Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2001,2,Mod(1,2001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2001, 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("2001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2001 = 3 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2001.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: | \(15.9780654445\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - x^{9} - 17x^{8} + 23x^{7} + 69x^{6} - 88x^{5} - 106x^{4} + 101x^{3} + 60x^{2} - 23x - 11 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(2.78422\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.611391 | 0.432318 | 0.216159 | − | 0.976358i | \(-0.430647\pi\) | ||||
0.216159 | + | 0.976358i | \(0.430647\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.62620 | −0.813101 | ||||||||
\(5\) | 0.834863 | 0.373362 | 0.186681 | − | 0.982421i | \(-0.440227\pi\) | ||||
0.186681 | + | 0.982421i | \(0.440227\pi\) | |||||||
\(6\) | −0.611391 | −0.249599 | ||||||||
\(7\) | −0.685491 | −0.259091 | −0.129546 | − | 0.991573i | \(-0.541352\pi\) | ||||
−0.129546 | + | 0.991573i | \(0.541352\pi\) | |||||||
\(8\) | −2.21703 | −0.783837 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.510427 | 0.161411 | ||||||||
\(11\) | −4.30989 | −1.29948 | −0.649741 | − | 0.760156i | \(-0.725122\pi\) | ||||
−0.649741 | + | 0.760156i | \(0.725122\pi\) | |||||||
\(12\) | 1.62620 | 0.469444 | ||||||||
\(13\) | −6.93620 | −1.92375 | −0.961877 | − | 0.273482i | \(-0.911825\pi\) | ||||
−0.961877 | + | 0.273482i | \(0.911825\pi\) | |||||||
\(14\) | −0.419103 | −0.112010 | ||||||||
\(15\) | −0.834863 | −0.215561 | ||||||||
\(16\) | 1.89693 | 0.474234 | ||||||||
\(17\) | 4.35585 | 1.05645 | 0.528225 | − | 0.849105i | \(-0.322858\pi\) | ||||
0.528225 | + | 0.849105i | \(0.322858\pi\) | |||||||
\(18\) | 0.611391 | 0.144106 | ||||||||
\(19\) | 5.00543 | 1.14832 | 0.574162 | − | 0.818742i | \(-0.305328\pi\) | ||||
0.574162 | + | 0.818742i | \(0.305328\pi\) | |||||||
\(20\) | −1.35766 | −0.303581 | ||||||||
\(21\) | 0.685491 | 0.149586 | ||||||||
\(22\) | −2.63503 | −0.561790 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 2.21703 | 0.452548 | ||||||||
\(25\) | −4.30300 | −0.860601 | ||||||||
\(26\) | −4.24072 | −0.831674 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.11475 | 0.210667 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | −0.510427 | −0.0931908 | ||||||||
\(31\) | 9.44967 | 1.69721 | 0.848606 | − | 0.529026i | \(-0.177442\pi\) | ||||
0.848606 | + | 0.529026i | \(0.177442\pi\) | |||||||
\(32\) | 5.59382 | 0.988857 | ||||||||
\(33\) | 4.30989 | 0.750256 | ||||||||
\(34\) | 2.66313 | 0.456723 | ||||||||
\(35\) | −0.572291 | −0.0967348 | ||||||||
\(36\) | −1.62620 | −0.271034 | ||||||||
\(37\) | 7.15237 | 1.17584 | 0.587921 | − | 0.808918i | \(-0.299946\pi\) | ||||
0.587921 | + | 0.808918i | \(0.299946\pi\) | |||||||
\(38\) | 3.06027 | 0.496441 | ||||||||
\(39\) | 6.93620 | 1.11068 | ||||||||
\(40\) | −1.85091 | −0.292655 | ||||||||
\(41\) | −3.83893 | −0.599540 | −0.299770 | − | 0.954011i | \(-0.596910\pi\) | ||||
−0.299770 | + | 0.954011i | \(0.596910\pi\) | |||||||
\(42\) | 0.419103 | 0.0646689 | ||||||||
\(43\) | −7.88050 | −1.20176 | −0.600882 | − | 0.799337i | \(-0.705184\pi\) | ||||
−0.600882 | + | 0.799337i | \(0.705184\pi\) | |||||||
\(44\) | 7.00875 | 1.05661 | ||||||||
\(45\) | 0.834863 | 0.124454 | ||||||||
\(46\) | −0.611391 | −0.0901446 | ||||||||
\(47\) | 6.51919 | 0.950922 | 0.475461 | − | 0.879737i | \(-0.342281\pi\) | ||||
0.475461 | + | 0.879737i | \(0.342281\pi\) | |||||||
\(48\) | −1.89693 | −0.273799 | ||||||||
\(49\) | −6.53010 | −0.932872 | ||||||||
\(50\) | −2.63082 | −0.372054 | ||||||||
\(51\) | −4.35585 | −0.609942 | ||||||||
\(52\) | 11.2797 | 1.56421 | ||||||||
\(53\) | −5.81406 | −0.798623 | −0.399312 | − | 0.916815i | \(-0.630751\pi\) | ||||
−0.399312 | + | 0.916815i | \(0.630751\pi\) | |||||||
\(54\) | −0.611391 | −0.0831997 | ||||||||
\(55\) | −3.59817 | −0.485177 | ||||||||
\(56\) | 1.51975 | 0.203085 | ||||||||
\(57\) | −5.00543 | −0.662985 | ||||||||
\(58\) | 0.611391 | 0.0802795 | ||||||||
\(59\) | 12.3793 | 1.61165 | 0.805826 | − | 0.592152i | \(-0.201722\pi\) | ||||
0.805826 | + | 0.592152i | \(0.201722\pi\) | |||||||
\(60\) | 1.35766 | 0.175273 | ||||||||
\(61\) | 14.2688 | 1.82693 | 0.913465 | − | 0.406916i | \(-0.133396\pi\) | ||||
0.913465 | + | 0.406916i | \(0.133396\pi\) | |||||||
\(62\) | 5.77744 | 0.733736 | ||||||||
\(63\) | −0.685491 | −0.0863637 | ||||||||
\(64\) | −0.373862 | −0.0467327 | ||||||||
\(65\) | −5.79077 | −0.718257 | ||||||||
\(66\) | 2.63503 | 0.324349 | ||||||||
\(67\) | 5.19008 | 0.634069 | 0.317035 | − | 0.948414i | \(-0.397313\pi\) | ||||
0.317035 | + | 0.948414i | \(0.397313\pi\) | |||||||
\(68\) | −7.08350 | −0.859000 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | −0.349893 | −0.0418202 | ||||||||
\(71\) | −9.86256 | −1.17047 | −0.585235 | − | 0.810864i | \(-0.698998\pi\) | ||||
−0.585235 | + | 0.810864i | \(0.698998\pi\) | |||||||
\(72\) | −2.21703 | −0.261279 | ||||||||
\(73\) | 10.3402 | 1.21023 | 0.605113 | − | 0.796140i | \(-0.293128\pi\) | ||||
0.605113 | + | 0.796140i | \(0.293128\pi\) | |||||||
\(74\) | 4.37289 | 0.508339 | ||||||||
\(75\) | 4.30300 | 0.496868 | ||||||||
\(76\) | −8.13983 | −0.933703 | ||||||||
\(77\) | 2.95439 | 0.336684 | ||||||||
\(78\) | 4.24072 | 0.480167 | ||||||||
\(79\) | −0.255706 | −0.0287692 | −0.0143846 | − | 0.999897i | \(-0.504579\pi\) | ||||
−0.0143846 | + | 0.999897i | \(0.504579\pi\) | |||||||
\(80\) | 1.58368 | 0.177061 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −2.34709 | −0.259192 | ||||||||
\(83\) | 3.16558 | 0.347467 | 0.173734 | − | 0.984793i | \(-0.444417\pi\) | ||||
0.173734 | + | 0.984793i | \(0.444417\pi\) | |||||||
\(84\) | −1.11475 | −0.121629 | ||||||||
\(85\) | 3.63654 | 0.394438 | ||||||||
\(86\) | −4.81806 | −0.519545 | ||||||||
\(87\) | −1.00000 | −0.107211 | ||||||||
\(88\) | 9.55514 | 1.01858 | ||||||||
\(89\) | 11.3236 | 1.20030 | 0.600148 | − | 0.799889i | \(-0.295108\pi\) | ||||
0.600148 | + | 0.799889i | \(0.295108\pi\) | |||||||
\(90\) | 0.510427 | 0.0538038 | ||||||||
\(91\) | 4.75470 | 0.498428 | ||||||||
\(92\) | 1.62620 | 0.169543 | ||||||||
\(93\) | −9.44967 | −0.979886 | ||||||||
\(94\) | 3.98577 | 0.411101 | ||||||||
\(95\) | 4.17884 | 0.428740 | ||||||||
\(96\) | −5.59382 | −0.570917 | ||||||||
\(97\) | 5.84187 | 0.593152 | 0.296576 | − | 0.955009i | \(-0.404155\pi\) | ||||
0.296576 | + | 0.955009i | \(0.404155\pi\) | |||||||
\(98\) | −3.99244 | −0.403298 | ||||||||
\(99\) | −4.30989 | −0.433160 | ||||||||
\(100\) | 6.99755 | 0.699755 | ||||||||
\(101\) | 12.7292 | 1.26660 | 0.633302 | − | 0.773905i | \(-0.281699\pi\) | ||||
0.633302 | + | 0.773905i | \(0.281699\pi\) | |||||||
\(102\) | −2.66313 | −0.263689 | ||||||||
\(103\) | −15.6336 | −1.54042 | −0.770212 | − | 0.637788i | \(-0.779850\pi\) | ||||
−0.770212 | + | 0.637788i | \(0.779850\pi\) | |||||||
\(104\) | 15.3777 | 1.50791 | ||||||||
\(105\) | 0.572291 | 0.0558499 | ||||||||
\(106\) | −3.55466 | −0.345259 | ||||||||
\(107\) | 4.65571 | 0.450084 | 0.225042 | − | 0.974349i | \(-0.427748\pi\) | ||||
0.225042 | + | 0.974349i | \(0.427748\pi\) | |||||||
\(108\) | 1.62620 | 0.156481 | ||||||||
\(109\) | −4.75799 | −0.455732 | −0.227866 | − | 0.973692i | \(-0.573175\pi\) | ||||
−0.227866 | + | 0.973692i | \(0.573175\pi\) | |||||||
\(110\) | −2.19989 | −0.209751 | ||||||||
\(111\) | −7.15237 | −0.678873 | ||||||||
\(112\) | −1.30033 | −0.122870 | ||||||||
\(113\) | −10.5909 | −0.996306 | −0.498153 | − | 0.867089i | \(-0.665988\pi\) | ||||
−0.498153 | + | 0.867089i | \(0.665988\pi\) | |||||||
\(114\) | −3.06027 | −0.286621 | ||||||||
\(115\) | −0.834863 | −0.0778514 | ||||||||
\(116\) | −1.62620 | −0.150989 | ||||||||
\(117\) | −6.93620 | −0.641251 | ||||||||
\(118\) | 7.56861 | 0.696747 | ||||||||
\(119\) | −2.98590 | −0.273717 | ||||||||
\(120\) | 1.85091 | 0.168964 | ||||||||
\(121\) | 7.57516 | 0.688651 | ||||||||
\(122\) | 8.72380 | 0.789816 | ||||||||
\(123\) | 3.83893 | 0.346145 | ||||||||
\(124\) | −15.3671 | −1.38000 | ||||||||
\(125\) | −7.76673 | −0.694678 | ||||||||
\(126\) | −0.419103 | −0.0373366 | ||||||||
\(127\) | 8.28369 | 0.735058 | 0.367529 | − | 0.930012i | \(-0.380204\pi\) | ||||
0.367529 | + | 0.930012i | \(0.380204\pi\) | |||||||
\(128\) | −11.4162 | −1.00906 | ||||||||
\(129\) | 7.88050 | 0.693839 | ||||||||
\(130\) | −3.54042 | −0.310516 | ||||||||
\(131\) | 1.34215 | 0.117264 | 0.0586320 | − | 0.998280i | \(-0.481326\pi\) | ||||
0.0586320 | + | 0.998280i | \(0.481326\pi\) | |||||||
\(132\) | −7.00875 | −0.610034 | ||||||||
\(133\) | −3.43117 | −0.297521 | ||||||||
\(134\) | 3.17317 | 0.274120 | ||||||||
\(135\) | −0.834863 | −0.0718535 | ||||||||
\(136\) | −9.65704 | −0.828084 | ||||||||
\(137\) | 2.09029 | 0.178585 | 0.0892926 | − | 0.996005i | \(-0.471539\pi\) | ||||
0.0892926 | + | 0.996005i | \(0.471539\pi\) | |||||||
\(138\) | 0.611391 | 0.0520450 | ||||||||
\(139\) | 3.71254 | 0.314893 | 0.157447 | − | 0.987528i | \(-0.449674\pi\) | ||||
0.157447 | + | 0.987528i | \(0.449674\pi\) | |||||||
\(140\) | 0.930660 | 0.0786551 | ||||||||
\(141\) | −6.51919 | −0.549015 | ||||||||
\(142\) | −6.02988 | −0.506016 | ||||||||
\(143\) | 29.8942 | 2.49988 | ||||||||
\(144\) | 1.89693 | 0.158078 | ||||||||
\(145\) | 0.834863 | 0.0693316 | ||||||||
\(146\) | 6.32189 | 0.523203 | ||||||||
\(147\) | 6.53010 | 0.538594 | ||||||||
\(148\) | −11.6312 | −0.956079 | ||||||||
\(149\) | 0.963445 | 0.0789285 | 0.0394642 | − | 0.999221i | \(-0.487435\pi\) | ||||
0.0394642 | + | 0.999221i | \(0.487435\pi\) | |||||||
\(150\) | 2.63082 | 0.214805 | ||||||||
\(151\) | 21.5727 | 1.75556 | 0.877779 | − | 0.479065i | \(-0.159024\pi\) | ||||
0.877779 | + | 0.479065i | \(0.159024\pi\) | |||||||
\(152\) | −11.0972 | −0.900098 | ||||||||
\(153\) | 4.35585 | 0.352150 | ||||||||
\(154\) | 1.80629 | 0.145555 | ||||||||
\(155\) | 7.88918 | 0.633674 | ||||||||
\(156\) | −11.2797 | −0.903095 | ||||||||
\(157\) | −9.60822 | −0.766820 | −0.383410 | − | 0.923578i | \(-0.625250\pi\) | ||||
−0.383410 | + | 0.923578i | \(0.625250\pi\) | |||||||
\(158\) | −0.156336 | −0.0124375 | ||||||||
\(159\) | 5.81406 | 0.461085 | ||||||||
\(160\) | 4.67007 | 0.369202 | ||||||||
\(161\) | 0.685491 | 0.0540242 | ||||||||
\(162\) | 0.611391 | 0.0480354 | ||||||||
\(163\) | 22.2529 | 1.74298 | 0.871489 | − | 0.490415i | \(-0.163155\pi\) | ||||
0.871489 | + | 0.490415i | \(0.163155\pi\) | |||||||
\(164\) | 6.24288 | 0.487487 | ||||||||
\(165\) | 3.59817 | 0.280117 | ||||||||
\(166\) | 1.93540 | 0.150216 | ||||||||
\(167\) | 17.6567 | 1.36632 | 0.683158 | − | 0.730270i | \(-0.260606\pi\) | ||||
0.683158 | + | 0.730270i | \(0.260606\pi\) | |||||||
\(168\) | −1.51975 | −0.117251 | ||||||||
\(169\) | 35.1108 | 2.70083 | ||||||||
\(170\) | 2.22335 | 0.170523 | ||||||||
\(171\) | 5.00543 | 0.382775 | ||||||||
\(172\) | 12.8153 | 0.977156 | ||||||||
\(173\) | 5.17476 | 0.393430 | 0.196715 | − | 0.980461i | \(-0.436973\pi\) | ||||
0.196715 | + | 0.980461i | \(0.436973\pi\) | |||||||
\(174\) | −0.611391 | −0.0463494 | ||||||||
\(175\) | 2.94967 | 0.222974 | ||||||||
\(176\) | −8.17558 | −0.616258 | ||||||||
\(177\) | −12.3793 | −0.930488 | ||||||||
\(178\) | 6.92312 | 0.518910 | ||||||||
\(179\) | −3.93984 | −0.294477 | −0.147239 | − | 0.989101i | \(-0.547039\pi\) | ||||
−0.147239 | + | 0.989101i | \(0.547039\pi\) | |||||||
\(180\) | −1.35766 | −0.101194 | ||||||||
\(181\) | 4.69684 | 0.349114 | 0.174557 | − | 0.984647i | \(-0.444151\pi\) | ||||
0.174557 | + | 0.984647i | \(0.444151\pi\) | |||||||
\(182\) | 2.90698 | 0.215480 | ||||||||
\(183\) | −14.2688 | −1.05478 | ||||||||
\(184\) | 2.21703 | 0.163441 | ||||||||
\(185\) | 5.97125 | 0.439015 | ||||||||
\(186\) | −5.77744 | −0.423623 | ||||||||
\(187\) | −18.7733 | −1.37284 | ||||||||
\(188\) | −10.6015 | −0.773195 | ||||||||
\(189\) | 0.685491 | 0.0498621 | ||||||||
\(190\) | 2.55491 | 0.185352 | ||||||||
\(191\) | 18.7144 | 1.35413 | 0.677064 | − | 0.735924i | \(-0.263252\pi\) | ||||
0.677064 | + | 0.735924i | \(0.263252\pi\) | |||||||
\(192\) | 0.373862 | 0.0269812 | ||||||||
\(193\) | −23.7007 | −1.70602 | −0.853008 | − | 0.521898i | \(-0.825224\pi\) | ||||
−0.853008 | + | 0.521898i | \(0.825224\pi\) | |||||||
\(194\) | 3.57167 | 0.256431 | ||||||||
\(195\) | 5.79077 | 0.414686 | ||||||||
\(196\) | 10.6193 | 0.758519 | ||||||||
\(197\) | −21.4337 | −1.52709 | −0.763544 | − | 0.645756i | \(-0.776542\pi\) | ||||
−0.763544 | + | 0.645756i | \(0.776542\pi\) | |||||||
\(198\) | −2.63503 | −0.187263 | ||||||||
\(199\) | −2.13493 | −0.151341 | −0.0756707 | − | 0.997133i | \(-0.524110\pi\) | ||||
−0.0756707 | + | 0.997133i | \(0.524110\pi\) | |||||||
\(200\) | 9.53987 | 0.674571 | ||||||||
\(201\) | −5.19008 | −0.366080 | ||||||||
\(202\) | 7.78252 | 0.547576 | ||||||||
\(203\) | −0.685491 | −0.0481120 | ||||||||
\(204\) | 7.08350 | 0.495944 | ||||||||
\(205\) | −3.20498 | −0.223846 | ||||||||
\(206\) | −9.55824 | −0.665954 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | −13.1575 | −0.912309 | ||||||||
\(209\) | −21.5728 | −1.49222 | ||||||||
\(210\) | 0.349893 | 0.0241449 | ||||||||
\(211\) | 0.324360 | 0.0223299 | 0.0111649 | − | 0.999938i | \(-0.496446\pi\) | ||||
0.0111649 | + | 0.999938i | \(0.496446\pi\) | |||||||
\(212\) | 9.45484 | 0.649361 | ||||||||
\(213\) | 9.86256 | 0.675771 | ||||||||
\(214\) | 2.84646 | 0.194580 | ||||||||
\(215\) | −6.57914 | −0.448693 | ||||||||
\(216\) | 2.21703 | 0.150849 | ||||||||
\(217\) | −6.47767 | −0.439733 | ||||||||
\(218\) | −2.90899 | −0.197021 | ||||||||
\(219\) | −10.3402 | −0.698724 | ||||||||
\(220\) | 5.85135 | 0.394498 | ||||||||
\(221\) | −30.2131 | −2.03235 | ||||||||
\(222\) | −4.37289 | −0.293489 | ||||||||
\(223\) | −10.7572 | −0.720354 | −0.360177 | − | 0.932884i | \(-0.617284\pi\) | ||||
−0.360177 | + | 0.932884i | \(0.617284\pi\) | |||||||
\(224\) | −3.83451 | −0.256204 | ||||||||
\(225\) | −4.30300 | −0.286867 | ||||||||
\(226\) | −6.47516 | −0.430721 | ||||||||
\(227\) | 18.4688 | 1.22582 | 0.612908 | − | 0.790154i | \(-0.290000\pi\) | ||||
0.612908 | + | 0.790154i | \(0.290000\pi\) | |||||||
\(228\) | 8.13983 | 0.539074 | ||||||||
\(229\) | −21.7562 | −1.43769 | −0.718846 | − | 0.695169i | \(-0.755330\pi\) | ||||
−0.718846 | + | 0.695169i | \(0.755330\pi\) | |||||||
\(230\) | −0.510427 | −0.0336566 | ||||||||
\(231\) | −2.95439 | −0.194385 | ||||||||
\(232\) | −2.21703 | −0.145555 | ||||||||
\(233\) | 5.18209 | 0.339490 | 0.169745 | − | 0.985488i | \(-0.445706\pi\) | ||||
0.169745 | + | 0.985488i | \(0.445706\pi\) | |||||||
\(234\) | −4.24072 | −0.277225 | ||||||||
\(235\) | 5.44263 | 0.355038 | ||||||||
\(236\) | −20.1313 | −1.31044 | ||||||||
\(237\) | 0.255706 | 0.0166099 | ||||||||
\(238\) | −1.82555 | −0.118333 | ||||||||
\(239\) | 2.60340 | 0.168400 | 0.0841999 | − | 0.996449i | \(-0.473167\pi\) | ||||
0.0841999 | + | 0.996449i | \(0.473167\pi\) | |||||||
\(240\) | −1.58368 | −0.102226 | ||||||||
\(241\) | 4.88851 | 0.314896 | 0.157448 | − | 0.987527i | \(-0.449673\pi\) | ||||
0.157448 | + | 0.987527i | \(0.449673\pi\) | |||||||
\(242\) | 4.63138 | 0.297717 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −23.2039 | −1.48548 | ||||||||
\(245\) | −5.45174 | −0.348299 | ||||||||
\(246\) | 2.34709 | 0.149645 | ||||||||
\(247\) | −34.7186 | −2.20909 | ||||||||
\(248\) | −20.9502 | −1.33034 | ||||||||
\(249\) | −3.16558 | −0.200610 | ||||||||
\(250\) | −4.74851 | −0.300322 | ||||||||
\(251\) | 12.7129 | 0.802432 | 0.401216 | − | 0.915984i | \(-0.368588\pi\) | ||||
0.401216 | + | 0.915984i | \(0.368588\pi\) | |||||||
\(252\) | 1.11475 | 0.0702224 | ||||||||
\(253\) | 4.30989 | 0.270961 | ||||||||
\(254\) | 5.06457 | 0.317779 | ||||||||
\(255\) | −3.63654 | −0.227729 | ||||||||
\(256\) | −6.23204 | −0.389503 | ||||||||
\(257\) | 16.1859 | 1.00965 | 0.504825 | − | 0.863222i | \(-0.331557\pi\) | ||||
0.504825 | + | 0.863222i | \(0.331557\pi\) | |||||||
\(258\) | 4.81806 | 0.299959 | ||||||||
\(259\) | −4.90289 | −0.304651 | ||||||||
\(260\) | 9.41696 | 0.584015 | ||||||||
\(261\) | 1.00000 | 0.0618984 | ||||||||
\(262\) | 0.820577 | 0.0506954 | ||||||||
\(263\) | 12.8887 | 0.794749 | 0.397374 | − | 0.917657i | \(-0.369921\pi\) | ||||
0.397374 | + | 0.917657i | \(0.369921\pi\) | |||||||
\(264\) | −9.55514 | −0.588078 | ||||||||
\(265\) | −4.85395 | −0.298176 | ||||||||
\(266\) | −2.09779 | −0.128624 | ||||||||
\(267\) | −11.3236 | −0.692991 | ||||||||
\(268\) | −8.44011 | −0.515562 | ||||||||
\(269\) | −1.11547 | −0.0680112 | −0.0340056 | − | 0.999422i | \(-0.510826\pi\) | ||||
−0.0340056 | + | 0.999422i | \(0.510826\pi\) | |||||||
\(270\) | −0.510427 | −0.0310636 | ||||||||
\(271\) | −5.92399 | −0.359857 | −0.179928 | − | 0.983680i | \(-0.557587\pi\) | ||||
−0.179928 | + | 0.983680i | \(0.557587\pi\) | |||||||
\(272\) | 8.26277 | 0.501004 | ||||||||
\(273\) | −4.75470 | −0.287767 | ||||||||
\(274\) | 1.27798 | 0.0772057 | ||||||||
\(275\) | 18.5455 | 1.11833 | ||||||||
\(276\) | −1.62620 | −0.0978858 | ||||||||
\(277\) | −25.0512 | −1.50518 | −0.752589 | − | 0.658491i | \(-0.771195\pi\) | ||||
−0.752589 | + | 0.658491i | \(0.771195\pi\) | |||||||
\(278\) | 2.26981 | 0.136134 | ||||||||
\(279\) | 9.44967 | 0.565737 | ||||||||
\(280\) | 1.26878 | 0.0758243 | ||||||||
\(281\) | −16.4921 | −0.983834 | −0.491917 | − | 0.870642i | \(-0.663704\pi\) | ||||
−0.491917 | + | 0.870642i | \(0.663704\pi\) | |||||||
\(282\) | −3.98577 | −0.237349 | ||||||||
\(283\) | −26.8068 | −1.59350 | −0.796751 | − | 0.604308i | \(-0.793450\pi\) | ||||
−0.796751 | + | 0.604308i | \(0.793450\pi\) | |||||||
\(284\) | 16.0385 | 0.951710 | ||||||||
\(285\) | −4.17884 | −0.247533 | ||||||||
\(286\) | 18.2771 | 1.08075 | ||||||||
\(287\) | 2.63155 | 0.155336 | ||||||||
\(288\) | 5.59382 | 0.329619 | ||||||||
\(289\) | 1.97346 | 0.116086 | ||||||||
\(290\) | 0.510427 | 0.0299733 | ||||||||
\(291\) | −5.84187 | −0.342457 | ||||||||
\(292\) | −16.8152 | −0.984036 | ||||||||
\(293\) | −11.2496 | −0.657210 | −0.328605 | − | 0.944467i | \(-0.606579\pi\) | ||||
−0.328605 | + | 0.944467i | \(0.606579\pi\) | |||||||
\(294\) | 3.99244 | 0.232844 | ||||||||
\(295\) | 10.3350 | 0.601730 | ||||||||
\(296\) | −15.8570 | −0.921669 | ||||||||
\(297\) | 4.30989 | 0.250085 | ||||||||
\(298\) | 0.589041 | 0.0341222 | ||||||||
\(299\) | 6.93620 | 0.401131 | ||||||||
\(300\) | −6.99755 | −0.404004 | ||||||||
\(301\) | 5.40201 | 0.311367 | ||||||||
\(302\) | 13.1893 | 0.758960 | ||||||||
\(303\) | −12.7292 | −0.731274 | ||||||||
\(304\) | 9.49497 | 0.544574 | ||||||||
\(305\) | 11.9125 | 0.682107 | ||||||||
\(306\) | 2.66313 | 0.152241 | ||||||||
\(307\) | −3.26882 | −0.186562 | −0.0932808 | − | 0.995640i | \(-0.529735\pi\) | ||||
−0.0932808 | + | 0.995640i | \(0.529735\pi\) | |||||||
\(308\) | −4.80443 | −0.273758 | ||||||||
\(309\) | 15.6336 | 0.889365 | ||||||||
\(310\) | 4.82337 | 0.273949 | ||||||||
\(311\) | −6.84083 | −0.387908 | −0.193954 | − | 0.981011i | \(-0.562131\pi\) | ||||
−0.193954 | + | 0.981011i | \(0.562131\pi\) | |||||||
\(312\) | −15.3777 | −0.870592 | ||||||||
\(313\) | −10.8195 | −0.611552 | −0.305776 | − | 0.952103i | \(-0.598916\pi\) | ||||
−0.305776 | + | 0.952103i | \(0.598916\pi\) | |||||||
\(314\) | −5.87438 | −0.331510 | ||||||||
\(315\) | −0.572291 | −0.0322449 | ||||||||
\(316\) | 0.415830 | 0.0233923 | ||||||||
\(317\) | 21.5866 | 1.21242 | 0.606212 | − | 0.795303i | \(-0.292688\pi\) | ||||
0.606212 | + | 0.795303i | \(0.292688\pi\) | |||||||
\(318\) | 3.55466 | 0.199336 | ||||||||
\(319\) | −4.30989 | −0.241308 | ||||||||
\(320\) | −0.312123 | −0.0174482 | ||||||||
\(321\) | −4.65571 | −0.259856 | ||||||||
\(322\) | 0.419103 | 0.0233557 | ||||||||
\(323\) | 21.8029 | 1.21315 | ||||||||
\(324\) | −1.62620 | −0.0903445 | ||||||||
\(325\) | 29.8465 | 1.65558 | ||||||||
\(326\) | 13.6052 | 0.753522 | ||||||||
\(327\) | 4.75799 | 0.263117 | ||||||||
\(328\) | 8.51101 | 0.469942 | ||||||||
\(329\) | −4.46884 | −0.246375 | ||||||||
\(330\) | 2.19989 | 0.121100 | ||||||||
\(331\) | −26.1848 | −1.43925 | −0.719624 | − | 0.694364i | \(-0.755686\pi\) | ||||
−0.719624 | + | 0.694364i | \(0.755686\pi\) | |||||||
\(332\) | −5.14786 | −0.282526 | ||||||||
\(333\) | 7.15237 | 0.391948 | ||||||||
\(334\) | 10.7951 | 0.590684 | ||||||||
\(335\) | 4.33300 | 0.236737 | ||||||||
\(336\) | 1.30033 | 0.0709389 | ||||||||
\(337\) | −4.93868 | −0.269027 | −0.134513 | − | 0.990912i | \(-0.542947\pi\) | ||||
−0.134513 | + | 0.990912i | \(0.542947\pi\) | |||||||
\(338\) | 21.4664 | 1.16762 | ||||||||
\(339\) | 10.5909 | 0.575218 | ||||||||
\(340\) | −5.91375 | −0.320718 | ||||||||
\(341\) | −40.7271 | −2.20549 | ||||||||
\(342\) | 3.06027 | 0.165480 | ||||||||
\(343\) | 9.27476 | 0.500790 | ||||||||
\(344\) | 17.4713 | 0.941988 | ||||||||
\(345\) | 0.834863 | 0.0449475 | ||||||||
\(346\) | 3.16380 | 0.170087 | ||||||||
\(347\) | −23.6045 | −1.26716 | −0.633579 | − | 0.773678i | \(-0.718415\pi\) | ||||
−0.633579 | + | 0.773678i | \(0.718415\pi\) | |||||||
\(348\) | 1.62620 | 0.0871736 | ||||||||
\(349\) | −11.7720 | −0.630141 | −0.315070 | − | 0.949068i | \(-0.602028\pi\) | ||||
−0.315070 | + | 0.949068i | \(0.602028\pi\) | |||||||
\(350\) | 1.80340 | 0.0963958 | ||||||||
\(351\) | 6.93620 | 0.370227 | ||||||||
\(352\) | −24.1088 | −1.28500 | ||||||||
\(353\) | 17.0723 | 0.908669 | 0.454334 | − | 0.890831i | \(-0.349877\pi\) | ||||
0.454334 | + | 0.890831i | \(0.349877\pi\) | |||||||
\(354\) | −7.56861 | −0.402267 | ||||||||
\(355\) | −8.23388 | −0.437009 | ||||||||
\(356\) | −18.4144 | −0.975961 | ||||||||
\(357\) | 2.98590 | 0.158030 | ||||||||
\(358\) | −2.40878 | −0.127308 | ||||||||
\(359\) | 33.2963 | 1.75731 | 0.878655 | − | 0.477456i | \(-0.158441\pi\) | ||||
0.878655 | + | 0.477456i | \(0.158441\pi\) | |||||||
\(360\) | −1.85091 | −0.0975516 | ||||||||
\(361\) | 6.05430 | 0.318647 | ||||||||
\(362\) | 2.87160 | 0.150928 | ||||||||
\(363\) | −7.57516 | −0.397593 | ||||||||
\(364\) | −7.73210 | −0.405272 | ||||||||
\(365\) | 8.63263 | 0.451852 | ||||||||
\(366\) | −8.72380 | −0.456000 | ||||||||
\(367\) | −17.4010 | −0.908327 | −0.454163 | − | 0.890918i | \(-0.650062\pi\) | ||||
−0.454163 | + | 0.890918i | \(0.650062\pi\) | |||||||
\(368\) | −1.89693 | −0.0988846 | ||||||||
\(369\) | −3.83893 | −0.199847 | ||||||||
\(370\) | 3.65077 | 0.189794 | ||||||||
\(371\) | 3.98549 | 0.206916 | ||||||||
\(372\) | 15.3671 | 0.796746 | ||||||||
\(373\) | −27.0425 | −1.40021 | −0.700104 | − | 0.714041i | \(-0.746863\pi\) | ||||
−0.700104 | + | 0.714041i | \(0.746863\pi\) | |||||||
\(374\) | −11.4778 | −0.593502 | ||||||||
\(375\) | 7.76673 | 0.401072 | ||||||||
\(376\) | −14.4532 | −0.745367 | ||||||||
\(377\) | −6.93620 | −0.357232 | ||||||||
\(378\) | 0.419103 | 0.0215563 | ||||||||
\(379\) | −5.91128 | −0.303642 | −0.151821 | − | 0.988408i | \(-0.548514\pi\) | ||||
−0.151821 | + | 0.988408i | \(0.548514\pi\) | |||||||
\(380\) | −6.79564 | −0.348609 | ||||||||
\(381\) | −8.28369 | −0.424386 | ||||||||
\(382\) | 11.4418 | 0.585414 | ||||||||
\(383\) | 33.5241 | 1.71300 | 0.856502 | − | 0.516144i | \(-0.172633\pi\) | ||||
0.856502 | + | 0.516144i | \(0.172633\pi\) | |||||||
\(384\) | 11.4162 | 0.582581 | ||||||||
\(385\) | 2.46651 | 0.125705 | ||||||||
\(386\) | −14.4904 | −0.737542 | ||||||||
\(387\) | −7.88050 | −0.400588 | ||||||||
\(388\) | −9.50006 | −0.482293 | ||||||||
\(389\) | −36.5143 | −1.85135 | −0.925674 | − | 0.378321i | \(-0.876501\pi\) | ||||
−0.925674 | + | 0.378321i | \(0.876501\pi\) | |||||||
\(390\) | 3.54042 | 0.179276 | ||||||||
\(391\) | −4.35585 | −0.220285 | ||||||||
\(392\) | 14.4774 | 0.731219 | ||||||||
\(393\) | −1.34215 | −0.0677024 | ||||||||
\(394\) | −13.1044 | −0.660188 | ||||||||
\(395\) | −0.213480 | −0.0107413 | ||||||||
\(396\) | 7.00875 | 0.352203 | ||||||||
\(397\) | 6.90723 | 0.346664 | 0.173332 | − | 0.984863i | \(-0.444547\pi\) | ||||
0.173332 | + | 0.984863i | \(0.444547\pi\) | |||||||
\(398\) | −1.30528 | −0.0654276 | ||||||||
\(399\) | 3.43117 | 0.171774 | ||||||||
\(400\) | −8.16252 | −0.408126 | ||||||||
\(401\) | 17.0761 | 0.852739 | 0.426370 | − | 0.904549i | \(-0.359792\pi\) | ||||
0.426370 | + | 0.904549i | \(0.359792\pi\) | |||||||
\(402\) | −3.17317 | −0.158263 | ||||||||
\(403\) | −65.5448 | −3.26502 | ||||||||
\(404\) | −20.7003 | −1.02988 | ||||||||
\(405\) | 0.834863 | 0.0414847 | ||||||||
\(406\) | −0.419103 | −0.0207997 | ||||||||
\(407\) | −30.8260 | −1.52799 | ||||||||
\(408\) | 9.65704 | 0.478095 | ||||||||
\(409\) | 19.7240 | 0.975291 | 0.487646 | − | 0.873042i | \(-0.337856\pi\) | ||||
0.487646 | + | 0.873042i | \(0.337856\pi\) | |||||||
\(410\) | −1.95950 | −0.0967726 | ||||||||
\(411\) | −2.09029 | −0.103106 | ||||||||
\(412\) | 25.4234 | 1.25252 | ||||||||
\(413\) | −8.48592 | −0.417565 | ||||||||
\(414\) | −0.611391 | −0.0300482 | ||||||||
\(415\) | 2.64282 | 0.129731 | ||||||||
\(416\) | −38.7998 | −1.90232 | ||||||||
\(417\) | −3.71254 | −0.181804 | ||||||||
\(418\) | −13.1894 | −0.645116 | ||||||||
\(419\) | −8.17325 | −0.399289 | −0.199645 | − | 0.979868i | \(-0.563979\pi\) | ||||
−0.199645 | + | 0.979868i | \(0.563979\pi\) | |||||||
\(420\) | −0.930660 | −0.0454116 | ||||||||
\(421\) | −19.2844 | −0.939865 | −0.469932 | − | 0.882702i | \(-0.655722\pi\) | ||||
−0.469932 | + | 0.882702i | \(0.655722\pi\) | |||||||
\(422\) | 0.198311 | 0.00965361 | ||||||||
\(423\) | 6.51919 | 0.316974 | ||||||||
\(424\) | 12.8899 | 0.625990 | ||||||||
\(425\) | −18.7433 | −0.909182 | ||||||||
\(426\) | 6.02988 | 0.292148 | ||||||||
\(427\) | −9.78112 | −0.473342 | ||||||||
\(428\) | −7.57112 | −0.365964 | ||||||||
\(429\) | −29.8942 | −1.44331 | ||||||||
\(430\) | −4.02242 | −0.193978 | ||||||||
\(431\) | 38.4805 | 1.85354 | 0.926771 | − | 0.375627i | \(-0.122573\pi\) | ||||
0.926771 | + | 0.375627i | \(0.122573\pi\) | |||||||
\(432\) | −1.89693 | −0.0912663 | ||||||||
\(433\) | −6.78157 | −0.325902 | −0.162951 | − | 0.986634i | \(-0.552101\pi\) | ||||
−0.162951 | + | 0.986634i | \(0.552101\pi\) | |||||||
\(434\) | −3.96038 | −0.190104 | ||||||||
\(435\) | −0.834863 | −0.0400286 | ||||||||
\(436\) | 7.73744 | 0.370556 | ||||||||
\(437\) | −5.00543 | −0.239442 | ||||||||
\(438\) | −6.32189 | −0.302071 | ||||||||
\(439\) | 25.2260 | 1.20397 | 0.601985 | − | 0.798508i | \(-0.294377\pi\) | ||||
0.601985 | + | 0.798508i | \(0.294377\pi\) | |||||||
\(440\) | 7.97723 | 0.380299 | ||||||||
\(441\) | −6.53010 | −0.310957 | ||||||||
\(442\) | −18.4720 | −0.878622 | ||||||||
\(443\) | 2.71891 | 0.129180 | 0.0645898 | − | 0.997912i | \(-0.479426\pi\) | ||||
0.0645898 | + | 0.997912i | \(0.479426\pi\) | |||||||
\(444\) | 11.6312 | 0.551992 | ||||||||
\(445\) | 9.45362 | 0.448145 | ||||||||
\(446\) | −6.57684 | −0.311422 | ||||||||
\(447\) | −0.963445 | −0.0455694 | ||||||||
\(448\) | 0.256279 | 0.0121080 | ||||||||
\(449\) | 1.22087 | 0.0576166 | 0.0288083 | − | 0.999585i | \(-0.490829\pi\) | ||||
0.0288083 | + | 0.999585i | \(0.490829\pi\) | |||||||
\(450\) | −2.63082 | −0.124018 | ||||||||
\(451\) | 16.5454 | 0.779091 | ||||||||
\(452\) | 17.2229 | 0.810097 | ||||||||
\(453\) | −21.5727 | −1.01357 | ||||||||
\(454\) | 11.2916 | 0.529943 | ||||||||
\(455\) | 3.96952 | 0.186094 | ||||||||
\(456\) | 11.0972 | 0.519672 | ||||||||
\(457\) | 37.0693 | 1.73403 | 0.867014 | − | 0.498284i | \(-0.166036\pi\) | ||||
0.867014 | + | 0.498284i | \(0.166036\pi\) | |||||||
\(458\) | −13.3016 | −0.621541 | ||||||||
\(459\) | −4.35585 | −0.203314 | ||||||||
\(460\) | 1.35766 | 0.0633010 | ||||||||
\(461\) | 32.1018 | 1.49513 | 0.747566 | − | 0.664188i | \(-0.231222\pi\) | ||||
0.747566 | + | 0.664188i | \(0.231222\pi\) | |||||||
\(462\) | −1.80629 | −0.0840361 | ||||||||
\(463\) | 17.4487 | 0.810911 | 0.405456 | − | 0.914115i | \(-0.367113\pi\) | ||||
0.405456 | + | 0.914115i | \(0.367113\pi\) | |||||||
\(464\) | 1.89693 | 0.0880630 | ||||||||
\(465\) | −7.88918 | −0.365852 | ||||||||
\(466\) | 3.16828 | 0.146768 | ||||||||
\(467\) | 18.3114 | 0.847353 | 0.423676 | − | 0.905814i | \(-0.360739\pi\) | ||||
0.423676 | + | 0.905814i | \(0.360739\pi\) | |||||||
\(468\) | 11.2797 | 0.521402 | ||||||||
\(469\) | −3.55775 | −0.164282 | ||||||||
\(470\) | 3.32757 | 0.153489 | ||||||||
\(471\) | 9.60822 | 0.442724 | ||||||||
\(472\) | −27.4453 | −1.26327 | ||||||||
\(473\) | 33.9641 | 1.56167 | ||||||||
\(474\) | 0.156336 | 0.00718077 | ||||||||
\(475\) | −21.5384 | −0.988248 | ||||||||
\(476\) | 4.85567 | 0.222559 | ||||||||
\(477\) | −5.81406 | −0.266208 | ||||||||
\(478\) | 1.59169 | 0.0728024 | ||||||||
\(479\) | −3.40517 | −0.155586 | −0.0777931 | − | 0.996970i | \(-0.524787\pi\) | ||||
−0.0777931 | + | 0.996970i | \(0.524787\pi\) | |||||||
\(480\) | −4.67007 | −0.213159 | ||||||||
\(481\) | −49.6103 | −2.26203 | ||||||||
\(482\) | 2.98879 | 0.136136 | ||||||||
\(483\) | −0.685491 | −0.0311909 | ||||||||
\(484\) | −12.3187 | −0.559943 | ||||||||
\(485\) | 4.87716 | 0.221461 | ||||||||
\(486\) | −0.611391 | −0.0277332 | ||||||||
\(487\) | −28.7100 | −1.30097 | −0.650487 | − | 0.759518i | \(-0.725435\pi\) | ||||
−0.650487 | + | 0.759518i | \(0.725435\pi\) | |||||||
\(488\) | −31.6343 | −1.43202 | ||||||||
\(489\) | −22.2529 | −1.00631 | ||||||||
\(490\) | −3.33314 | −0.150576 | ||||||||
\(491\) | 14.5823 | 0.658089 | 0.329045 | − | 0.944314i | \(-0.393273\pi\) | ||||
0.329045 | + | 0.944314i | \(0.393273\pi\) | |||||||
\(492\) | −6.24288 | −0.281451 | ||||||||
\(493\) | 4.35585 | 0.196178 | ||||||||
\(494\) | −21.2266 | −0.955032 | ||||||||
\(495\) | −3.59817 | −0.161726 | ||||||||
\(496\) | 17.9254 | 0.804875 | ||||||||
\(497\) | 6.76069 | 0.303259 | ||||||||
\(498\) | −1.93540 | −0.0867275 | ||||||||
\(499\) | 23.7734 | 1.06425 | 0.532123 | − | 0.846667i | \(-0.321395\pi\) | ||||
0.532123 | + | 0.846667i | \(0.321395\pi\) | |||||||
\(500\) | 12.6303 | 0.564843 | ||||||||
\(501\) | −17.6567 | −0.788843 | ||||||||
\(502\) | 7.77255 | 0.346906 | ||||||||
\(503\) | 41.4368 | 1.84758 | 0.923788 | − | 0.382904i | \(-0.125076\pi\) | ||||
0.923788 | + | 0.382904i | \(0.125076\pi\) | |||||||
\(504\) | 1.51975 | 0.0676951 | ||||||||
\(505\) | 10.6271 | 0.472902 | ||||||||
\(506\) | 2.63503 | 0.117141 | ||||||||
\(507\) | −35.1108 | −1.55933 | ||||||||
\(508\) | −13.4709 | −0.597677 | ||||||||
\(509\) | 4.51731 | 0.200226 | 0.100113 | − | 0.994976i | \(-0.468080\pi\) | ||||
0.100113 | + | 0.994976i | \(0.468080\pi\) | |||||||
\(510\) | −2.22335 | −0.0984514 | ||||||||
\(511\) | −7.08809 | −0.313559 | ||||||||
\(512\) | 19.0222 | 0.840671 | ||||||||
\(513\) | −5.00543 | −0.220995 | ||||||||
\(514\) | 9.89592 | 0.436490 | ||||||||
\(515\) | −13.0519 | −0.575136 | ||||||||
\(516\) | −12.8153 | −0.564161 | ||||||||
\(517\) | −28.0970 | −1.23570 | ||||||||
\(518\) | −2.99758 | −0.131706 | ||||||||
\(519\) | −5.17476 | −0.227147 | ||||||||
\(520\) | 12.8383 | 0.562996 | ||||||||
\(521\) | −19.6782 | −0.862119 | −0.431059 | − | 0.902324i | \(-0.641860\pi\) | ||||
−0.431059 | + | 0.902324i | \(0.641860\pi\) | |||||||
\(522\) | 0.611391 | 0.0267598 | ||||||||
\(523\) | 23.9065 | 1.04536 | 0.522678 | − | 0.852530i | \(-0.324933\pi\) | ||||
0.522678 | + | 0.852530i | \(0.324933\pi\) | |||||||
\(524\) | −2.18260 | −0.0953475 | ||||||||
\(525\) | −2.94967 | −0.128734 | ||||||||
\(526\) | 7.88000 | 0.343584 | ||||||||
\(527\) | 41.1614 | 1.79302 | ||||||||
\(528\) | 8.17558 | 0.355797 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −2.96766 | −0.128907 | ||||||||
\(531\) | 12.3793 | 0.537217 | ||||||||
\(532\) | 5.57978 | 0.241914 | ||||||||
\(533\) | 26.6276 | 1.15337 | ||||||||
\(534\) | −6.92312 | −0.299593 | ||||||||
\(535\) | 3.88688 | 0.168044 | ||||||||
\(536\) | −11.5065 | −0.497007 | ||||||||
\(537\) | 3.93984 | 0.170016 | ||||||||
\(538\) | −0.681986 | −0.0294025 | ||||||||
\(539\) | 28.1440 | 1.21225 | ||||||||
\(540\) | 1.35766 | 0.0584242 | ||||||||
\(541\) | −21.9779 | −0.944902 | −0.472451 | − | 0.881357i | \(-0.656631\pi\) | ||||
−0.472451 | + | 0.881357i | \(0.656631\pi\) | |||||||
\(542\) | −3.62187 | −0.155573 | ||||||||
\(543\) | −4.69684 | −0.201561 | ||||||||
\(544\) | 24.3659 | 1.04468 | ||||||||
\(545\) | −3.97227 | −0.170153 | ||||||||
\(546\) | −2.90698 | −0.124407 | ||||||||
\(547\) | −27.7223 | −1.18532 | −0.592659 | − | 0.805453i | \(-0.701922\pi\) | ||||
−0.592659 | + | 0.805453i | \(0.701922\pi\) | |||||||
\(548\) | −3.39923 | −0.145208 | ||||||||
\(549\) | 14.2688 | 0.608977 | ||||||||
\(550\) | 11.3385 | 0.483477 | ||||||||
\(551\) | 5.00543 | 0.213238 | ||||||||
\(552\) | −2.21703 | −0.0943629 | ||||||||
\(553\) | 0.175284 | 0.00745385 | ||||||||
\(554\) | −15.3160 | −0.650716 | ||||||||
\(555\) | −5.97125 | −0.253465 | ||||||||
\(556\) | −6.03733 | −0.256040 | ||||||||
\(557\) | 4.05940 | 0.172002 | 0.0860012 | − | 0.996295i | \(-0.472591\pi\) | ||||
0.0860012 | + | 0.996295i | \(0.472591\pi\) | |||||||
\(558\) | 5.77744 | 0.244579 | ||||||||
\(559\) | 54.6607 | 2.31190 | ||||||||
\(560\) | −1.08560 | −0.0458749 | ||||||||
\(561\) | 18.7733 | 0.792608 | ||||||||
\(562\) | −10.0831 | −0.425329 | ||||||||
\(563\) | −8.97405 | −0.378211 | −0.189106 | − | 0.981957i | \(-0.560559\pi\) | ||||
−0.189106 | + | 0.981957i | \(0.560559\pi\) | |||||||
\(564\) | 10.6015 | 0.446404 | ||||||||
\(565\) | −8.84193 | −0.371983 | ||||||||
\(566\) | −16.3895 | −0.688900 | ||||||||
\(567\) | −0.685491 | −0.0287879 | ||||||||
\(568\) | 21.8655 | 0.917458 | ||||||||
\(569\) | −13.0274 | −0.546137 | −0.273069 | − | 0.961995i | \(-0.588039\pi\) | ||||
−0.273069 | + | 0.961995i | \(0.588039\pi\) | |||||||
\(570\) | −2.55491 | −0.107013 | ||||||||
\(571\) | −8.27190 | −0.346168 | −0.173084 | − | 0.984907i | \(-0.555373\pi\) | ||||
−0.173084 | + | 0.984907i | \(0.555373\pi\) | |||||||
\(572\) | −48.6141 | −2.03266 | ||||||||
\(573\) | −18.7144 | −0.781806 | ||||||||
\(574\) | 1.60891 | 0.0671545 | ||||||||
\(575\) | 4.30300 | 0.179448 | ||||||||
\(576\) | −0.373862 | −0.0155776 | ||||||||
\(577\) | 27.0737 | 1.12709 | 0.563547 | − | 0.826084i | \(-0.309436\pi\) | ||||
0.563547 | + | 0.826084i | \(0.309436\pi\) | |||||||
\(578\) | 1.20656 | 0.0501862 | ||||||||
\(579\) | 23.7007 | 0.984969 | ||||||||
\(580\) | −1.35766 | −0.0563736 | ||||||||
\(581\) | −2.16997 | −0.0900256 | ||||||||
\(582\) | −3.57167 | −0.148050 | ||||||||
\(583\) | 25.0580 | 1.03780 | ||||||||
\(584\) | −22.9244 | −0.948620 | ||||||||
\(585\) | −5.79077 | −0.239419 | ||||||||
\(586\) | −6.87792 | −0.284124 | ||||||||
\(587\) | 17.0434 | 0.703458 | 0.351729 | − | 0.936102i | \(-0.385594\pi\) | ||||
0.351729 | + | 0.936102i | \(0.385594\pi\) | |||||||
\(588\) | −10.6193 | −0.437931 | ||||||||
\(589\) | 47.2997 | 1.94895 | ||||||||
\(590\) | 6.31875 | 0.260139 | ||||||||
\(591\) | 21.4337 | 0.881664 | ||||||||
\(592\) | 13.5676 | 0.557624 | ||||||||
\(593\) | 14.4296 | 0.592554 | 0.296277 | − | 0.955102i | \(-0.404255\pi\) | ||||
0.296277 | + | 0.955102i | \(0.404255\pi\) | |||||||
\(594\) | 2.63503 | 0.108116 | ||||||||
\(595\) | −2.49281 | −0.102195 | ||||||||
\(596\) | −1.56676 | −0.0641768 | ||||||||
\(597\) | 2.13493 | 0.0873769 | ||||||||
\(598\) | 4.24072 | 0.173416 | ||||||||
\(599\) | 26.5520 | 1.08488 | 0.542442 | − | 0.840093i | \(-0.317500\pi\) | ||||
0.542442 | + | 0.840093i | \(0.317500\pi\) | |||||||
\(600\) | −9.53987 | −0.389464 | ||||||||
\(601\) | −0.281069 | −0.0114651 | −0.00573253 | − | 0.999984i | \(-0.501825\pi\) | ||||
−0.00573253 | + | 0.999984i | \(0.501825\pi\) | |||||||
\(602\) | 3.30274 | 0.134610 | ||||||||
\(603\) | 5.19008 | 0.211356 | ||||||||
\(604\) | −35.0815 | −1.42745 | ||||||||
\(605\) | 6.32422 | 0.257116 | ||||||||
\(606\) | −7.78252 | −0.316143 | ||||||||
\(607\) | 36.7176 | 1.49032 | 0.745161 | − | 0.666885i | \(-0.232373\pi\) | ||||
0.745161 | + | 0.666885i | \(0.232373\pi\) | |||||||
\(608\) | 27.9995 | 1.13553 | ||||||||
\(609\) | 0.685491 | 0.0277775 | ||||||||
\(610\) | 7.28318 | 0.294887 | ||||||||
\(611\) | −45.2184 | −1.82934 | ||||||||
\(612\) | −7.08350 | −0.286333 | ||||||||
\(613\) | 26.1991 | 1.05817 | 0.529085 | − | 0.848569i | \(-0.322535\pi\) | ||||
0.529085 | + | 0.848569i | \(0.322535\pi\) | |||||||
\(614\) | −1.99853 | −0.0806541 | ||||||||
\(615\) | 3.20498 | 0.129237 | ||||||||
\(616\) | −6.54996 | −0.263905 | ||||||||
\(617\) | −7.82574 | −0.315052 | −0.157526 | − | 0.987515i | \(-0.550352\pi\) | ||||
−0.157526 | + | 0.987515i | \(0.550352\pi\) | |||||||
\(618\) | 9.55824 | 0.384489 | ||||||||
\(619\) | −5.62966 | −0.226275 | −0.113137 | − | 0.993579i | \(-0.536090\pi\) | ||||
−0.113137 | + | 0.993579i | \(0.536090\pi\) | |||||||
\(620\) | −12.8294 | −0.515241 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | −4.18242 | −0.167700 | ||||||||
\(623\) | −7.76220 | −0.310986 | ||||||||
\(624\) | 13.1575 | 0.526722 | ||||||||
\(625\) | 15.0309 | 0.601235 | ||||||||
\(626\) | −6.61492 | −0.264385 | ||||||||
\(627\) | 21.5728 | 0.861537 | ||||||||
\(628\) | 15.6249 | 0.623502 | ||||||||
\(629\) | 31.1547 | 1.24222 | ||||||||
\(630\) | −0.349893 | −0.0139401 | ||||||||
\(631\) | −11.4063 | −0.454078 | −0.227039 | − | 0.973886i | \(-0.572904\pi\) | ||||
−0.227039 | + | 0.973886i | \(0.572904\pi\) | |||||||
\(632\) | 0.566908 | 0.0225504 | ||||||||
\(633\) | −0.324360 | −0.0128921 | ||||||||
\(634\) | 13.1978 | 0.524153 | ||||||||
\(635\) | 6.91574 | 0.274443 | ||||||||
\(636\) | −9.45484 | −0.374909 | ||||||||
\(637\) | 45.2941 | 1.79462 | ||||||||
\(638\) | −2.63503 | −0.104322 | ||||||||
\(639\) | −9.86256 | −0.390157 | ||||||||
\(640\) | −9.53097 | −0.376745 | ||||||||
\(641\) | 25.2121 | 0.995818 | 0.497909 | − | 0.867229i | \(-0.334101\pi\) | ||||
0.497909 | + | 0.867229i | \(0.334101\pi\) | |||||||
\(642\) | −2.84646 | −0.112341 | ||||||||
\(643\) | −4.38300 | −0.172849 | −0.0864243 | − | 0.996258i | \(-0.527544\pi\) | ||||
−0.0864243 | + | 0.996258i | \(0.527544\pi\) | |||||||
\(644\) | −1.11475 | −0.0439272 | ||||||||
\(645\) | 6.57914 | 0.259053 | ||||||||
\(646\) | 13.3301 | 0.524465 | ||||||||
\(647\) | 2.22353 | 0.0874162 | 0.0437081 | − | 0.999044i | \(-0.486083\pi\) | ||||
0.0437081 | + | 0.999044i | \(0.486083\pi\) | |||||||
\(648\) | −2.21703 | −0.0870930 | ||||||||
\(649\) | −53.3536 | −2.09431 | ||||||||
\(650\) | 18.2479 | 0.715740 | ||||||||
\(651\) | 6.47767 | 0.253880 | ||||||||
\(652\) | −36.1876 | −1.41722 | ||||||||
\(653\) | −14.2881 | −0.559137 | −0.279568 | − | 0.960126i | \(-0.590191\pi\) | ||||
−0.279568 | + | 0.960126i | \(0.590191\pi\) | |||||||
\(654\) | 2.90899 | 0.113750 | ||||||||
\(655\) | 1.12051 | 0.0437819 | ||||||||
\(656\) | −7.28220 | −0.284322 | ||||||||
\(657\) | 10.3402 | 0.403409 | ||||||||
\(658\) | −2.73221 | −0.106513 | ||||||||
\(659\) | −15.4293 | −0.601040 | −0.300520 | − | 0.953776i | \(-0.597160\pi\) | ||||
−0.300520 | + | 0.953776i | \(0.597160\pi\) | |||||||
\(660\) | −5.85135 | −0.227763 | ||||||||
\(661\) | 31.7825 | 1.23620 | 0.618098 | − | 0.786101i | \(-0.287903\pi\) | ||||
0.618098 | + | 0.786101i | \(0.287903\pi\) | |||||||
\(662\) | −16.0092 | −0.622214 | ||||||||
\(663\) | 30.2131 | 1.17338 | ||||||||
\(664\) | −7.01816 | −0.272357 | ||||||||
\(665\) | −2.86456 | −0.111083 | ||||||||
\(666\) | 4.37289 | 0.169446 | ||||||||
\(667\) | −1.00000 | −0.0387202 | ||||||||
\(668\) | −28.7134 | −1.11095 | ||||||||
\(669\) | 10.7572 | 0.415897 | ||||||||
\(670\) | 2.64916 | 0.102346 | ||||||||
\(671\) | −61.4969 | −2.37406 | ||||||||
\(672\) | 3.83451 | 0.147919 | ||||||||
\(673\) | −0.00588219 | −0.000226742 0 | −0.000113371 | − | 1.00000i | \(-0.500036\pi\) | ||||
−0.000113371 | 1.00000i | \(0.500036\pi\) | ||||||||
\(674\) | −3.01946 | −0.116305 | ||||||||
\(675\) | 4.30300 | 0.165623 | ||||||||
\(676\) | −57.0972 | −2.19605 | ||||||||
\(677\) | −27.8314 | −1.06965 | −0.534824 | − | 0.844964i | \(-0.679622\pi\) | ||||
−0.534824 | + | 0.844964i | \(0.679622\pi\) | |||||||
\(678\) | 6.47516 | 0.248677 | ||||||||
\(679\) | −4.00455 | −0.153681 | ||||||||
\(680\) | −8.06230 | −0.309175 | ||||||||
\(681\) | −18.4688 | −0.707725 | ||||||||
\(682\) | −24.9001 | −0.953476 | ||||||||
\(683\) | 5.92751 | 0.226810 | 0.113405 | − | 0.993549i | \(-0.463824\pi\) | ||||
0.113405 | + | 0.993549i | \(0.463824\pi\) | |||||||
\(684\) | −8.13983 | −0.311234 | ||||||||
\(685\) | 1.74510 | 0.0666769 | ||||||||
\(686\) | 5.67050 | 0.216501 | ||||||||
\(687\) | 21.7562 | 0.830052 | ||||||||
\(688\) | −14.9488 | −0.569917 | ||||||||
\(689\) | 40.3275 | 1.53635 | ||||||||
\(690\) | 0.510427 | 0.0194316 | ||||||||
\(691\) | 25.7814 | 0.980771 | 0.490386 | − | 0.871506i | \(-0.336856\pi\) | ||||
0.490386 | + | 0.871506i | \(0.336856\pi\) | |||||||
\(692\) | −8.41520 | −0.319898 | ||||||||
\(693\) | 2.95439 | 0.112228 | ||||||||
\(694\) | −14.4316 | −0.547816 | ||||||||
\(695\) | 3.09946 | 0.117569 | ||||||||
\(696\) | 2.21703 | 0.0840361 | ||||||||
\(697\) | −16.7218 | −0.633384 | ||||||||
\(698\) | −7.19729 | −0.272422 | ||||||||
\(699\) | −5.18209 | −0.196005 | ||||||||
\(700\) | −4.79676 | −0.181300 | ||||||||
\(701\) | 2.22483 | 0.0840307 | 0.0420154 | − | 0.999117i | \(-0.486622\pi\) | ||||
0.0420154 | + | 0.999117i | \(0.486622\pi\) | |||||||
\(702\) | 4.24072 | 0.160056 | ||||||||
\(703\) | 35.8007 | 1.35025 | ||||||||
\(704\) | 1.61130 | 0.0607283 | ||||||||
\(705\) | −5.44263 | −0.204981 | ||||||||
\(706\) | 10.4379 | 0.392834 | ||||||||
\(707\) | −8.72575 | −0.328166 | ||||||||
\(708\) | 20.1313 | 0.756580 | ||||||||
\(709\) | 25.5951 | 0.961243 | 0.480621 | − | 0.876928i | \(-0.340411\pi\) | ||||
0.480621 | + | 0.876928i | \(0.340411\pi\) | |||||||
\(710\) | −5.03412 | −0.188927 | ||||||||
\(711\) | −0.255706 | −0.00958974 | ||||||||
\(712\) | −25.1046 | −0.940836 | ||||||||
\(713\) | −9.44967 | −0.353893 | ||||||||
\(714\) | 1.82555 | 0.0683195 | ||||||||
\(715\) | 24.9576 | 0.933361 | ||||||||
\(716\) | 6.40697 | 0.239440 | ||||||||
\(717\) | −2.60340 | −0.0972257 | ||||||||
\(718\) | 20.3570 | 0.759718 | ||||||||
\(719\) | 7.78746 | 0.290423 | 0.145212 | − | 0.989401i | \(-0.453614\pi\) | ||||
0.145212 | + | 0.989401i | \(0.453614\pi\) | |||||||
\(720\) | 1.58368 | 0.0590203 | ||||||||
\(721\) | 10.7167 | 0.399110 | ||||||||
\(722\) | 3.70154 | 0.137757 | ||||||||
\(723\) | −4.88851 | −0.181806 | ||||||||
\(724\) | −7.63801 | −0.283864 | ||||||||
\(725\) | −4.30300 | −0.159810 | ||||||||
\(726\) | −4.63138 | −0.171887 | ||||||||
\(727\) | 27.2912 | 1.01217 | 0.506087 | − | 0.862482i | \(-0.331092\pi\) | ||||
0.506087 | + | 0.862482i | \(0.331092\pi\) | |||||||
\(728\) | −10.5413 | −0.390686 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 5.27791 | 0.195344 | ||||||||
\(731\) | −34.3263 | −1.26960 | ||||||||
\(732\) | 23.2039 | 0.857642 | ||||||||
\(733\) | 4.37066 | 0.161434 | 0.0807171 | − | 0.996737i | \(-0.474279\pi\) | ||||
0.0807171 | + | 0.996737i | \(0.474279\pi\) | |||||||
\(734\) | −10.6388 | −0.392686 | ||||||||
\(735\) | 5.45174 | 0.201090 | ||||||||
\(736\) | −5.59382 | −0.206191 | ||||||||
\(737\) | −22.3687 | −0.823961 | ||||||||
\(738\) | −2.34709 | −0.0863975 | ||||||||
\(739\) | −9.64767 | −0.354895 | −0.177448 | − | 0.984130i | \(-0.556784\pi\) | ||||
−0.177448 | + | 0.984130i | \(0.556784\pi\) | |||||||
\(740\) | −9.71046 | −0.356963 | ||||||||
\(741\) | 34.7186 | 1.27542 | ||||||||
\(742\) | 2.43669 | 0.0894537 | ||||||||
\(743\) | 0.995847 | 0.0365341 | 0.0182670 | − | 0.999833i | \(-0.494185\pi\) | ||||
0.0182670 | + | 0.999833i | \(0.494185\pi\) | |||||||
\(744\) | 20.9502 | 0.768070 | ||||||||
\(745\) | 0.804344 | 0.0294689 | ||||||||
\(746\) | −16.5335 | −0.605336 | ||||||||
\(747\) | 3.16558 | 0.115822 | ||||||||
\(748\) | 30.5291 | 1.11625 | ||||||||
\(749\) | −3.19145 | −0.116613 | ||||||||
\(750\) | 4.74851 | 0.173391 | ||||||||
\(751\) | 4.60712 | 0.168116 | 0.0840581 | − | 0.996461i | \(-0.473212\pi\) | ||||
0.0840581 | + | 0.996461i | \(0.473212\pi\) | |||||||
\(752\) | 12.3665 | 0.450959 | ||||||||
\(753\) | −12.7129 | −0.463284 | ||||||||
\(754\) | −4.24072 | −0.154438 | ||||||||
\(755\) | 18.0102 | 0.655459 | ||||||||
\(756\) | −1.11475 | −0.0405429 | ||||||||
\(757\) | −15.3820 | −0.559069 | −0.279535 | − | 0.960136i | \(-0.590180\pi\) | ||||
−0.279535 | + | 0.960136i | \(0.590180\pi\) | |||||||
\(758\) | −3.61410 | −0.131270 | ||||||||
\(759\) | −4.30989 | −0.156439 | ||||||||
\(760\) | −9.26460 | −0.336063 | ||||||||
\(761\) | 10.2638 | 0.372062 | 0.186031 | − | 0.982544i | \(-0.440438\pi\) | ||||
0.186031 | + | 0.982544i | \(0.440438\pi\) | |||||||
\(762\) | −5.06457 | −0.183470 | ||||||||
\(763\) | 3.26156 | 0.118076 | ||||||||
\(764\) | −30.4334 | −1.10104 | ||||||||
\(765\) | 3.63654 | 0.131479 | ||||||||
\(766\) | 20.4963 | 0.740563 | ||||||||
\(767\) | −85.8655 | −3.10042 | ||||||||
\(768\) | 6.23204 | 0.224879 | ||||||||
\(769\) | −37.4723 | −1.35128 | −0.675642 | − | 0.737230i | \(-0.736133\pi\) | ||||
−0.675642 | + | 0.737230i | \(0.736133\pi\) | |||||||
\(770\) | 1.50800 | 0.0543446 | ||||||||
\(771\) | −16.1859 | −0.582922 | ||||||||
\(772\) | 38.5422 | 1.38716 | ||||||||
\(773\) | 24.8016 | 0.892053 | 0.446026 | − | 0.895020i | \(-0.352839\pi\) | ||||
0.446026 | + | 0.895020i | \(0.352839\pi\) | |||||||
\(774\) | −4.81806 | −0.173182 | ||||||||
\(775\) | −40.6620 | −1.46062 | ||||||||
\(776\) | −12.9516 | −0.464935 | ||||||||
\(777\) | 4.90289 | 0.175890 | ||||||||
\(778\) | −22.3245 | −0.800372 | ||||||||
\(779\) | −19.2155 | −0.688467 | ||||||||
\(780\) | −9.41696 | −0.337181 | ||||||||
\(781\) | 42.5066 | 1.52100 | ||||||||
\(782\) | −2.66313 | −0.0952333 | ||||||||
\(783\) | −1.00000 | −0.0357371 | ||||||||
\(784\) | −12.3872 | −0.442399 | ||||||||
\(785\) | −8.02155 | −0.286301 | ||||||||
\(786\) | −0.820577 | −0.0292690 | ||||||||
\(787\) | −11.3807 | −0.405677 | −0.202839 | − | 0.979212i | \(-0.565017\pi\) | ||||
−0.202839 | + | 0.979212i | \(0.565017\pi\) | |||||||
\(788\) | 34.8555 | 1.24168 | ||||||||
\(789\) | −12.8887 | −0.458848 | ||||||||
\(790\) | −0.130520 | −0.00464368 | ||||||||
\(791\) | 7.25995 | 0.258134 | ||||||||
\(792\) | 9.55514 | 0.339527 | ||||||||
\(793\) | −98.9711 | −3.51457 | ||||||||
\(794\) | 4.22301 | 0.149869 | ||||||||
\(795\) | 4.85395 | 0.172152 | ||||||||
\(796\) | 3.47183 | 0.123056 | ||||||||
\(797\) | 17.9080 | 0.634333 | 0.317167 | − | 0.948370i | \(-0.397269\pi\) | ||||
0.317167 | + | 0.948370i | \(0.397269\pi\) | |||||||
\(798\) | 2.09779 | 0.0742609 | ||||||||
\(799\) | 28.3966 | 1.00460 | ||||||||
\(800\) | −24.0702 | −0.851011 | ||||||||
\(801\) | 11.3236 | 0.400099 | ||||||||
\(802\) | 10.4402 | 0.368655 | ||||||||
\(803\) | −44.5650 | −1.57267 | ||||||||
\(804\) | 8.44011 | 0.297660 | ||||||||
\(805\) | 0.572291 | 0.0201706 | ||||||||
\(806\) | −40.0735 | −1.41153 | ||||||||
\(807\) | 1.11547 | 0.0392663 | ||||||||
\(808\) | −28.2210 | −0.992810 | ||||||||
\(809\) | 31.3051 | 1.10063 | 0.550314 | − | 0.834958i | \(-0.314508\pi\) | ||||
0.550314 | + | 0.834958i | \(0.314508\pi\) | |||||||
\(810\) | 0.510427 | 0.0179346 | ||||||||
\(811\) | 34.5718 | 1.21398 | 0.606990 | − | 0.794709i | \(-0.292377\pi\) | ||||
0.606990 | + | 0.794709i | \(0.292377\pi\) | |||||||
\(812\) | 1.11475 | 0.0391199 | ||||||||
\(813\) | 5.92399 | 0.207763 | ||||||||
\(814\) | −18.8467 | −0.660576 | ||||||||
\(815\) | 18.5781 | 0.650762 | ||||||||
\(816\) | −8.26277 | −0.289255 | ||||||||
\(817\) | −39.4453 | −1.38002 | ||||||||
\(818\) | 12.0591 | 0.421636 | ||||||||
\(819\) | 4.75470 | 0.166143 | ||||||||
\(820\) | 5.21195 | 0.182009 | ||||||||
\(821\) | −3.89321 | −0.135874 | −0.0679369 | − | 0.997690i | \(-0.521642\pi\) | ||||
−0.0679369 | + | 0.997690i | \(0.521642\pi\) | |||||||
\(822\) | −1.27798 | −0.0445747 | ||||||||
\(823\) | 8.32208 | 0.290089 | 0.145045 | − | 0.989425i | \(-0.453667\pi\) | ||||
0.145045 | + | 0.989425i | \(0.453667\pi\) | |||||||
\(824\) | 34.6601 | 1.20744 | ||||||||
\(825\) | −18.5455 | −0.645671 | ||||||||
\(826\) | −5.18821 | −0.180521 | ||||||||
\(827\) | −38.7597 | −1.34781 | −0.673904 | − | 0.738819i | \(-0.735384\pi\) | ||||
−0.673904 | + | 0.738819i | \(0.735384\pi\) | |||||||
\(828\) | 1.62620 | 0.0565144 | ||||||||
\(829\) | −16.5657 | −0.575352 | −0.287676 | − | 0.957728i | \(-0.592883\pi\) | ||||
−0.287676 | + | 0.957728i | \(0.592883\pi\) | |||||||
\(830\) | 1.61580 | 0.0560851 | ||||||||
\(831\) | 25.0512 | 0.869015 | ||||||||
\(832\) | 2.59318 | 0.0899023 | ||||||||
\(833\) | −28.4442 | −0.985532 | ||||||||
\(834\) | −2.26981 | −0.0785971 | ||||||||
\(835\) | 14.7409 | 0.510131 | ||||||||
\(836\) | 35.0818 | 1.21333 | ||||||||
\(837\) | −9.44967 | −0.326629 | ||||||||
\(838\) | −4.99705 | −0.172620 | ||||||||
\(839\) | −35.5005 | −1.22561 | −0.612807 | − | 0.790233i | \(-0.709960\pi\) | ||||
−0.612807 | + | 0.790233i | \(0.709960\pi\) | |||||||
\(840\) | −1.26878 | −0.0437772 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −11.7903 | −0.406321 | ||||||||
\(843\) | 16.4921 | 0.568017 | ||||||||
\(844\) | −0.527475 | −0.0181564 | ||||||||
\(845\) | 29.3127 | 1.00839 | ||||||||
\(846\) | 3.98577 | 0.137034 | ||||||||
\(847\) | −5.19270 | −0.178423 | ||||||||
\(848\) | −11.0289 | −0.378734 | ||||||||
\(849\) | 26.8068 | 0.920009 | ||||||||
\(850\) | −11.4595 | −0.393056 | ||||||||
\(851\) | −7.15237 | −0.245180 | ||||||||
\(852\) | −16.0385 | −0.549470 | ||||||||
\(853\) | 0.569695 | 0.0195060 | 0.00975299 | − | 0.999952i | \(-0.496895\pi\) | ||||
0.00975299 | + | 0.999952i | \(0.496895\pi\) | |||||||
\(854\) | −5.98009 | −0.204634 | ||||||||
\(855\) | 4.17884 | 0.142913 | ||||||||
\(856\) | −10.3218 | −0.352793 | ||||||||
\(857\) | −42.6670 | −1.45748 | −0.728739 | − | 0.684792i | \(-0.759893\pi\) | ||||
−0.728739 | + | 0.684792i | \(0.759893\pi\) | |||||||
\(858\) | −18.2771 | −0.623969 | ||||||||
\(859\) | 10.0786 | 0.343877 | 0.171939 | − | 0.985108i | \(-0.444997\pi\) | ||||
0.171939 | + | 0.985108i | \(0.444997\pi\) | |||||||
\(860\) | 10.6990 | 0.364833 | ||||||||
\(861\) | −2.63155 | −0.0896831 | ||||||||
\(862\) | 23.5266 | 0.801320 | ||||||||
\(863\) | 39.0533 | 1.32939 | 0.664695 | − | 0.747115i | \(-0.268561\pi\) | ||||
0.664695 | + | 0.747115i | \(0.268561\pi\) | |||||||
\(864\) | −5.59382 | −0.190306 | ||||||||
\(865\) | 4.32022 | 0.146892 | ||||||||
\(866\) | −4.14619 | −0.140893 | ||||||||
\(867\) | −1.97346 | −0.0670223 | ||||||||
\(868\) | 10.5340 | 0.357547 | ||||||||
\(869\) | 1.10207 | 0.0373851 | ||||||||
\(870\) | −0.510427 | −0.0173051 | ||||||||
\(871\) | −35.9994 | −1.21979 | ||||||||
\(872\) | 10.5486 | 0.357220 | ||||||||
\(873\) | 5.84187 | 0.197717 | ||||||||
\(874\) | −3.06027 | −0.103515 | ||||||||
\(875\) | 5.32402 | 0.179985 | ||||||||
\(876\) | 16.8152 | 0.568133 | ||||||||
\(877\) | 13.8533 | 0.467794 | 0.233897 | − | 0.972261i | \(-0.424852\pi\) | ||||
0.233897 | + | 0.972261i | \(0.424852\pi\) | |||||||
\(878\) | 15.4229 | 0.520498 | ||||||||
\(879\) | 11.2496 | 0.379441 | ||||||||
\(880\) | −6.82549 | −0.230087 | ||||||||
\(881\) | 40.8796 | 1.37727 | 0.688635 | − | 0.725108i | \(-0.258210\pi\) | ||||
0.688635 | + | 0.725108i | \(0.258210\pi\) | |||||||
\(882\) | −3.99244 | −0.134433 | ||||||||
\(883\) | 7.40254 | 0.249115 | 0.124558 | − | 0.992212i | \(-0.460249\pi\) | ||||
0.124558 | + | 0.992212i | \(0.460249\pi\) | |||||||
\(884\) | 49.1325 | 1.65251 | ||||||||
\(885\) | −10.3350 | −0.347409 | ||||||||
\(886\) | 1.66232 | 0.0558467 | ||||||||
\(887\) | 24.3437 | 0.817380 | 0.408690 | − | 0.912673i | \(-0.365986\pi\) | ||||
0.408690 | + | 0.912673i | \(0.365986\pi\) | |||||||
\(888\) | 15.8570 | 0.532126 | ||||||||
\(889\) | −5.67839 | −0.190447 | ||||||||
\(890\) | 5.77986 | 0.193741 | ||||||||
\(891\) | −4.30989 | −0.144387 | ||||||||
\(892\) | 17.4934 | 0.585721 | ||||||||
\(893\) | 32.6313 | 1.09197 | ||||||||
\(894\) | −0.589041 | −0.0197005 | ||||||||
\(895\) | −3.28922 | −0.109947 | ||||||||
\(896\) | 7.82571 | 0.261439 | ||||||||
\(897\) | −6.93620 | −0.231593 | ||||||||
\(898\) | 0.746430 | 0.0249087 | ||||||||
\(899\) | 9.44967 | 0.315164 | ||||||||
\(900\) | 6.99755 | 0.233252 | ||||||||
\(901\) | −25.3252 | −0.843705 | ||||||||
\(902\) | 10.1157 | 0.336816 | ||||||||
\(903\) | −5.40201 | −0.179768 | ||||||||
\(904\) | 23.4802 | 0.780941 | ||||||||
\(905\) | 3.92122 | 0.130346 | ||||||||
\(906\) | −13.1893 | −0.438186 | ||||||||
\(907\) | −29.8887 | −0.992439 | −0.496219 | − | 0.868197i | \(-0.665279\pi\) | ||||
−0.496219 | + | 0.868197i | \(0.665279\pi\) | |||||||
\(908\) | −30.0340 | −0.996712 | ||||||||
\(909\) | 12.7292 | 0.422201 | ||||||||
\(910\) | 2.42693 | 0.0804519 | ||||||||
\(911\) | 43.4237 | 1.43869 | 0.719345 | − | 0.694653i | \(-0.244442\pi\) | ||||
0.719345 | + | 0.694653i | \(0.244442\pi\) | |||||||
\(912\) | −9.49497 | −0.314410 | ||||||||
\(913\) | −13.6433 | −0.451527 | ||||||||
\(914\) | 22.6638 | 0.749652 | ||||||||
\(915\) | −11.9125 | −0.393814 | ||||||||
\(916\) | 35.3800 | 1.16899 | ||||||||
\(917\) | −0.920031 | −0.0303821 | ||||||||
\(918\) | −2.66313 | −0.0878963 | ||||||||
\(919\) | −9.90012 | −0.326575 | −0.163287 | − | 0.986579i | \(-0.552210\pi\) | ||||
−0.163287 | + | 0.986579i | \(0.552210\pi\) | |||||||
\(920\) | 1.85091 | 0.0610228 | ||||||||
\(921\) | 3.26882 | 0.107711 | ||||||||
\(922\) | 19.6268 | 0.646373 | ||||||||
\(923\) | 68.4086 | 2.25170 | ||||||||
\(924\) | 4.80443 | 0.158054 | ||||||||
\(925\) | −30.7767 | −1.01193 | ||||||||
\(926\) | 10.6680 | 0.350572 | ||||||||
\(927\) | −15.6336 | −0.513475 | ||||||||
\(928\) | 5.59382 | 0.183626 | ||||||||
\(929\) | −32.1938 | −1.05624 | −0.528122 | − | 0.849168i | \(-0.677104\pi\) | ||||
−0.528122 | + | 0.849168i | \(0.677104\pi\) | |||||||
\(930\) | −4.82337 | −0.158165 | ||||||||
\(931\) | −32.6860 | −1.07124 | ||||||||
\(932\) | −8.42713 | −0.276040 | ||||||||
\(933\) | 6.84083 | 0.223959 | ||||||||
\(934\) | 11.1954 | 0.366326 | ||||||||
\(935\) | −15.6731 | −0.512565 | ||||||||
\(936\) | 15.3777 | 0.502637 | ||||||||
\(937\) | −10.2659 | −0.335372 | −0.167686 | − | 0.985840i | \(-0.553629\pi\) | ||||
−0.167686 | + | 0.985840i | \(0.553629\pi\) | |||||||
\(938\) | −2.17518 | −0.0710220 | ||||||||
\(939\) | 10.8195 | 0.353080 | ||||||||
\(940\) | −8.85081 | −0.288682 | ||||||||
\(941\) | 32.3494 | 1.05456 | 0.527279 | − | 0.849692i | \(-0.323212\pi\) | ||||
0.527279 | + | 0.849692i | \(0.323212\pi\) | |||||||
\(942\) | 5.87438 | 0.191398 | ||||||||
\(943\) | 3.83893 | 0.125013 | ||||||||
\(944\) | 23.4828 | 0.764300 | ||||||||
\(945\) | 0.572291 | 0.0186166 | ||||||||
\(946\) | 20.7653 | 0.675139 | ||||||||
\(947\) | −42.5434 | −1.38247 | −0.691237 | − | 0.722628i | \(-0.742934\pi\) | ||||
−0.691237 | + | 0.722628i | \(0.742934\pi\) | |||||||
\(948\) | −0.415830 | −0.0135055 | ||||||||
\(949\) | −71.7215 | −2.32818 | ||||||||
\(950\) | −13.1684 | −0.427238 | ||||||||
\(951\) | −21.5866 | −0.699993 | ||||||||
\(952\) | 6.61981 | 0.214549 | ||||||||
\(953\) | −11.4943 | −0.372338 | −0.186169 | − | 0.982518i | \(-0.559607\pi\) | ||||
−0.186169 | + | 0.982518i | \(0.559607\pi\) | |||||||
\(954\) | −3.55466 | −0.115086 | ||||||||
\(955\) | 15.6240 | 0.505580 | ||||||||
\(956\) | −4.23365 | −0.136926 | ||||||||
\(957\) | 4.30989 | 0.139319 | ||||||||
\(958\) | −2.08189 | −0.0672628 | ||||||||
\(959\) | −1.43287 | −0.0462698 | ||||||||
\(960\) | 0.312123 | 0.0100737 | ||||||||
\(961\) | 58.2964 | 1.88053 | ||||||||
\(962\) | −30.3312 | −0.977919 | ||||||||
\(963\) | 4.65571 | 0.150028 | ||||||||
\(964\) | −7.94970 | −0.256043 | ||||||||
\(965\) | −19.7869 | −0.636961 | ||||||||
\(966\) | −0.419103 | −0.0134844 | ||||||||
\(967\) | 16.6068 | 0.534037 | 0.267019 | − | 0.963691i | \(-0.413961\pi\) | ||||
0.267019 | + | 0.963691i | \(0.413961\pi\) | |||||||
\(968\) | −16.7943 | −0.539790 | ||||||||
\(969\) | −21.8029 | −0.700410 | ||||||||
\(970\) | 2.98185 | 0.0957415 | ||||||||
\(971\) | 15.8282 | 0.507953 | 0.253976 | − | 0.967210i | \(-0.418261\pi\) | ||||
0.253976 | + | 0.967210i | \(0.418261\pi\) | |||||||
\(972\) | 1.62620 | 0.0521604 | ||||||||
\(973\) | −2.54491 | −0.0815860 | ||||||||
\(974\) | −17.5530 | −0.562435 | ||||||||
\(975\) | −29.8465 | −0.955852 | ||||||||
\(976\) | 27.0670 | 0.866392 | ||||||||
\(977\) | 21.2614 | 0.680213 | 0.340106 | − | 0.940387i | \(-0.389537\pi\) | ||||
0.340106 | + | 0.940387i | \(0.389537\pi\) | |||||||
\(978\) | −13.6052 | −0.435046 | ||||||||
\(979\) | −48.8033 | −1.55976 | ||||||||
\(980\) | 8.86563 | 0.283202 | ||||||||
\(981\) | −4.75799 | −0.151911 | ||||||||
\(982\) | 8.91547 | 0.284504 | ||||||||
\(983\) | 50.5034 | 1.61081 | 0.805404 | − | 0.592727i | \(-0.201949\pi\) | ||||
0.805404 | + | 0.592727i | \(0.201949\pi\) | |||||||
\(984\) | −8.51101 | −0.271321 | ||||||||
\(985\) | −17.8942 | −0.570156 | ||||||||
\(986\) | 2.66313 | 0.0848113 | ||||||||
\(987\) | 4.46884 | 0.142245 | ||||||||
\(988\) | 56.4595 | 1.79622 | ||||||||
\(989\) | 7.88050 | 0.250585 | ||||||||
\(990\) | −2.19989 | −0.0699170 | ||||||||
\(991\) | 18.7508 | 0.595640 | 0.297820 | − | 0.954622i | \(-0.403741\pi\) | ||||
0.297820 | + | 0.954622i | \(0.403741\pi\) | |||||||
\(992\) | 52.8598 | 1.67830 | ||||||||
\(993\) | 26.1848 | 0.830951 | ||||||||
\(994\) | 4.13342 | 0.131104 | ||||||||
\(995\) | −1.78238 | −0.0565051 | ||||||||
\(996\) | 5.14786 | 0.163116 | ||||||||
\(997\) | 6.97463 | 0.220889 | 0.110444 | − | 0.993882i | \(-0.464773\pi\) | ||||
0.110444 | + | 0.993882i | \(0.464773\pi\) | |||||||
\(998\) | 14.5349 | 0.460093 | ||||||||
\(999\) | −7.15237 | −0.226291 |
(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 | 2001.2.a.k.1.5 | ✓ | 10 | |
3.2 | odd | 2 | 6003.2.a.k.1.6 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2001.2.a.k.1.5 | ✓ | 10 | 1.1 | even | 1 | trivial | |
6003.2.a.k.1.6 | 10 | 3.2 | odd | 2 |