946975i | \(-0.395878\pi\) | ||||
0.321308 | + | 0.946975i | \(0.395878\pi\) | |||||||
\(884\) | −1.86522 | −0.0627343 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 22.6132 | 0.759705 | ||||||||
\(887\) | 46.8091 | 1.57169 | 0.785847 | − | 0.618420i | \(-0.212227\pi\) | ||||
0.785847 | + | 0.618420i | \(0.212227\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.8833 | 0.365015 | ||||||||
\(890\) | 44.4113 | 1.48867 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 23.1746 | 0.775945 | ||||||||
\(893\) | 30.9767 | 1.03660 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −21.6685 | −0.724299 | ||||||||
\(896\) | −2.79628 | −0.0934173 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −23.4810 | −0.783573 | ||||||||
\(899\) | 14.6035 | 0.487055 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.68866 | −0.189517 | ||||||||
\(902\) | 26.4111 | 0.879392 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −11.3336 | −0.376950 | ||||||||
\(905\) | −14.7572 | −0.490545 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −21.2858 | −0.706784 | −0.353392 | − | 0.935475i | \(-0.614972\pi\) | ||||
−0.353392 | + | 0.935475i | \(0.614972\pi\) | |||||||
\(908\) | 11.7427 | 0.389694 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −22.2172 | −0.736493 | ||||||||
\(911\) | −44.5040 | −1.47448 | −0.737241 | − | 0.675629i | \(-0.763872\pi\) | ||||
−0.737241 | + | 0.675629i | \(0.763872\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 17.1583 | 0.567857 | ||||||||
\(914\) | −10.3125 | −0.341108 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −13.1092 | −0.433140 | ||||||||
\(917\) | −3.85762 | −0.127390 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −35.3524 | −1.16617 | −0.583083 | − | 0.812412i | \(-0.698154\pi\) | ||||
−0.583083 | + | 0.812412i | \(0.698154\pi\) | |||||||
\(920\) | 3.61944 | 0.119329 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −28.1519 | −0.927132 | ||||||||
\(923\) | 48.4794 | 1.59572 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.06698 | 0.265241 | ||||||||
\(926\) | 23.6846 | 0.778323 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3.22092 | −0.105732 | ||||||||
\(929\) | 44.0940 | 1.44668 | 0.723338 | − | 0.690494i | \(-0.242607\pi\) | ||||
0.723338 | + | 0.690494i | \(0.242607\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.67413 | 0.153188 | ||||||||
\(932\) | −4.00233 | −0.131101 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −17.9826 | −0.588407 | ||||||||
\(935\) | −5.68584 | −0.185947 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.16133 | 0.168613 | 0.0843066 | − | 0.996440i | \(-0.473132\pi\) | ||||
0.0843066 | + | 0.996440i | \(0.473132\pi\) | |||||||
\(938\) | −31.7209 | −1.03572 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −14.7956 | −0.482581 | ||||||||
\(941\) | −25.8702 | −0.843344 | −0.421672 | − | 0.906748i | \(-0.638557\pi\) | ||||
−0.421672 | + | 0.906748i | \(0.638557\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10.7563 | −0.350273 | ||||||||
\(944\) | 0.723299 | 0.0235414 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 38.7455 | 1.25972 | ||||||||
\(947\) | 14.1037 | 0.458308 | 0.229154 | − | 0.973390i | \(-0.426404\pi\) | ||||
0.229154 | + | 0.973390i | \(0.426404\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 42.3594 | 1.37504 | ||||||||
\(950\) | 13.8478 | 0.449284 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.78900 | −0.0579820 | ||||||||
\(953\) | 12.3360 | 0.399603 | 0.199801 | − | 0.979836i | \(-0.435970\pi\) | ||||
0.199801 | + | 0.979836i | \(0.435970\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −22.4770 | −0.727340 | ||||||||
\(956\) | 22.3878 | 0.724074 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −8.58630 | −0.277411 | ||||||||
\(959\) | −43.5573 | −1.40654 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10.4432 | −0.336878 | ||||||||
\(962\) | −9.69033 | −0.312429 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −22.8159 | −0.734852 | ||||||||
\(965\) | −10.7651 | −0.346541 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −16.0689 | −0.516740 | −0.258370 | − | 0.966046i | \(-0.583185\pi\) | ||||
−0.258370 | + | 0.966046i | \(0.583185\pi\) | |||||||
\(968\) | −0.365561 | −0.0117496 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 43.7576 | 1.40497 | ||||||||
\(971\) | 51.5433 | 1.65410 | 0.827051 | − | 0.562126i | \(-0.190017\pi\) | ||||
0.827051 | + | 0.562126i | \(0.190017\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 10.3991 | 0.333378 | ||||||||
\(974\) | −4.72199 | −0.151302 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.58006 | 0.114595 | ||||||||
\(977\) | 47.6254 | 1.52367 | 0.761836 | − | 0.647770i | \(-0.224298\pi\) | ||||
0.761836 | + | 0.647770i | \(0.224298\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −53.1427 | −1.69845 | ||||||||
\(980\) | −2.23254 | −0.0713158 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −2.83154 | −0.0903582 | ||||||||
\(983\) | −24.2854 | −0.774585 | −0.387293 | − | 0.921957i | \(-0.626590\pi\) | ||||
−0.387293 | + | 0.921957i | \(0.626590\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −49.4829 | −1.57666 | ||||||||
\(986\) | −2.06068 | −0.0656253 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −16.6345 | −0.529214 | ||||||||
\(989\) | −15.7796 | −0.501764 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.8119 | 0.534048 | 0.267024 | − | 0.963690i | \(-0.413960\pi\) | ||||
0.267024 | + | 0.963690i | \(0.413960\pi\) | |||||||
\(992\) | −4.53396 | −0.143953 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 46.4983 | 1.47484 | ||||||||
\(995\) | 21.8901 | 0.693962 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 33.9833 | 1.07626 | 0.538132 | − | 0.842861i | \(-0.319130\pi\) | ||||
0.538132 | + | 0.842861i | \(0.319130\pi\) | |||||||
\(998\) | −35.6782 | −1.12937 | ||||||||
\(999\) | 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 | 8046.2.a.h.1.2 | yes | 9 | |
3.2 | odd | 2 | 8046.2.a.g.1.8 | ✓ | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8046.2.a.g.1.8 | ✓ | 9 | 3.2 | odd | 2 | ||
8046.2.a.h.1.2 | yes | 9 | 1.1 | even | 1 | trivial |