Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8048,2,Mod(1,8048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8048, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("8048.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8048 = 2^{4} \cdot 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8048.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: | \(64.2636035467\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4 x^{11} - 22 x^{10} + 67 x^{9} + 180 x^{8} - 383 x^{7} - 674 x^{6} + 875 x^{5} + 1077 x^{4} + \cdots + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 1006) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(0.753640\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8048.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.49671 | −1.44147 | −0.720737 | − | 0.693208i | \(-0.756197\pi\) | ||||
−0.720737 | + | 0.693208i | \(0.756197\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.79920 | 1.25184 | 0.625920 | − | 0.779887i | \(-0.284723\pi\) | ||||
0.625920 | + | 0.779887i | \(0.284723\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.31469 | −0.496907 | −0.248453 | − | 0.968644i | \(-0.579922\pi\) | ||||
−0.248453 | + | 0.968644i | \(0.579922\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.23355 | 1.07785 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.214910 | −0.0647978 | −0.0323989 | − | 0.999475i | \(-0.510315\pi\) | ||||
−0.0323989 | + | 0.999475i | \(0.510315\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.48880 | 1.24497 | 0.622485 | − | 0.782632i | \(-0.286123\pi\) | ||||
0.622485 | + | 0.782632i | \(0.286123\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −6.98879 | −1.80450 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.531363 | 0.128875 | 0.0644373 | − | 0.997922i | \(-0.479475\pi\) | ||||
0.0644373 | + | 0.997922i | \(0.479475\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.59936 | 1.74341 | 0.871706 | − | 0.490029i | \(-0.163014\pi\) | ||||
0.871706 | + | 0.490029i | \(0.163014\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.28240 | 0.716279 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.80244 | 1.41841 | 0.709203 | − | 0.705004i | \(-0.249055\pi\) | ||||
0.709203 | + | 0.705004i | \(0.249055\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.83553 | 0.567106 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.583104 | −0.112218 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 10.5592 | 1.96080 | 0.980398 | − | 0.197025i | \(-0.0631280\pi\) | ||||
0.980398 | + | 0.197025i | \(0.0631280\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.24171 | −0.582228 | −0.291114 | − | 0.956688i | \(-0.594026\pi\) | ||||
−0.291114 | + | 0.956688i | \(0.594026\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.536567 | 0.0934044 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.68009 | −0.622048 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.24012 | −0.861471 | −0.430736 | − | 0.902478i | \(-0.641746\pi\) | ||||
−0.430736 | + | 0.902478i | \(0.641746\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −11.2072 | −1.79459 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.41910 | 0.533973 | 0.266987 | − | 0.963700i | \(-0.413972\pi\) | ||||
0.266987 | + | 0.963700i | \(0.413972\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.59335 | 1.15798 | 0.578988 | − | 0.815336i | \(-0.303448\pi\) | ||||
0.578988 | + | 0.815336i | \(0.303448\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 9.05136 | 1.34930 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.87068 | 0.856327 | 0.428164 | − | 0.903701i | \(-0.359161\pi\) | ||||
0.428164 | + | 0.903701i | \(0.359161\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.27159 | −0.753084 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.32666 | −0.185769 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.35707 | 0.461129 | 0.230564 | − | 0.973057i | \(-0.425943\pi\) | ||||
0.230564 | + | 0.973057i | \(0.425943\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.601576 | −0.0811165 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −18.9734 | −2.51308 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.93028 | 1.29281 | 0.646406 | − | 0.762993i | \(-0.276271\pi\) | ||||
0.646406 | + | 0.762993i | \(0.276271\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.7166 | −1.37213 | −0.686063 | − | 0.727542i | \(-0.740662\pi\) | ||||
−0.686063 | + | 0.727542i | \(0.740662\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.25112 | −0.535591 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 12.5651 | 1.55850 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −13.4958 | −1.64877 | −0.824387 | − | 0.566027i | \(-0.808480\pi\) | ||||
−0.824387 | + | 0.566027i | \(0.808480\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −16.9837 | −2.04460 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.31548 | −0.393475 | −0.196737 | − | 0.980456i | \(-0.563035\pi\) | ||||
−0.196737 | + | 0.980456i | \(0.563035\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.20600 | −0.258193 | −0.129096 | − | 0.991632i | \(-0.541208\pi\) | ||||
−0.129096 | + | 0.991632i | \(0.541208\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −7.07948 | −0.817468 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.282540 | 0.0321985 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.11263 | 0.350198 | 0.175099 | − | 0.984551i | \(-0.443975\pi\) | ||||
0.175099 | + | 0.984551i | \(0.443975\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.24481 | −0.916090 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.88502 | 0.426436 | 0.213218 | − | 0.977005i | \(-0.431606\pi\) | ||||
0.213218 | + | 0.977005i | \(0.431606\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.48739 | 0.161330 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −26.3633 | −2.82644 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.38189 | −0.676479 | −0.338240 | − | 0.941060i | \(-0.609831\pi\) | ||||
−0.338240 | + | 0.941060i | \(0.609831\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.90139 | −0.618634 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.09360 | 0.839268 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 21.2721 | 2.18247 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.8118 | 1.30084 | 0.650419 | − | 0.759575i | \(-0.274593\pi\) | ||||
0.650419 | + | 0.759575i | \(0.274593\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.694922 | −0.0698423 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.1509 | 1.20906 | 0.604530 | − | 0.796582i | \(-0.293361\pi\) | ||||
0.604530 | + | 0.796582i | \(0.293361\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.64846 | −0.359494 | −0.179747 | − | 0.983713i | \(-0.557528\pi\) | ||||
−0.179747 | + | 0.983713i | \(0.557528\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 9.18810 | 0.896667 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.15421 | −0.594950 | −0.297475 | − | 0.954730i | \(-0.596144\pi\) | ||||
−0.297475 | + | 0.954730i | \(0.596144\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 16.0449 | 1.53683 | 0.768413 | − | 0.639954i | \(-0.221047\pi\) | ||||
0.768413 | + | 0.639954i | \(0.221047\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 13.0831 | 1.24179 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.87399 | 0.646651 | 0.323325 | − | 0.946288i | \(-0.395199\pi\) | ||||
0.323325 | + | 0.946288i | \(0.395199\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 19.0414 | 1.77562 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 14.5148 | 1.34189 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.698579 | −0.0640386 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9538 | −0.995801 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −8.53648 | −0.769709 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.05879 | −0.541915 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.45181 | −0.838713 | −0.419356 | − | 0.907822i | \(-0.637744\pi\) | ||||
−0.419356 | + | 0.907822i | \(0.637744\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −18.9584 | −1.66919 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.60429 | −0.839131 | −0.419566 | − | 0.907725i | \(-0.637818\pi\) | ||||
−0.419566 | + | 0.907725i | \(0.637818\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −9.99081 | −0.866313 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.63223 | −0.140480 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.2873 | 1.04977 | 0.524887 | − | 0.851172i | \(-0.324107\pi\) | ||||
0.524887 | + | 0.851172i | \(0.324107\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.3864 | 1.30506 | 0.652530 | − | 0.757763i | \(-0.273708\pi\) | ||||
0.652530 | + | 0.757763i | \(0.273708\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −14.6574 | −1.23437 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.964689 | −0.0806714 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 29.5574 | 2.45461 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 13.1616 | 1.08555 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12.5606 | −1.02901 | −0.514503 | − | 0.857489i | \(-0.672024\pi\) | ||||
−0.514503 | + | 0.857489i | \(0.672024\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.82680 | −0.636936 | −0.318468 | − | 0.947934i | \(-0.603168\pi\) | ||||
−0.318468 | + | 0.947934i | \(0.603168\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.71819 | 0.138907 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.07420 | −0.728857 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −18.6010 | −1.48452 | −0.742262 | − | 0.670109i | \(-0.766247\pi\) | ||||
−0.742262 | + | 0.670109i | \(0.766247\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −8.38161 | −0.664705 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.94311 | −0.704816 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.36672 | 0.577006 | 0.288503 | − | 0.957479i | \(-0.406842\pi\) | ||||
0.288503 | + | 0.957479i | \(0.406842\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.50196 | 0.116927 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −12.6120 | −0.975948 | −0.487974 | − | 0.872858i | \(-0.662264\pi\) | ||||
−0.487974 | + | 0.872858i | \(0.662264\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.14937 | 0.549951 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 24.5729 | 1.87914 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 14.5677 | 1.10756 | 0.553780 | − | 0.832663i | \(-0.313185\pi\) | ||||
0.553780 | + | 0.832663i | \(0.313185\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.72785 | −0.281799 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −24.7930 | −1.86356 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −14.8248 | −1.10806 | −0.554028 | − | 0.832498i | \(-0.686910\pi\) | ||||
−0.554028 | + | 0.832498i | \(0.686910\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.29653 | −0.0963700 | −0.0481850 | − | 0.998838i | \(-0.515344\pi\) | ||||
−0.0481850 | + | 0.998838i | \(0.515344\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 26.7563 | 1.97788 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −14.6682 | −1.07842 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.114195 | −0.00835079 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.766602 | 0.0557621 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.61849 | 0.478897 | 0.239449 | − | 0.970909i | \(-0.423033\pi\) | ||||
0.239449 | + | 0.970909i | \(0.423033\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −15.2763 | −1.09961 | −0.549806 | − | 0.835293i | \(-0.685298\pi\) | ||||
−0.549806 | + | 0.835293i | \(0.685298\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −31.3713 | −2.24655 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.2507 | 1.30031 | 0.650154 | − | 0.759803i | \(-0.274705\pi\) | ||||
0.650154 | + | 0.759803i | \(0.274705\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.96715 | 0.281224 | 0.140612 | − | 0.990065i | \(-0.455093\pi\) | ||||
0.140612 | + | 0.990065i | \(0.455093\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 33.6950 | 2.37666 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −13.8821 | −0.974333 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.57074 | 0.668449 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 21.9960 | 1.52883 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.63318 | −0.112969 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.4060 | −0.922908 | −0.461454 | − | 0.887164i | \(-0.652672\pi\) | ||||
−0.461454 | + | 0.887164i | \(0.652672\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8.27777 | 0.567184 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 21.2553 | 1.44960 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.26185 | 0.289313 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.50774 | 0.372178 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.38519 | 0.160445 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 24.7289 | 1.65597 | 0.827985 | − | 0.560751i | \(-0.189487\pi\) | ||||
0.827985 | + | 0.560751i | \(0.189487\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 9.16882 | 0.611255 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −15.5037 | −1.02902 | −0.514509 | − | 0.857485i | \(-0.672026\pi\) | ||||
−0.514509 | + | 0.857485i | \(0.672026\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.7101 | −0.707745 | −0.353873 | − | 0.935294i | \(-0.615135\pi\) | ||||
−0.353873 | + | 0.935294i | \(0.615135\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.705421 | −0.0464133 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 21.8231 | 1.42968 | 0.714840 | − | 0.699288i | \(-0.246500\pi\) | ||||
0.714840 | + | 0.699288i | \(0.246500\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 16.4332 | 1.07199 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −7.77133 | −0.504802 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.2065 | 0.660201 | 0.330101 | − | 0.943946i | \(-0.392917\pi\) | ||||
0.330101 | + | 0.943946i | \(0.392917\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.9915 | −0.965690 | −0.482845 | − | 0.875706i | \(-0.660397\pi\) | ||||
−0.482845 | + | 0.875706i | \(0.660397\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 22.3342 | 1.43274 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −14.7562 | −0.942741 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 34.1120 | 2.17050 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −9.69975 | −0.614696 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −19.8887 | −1.25536 | −0.627682 | − | 0.778470i | \(-0.715996\pi\) | ||||
−0.627682 | + | 0.778470i | \(0.715996\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.46191 | −0.0919096 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.71359 | −0.232554 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −30.4500 | −1.89942 | −0.949709 | − | 0.313135i | \(-0.898621\pi\) | ||||
−0.949709 | + | 0.313135i | \(0.898621\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.88915 | 0.428071 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 34.1437 | 2.11344 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.72105 | 0.291112 | 0.145556 | − | 0.989350i | \(-0.453503\pi\) | ||||
0.145556 | + | 0.989350i | \(0.453503\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.39710 | 0.577260 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 15.9337 | 0.975128 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −21.3513 | −1.30181 | −0.650907 | − | 0.759158i | \(-0.725611\pi\) | ||||
−0.650907 | + | 0.759158i | \(0.725611\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.0054 | −0.607783 | −0.303891 | − | 0.952707i | \(-0.598286\pi\) | ||||
−0.303891 | + | 0.952707i | \(0.598286\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 14.7341 | 0.891746 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.609383 | −0.0367472 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −22.6138 | −1.35873 | −0.679367 | − | 0.733799i | \(-0.737745\pi\) | ||||
−0.679367 | + | 0.733799i | \(0.737745\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −10.4822 | −0.627555 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.5518 | 1.34533 | 0.672663 | − | 0.739949i | \(-0.265151\pi\) | ||||
0.672663 | + | 0.739949i | \(0.265151\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 21.6726 | 1.28830 | 0.644152 | − | 0.764898i | \(-0.277211\pi\) | ||||
0.644152 | + | 0.764898i | \(0.277211\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −53.1103 | −3.14598 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.49506 | −0.265335 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.7177 | −0.983391 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −31.9873 | −1.87513 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.0357357 | 0.00208770 | 0.00104385 | − | 0.999999i | \(-0.499668\pi\) | ||||
0.00104385 | + | 0.999999i | \(0.499668\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 27.7969 | 1.61840 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.125315 | 0.00727151 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 30.5348 | 1.76587 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.98292 | −0.575406 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −30.3373 | −1.74283 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −29.9980 | −1.71768 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 32.1186 | 1.83311 | 0.916554 | − | 0.399911i | \(-0.130959\pi\) | ||||
0.916554 | + | 0.399911i | \(0.130959\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 9.10914 | 0.518201 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.2371 | 0.580492 | 0.290246 | − | 0.956952i | \(-0.406263\pi\) | ||||
0.290246 | + | 0.956952i | \(0.406263\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.28376 | −0.355179 | −0.177589 | − | 0.984105i | \(-0.556830\pi\) | ||||
−0.177589 | + | 0.984105i | \(0.556830\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −11.8997 | −0.670474 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −11.3267 | −0.636173 | −0.318087 | − | 0.948062i | \(-0.603040\pi\) | ||||
−0.318087 | + | 0.948062i | \(0.603040\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.26928 | −0.127055 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 15.3653 | 0.857605 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.03802 | 0.224681 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12.7281 | 0.706030 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −40.0595 | −2.21530 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.71814 | −0.425515 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −21.5175 | −1.18271 | −0.591355 | − | 0.806411i | \(-0.701407\pi\) | ||||
−0.591355 | + | 0.806411i | \(0.701407\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −16.9442 | −0.928536 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −37.7774 | −2.06400 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.19687 | 0.337565 | 0.168783 | − | 0.985653i | \(-0.446016\pi\) | ||||
0.168783 | + | 0.985653i | \(0.446016\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −17.1623 | −0.932131 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.696676 | 0.0377271 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.1334 | 0.871119 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −47.5408 | −2.55951 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −19.6683 | −1.05585 | −0.527924 | − | 0.849292i | \(-0.677029\pi\) | ||||
−0.527924 | + | 0.849292i | \(0.677029\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 32.0717 | 1.71676 | 0.858379 | − | 0.513015i | \(-0.171472\pi\) | ||||
0.858379 | + | 0.513015i | \(0.171472\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.61744 | −0.139709 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.66289 | −0.0885065 | −0.0442532 | − | 0.999020i | \(-0.514091\pi\) | ||||
−0.0442532 | + | 0.999020i | \(0.514091\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.28068 | −0.492568 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.74415 | 0.0923101 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.62921 | 0.349876 | 0.174938 | − | 0.984579i | \(-0.444027\pi\) | ||||
0.174938 | + | 0.984579i | \(0.444027\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 38.7502 | 2.03949 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 27.3485 | 1.43542 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.17504 | −0.323216 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.90874 | −0.151835 | −0.0759174 | − | 0.997114i | \(-0.524189\pi\) | ||||
−0.0759174 | + | 0.997114i | \(0.524189\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 11.0558 | 0.575543 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.41351 | −0.229138 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.59871 | 0.186334 | 0.0931671 | − | 0.995650i | \(-0.470301\pi\) | ||||
0.0931671 | + | 0.995650i | \(0.470301\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 15.1270 | 0.781157 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 47.3982 | 2.44113 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.9376 | −0.870026 | −0.435013 | − | 0.900424i | \(-0.643256\pi\) | ||||
−0.435013 | + | 0.900424i | \(0.643256\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 23.5984 | 1.20898 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 18.1570 | 0.927781 | 0.463891 | − | 0.885893i | \(-0.346453\pi\) | ||||
0.463891 | + | 0.885893i | \(0.346453\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.790888 | 0.0403074 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 24.5535 | 1.24812 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.79403 | −0.344471 | −0.172235 | − | 0.985056i | \(-0.555099\pi\) | ||||
−0.172235 | + | 0.985056i | \(0.555099\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.61457 | 0.182796 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 23.9791 | 1.20959 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.71288 | 0.438393 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.28781 | −0.165010 | −0.0825052 | − | 0.996591i | \(-0.526292\pi\) | ||||
−0.0825052 | + | 0.996591i | \(0.526292\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 24.9441 | 1.24877 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 24.3263 | 1.21480 | 0.607399 | − | 0.794397i | \(-0.292213\pi\) | ||||
0.607399 | + | 0.794397i | \(0.292213\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −14.5514 | −0.724857 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −23.0789 | −1.14680 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.12616 | 0.0558214 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16.6999 | 0.825755 | 0.412878 | − | 0.910787i | \(-0.364524\pi\) | ||||
0.412878 | + | 0.910787i | \(0.364524\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −30.6778 | −1.51322 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −13.0553 | −0.642407 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10.8749 | 0.533830 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −38.4154 | −1.88121 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8.61001 | −0.420627 | −0.210313 | − | 0.977634i | \(-0.567448\pi\) | ||||
−0.210313 | + | 0.977634i | \(0.567448\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.16303 | −0.349105 | −0.174552 | − | 0.984648i | \(-0.555848\pi\) | ||||
−0.174552 | + | 0.984648i | \(0.555848\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 18.9831 | 0.922992 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.50670 | 0.0730855 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 14.0891 | 0.681818 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.40855 | 0.116286 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.82687 | −0.136165 | −0.0680827 | − | 0.997680i | \(-0.521688\pi\) | ||||
−0.0680827 | + | 0.997680i | \(0.521688\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.8263 | 0.568336 | 0.284168 | − | 0.958775i | \(-0.408283\pi\) | ||||
0.284168 | + | 0.958775i | \(0.408283\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −73.7961 | −3.53825 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 51.6942 | 2.47287 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.1184 | 0.769287 | 0.384644 | − | 0.923065i | \(-0.374324\pi\) | ||||
0.384644 | + | 0.923065i | \(0.374324\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −17.0459 | −0.811711 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 33.1314 | 1.57412 | 0.787060 | − | 0.616877i | \(-0.211602\pi\) | ||||
0.787060 | + | 0.616877i | \(0.211602\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −17.8642 | −0.846844 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 31.3602 | 1.48329 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.39951 | −0.160433 | −0.0802164 | − | 0.996777i | \(-0.525561\pi\) | ||||
−0.0802164 | + | 0.996777i | \(0.525561\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.734798 | −0.0346003 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 19.5412 | 0.918127 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −16.5192 | −0.774432 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −35.5847 | −1.66458 | −0.832291 | − | 0.554338i | \(-0.812971\pi\) | ||||
−0.832291 | + | 0.554338i | \(0.812971\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.309840 | −0.0144621 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 34.9030 | 1.62560 | 0.812798 | − | 0.582545i | \(-0.197943\pi\) | ||||
0.812798 | + | 0.582545i | \(0.197943\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.3855 | −0.668550 | −0.334275 | − | 0.942476i | \(-0.608491\pi\) | ||||
−0.334275 | + | 0.942476i | \(0.608491\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 22.6556 | 1.05063 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −14.3321 | −0.663213 | −0.331606 | − | 0.943418i | \(-0.607591\pi\) | ||||
−0.331606 | + | 0.943418i | \(0.607591\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 17.7428 | 0.819286 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 46.4414 | 2.13990 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.63189 | −0.0750343 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 21.5482 | 0.988699 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.8552 | 0.497027 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 36.3487 | 1.66082 | 0.830408 | − | 0.557156i | \(-0.188108\pi\) | ||||
0.830408 | + | 0.557156i | \(0.188108\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −23.5219 | −1.07251 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 22.3283 | 1.01597 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 35.8627 | 1.62844 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 33.5406 | 1.51987 | 0.759935 | − | 0.650000i | \(-0.225231\pi\) | ||||
0.759935 | + | 0.650000i | \(0.225231\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −18.3925 | −0.831739 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −37.3160 | −1.68405 | −0.842024 | − | 0.539441i | \(-0.818636\pi\) | ||||
−0.842024 | + | 0.539441i | \(0.818636\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.61078 | 0.252697 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.94523 | −0.0874314 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.35883 | 0.195520 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.12726 | −0.139995 | −0.0699977 | − | 0.997547i | \(-0.522299\pi\) | ||||
−0.0699977 | + | 0.997547i | \(0.522299\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 31.4886 | 1.40680 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.00000 | −0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 34.0128 | 1.51355 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −17.8499 | −0.792741 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 38.0821 | 1.68796 | 0.843980 | − | 0.536375i | \(-0.180207\pi\) | ||||
0.843980 | + | 0.536375i | \(0.180207\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.90021 | 0.128298 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.43122 | −0.195643 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −10.2128 | −0.450029 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.26167 | −0.0554881 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −36.3713 | −1.59652 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −23.0831 | −1.01129 | −0.505645 | − | 0.862742i | \(-0.668745\pi\) | ||||
−0.505645 | + | 0.862742i | \(0.668745\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −26.4097 | −1.15482 | −0.577409 | − | 0.816455i | \(-0.695936\pi\) | ||||
−0.577409 | + | 0.816455i | \(0.695936\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 9.30734 | 0.406206 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.72253 | −0.0750344 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 23.2732 | 1.01188 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 32.1100 | 1.39346 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 15.3477 | 0.664781 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −17.2269 | −0.744783 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 37.0132 | 1.59724 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.13292 | 0.0487982 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.30510 | −0.228084 | −0.114042 | − | 0.993476i | \(-0.536380\pi\) | ||||
−0.114042 | + | 0.993476i | \(0.536380\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.23704 | 0.138915 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 44.9130 | 1.92386 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.08255 | 0.388342 | 0.194171 | − | 0.980968i | \(-0.437798\pi\) | ||||
0.194171 | + | 0.980968i | \(0.437798\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −34.6528 | −1.47895 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 80.2432 | 3.41848 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.09215 | −0.174016 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 36.6221 | 1.55452 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.19469 | −0.0929922 | −0.0464961 | − | 0.998918i | \(-0.514806\pi\) | ||||
−0.0464961 | + | 0.998918i | \(0.514806\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 34.0851 | 1.44165 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.285112 | 0.0120375 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 36.1536 | 1.52369 | 0.761846 | − | 0.647758i | \(-0.224293\pi\) | ||||
0.761846 | + | 0.647758i | \(0.224293\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 19.2417 | 0.809504 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 10.8394 | 0.455211 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −16.2612 | −0.681706 | −0.340853 | − | 0.940117i | \(-0.610716\pi\) | ||||
−0.340853 | + | 0.940117i | \(0.610716\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12.2329 | −0.511932 | −0.255966 | − | 0.966686i | \(-0.582394\pi\) | ||||
−0.255966 | + | 0.966686i | \(0.582394\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −16.5244 | −0.690318 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 19.2885 | 0.804386 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 30.4384 | 1.26717 | 0.633584 | − | 0.773674i | \(-0.281583\pi\) | ||||
0.633584 | + | 0.773674i | \(0.281583\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 38.1404 | 1.58506 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.10760 | −0.211899 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.721467 | −0.0298801 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 40.6298 | 1.67983 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.33753 | −0.0552056 | −0.0276028 | − | 0.999619i | \(-0.508787\pi\) | ||||
−0.0276028 | + | 0.999619i | \(0.508787\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −24.6349 | −1.01506 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −45.5666 | −1.87436 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 39.2257 | 1.61081 | 0.805404 | − | 0.592726i | \(-0.201948\pi\) | ||||
0.805404 | + | 0.592726i | \(0.201948\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.95546 | −0.0801662 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −9.90481 | −0.405377 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.25729 | −0.173948 | −0.0869741 | − | 0.996211i | \(-0.527720\pi\) | ||||
−0.0869741 | + | 0.996211i | \(0.527720\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.16250 | −0.129001 | −0.0645005 | − | 0.997918i | \(-0.520545\pi\) | ||||
−0.0645005 | + | 0.997918i | \(0.520545\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −43.6393 | −1.77713 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −30.6619 | −1.24658 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −27.6650 | −1.12289 | −0.561445 | − | 0.827514i | \(-0.689754\pi\) | ||||
−0.561445 | + | 0.827514i | \(0.689754\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 34.6596 | 1.40448 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 26.3523 | 1.06610 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 36.3191 | 1.46691 | 0.733457 | − | 0.679736i | \(-0.237906\pi\) | ||||
0.733457 | + | 0.679736i | \(0.237906\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −23.8953 | −0.963553 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.90613 | −0.157255 | −0.0786273 | − | 0.996904i | \(-0.525054\pi\) | ||||
−0.0786273 | + | 0.996904i | \(0.525054\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −17.7479 | −0.713348 | −0.356674 | − | 0.934229i | \(-0.616089\pi\) | ||||
−0.356674 | + | 0.934229i | \(0.616089\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.96653 | −0.159171 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.39022 | 0.336147 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.1374 | −1.24550 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.07757 | 0.162842 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.78441 | −0.111022 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.6000 | 0.541407 | 0.270703 | − | 0.962663i | \(-0.412744\pi\) | ||||
0.270703 | + | 0.962663i | \(0.412744\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 33.4709 | 1.33035 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −26.4575 | −1.04993 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −23.6631 | −0.937567 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −10.7208 | −0.424106 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 13.9364 | 0.550456 | 0.275228 | − | 0.961379i | \(-0.411247\pi\) | ||||
0.275228 | + | 0.961379i | \(0.411247\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −18.5556 | −0.731763 | −0.365881 | − | 0.930662i | \(-0.619232\pi\) | ||||
−0.365881 | + | 0.930662i | \(0.619232\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −53.0683 | −2.08956 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 13.8632 | 0.545018 | 0.272509 | − | 0.962153i | \(-0.412146\pi\) | ||||
0.272509 | + | 0.962153i | \(0.412146\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.13412 | −0.0837714 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −10.6406 | −0.417038 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −26.8331 | −1.05006 | −0.525031 | − | 0.851083i | \(-0.675946\pi\) | ||||
−0.525031 | + | 0.851083i | \(0.675946\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −26.8844 | −1.05046 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −7.13321 | −0.278293 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19.2991 | −0.751785 | −0.375892 | − | 0.926663i | \(-0.622664\pi\) | ||||
−0.375892 | + | 0.926663i | \(0.622664\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.1669 | 0.473238 | 0.236619 | − | 0.971603i | \(-0.423961\pi\) | ||||
0.236619 | + | 0.971603i | \(0.423961\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.95511 | −0.231277 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −27.9663 | −1.08449 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 71.8284 | 2.78121 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −61.7408 | −2.38704 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.30311 | 0.0889107 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16.8266 | 0.648618 | 0.324309 | − | 0.945951i | \(-0.394868\pi\) | ||||
0.324309 | + | 0.945951i | \(0.394868\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.65341 | −0.0636397 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9.81619 | 0.377267 | 0.188633 | − | 0.982048i | \(-0.439594\pi\) | ||||
0.188633 | + | 0.982048i | \(0.439594\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −16.8435 | −0.646395 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 38.7082 | 1.48330 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −43.0568 | −1.64752 | −0.823761 | − | 0.566937i | \(-0.808128\pi\) | ||||
−0.823761 | + | 0.566937i | \(0.808128\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 34.3946 | 1.31415 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 26.7401 | 1.02020 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 15.0692 | 0.574091 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −31.0812 | −1.18239 | −0.591193 | − | 0.806530i | \(-0.701343\pi\) | ||||
−0.591193 | + | 0.806530i | \(0.701343\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.913608 | 0.0347051 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 43.0697 | 1.63373 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.81678 | 0.0688155 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −54.4859 | −2.06085 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −14.9328 | −0.564003 | −0.282002 | − | 0.959414i | \(-0.590998\pi\) | ||||
−0.282002 | + | 0.959414i | \(0.590998\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −39.8216 | −1.50190 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −41.0290 | −1.54524 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −15.9747 | −0.600790 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17.7868 | 0.667998 | 0.333999 | − | 0.942573i | \(-0.391602\pi\) | ||||
0.333999 | + | 0.942573i | \(0.391602\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 10.0648 | 0.377461 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −22.0515 | −0.825837 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.70036 | −0.100988 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −25.4825 | −0.951663 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.34669 | −0.0875169 | −0.0437585 | − | 0.999042i | \(-0.513933\pi\) | ||||
−0.0437585 | + | 0.999042i | \(0.513933\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.79660 | 0.178635 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 37.4295 | 1.39202 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 29.9409 | 1.11198 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13.2559 | −0.491636 | −0.245818 | − | 0.969316i | \(-0.579056\pi\) | ||||
−0.245818 | + | 0.969316i | \(0.579056\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −31.0275 | −1.14917 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.03483 | 0.149234 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 41.9658 | 1.55004 | 0.775021 | − | 0.631936i | \(-0.217739\pi\) | ||||
0.775021 | + | 0.631936i | \(0.217739\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 36.8420 | 1.35894 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.90038 | 0.106837 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15.7393 | 0.578979 | 0.289489 | − | 0.957181i | \(-0.406514\pi\) | ||||
0.289489 | + | 0.957181i | \(0.406514\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −85.1678 | −3.12872 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 48.6983 | 1.78657 | 0.893284 | − | 0.449494i | \(-0.148396\pi\) | ||||
0.893284 | + | 0.449494i | \(0.148396\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −35.1597 | −1.28815 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 12.5624 | 0.459634 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.09089 | 0.295635 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 19.3337 | 0.705496 | 0.352748 | − | 0.935718i | \(-0.385247\pi\) | ||||
0.352748 | + | 0.935718i | \(0.385247\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 49.6563 | 1.80958 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −21.9088 | −0.797343 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −49.3985 | −1.79542 | −0.897710 | − | 0.440587i | \(-0.854770\pi\) | ||||
−0.897710 | + | 0.440587i | \(0.854770\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.64997 | 0.132485 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −10.3490 | −0.375153 | −0.187576 | − | 0.982250i | \(-0.560063\pi\) | ||||
−0.187576 | + | 0.982250i | \(0.560063\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −21.0941 | −0.763659 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.80956 | 0.173890 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 44.5751 | 1.60951 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 15.7765 | 0.568914 | 0.284457 | − | 0.958689i | \(-0.408187\pi\) | ||||
0.284457 | + | 0.958689i | \(0.408187\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 76.0247 | 2.73796 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −33.7577 | −1.21418 | −0.607089 | − | 0.794634i | \(-0.707663\pi\) | ||||
−0.607089 | + | 0.794634i | \(0.707663\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.19196 | −0.330185 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −17.2002 | −0.617053 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 25.9829 | 0.930935 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.712529 | 0.0254963 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6.15712 | −0.220038 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −52.0681 | −1.85839 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 29.6976 | 1.05861 | 0.529303 | − | 0.848433i | \(-0.322453\pi\) | ||||
0.529303 | + | 0.848433i | \(0.322453\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −11.7871 | −0.419631 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.03718 | −0.321325 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −48.1049 | −1.70826 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −23.4618 | −0.832105 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 22.0734 | 0.781882 | 0.390941 | − | 0.920416i | \(-0.372150\pi\) | ||||
0.390941 | + | 0.920416i | \(0.372150\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.11947 | 0.110359 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −20.6362 | −0.729143 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.474091 | 0.0167303 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −25.0336 | −0.882317 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 53.3080 | 1.87653 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 30.0030 | 1.05485 | 0.527424 | − | 0.849602i | \(-0.323158\pi\) | ||||
0.527424 | + | 0.849602i | \(0.323158\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19.1169 | 0.671287 | 0.335643 | − | 0.941989i | \(-0.391046\pi\) | ||||
0.335643 | + | 0.941989i | \(0.391046\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 24.9805 | 0.876104 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 20.6209 | 0.722320 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 57.7046 | 2.01883 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −19.0824 | −0.666795 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 25.6672 | 0.895792 | 0.447896 | − | 0.894086i | \(-0.352173\pi\) | ||||
0.447896 | + | 0.894086i | \(0.352173\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11.1225 | −0.387705 | −0.193853 | − | 0.981031i | \(-0.562098\pi\) | ||||
−0.193853 | + | 0.981031i | \(0.562098\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.52145 | 0.0529702 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 36.5469 | 1.27086 | 0.635430 | − | 0.772158i | \(-0.280823\pi\) | ||||
0.635430 | + | 0.772158i | \(0.280823\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −12.9358 | −0.449277 | −0.224639 | − | 0.974442i | \(-0.572120\pi\) | ||||
−0.224639 | + | 0.974442i | \(0.572120\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 56.4601 | 1.95858 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.80113 | −0.0970533 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −35.3036 | −1.22173 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.89025 | 0.0653368 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 12.5439 | 0.433062 | 0.216531 | − | 0.976276i | \(-0.430526\pi\) | ||||
0.216531 | + | 0.976276i | \(0.430526\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 82.4970 | 2.84472 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −56.3051 | −1.93925 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 20.0125 | 0.688451 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 14.4009 | 0.494820 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −54.1102 | −1.85706 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −35.6456 | −1.22192 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10.9760 | 0.375813 | 0.187906 | − | 0.982187i | \(-0.439830\pi\) | ||||
0.187906 | + | 0.982187i | \(0.439830\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 68.7845 | 2.35238 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −36.4080 | −1.24367 | −0.621837 | − | 0.783146i | \(-0.713614\pi\) | ||||
−0.621837 | + | 0.783146i | \(0.713614\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −21.8751 | −0.746370 | −0.373185 | − | 0.927757i | \(-0.621734\pi\) | ||||
−0.373185 | + | 0.927757i | \(0.621734\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 11.2228 | 0.382474 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −55.3352 | −1.88363 | −0.941817 | − | 0.336127i | \(-0.890883\pi\) | ||||
−0.941817 | + | 0.336127i | \(0.890883\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 40.7779 | 1.38649 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 41.7391 | 1.41753 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.668936 | −0.0226921 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −60.5800 | −2.05267 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 41.4275 | 1.40211 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 7.96544 | 0.269281 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 43.4681 | 1.46781 | 0.733907 | − | 0.679250i | \(-0.237695\pi\) | ||||
0.733907 | + | 0.679250i | \(0.237695\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −0.0892216 | −0.00300937 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −12.7587 | −0.429851 | −0.214925 | − | 0.976630i | \(-0.568951\pi\) | ||||
−0.214925 | + | 0.976630i | \(0.568951\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 29.3044 | 0.986172 | 0.493086 | − | 0.869981i | \(-0.335869\pi\) | ||||
0.493086 | + | 0.869981i | \(0.335869\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −69.4006 | −2.33288 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −39.5947 | −1.32946 | −0.664730 | − | 0.747084i | \(-0.731453\pi\) | ||||
−0.664730 | + | 0.747084i | \(0.731453\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 12.4262 | 0.416762 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.77189 | 0.0593606 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 44.6134 | 1.49293 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −41.4976 | −1.38711 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −76.2365 | −2.54546 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −34.2299 | −1.14163 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.78382 | 0.0594277 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 24.9244 | 0.829433 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −3.62923 | −0.120640 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.16892 | −0.105222 | −0.0526111 | − | 0.998615i | \(-0.516754\pi\) | ||||
−0.0526111 | + | 0.998615i | \(0.516754\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 39.2905 | 1.30319 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.58375 | 0.184998 | 0.0924989 | − | 0.995713i | \(-0.470515\pi\) | ||||
0.0924989 | + | 0.995713i | \(0.470515\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.834929 | −0.0276321 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 74.8963 | 2.47600 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 12.6267 | 0.416970 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −56.4947 | −1.86359 | −0.931794 | − | 0.362988i | \(-0.881756\pi\) | ||||
−0.931794 | + | 0.362988i | \(0.881756\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −80.1909 | −2.64238 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −14.8825 | −0.489864 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −14.8585 | −0.488545 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −11.7975 | −0.387480 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −25.8228 | −0.847218 | −0.423609 | − | 0.905845i | \(-0.639237\pi\) | ||||
−0.423609 | + | 0.905845i | \(0.639237\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −40.0607 | −1.31294 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −25.5590 | −0.836765 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.319656 | −0.0104539 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −13.6840 | −0.447037 | −0.223518 | − | 0.974700i | \(-0.571754\pi\) | ||||
−0.223518 | + | 0.974700i | \(0.571754\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 15.6887 | 0.511981 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 27.5733 | 0.898862 | 0.449431 | − | 0.893315i | \(-0.351627\pi\) | ||||
0.449431 | + | 0.893315i | \(0.351627\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 23.2582 | 0.757391 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.14587 | 0.0698053 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 24.7426 | 0.804026 | 0.402013 | − | 0.915634i | \(-0.368311\pi\) | ||||
0.402013 | + | 0.915634i | \(0.368311\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.90230 | −0.321442 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 28.2796 | 0.917028 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 58.1228 | 1.88278 | 0.941391 | − | 0.337317i | \(-0.109520\pi\) | ||||
0.941391 | + | 0.337317i | \(0.109520\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 18.5265 | 0.599503 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5.66573 | 0.183147 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −16.1540 | −0.521640 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.4913 | −0.661010 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −19.8999 | −0.641267 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −42.7614 | −1.37654 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.56870 | 0.243393 | 0.121697 | − | 0.992567i | \(-0.461167\pi\) | ||||
0.121697 | + | 0.992567i | \(0.461167\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −10.0818 | −0.323873 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 16.0968 | 0.516571 | 0.258286 | − | 0.966069i | \(-0.416842\pi\) | ||||
0.258286 | + | 0.966069i | \(0.416842\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −20.2284 | −0.648493 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −31.7784 | −1.01772 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −17.1730 | −0.549413 | −0.274707 | − | 0.961528i | \(-0.588581\pi\) | ||||
−0.274707 | + | 0.961528i | \(0.588581\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.37153 | 0.0438344 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 51.8821 | 1.65647 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −20.0335 | −0.638970 | −0.319485 | − | 0.947591i | \(-0.603510\pi\) | ||||
−0.319485 | + | 0.947591i | \(0.603510\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 51.0873 | 1.62778 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 19.2699 | 0.613369 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 51.6533 | 1.64248 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −32.5514 | −1.03403 | −0.517014 | − | 0.855977i | \(-0.672957\pi\) | ||||
−0.517014 | + | 0.855977i | \(0.672957\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 53.7230 | 1.70485 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 11.1049 | 0.352047 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20.4199 | 0.646703 | 0.323352 | − | 0.946279i | \(-0.395190\pi\) | ||||
0.323352 | + | 0.946279i | \(0.395190\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.05554 | 0.0966729 |
(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 | 8048.2.a.r.1.3 | 12 | ||
4.3 | odd | 2 | 1006.2.a.i.1.10 | ✓ | 12 | ||
12.11 | even | 2 | 9054.2.a.bj.1.4 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1006.2.a.i.1.10 | ✓ | 12 | 4.3 | odd | 2 | ||
8048.2.a.r.1.3 | 12 | 1.1 | even | 1 | trivial | ||
9054.2.a.bj.1.4 | 12 | 12.11 | even | 2 |