Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6003,2,Mod(1,6003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6003, 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("6003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6003 = 3^{2} \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6003.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: | \(47.9341963334\) |
Analytic rank: | \(1\) |
Dimension: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{11} - 2 x^{10} - 18 x^{9} + 30 x^{8} + 124 x^{7} - 152 x^{6} - 408 x^{5} + 285 x^{4} + 634 x^{3} - 93 x^{2} - 369 x - 108 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 2001) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(1.76484\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6003.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.76484 | −1.24793 | −0.623964 | − | 0.781453i | \(-0.714479\pi\) | ||||
−0.623964 | + | 0.781453i | \(0.714479\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.11465 | 0.557325 | ||||||||
\(5\) | 2.54815 | 1.13957 | 0.569784 | − | 0.821795i | \(-0.307027\pi\) | ||||
0.569784 | + | 0.821795i | \(0.307027\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.97592 | −1.88072 | −0.940360 | − | 0.340182i | \(-0.889511\pi\) | ||||
−0.940360 | + | 0.340182i | \(0.889511\pi\) | |||||||
\(8\) | 1.56250 | 0.552427 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −4.49707 | −1.42210 | ||||||||
\(11\) | −0.283045 | −0.0853411 | −0.0426706 | − | 0.999089i | \(-0.513587\pi\) | ||||
−0.0426706 | + | 0.999089i | \(0.513587\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.170966 | −0.0474175 | −0.0237087 | − | 0.999719i | \(-0.507547\pi\) | ||||
−0.0237087 | + | 0.999719i | \(0.507547\pi\) | |||||||
\(14\) | 8.78168 | 2.34700 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.98686 | −1.24671 | ||||||||
\(17\) | −5.92041 | −1.43591 | −0.717956 | − | 0.696089i | \(-0.754922\pi\) | ||||
−0.717956 | + | 0.696089i | \(0.754922\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.65876 | 1.06879 | 0.534396 | − | 0.845234i | \(-0.320539\pi\) | ||||
0.534396 | + | 0.845234i | \(0.320539\pi\) | |||||||
\(20\) | 2.84029 | 0.635109 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.499527 | 0.106500 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.49307 | 0.298613 | ||||||||
\(26\) | 0.301727 | 0.0591736 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −5.54640 | −1.04817 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.96888 | 1.61086 | 0.805429 | − | 0.592692i | \(-0.201935\pi\) | ||||
0.805429 | + | 0.592692i | \(0.201935\pi\) | |||||||
\(32\) | 5.67599 | 1.00338 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 10.4486 | 1.79191 | ||||||||
\(35\) | −12.6794 | −2.14321 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.201428 | 0.0331146 | 0.0165573 | − | 0.999863i | \(-0.494729\pi\) | ||||
0.0165573 | + | 0.999863i | \(0.494729\pi\) | |||||||
\(38\) | −8.22195 | −1.33378 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.98148 | 0.629528 | ||||||||
\(41\) | 6.77658 | 1.05832 | 0.529162 | − | 0.848521i | \(-0.322507\pi\) | ||||
0.529162 | + | 0.848521i | \(0.322507\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.97728 | −0.454031 | −0.227015 | − | 0.973891i | \(-0.572897\pi\) | ||||
−0.227015 | + | 0.973891i | \(0.572897\pi\) | |||||||
\(44\) | −0.315495 | −0.0475627 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.76484 | 0.260211 | ||||||||
\(47\) | −7.64176 | −1.11466 | −0.557332 | − | 0.830290i | \(-0.688175\pi\) | ||||
−0.557332 | + | 0.830290i | \(0.688175\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 17.7597 | 2.53711 | ||||||||
\(50\) | −2.63502 | −0.372648 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.190567 | −0.0264269 | ||||||||
\(53\) | −2.22897 | −0.306173 | −0.153087 | − | 0.988213i | \(-0.548921\pi\) | ||||
−0.153087 | + | 0.988213i | \(0.548921\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.721240 | −0.0972520 | ||||||||
\(56\) | −7.77487 | −1.03896 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.76484 | −0.231734 | ||||||||
\(59\) | 15.2006 | 1.97895 | 0.989474 | − | 0.144711i | \(-0.0462252\pi\) | ||||
0.989474 | + | 0.144711i | \(0.0462252\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.08366 | 0.138748 | 0.0693741 | − | 0.997591i | \(-0.477900\pi\) | ||||
0.0693741 | + | 0.997591i | \(0.477900\pi\) | |||||||
\(62\) | −15.8286 | −2.01023 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.0434802 | −0.00543502 | ||||||||
\(65\) | −0.435647 | −0.0540354 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.78799 | −0.584946 | −0.292473 | − | 0.956274i | \(-0.594478\pi\) | ||||
−0.292473 | + | 0.956274i | \(0.594478\pi\) | |||||||
\(68\) | −6.59918 | −0.800269 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 22.3770 | 2.67457 | ||||||||
\(71\) | −15.9000 | −1.88698 | −0.943489 | − | 0.331404i | \(-0.892478\pi\) | ||||
−0.943489 | + | 0.331404i | \(0.892478\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.09595 | 0.596436 | 0.298218 | − | 0.954498i | \(-0.403608\pi\) | ||||
0.298218 | + | 0.954498i | \(0.403608\pi\) | |||||||
\(74\) | −0.355488 | −0.0413247 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.19288 | 0.595664 | ||||||||
\(77\) | 1.40841 | 0.160503 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 15.8153 | 1.77936 | 0.889678 | − | 0.456588i | \(-0.150929\pi\) | ||||
0.889678 | + | 0.456588i | \(0.150929\pi\) | |||||||
\(80\) | −12.7073 | −1.42071 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −11.9596 | −1.32071 | ||||||||
\(83\) | 4.95563 | 0.543951 | 0.271976 | − | 0.962304i | \(-0.412323\pi\) | ||||
0.271976 | + | 0.962304i | \(0.412323\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −15.0861 | −1.63632 | ||||||||
\(86\) | 5.25441 | 0.566597 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.442257 | −0.0471448 | ||||||||
\(89\) | 3.87577 | 0.410830 | 0.205415 | − | 0.978675i | \(-0.434146\pi\) | ||||
0.205415 | + | 0.978675i | \(0.434146\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.850713 | 0.0891790 | ||||||||
\(92\) | −1.11465 | −0.116210 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 13.4865 | 1.39102 | ||||||||
\(95\) | 11.8712 | 1.21796 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −16.0439 | −1.62901 | −0.814507 | − | 0.580154i | \(-0.802992\pi\) | ||||
−0.814507 | + | 0.580154i | \(0.802992\pi\) | |||||||
\(98\) | −31.3430 | −3.16613 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.66425 | 0.166425 | ||||||||
\(101\) | −5.49297 | −0.546571 | −0.273285 | − | 0.961933i | \(-0.588110\pi\) | ||||
−0.273285 | + | 0.961933i | \(0.588110\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.1030 | −1.09401 | −0.547004 | − | 0.837130i | \(-0.684232\pi\) | ||||
−0.547004 | + | 0.837130i | \(0.684232\pi\) | |||||||
\(104\) | −0.267135 | −0.0261947 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.93378 | 0.382082 | ||||||||
\(107\) | −4.19747 | −0.405785 | −0.202892 | − | 0.979201i | \(-0.565034\pi\) | ||||
−0.202892 | + | 0.979201i | \(0.565034\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.34044 | −0.128391 | −0.0641954 | − | 0.997937i | \(-0.520448\pi\) | ||||
−0.0641954 | + | 0.997937i | \(0.520448\pi\) | |||||||
\(110\) | 1.27287 | 0.121363 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 24.8142 | 2.34472 | ||||||||
\(113\) | 6.13822 | 0.577435 | 0.288718 | − | 0.957414i | \(-0.406771\pi\) | ||||
0.288718 | + | 0.957414i | \(0.406771\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.54815 | −0.237616 | ||||||||
\(116\) | 1.11465 | 0.103493 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −26.8266 | −2.46958 | ||||||||
\(119\) | 29.4595 | 2.70055 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9199 | −0.992717 | ||||||||
\(122\) | −1.91248 | −0.173148 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 9.99715 | 0.897771 | ||||||||
\(125\) | −8.93619 | −0.799277 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 20.6626 | 1.83351 | 0.916755 | − | 0.399450i | \(-0.130799\pi\) | ||||
0.916755 | + | 0.399450i | \(0.130799\pi\) | |||||||
\(128\) | −11.2752 | −0.996600 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.768847 | 0.0674323 | ||||||||
\(131\) | −14.9676 | −1.30772 | −0.653861 | − | 0.756614i | \(-0.726852\pi\) | ||||
−0.653861 | + | 0.756614i | \(0.726852\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −23.1816 | −2.01010 | ||||||||
\(134\) | 8.45002 | 0.729970 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −9.25064 | −0.793236 | ||||||||
\(137\) | −7.68590 | −0.656651 | −0.328326 | − | 0.944565i | \(-0.606484\pi\) | ||||
−0.328326 | + | 0.944565i | \(0.606484\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 18.0155 | 1.52806 | 0.764029 | − | 0.645182i | \(-0.223218\pi\) | ||||
0.764029 | + | 0.645182i | \(0.223218\pi\) | |||||||
\(140\) | −14.1331 | −1.19446 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 28.0608 | 2.35481 | ||||||||
\(143\) | 0.0483910 | 0.00404666 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.54815 | 0.211612 | ||||||||
\(146\) | −8.99353 | −0.744310 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.224522 | 0.0184556 | ||||||||
\(149\) | −19.5667 | −1.60297 | −0.801485 | − | 0.598015i | \(-0.795956\pi\) | ||||
−0.801485 | + | 0.598015i | \(0.795956\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.32858 | −0.270876 | −0.135438 | − | 0.990786i | \(-0.543244\pi\) | ||||
−0.135438 | + | 0.990786i | \(0.543244\pi\) | |||||||
\(152\) | 7.27931 | 0.590430 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.48561 | −0.200296 | ||||||||
\(155\) | 22.8540 | 1.83568 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −18.4270 | −1.47063 | −0.735317 | − | 0.677723i | \(-0.762967\pi\) | ||||
−0.735317 | + | 0.677723i | \(0.762967\pi\) | |||||||
\(158\) | −27.9114 | −2.22051 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 14.4633 | 1.14342 | ||||||||
\(161\) | 4.97592 | 0.392157 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.52999 | 0.198164 | 0.0990822 | − | 0.995079i | \(-0.468409\pi\) | ||||
0.0990822 | + | 0.995079i | \(0.468409\pi\) | |||||||
\(164\) | 7.55350 | 0.589830 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.74588 | −0.678812 | ||||||||
\(167\) | 1.30974 | 0.101350 | 0.0506752 | − | 0.998715i | \(-0.483863\pi\) | ||||
0.0506752 | + | 0.998715i | \(0.483863\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9708 | −0.997752 | ||||||||
\(170\) | 26.6245 | 2.04201 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3.31862 | −0.253042 | ||||||||
\(173\) | −13.3226 | −1.01290 | −0.506451 | − | 0.862269i | \(-0.669043\pi\) | ||||
−0.506451 | + | 0.862269i | \(0.669043\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.42938 | −0.561608 | ||||||||
\(176\) | 1.41150 | 0.106396 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −6.84009 | −0.512687 | ||||||||
\(179\) | 6.31895 | 0.472300 | 0.236150 | − | 0.971717i | \(-0.424114\pi\) | ||||
0.236150 | + | 0.971717i | \(0.424114\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.65286 | −0.717491 | −0.358746 | − | 0.933435i | \(-0.616795\pi\) | ||||
−0.358746 | + | 0.933435i | \(0.616795\pi\) | |||||||
\(182\) | −1.50137 | −0.111289 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.56250 | −0.115189 | ||||||||
\(185\) | 0.513270 | 0.0377364 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.67574 | 0.122542 | ||||||||
\(188\) | −8.51788 | −0.621230 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −20.9508 | −1.51993 | ||||||||
\(191\) | 1.31803 | 0.0953691 | 0.0476846 | − | 0.998862i | \(-0.484816\pi\) | ||||
0.0476846 | + | 0.998862i | \(0.484816\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 21.0522 | 1.51537 | 0.757685 | − | 0.652620i | \(-0.226330\pi\) | ||||
0.757685 | + | 0.652620i | \(0.226330\pi\) | |||||||
\(194\) | 28.3149 | 2.03289 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 19.7959 | 1.41399 | ||||||||
\(197\) | −6.15267 | −0.438359 | −0.219180 | − | 0.975684i | \(-0.570338\pi\) | ||||
−0.219180 | + | 0.975684i | \(0.570338\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.2203 | 0.866274 | 0.433137 | − | 0.901328i | \(-0.357407\pi\) | ||||
0.433137 | + | 0.901328i | \(0.357407\pi\) | |||||||
\(200\) | 2.33292 | 0.164962 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 9.69419 | 0.682081 | ||||||||
\(203\) | −4.97592 | −0.349241 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 17.2677 | 1.20603 | ||||||||
\(206\) | 19.5949 | 1.36524 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.852584 | 0.0591160 | ||||||||
\(209\) | −1.31864 | −0.0912120 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.47990 | 0.308409 | 0.154205 | − | 0.988039i | \(-0.450719\pi\) | ||||
0.154205 | + | 0.988039i | \(0.450719\pi\) | |||||||
\(212\) | −2.48452 | −0.170638 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 7.40785 | 0.506390 | ||||||||
\(215\) | −7.58655 | −0.517398 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −44.6284 | −3.02957 | ||||||||
\(218\) | 2.36566 | 0.160223 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.803929 | −0.0542009 | ||||||||
\(221\) | 1.01219 | 0.0680873 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.63867 | 0.176699 | 0.0883493 | − | 0.996090i | \(-0.471841\pi\) | ||||
0.0883493 | + | 0.996090i | \(0.471841\pi\) | |||||||
\(224\) | −28.2432 | −1.88708 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −10.8330 | −0.720598 | ||||||||
\(227\) | −14.3265 | −0.950885 | −0.475442 | − | 0.879747i | \(-0.657712\pi\) | ||||
−0.475442 | + | 0.879747i | \(0.657712\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −24.0371 | −1.58842 | −0.794208 | − | 0.607647i | \(-0.792114\pi\) | ||||
−0.794208 | + | 0.607647i | \(0.792114\pi\) | |||||||
\(230\) | 4.49707 | 0.296528 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.56250 | 0.102583 | ||||||||
\(233\) | 0.647548 | 0.0424223 | 0.0212111 | − | 0.999775i | \(-0.493248\pi\) | ||||
0.0212111 | + | 0.999775i | \(0.493248\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −19.4723 | −1.27024 | ||||||||
\(236\) | 16.9433 | 1.10292 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −51.9912 | −3.37009 | ||||||||
\(239\) | −23.0226 | −1.48921 | −0.744603 | − | 0.667508i | \(-0.767361\pi\) | ||||
−0.744603 | + | 0.667508i | \(0.767361\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.27926 | 0.275652 | 0.137826 | − | 0.990456i | \(-0.455989\pi\) | ||||
0.137826 | + | 0.990456i | \(0.455989\pi\) | |||||||
\(242\) | 19.2718 | 1.23884 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.20790 | 0.0773278 | ||||||||
\(245\) | 45.2545 | 2.89120 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.796490 | −0.0506795 | ||||||||
\(248\) | 14.0139 | 0.889881 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 15.7709 | 0.997440 | ||||||||
\(251\) | 13.5637 | 0.856132 | 0.428066 | − | 0.903747i | \(-0.359195\pi\) | ||||
0.428066 | + | 0.903747i | \(0.359195\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.283045 | 0.0177949 | ||||||||
\(254\) | −36.4661 | −2.28809 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 19.9859 | 1.24912 | ||||||||
\(257\) | 2.03382 | 0.126866 | 0.0634330 | − | 0.997986i | \(-0.479795\pi\) | ||||
0.0634330 | + | 0.997986i | \(0.479795\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.00229 | −0.0622793 | ||||||||
\(260\) | −0.485594 | −0.0301153 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 26.4153 | 1.63194 | ||||||||
\(263\) | −11.9405 | −0.736283 | −0.368142 | − | 0.929770i | \(-0.620006\pi\) | ||||
−0.368142 | + | 0.929770i | \(0.620006\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.67976 | −0.348905 | ||||||||
\(266\) | 40.9117 | 2.50846 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −5.33693 | −0.326005 | ||||||||
\(269\) | −15.1479 | −0.923587 | −0.461793 | − | 0.886988i | \(-0.652794\pi\) | ||||
−0.461793 | + | 0.886988i | \(0.652794\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.1868 | 1.22626 | 0.613132 | − | 0.789981i | \(-0.289909\pi\) | ||||
0.613132 | + | 0.789981i | \(0.289909\pi\) | |||||||
\(272\) | 29.5242 | 1.79017 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 13.5644 | 0.819453 | ||||||||
\(275\) | −0.422604 | −0.0254840 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.22660 | −0.133783 | −0.0668917 | − | 0.997760i | \(-0.521308\pi\) | ||||
−0.0668917 | + | 0.997760i | \(0.521308\pi\) | |||||||
\(278\) | −31.7945 | −1.90691 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −19.8115 | −1.18397 | ||||||||
\(281\) | −21.9565 | −1.30981 | −0.654907 | − | 0.755710i | \(-0.727292\pi\) | ||||
−0.654907 | + | 0.755710i | \(0.727292\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.53617 | 0.269647 | 0.134824 | − | 0.990870i | \(-0.456953\pi\) | ||||
0.134824 | + | 0.990870i | \(0.456953\pi\) | |||||||
\(284\) | −17.7229 | −1.05166 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.0854023 | −0.00504994 | ||||||||
\(287\) | −33.7197 | −1.99041 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 18.0513 | 1.06184 | ||||||||
\(290\) | −4.49707 | −0.264077 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 5.68020 | 0.332409 | ||||||||
\(293\) | 11.0848 | 0.647581 | 0.323790 | − | 0.946129i | \(-0.395043\pi\) | ||||
0.323790 | + | 0.946129i | \(0.395043\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 38.7334 | 2.25514 | ||||||||
\(296\) | 0.314732 | 0.0182934 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 34.5321 | 2.00039 | ||||||||
\(299\) | 0.170966 | 0.00988723 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 14.8147 | 0.853904 | ||||||||
\(302\) | 5.87440 | 0.338034 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −23.2326 | −1.33248 | ||||||||
\(305\) | 2.76132 | 0.158113 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.6843 | −0.666856 | −0.333428 | − | 0.942776i | \(-0.608205\pi\) | ||||
−0.333428 | + | 0.942776i | \(0.608205\pi\) | |||||||
\(308\) | 1.56988 | 0.0894521 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −40.3337 | −2.29080 | ||||||||
\(311\) | −18.4799 | −1.04790 | −0.523949 | − | 0.851750i | \(-0.675542\pi\) | ||||
−0.523949 | + | 0.851750i | \(0.675542\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.66419 | 0.0940656 | 0.0470328 | − | 0.998893i | \(-0.485023\pi\) | ||||
0.0470328 | + | 0.998893i | \(0.485023\pi\) | |||||||
\(314\) | 32.5206 | 1.83525 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 17.6285 | 0.991679 | ||||||||
\(317\) | −6.66769 | −0.374495 | −0.187247 | − | 0.982313i | \(-0.559957\pi\) | ||||
−0.187247 | + | 0.982313i | \(0.559957\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.283045 | −0.0158475 | ||||||||
\(320\) | −0.110794 | −0.00619357 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −8.78168 | −0.489384 | ||||||||
\(323\) | −27.5818 | −1.53469 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.255264 | −0.0141595 | ||||||||
\(326\) | −4.46503 | −0.247295 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 10.5884 | 0.584646 | ||||||||
\(329\) | 38.0247 | 2.09637 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.8701 | 1.09216 | 0.546080 | − | 0.837733i | \(-0.316119\pi\) | ||||
0.546080 | + | 0.837733i | \(0.316119\pi\) | |||||||
\(332\) | 5.52379 | 0.303157 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.31147 | −0.126478 | ||||||||
\(335\) | −12.2005 | −0.666585 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12.8728 | −0.701228 | −0.350614 | − | 0.936520i | \(-0.614027\pi\) | ||||
−0.350614 | + | 0.936520i | \(0.614027\pi\) | |||||||
\(338\) | 22.8913 | 1.24512 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −16.8157 | −0.911960 | ||||||||
\(341\) | −2.53859 | −0.137472 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −53.5396 | −2.89087 | ||||||||
\(344\) | −4.65199 | −0.250819 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 23.5123 | 1.26403 | ||||||||
\(347\) | −9.77259 | −0.524620 | −0.262310 | − | 0.964984i | \(-0.584484\pi\) | ||||
−0.262310 | + | 0.964984i | \(0.584484\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.1699 | 0.704971 | 0.352486 | − | 0.935817i | \(-0.385337\pi\) | ||||
0.352486 | + | 0.935817i | \(0.385337\pi\) | |||||||
\(350\) | 13.1116 | 0.700846 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.60656 | −0.0856298 | ||||||||
\(353\) | 14.5533 | 0.774593 | 0.387297 | − | 0.921955i | \(-0.373409\pi\) | ||||
0.387297 | + | 0.921955i | \(0.373409\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −40.5155 | −2.15034 | ||||||||
\(356\) | 4.32012 | 0.228966 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −11.1519 | −0.589397 | ||||||||
\(359\) | 11.6926 | 0.617113 | 0.308556 | − | 0.951206i | \(-0.400154\pi\) | ||||
0.308556 | + | 0.951206i | \(0.400154\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.70404 | 0.142318 | ||||||||
\(362\) | 17.0357 | 0.895378 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.948247 | 0.0497016 | ||||||||
\(365\) | 12.9853 | 0.679679 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.437440 | −0.0228342 | −0.0114171 | − | 0.999935i | \(-0.503634\pi\) | ||||
−0.0114171 | + | 0.999935i | \(0.503634\pi\) | |||||||
\(368\) | 4.98686 | 0.259958 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.905838 | −0.0470923 | ||||||||
\(371\) | 11.0912 | 0.575826 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.7884 | 0.765714 | 0.382857 | − | 0.923808i | \(-0.374940\pi\) | ||||
0.382857 | + | 0.923808i | \(0.374940\pi\) | |||||||
\(374\) | −2.95741 | −0.152924 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −11.9402 | −0.615771 | ||||||||
\(377\) | −0.170966 | −0.00880521 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.0767 | −0.723073 | −0.361537 | − | 0.932358i | \(-0.617748\pi\) | ||||
−0.361537 | + | 0.932358i | \(0.617748\pi\) | |||||||
\(380\) | 13.2322 | 0.678800 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2.32610 | −0.119014 | ||||||||
\(383\) | 14.7132 | 0.751809 | 0.375905 | − | 0.926658i | \(-0.377332\pi\) | ||||
0.375905 | + | 0.926658i | \(0.377332\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.58883 | 0.182904 | ||||||||
\(386\) | −37.1537 | −1.89107 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −17.8833 | −0.907889 | ||||||||
\(389\) | −11.4361 | −0.579835 | −0.289917 | − | 0.957052i | \(-0.593628\pi\) | ||||
−0.289917 | + | 0.957052i | \(0.593628\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.92041 | 0.299408 | ||||||||
\(392\) | 27.7496 | 1.40157 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 10.8585 | 0.547041 | ||||||||
\(395\) | 40.2997 | 2.02770 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 31.0202 | 1.55686 | 0.778430 | − | 0.627732i | \(-0.216016\pi\) | ||||
0.778430 | + | 0.627732i | \(0.216016\pi\) | |||||||
\(398\) | −21.5668 | −1.08105 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −7.44571 | −0.372285 | ||||||||
\(401\) | 37.4659 | 1.87096 | 0.935480 | − | 0.353379i | \(-0.114968\pi\) | ||||
0.935480 | + | 0.353379i | \(0.114968\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.53337 | −0.0763828 | ||||||||
\(404\) | −6.12273 | −0.304617 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8.78168 | 0.435827 | ||||||||
\(407\) | −0.0570132 | −0.00282604 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −30.1554 | −1.49109 | −0.745544 | − | 0.666456i | \(-0.767810\pi\) | ||||
−0.745544 | + | 0.666456i | \(0.767810\pi\) | |||||||
\(410\) | −30.4747 | −1.50504 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −12.3759 | −0.609718 | ||||||||
\(413\) | −75.6369 | −3.72185 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12.6277 | 0.619869 | ||||||||
\(416\) | −0.970402 | −0.0475779 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.32718 | 0.113826 | ||||||||
\(419\) | −21.3187 | −1.04149 | −0.520745 | − | 0.853713i | \(-0.674346\pi\) | ||||
−0.520745 | + | 0.853713i | \(0.674346\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −39.1557 | −1.90833 | −0.954165 | − | 0.299280i | \(-0.903254\pi\) | ||||
−0.954165 | + | 0.299280i | \(0.903254\pi\) | |||||||
\(422\) | −7.90629 | −0.384872 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.48277 | −0.169138 | ||||||||
\(425\) | −8.83957 | −0.428782 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.39219 | −0.260946 | ||||||||
\(428\) | −4.67871 | −0.226154 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 13.3890 | 0.645676 | ||||||||
\(431\) | −17.4143 | −0.838818 | −0.419409 | − | 0.907797i | \(-0.637763\pi\) | ||||
−0.419409 | + | 0.907797i | \(0.637763\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12.3095 | −0.591555 | −0.295778 | − | 0.955257i | \(-0.595579\pi\) | ||||
−0.295778 | + | 0.955257i | \(0.595579\pi\) | |||||||
\(434\) | 78.7618 | 3.78069 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.49412 | −0.0715554 | ||||||||
\(437\) | −4.65876 | −0.222859 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14.3065 | −0.682814 | −0.341407 | − | 0.939916i | \(-0.610903\pi\) | ||||
−0.341407 | + | 0.939916i | \(0.610903\pi\) | |||||||
\(440\) | −1.12694 | −0.0537246 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.78635 | −0.0849680 | ||||||||
\(443\) | 13.9006 | 0.660439 | 0.330220 | − | 0.943904i | \(-0.392877\pi\) | ||||
0.330220 | + | 0.943904i | \(0.392877\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.87603 | 0.468169 | ||||||||
\(446\) | −4.65683 | −0.220507 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.216354 | 0.0102217 | ||||||||
\(449\) | −29.6600 | −1.39974 | −0.699872 | − | 0.714268i | \(-0.746760\pi\) | ||||
−0.699872 | + | 0.714268i | \(0.746760\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.91807 | −0.0903185 | ||||||||
\(452\) | 6.84196 | 0.321819 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 25.2840 | 1.18664 | ||||||||
\(455\) | 2.16774 | 0.101625 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 38.3682 | 1.79479 | 0.897394 | − | 0.441230i | \(-0.145458\pi\) | ||||
0.897394 | + | 0.441230i | \(0.145458\pi\) | |||||||
\(458\) | 42.4215 | 1.98223 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2.84029 | −0.132429 | ||||||||
\(461\) | 28.6130 | 1.33264 | 0.666321 | − | 0.745665i | \(-0.267868\pi\) | ||||
0.666321 | + | 0.745665i | \(0.267868\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.51659 | 0.302852 | 0.151426 | − | 0.988469i | \(-0.451614\pi\) | ||||
0.151426 | + | 0.988469i | \(0.451614\pi\) | |||||||
\(464\) | −4.98686 | −0.231509 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.14282 | −0.0529400 | ||||||||
\(467\) | 16.6592 | 0.770895 | 0.385448 | − | 0.922730i | \(-0.374047\pi\) | ||||
0.385448 | + | 0.922730i | \(0.374047\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 23.8246 | 1.10012 | ||||||||
\(470\) | 34.3655 | 1.58516 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 23.7509 | 1.09322 | ||||||||
\(473\) | 0.842702 | 0.0387475 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.95584 | 0.319156 | ||||||||
\(476\) | 32.8370 | 1.50508 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 40.6310 | 1.85842 | ||||||||
\(479\) | 9.73200 | 0.444666 | 0.222333 | − | 0.974971i | \(-0.428633\pi\) | ||||
0.222333 | + | 0.974971i | \(0.428633\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.0344375 | −0.00157021 | ||||||||
\(482\) | −7.55220 | −0.343993 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −12.1718 | −0.553266 | ||||||||
\(485\) | −40.8823 | −1.85637 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10.4945 | −0.475551 | −0.237775 | − | 0.971320i | \(-0.576418\pi\) | ||||
−0.237775 | + | 0.971320i | \(0.576418\pi\) | |||||||
\(488\) | 1.69321 | 0.0766482 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −79.8668 | −3.60801 | ||||||||
\(491\) | −31.9404 | −1.44145 | −0.720726 | − | 0.693220i | \(-0.756191\pi\) | ||||
−0.720726 | + | 0.693220i | \(0.756191\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.92041 | −0.266642 | ||||||||
\(494\) | 1.40568 | 0.0632443 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −44.7265 | −2.00828 | ||||||||
\(497\) | 79.1169 | 3.54888 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.06782 | 0.0925684 | 0.0462842 | − | 0.998928i | \(-0.485262\pi\) | ||||
0.0462842 | + | 0.998928i | \(0.485262\pi\) | |||||||
\(500\) | −9.96072 | −0.445457 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −23.9377 | −1.06839 | ||||||||
\(503\) | 39.4576 | 1.75933 | 0.879663 | − | 0.475598i | \(-0.157768\pi\) | ||||
0.879663 | + | 0.475598i | \(0.157768\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −13.9969 | −0.622854 | ||||||||
\(506\) | −0.499527 | −0.0222067 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 23.0316 | 1.02186 | ||||||||
\(509\) | −26.0870 | −1.15629 | −0.578143 | − | 0.815935i | \(-0.696223\pi\) | ||||
−0.578143 | + | 0.815935i | \(0.696223\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −25.3570 | −1.12173 | ||||||||
\(512\) | −12.7214 | −0.562212 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3.58936 | −0.158320 | ||||||||
\(515\) | −28.2920 | −1.24670 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.16296 | 0.0951267 | ||||||||
\(518\) | 1.76888 | 0.0777202 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −0.680699 | −0.0298506 | ||||||||
\(521\) | −35.0010 | −1.53342 | −0.766711 | − | 0.641992i | \(-0.778108\pi\) | ||||
−0.766711 | + | 0.641992i | \(0.778108\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −14.5683 | −0.637026 | −0.318513 | − | 0.947919i | \(-0.603183\pi\) | ||||
−0.318513 | + | 0.947919i | \(0.603183\pi\) | |||||||
\(524\) | −16.6836 | −0.728826 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 21.0730 | 0.918828 | ||||||||
\(527\) | −53.0995 | −2.31305 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 10.0238 | 0.435408 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −25.8393 | −1.12028 | ||||||||
\(533\) | −1.15857 | −0.0501830 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −10.6958 | −0.462419 | ||||||||
\(536\) | −7.48123 | −0.323140 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 26.7337 | 1.15257 | ||||||||
\(539\) | −5.02680 | −0.216519 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −25.5258 | −1.09744 | −0.548719 | − | 0.836007i | \(-0.684884\pi\) | ||||
−0.548719 | + | 0.836007i | \(0.684884\pi\) | |||||||
\(542\) | −35.6265 | −1.53029 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −33.6042 | −1.44077 | ||||||||
\(545\) | −3.41564 | −0.146310 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.84906 | 0.378358 | 0.189179 | − | 0.981943i | \(-0.439417\pi\) | ||||
0.189179 | + | 0.981943i | \(0.439417\pi\) | |||||||
\(548\) | −8.56709 | −0.365968 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.745828 | 0.0318022 | ||||||||
\(551\) | 4.65876 | 0.198470 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −78.6955 | −3.34647 | ||||||||
\(554\) | 3.92959 | 0.166952 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 20.0810 | 0.851625 | ||||||||
\(557\) | −26.6759 | −1.13029 | −0.565147 | − | 0.824990i | \(-0.691181\pi\) | ||||
−0.565147 | + | 0.824990i | \(0.691181\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.509014 | 0.0215290 | ||||||||
\(560\) | 63.2302 | 2.67197 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 38.7496 | 1.63455 | ||||||||
\(563\) | 16.5834 | 0.698906 | 0.349453 | − | 0.936954i | \(-0.386367\pi\) | ||||
0.349453 | + | 0.936954i | \(0.386367\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 15.6411 | 0.658026 | ||||||||
\(566\) | −8.00560 | −0.336501 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −24.8437 | −1.04242 | ||||||||
\(569\) | −24.5455 | −1.02900 | −0.514500 | − | 0.857491i | \(-0.672022\pi\) | ||||
−0.514500 | + | 0.857491i | \(0.672022\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −26.4099 | −1.10522 | −0.552611 | − | 0.833439i | \(-0.686368\pi\) | ||||
−0.552611 | + | 0.833439i | \(0.686368\pi\) | |||||||
\(572\) | 0.0539390 | 0.00225530 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 59.5097 | 2.48389 | ||||||||
\(575\) | −1.49307 | −0.0622652 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −20.0446 | −0.834469 | −0.417234 | − | 0.908799i | \(-0.637001\pi\) | ||||
−0.417234 | + | 0.908799i | \(0.637001\pi\) | |||||||
\(578\) | −31.8576 | −1.32510 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2.84029 | 0.117937 | ||||||||
\(581\) | −24.6588 | −1.02302 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.630899 | 0.0261292 | ||||||||
\(584\) | 7.96243 | 0.329488 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −19.5629 | −0.808134 | ||||||||
\(587\) | −2.29610 | −0.0947702 | −0.0473851 | − | 0.998877i | \(-0.515089\pi\) | ||||
−0.0473851 | + | 0.998877i | \(0.515089\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 41.7838 | 1.72167 | ||||||||
\(590\) | −68.3581 | −2.81426 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.00449 | −0.0412845 | ||||||||
\(593\) | 12.5883 | 0.516940 | 0.258470 | − | 0.966019i | \(-0.416782\pi\) | ||||
0.258470 | + | 0.966019i | \(0.416782\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 75.0672 | 3.07745 | ||||||||
\(596\) | −21.8101 | −0.893375 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −0.301727 | −0.0123386 | ||||||||
\(599\) | −26.0338 | −1.06371 | −0.531857 | − | 0.846834i | \(-0.678506\pi\) | ||||
−0.531857 | + | 0.846834i | \(0.678506\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.9942 | 0.611628 | 0.305814 | − | 0.952091i | \(-0.401071\pi\) | ||||
0.305814 | + | 0.952091i | \(0.401071\pi\) | |||||||
\(602\) | −26.1455 | −1.06561 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3.71020 | −0.150966 | ||||||||
\(605\) | −27.8255 | −1.13127 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.38075 | −0.258987 | −0.129493 | − | 0.991580i | \(-0.541335\pi\) | ||||
−0.129493 | + | 0.991580i | \(0.541335\pi\) | |||||||
\(608\) | 26.4431 | 1.07241 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4.87328 | −0.197313 | ||||||||
\(611\) | 1.30648 | 0.0528546 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −21.4514 | −0.866413 | −0.433206 | − | 0.901295i | \(-0.642618\pi\) | ||||
−0.433206 | + | 0.901295i | \(0.642618\pi\) | |||||||
\(614\) | 20.6208 | 0.832188 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.20063 | 0.0886661 | ||||||||
\(617\) | −27.6955 | −1.11498 | −0.557489 | − | 0.830184i | \(-0.688235\pi\) | ||||
−0.557489 | + | 0.830184i | \(0.688235\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.3783 | 0.457332 | 0.228666 | − | 0.973505i | \(-0.426564\pi\) | ||||
0.228666 | + | 0.973505i | \(0.426564\pi\) | |||||||
\(620\) | 25.4742 | 1.02307 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 32.6140 | 1.30770 | ||||||||
\(623\) | −19.2855 | −0.772657 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.2361 | −1.20944 | ||||||||
\(626\) | −2.93702 | −0.117387 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −20.5396 | −0.819621 | ||||||||
\(629\) | −1.19254 | −0.0475497 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −45.9809 | −1.83047 | −0.915235 | − | 0.402921i | \(-0.867995\pi\) | ||||
−0.915235 | + | 0.402921i | \(0.867995\pi\) | |||||||
\(632\) | 24.7114 | 0.982965 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 11.7674 | 0.467342 | ||||||||
\(635\) | 52.6514 | 2.08941 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.03632 | −0.120303 | ||||||||
\(638\) | 0.499527 | 0.0197765 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −28.7310 | −1.13569 | ||||||||
\(641\) | −8.77087 | −0.346428 | −0.173214 | − | 0.984884i | \(-0.555415\pi\) | ||||
−0.173214 | + | 0.984884i | \(0.555415\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −42.4849 | −1.67544 | −0.837721 | − | 0.546098i | \(-0.816113\pi\) | ||||
−0.837721 | + | 0.546098i | \(0.816113\pi\) | |||||||
\(644\) | 5.54640 | 0.218559 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 48.6773 | 1.91518 | ||||||||
\(647\) | 7.83180 | 0.307900 | 0.153950 | − | 0.988079i | \(-0.450801\pi\) | ||||
0.153950 | + | 0.988079i | \(0.450801\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.30244 | −0.168886 | ||||||||
\(650\) | 0.450499 | 0.0176700 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.82006 | 0.110442 | ||||||||
\(653\) | 19.9384 | 0.780248 | 0.390124 | − | 0.920762i | \(-0.372432\pi\) | ||||
0.390124 | + | 0.920762i | \(0.372432\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −38.1396 | −1.49024 | ||||||||
\(656\) | −33.7938 | −1.31943 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −67.1075 | −2.61612 | ||||||||
\(659\) | −13.1611 | −0.512684 | −0.256342 | − | 0.966586i | \(-0.582517\pi\) | ||||
−0.256342 | + | 0.966586i | \(0.582517\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.99619 | −0.388807 | −0.194403 | − | 0.980922i | \(-0.562277\pi\) | ||||
−0.194403 | + | 0.980922i | \(0.562277\pi\) | |||||||
\(662\) | −35.0675 | −1.36294 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 7.74317 | 0.300493 | ||||||||
\(665\) | −59.0702 | −2.29064 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.00000 | −0.0387202 | ||||||||
\(668\) | 1.45990 | 0.0564851 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 21.5319 | 0.831850 | ||||||||
\(671\) | −0.306723 | −0.0118409 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −44.4817 | −1.71464 | −0.857322 | − | 0.514781i | \(-0.827873\pi\) | ||||
−0.857322 | + | 0.514781i | \(0.827873\pi\) | |||||||
\(674\) | 22.7185 | 0.875082 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −14.4579 | −0.556071 | ||||||||
\(677\) | −23.2960 | −0.895339 | −0.447670 | − | 0.894199i | \(-0.647746\pi\) | ||||
−0.447670 | + | 0.894199i | \(0.647746\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 79.8332 | 3.06372 | ||||||||
\(680\) | −23.5720 | −0.903946 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 4.48020 | 0.171556 | ||||||||
\(683\) | −46.6962 | −1.78678 | −0.893391 | − | 0.449280i | \(-0.851680\pi\) | ||||
−0.893391 | + | 0.449280i | \(0.851680\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −19.5848 | −0.748298 | ||||||||
\(686\) | 94.4886 | 3.60759 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 14.8473 | 0.566046 | ||||||||
\(689\) | 0.381079 | 0.0145180 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −47.2859 | −1.79884 | −0.899421 | − | 0.437084i | \(-0.856011\pi\) | ||||
−0.899421 | + | 0.437084i | \(0.856011\pi\) | |||||||
\(692\) | −14.8501 | −0.564515 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 17.2470 | 0.654688 | ||||||||
\(695\) | 45.9063 | 1.74133 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −40.1201 | −1.51966 | ||||||||
\(698\) | −23.2428 | −0.879753 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −8.28115 | −0.312998 | ||||||||
\(701\) | −46.4140 | −1.75303 | −0.876517 | − | 0.481371i | \(-0.840139\pi\) | ||||
−0.876517 | + | 0.481371i | \(0.840139\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.938407 | 0.0353927 | ||||||||
\(704\) | 0.0123068 | 0.000463831 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −25.6842 | −0.966637 | ||||||||
\(707\) | 27.3326 | 1.02795 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11.3444 | 0.426047 | 0.213024 | − | 0.977047i | \(-0.431669\pi\) | ||||
0.213024 | + | 0.977047i | \(0.431669\pi\) | |||||||
\(710\) | 71.5032 | 2.68347 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 6.05588 | 0.226954 | ||||||||
\(713\) | −8.96888 | −0.335887 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.123308 | 0.00461144 | ||||||||
\(716\) | 7.04341 | 0.263225 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −20.6356 | −0.770112 | ||||||||
\(719\) | −37.1842 | −1.38674 | −0.693369 | − | 0.720582i | \(-0.743874\pi\) | ||||
−0.693369 | + | 0.720582i | \(0.743874\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 55.2475 | 2.05752 | ||||||||
\(722\) | −4.77218 | −0.177602 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −10.7596 | −0.399876 | ||||||||
\(725\) | 1.49307 | 0.0554511 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.0657 | 0.595843 | 0.297922 | − | 0.954590i | \(-0.403707\pi\) | ||||
0.297922 | + | 0.954590i | \(0.403707\pi\) | |||||||
\(728\) | 1.32924 | 0.0492649 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −22.9169 | −0.848191 | ||||||||
\(731\) | 17.6267 | 0.651948 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 35.3061 | 1.30406 | 0.652031 | − | 0.758193i | \(-0.273917\pi\) | ||||
0.652031 | + | 0.758193i | \(0.273917\pi\) | |||||||
\(734\) | 0.772009 | 0.0284954 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.67599 | −0.209220 | ||||||||
\(737\) | 1.35521 | 0.0499199 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.60959 | −0.132781 | −0.0663905 | − | 0.997794i | \(-0.521148\pi\) | ||||
−0.0663905 | + | 0.997794i | \(0.521148\pi\) | |||||||
\(740\) | 0.572116 | 0.0210314 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −19.5741 | −0.718589 | ||||||||
\(743\) | −31.2299 | −1.14572 | −0.572858 | − | 0.819655i | \(-0.694165\pi\) | ||||
−0.572858 | + | 0.819655i | \(0.694165\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −49.8590 | −1.82669 | ||||||||
\(746\) | −26.0991 | −0.955556 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.86786 | 0.0682958 | ||||||||
\(749\) | 20.8863 | 0.763167 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.0119 | 0.730246 | 0.365123 | − | 0.930959i | \(-0.381027\pi\) | ||||
0.365123 | + | 0.930959i | \(0.381027\pi\) | |||||||
\(752\) | 38.1083 | 1.38967 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0.301727 | 0.0109883 | ||||||||
\(755\) | −8.48172 | −0.308681 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 31.3437 | 1.13921 | 0.569604 | − | 0.821920i | \(-0.307097\pi\) | ||||
0.569604 | + | 0.821920i | \(0.307097\pi\) | |||||||
\(758\) | 24.8431 | 0.902343 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 18.5488 | 0.672835 | ||||||||
\(761\) | −14.4059 | −0.522215 | −0.261107 | − | 0.965310i | \(-0.584088\pi\) | ||||
−0.261107 | + | 0.965310i | \(0.584088\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.66992 | 0.241467 | ||||||||
\(764\) | 1.46914 | 0.0531516 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −25.9664 | −0.938204 | ||||||||
\(767\) | −2.59879 | −0.0938367 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −19.9701 | −0.720140 | −0.360070 | − | 0.932925i | \(-0.617247\pi\) | ||||
−0.360070 | + | 0.932925i | \(0.617247\pi\) | |||||||
\(770\) | −6.33370 | −0.228251 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 23.4658 | 0.844553 | ||||||||
\(773\) | 9.65289 | 0.347190 | 0.173595 | − | 0.984817i | \(-0.444462\pi\) | ||||
0.173595 | + | 0.984817i | \(0.444462\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 13.3911 | 0.481024 | ||||||||
\(776\) | −25.0686 | −0.899911 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 20.1829 | 0.723592 | ||||||||
\(779\) | 31.5704 | 1.13113 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.50040 | 0.161037 | ||||||||
\(782\) | −10.4486 | −0.373640 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −88.5653 | −3.16305 | ||||||||
\(785\) | −46.9547 | −1.67589 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 37.1608 | 1.32464 | 0.662320 | − | 0.749221i | \(-0.269572\pi\) | ||||
0.662320 | + | 0.749221i | \(0.269572\pi\) | |||||||
\(788\) | −6.85807 | −0.244309 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −71.1223 | −2.53042 | ||||||||
\(791\) | −30.5433 | −1.08599 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.185269 | −0.00657909 | ||||||||
\(794\) | −54.7456 | −1.94285 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 13.6213 | 0.482796 | ||||||||
\(797\) | 18.0087 | 0.637900 | 0.318950 | − | 0.947772i | \(-0.396670\pi\) | ||||
0.318950 | + | 0.947772i | \(0.396670\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 45.2424 | 1.60056 | ||||||||
\(800\) | 8.47463 | 0.299623 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −66.1213 | −2.33482 | ||||||||
\(803\) | −1.44238 | −0.0509006 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 12.6794 | 0.446889 | ||||||||
\(806\) | 2.70616 | 0.0953203 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −8.58276 | −0.301941 | ||||||||
\(809\) | −4.86545 | −0.171060 | −0.0855301 | − | 0.996336i | \(-0.527258\pi\) | ||||
−0.0855301 | + | 0.996336i | \(0.527258\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13.8980 | 0.488025 | 0.244012 | − | 0.969772i | \(-0.421536\pi\) | ||||
0.244012 | + | 0.969772i | \(0.421536\pi\) | |||||||
\(812\) | −5.54640 | −0.194641 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.100619 | 0.00352670 | ||||||||
\(815\) | 6.44680 | 0.225822 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −13.8704 | −0.485264 | ||||||||
\(818\) | 53.2193 | 1.86077 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 19.2475 | 0.672150 | ||||||||
\(821\) | 45.1277 | 1.57497 | 0.787483 | − | 0.616336i | \(-0.211384\pi\) | ||||
0.787483 | + | 0.616336i | \(0.211384\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20.1767 | −0.703315 | −0.351658 | − | 0.936129i | \(-0.614382\pi\) | ||||
−0.351658 | + | 0.936129i | \(0.614382\pi\) | |||||||
\(824\) | −17.3484 | −0.604360 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 133.487 | 4.64460 | ||||||||
\(827\) | −54.0105 | −1.87813 | −0.939064 | − | 0.343742i | \(-0.888305\pi\) | ||||
−0.939064 | + | 0.343742i | \(0.888305\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −15.7634 | −0.547485 | −0.273742 | − | 0.961803i | \(-0.588262\pi\) | ||||
−0.273742 | + | 0.961803i | \(0.588262\pi\) | |||||||
\(830\) | −22.2858 | −0.773552 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.00743364 | 0.000257715 0 | ||||||||
\(833\) | −105.145 | −3.64306 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.33740 | 0.115496 | ||||||||
\(836\) | −1.46982 | −0.0508347 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 37.6241 | 1.29970 | ||||||||
\(839\) | −19.8149 | −0.684086 | −0.342043 | − | 0.939684i | \(-0.611119\pi\) | ||||
−0.342043 | + | 0.939684i | \(0.611119\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 69.1034 | 2.38146 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 4.99352 | 0.171884 | ||||||||
\(845\) | −33.0515 | −1.13700 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 54.3364 | 1.86702 | ||||||||
\(848\) | 11.1156 | 0.381710 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 15.6004 | 0.535089 | ||||||||
\(851\) | −0.201428 | −0.00690488 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −28.3860 | −0.971918 | −0.485959 | − | 0.873982i | \(-0.661529\pi\) | ||||
−0.485959 | + | 0.873982i | \(0.661529\pi\) | |||||||
\(854\) | 9.51634 | 0.325642 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.55855 | −0.224167 | ||||||||
\(857\) | 46.0087 | 1.57163 | 0.785814 | − | 0.618462i | \(-0.212244\pi\) | ||||
0.785814 | + | 0.618462i | \(0.212244\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 46.3189 | 1.58038 | 0.790191 | − | 0.612861i | \(-0.209982\pi\) | ||||
0.790191 | + | 0.612861i | \(0.209982\pi\) | |||||||
\(860\) | −8.45634 | −0.288359 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 30.7334 | 1.04678 | ||||||||
\(863\) | −17.1707 | −0.584497 | −0.292249 | − | 0.956342i | \(-0.594403\pi\) | ||||
−0.292249 | + | 0.956342i | \(0.594403\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −33.9481 | −1.15427 | ||||||||
\(866\) | 21.7242 | 0.738219 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −49.7450 | −1.68845 | ||||||||
\(869\) | −4.47642 | −0.151852 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.818584 | 0.0277367 | ||||||||
\(872\) | −2.09444 | −0.0709266 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 8.22195 | 0.278112 | ||||||||
\(875\) | 44.4657 | 1.50322 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −41.0178 | −1.38507 | −0.692537 | − | 0.721383i | \(-0.743507\pi\) | ||||
−0.692537 | + | 0.721383i | \(0.743507\pi\) | |||||||
\(878\) | 25.2487 | 0.852103 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 3.59672 | 0.121245 | ||||||||
\(881\) | 12.1431 | 0.409111 | 0.204556 | − | 0.978855i | \(-0.434425\pi\) | ||||
0.204556 | + | 0.978855i | \(0.434425\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 13.3621 | 0.449669 | 0.224835 | − | 0.974397i | \(-0.427816\pi\) | ||||
0.224835 | + | 0.974397i | \(0.427816\pi\) | |||||||
\(884\) | 1.12824 | 0.0379467 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −24.5324 | −0.824181 | ||||||||
\(887\) | −5.50891 | −0.184971 | −0.0924856 | − | 0.995714i | \(-0.529481\pi\) | ||||
−0.0924856 | + | 0.995714i | \(0.529481\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −102.815 | −3.44832 | ||||||||
\(890\) | −17.4296 | −0.584241 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2.94119 | 0.0984785 | ||||||||
\(893\) | −35.6011 | −1.19135 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 16.1016 | 0.538218 | ||||||||
\(896\) | 56.1046 | 1.87432 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 52.3451 | 1.74678 | ||||||||
\(899\) | 8.96888 | 0.299129 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13.1964 | 0.439637 | ||||||||
\(902\) | 3.38509 | 0.112711 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 9.59097 | 0.318991 | ||||||||
\(905\) | −24.5969 | −0.817630 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −19.7017 | −0.654184 | −0.327092 | − | 0.944993i | \(-0.606069\pi\) | ||||
−0.327092 | + | 0.944993i | \(0.606069\pi\) | |||||||
\(908\) | −15.9690 | −0.529951 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −3.82572 | −0.126821 | ||||||||
\(911\) | −43.9735 | −1.45691 | −0.728453 | − | 0.685096i | \(-0.759760\pi\) | ||||
−0.728453 | + | 0.685096i | \(0.759760\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.40266 | −0.0464214 | ||||||||
\(914\) | −67.7136 | −2.23977 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −26.7929 | −0.885263 | ||||||||
\(917\) | 74.4774 | 2.45946 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 27.3654 | 0.902703 | 0.451351 | − | 0.892346i | \(-0.350942\pi\) | ||||
0.451351 | + | 0.892346i | \(0.350942\pi\) | |||||||
\(920\) | −3.98148 | −0.131266 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −50.4973 | −1.66304 | ||||||||
\(923\) | 2.71835 | 0.0894757 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.300746 | 0.00988847 | ||||||||
\(926\) | −11.5007 | −0.377937 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 5.67599 | 0.186323 | ||||||||
\(929\) | −48.2798 | −1.58401 | −0.792004 | − | 0.610516i | \(-0.790962\pi\) | ||||
−0.792004 | + | 0.610516i | \(0.790962\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 82.7384 | 2.71164 | ||||||||
\(932\) | 0.721789 | 0.0236430 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −29.4007 | −0.962022 | ||||||||
\(935\) | 4.27004 | 0.139645 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 24.8928 | 0.813213 | 0.406607 | − | 0.913603i | \(-0.366712\pi\) | ||||
0.406607 | + | 0.913603i | \(0.366712\pi\) | |||||||
\(938\) | −42.0466 | −1.37287 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −21.7048 | −0.707933 | ||||||||
\(941\) | 5.98909 | 0.195239 | 0.0976193 | − | 0.995224i | \(-0.468877\pi\) | ||||
0.0976193 | + | 0.995224i | \(0.468877\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.77658 | −0.220676 | ||||||||
\(944\) | −75.8031 | −2.46718 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.48723 | −0.0483541 | ||||||||
\(947\) | 45.5443 | 1.47999 | 0.739995 | − | 0.672613i | \(-0.234828\pi\) | ||||
0.739995 | + | 0.672613i | \(0.234828\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.871236 | −0.0282815 | ||||||||
\(950\) | −12.2759 | −0.398283 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 46.0304 | 1.49185 | ||||||||
\(953\) | 36.5769 | 1.18484 | 0.592422 | − | 0.805628i | \(-0.298172\pi\) | ||||
0.592422 | + | 0.805628i | \(0.298172\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.35853 | 0.108680 | ||||||||
\(956\) | −25.6621 | −0.829971 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −17.1754 | −0.554912 | ||||||||
\(959\) | 38.2444 | 1.23498 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 49.4407 | 1.59486 | ||||||||
\(962\) | 0.0607765 | 0.00195951 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 4.76988 | 0.153627 | ||||||||
\(965\) | 53.6442 | 1.72687 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.29341 | 0.138067 | 0.0690334 | − | 0.997614i | \(-0.478009\pi\) | ||||
0.0690334 | + | 0.997614i | \(0.478009\pi\) | |||||||
\(968\) | −17.0623 | −0.548404 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 72.1506 | 2.31662 | ||||||||
\(971\) | −12.3990 | −0.397902 | −0.198951 | − | 0.980009i | \(-0.563754\pi\) | ||||
−0.198951 | + | 0.980009i | \(0.563754\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −89.6438 | −2.87385 | ||||||||
\(974\) | 18.5211 | 0.593453 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.40404 | −0.172979 | ||||||||
\(977\) | −5.07082 | −0.162230 | −0.0811150 | − | 0.996705i | \(-0.525848\pi\) | ||||
−0.0811150 | + | 0.996705i | \(0.525848\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.09701 | −0.0350607 | ||||||||
\(980\) | 50.4429 | 1.61134 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 56.3697 | 1.79883 | ||||||||
\(983\) | −7.83628 | −0.249939 | −0.124969 | − | 0.992161i | \(-0.539883\pi\) | ||||
−0.124969 | + | 0.992161i | \(0.539883\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −15.6779 | −0.499540 | ||||||||
\(986\) | 10.4486 | 0.332750 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.887807 | −0.0282449 | ||||||||
\(989\) | 2.97728 | 0.0946719 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 58.1336 | 1.84667 | 0.923337 | − | 0.383990i | \(-0.125450\pi\) | ||||
0.923337 | + | 0.383990i | \(0.125450\pi\) | |||||||
\(992\) | 50.9072 | 1.61631 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −139.628 | −4.42874 | ||||||||
\(995\) | 31.1392 | 0.987178 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −62.9965 | −1.99512 | −0.997560 | − | 0.0698195i | \(-0.977758\pi\) | ||||
−0.997560 | + | 0.0698195i | \(0.977758\pi\) | |||||||
\(998\) | −3.64937 | −0.115519 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6003.2.a.m.1.4 | 11 | ||
3.2 | odd | 2 | 2001.2.a.l.1.8 | ✓ | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2001.2.a.l.1.8 | ✓ | 11 | 3.2 | odd | 2 | ||
6003.2.a.m.1.4 | 11 | 1.1 | even | 1 | trivial |