Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8015,2,Mod(1,8015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8015, 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("8015.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8015 = 5 \cdot 7 \cdot 229 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8015.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.0000972201\) |
Analytic rank: | \(0\) |
Dimension: | \(62\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.40 | ||
Character | \(\chi\) | \(=\) | 8015.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.970097 | 0.685962 | 0.342981 | − | 0.939342i | \(-0.388563\pi\) | ||||
0.342981 | + | 0.939342i | \(0.388563\pi\) | |||||||
\(3\) | −0.396968 | −0.229190 | −0.114595 | − | 0.993412i | \(-0.536557\pi\) | ||||
−0.114595 | + | 0.993412i | \(0.536557\pi\) | |||||||
\(4\) | −1.05891 | −0.529456 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −0.385098 | −0.157216 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −2.96744 | −1.04915 | ||||||||
\(9\) | −2.84242 | −0.947472 | ||||||||
\(10\) | −0.970097 | −0.306772 | ||||||||
\(11\) | −2.20338 | −0.664343 | −0.332172 | − | 0.943219i | \(-0.607781\pi\) | ||||
−0.332172 | + | 0.943219i | \(0.607781\pi\) | |||||||
\(12\) | 0.420355 | 0.121346 | ||||||||
\(13\) | 4.66808 | 1.29469 | 0.647347 | − | 0.762196i | \(-0.275879\pi\) | ||||
0.647347 | + | 0.762196i | \(0.275879\pi\) | |||||||
\(14\) | −0.970097 | −0.259269 | ||||||||
\(15\) | 0.396968 | 0.102497 | ||||||||
\(16\) | −0.760881 | −0.190220 | ||||||||
\(17\) | −3.82317 | −0.927255 | −0.463628 | − | 0.886030i | \(-0.653452\pi\) | ||||
−0.463628 | + | 0.886030i | \(0.653452\pi\) | |||||||
\(18\) | −2.75742 | −0.649930 | ||||||||
\(19\) | −5.08764 | −1.16718 | −0.583592 | − | 0.812047i | \(-0.698353\pi\) | ||||
−0.583592 | + | 0.812047i | \(0.698353\pi\) | |||||||
\(20\) | 1.05891 | 0.236780 | ||||||||
\(21\) | 0.396968 | 0.0866256 | ||||||||
\(22\) | −2.13749 | −0.455714 | ||||||||
\(23\) | −8.61116 | −1.79555 | −0.897775 | − | 0.440454i | \(-0.854817\pi\) | ||||
−0.897775 | + | 0.440454i | \(0.854817\pi\) | |||||||
\(24\) | 1.17798 | 0.240454 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 4.52849 | 0.888110 | ||||||||
\(27\) | 2.31925 | 0.446341 | ||||||||
\(28\) | 1.05891 | 0.200116 | ||||||||
\(29\) | −6.53813 | −1.21410 | −0.607050 | − | 0.794664i | \(-0.707647\pi\) | ||||
−0.607050 | + | 0.794664i | \(0.707647\pi\) | |||||||
\(30\) | 0.385098 | 0.0703089 | ||||||||
\(31\) | −3.90594 | −0.701527 | −0.350764 | − | 0.936464i | \(-0.614078\pi\) | ||||
−0.350764 | + | 0.936464i | \(0.614078\pi\) | |||||||
\(32\) | 5.19675 | 0.918665 | ||||||||
\(33\) | 0.874671 | 0.152261 | ||||||||
\(34\) | −3.70885 | −0.636062 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 3.00987 | 0.501645 | ||||||||
\(37\) | 1.56682 | 0.257584 | 0.128792 | − | 0.991672i | \(-0.458890\pi\) | ||||
0.128792 | + | 0.991672i | \(0.458890\pi\) | |||||||
\(38\) | −4.93550 | −0.800644 | ||||||||
\(39\) | −1.85308 | −0.296731 | ||||||||
\(40\) | 2.96744 | 0.469194 | ||||||||
\(41\) | −10.3901 | −1.62265 | −0.811327 | − | 0.584592i | \(-0.801254\pi\) | ||||
−0.811327 | + | 0.584592i | \(0.801254\pi\) | |||||||
\(42\) | 0.385098 | 0.0594219 | ||||||||
\(43\) | −5.42344 | −0.827067 | −0.413533 | − | 0.910489i | \(-0.635705\pi\) | ||||
−0.413533 | + | 0.910489i | \(0.635705\pi\) | |||||||
\(44\) | 2.33318 | 0.351740 | ||||||||
\(45\) | 2.84242 | 0.423722 | ||||||||
\(46\) | −8.35365 | −1.23168 | ||||||||
\(47\) | 4.14775 | 0.605011 | 0.302505 | − | 0.953148i | \(-0.402177\pi\) | ||||
0.302505 | + | 0.953148i | \(0.402177\pi\) | |||||||
\(48\) | 0.302046 | 0.0435966 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0.970097 | 0.137192 | ||||||||
\(51\) | 1.51768 | 0.212517 | ||||||||
\(52\) | −4.94309 | −0.685483 | ||||||||
\(53\) | −1.57645 | −0.216541 | −0.108271 | − | 0.994121i | \(-0.534531\pi\) | ||||
−0.108271 | + | 0.994121i | \(0.534531\pi\) | |||||||
\(54\) | 2.24990 | 0.306173 | ||||||||
\(55\) | 2.20338 | 0.297103 | ||||||||
\(56\) | 2.96744 | 0.396541 | ||||||||
\(57\) | 2.01963 | 0.267507 | ||||||||
\(58\) | −6.34262 | −0.832827 | ||||||||
\(59\) | 8.65116 | 1.12628 | 0.563142 | − | 0.826360i | \(-0.309592\pi\) | ||||
0.563142 | + | 0.826360i | \(0.309592\pi\) | |||||||
\(60\) | −0.420355 | −0.0542675 | ||||||||
\(61\) | 1.84183 | 0.235822 | 0.117911 | − | 0.993024i | \(-0.462380\pi\) | ||||
0.117911 | + | 0.993024i | \(0.462380\pi\) | |||||||
\(62\) | −3.78914 | −0.481221 | ||||||||
\(63\) | 2.84242 | 0.358111 | ||||||||
\(64\) | 6.56312 | 0.820390 | ||||||||
\(65\) | −4.66808 | −0.579004 | ||||||||
\(66\) | 0.848516 | 0.104445 | ||||||||
\(67\) | 10.0744 | 1.23078 | 0.615392 | − | 0.788222i | \(-0.288998\pi\) | ||||
0.615392 | + | 0.788222i | \(0.288998\pi\) | |||||||
\(68\) | 4.04840 | 0.490941 | ||||||||
\(69\) | 3.41836 | 0.411522 | ||||||||
\(70\) | 0.970097 | 0.115949 | ||||||||
\(71\) | 2.25770 | 0.267939 | 0.133970 | − | 0.990985i | \(-0.457228\pi\) | ||||
0.133970 | + | 0.990985i | \(0.457228\pi\) | |||||||
\(72\) | 8.43470 | 0.994039 | ||||||||
\(73\) | −10.5309 | −1.23255 | −0.616275 | − | 0.787531i | \(-0.711359\pi\) | ||||
−0.616275 | + | 0.787531i | \(0.711359\pi\) | |||||||
\(74\) | 1.51997 | 0.176693 | ||||||||
\(75\) | −0.396968 | −0.0458380 | ||||||||
\(76\) | 5.38736 | 0.617973 | ||||||||
\(77\) | 2.20338 | 0.251098 | ||||||||
\(78\) | −1.79767 | −0.203546 | ||||||||
\(79\) | 8.74949 | 0.984394 | 0.492197 | − | 0.870484i | \(-0.336194\pi\) | ||||
0.492197 | + | 0.870484i | \(0.336194\pi\) | |||||||
\(80\) | 0.760881 | 0.0850691 | ||||||||
\(81\) | 7.60658 | 0.845175 | ||||||||
\(82\) | −10.0794 | −1.11308 | ||||||||
\(83\) | −13.9029 | −1.52604 | −0.763022 | − | 0.646373i | \(-0.776285\pi\) | ||||
−0.763022 | + | 0.646373i | \(0.776285\pi\) | |||||||
\(84\) | −0.420355 | −0.0458645 | ||||||||
\(85\) | 3.82317 | 0.414681 | ||||||||
\(86\) | −5.26126 | −0.567336 | ||||||||
\(87\) | 2.59543 | 0.278259 | ||||||||
\(88\) | 6.53839 | 0.696995 | ||||||||
\(89\) | −8.53761 | −0.904985 | −0.452492 | − | 0.891768i | \(-0.649465\pi\) | ||||
−0.452492 | + | 0.891768i | \(0.649465\pi\) | |||||||
\(90\) | 2.75742 | 0.290657 | ||||||||
\(91\) | −4.66808 | −0.489348 | ||||||||
\(92\) | 9.11846 | 0.950665 | ||||||||
\(93\) | 1.55053 | 0.160783 | ||||||||
\(94\) | 4.02372 | 0.415015 | ||||||||
\(95\) | 5.08764 | 0.521981 | ||||||||
\(96\) | −2.06295 | −0.210549 | ||||||||
\(97\) | −14.8303 | −1.50578 | −0.752892 | − | 0.658144i | \(-0.771342\pi\) | ||||
−0.752892 | + | 0.658144i | \(0.771342\pi\) | |||||||
\(98\) | 0.970097 | 0.0979946 | ||||||||
\(99\) | 6.26291 | 0.629446 | ||||||||
\(100\) | −1.05891 | −0.105891 | ||||||||
\(101\) | 3.96350 | 0.394383 | 0.197191 | − | 0.980365i | \(-0.436818\pi\) | ||||
0.197191 | + | 0.980365i | \(0.436818\pi\) | |||||||
\(102\) | 1.47229 | 0.145779 | ||||||||
\(103\) | −8.14891 | −0.802936 | −0.401468 | − | 0.915873i | \(-0.631500\pi\) | ||||
−0.401468 | + | 0.915873i | \(0.631500\pi\) | |||||||
\(104\) | −13.8523 | −1.35833 | ||||||||
\(105\) | −0.396968 | −0.0387402 | ||||||||
\(106\) | −1.52931 | −0.148539 | ||||||||
\(107\) | −9.09956 | −0.879688 | −0.439844 | − | 0.898074i | \(-0.644966\pi\) | ||||
−0.439844 | + | 0.898074i | \(0.644966\pi\) | |||||||
\(108\) | −2.45589 | −0.236318 | ||||||||
\(109\) | 11.2079 | 1.07352 | 0.536760 | − | 0.843735i | \(-0.319648\pi\) | ||||
0.536760 | + | 0.843735i | \(0.319648\pi\) | |||||||
\(110\) | 2.13749 | 0.203802 | ||||||||
\(111\) | −0.621979 | −0.0590356 | ||||||||
\(112\) | 0.760881 | 0.0718965 | ||||||||
\(113\) | 0.420027 | 0.0395129 | 0.0197564 | − | 0.999805i | \(-0.493711\pi\) | ||||
0.0197564 | + | 0.999805i | \(0.493711\pi\) | |||||||
\(114\) | 1.95924 | 0.183499 | ||||||||
\(115\) | 8.61116 | 0.802994 | ||||||||
\(116\) | 6.92330 | 0.642813 | ||||||||
\(117\) | −13.2686 | −1.22669 | ||||||||
\(118\) | 8.39246 | 0.772589 | ||||||||
\(119\) | 3.82317 | 0.350470 | ||||||||
\(120\) | −1.17798 | −0.107534 | ||||||||
\(121\) | −6.14513 | −0.558648 | ||||||||
\(122\) | 1.78675 | 0.161765 | ||||||||
\(123\) | 4.12452 | 0.371896 | ||||||||
\(124\) | 4.13605 | 0.371428 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 2.75742 | 0.245650 | ||||||||
\(127\) | 4.25797 | 0.377834 | 0.188917 | − | 0.981993i | \(-0.439502\pi\) | ||||
0.188917 | + | 0.981993i | \(0.439502\pi\) | |||||||
\(128\) | −4.02665 | −0.355909 | ||||||||
\(129\) | 2.15293 | 0.189555 | ||||||||
\(130\) | −4.52849 | −0.397175 | ||||||||
\(131\) | −8.77509 | −0.766683 | −0.383342 | − | 0.923607i | \(-0.625227\pi\) | ||||
−0.383342 | + | 0.923607i | \(0.625227\pi\) | |||||||
\(132\) | −0.926200 | −0.0806153 | ||||||||
\(133\) | 5.08764 | 0.441154 | ||||||||
\(134\) | 9.77314 | 0.844271 | ||||||||
\(135\) | −2.31925 | −0.199610 | ||||||||
\(136\) | 11.3450 | 0.972829 | ||||||||
\(137\) | −0.00613626 | −0.000524256 0 | −0.000262128 | − | 1.00000i | \(-0.500083\pi\) | ||||
−0.000262128 | 1.00000i | \(0.500083\pi\) | ||||||||
\(138\) | 3.31614 | 0.282288 | ||||||||
\(139\) | −9.63822 | −0.817503 | −0.408752 | − | 0.912646i | \(-0.634036\pi\) | ||||
−0.408752 | + | 0.912646i | \(0.634036\pi\) | |||||||
\(140\) | −1.05891 | −0.0894944 | ||||||||
\(141\) | −1.64652 | −0.138662 | ||||||||
\(142\) | 2.19018 | 0.183796 | ||||||||
\(143\) | −10.2855 | −0.860120 | ||||||||
\(144\) | 2.16274 | 0.180228 | ||||||||
\(145\) | 6.53813 | 0.542962 | ||||||||
\(146\) | −10.2160 | −0.845483 | ||||||||
\(147\) | −0.396968 | −0.0327414 | ||||||||
\(148\) | −1.65913 | −0.136379 | ||||||||
\(149\) | 13.3212 | 1.09131 | 0.545657 | − | 0.838009i | \(-0.316280\pi\) | ||||
0.545657 | + | 0.838009i | \(0.316280\pi\) | |||||||
\(150\) | −0.385098 | −0.0314431 | ||||||||
\(151\) | −5.14788 | −0.418929 | −0.209464 | − | 0.977816i | \(-0.567172\pi\) | ||||
−0.209464 | + | 0.977816i | \(0.567172\pi\) | |||||||
\(152\) | 15.0973 | 1.22455 | ||||||||
\(153\) | 10.8670 | 0.878548 | ||||||||
\(154\) | 2.13749 | 0.172244 | ||||||||
\(155\) | 3.90594 | 0.313733 | ||||||||
\(156\) | 1.96225 | 0.157106 | ||||||||
\(157\) | 9.06063 | 0.723117 | 0.361558 | − | 0.932349i | \(-0.382245\pi\) | ||||
0.361558 | + | 0.932349i | \(0.382245\pi\) | |||||||
\(158\) | 8.48785 | 0.675257 | ||||||||
\(159\) | 0.625799 | 0.0496291 | ||||||||
\(160\) | −5.19675 | −0.410839 | ||||||||
\(161\) | 8.61116 | 0.678654 | ||||||||
\(162\) | 7.37912 | 0.579758 | ||||||||
\(163\) | −0.996155 | −0.0780249 | −0.0390124 | − | 0.999239i | \(-0.512421\pi\) | ||||
−0.0390124 | + | 0.999239i | \(0.512421\pi\) | |||||||
\(164\) | 11.0022 | 0.859124 | ||||||||
\(165\) | −0.874671 | −0.0680930 | ||||||||
\(166\) | −13.4872 | −1.04681 | ||||||||
\(167\) | −12.3079 | −0.952412 | −0.476206 | − | 0.879334i | \(-0.657988\pi\) | ||||
−0.476206 | + | 0.879334i | \(0.657988\pi\) | |||||||
\(168\) | −1.17798 | −0.0908832 | ||||||||
\(169\) | 8.79100 | 0.676231 | ||||||||
\(170\) | 3.70885 | 0.284456 | ||||||||
\(171\) | 14.4612 | 1.10587 | ||||||||
\(172\) | 5.74294 | 0.437895 | ||||||||
\(173\) | 16.4452 | 1.25031 | 0.625154 | − | 0.780501i | \(-0.285036\pi\) | ||||
0.625154 | + | 0.780501i | \(0.285036\pi\) | |||||||
\(174\) | 2.51782 | 0.190875 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 1.67651 | 0.126372 | ||||||||
\(177\) | −3.43424 | −0.258133 | ||||||||
\(178\) | −8.28231 | −0.620785 | ||||||||
\(179\) | 5.29031 | 0.395416 | 0.197708 | − | 0.980261i | \(-0.436650\pi\) | ||||
0.197708 | + | 0.980261i | \(0.436650\pi\) | |||||||
\(180\) | −3.00987 | −0.224342 | ||||||||
\(181\) | 11.0371 | 0.820378 | 0.410189 | − | 0.912001i | \(-0.365463\pi\) | ||||
0.410189 | + | 0.912001i | \(0.365463\pi\) | |||||||
\(182\) | −4.52849 | −0.335674 | ||||||||
\(183\) | −0.731149 | −0.0540481 | ||||||||
\(184\) | 25.5531 | 1.88380 | ||||||||
\(185\) | −1.56682 | −0.115195 | ||||||||
\(186\) | 1.50417 | 0.110291 | ||||||||
\(187\) | 8.42389 | 0.616016 | ||||||||
\(188\) | −4.39210 | −0.320327 | ||||||||
\(189\) | −2.31925 | −0.168701 | ||||||||
\(190\) | 4.93550 | 0.358059 | ||||||||
\(191\) | −11.7995 | −0.853782 | −0.426891 | − | 0.904303i | \(-0.640391\pi\) | ||||
−0.426891 | + | 0.904303i | \(0.640391\pi\) | |||||||
\(192\) | −2.60535 | −0.188025 | ||||||||
\(193\) | 6.22737 | 0.448256 | 0.224128 | − | 0.974560i | \(-0.428047\pi\) | ||||
0.224128 | + | 0.974560i | \(0.428047\pi\) | |||||||
\(194\) | −14.3868 | −1.03291 | ||||||||
\(195\) | 1.85308 | 0.132702 | ||||||||
\(196\) | −1.05891 | −0.0756366 | ||||||||
\(197\) | −6.52208 | −0.464679 | −0.232339 | − | 0.972635i | \(-0.574638\pi\) | ||||
−0.232339 | + | 0.972635i | \(0.574638\pi\) | |||||||
\(198\) | 6.07563 | 0.431776 | ||||||||
\(199\) | −0.945655 | −0.0670357 | −0.0335179 | − | 0.999438i | \(-0.510671\pi\) | ||||
−0.0335179 | + | 0.999438i | \(0.510671\pi\) | |||||||
\(200\) | −2.96744 | −0.209830 | ||||||||
\(201\) | −3.99922 | −0.282083 | ||||||||
\(202\) | 3.84497 | 0.270531 | ||||||||
\(203\) | 6.53813 | 0.458887 | ||||||||
\(204\) | −1.60709 | −0.112519 | ||||||||
\(205\) | 10.3901 | 0.725673 | ||||||||
\(206\) | −7.90524 | −0.550784 | ||||||||
\(207\) | 24.4765 | 1.70123 | ||||||||
\(208\) | −3.55186 | −0.246277 | ||||||||
\(209\) | 11.2100 | 0.775410 | ||||||||
\(210\) | −0.385098 | −0.0265743 | ||||||||
\(211\) | −2.49474 | −0.171745 | −0.0858725 | − | 0.996306i | \(-0.527368\pi\) | ||||
−0.0858725 | + | 0.996306i | \(0.527368\pi\) | |||||||
\(212\) | 1.66932 | 0.114649 | ||||||||
\(213\) | −0.896234 | −0.0614089 | ||||||||
\(214\) | −8.82746 | −0.603433 | ||||||||
\(215\) | 5.42344 | 0.369875 | ||||||||
\(216\) | −6.88225 | −0.468278 | ||||||||
\(217\) | 3.90594 | 0.265152 | ||||||||
\(218\) | 10.8727 | 0.736394 | ||||||||
\(219\) | 4.18044 | 0.282488 | ||||||||
\(220\) | −2.33318 | −0.157303 | ||||||||
\(221\) | −17.8469 | −1.20051 | ||||||||
\(222\) | −0.603380 | −0.0404962 | ||||||||
\(223\) | 23.9274 | 1.60230 | 0.801149 | − | 0.598465i | \(-0.204222\pi\) | ||||
0.801149 | + | 0.598465i | \(0.204222\pi\) | |||||||
\(224\) | −5.19675 | −0.347223 | ||||||||
\(225\) | −2.84242 | −0.189494 | ||||||||
\(226\) | 0.407467 | 0.0271043 | ||||||||
\(227\) | 12.3622 | 0.820510 | 0.410255 | − | 0.911971i | \(-0.365440\pi\) | ||||
0.410255 | + | 0.911971i | \(0.365440\pi\) | |||||||
\(228\) | −2.13861 | −0.141633 | ||||||||
\(229\) | 1.00000 | 0.0660819 | ||||||||
\(230\) | 8.35365 | 0.550824 | ||||||||
\(231\) | −0.874671 | −0.0575491 | ||||||||
\(232\) | 19.4015 | 1.27377 | ||||||||
\(233\) | −21.9933 | −1.44083 | −0.720414 | − | 0.693544i | \(-0.756048\pi\) | ||||
−0.720414 | + | 0.693544i | \(0.756048\pi\) | |||||||
\(234\) | −12.8719 | −0.841460 | ||||||||
\(235\) | −4.14775 | −0.270569 | ||||||||
\(236\) | −9.16081 | −0.596318 | ||||||||
\(237\) | −3.47327 | −0.225613 | ||||||||
\(238\) | 3.70885 | 0.240409 | ||||||||
\(239\) | 16.6728 | 1.07847 | 0.539236 | − | 0.842155i | \(-0.318713\pi\) | ||||
0.539236 | + | 0.842155i | \(0.318713\pi\) | |||||||
\(240\) | −0.302046 | −0.0194970 | ||||||||
\(241\) | 5.79359 | 0.373198 | 0.186599 | − | 0.982436i | \(-0.440254\pi\) | ||||
0.186599 | + | 0.982436i | \(0.440254\pi\) | |||||||
\(242\) | −5.96137 | −0.383212 | ||||||||
\(243\) | −9.97733 | −0.640046 | ||||||||
\(244\) | −1.95034 | −0.124858 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | 4.00119 | 0.255106 | ||||||||
\(247\) | −23.7495 | −1.51115 | ||||||||
\(248\) | 11.5906 | 0.736007 | ||||||||
\(249\) | 5.51902 | 0.349754 | ||||||||
\(250\) | −0.970097 | −0.0613543 | ||||||||
\(251\) | 22.9827 | 1.45066 | 0.725328 | − | 0.688404i | \(-0.241688\pi\) | ||||
0.725328 | + | 0.688404i | \(0.241688\pi\) | |||||||
\(252\) | −3.00987 | −0.189604 | ||||||||
\(253\) | 18.9736 | 1.19286 | ||||||||
\(254\) | 4.13065 | 0.259180 | ||||||||
\(255\) | −1.51768 | −0.0950407 | ||||||||
\(256\) | −17.0325 | −1.06453 | ||||||||
\(257\) | 9.03120 | 0.563351 | 0.281675 | − | 0.959510i | \(-0.409110\pi\) | ||||
0.281675 | + | 0.959510i | \(0.409110\pi\) | |||||||
\(258\) | 2.08855 | 0.130028 | ||||||||
\(259\) | −1.56682 | −0.0973576 | ||||||||
\(260\) | 4.94309 | 0.306557 | ||||||||
\(261\) | 18.5841 | 1.15033 | ||||||||
\(262\) | −8.51269 | −0.525915 | ||||||||
\(263\) | −7.40733 | −0.456755 | −0.228378 | − | 0.973573i | \(-0.573342\pi\) | ||||
−0.228378 | + | 0.973573i | \(0.573342\pi\) | |||||||
\(264\) | −2.59553 | −0.159744 | ||||||||
\(265\) | 1.57645 | 0.0968403 | ||||||||
\(266\) | 4.93550 | 0.302615 | ||||||||
\(267\) | 3.38916 | 0.207413 | ||||||||
\(268\) | −10.6679 | −0.651646 | ||||||||
\(269\) | 16.2546 | 0.991063 | 0.495531 | − | 0.868590i | \(-0.334973\pi\) | ||||
0.495531 | + | 0.868590i | \(0.334973\pi\) | |||||||
\(270\) | −2.24990 | −0.136925 | ||||||||
\(271\) | 25.9362 | 1.57551 | 0.787757 | − | 0.615986i | \(-0.211242\pi\) | ||||
0.787757 | + | 0.615986i | \(0.211242\pi\) | |||||||
\(272\) | 2.90898 | 0.176383 | ||||||||
\(273\) | 1.85308 | 0.112154 | ||||||||
\(274\) | −0.00595277 | −0.000359620 0 | ||||||||
\(275\) | −2.20338 | −0.132869 | ||||||||
\(276\) | −3.61974 | −0.217883 | ||||||||
\(277\) | −7.44191 | −0.447141 | −0.223570 | − | 0.974688i | \(-0.571771\pi\) | ||||
−0.223570 | + | 0.974688i | \(0.571771\pi\) | |||||||
\(278\) | −9.35001 | −0.560776 | ||||||||
\(279\) | 11.1023 | 0.664678 | ||||||||
\(280\) | −2.96744 | −0.177339 | ||||||||
\(281\) | −17.8273 | −1.06349 | −0.531743 | − | 0.846906i | \(-0.678463\pi\) | ||||
−0.531743 | + | 0.846906i | \(0.678463\pi\) | |||||||
\(282\) | −1.59729 | −0.0951171 | ||||||||
\(283\) | 11.3850 | 0.676768 | 0.338384 | − | 0.941008i | \(-0.390120\pi\) | ||||
0.338384 | + | 0.941008i | \(0.390120\pi\) | |||||||
\(284\) | −2.39070 | −0.141862 | ||||||||
\(285\) | −2.01963 | −0.119633 | ||||||||
\(286\) | −9.97797 | −0.590010 | ||||||||
\(287\) | 10.3901 | 0.613306 | ||||||||
\(288\) | −14.7713 | −0.870409 | ||||||||
\(289\) | −2.38336 | −0.140198 | ||||||||
\(290\) | 6.34262 | 0.372451 | ||||||||
\(291\) | 5.88715 | 0.345111 | ||||||||
\(292\) | 11.1513 | 0.652581 | ||||||||
\(293\) | −14.6010 | −0.852997 | −0.426498 | − | 0.904488i | \(-0.640253\pi\) | ||||
−0.426498 | + | 0.904488i | \(0.640253\pi\) | |||||||
\(294\) | −0.385098 | −0.0224594 | ||||||||
\(295\) | −8.65116 | −0.503690 | ||||||||
\(296\) | −4.64945 | −0.270244 | ||||||||
\(297\) | −5.11019 | −0.296523 | ||||||||
\(298\) | 12.9228 | 0.748600 | ||||||||
\(299\) | −40.1976 | −2.32469 | ||||||||
\(300\) | 0.420355 | 0.0242692 | ||||||||
\(301\) | 5.42344 | 0.312602 | ||||||||
\(302\) | −4.99394 | −0.287369 | ||||||||
\(303\) | −1.57338 | −0.0903885 | ||||||||
\(304\) | 3.87109 | 0.222022 | ||||||||
\(305\) | −1.84183 | −0.105463 | ||||||||
\(306\) | 10.5421 | 0.602651 | ||||||||
\(307\) | 4.07326 | 0.232473 | 0.116237 | − | 0.993222i | \(-0.462917\pi\) | ||||
0.116237 | + | 0.993222i | \(0.462917\pi\) | |||||||
\(308\) | −2.33318 | −0.132945 | ||||||||
\(309\) | 3.23486 | 0.184025 | ||||||||
\(310\) | 3.78914 | 0.215209 | ||||||||
\(311\) | 6.74219 | 0.382314 | 0.191157 | − | 0.981559i | \(-0.438776\pi\) | ||||
0.191157 | + | 0.981559i | \(0.438776\pi\) | |||||||
\(312\) | 5.49891 | 0.311314 | ||||||||
\(313\) | 4.88163 | 0.275926 | 0.137963 | − | 0.990437i | \(-0.455944\pi\) | ||||
0.137963 | + | 0.990437i | \(0.455944\pi\) | |||||||
\(314\) | 8.78969 | 0.496031 | ||||||||
\(315\) | −2.84242 | −0.160152 | ||||||||
\(316\) | −9.26494 | −0.521193 | ||||||||
\(317\) | 26.1274 | 1.46746 | 0.733729 | − | 0.679442i | \(-0.237778\pi\) | ||||
0.733729 | + | 0.679442i | \(0.237778\pi\) | |||||||
\(318\) | 0.607086 | 0.0340437 | ||||||||
\(319\) | 14.4060 | 0.806579 | ||||||||
\(320\) | −6.56312 | −0.366889 | ||||||||
\(321\) | 3.61224 | 0.201616 | ||||||||
\(322\) | 8.35365 | 0.465531 | ||||||||
\(323\) | 19.4509 | 1.08228 | ||||||||
\(324\) | −8.05470 | −0.447483 | ||||||||
\(325\) | 4.66808 | 0.258939 | ||||||||
\(326\) | −0.966367 | −0.0535221 | ||||||||
\(327\) | −4.44917 | −0.246040 | ||||||||
\(328\) | 30.8319 | 1.70241 | ||||||||
\(329\) | −4.14775 | −0.228673 | ||||||||
\(330\) | −0.848516 | −0.0467092 | ||||||||
\(331\) | 24.1488 | 1.32734 | 0.663669 | − | 0.748026i | \(-0.268998\pi\) | ||||
0.663669 | + | 0.748026i | \(0.268998\pi\) | |||||||
\(332\) | 14.7220 | 0.807973 | ||||||||
\(333\) | −4.45356 | −0.244054 | ||||||||
\(334\) | −11.9398 | −0.653318 | ||||||||
\(335\) | −10.0744 | −0.550423 | ||||||||
\(336\) | −0.302046 | −0.0164779 | ||||||||
\(337\) | 31.0135 | 1.68941 | 0.844707 | − | 0.535230i | \(-0.179775\pi\) | ||||
0.844707 | + | 0.535230i | \(0.179775\pi\) | |||||||
\(338\) | 8.52812 | 0.463869 | ||||||||
\(339\) | −0.166738 | −0.00905594 | ||||||||
\(340\) | −4.04840 | −0.219555 | ||||||||
\(341\) | 8.60626 | 0.466055 | ||||||||
\(342\) | 14.0287 | 0.758588 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 16.0937 | 0.867716 | ||||||||
\(345\) | −3.41836 | −0.184038 | ||||||||
\(346\) | 15.9535 | 0.857664 | ||||||||
\(347\) | 0.0306680 | 0.00164634 | 0.000823172 | − | 1.00000i | \(-0.499738\pi\) | ||||
0.000823172 | 1.00000i | \(0.499738\pi\) | ||||||||
\(348\) | −2.74833 | −0.147326 | ||||||||
\(349\) | 21.6364 | 1.15817 | 0.579085 | − | 0.815267i | \(-0.303410\pi\) | ||||
0.579085 | + | 0.815267i | \(0.303410\pi\) | |||||||
\(350\) | −0.970097 | −0.0518539 | ||||||||
\(351\) | 10.8265 | 0.577874 | ||||||||
\(352\) | −11.4504 | −0.610309 | ||||||||
\(353\) | 2.83747 | 0.151023 | 0.0755117 | − | 0.997145i | \(-0.475941\pi\) | ||||
0.0755117 | + | 0.997145i | \(0.475941\pi\) | |||||||
\(354\) | −3.33154 | −0.177069 | ||||||||
\(355\) | −2.25770 | −0.119826 | ||||||||
\(356\) | 9.04058 | 0.479150 | ||||||||
\(357\) | −1.51768 | −0.0803241 | ||||||||
\(358\) | 5.13211 | 0.271241 | ||||||||
\(359\) | −33.7911 | −1.78342 | −0.891712 | − | 0.452603i | \(-0.850495\pi\) | ||||
−0.891712 | + | 0.452603i | \(0.850495\pi\) | |||||||
\(360\) | −8.43470 | −0.444548 | ||||||||
\(361\) | 6.88405 | 0.362318 | ||||||||
\(362\) | 10.7070 | 0.562748 | ||||||||
\(363\) | 2.43942 | 0.128037 | ||||||||
\(364\) | 4.94309 | 0.259088 | ||||||||
\(365\) | 10.5309 | 0.551213 | ||||||||
\(366\) | −0.709285 | −0.0370749 | ||||||||
\(367\) | 6.12803 | 0.319881 | 0.159940 | − | 0.987127i | \(-0.448870\pi\) | ||||
0.159940 | + | 0.987127i | \(0.448870\pi\) | |||||||
\(368\) | 6.55207 | 0.341550 | ||||||||
\(369\) | 29.5329 | 1.53742 | ||||||||
\(370\) | −1.51997 | −0.0790194 | ||||||||
\(371\) | 1.57645 | 0.0818450 | ||||||||
\(372\) | −1.64188 | −0.0851275 | ||||||||
\(373\) | 11.3406 | 0.587195 | 0.293597 | − | 0.955929i | \(-0.405148\pi\) | ||||
0.293597 | + | 0.955929i | \(0.405148\pi\) | |||||||
\(374\) | 8.17199 | 0.422563 | ||||||||
\(375\) | 0.396968 | 0.0204994 | ||||||||
\(376\) | −12.3082 | −0.634746 | ||||||||
\(377\) | −30.5205 | −1.57189 | ||||||||
\(378\) | −2.24990 | −0.115722 | ||||||||
\(379\) | −34.4420 | −1.76917 | −0.884583 | − | 0.466383i | \(-0.845557\pi\) | ||||
−0.884583 | + | 0.466383i | \(0.845557\pi\) | |||||||
\(380\) | −5.38736 | −0.276366 | ||||||||
\(381\) | −1.69028 | −0.0865957 | ||||||||
\(382\) | −11.4467 | −0.585662 | ||||||||
\(383\) | −36.0412 | −1.84162 | −0.920810 | − | 0.390010i | \(-0.872471\pi\) | ||||
−0.920810 | + | 0.390010i | \(0.872471\pi\) | |||||||
\(384\) | 1.59845 | 0.0815707 | ||||||||
\(385\) | −2.20338 | −0.112294 | ||||||||
\(386\) | 6.04115 | 0.307487 | ||||||||
\(387\) | 15.4157 | 0.783623 | ||||||||
\(388\) | 15.7039 | 0.797247 | ||||||||
\(389\) | 30.7369 | 1.55842 | 0.779211 | − | 0.626762i | \(-0.215620\pi\) | ||||
0.779211 | + | 0.626762i | \(0.215620\pi\) | |||||||
\(390\) | 1.79767 | 0.0910285 | ||||||||
\(391\) | 32.9219 | 1.66493 | ||||||||
\(392\) | −2.96744 | −0.149878 | ||||||||
\(393\) | 3.48343 | 0.175716 | ||||||||
\(394\) | −6.32705 | −0.318752 | ||||||||
\(395\) | −8.74949 | −0.440234 | ||||||||
\(396\) | −6.63187 | −0.333264 | ||||||||
\(397\) | 25.6295 | 1.28631 | 0.643153 | − | 0.765737i | \(-0.277626\pi\) | ||||
0.643153 | + | 0.765737i | \(0.277626\pi\) | |||||||
\(398\) | −0.917377 | −0.0459839 | ||||||||
\(399\) | −2.01963 | −0.101108 | ||||||||
\(400\) | −0.760881 | −0.0380441 | ||||||||
\(401\) | 1.76129 | 0.0879547 | 0.0439773 | − | 0.999033i | \(-0.485997\pi\) | ||||
0.0439773 | + | 0.999033i | \(0.485997\pi\) | |||||||
\(402\) | −3.87963 | −0.193498 | ||||||||
\(403\) | −18.2333 | −0.908263 | ||||||||
\(404\) | −4.19699 | −0.208808 | ||||||||
\(405\) | −7.60658 | −0.377974 | ||||||||
\(406\) | 6.34262 | 0.314779 | ||||||||
\(407\) | −3.45230 | −0.171124 | ||||||||
\(408\) | −4.50362 | −0.222962 | ||||||||
\(409\) | 22.9828 | 1.13643 | 0.568214 | − | 0.822881i | \(-0.307635\pi\) | ||||
0.568214 | + | 0.822881i | \(0.307635\pi\) | |||||||
\(410\) | 10.0794 | 0.497784 | ||||||||
\(411\) | 0.00243590 | 0.000120154 0 | ||||||||
\(412\) | 8.62898 | 0.425119 | ||||||||
\(413\) | −8.65116 | −0.425696 | ||||||||
\(414\) | 23.7446 | 1.16698 | ||||||||
\(415\) | 13.9029 | 0.682467 | ||||||||
\(416\) | 24.2589 | 1.18939 | ||||||||
\(417\) | 3.82607 | 0.187363 | ||||||||
\(418\) | 10.8748 | 0.531902 | ||||||||
\(419\) | −12.9493 | −0.632614 | −0.316307 | − | 0.948657i | \(-0.602443\pi\) | ||||
−0.316307 | + | 0.948657i | \(0.602443\pi\) | |||||||
\(420\) | 0.420355 | 0.0205112 | ||||||||
\(421\) | −29.2841 | −1.42722 | −0.713610 | − | 0.700543i | \(-0.752941\pi\) | ||||
−0.713610 | + | 0.700543i | \(0.752941\pi\) | |||||||
\(422\) | −2.42014 | −0.117811 | ||||||||
\(423\) | −11.7896 | −0.573231 | ||||||||
\(424\) | 4.67801 | 0.227184 | ||||||||
\(425\) | −3.82317 | −0.185451 | ||||||||
\(426\) | −0.869434 | −0.0421242 | ||||||||
\(427\) | −1.84183 | −0.0891324 | ||||||||
\(428\) | 9.63564 | 0.465756 | ||||||||
\(429\) | 4.08304 | 0.197131 | ||||||||
\(430\) | 5.26126 | 0.253721 | ||||||||
\(431\) | 14.3388 | 0.690675 | 0.345337 | − | 0.938479i | \(-0.387765\pi\) | ||||
0.345337 | + | 0.938479i | \(0.387765\pi\) | |||||||
\(432\) | −1.76468 | −0.0849031 | ||||||||
\(433\) | 5.82467 | 0.279916 | 0.139958 | − | 0.990157i | \(-0.455303\pi\) | ||||
0.139958 | + | 0.990157i | \(0.455303\pi\) | |||||||
\(434\) | 3.78914 | 0.181885 | ||||||||
\(435\) | −2.59543 | −0.124441 | ||||||||
\(436\) | −11.8682 | −0.568382 | ||||||||
\(437\) | 43.8104 | 2.09574 | ||||||||
\(438\) | 4.05543 | 0.193776 | ||||||||
\(439\) | −33.2124 | −1.58514 | −0.792570 | − | 0.609780i | \(-0.791258\pi\) | ||||
−0.792570 | + | 0.609780i | \(0.791258\pi\) | |||||||
\(440\) | −6.53839 | −0.311706 | ||||||||
\(441\) | −2.84242 | −0.135353 | ||||||||
\(442\) | −17.3132 | −0.823505 | ||||||||
\(443\) | −16.1169 | −0.765738 | −0.382869 | − | 0.923803i | \(-0.625064\pi\) | ||||
−0.382869 | + | 0.923803i | \(0.625064\pi\) | |||||||
\(444\) | 0.658621 | 0.0312568 | ||||||||
\(445\) | 8.53761 | 0.404721 | ||||||||
\(446\) | 23.2119 | 1.09912 | ||||||||
\(447\) | −5.28809 | −0.250118 | ||||||||
\(448\) | −6.56312 | −0.310078 | ||||||||
\(449\) | 0.840226 | 0.0396527 | 0.0198264 | − | 0.999803i | \(-0.493689\pi\) | ||||
0.0198264 | + | 0.999803i | \(0.493689\pi\) | |||||||
\(450\) | −2.75742 | −0.129986 | ||||||||
\(451\) | 22.8932 | 1.07800 | ||||||||
\(452\) | −0.444772 | −0.0209203 | ||||||||
\(453\) | 2.04355 | 0.0960142 | ||||||||
\(454\) | 11.9926 | 0.562839 | ||||||||
\(455\) | 4.66808 | 0.218843 | ||||||||
\(456\) | −5.99314 | −0.280654 | ||||||||
\(457\) | −9.74058 | −0.455645 | −0.227823 | − | 0.973703i | \(-0.573161\pi\) | ||||
−0.227823 | + | 0.973703i | \(0.573161\pi\) | |||||||
\(458\) | 0.970097 | 0.0453297 | ||||||||
\(459\) | −8.86691 | −0.413872 | ||||||||
\(460\) | −9.11846 | −0.425150 | ||||||||
\(461\) | −14.7555 | −0.687231 | −0.343615 | − | 0.939110i | \(-0.611652\pi\) | ||||
−0.343615 | + | 0.939110i | \(0.611652\pi\) | |||||||
\(462\) | −0.848516 | −0.0394765 | ||||||||
\(463\) | −17.7643 | −0.825577 | −0.412788 | − | 0.910827i | \(-0.635445\pi\) | ||||
−0.412788 | + | 0.910827i | \(0.635445\pi\) | |||||||
\(464\) | 4.97474 | 0.230946 | ||||||||
\(465\) | −1.55053 | −0.0719043 | ||||||||
\(466\) | −21.3356 | −0.988353 | ||||||||
\(467\) | 11.1165 | 0.514410 | 0.257205 | − | 0.966357i | \(-0.417198\pi\) | ||||
0.257205 | + | 0.966357i | \(0.417198\pi\) | |||||||
\(468\) | 14.0503 | 0.649476 | ||||||||
\(469\) | −10.0744 | −0.465192 | ||||||||
\(470\) | −4.02372 | −0.185600 | ||||||||
\(471\) | −3.59678 | −0.165731 | ||||||||
\(472\) | −25.6718 | −1.18164 | ||||||||
\(473\) | 11.9499 | 0.549456 | ||||||||
\(474\) | −3.36941 | −0.154762 | ||||||||
\(475\) | −5.08764 | −0.233437 | ||||||||
\(476\) | −4.04840 | −0.185558 | ||||||||
\(477\) | 4.48092 | 0.205167 | ||||||||
\(478\) | 16.1742 | 0.739790 | ||||||||
\(479\) | −40.0322 | −1.82912 | −0.914559 | − | 0.404452i | \(-0.867462\pi\) | ||||
−0.914559 | + | 0.404452i | \(0.867462\pi\) | |||||||
\(480\) | 2.06295 | 0.0941602 | ||||||||
\(481\) | 7.31406 | 0.333492 | ||||||||
\(482\) | 5.62034 | 0.255999 | ||||||||
\(483\) | −3.41836 | −0.155541 | ||||||||
\(484\) | 6.50715 | 0.295780 | ||||||||
\(485\) | 14.8303 | 0.673408 | ||||||||
\(486\) | −9.67898 | −0.439048 | ||||||||
\(487\) | −16.2358 | −0.735716 | −0.367858 | − | 0.929882i | \(-0.619909\pi\) | ||||
−0.367858 | + | 0.929882i | \(0.619909\pi\) | |||||||
\(488\) | −5.46552 | −0.247413 | ||||||||
\(489\) | 0.395442 | 0.0178825 | ||||||||
\(490\) | −0.970097 | −0.0438245 | ||||||||
\(491\) | −22.9333 | −1.03497 | −0.517483 | − | 0.855694i | \(-0.673131\pi\) | ||||
−0.517483 | + | 0.855694i | \(0.673131\pi\) | |||||||
\(492\) | −4.36751 | −0.196903 | ||||||||
\(493\) | 24.9964 | 1.12578 | ||||||||
\(494\) | −23.0393 | −1.03659 | ||||||||
\(495\) | −6.26291 | −0.281497 | ||||||||
\(496\) | 2.97196 | 0.133445 | ||||||||
\(497\) | −2.25770 | −0.101271 | ||||||||
\(498\) | 5.35398 | 0.239918 | ||||||||
\(499\) | 17.0699 | 0.764154 | 0.382077 | − | 0.924131i | \(-0.375209\pi\) | ||||
0.382077 | + | 0.924131i | \(0.375209\pi\) | |||||||
\(500\) | 1.05891 | 0.0473560 | ||||||||
\(501\) | 4.88584 | 0.218283 | ||||||||
\(502\) | 22.2954 | 0.995094 | ||||||||
\(503\) | −15.3081 | −0.682554 | −0.341277 | − | 0.939963i | \(-0.610859\pi\) | ||||
−0.341277 | + | 0.939963i | \(0.610859\pi\) | |||||||
\(504\) | −8.43470 | −0.375711 | ||||||||
\(505\) | −3.96350 | −0.176373 | ||||||||
\(506\) | 18.4062 | 0.818257 | ||||||||
\(507\) | −3.48975 | −0.154985 | ||||||||
\(508\) | −4.50882 | −0.200046 | ||||||||
\(509\) | −9.62930 | −0.426811 | −0.213406 | − | 0.976964i | \(-0.568456\pi\) | ||||
−0.213406 | + | 0.976964i | \(0.568456\pi\) | |||||||
\(510\) | −1.47229 | −0.0651943 | ||||||||
\(511\) | 10.5309 | 0.465860 | ||||||||
\(512\) | −8.46985 | −0.374318 | ||||||||
\(513\) | −11.7995 | −0.520962 | ||||||||
\(514\) | 8.76114 | 0.386437 | ||||||||
\(515\) | 8.14891 | 0.359084 | ||||||||
\(516\) | −2.27977 | −0.100361 | ||||||||
\(517\) | −9.13905 | −0.401935 | ||||||||
\(518\) | −1.51997 | −0.0667836 | ||||||||
\(519\) | −6.52824 | −0.286558 | ||||||||
\(520\) | 13.8523 | 0.607462 | ||||||||
\(521\) | 3.33359 | 0.146047 | 0.0730237 | − | 0.997330i | \(-0.476735\pi\) | ||||
0.0730237 | + | 0.997330i | \(0.476735\pi\) | |||||||
\(522\) | 18.0284 | 0.789080 | ||||||||
\(523\) | −10.8231 | −0.473262 | −0.236631 | − | 0.971600i | \(-0.576043\pi\) | ||||
−0.236631 | + | 0.971600i | \(0.576043\pi\) | |||||||
\(524\) | 9.29205 | 0.405925 | ||||||||
\(525\) | 0.396968 | 0.0173251 | ||||||||
\(526\) | −7.18583 | −0.313317 | ||||||||
\(527\) | 14.9331 | 0.650495 | ||||||||
\(528\) | −0.665521 | −0.0289631 | ||||||||
\(529\) | 51.1520 | 2.22400 | ||||||||
\(530\) | 1.52931 | 0.0664288 | ||||||||
\(531\) | −24.5902 | −1.06712 | ||||||||
\(532\) | −5.38736 | −0.233572 | ||||||||
\(533\) | −48.5017 | −2.10084 | ||||||||
\(534\) | 3.28781 | 0.142278 | ||||||||
\(535\) | 9.09956 | 0.393408 | ||||||||
\(536\) | −29.8952 | −1.29127 | ||||||||
\(537\) | −2.10009 | −0.0906254 | ||||||||
\(538\) | 15.7686 | 0.679832 | ||||||||
\(539\) | −2.20338 | −0.0949061 | ||||||||
\(540\) | 2.45589 | 0.105685 | ||||||||
\(541\) | 30.1401 | 1.29582 | 0.647911 | − | 0.761716i | \(-0.275643\pi\) | ||||
0.647911 | + | 0.761716i | \(0.275643\pi\) | |||||||
\(542\) | 25.1607 | 1.08074 | ||||||||
\(543\) | −4.38136 | −0.188022 | ||||||||
\(544\) | −19.8681 | −0.851837 | ||||||||
\(545\) | −11.2079 | −0.480093 | ||||||||
\(546\) | 1.79767 | 0.0769331 | ||||||||
\(547\) | −22.9241 | −0.980166 | −0.490083 | − | 0.871676i | \(-0.663033\pi\) | ||||
−0.490083 | + | 0.871676i | \(0.663033\pi\) | |||||||
\(548\) | 0.00649776 | 0.000277571 0 | ||||||||
\(549\) | −5.23525 | −0.223435 | ||||||||
\(550\) | −2.13749 | −0.0911428 | ||||||||
\(551\) | 33.2636 | 1.41708 | ||||||||
\(552\) | −10.1438 | −0.431748 | ||||||||
\(553\) | −8.74949 | −0.372066 | ||||||||
\(554\) | −7.21937 | −0.306722 | ||||||||
\(555\) | 0.621979 | 0.0264015 | ||||||||
\(556\) | 10.2060 | 0.432832 | ||||||||
\(557\) | 9.20116 | 0.389866 | 0.194933 | − | 0.980817i | \(-0.437551\pi\) | ||||
0.194933 | + | 0.980817i | \(0.437551\pi\) | |||||||
\(558\) | 10.7703 | 0.455944 | ||||||||
\(559\) | −25.3171 | −1.07080 | ||||||||
\(560\) | −0.760881 | −0.0321531 | ||||||||
\(561\) | −3.34402 | −0.141184 | ||||||||
\(562\) | −17.2942 | −0.729511 | ||||||||
\(563\) | −21.4310 | −0.903207 | −0.451604 | − | 0.892219i | \(-0.649148\pi\) | ||||
−0.451604 | + | 0.892219i | \(0.649148\pi\) | |||||||
\(564\) | 1.74352 | 0.0734156 | ||||||||
\(565\) | −0.420027 | −0.0176707 | ||||||||
\(566\) | 11.0446 | 0.464237 | ||||||||
\(567\) | −7.60658 | −0.319446 | ||||||||
\(568\) | −6.69958 | −0.281108 | ||||||||
\(569\) | 4.44920 | 0.186520 | 0.0932600 | − | 0.995642i | \(-0.470271\pi\) | ||||
0.0932600 | + | 0.995642i | \(0.470271\pi\) | |||||||
\(570\) | −1.95924 | −0.0820634 | ||||||||
\(571\) | −42.8836 | −1.79462 | −0.897312 | − | 0.441397i | \(-0.854483\pi\) | ||||
−0.897312 | + | 0.441397i | \(0.854483\pi\) | |||||||
\(572\) | 10.8915 | 0.455396 | ||||||||
\(573\) | 4.68403 | 0.195678 | ||||||||
\(574\) | 10.0794 | 0.420704 | ||||||||
\(575\) | −8.61116 | −0.359110 | ||||||||
\(576\) | −18.6551 | −0.777296 | ||||||||
\(577\) | −35.9822 | −1.49796 | −0.748979 | − | 0.662594i | \(-0.769455\pi\) | ||||
−0.748979 | + | 0.662594i | \(0.769455\pi\) | |||||||
\(578\) | −2.31209 | −0.0961703 | ||||||||
\(579\) | −2.47207 | −0.102736 | ||||||||
\(580\) | −6.92330 | −0.287474 | ||||||||
\(581\) | 13.9029 | 0.576790 | ||||||||
\(582\) | 5.71110 | 0.236733 | ||||||||
\(583\) | 3.47350 | 0.143858 | ||||||||
\(584\) | 31.2499 | 1.29313 | ||||||||
\(585\) | 13.2686 | 0.548590 | ||||||||
\(586\) | −14.1643 | −0.585124 | ||||||||
\(587\) | −3.77637 | −0.155867 | −0.0779337 | − | 0.996959i | \(-0.524832\pi\) | ||||
−0.0779337 | + | 0.996959i | \(0.524832\pi\) | |||||||
\(588\) | 0.420355 | 0.0173351 | ||||||||
\(589\) | 19.8720 | 0.818812 | ||||||||
\(590\) | −8.39246 | −0.345512 | ||||||||
\(591\) | 2.58906 | 0.106500 | ||||||||
\(592\) | −1.19217 | −0.0489977 | ||||||||
\(593\) | −47.9537 | −1.96922 | −0.984612 | − | 0.174755i | \(-0.944087\pi\) | ||||
−0.984612 | + | 0.174755i | \(0.944087\pi\) | |||||||
\(594\) | −4.95738 | −0.203404 | ||||||||
\(595\) | −3.82317 | −0.156735 | ||||||||
\(596\) | −14.1060 | −0.577803 | ||||||||
\(597\) | 0.375395 | 0.0153639 | ||||||||
\(598\) | −38.9956 | −1.59465 | ||||||||
\(599\) | 8.62497 | 0.352407 | 0.176203 | − | 0.984354i | \(-0.443618\pi\) | ||||
0.176203 | + | 0.984354i | \(0.443618\pi\) | |||||||
\(600\) | 1.17798 | 0.0480908 | ||||||||
\(601\) | −25.0778 | −1.02294 | −0.511471 | − | 0.859300i | \(-0.670899\pi\) | ||||
−0.511471 | + | 0.859300i | \(0.670899\pi\) | |||||||
\(602\) | 5.26126 | 0.214433 | ||||||||
\(603\) | −28.6356 | −1.16613 | ||||||||
\(604\) | 5.45115 | 0.221804 | ||||||||
\(605\) | 6.14513 | 0.249835 | ||||||||
\(606\) | −1.52633 | −0.0620031 | ||||||||
\(607\) | 22.0772 | 0.896088 | 0.448044 | − | 0.894012i | \(-0.352121\pi\) | ||||
0.448044 | + | 0.894012i | \(0.352121\pi\) | |||||||
\(608\) | −26.4392 | −1.07225 | ||||||||
\(609\) | −2.59543 | −0.105172 | ||||||||
\(610\) | −1.78675 | −0.0723436 | ||||||||
\(611\) | 19.3620 | 0.783304 | ||||||||
\(612\) | −11.5072 | −0.465153 | ||||||||
\(613\) | 22.9679 | 0.927664 | 0.463832 | − | 0.885923i | \(-0.346474\pi\) | ||||
0.463832 | + | 0.885923i | \(0.346474\pi\) | |||||||
\(614\) | 3.95146 | 0.159468 | ||||||||
\(615\) | −4.12452 | −0.166317 | ||||||||
\(616\) | −6.53839 | −0.263439 | ||||||||
\(617\) | −42.8701 | −1.72589 | −0.862943 | − | 0.505301i | \(-0.831381\pi\) | ||||
−0.862943 | + | 0.505301i | \(0.831381\pi\) | |||||||
\(618\) | 3.13813 | 0.126234 | ||||||||
\(619\) | −8.22940 | −0.330767 | −0.165384 | − | 0.986229i | \(-0.552886\pi\) | ||||
−0.165384 | + | 0.986229i | \(0.552886\pi\) | |||||||
\(620\) | −4.13605 | −0.166108 | ||||||||
\(621\) | −19.9715 | −0.801427 | ||||||||
\(622\) | 6.54058 | 0.262253 | ||||||||
\(623\) | 8.53761 | 0.342052 | ||||||||
\(624\) | 1.40997 | 0.0564442 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 4.73566 | 0.189275 | ||||||||
\(627\) | −4.45001 | −0.177716 | ||||||||
\(628\) | −9.59441 | −0.382859 | ||||||||
\(629\) | −5.99023 | −0.238846 | ||||||||
\(630\) | −2.75742 | −0.109858 | ||||||||
\(631\) | 6.97229 | 0.277562 | 0.138781 | − | 0.990323i | \(-0.455682\pi\) | ||||
0.138781 | + | 0.990323i | \(0.455682\pi\) | |||||||
\(632\) | −25.9636 | −1.03278 | ||||||||
\(633\) | 0.990333 | 0.0393622 | ||||||||
\(634\) | 25.3461 | 1.00662 | ||||||||
\(635\) | −4.25797 | −0.168972 | ||||||||
\(636\) | −0.662666 | −0.0262764 | ||||||||
\(637\) | 4.66808 | 0.184956 | ||||||||
\(638\) | 13.9752 | 0.553282 | ||||||||
\(639\) | −6.41731 | −0.253865 | ||||||||
\(640\) | 4.02665 | 0.159167 | ||||||||
\(641\) | 20.5071 | 0.809980 | 0.404990 | − | 0.914321i | \(-0.367275\pi\) | ||||
0.404990 | + | 0.914321i | \(0.367275\pi\) | |||||||
\(642\) | 3.50422 | 0.138301 | ||||||||
\(643\) | 8.28256 | 0.326632 | 0.163316 | − | 0.986574i | \(-0.447781\pi\) | ||||
0.163316 | + | 0.986574i | \(0.447781\pi\) | |||||||
\(644\) | −9.11846 | −0.359317 | ||||||||
\(645\) | −2.15293 | −0.0847717 | ||||||||
\(646\) | 18.8693 | 0.742401 | ||||||||
\(647\) | 13.7628 | 0.541073 | 0.270536 | − | 0.962710i | \(-0.412799\pi\) | ||||
0.270536 | + | 0.962710i | \(0.412799\pi\) | |||||||
\(648\) | −22.5721 | −0.886715 | ||||||||
\(649\) | −19.0618 | −0.748239 | ||||||||
\(650\) | 4.52849 | 0.177622 | ||||||||
\(651\) | −1.55053 | −0.0607702 | ||||||||
\(652\) | 1.05484 | 0.0413107 | ||||||||
\(653\) | −15.1249 | −0.591882 | −0.295941 | − | 0.955206i | \(-0.595633\pi\) | ||||
−0.295941 | + | 0.955206i | \(0.595633\pi\) | |||||||
\(654\) | −4.31613 | −0.168774 | ||||||||
\(655\) | 8.77509 | 0.342871 | ||||||||
\(656\) | 7.90560 | 0.308662 | ||||||||
\(657\) | 29.9333 | 1.16781 | ||||||||
\(658\) | −4.02372 | −0.156861 | ||||||||
\(659\) | −13.4571 | −0.524216 | −0.262108 | − | 0.965039i | \(-0.584418\pi\) | ||||
−0.262108 | + | 0.965039i | \(0.584418\pi\) | |||||||
\(660\) | 0.926200 | 0.0360523 | ||||||||
\(661\) | −36.1753 | −1.40706 | −0.703528 | − | 0.710667i | \(-0.748393\pi\) | ||||
−0.703528 | + | 0.710667i | \(0.748393\pi\) | |||||||
\(662\) | 23.4267 | 0.910504 | ||||||||
\(663\) | 7.08465 | 0.275145 | ||||||||
\(664\) | 41.2561 | 1.60105 | ||||||||
\(665\) | −5.08764 | −0.197290 | ||||||||
\(666\) | −4.32039 | −0.167412 | ||||||||
\(667\) | 56.3008 | 2.17998 | ||||||||
\(668\) | 13.0330 | 0.504260 | ||||||||
\(669\) | −9.49843 | −0.367230 | ||||||||
\(670\) | −9.77314 | −0.377569 | ||||||||
\(671\) | −4.05825 | −0.156667 | ||||||||
\(672\) | 2.06295 | 0.0795799 | ||||||||
\(673\) | −33.6626 | −1.29760 | −0.648799 | − | 0.760959i | \(-0.724729\pi\) | ||||
−0.648799 | + | 0.760959i | \(0.724729\pi\) | |||||||
\(674\) | 30.0861 | 1.15887 | ||||||||
\(675\) | 2.31925 | 0.0892682 | ||||||||
\(676\) | −9.30889 | −0.358034 | ||||||||
\(677\) | −11.3713 | −0.437033 | −0.218517 | − | 0.975833i | \(-0.570122\pi\) | ||||
−0.218517 | + | 0.975833i | \(0.570122\pi\) | |||||||
\(678\) | −0.161752 | −0.00621203 | ||||||||
\(679\) | 14.8303 | 0.569133 | ||||||||
\(680\) | −11.3450 | −0.435062 | ||||||||
\(681\) | −4.90741 | −0.188052 | ||||||||
\(682\) | 8.34890 | 0.319696 | ||||||||
\(683\) | −11.6951 | −0.447502 | −0.223751 | − | 0.974646i | \(-0.571830\pi\) | ||||
−0.223751 | + | 0.974646i | \(0.571830\pi\) | |||||||
\(684\) | −15.3131 | −0.585512 | ||||||||
\(685\) | 0.00613626 | 0.000234455 0 | ||||||||
\(686\) | −0.970097 | −0.0370385 | ||||||||
\(687\) | −0.396968 | −0.0151453 | ||||||||
\(688\) | 4.12659 | 0.157325 | ||||||||
\(689\) | −7.35898 | −0.280355 | ||||||||
\(690\) | −3.31614 | −0.126243 | ||||||||
\(691\) | −27.1242 | −1.03185 | −0.515927 | − | 0.856632i | \(-0.672552\pi\) | ||||
−0.515927 | + | 0.856632i | \(0.672552\pi\) | |||||||
\(692\) | −17.4141 | −0.661983 | ||||||||
\(693\) | −6.26291 | −0.237908 | ||||||||
\(694\) | 0.0297509 | 0.00112933 | ||||||||
\(695\) | 9.63822 | 0.365599 | ||||||||
\(696\) | −7.70179 | −0.291935 | ||||||||
\(697\) | 39.7230 | 1.50461 | ||||||||
\(698\) | 20.9894 | 0.794461 | ||||||||
\(699\) | 8.73064 | 0.330223 | ||||||||
\(700\) | 1.05891 | 0.0400231 | ||||||||
\(701\) | 28.6667 | 1.08272 | 0.541362 | − | 0.840789i | \(-0.317909\pi\) | ||||
0.541362 | + | 0.840789i | \(0.317909\pi\) | |||||||
\(702\) | 10.5027 | 0.396400 | ||||||||
\(703\) | −7.97142 | −0.300648 | ||||||||
\(704\) | −14.4610 | −0.545020 | ||||||||
\(705\) | 1.64652 | 0.0620117 | ||||||||
\(706\) | 2.75262 | 0.103596 | ||||||||
\(707\) | −3.96350 | −0.149063 | ||||||||
\(708\) | 3.63655 | 0.136670 | ||||||||
\(709\) | −28.2128 | −1.05955 | −0.529776 | − | 0.848137i | \(-0.677724\pi\) | ||||
−0.529776 | + | 0.848137i | \(0.677724\pi\) | |||||||
\(710\) | −2.19018 | −0.0821961 | ||||||||
\(711\) | −24.8697 | −0.932686 | ||||||||
\(712\) | 25.3349 | 0.949464 | ||||||||
\(713\) | 33.6347 | 1.25963 | ||||||||
\(714\) | −1.47229 | −0.0550993 | ||||||||
\(715\) | 10.2855 | 0.384658 | ||||||||
\(716\) | −5.60197 | −0.209356 | ||||||||
\(717\) | −6.61856 | −0.247175 | ||||||||
\(718\) | −32.7806 | −1.22336 | ||||||||
\(719\) | −9.99293 | −0.372674 | −0.186337 | − | 0.982486i | \(-0.559662\pi\) | ||||
−0.186337 | + | 0.982486i | \(0.559662\pi\) | |||||||
\(720\) | −2.16274 | −0.0806006 | ||||||||
\(721\) | 8.14891 | 0.303481 | ||||||||
\(722\) | 6.67819 | 0.248537 | ||||||||
\(723\) | −2.29987 | −0.0855331 | ||||||||
\(724\) | −11.6873 | −0.434354 | ||||||||
\(725\) | −6.53813 | −0.242820 | ||||||||
\(726\) | 2.36648 | 0.0878282 | ||||||||
\(727\) | 20.9421 | 0.776699 | 0.388350 | − | 0.921512i | \(-0.373045\pi\) | ||||
0.388350 | + | 0.921512i | \(0.373045\pi\) | |||||||
\(728\) | 13.8523 | 0.513399 | ||||||||
\(729\) | −18.8590 | −0.698483 | ||||||||
\(730\) | 10.2160 | 0.378112 | ||||||||
\(731\) | 20.7347 | 0.766902 | ||||||||
\(732\) | 0.774222 | 0.0286161 | ||||||||
\(733\) | 21.0024 | 0.775740 | 0.387870 | − | 0.921714i | \(-0.373211\pi\) | ||||
0.387870 | + | 0.921714i | \(0.373211\pi\) | |||||||
\(734\) | 5.94478 | 0.219426 | ||||||||
\(735\) | 0.396968 | 0.0146424 | ||||||||
\(736\) | −44.7501 | −1.64951 | ||||||||
\(737\) | −22.1977 | −0.817662 | ||||||||
\(738\) | 28.6497 | 1.05461 | ||||||||
\(739\) | 14.8485 | 0.546210 | 0.273105 | − | 0.961984i | \(-0.411949\pi\) | ||||
0.273105 | + | 0.961984i | \(0.411949\pi\) | |||||||
\(740\) | 1.65913 | 0.0609907 | ||||||||
\(741\) | 9.42781 | 0.346339 | ||||||||
\(742\) | 1.52931 | 0.0561426 | ||||||||
\(743\) | −33.9274 | −1.24468 | −0.622338 | − | 0.782749i | \(-0.713817\pi\) | ||||
−0.622338 | + | 0.782749i | \(0.713817\pi\) | |||||||
\(744\) | −4.60112 | −0.168685 | ||||||||
\(745\) | −13.3212 | −0.488050 | ||||||||
\(746\) | 11.0015 | 0.402793 | ||||||||
\(747\) | 39.5179 | 1.44588 | ||||||||
\(748\) | −8.92015 | −0.326153 | ||||||||
\(749\) | 9.09956 | 0.332491 | ||||||||
\(750\) | 0.385098 | 0.0140618 | ||||||||
\(751\) | −43.6902 | −1.59428 | −0.797139 | − | 0.603795i | \(-0.793654\pi\) | ||||
−0.797139 | + | 0.603795i | \(0.793654\pi\) | |||||||
\(752\) | −3.15594 | −0.115085 | ||||||||
\(753\) | −9.12341 | −0.332475 | ||||||||
\(754\) | −29.6079 | −1.07825 | ||||||||
\(755\) | 5.14788 | 0.187351 | ||||||||
\(756\) | 2.45589 | 0.0893197 | ||||||||
\(757\) | 15.9082 | 0.578194 | 0.289097 | − | 0.957300i | \(-0.406645\pi\) | ||||
0.289097 | + | 0.957300i | \(0.406645\pi\) | |||||||
\(758\) | −33.4121 | −1.21358 | ||||||||
\(759\) | −7.53193 | −0.273392 | ||||||||
\(760\) | −15.0973 | −0.547635 | ||||||||
\(761\) | −16.0488 | −0.581768 | −0.290884 | − | 0.956758i | \(-0.593949\pi\) | ||||
−0.290884 | + | 0.956758i | \(0.593949\pi\) | |||||||
\(762\) | −1.63974 | −0.0594014 | ||||||||
\(763\) | −11.2079 | −0.405752 | ||||||||
\(764\) | 12.4946 | 0.452040 | ||||||||
\(765\) | −10.8670 | −0.392899 | ||||||||
\(766\) | −34.9635 | −1.26328 | ||||||||
\(767\) | 40.3843 | 1.45819 | ||||||||
\(768\) | 6.76135 | 0.243979 | ||||||||
\(769\) | −43.2353 | −1.55911 | −0.779553 | − | 0.626337i | \(-0.784554\pi\) | ||||
−0.779553 | + | 0.626337i | \(0.784554\pi\) | |||||||
\(770\) | −2.13749 | −0.0770297 | ||||||||
\(771\) | −3.58510 | −0.129114 | ||||||||
\(772\) | −6.59424 | −0.237332 | ||||||||
\(773\) | −4.00538 | −0.144064 | −0.0720318 | − | 0.997402i | \(-0.522948\pi\) | ||||
−0.0720318 | + | 0.997402i | \(0.522948\pi\) | |||||||
\(774\) | 14.9547 | 0.537535 | ||||||||
\(775\) | −3.90594 | −0.140305 | ||||||||
\(776\) | 44.0079 | 1.57979 | ||||||||
\(777\) | 0.621979 | 0.0223134 | ||||||||
\(778\) | 29.8177 | 1.06902 | ||||||||
\(779\) | 52.8608 | 1.89394 | ||||||||
\(780\) | −1.96225 | −0.0702598 | ||||||||
\(781\) | −4.97455 | −0.178004 | ||||||||
\(782\) | 31.9375 | 1.14208 | ||||||||
\(783\) | −15.1636 | −0.541902 | ||||||||
\(784\) | −0.760881 | −0.0271743 | ||||||||
\(785\) | −9.06063 | −0.323388 | ||||||||
\(786\) | 3.37927 | 0.120534 | ||||||||
\(787\) | 38.6808 | 1.37882 | 0.689411 | − | 0.724370i | \(-0.257869\pi\) | ||||
0.689411 | + | 0.724370i | \(0.257869\pi\) | |||||||
\(788\) | 6.90631 | 0.246027 | ||||||||
\(789\) | 2.94048 | 0.104684 | ||||||||
\(790\) | −8.48785 | −0.301984 | ||||||||
\(791\) | −0.420027 | −0.0149345 | ||||||||
\(792\) | −18.5848 | −0.660383 | ||||||||
\(793\) | 8.59782 | 0.305318 | ||||||||
\(794\) | 24.8631 | 0.882358 | ||||||||
\(795\) | −0.625799 | −0.0221948 | ||||||||
\(796\) | 1.00137 | 0.0354925 | ||||||||
\(797\) | 0.586778 | 0.0207847 | 0.0103924 | − | 0.999946i | \(-0.496692\pi\) | ||||
0.0103924 | + | 0.999946i | \(0.496692\pi\) | |||||||
\(798\) | −1.95924 | −0.0693563 | ||||||||
\(799\) | −15.8575 | −0.561000 | ||||||||
\(800\) | 5.19675 | 0.183733 | ||||||||
\(801\) | 24.2674 | 0.857448 | ||||||||
\(802\) | 1.70862 | 0.0603336 | ||||||||
\(803\) | 23.2036 | 0.818837 | ||||||||
\(804\) | 4.23482 | 0.149351 | ||||||||
\(805\) | −8.61116 | −0.303503 | ||||||||
\(806\) | −17.6880 | −0.623034 | ||||||||
\(807\) | −6.45258 | −0.227142 | ||||||||
\(808\) | −11.7614 | −0.413766 | ||||||||
\(809\) | −43.0287 | −1.51281 | −0.756404 | − | 0.654104i | \(-0.773046\pi\) | ||||
−0.756404 | + | 0.654104i | \(0.773046\pi\) | |||||||
\(810\) | −7.37912 | −0.259276 | ||||||||
\(811\) | −42.8131 | −1.50337 | −0.751686 | − | 0.659521i | \(-0.770759\pi\) | ||||
−0.751686 | + | 0.659521i | \(0.770759\pi\) | |||||||
\(812\) | −6.92330 | −0.242960 | ||||||||
\(813\) | −10.2959 | −0.361092 | ||||||||
\(814\) | −3.34906 | −0.117385 | ||||||||
\(815\) | 0.996155 | 0.0348938 | ||||||||
\(816\) | −1.15477 | −0.0404251 | ||||||||
\(817\) | 27.5925 | 0.965339 | ||||||||
\(818\) | 22.2956 | 0.779546 | ||||||||
\(819\) | 13.2686 | 0.463644 | ||||||||
\(820\) | −11.0022 | −0.384212 | ||||||||
\(821\) | 35.5694 | 1.24138 | 0.620690 | − | 0.784056i | \(-0.286852\pi\) | ||||
0.620690 | + | 0.784056i | \(0.286852\pi\) | |||||||
\(822\) | 0.00236306 | 8.24213e−5 0 | ||||||||
\(823\) | −9.24595 | −0.322293 | −0.161147 | − | 0.986930i | \(-0.551519\pi\) | ||||
−0.161147 | + | 0.986930i | \(0.551519\pi\) | |||||||
\(824\) | 24.1814 | 0.842400 | ||||||||
\(825\) | 0.874671 | 0.0304521 | ||||||||
\(826\) | −8.39246 | −0.292011 | ||||||||
\(827\) | 21.7702 | 0.757025 | 0.378513 | − | 0.925596i | \(-0.376436\pi\) | ||||
0.378513 | + | 0.925596i | \(0.376436\pi\) | |||||||
\(828\) | −25.9184 | −0.900728 | ||||||||
\(829\) | 32.8043 | 1.13934 | 0.569671 | − | 0.821873i | \(-0.307071\pi\) | ||||
0.569671 | + | 0.821873i | \(0.307071\pi\) | |||||||
\(830\) | 13.4872 | 0.468147 | ||||||||
\(831\) | 2.95420 | 0.102480 | ||||||||
\(832\) | 30.6372 | 1.06215 | ||||||||
\(833\) | −3.82317 | −0.132465 | ||||||||
\(834\) | 3.71166 | 0.128524 | ||||||||
\(835\) | 12.3079 | 0.425932 | ||||||||
\(836\) | −11.8704 | −0.410546 | ||||||||
\(837\) | −9.05887 | −0.313120 | ||||||||
\(838\) | −12.5621 | −0.433949 | ||||||||
\(839\) | 21.9111 | 0.756456 | 0.378228 | − | 0.925712i | \(-0.376534\pi\) | ||||
0.378228 | + | 0.925712i | \(0.376534\pi\) | |||||||
\(840\) | 1.17798 | 0.0406442 | ||||||||
\(841\) | 13.7471 | 0.474039 | ||||||||
\(842\) | −28.4084 | −0.979019 | ||||||||
\(843\) | 7.07687 | 0.243740 | ||||||||
\(844\) | 2.64171 | 0.0909314 | ||||||||
\(845\) | −8.79100 | −0.302420 | ||||||||
\(846\) | −11.4371 | −0.393215 | ||||||||
\(847\) | 6.14513 | 0.211149 | ||||||||
\(848\) | 1.19949 | 0.0411906 | ||||||||
\(849\) | −4.51949 | −0.155108 | ||||||||
\(850\) | −3.70885 | −0.127212 | ||||||||
\(851\) | −13.4921 | −0.462505 | ||||||||
\(852\) | 0.949033 | 0.0325133 | ||||||||
\(853\) | 27.1671 | 0.930183 | 0.465091 | − | 0.885263i | \(-0.346021\pi\) | ||||
0.465091 | + | 0.885263i | \(0.346021\pi\) | |||||||
\(854\) | −1.78675 | −0.0611415 | ||||||||
\(855\) | −14.4612 | −0.494562 | ||||||||
\(856\) | 27.0024 | 0.922924 | ||||||||
\(857\) | 46.1986 | 1.57812 | 0.789058 | − | 0.614319i | \(-0.210569\pi\) | ||||
0.789058 | + | 0.614319i | \(0.210569\pi\) | |||||||
\(858\) | 3.96094 | 0.135224 | ||||||||
\(859\) | −11.6704 | −0.398190 | −0.199095 | − | 0.979980i | \(-0.563800\pi\) | ||||
−0.199095 | + | 0.979980i | \(0.563800\pi\) | |||||||
\(860\) | −5.74294 | −0.195833 | ||||||||
\(861\) | −4.12452 | −0.140563 | ||||||||
\(862\) | 13.9100 | 0.473777 | ||||||||
\(863\) | 15.2359 | 0.518635 | 0.259317 | − | 0.965792i | \(-0.416502\pi\) | ||||
0.259317 | + | 0.965792i | \(0.416502\pi\) | |||||||
\(864\) | 12.0526 | 0.410038 | ||||||||
\(865\) | −16.4452 | −0.559155 | ||||||||
\(866\) | 5.65050 | 0.192012 | ||||||||
\(867\) | 0.946119 | 0.0321319 | ||||||||
\(868\) | −4.13605 | −0.140387 | ||||||||
\(869\) | −19.2784 | −0.653975 | ||||||||
\(870\) | −2.51782 | −0.0853621 | ||||||||
\(871\) | 47.0281 | 1.59349 | ||||||||
\(872\) | −33.2587 | −1.12628 | ||||||||
\(873\) | 42.1538 | 1.42669 | ||||||||
\(874\) | 42.5004 | 1.43760 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | −4.42672 | −0.149565 | ||||||||
\(877\) | −7.57101 | −0.255655 | −0.127827 | − | 0.991796i | \(-0.540800\pi\) | ||||
−0.127827 | + | 0.991796i | \(0.540800\pi\) | |||||||
\(878\) | −32.2192 | −1.08735 | ||||||||
\(879\) | 5.79612 | 0.195498 | ||||||||
\(880\) | −1.67651 | −0.0565151 | ||||||||
\(881\) | −2.47954 | −0.0835379 | −0.0417689 | − | 0.999127i | \(-0.513299\pi\) | ||||
−0.0417689 | + | 0.999127i | \(0.513299\pi\) | |||||||
\(882\) | −2.75742 | −0.0928471 | ||||||||
\(883\) | −31.3125 | −1.05375 | −0.526874 | − | 0.849943i | \(-0.676636\pi\) | ||||
−0.526874 | + | 0.849943i | \(0.676636\pi\) | |||||||
\(884\) | 18.8983 | 0.635618 | ||||||||
\(885\) | 3.43424 | 0.115441 | ||||||||
\(886\) | −15.6350 | −0.525267 | ||||||||
\(887\) | 2.61870 | 0.0879272 | 0.0439636 | − | 0.999033i | \(-0.486001\pi\) | ||||
0.0439636 | + | 0.999033i | \(0.486001\pi\) | |||||||
\(888\) | 1.84569 | 0.0619372 | ||||||||
\(889\) | −4.25797 | −0.142808 | ||||||||
\(890\) | 8.28231 | 0.277624 | ||||||||
\(891\) | −16.7602 | −0.561486 | ||||||||
\(892\) | −25.3370 | −0.848346 | ||||||||
\(893\) | −21.1022 | −0.706159 | ||||||||
\(894\) | −5.12996 | −0.171571 | ||||||||
\(895\) | −5.29031 | −0.176836 | ||||||||
\(896\) | 4.02665 | 0.134521 | ||||||||
\(897\) | 15.9572 | 0.532794 | ||||||||
\(898\) | 0.815101 | 0.0272003 | ||||||||
\(899\) | 25.5375 | 0.851724 | ||||||||
\(900\) | 3.00987 | 0.100329 | ||||||||
\(901\) | 6.02702 | 0.200789 | ||||||||
\(902\) | 22.2086 | 0.739467 | ||||||||
\(903\) | −2.15293 | −0.0716452 | ||||||||
\(904\) | −1.24641 | −0.0414549 | ||||||||
\(905\) | −11.0371 | −0.366884 | ||||||||
\(906\) | 1.98244 | 0.0658621 | ||||||||
\(907\) | −2.40941 | −0.0800032 | −0.0400016 | − | 0.999200i | \(-0.512736\pi\) | ||||
−0.0400016 | + | 0.999200i | \(0.512736\pi\) | |||||||
\(908\) | −13.0905 | −0.434424 | ||||||||
\(909\) | −11.2659 | −0.373666 | ||||||||
\(910\) | 4.52849 | 0.150118 | ||||||||
\(911\) | 12.5161 | 0.414676 | 0.207338 | − | 0.978269i | \(-0.433520\pi\) | ||||
0.207338 | + | 0.978269i | \(0.433520\pi\) | |||||||
\(912\) | −1.53670 | −0.0508852 | ||||||||
\(913\) | 30.6334 | 1.01382 | ||||||||
\(914\) | −9.44931 | −0.312555 | ||||||||
\(915\) | 0.731149 | 0.0241710 | ||||||||
\(916\) | −1.05891 | −0.0349874 | ||||||||
\(917\) | 8.77509 | 0.289779 | ||||||||
\(918\) | −8.60176 | −0.283900 | ||||||||
\(919\) | −5.20958 | −0.171848 | −0.0859242 | − | 0.996302i | \(-0.527384\pi\) | ||||
−0.0859242 | + | 0.996302i | \(0.527384\pi\) | |||||||
\(920\) | −25.5531 | −0.842461 | ||||||||
\(921\) | −1.61696 | −0.0532805 | ||||||||
\(922\) | −14.3142 | −0.471414 | ||||||||
\(923\) | 10.5391 | 0.346899 | ||||||||
\(924\) | 0.926200 | 0.0304697 | ||||||||
\(925\) | 1.56682 | 0.0515168 | ||||||||
\(926\) | −17.2331 | −0.566314 | ||||||||
\(927\) | 23.1626 | 0.760760 | ||||||||
\(928\) | −33.9770 | −1.11535 | ||||||||
\(929\) | 41.4038 | 1.35841 | 0.679207 | − | 0.733947i | \(-0.262324\pi\) | ||||
0.679207 | + | 0.733947i | \(0.262324\pi\) | |||||||
\(930\) | −1.50417 | −0.0493236 | ||||||||
\(931\) | −5.08764 | −0.166741 | ||||||||
\(932\) | 23.2890 | 0.762855 | ||||||||
\(933\) | −2.67644 | −0.0876226 | ||||||||
\(934\) | 10.7841 | 0.352866 | ||||||||
\(935\) | −8.42389 | −0.275491 | ||||||||
\(936\) | 39.3739 | 1.28698 | ||||||||
\(937\) | 13.0517 | 0.426379 | 0.213190 | − | 0.977011i | \(-0.431615\pi\) | ||||
0.213190 | + | 0.977011i | \(0.431615\pi\) | |||||||
\(938\) | −9.77314 | −0.319104 | ||||||||
\(939\) | −1.93785 | −0.0632395 | ||||||||
\(940\) | 4.39210 | 0.143254 | ||||||||
\(941\) | −43.4066 | −1.41501 | −0.707507 | − | 0.706706i | \(-0.750180\pi\) | ||||
−0.707507 | + | 0.706706i | \(0.750180\pi\) | |||||||
\(942\) | −3.48923 | −0.113685 | ||||||||
\(943\) | 89.4704 | 2.91356 | ||||||||
\(944\) | −6.58250 | −0.214242 | ||||||||
\(945\) | 2.31925 | 0.0754454 | ||||||||
\(946\) | 11.5925 | 0.376906 | ||||||||
\(947\) | 45.7348 | 1.48618 | 0.743091 | − | 0.669191i | \(-0.233359\pi\) | ||||
0.743091 | + | 0.669191i | \(0.233359\pi\) | |||||||
\(948\) | 3.67789 | 0.119452 | ||||||||
\(949\) | −49.1592 | −1.59578 | ||||||||
\(950\) | −4.93550 | −0.160129 | ||||||||
\(951\) | −10.3717 | −0.336326 | ||||||||
\(952\) | −11.3450 | −0.367695 | ||||||||
\(953\) | −36.0278 | −1.16706 | −0.583528 | − | 0.812093i | \(-0.698328\pi\) | ||||
−0.583528 | + | 0.812093i | \(0.698328\pi\) | |||||||
\(954\) | 4.34692 | 0.140737 | ||||||||
\(955\) | 11.7995 | 0.381823 | ||||||||
\(956\) | −17.6550 | −0.571003 | ||||||||
\(957\) | −5.71871 | −0.184860 | ||||||||
\(958\) | −38.8351 | −1.25471 | ||||||||
\(959\) | 0.00613626 | 0.000198150 0 | ||||||||
\(960\) | 2.60535 | 0.0840873 | ||||||||
\(961\) | −15.7436 | −0.507859 | ||||||||
\(962\) | 7.09534 | 0.228763 | ||||||||
\(963\) | 25.8647 | 0.833480 | ||||||||
\(964\) | −6.13490 | −0.197592 | ||||||||
\(965\) | −6.22737 | −0.200466 | ||||||||
\(966\) | −3.31614 | −0.106695 | ||||||||
\(967\) | −31.8922 | −1.02558 | −0.512792 | − | 0.858513i | \(-0.671389\pi\) | ||||
−0.512792 | + | 0.858513i | \(0.671389\pi\) | |||||||
\(968\) | 18.2353 | 0.586105 | ||||||||
\(969\) | −7.72140 | −0.248047 | ||||||||
\(970\) | 14.3868 | 0.461932 | ||||||||
\(971\) | 39.9911 | 1.28338 | 0.641688 | − | 0.766966i | \(-0.278234\pi\) | ||||
0.641688 | + | 0.766966i | \(0.278234\pi\) | |||||||
\(972\) | 10.5651 | 0.338876 | ||||||||
\(973\) | 9.63822 | 0.308987 | ||||||||
\(974\) | −15.7503 | −0.504674 | ||||||||
\(975\) | −1.85308 | −0.0593461 | ||||||||
\(976\) | −1.40141 | −0.0448582 | ||||||||
\(977\) | 26.3668 | 0.843549 | 0.421774 | − | 0.906701i | \(-0.361407\pi\) | ||||
0.421774 | + | 0.906701i | \(0.361407\pi\) | |||||||
\(978\) | 0.383617 | 0.0122667 | ||||||||
\(979\) | 18.8116 | 0.601220 | ||||||||
\(980\) | 1.05891 | 0.0338257 | ||||||||
\(981\) | −31.8574 | −1.01713 | ||||||||
\(982\) | −22.2475 | −0.709947 | ||||||||
\(983\) | 6.84062 | 0.218182 | 0.109091 | − | 0.994032i | \(-0.465206\pi\) | ||||
0.109091 | + | 0.994032i | \(0.465206\pi\) | |||||||
\(984\) | −12.2393 | −0.390174 | ||||||||
\(985\) | 6.52208 | 0.207811 | ||||||||
\(986\) | 24.2489 | 0.772243 | ||||||||
\(987\) | 1.64652 | 0.0524094 | ||||||||
\(988\) | 25.1486 | 0.800085 | ||||||||
\(989\) | 46.7021 | 1.48504 | ||||||||
\(990\) | −6.07563 | −0.193096 | ||||||||
\(991\) | −10.4466 | −0.331847 | −0.165924 | − | 0.986139i | \(-0.553061\pi\) | ||||
−0.165924 | + | 0.986139i | \(0.553061\pi\) | |||||||
\(992\) | −20.2982 | −0.644469 | ||||||||
\(993\) | −9.58632 | −0.304213 | ||||||||
\(994\) | −2.19018 | −0.0694684 | ||||||||
\(995\) | 0.945655 | 0.0299793 | ||||||||
\(996\) | −5.84415 | −0.185179 | ||||||||
\(997\) | −33.4358 | −1.05892 | −0.529461 | − | 0.848334i | \(-0.677606\pi\) | ||||
−0.529461 | + | 0.848334i | \(0.677606\pi\) | |||||||
\(998\) | 16.5595 | 0.524180 | ||||||||
\(999\) | 3.63386 | 0.114970 |
(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 | 8015.2.a.l.1.40 | ✓ | 62 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8015.2.a.l.1.40 | ✓ | 62 | 1.1 | even | 1 | trivial |