Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1344,4,Mod(895,1344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1344, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1344.895");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1344 = 2^{6} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1344.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(79.2985670477\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 158x^{6} + 8461x^{4} + 180672x^{2} + 1232100 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{15}\cdot 3^{3} \) |
Twist minimal: | no (minimal twist has level 336) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 895.4 | ||
Root | \(-3.58293i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1344.895 |
Dual form | 1344.4.b.f.895.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(449\) | \(577\) | \(1093\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 4.33129i | − | 0.387403i | −0.981061 | − | 0.193701i | \(-0.937951\pi\) | ||
0.981061 | − | 0.193701i | \(-0.0620493\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 18.4617 | + | 1.47188i | 0.996837 | + | 0.0794739i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 21.1315i | − | 0.579216i | −0.957145 | − | 0.289608i | \(-0.906475\pi\) | ||
0.957145 | − | 0.289608i | \(-0.0935249\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 36.7607i | 0.784275i | 0.919907 | + | 0.392137i | \(0.128264\pi\) | ||||
−0.919907 | + | 0.392137i | \(0.871736\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 12.9939i | − | 0.223667i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 46.5942i | − | 0.664750i | −0.943147 | − | 0.332375i | \(-0.892150\pi\) | ||
0.943147 | − | 0.332375i | \(-0.107850\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 89.7520 | 1.08371 | 0.541856 | − | 0.840471i | \(-0.317722\pi\) | ||||
0.541856 | + | 0.840471i | \(0.317722\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 55.3850 | + | 4.41563i | 0.575524 | + | 0.0458843i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 190.308i | 1.72530i | 0.505800 | + | 0.862651i | \(0.331197\pi\) | ||||
−0.505800 | + | 0.862651i | \(0.668803\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 106.240 | 0.849919 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −196.881 | −1.26069 | −0.630343 | − | 0.776317i | \(-0.717086\pi\) | ||||
−0.630343 | + | 0.776317i | \(0.717086\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 87.5824 | 0.507428 | 0.253714 | − | 0.967279i | \(-0.418348\pi\) | ||||
0.253714 | + | 0.967279i | \(0.418348\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 63.3944i | − | 0.334410i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.37513 | − | 79.9629i | 0.0307884 | − | 0.386177i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 17.9215 | 0.0796289 | 0.0398145 | − | 0.999207i | \(-0.487323\pi\) | ||||
0.0398145 | + | 0.999207i | \(0.487323\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 110.282i | 0.452801i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 374.897i | 1.42803i | 0.700132 | + | 0.714013i | \(0.253124\pi\) | ||||
−0.700132 | + | 0.714013i | \(0.746876\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 504.442i | − | 1.78899i | −0.447075 | − | 0.894496i | \(-0.647534\pi\) | ||
0.447075 | − | 0.894496i | \(-0.352466\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 38.9816i | − | 0.129134i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 399.286 | 1.23919 | 0.619594 | − | 0.784923i | \(-0.287297\pi\) | ||||
0.619594 | + | 0.784923i | \(0.287297\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 338.667 | + | 54.3467i | 0.987368 | + | 0.158445i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 139.783i | − | 0.383794i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 19.8855 | 0.0515374 | 0.0257687 | − | 0.999668i | \(-0.491797\pi\) | ||||
0.0257687 | + | 0.999668i | \(0.491797\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −91.5265 | −0.224390 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 269.256 | 0.625681 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 74.2866 | 0.163920 | 0.0819601 | − | 0.996636i | \(-0.473882\pi\) | ||||
0.0819601 | + | 0.996636i | \(0.473882\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 5.16488i | − | 0.0108409i | −0.999985 | − | 0.00542046i | \(-0.998275\pi\) | ||
0.999985 | − | 0.00542046i | \(-0.00172539\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 166.155 | + | 13.2469i | 0.332279 | + | 0.0264913i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 159.221 | 0.303830 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 276.852i | − | 0.504818i | −0.967621 | − | 0.252409i | \(-0.918777\pi\) | ||
0.967621 | − | 0.252409i | \(-0.0812229\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 570.924i | 0.996103i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 474.674i | 0.793428i | 0.917942 | + | 0.396714i | \(0.129850\pi\) | ||||
−0.917942 | + | 0.396714i | \(0.870150\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 653.765i | − | 1.04818i | −0.851662 | − | 0.524092i | \(-0.824405\pi\) | ||
0.851662 | − | 0.524092i | \(-0.175595\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 318.720 | 0.490701 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 31.1029 | − | 390.122i | 0.0460326 | − | 0.577384i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 586.924i | 0.835875i | 0.908476 | + | 0.417937i | \(0.137247\pi\) | ||||
−0.908476 | + | 0.417937i | \(0.862753\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −441.028 | −0.583242 | −0.291621 | − | 0.956534i | \(-0.594195\pi\) | ||||
−0.291621 | + | 0.956534i | \(0.594195\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −201.813 | −0.257526 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −590.643 | −0.727857 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 862.965i | 1.02780i | 0.857850 | + | 0.513899i | \(0.171800\pi\) | ||||
−0.857850 | + | 0.513899i | \(0.828200\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −54.1072 | + | 678.664i | −0.0623294 | + | 0.781794i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 262.747 | 0.292964 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 388.742i | − | 0.419833i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 890.287i | − | 0.931907i | −0.884809 | − | 0.465953i | \(-0.845711\pi\) | ||
0.884809 | − | 0.465953i | \(-0.154289\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 190.183i | − | 0.193072i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 684.148i | − | 0.674013i | −0.941502 | − | 0.337006i | \(-0.890586\pi\) | ||
0.941502 | − | 0.337006i | \(-0.109414\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −385.671 | −0.368944 | −0.184472 | − | 0.982838i | \(-0.559058\pi\) | ||||
−0.184472 | + | 0.982838i | \(0.559058\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 19.1254 | − | 239.889i | 0.0177757 | − | 0.222960i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 341.995i | 0.308990i | 0.987994 | + | 0.154495i | \(0.0493751\pi\) | ||||
−0.987994 | + | 0.154495i | \(0.950625\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1807.72 | 1.58852 | 0.794259 | − | 0.607579i | \(-0.207859\pi\) | ||||
0.794259 | + | 0.607579i | \(0.207859\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 53.7644 | 0.0459738 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 707.257 | 0.588789 | 0.294394 | − | 0.955684i | \(-0.404882\pi\) | ||||
0.294394 | + | 0.955684i | \(0.404882\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 824.279 | 0.668386 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 330.846i | 0.261425i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 68.5810 | − | 860.207i | 0.0528303 | − | 0.662648i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 884.462 | 0.664509 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1124.69i | 0.824471i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 1001.57i | − | 0.716664i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 1282.50i | − | 0.896092i | −0.894010 | − | 0.448046i | \(-0.852120\pi\) | ||
0.894010 | − | 0.448046i | \(-0.147880\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 1513.33i | − | 1.03288i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2295.10 | −1.53071 | −0.765357 | − | 0.643606i | \(-0.777438\pi\) | ||||
−0.765357 | + | 0.643606i | \(0.777438\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1656.97 | + | 132.104i | 1.08028 | + | 0.0861268i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 116.945i | − | 0.0745557i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 375.692 | 0.234288 | 0.117144 | − | 0.993115i | \(-0.462626\pi\) | ||||
0.117144 | + | 0.993115i | \(0.462626\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1346.64 | 0.821728 | 0.410864 | − | 0.911697i | \(-0.365227\pi\) | ||||
0.410864 | + | 0.911697i | \(0.365227\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1197.86 | 0.715445 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 776.806 | 0.454264 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 852.749i | 0.488393i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1016.00 | + | 163.040i | 0.570057 | + | 0.0914783i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2440.27 | 1.34171 | 0.670855 | − | 0.741588i | \(-0.265927\pi\) | ||||
0.670855 | + | 0.741588i | \(0.265927\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 1896.11i | − | 1.02188i | −0.859618 | − | 0.510938i | \(-0.829298\pi\) | ||
0.859618 | − | 0.510938i | \(-0.170702\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 419.348i | − | 0.221583i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 379.345i | − | 0.196579i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3198.03i | 1.62567i | 0.582493 | + | 0.812836i | \(0.302077\pi\) | ||||
−0.582493 | + | 0.812836i | \(0.697923\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 59.6565 | 0.0297551 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −280.110 | + | 3513.40i | −0.137116 | + | 1.71984i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2106.63i | 1.01229i | 0.862447 | + | 0.506147i | \(0.168931\pi\) | ||||
−0.862447 | + | 0.506147i | \(0.831069\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −274.580 | −0.129551 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 82.8763 | 0.0384022 | 0.0192011 | − | 0.999816i | \(-0.493888\pi\) | ||||
0.0192011 | + | 0.999816i | \(0.493888\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 845.654 | 0.384913 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 807.768 | 0.361237 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 4383.57i | − | 1.92646i | −0.268687 | − | 0.963228i | \(-0.586590\pi\) | ||
0.268687 | − | 0.963228i | \(-0.413410\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1961.37 | + | 156.372i | 0.847231 | + | 0.0675464i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 222.860 | 0.0946394 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2994.66i | 1.25045i | 0.780443 | + | 0.625227i | \(0.214994\pi\) | ||||
−0.780443 | + | 0.625227i | \(0.785006\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 518.569i | − | 0.212956i | −0.994315 | − | 0.106478i | \(-0.966043\pi\) | ||
0.994315 | − | 0.106478i | \(-0.0339573\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 15.4947i | − | 0.00625900i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 77.6231i | − | 0.0308485i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −984.603 | −0.385034 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 498.465 | + | 39.7407i | 0.191841 | + | 0.0152948i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 2580.23i | − | 0.977482i | −0.872429 | − | 0.488741i | \(-0.837456\pi\) | ||
0.872429 | − | 0.488741i | \(-0.162544\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 861.276 | 0.321223 | 0.160611 | − | 0.987018i | \(-0.448653\pi\) | ||||
0.160611 | + | 0.987018i | \(0.448653\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 477.664 | 0.175416 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2206.28 | 0.797922 | 0.398961 | − | 0.916968i | \(-0.369371\pi\) | ||||
0.398961 | + | 0.916968i | \(0.369371\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2855.66 | −1.01725 | −0.508624 | − | 0.860989i | \(-0.669846\pi\) | ||||
−0.508624 | + | 0.860989i | \(0.669846\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 830.555i | − | 0.291457i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3634.75 | − | 289.785i | −1.25670 | − | 0.100192i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1623.79 | 0.553221 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1712.77i | 0.575100i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 1896.59i | − | 0.627703i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 2314.89i | − | 0.755279i | −0.925953 | − | 0.377640i | \(-0.876736\pi\) | ||
0.925953 | − | 0.377640i | \(-0.123264\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1424.02i | 0.458086i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2184.89 | −0.693060 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1616.92 | + | 128.911i | 0.505823 | + | 0.0403273i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 1961.29i | − | 0.605169i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1712.83 | 0.521347 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2776.63 | −0.833799 | −0.416899 | − | 0.908953i | \(-0.636883\pi\) | ||||
−0.416899 | + | 0.908953i | \(0.636883\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 956.159 | 0.283306 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2451.68 | 0.716846 | 0.358423 | − | 0.933559i | \(-0.383315\pi\) | ||||
0.358423 | + | 0.933559i | \(0.383315\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 362.328i | 0.104556i | 0.998633 | + | 0.0522780i | \(0.0166482\pi\) | ||||
−0.998633 | + | 0.0522780i | \(0.983352\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 93.3088 | − | 1170.37i | 0.0265769 | − | 0.333353i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6493.96 | 1.82589 | 0.912947 | − | 0.408078i | \(-0.133801\pi\) | ||||
0.912947 | + | 0.408078i | \(0.133801\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 1729.42i | − | 0.480065i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1760.77i | 0.482593i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 272.296i | 0.0736962i | 0.999321 | + | 0.0368481i | \(0.0117318\pi\) | ||||
−0.999321 | + | 0.0368481i | \(0.988268\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 5941.82i | − | 1.58816i | −0.607814 | − | 0.794079i | \(-0.707953\pi\) | ||
0.607814 | − | 0.794079i | \(-0.292047\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 235.391 | − | 1466.87i | 0.0613820 | − | 0.382509i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3299.34i | 0.849928i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1323.08 | −0.336735 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3810.08 | −0.958129 | −0.479065 | − | 0.877780i | \(-0.659024\pi\) | ||||
−0.479065 | + | 0.877780i | \(0.659024\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4021.48 | 0.999322 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −605.439 | −0.148683 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3955.09i | 0.959967i | 0.877278 | + | 0.479983i | \(0.159357\pi\) | ||||
−0.877278 | + | 0.479983i | \(0.840643\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 330.860 | + | 26.3782i | 0.0793771 | + | 0.00632842i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1771.93 | −0.420228 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5506.53i | 1.29105i | 0.763737 | + | 0.645527i | \(0.223362\pi\) | ||||
−0.763737 | + | 0.645527i | \(0.776638\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 86.1299i | − | 0.0199657i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2588.90i | 0.593400i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7132.82i | 1.61671i | 0.588694 | + | 0.808356i | \(0.299642\pi\) | ||||
−0.588694 | + | 0.808356i | \(0.700358\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5017.04 | 1.12459 | 0.562294 | − | 0.826937i | \(-0.309919\pi\) | ||||
0.562294 | + | 0.826937i | \(0.309919\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −162.322 | + | 2035.99i | −0.0359859 | + | 0.451369i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 2245.00i | − | 0.492287i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6117.95 | −1.32705 | −0.663524 | − | 0.748155i | \(-0.730940\pi\) | ||||
−0.663524 | + | 0.748155i | \(0.730940\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 788.242 | 0.169143 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5293.44 | 1.12377 | 0.561886 | − | 0.827214i | \(-0.310076\pi\) | ||||
0.561886 | + | 0.827214i | \(0.310076\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 402.940 | 0.0846371 | 0.0423185 | − | 0.999104i | \(-0.486526\pi\) | ||||
0.0423185 | + | 0.999104i | \(0.486526\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − | 1166.23i | − | 0.242391i | ||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −551.803 | + | 6921.23i | −0.113491 | + | 1.42351i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2741.98 | 0.558107 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 2670.86i | − | 0.538037i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 900.733i | − | 0.179595i | −0.995960 | − | 0.0897976i | \(-0.971378\pi\) | ||
0.995960 | − | 0.0897976i | \(-0.0286220\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 321.757i | − | 0.0635031i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 570.549i | − | 0.111470i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6995.84 | −1.35311 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 742.477 | − | 9312.85i | 0.142178 | − | 1.78333i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 2052.44i | − | 0.389141i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −22.3706 | −0.00419980 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2809.28 | 0.522262 | 0.261131 | − | 0.965303i | \(-0.415905\pi\) | ||||
0.261131 | + | 0.965303i | \(0.415905\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1157.01 | −0.213010 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8837.72 | −1.61139 | −0.805693 | − | 0.592333i | \(-0.798207\pi\) | ||||
−0.805693 | + | 0.592333i | \(0.798207\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7844.03i | 1.41652i | 0.705952 | + | 0.708260i | \(0.250519\pi\) | ||||
−0.705952 | + | 0.708260i | \(0.749481\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 57.3762 | − | 719.666i | 0.0102628 | − | 0.128726i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5733.24 | 1.01581 | 0.507904 | − | 0.861414i | \(-0.330421\pi\) | ||||
0.507904 | + | 0.861414i | \(0.330421\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4160.38i | 0.730209i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1025.99i | 0.178395i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 4181.92i | − | 0.720398i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3905.45i | 0.666570i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5423.17 | 0.917132 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7371.49 | + | 587.700i | 1.23527 | + | 0.0984831i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 6075.19i | − | 1.00883i | −0.863461 | − | 0.504415i | \(-0.831708\pi\) | ||
0.863461 | − | 0.504415i | \(-0.168292\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 161.293 | 0.0265430 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1199.13 | −0.195568 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1154.68 | −0.186646 | −0.0933230 | − | 0.995636i | \(-0.529749\pi\) | ||||
−0.0933230 | + | 0.995636i | \(0.529749\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2121.77 | 0.339937 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 1850.74i | − | 0.293910i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6172.37 | + | 1501.81i | 0.971652 | + | 0.236414i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2472.84 | 0.385893 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 3063.66i | − | 0.473965i | −0.971514 | − | 0.236982i | \(-0.923842\pi\) | ||
0.971514 | − | 0.236982i | \(-0.0761583\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7903.85i | 1.21227i | 0.795361 | + | 0.606136i | \(0.207281\pi\) | ||||
−0.795361 | + | 0.606136i | \(0.792719\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 992.538i | 0.150934i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 10440.0i | − | 1.57411i | −0.616880 | − | 0.787057i | \(-0.711603\pi\) | ||
0.616880 | − | 0.787057i | \(-0.288397\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2055.95 | 0.307376 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 205.743 | − | 2580.62i | 0.0305016 | − | 0.382580i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 7891.79i | − | 1.16020i | −0.814544 | − | 0.580101i | \(-0.803013\pi\) | ||
0.814544 | − | 0.580101i | \(-0.196987\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1196.42 | 0.174431 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2653.38 | 0.383655 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2831.65 | −0.406069 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 69.3175 | 0.00985924 | 0.00492962 | − | 0.999988i | \(-0.498431\pi\) | ||||
0.00492962 | + | 0.999988i | \(0.498431\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3374.07i | 0.476009i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 367.120 | + | 29.2690i | 0.0513744 | + | 0.00409588i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1221.71 | 0.169591 | 0.0847956 | − | 0.996398i | \(-0.472976\pi\) | ||||
0.0847956 | + | 0.996398i | \(0.472976\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 3004.70i | − | 0.413766i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 7237.47i | − | 0.988724i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9565.80i | 1.29647i | 0.761440 | + | 0.648235i | \(0.224493\pi\) | ||||
−0.761440 | + | 0.648235i | \(0.775507\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 3847.51i | − | 0.517359i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5413.33 | −0.722215 | −0.361107 | − | 0.932524i | \(-0.617601\pi\) | ||||
−0.361107 | + | 0.932524i | \(0.617601\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1689.73 | − | 134.716i | −0.223680 | − | 0.0178331i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 4539.98i | − | 0.596331i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5222.11 | −0.680647 | −0.340323 | − | 0.940308i | \(-0.610537\pi\) | ||||
−0.340323 | + | 0.940308i | \(0.610537\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8867.24 | 1.14689 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6885.29 | −0.883758 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2542.14 | 0.323820 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 13550.8i | − | 1.71308i | −0.516079 | − | 0.856541i | \(-0.672609\pi\) | ||
0.516079 | − | 0.856541i | \(-0.327391\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4970.92 | + | 396.312i | 0.623702 | + | 0.0497254i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −14908.0 | −1.85654 | −0.928268 | − | 0.371912i | \(-0.878702\pi\) | ||||
−0.928268 | + | 0.371912i | \(0.878702\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3219.59i | 0.397963i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 350.835i | − | 0.0430447i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 378.707i | − | 0.0461223i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 5137.85i | − | 0.621150i | −0.950549 | − | 0.310575i | \(-0.899478\pi\) | ||
0.950549 | − | 0.310575i | \(-0.100522\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1127.07 | 0.135266 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1371.46 | + | 109.341i | 0.163402 | + | 0.0130274i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1910.22i | 0.225949i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4039.91 | 0.474425 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 11861.5 | 1.38299 | 0.691494 | − | 0.722382i | \(-0.256953\pi\) | ||||
0.691494 | + | 0.722382i | \(0.256953\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5965.71 | −0.690619 | −0.345310 | − | 0.938489i | \(-0.612226\pi\) | ||||
−0.345310 | + | 0.938489i | \(0.612226\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3593.57 | 0.413063 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 4950.16i | − | 0.564984i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.60208 | − | 95.3524i | 0.000861570 | − | 0.0108066i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2330.42 | 0.262270 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 9360.31i | − | 1.04610i | −0.852301 | − | 0.523051i | \(-0.824794\pi\) | ||
0.852301 | − | 0.523051i | \(-0.175206\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9022.58i | 1.00138i | 0.865627 | + | 0.500690i | \(0.166920\pi\) | ||||
−0.865627 | + | 0.500690i | \(0.833080\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2558.25i | 0.281974i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 17080.5i | 1.86973i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2551.97 | 0.277446 | 0.138723 | − | 0.990331i | \(-0.455700\pi\) | ||||
0.138723 | + | 0.990331i | \(0.455700\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3048.00 | + | 489.120i | 0.329123 | + | 0.0528150i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14077.7i | 1.50983i | 0.655824 | + | 0.754914i | \(0.272321\pi\) | ||||
−0.655824 | + | 0.754914i | \(0.727679\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3737.75 | 0.398172 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 7320.82 | 0.774637 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −15244.7 | −1.60232 | −0.801162 | − | 0.598448i | \(-0.795784\pi\) | ||||
−0.801162 | + | 0.598448i | \(0.795784\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7922.12 | 0.827135 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 5688.33i | − | 0.589980i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2939.49 | + | 234.354i | 0.302869 | + | 0.0241466i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2533.83 | 0.259360 | 0.129680 | − | 0.991556i | \(-0.458605\pi\) | ||||
0.129680 | + | 0.991556i | \(0.458605\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 1258.04i | − | 0.127931i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9315.46i | 0.941137i | 0.882363 | + | 0.470569i | \(0.155951\pi\) | ||||
−0.882363 | + | 0.470569i | \(0.844049\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 15998.0i | − | 1.60581i | −0.596104 | − | 0.802907i | \(-0.703286\pi\) | ||
0.596104 | − | 0.802907i | \(-0.296714\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 1138.04i | − | 0.113495i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −13869.3 | −1.37430 | −0.687148 | − | 0.726518i | \(-0.741138\pi\) | ||||
−0.687148 | + | 0.726518i | \(0.741138\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 407.492 | − | 5111.15i | 0.0401199 | − | 0.503221i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9594.08i | 0.938582i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −10659.6 | −1.03621 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 9535.25 | 0.921068 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 178.970 | 0.0171791 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −16338.3 | −1.55849 | −0.779245 | − | 0.626719i | \(-0.784397\pi\) | ||||
−0.779245 | + | 0.626719i | \(0.784397\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 658.805i | 0.0624510i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −840.330 | + | 10540.2i | −0.0791642 | + | 0.992952i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3856.09 | −0.361023 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5149.77i | 0.479175i | 0.970875 | + | 0.239588i | \(0.0770122\pi\) | ||||
−0.970875 | + | 0.239588i | \(0.922988\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6319.89i | 0.584448i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1425.88i | 0.131057i | 0.997851 | + | 0.0655287i | \(0.0208734\pi\) | ||||
−0.997851 | + | 0.0655287i | \(0.979127\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9173.51i | 0.838041i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −823.739 | −0.0747966 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −698.662 | + | 8763.28i | −0.0630569 | + | 0.790919i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9498.21i | 0.852101i | 0.904699 | + | 0.426050i | \(0.140095\pi\) | ||||
−0.904699 | + | 0.426050i | \(0.859905\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 248.629 | 0.0221715 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −16057.1 | −1.42336 | −0.711680 | − | 0.702503i | \(-0.752066\pi\) | ||||
−0.711680 | + | 0.702503i | \(0.752066\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2963.25 | −0.261114 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2536.96 | 0.222230 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3313.42i | 0.288536i | 0.989539 | + | 0.144268i | \(0.0460828\pi\) | ||||
−0.989539 | + | 0.144268i | \(0.953917\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 962.262 | − | 12069.6i | 0.0833032 | − | 1.04487i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2423.30 | 0.208560 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1670.45i | 0.142930i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 8437.49i | − | 0.717757i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 13150.7i | − | 1.11224i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 7862.04i | − | 0.661118i | −0.943785 | − | 0.330559i | \(-0.892763\pi\) | ||
0.943785 | − | 0.330559i | \(-0.107237\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −17648.7 | −1.47557 | −0.737784 | − | 0.675037i | \(-0.764127\pi\) | ||||
−0.737784 | + | 0.675037i | \(0.764127\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5884.10 | + | 469.116i | 0.489149 | + | 0.0389979i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 4080.83i | − | 0.337313i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −24050.1 | −1.97666 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 668.580 | 0.0546401 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −13781.5 | −1.11997 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1481.28 | 0.119704 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 8983.97i | 0.721950i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1148.42 | − | 7156.53i | 0.0917739 | − | 0.571899i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −744.076 | −0.0591319 | −0.0295659 | − | 0.999563i | \(-0.509413\pi\) | ||||
−0.0295659 | + | 0.999563i | \(0.509413\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 1555.71i | − | 0.122950i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 7829.78i | − | 0.615396i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 9139.33i | − | 0.714387i | −0.934031 | − | 0.357193i | \(-0.883734\pi\) | ||
0.934031 | − | 0.357193i | \(-0.116266\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 46.4840i | − | 0.00361364i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −17670.5 | −1.36622 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −863.880 | + | 10835.6i | −0.0664303 | + | 0.833231i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − | 232.869i | − | 0.0178104i | ||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6925.09 | −0.526796 | −0.263398 | − | 0.964687i | \(-0.584843\pi\) | ||||
−0.263398 | + | 0.964687i | \(0.584843\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 18543.6 | 1.40306 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2953.81 | −0.222299 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −22776.2 | −1.70497 | −0.852487 | − | 0.522748i | \(-0.824907\pi\) | ||||
−0.852487 | + | 0.522748i | \(0.824907\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 3063.34i | − | 0.228098i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1495.40 | + | 119.222i | 0.110760 | + | 0.00883044i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9189.15 | −0.677028 | −0.338514 | − | 0.940961i | \(-0.609924\pi\) | ||||
−0.338514 | + | 0.940961i | \(0.609924\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7124.04i | 0.522122i | 0.965322 | + | 0.261061i | \(0.0840724\pi\) | ||||
−0.965322 | + | 0.261061i | \(0.915928\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 7740.70i | − | 0.564349i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 20218.3i | 1.46637i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 20110.0i | 1.45094i | 0.688255 | + | 0.725469i | \(0.258377\pi\) | ||||
−0.688255 | + | 0.725469i | \(0.741623\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2583.83 | 0.185458 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8142.11 | − | 649.139i | −0.581397 | − | 0.0463525i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 420.210i | − | 0.0298513i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1432.99 | 0.101277 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −11857.5 | −0.833753 | −0.416876 | − | 0.908963i | \(-0.636875\pi\) | ||||
−0.416876 | + | 0.908963i | \(0.636875\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7860.70 | 0.549906 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6618.83 | 0.460681 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 195.777i | − | 0.0135575i | −0.999977 | − | 0.00677876i | \(-0.997842\pi\) | ||
0.999977 | − | 0.00677876i | \(-0.00215776\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3725.81 | − | 297.044i | −0.256711 | − | 0.0204666i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8566.98 | −0.587308 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 12375.6i | − | 0.844161i | −0.906558 | − | 0.422081i | \(-0.861300\pi\) | ||
0.906558 | − | 0.422081i | \(-0.138700\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 20034.3i | − | 1.35976i | −0.733322 | − | 0.679882i | \(-0.762031\pi\) | ||
0.733322 | − | 0.679882i | \(-0.237969\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 2491.67i | − | 0.168273i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 3830.86i | − | 0.257433i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14743.8 | −0.985883 | −0.492941 | − | 0.870062i | \(-0.664078\pi\) | ||||
−0.492941 | + | 0.870062i | \(0.664078\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −10904.3 | − | 869.354i | −0.725555 | − | 0.0578457i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 14678.0i | 0.971864i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −25967.4 | −1.71095 | −0.855476 | − | 0.517843i | \(-0.826735\pi\) | ||||
−0.855476 | + | 0.517843i | \(0.826735\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4871.37 | 0.319402 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23573.3 | 1.53813 | 0.769064 | − | 0.639172i | \(-0.220723\pi\) | ||||
0.769064 | + | 0.639172i | \(0.220723\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 19905.1 | 1.29250 | 0.646248 | − | 0.763127i | \(-0.276337\pi\) | ||||
0.646248 | + | 0.763127i | \(0.276337\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5138.31i | 0.332034i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1270.18 | + | 15931.8i | −0.0816832 | + | 1.02455i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8941.90 | 0.572282 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 5689.77i | − | 0.362404i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 835.036i | − | 0.0529333i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17257.1i | 1.08874i | 0.838845 | + | 0.544370i | \(0.183231\pi\) | ||||
−0.838845 | + | 0.544370i | \(0.816769\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 6944.68i | − | 0.436061i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5554.89 | −0.347148 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1997.82 | + | 12449.6i | −0.124265 | + | 0.774368i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4272.06i | 0.264476i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −22540.0 | −1.38889 | −0.694443 | − | 0.719547i | \(-0.744349\pi\) | ||||
−0.694443 | + | 0.719547i | \(0.744349\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2084.87 | −0.127868 | −0.0639341 | − | 0.997954i | \(-0.520365\pi\) | ||||
−0.0639341 | + | 0.997954i | \(0.520365\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6554.66 | −0.400139 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −19323.6 | −1.17417 | −0.587087 | − | 0.809524i | \(-0.699725\pi\) | ||||
−0.587087 | + | 0.809524i | \(0.699725\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 1569.78i | − | 0.0949452i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4850.76 | + | 386.732i | 0.292037 | + | 0.0232830i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10267.1 | 0.615287 | 0.307643 | − | 0.951502i | \(-0.400460\pi\) | ||||
0.307643 | + | 0.951502i | \(0.400460\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9940.74i | 0.593003i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 5883.88i | − | 0.349394i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 16592.3i | − | 0.980797i | −0.871498 | − | 0.490398i | \(-0.836851\pi\) | ||
0.871498 | − | 0.490398i | \(-0.163149\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6908.93i | 0.406545i | 0.979122 | + | 0.203272i | \(0.0651577\pi\) | ||||
−0.979122 | + | 0.203272i | \(0.934842\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5138.50 | 0.301000 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 572.181 | − | 7176.84i | 0.0333658 | − | 0.418505i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 37468.0i | − | 2.17506i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8329.90 | −0.481394 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −109.142 | −0.00627923 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −26133.0 | −1.49681 | −0.748404 | − | 0.663243i | \(-0.769180\pi\) | ||||
−0.748404 | + | 0.663243i | \(0.769180\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2868.48 | 0.163567 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5448.04i | 0.309284i | 0.987971 | + | 0.154642i | \(0.0494224\pi\) | ||||
−0.987971 | + | 0.154642i | \(0.950578\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1310.39 | − | 16436.2i | 0.0740623 | − | 0.928959i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7355.05 | 0.413871 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3401.50i | 0.190564i | 0.995450 | + | 0.0952818i | \(0.0303752\pi\) | ||||
−0.995450 | + | 0.0952818i | \(0.969625\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 1627.23i | − | 0.0907639i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1086.99i | 0.0603655i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 731.004i | 0.0404195i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2782.64 | −0.153193 | −0.0765967 | − | 0.997062i | \(-0.524405\pi\) | ||||
−0.0765967 | + | 0.997062i | \(0.524405\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 279.926 | − | 3511.10i | 0.0153442 | − | 0.192461i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 5832.67i | − | 0.318339i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 17468.0 | 0.949281 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 19481.9 | 1.05418 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7163.73 | −0.385978 | −0.192989 | − | 0.981201i | \(-0.561818\pi\) | ||||
−0.192989 | + | 0.981201i | \(0.561818\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1608.49 | 0.0862948 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 5188.27i | − | 0.277165i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1006.98 | − | 12630.5i | 0.0535664 | − | 0.671881i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −30301.5 | −1.60507 | −0.802537 | − | 0.596602i | \(-0.796517\pi\) | ||||
−0.802537 | + | 0.596602i | \(0.796517\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5282.32i | 0.278625i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 16667.6i | 0.875466i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 3364.58i | − | 0.175983i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 816.889i | 0.0425485i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4035.13 | −0.209298 | −0.104649 | − | 0.994509i | \(-0.533372\pi\) | ||||
−0.104649 | + | 0.994509i | \(0.533372\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7120.13 | − | 567.660i | −0.367777 | − | 0.0293215i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 17825.5i | − | 0.916924i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −20916.6 | −1.07148 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 390.945 | 0.0199441 | 0.00997205 | − | 0.999950i | \(-0.496826\pi\) | ||||
0.00997205 | + | 0.999950i | \(0.496826\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −23504.1 | −1.18923 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7225.92i | 0.364114i | 0.983288 | + | 0.182057i | \(0.0582755\pi\) | ||||
−0.983288 | + | 0.182057i | \(0.941724\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 706.174 | − | 4400.60i | 0.0354389 | − | 0.220842i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5850.28 | −0.292399 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 3342.36i | − | 0.166374i | −0.996534 | − | 0.0831872i | \(-0.973490\pi\) | ||
0.996534 | − | 0.0831872i | \(-0.0265100\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9898.03i | 0.490706i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 33993.8i | 1.67848i | 0.543761 | + | 0.839240i | \(0.317000\pi\) | ||||
−0.543761 | + | 0.839240i | \(0.683000\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 10569.5i | − | 0.519782i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3969.25 | −0.194414 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −503.375 | + | 6313.81i | −0.0245567 | + | 0.308013i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 30957.8i | 1.50422i | 0.659039 | + | 0.752109i | \(0.270963\pi\) | ||||
−0.659039 | + | 0.752109i | \(0.729037\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −11430.3 | −0.553176 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8212.61 | −0.395877 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −25919.3 | −1.24446 | −0.622228 | − | 0.782836i | \(-0.713772\pi\) | ||||
−0.622228 | + | 0.782836i | \(0.713772\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 12064.4 | 0.576959 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 29091.1i | 1.38575i | 0.721059 | + | 0.692873i | \(0.243656\pi\) | ||||
−0.721059 | + | 0.692873i | \(0.756344\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 33373.6 | + | 2660.75i | 1.58349 | + | 0.126246i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1816.32 | −0.0858420 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2730.83i | 0.128559i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11075.2i | 0.519352i | 0.965696 | + | 0.259676i | \(0.0836157\pi\) | ||||
−0.965696 | + | 0.259676i | \(0.916384\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11865.3i | 0.554237i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 36140.2i | − | 1.68160i | −0.541350 | − | 0.840798i | \(-0.682086\pi\) | ||
0.541350 | − | 0.840798i | \(-0.317914\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9304.75 | 0.431273 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 992.581 | + | 79.1346i | 0.0458284 | + | 0.00365372i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 33647.8i | 1.54757i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10030.5 | 0.459566 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5315.78 | −0.242619 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 13851.6 | 0.629789 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −28453.9 | −1.28878 | −0.644392 | − | 0.764695i | \(-0.722890\pi\) | ||||
−0.644392 | + | 0.764695i | \(0.722890\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 16519.6i | 0.745391i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 13057.1 | + | 1041.00i | 0.586926 | + | 0.0467933i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 189.865 | 0.00850226 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − | 258.390i | − | 0.0115272i | ||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 22987.4i | − | 1.02165i | −0.859684 | − | 0.510826i | \(-0.829340\pi\) | ||
0.859684 | − | 0.510826i | \(-0.170660\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 18604.4i | − | 0.823750i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7766.69i | 0.342600i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −13815.0 | −0.607124 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 15217.6 | + | 1213.24i | 0.666272 | + | 0.0531193i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 21398.5i | 0.933409i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4688.53 | 0.203758 | 0.101879 | − | 0.994797i | \(-0.467515\pi\) | ||||
0.101879 | + | 0.994797i | \(0.467515\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26381.0 | 1.14225 | 0.571124 | − | 0.820864i | \(-0.306508\pi\) | ||||
0.571124 | + | 0.820864i | \(0.306508\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 15051.1 | 0.649282 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 9124.43 | 0.392166 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 45274.7i | − | 1.93875i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −486.965 | + | 6107.97i | −0.0207765 | + | 0.260598i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1244.52 | 0.0529039 | 0.0264520 | − | 0.999650i | \(-0.491579\pi\) | ||||
0.0264520 | + | 0.999650i | \(0.491579\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 7926.32i | − | 0.335716i | −0.985811 | − | 0.167858i | \(-0.946315\pi\) | ||
0.985811 | − | 0.167858i | \(-0.0536850\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 6735.01i | − | 0.284222i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 32063.4i | − | 1.34819i | −0.738644 | − | 0.674095i | \(-0.764534\pi\) | ||
0.738644 | − | 0.674095i | \(-0.235466\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 41224.4i | − | 1.72712i | −0.504246 | − | 0.863560i | \(-0.668230\pi\) | ||
0.504246 | − | 0.863560i | \(-0.331770\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −18353.9 | −0.766171 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2532.24 | − | 15779.9i | 0.105326 | − | 0.656353i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 358.962i | − | 0.0148771i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2364.73 | 0.0976546 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 25040.7 | 1.03039 | 0.515197 | − | 0.857072i | \(-0.327719\pi\) | ||||
0.515197 | + | 0.857072i | \(0.327719\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14373.1 | 0.589327 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 15880.3 | 0.648810 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 3662.77i | − | 0.149116i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 16328.6 | + | 1301.82i | 0.662407 | + | 0.0528112i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1208.82 | 0.0488652 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3410.59i | 0.137384i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 35611.4i | 1.42944i | 0.699411 | + | 0.714720i | \(0.253446\pi\) | ||||
−0.699411 | + | 0.714720i | \(0.746554\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 3498.68i | − | 0.139944i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 20425.0i | 0.814125i | 0.913400 | + | 0.407063i | \(0.133447\pi\) | ||||
−0.913400 | + | 0.407063i | \(0.866553\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7823.05 | 0.310732 | 0.155366 | − | 0.987857i | \(-0.450344\pi\) | ||||
0.155366 | + | 0.987857i | \(0.450344\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1655.41 | + | 20763.7i | −0.0655240 | + | 0.821863i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 41712.4i | − | 1.64532i | −0.568536 | − | 0.822658i | \(-0.692490\pi\) | ||
0.568536 | − | 0.822658i | \(-0.307510\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −18986.5 | −0.746314 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 8225.94 | 0.322223 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12402.6 | 0.484152 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10177.3 | 0.395916 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 8012.58i | − | 0.310636i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1474.19 | − | 18490.6i | 0.0569561 | − | 0.714397i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10968.2 | 0.422316 | 0.211158 | − | 0.977452i | \(-0.432277\pi\) | ||||
0.211158 | + | 0.977452i | \(0.432277\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 2702.20i | − | 0.103689i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 29482.5i | 1.12746i | 0.825960 | + | 0.563729i | \(0.190634\pi\) | ||||
−0.825960 | + | 0.563729i | \(0.809366\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 39081.9i | 1.48948i | 0.667356 | + | 0.744739i | \(0.267426\pi\) | ||||
−0.667356 | + | 0.744739i | \(0.732574\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − | 965.271i | − | 0.0366636i | ||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −44545.5 | −1.68624 | −0.843118 | − | 0.537728i | \(-0.819283\pi\) | ||||
−0.843118 | + | 0.537728i | \(0.819283\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1887.69 | − | 23677.1i | 0.0712160 | − | 0.893258i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 1711.65i | − | 0.0643573i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 35836.7 | 1.34292 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12970.7 | 0.484429 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −20987.5 | −0.781219 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −17243.3 | −0.639707 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 926.549i | − | 0.0342595i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2227.43 | − | 27938.5i | 0.0820867 | − | 1.02961i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2246.08 | −0.0824995 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 12446.7i | − | 0.455662i | −0.973701 | − | 0.227831i | \(-0.926837\pi\) | ||
0.973701 | − | 0.227831i | \(-0.0731634\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 6157.33i | − | 0.224671i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 5652.41i | − | 0.205568i | −0.994704 | − | 0.102784i | \(-0.967225\pi\) | ||
0.994704 | − | 0.102784i | \(-0.0327751\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9319.56i | 0.337823i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −67.1119 | −0.00242475 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −42371.3 | − | 3378.10i | −1.52587 | − | 0.121652i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 27140.5i | − | 0.974191i | −0.873349 | − | 0.487096i | \(-0.838056\pi\) | ||
0.873349 | − | 0.487096i | \(-0.161944\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8427.85 | 0.301528 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −17449.3 | −0.622266 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1903.97 | 0.0676782 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3471.04 | −0.122981 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3257.14i | 0.115031i | 0.998345 | + | 0.0575153i | \(0.0183178\pi\) | ||||
−0.998345 | + | 0.0575153i | \(0.981682\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 30396.1 | + | 4877.72i | 1.07002 | + | 0.171709i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −26513.2 | −0.930334 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4264.61i | 0.149163i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20532.1i | 0.715852i | 0.933750 | + | 0.357926i | \(0.116516\pi\) | ||||
−0.933750 | + | 0.357926i | \(0.883484\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 23532.1i | 0.817828i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 39190.7i | − | 1.35768i | −0.734284 | − | 0.678842i | \(-0.762482\pi\) | ||
0.734284 | − | 0.678842i | \(-0.237518\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −71345.8 | −2.46378 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 172.129 | − | 2159.00i | 0.00592523 | − | 0.0743198i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 20071.9i | 0.688754i | 0.938831 | + | 0.344377i | \(0.111910\pi\) | ||||
−0.938831 | + | 0.344377i | \(0.888090\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 24032.8 | 0.822064 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 17199.7 | 0.586477 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 21364.2 | 0.726186 | 0.363093 | − | 0.931753i | \(-0.381721\pi\) | ||||
0.363093 | + | 0.931753i | \(0.381721\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −11175.7 | −0.378679 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 12481.1i | 0.421586i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6935.90 | + | 552.972i | 0.233547 | + | 0.0186198i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22120.3 | −0.742517 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3077.96i | 0.102997i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 3730.44i | − | 0.124443i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 437.986i | 0.0145654i | 0.999973 | + | 0.00728268i | \(0.00231817\pi\) | ||||
−0.999973 | + | 0.00728268i | \(0.997682\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 12545.8i | − | 0.415922i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −43517.0 | −1.43824 | −0.719118 | − | 0.694888i | \(-0.755454\pi\) | ||||
−0.719118 | + | 0.694888i | \(0.755454\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 24861.2 | + | 1982.08i | 0.819129 | + | 0.0653059i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 11716.3i | 0.384845i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3333.85 | 0.109170 | 0.0545851 | − | 0.998509i | \(-0.482616\pi\) | ||||
0.0545851 | + | 0.998509i | \(0.482616\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 18235.7 | 0.595317 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 16269.5 | 0.529506 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 10148.5 | 0.329284 | 0.164642 | − | 0.986353i | \(-0.447353\pi\) | ||||
0.164642 | + | 0.986353i | \(0.447353\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 9556.03i | − | 0.309117i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 22114.5 | + | 1763.10i | 0.713182 | + | 0.0568593i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 95999.3 | 3.08655 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 38849.6i | − | 1.24531i | −0.782498 | − | 0.622653i | \(-0.786055\pi\) | ||
0.782498 | − | 0.622653i | \(-0.213945\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 18225.6i | − | 0.582448i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 12368.7i | 0.394085i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 32853.3i | 1.04360i | 0.853066 | + | 0.521802i | \(0.174740\pi\) | ||||
−0.853066 | + | 0.521802i | \(0.825260\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 483.879 | 0.0153246 |
(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 | 1344.4.b.f.895.4 | 8 | ||
4.3 | odd | 2 | 1344.4.b.e.895.4 | 8 | |||
7.6 | odd | 2 | 1344.4.b.e.895.5 | 8 | |||
8.3 | odd | 2 | 336.4.b.f.223.5 | yes | 8 | ||
8.5 | even | 2 | 336.4.b.e.223.5 | yes | 8 | ||
24.5 | odd | 2 | 1008.4.b.i.559.4 | 8 | |||
24.11 | even | 2 | 1008.4.b.k.559.4 | 8 | |||
28.27 | even | 2 | inner | 1344.4.b.f.895.5 | 8 | ||
56.13 | odd | 2 | 336.4.b.f.223.4 | yes | 8 | ||
56.27 | even | 2 | 336.4.b.e.223.4 | ✓ | 8 | ||
168.83 | odd | 2 | 1008.4.b.i.559.5 | 8 | |||
168.125 | even | 2 | 1008.4.b.k.559.5 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
336.4.b.e.223.4 | ✓ | 8 | 56.27 | even | 2 | ||
336.4.b.e.223.5 | yes | 8 | 8.5 | even | 2 | ||
336.4.b.f.223.4 | yes | 8 | 56.13 | odd | 2 | ||
336.4.b.f.223.5 | yes | 8 | 8.3 | odd | 2 | ||
1008.4.b.i.559.4 | 8 | 24.5 | odd | 2 | |||
1008.4.b.i.559.5 | 8 | 168.83 | odd | 2 | |||
1008.4.b.k.559.4 | 8 | 24.11 | even | 2 | |||
1008.4.b.k.559.5 | 8 | 168.125 | even | 2 | |||
1344.4.b.e.895.4 | 8 | 4.3 | odd | 2 | |||
1344.4.b.e.895.5 | 8 | 7.6 | odd | 2 | |||
1344.4.b.f.895.4 | 8 | 1.1 | even | 1 | trivial | ||
1344.4.b.f.895.5 | 8 | 28.27 | even | 2 | inner |