Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6017,2,Mod(1,6017)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6017, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("6017.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6017 = 11 \cdot 547 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6017.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: | \(48.0459868962\) |
Analytic rank: | \(0\) |
Dimension: | \(121\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
Character | \(\chi\) | \(=\) | 6017.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.10704 | −1.48990 | −0.744951 | − | 0.667119i | \(-0.767527\pi\) | ||||
−0.744951 | + | 0.667119i | \(0.767527\pi\) | |||||||
\(3\) | −1.55624 | −0.898498 | −0.449249 | − | 0.893406i | \(-0.648308\pi\) | ||||
−0.449249 | + | 0.893406i | \(0.648308\pi\) | |||||||
\(4\) | 2.43961 | 1.21981 | ||||||||
\(5\) | −0.464512 | −0.207736 | −0.103868 | − | 0.994591i | \(-0.533122\pi\) | ||||
−0.103868 | + | 0.994591i | \(0.533122\pi\) | |||||||
\(6\) | 3.27907 | 1.33867 | ||||||||
\(7\) | −0.781558 | −0.295401 | −0.147701 | − | 0.989032i | \(-0.547187\pi\) | ||||
−0.147701 | + | 0.989032i | \(0.547187\pi\) | |||||||
\(8\) | −0.926282 | −0.327490 | ||||||||
\(9\) | −0.578102 | −0.192701 | ||||||||
\(10\) | 0.978744 | 0.309506 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | −3.79664 | −1.09599 | ||||||||
\(13\) | −6.89190 | −1.91147 | −0.955735 | − | 0.294229i | \(-0.904937\pi\) | ||||
−0.955735 | + | 0.294229i | \(0.904937\pi\) | |||||||
\(14\) | 1.64677 | 0.440119 | ||||||||
\(15\) | 0.722894 | 0.186650 | ||||||||
\(16\) | −2.92751 | −0.731879 | ||||||||
\(17\) | 4.41736 | 1.07137 | 0.535684 | − | 0.844419i | \(-0.320054\pi\) | ||||
0.535684 | + | 0.844419i | \(0.320054\pi\) | |||||||
\(18\) | 1.21808 | 0.287105 | ||||||||
\(19\) | 6.82809 | 1.56647 | 0.783236 | − | 0.621725i | \(-0.213568\pi\) | ||||
0.783236 | + | 0.621725i | \(0.213568\pi\) | |||||||
\(20\) | −1.13323 | −0.253398 | ||||||||
\(21\) | 1.21630 | 0.265418 | ||||||||
\(22\) | 2.10704 | 0.449222 | ||||||||
\(23\) | −0.0938169 | −0.0195622 | −0.00978109 | − | 0.999952i | \(-0.503113\pi\) | ||||
−0.00978109 | + | 0.999952i | \(0.503113\pi\) | |||||||
\(24\) | 1.44152 | 0.294249 | ||||||||
\(25\) | −4.78423 | −0.956846 | ||||||||
\(26\) | 14.5215 | 2.84790 | ||||||||
\(27\) | 5.56840 | 1.07164 | ||||||||
\(28\) | −1.90670 | −0.360332 | ||||||||
\(29\) | 6.75883 | 1.25508 | 0.627541 | − | 0.778583i | \(-0.284061\pi\) | ||||
0.627541 | + | 0.778583i | \(0.284061\pi\) | |||||||
\(30\) | −1.52317 | −0.278091 | ||||||||
\(31\) | −9.92986 | −1.78345 | −0.891727 | − | 0.452573i | \(-0.850506\pi\) | ||||
−0.891727 | + | 0.452573i | \(0.850506\pi\) | |||||||
\(32\) | 8.02095 | 1.41792 | ||||||||
\(33\) | 1.55624 | 0.270907 | ||||||||
\(34\) | −9.30755 | −1.59623 | ||||||||
\(35\) | 0.363043 | 0.0613654 | ||||||||
\(36\) | −1.41034 | −0.235057 | ||||||||
\(37\) | 1.09753 | 0.180433 | 0.0902165 | − | 0.995922i | \(-0.471244\pi\) | ||||
0.0902165 | + | 0.995922i | \(0.471244\pi\) | |||||||
\(38\) | −14.3871 | −2.33389 | ||||||||
\(39\) | 10.7255 | 1.71745 | ||||||||
\(40\) | 0.430269 | 0.0680314 | ||||||||
\(41\) | −10.0398 | −1.56796 | −0.783980 | − | 0.620786i | \(-0.786813\pi\) | ||||
−0.783980 | + | 0.620786i | \(0.786813\pi\) | |||||||
\(42\) | −2.56278 | −0.395446 | ||||||||
\(43\) | 10.8534 | 1.65513 | 0.827566 | − | 0.561368i | \(-0.189725\pi\) | ||||
0.827566 | + | 0.561368i | \(0.189725\pi\) | |||||||
\(44\) | −2.43961 | −0.367786 | ||||||||
\(45\) | 0.268535 | 0.0400308 | ||||||||
\(46\) | 0.197676 | 0.0291457 | ||||||||
\(47\) | −12.6125 | −1.83973 | −0.919865 | − | 0.392236i | \(-0.871702\pi\) | ||||
−0.919865 | + | 0.392236i | \(0.871702\pi\) | |||||||
\(48\) | 4.55593 | 0.657592 | ||||||||
\(49\) | −6.38917 | −0.912738 | ||||||||
\(50\) | 10.0806 | 1.42561 | ||||||||
\(51\) | −6.87450 | −0.962622 | ||||||||
\(52\) | −16.8136 | −2.33162 | ||||||||
\(53\) | 3.80944 | 0.523267 | 0.261634 | − | 0.965167i | \(-0.415739\pi\) | ||||
0.261634 | + | 0.965167i | \(0.415739\pi\) | |||||||
\(54\) | −11.7328 | −1.59664 | ||||||||
\(55\) | 0.464512 | 0.0626347 | ||||||||
\(56\) | 0.723943 | 0.0967410 | ||||||||
\(57\) | −10.6262 | −1.40747 | ||||||||
\(58\) | −14.2411 | −1.86995 | ||||||||
\(59\) | −0.976632 | −0.127147 | −0.0635733 | − | 0.997977i | \(-0.520250\pi\) | ||||
−0.0635733 | + | 0.997977i | \(0.520250\pi\) | |||||||
\(60\) | 1.76358 | 0.227677 | ||||||||
\(61\) | −3.58002 | −0.458374 | −0.229187 | − | 0.973382i | \(-0.573607\pi\) | ||||
−0.229187 | + | 0.973382i | \(0.573607\pi\) | |||||||
\(62\) | 20.9226 | 2.65717 | ||||||||
\(63\) | 0.451820 | 0.0569240 | ||||||||
\(64\) | −11.0454 | −1.38068 | ||||||||
\(65\) | 3.20137 | 0.397081 | ||||||||
\(66\) | −3.27907 | −0.403625 | ||||||||
\(67\) | −10.4523 | −1.27695 | −0.638476 | − | 0.769641i | \(-0.720435\pi\) | ||||
−0.638476 | + | 0.769641i | \(0.720435\pi\) | |||||||
\(68\) | 10.7767 | 1.30686 | ||||||||
\(69\) | 0.146002 | 0.0175766 | ||||||||
\(70\) | −0.764945 | −0.0914285 | ||||||||
\(71\) | −2.15531 | −0.255789 | −0.127894 | − | 0.991788i | \(-0.540822\pi\) | ||||
−0.127894 | + | 0.991788i | \(0.540822\pi\) | |||||||
\(72\) | 0.535485 | 0.0631075 | ||||||||
\(73\) | 2.99520 | 0.350562 | 0.175281 | − | 0.984518i | \(-0.443917\pi\) | ||||
0.175281 | + | 0.984518i | \(0.443917\pi\) | |||||||
\(74\) | −2.31254 | −0.268827 | ||||||||
\(75\) | 7.44543 | 0.859724 | ||||||||
\(76\) | 16.6579 | 1.91079 | ||||||||
\(77\) | 0.781558 | 0.0890668 | ||||||||
\(78\) | −22.5990 | −2.55884 | ||||||||
\(79\) | 4.36567 | 0.491176 | 0.245588 | − | 0.969374i | \(-0.421019\pi\) | ||||
0.245588 | + | 0.969374i | \(0.421019\pi\) | |||||||
\(80\) | 1.35986 | 0.152037 | ||||||||
\(81\) | −6.93149 | −0.770166 | ||||||||
\(82\) | 21.1543 | 2.33611 | ||||||||
\(83\) | −2.51149 | −0.275672 | −0.137836 | − | 0.990455i | \(-0.544015\pi\) | ||||
−0.137836 | + | 0.990455i | \(0.544015\pi\) | |||||||
\(84\) | 2.96729 | 0.323758 | ||||||||
\(85\) | −2.05192 | −0.222561 | ||||||||
\(86\) | −22.8686 | −2.46598 | ||||||||
\(87\) | −10.5184 | −1.12769 | ||||||||
\(88\) | 0.926282 | 0.0987420 | ||||||||
\(89\) | 2.79207 | 0.295959 | 0.147979 | − | 0.988990i | \(-0.452723\pi\) | ||||
0.147979 | + | 0.988990i | \(0.452723\pi\) | |||||||
\(90\) | −0.565814 | −0.0596420 | ||||||||
\(91\) | 5.38642 | 0.564651 | ||||||||
\(92\) | −0.228877 | −0.0238621 | ||||||||
\(93\) | 15.4533 | 1.60243 | ||||||||
\(94\) | 26.5751 | 2.74102 | ||||||||
\(95\) | −3.17173 | −0.325412 | ||||||||
\(96\) | −12.4826 | −1.27400 | ||||||||
\(97\) | −1.81420 | −0.184204 | −0.0921020 | − | 0.995750i | \(-0.529359\pi\) | ||||
−0.0921020 | + | 0.995750i | \(0.529359\pi\) | |||||||
\(98\) | 13.4622 | 1.35989 | ||||||||
\(99\) | 0.578102 | 0.0581014 | ||||||||
\(100\) | −11.6717 | −1.16717 | ||||||||
\(101\) | 14.4043 | 1.43328 | 0.716642 | − | 0.697441i | \(-0.245678\pi\) | ||||
0.716642 | + | 0.697441i | \(0.245678\pi\) | |||||||
\(102\) | 14.4848 | 1.43421 | ||||||||
\(103\) | −1.45789 | −0.143650 | −0.0718249 | − | 0.997417i | \(-0.522882\pi\) | ||||
−0.0718249 | + | 0.997417i | \(0.522882\pi\) | |||||||
\(104\) | 6.38384 | 0.625987 | ||||||||
\(105\) | −0.564984 | −0.0551367 | ||||||||
\(106\) | −8.02664 | −0.779617 | ||||||||
\(107\) | −13.0371 | −1.26035 | −0.630173 | − | 0.776454i | \(-0.717016\pi\) | ||||
−0.630173 | + | 0.776454i | \(0.717016\pi\) | |||||||
\(108\) | 13.5847 | 1.30719 | ||||||||
\(109\) | 12.1611 | 1.16482 | 0.582410 | − | 0.812895i | \(-0.302110\pi\) | ||||
0.582410 | + | 0.812895i | \(0.302110\pi\) | |||||||
\(110\) | −0.978744 | −0.0933196 | ||||||||
\(111\) | −1.70803 | −0.162119 | ||||||||
\(112\) | 2.28802 | 0.216198 | ||||||||
\(113\) | 2.11125 | 0.198610 | 0.0993049 | − | 0.995057i | \(-0.468338\pi\) | ||||
0.0993049 | + | 0.995057i | \(0.468338\pi\) | |||||||
\(114\) | 22.3898 | 2.09700 | ||||||||
\(115\) | 0.0435790 | 0.00406377 | ||||||||
\(116\) | 16.4889 | 1.53096 | ||||||||
\(117\) | 3.98422 | 0.368341 | ||||||||
\(118\) | 2.05780 | 0.189436 | ||||||||
\(119\) | −3.45243 | −0.316483 | ||||||||
\(120\) | −0.669603 | −0.0611261 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 7.54323 | 0.682932 | ||||||||
\(123\) | 15.6244 | 1.40881 | ||||||||
\(124\) | −24.2250 | −2.17547 | ||||||||
\(125\) | 4.54489 | 0.406507 | ||||||||
\(126\) | −0.952003 | −0.0848112 | ||||||||
\(127\) | −11.4929 | −1.01983 | −0.509915 | − | 0.860225i | \(-0.670323\pi\) | ||||
−0.509915 | + | 0.860225i | \(0.670323\pi\) | |||||||
\(128\) | 7.23124 | 0.639158 | ||||||||
\(129\) | −16.8906 | −1.48713 | ||||||||
\(130\) | −6.74541 | −0.591611 | ||||||||
\(131\) | −0.477214 | −0.0416944 | −0.0208472 | − | 0.999783i | \(-0.506636\pi\) | ||||
−0.0208472 | + | 0.999783i | \(0.506636\pi\) | |||||||
\(132\) | 3.79664 | 0.330455 | ||||||||
\(133\) | −5.33655 | −0.462738 | ||||||||
\(134\) | 22.0234 | 1.90253 | ||||||||
\(135\) | −2.58659 | −0.222618 | ||||||||
\(136\) | −4.09172 | −0.350862 | ||||||||
\(137\) | −9.02273 | −0.770864 | −0.385432 | − | 0.922736i | \(-0.625948\pi\) | ||||
−0.385432 | + | 0.922736i | \(0.625948\pi\) | |||||||
\(138\) | −0.307632 | −0.0261874 | ||||||||
\(139\) | −19.6593 | −1.66748 | −0.833742 | − | 0.552155i | \(-0.813806\pi\) | ||||
−0.833742 | + | 0.552155i | \(0.813806\pi\) | |||||||
\(140\) | 0.885684 | 0.0748540 | ||||||||
\(141\) | 19.6282 | 1.65299 | ||||||||
\(142\) | 4.54133 | 0.381100 | ||||||||
\(143\) | 6.89190 | 0.576330 | ||||||||
\(144\) | 1.69240 | 0.141033 | ||||||||
\(145\) | −3.13955 | −0.260726 | ||||||||
\(146\) | −6.31101 | −0.522303 | ||||||||
\(147\) | 9.94311 | 0.820094 | ||||||||
\(148\) | 2.67755 | 0.220093 | ||||||||
\(149\) | −19.0518 | −1.56079 | −0.780394 | − | 0.625288i | \(-0.784981\pi\) | ||||
−0.780394 | + | 0.625288i | \(0.784981\pi\) | |||||||
\(150\) | −15.6878 | −1.28090 | ||||||||
\(151\) | −10.6080 | −0.863266 | −0.431633 | − | 0.902049i | \(-0.642062\pi\) | ||||
−0.431633 | + | 0.902049i | \(0.642062\pi\) | |||||||
\(152\) | −6.32474 | −0.513004 | ||||||||
\(153\) | −2.55368 | −0.206453 | ||||||||
\(154\) | −1.64677 | −0.132701 | ||||||||
\(155\) | 4.61253 | 0.370488 | ||||||||
\(156\) | 26.1660 | 2.09496 | ||||||||
\(157\) | 16.8406 | 1.34403 | 0.672013 | − | 0.740539i | \(-0.265430\pi\) | ||||
0.672013 | + | 0.740539i | \(0.265430\pi\) | |||||||
\(158\) | −9.19863 | −0.731804 | ||||||||
\(159\) | −5.92843 | −0.470155 | ||||||||
\(160\) | −3.72582 | −0.294552 | ||||||||
\(161\) | 0.0733234 | 0.00577869 | ||||||||
\(162\) | 14.6049 | 1.14747 | ||||||||
\(163\) | 13.6243 | 1.06714 | 0.533569 | − | 0.845757i | \(-0.320851\pi\) | ||||
0.533569 | + | 0.845757i | \(0.320851\pi\) | |||||||
\(164\) | −24.4933 | −1.91261 | ||||||||
\(165\) | −0.722894 | −0.0562772 | ||||||||
\(166\) | 5.29181 | 0.410724 | ||||||||
\(167\) | 6.31044 | 0.488317 | 0.244158 | − | 0.969735i | \(-0.421488\pi\) | ||||
0.244158 | + | 0.969735i | \(0.421488\pi\) | |||||||
\(168\) | −1.12663 | −0.0869216 | ||||||||
\(169\) | 34.4983 | 2.65372 | ||||||||
\(170\) | 4.32347 | 0.331595 | ||||||||
\(171\) | −3.94733 | −0.301860 | ||||||||
\(172\) | 26.4782 | 2.01894 | ||||||||
\(173\) | −17.0807 | −1.29862 | −0.649310 | − | 0.760524i | \(-0.724942\pi\) | ||||
−0.649310 | + | 0.760524i | \(0.724942\pi\) | |||||||
\(174\) | 22.1627 | 1.68015 | ||||||||
\(175\) | 3.73915 | 0.282653 | ||||||||
\(176\) | 2.92751 | 0.220670 | ||||||||
\(177\) | 1.51988 | 0.114241 | ||||||||
\(178\) | −5.88300 | −0.440949 | ||||||||
\(179\) | −21.4178 | −1.60084 | −0.800421 | − | 0.599439i | \(-0.795391\pi\) | ||||
−0.800421 | + | 0.599439i | \(0.795391\pi\) | |||||||
\(180\) | 0.655121 | 0.0488299 | ||||||||
\(181\) | −14.1806 | −1.05404 | −0.527018 | − | 0.849854i | \(-0.676690\pi\) | ||||
−0.527018 | + | 0.849854i | \(0.676690\pi\) | |||||||
\(182\) | −11.3494 | −0.841274 | ||||||||
\(183\) | 5.57138 | 0.411848 | ||||||||
\(184\) | 0.0869009 | 0.00640642 | ||||||||
\(185\) | −0.509816 | −0.0374824 | ||||||||
\(186\) | −32.5607 | −2.38746 | ||||||||
\(187\) | −4.41736 | −0.323029 | ||||||||
\(188\) | −30.7697 | −2.24411 | ||||||||
\(189\) | −4.35203 | −0.316564 | ||||||||
\(190\) | 6.68295 | 0.484832 | ||||||||
\(191\) | −7.21785 | −0.522265 | −0.261133 | − | 0.965303i | \(-0.584096\pi\) | ||||
−0.261133 | + | 0.965303i | \(0.584096\pi\) | |||||||
\(192\) | 17.1894 | 1.24054 | ||||||||
\(193\) | −7.13565 | −0.513635 | −0.256818 | − | 0.966460i | \(-0.582674\pi\) | ||||
−0.256818 | + | 0.966460i | \(0.582674\pi\) | |||||||
\(194\) | 3.82259 | 0.274446 | ||||||||
\(195\) | −4.98211 | −0.356776 | ||||||||
\(196\) | −15.5871 | −1.11336 | ||||||||
\(197\) | 0.844817 | 0.0601907 | 0.0300953 | − | 0.999547i | \(-0.490419\pi\) | ||||
0.0300953 | + | 0.999547i | \(0.490419\pi\) | |||||||
\(198\) | −1.21808 | −0.0865654 | ||||||||
\(199\) | −11.9017 | −0.843692 | −0.421846 | − | 0.906668i | \(-0.638618\pi\) | ||||
−0.421846 | + | 0.906668i | \(0.638618\pi\) | |||||||
\(200\) | 4.43154 | 0.313358 | ||||||||
\(201\) | 16.2664 | 1.14734 | ||||||||
\(202\) | −30.3505 | −2.13545 | ||||||||
\(203\) | −5.28242 | −0.370753 | ||||||||
\(204\) | −16.7711 | −1.17421 | ||||||||
\(205\) | 4.66362 | 0.325721 | ||||||||
\(206\) | 3.07182 | 0.214024 | ||||||||
\(207\) | 0.0542357 | 0.00376964 | ||||||||
\(208\) | 20.1761 | 1.39896 | ||||||||
\(209\) | −6.82809 | −0.472309 | ||||||||
\(210\) | 1.19044 | 0.0821483 | ||||||||
\(211\) | −17.3963 | −1.19761 | −0.598804 | − | 0.800896i | \(-0.704357\pi\) | ||||
−0.598804 | + | 0.800896i | \(0.704357\pi\) | |||||||
\(212\) | 9.29357 | 0.638285 | ||||||||
\(213\) | 3.35420 | 0.229826 | ||||||||
\(214\) | 27.4697 | 1.87779 | ||||||||
\(215\) | −5.04154 | −0.343830 | ||||||||
\(216\) | −5.15791 | −0.350951 | ||||||||
\(217\) | 7.76076 | 0.526835 | ||||||||
\(218\) | −25.6238 | −1.73547 | ||||||||
\(219\) | −4.66127 | −0.314979 | ||||||||
\(220\) | 1.13323 | 0.0764022 | ||||||||
\(221\) | −30.4440 | −2.04789 | ||||||||
\(222\) | 3.59888 | 0.241541 | ||||||||
\(223\) | 24.5414 | 1.64342 | 0.821708 | − | 0.569908i | \(-0.193021\pi\) | ||||
0.821708 | + | 0.569908i | \(0.193021\pi\) | |||||||
\(224\) | −6.26884 | −0.418855 | ||||||||
\(225\) | 2.76577 | 0.184385 | ||||||||
\(226\) | −4.44849 | −0.295909 | ||||||||
\(227\) | 6.45910 | 0.428706 | 0.214353 | − | 0.976756i | \(-0.431236\pi\) | ||||
0.214353 | + | 0.976756i | \(0.431236\pi\) | |||||||
\(228\) | −25.9238 | −1.71684 | ||||||||
\(229\) | 21.5929 | 1.42690 | 0.713450 | − | 0.700706i | \(-0.247132\pi\) | ||||
0.713450 | + | 0.700706i | \(0.247132\pi\) | |||||||
\(230\) | −0.0918227 | −0.00605461 | ||||||||
\(231\) | −1.21630 | −0.0800264 | ||||||||
\(232\) | −6.26058 | −0.411027 | ||||||||
\(233\) | −5.67337 | −0.371675 | −0.185837 | − | 0.982580i | \(-0.559500\pi\) | ||||
−0.185837 | + | 0.982580i | \(0.559500\pi\) | |||||||
\(234\) | −8.39491 | −0.548792 | ||||||||
\(235\) | 5.85867 | 0.382178 | ||||||||
\(236\) | −2.38260 | −0.155094 | ||||||||
\(237\) | −6.79405 | −0.441321 | ||||||||
\(238\) | 7.27440 | 0.471529 | ||||||||
\(239\) | −20.4062 | −1.31996 | −0.659982 | − | 0.751281i | \(-0.729436\pi\) | ||||
−0.659982 | + | 0.751281i | \(0.729436\pi\) | |||||||
\(240\) | −2.11628 | −0.136605 | ||||||||
\(241\) | −16.5604 | −1.06675 | −0.533374 | − | 0.845880i | \(-0.679076\pi\) | ||||
−0.533374 | + | 0.845880i | \(0.679076\pi\) | |||||||
\(242\) | −2.10704 | −0.135446 | ||||||||
\(243\) | −5.91811 | −0.379647 | ||||||||
\(244\) | −8.73385 | −0.559128 | ||||||||
\(245\) | 2.96784 | 0.189608 | ||||||||
\(246\) | −32.9213 | −2.09899 | ||||||||
\(247\) | −47.0585 | −2.99426 | ||||||||
\(248\) | 9.19785 | 0.584064 | ||||||||
\(249\) | 3.90850 | 0.247691 | ||||||||
\(250\) | −9.57625 | −0.605655 | ||||||||
\(251\) | −0.221098 | −0.0139556 | −0.00697780 | − | 0.999976i | \(-0.502221\pi\) | ||||
−0.00697780 | + | 0.999976i | \(0.502221\pi\) | |||||||
\(252\) | 1.10227 | 0.0694363 | ||||||||
\(253\) | 0.0938169 | 0.00589822 | ||||||||
\(254\) | 24.2160 | 1.51945 | ||||||||
\(255\) | 3.19328 | 0.199971 | ||||||||
\(256\) | 6.85434 | 0.428396 | ||||||||
\(257\) | 26.0049 | 1.62214 | 0.811070 | − | 0.584950i | \(-0.198886\pi\) | ||||
0.811070 | + | 0.584950i | \(0.198886\pi\) | |||||||
\(258\) | 35.5891 | 2.21568 | ||||||||
\(259\) | −0.857784 | −0.0533001 | ||||||||
\(260\) | 7.81010 | 0.484362 | ||||||||
\(261\) | −3.90729 | −0.241855 | ||||||||
\(262\) | 1.00551 | 0.0621205 | ||||||||
\(263\) | 17.1565 | 1.05791 | 0.528957 | − | 0.848648i | \(-0.322583\pi\) | ||||
0.528957 | + | 0.848648i | \(0.322583\pi\) | |||||||
\(264\) | −1.44152 | −0.0887195 | ||||||||
\(265\) | −1.76953 | −0.108701 | ||||||||
\(266\) | 11.2443 | 0.689434 | ||||||||
\(267\) | −4.34514 | −0.265919 | ||||||||
\(268\) | −25.4996 | −1.55764 | ||||||||
\(269\) | −16.5038 | −1.00626 | −0.503128 | − | 0.864212i | \(-0.667818\pi\) | ||||
−0.503128 | + | 0.864212i | \(0.667818\pi\) | |||||||
\(270\) | 5.45004 | 0.331679 | ||||||||
\(271\) | 25.7543 | 1.56446 | 0.782230 | − | 0.622989i | \(-0.214082\pi\) | ||||
0.782230 | + | 0.622989i | \(0.214082\pi\) | |||||||
\(272\) | −12.9319 | −0.784111 | ||||||||
\(273\) | −8.38259 | −0.507338 | ||||||||
\(274\) | 19.0112 | 1.14851 | ||||||||
\(275\) | 4.78423 | 0.288500 | ||||||||
\(276\) | 0.356189 | 0.0214400 | ||||||||
\(277\) | −22.2862 | −1.33905 | −0.669524 | − | 0.742791i | \(-0.733502\pi\) | ||||
−0.669524 | + | 0.742791i | \(0.733502\pi\) | |||||||
\(278\) | 41.4230 | 2.48439 | ||||||||
\(279\) | 5.74047 | 0.343673 | ||||||||
\(280\) | −0.336280 | −0.0200966 | ||||||||
\(281\) | −1.63736 | −0.0976765 | −0.0488382 | − | 0.998807i | \(-0.515552\pi\) | ||||
−0.0488382 | + | 0.998807i | \(0.515552\pi\) | |||||||
\(282\) | −41.3574 | −2.46280 | ||||||||
\(283\) | 12.1106 | 0.719899 | 0.359950 | − | 0.932972i | \(-0.382794\pi\) | ||||
0.359950 | + | 0.932972i | \(0.382794\pi\) | |||||||
\(284\) | −5.25813 | −0.312013 | ||||||||
\(285\) | 4.93598 | 0.292382 | ||||||||
\(286\) | −14.5215 | −0.858675 | ||||||||
\(287\) | 7.84672 | 0.463177 | ||||||||
\(288\) | −4.63693 | −0.273233 | ||||||||
\(289\) | 2.51308 | 0.147828 | ||||||||
\(290\) | 6.61516 | 0.388456 | ||||||||
\(291\) | 2.82334 | 0.165507 | ||||||||
\(292\) | 7.30713 | 0.427618 | ||||||||
\(293\) | −10.8622 | −0.634575 | −0.317287 | − | 0.948329i | \(-0.602772\pi\) | ||||
−0.317287 | + | 0.948329i | \(0.602772\pi\) | |||||||
\(294\) | −20.9505 | −1.22186 | ||||||||
\(295\) | 0.453657 | 0.0264129 | ||||||||
\(296\) | −1.01662 | −0.0590900 | ||||||||
\(297\) | −5.56840 | −0.323111 | ||||||||
\(298\) | 40.1430 | 2.32542 | ||||||||
\(299\) | 0.646577 | 0.0373925 | ||||||||
\(300\) | 18.1640 | 1.04870 | ||||||||
\(301\) | −8.48259 | −0.488928 | ||||||||
\(302\) | 22.3515 | 1.28618 | ||||||||
\(303\) | −22.4167 | −1.28780 | ||||||||
\(304\) | −19.9893 | −1.14647 | ||||||||
\(305\) | 1.66296 | 0.0952207 | ||||||||
\(306\) | 5.38071 | 0.307595 | ||||||||
\(307\) | 29.5682 | 1.68755 | 0.843773 | − | 0.536701i | \(-0.180330\pi\) | ||||
0.843773 | + | 0.536701i | \(0.180330\pi\) | |||||||
\(308\) | 1.90670 | 0.108644 | ||||||||
\(309\) | 2.26883 | 0.129069 | ||||||||
\(310\) | −9.71879 | −0.551990 | ||||||||
\(311\) | −30.3015 | −1.71824 | −0.859121 | − | 0.511773i | \(-0.828989\pi\) | ||||
−0.859121 | + | 0.511773i | \(0.828989\pi\) | |||||||
\(312\) | −9.93483 | −0.562449 | ||||||||
\(313\) | −20.9506 | −1.18420 | −0.592099 | − | 0.805865i | \(-0.701701\pi\) | ||||
−0.592099 | + | 0.805865i | \(0.701701\pi\) | |||||||
\(314\) | −35.4838 | −2.00247 | ||||||||
\(315\) | −0.209876 | −0.0118252 | ||||||||
\(316\) | 10.6505 | 0.599139 | ||||||||
\(317\) | 0.351956 | 0.0197678 | 0.00988391 | − | 0.999951i | \(-0.496854\pi\) | ||||
0.00988391 | + | 0.999951i | \(0.496854\pi\) | |||||||
\(318\) | 12.4914 | 0.700484 | ||||||||
\(319\) | −6.75883 | −0.378422 | ||||||||
\(320\) | 5.13073 | 0.286816 | ||||||||
\(321\) | 20.2890 | 1.13242 | ||||||||
\(322\) | −0.154495 | −0.00860968 | ||||||||
\(323\) | 30.1622 | 1.67827 | ||||||||
\(324\) | −16.9102 | −0.939453 | ||||||||
\(325\) | 32.9724 | 1.82898 | ||||||||
\(326\) | −28.7069 | −1.58993 | ||||||||
\(327\) | −18.9256 | −1.04659 | ||||||||
\(328\) | 9.29972 | 0.513491 | ||||||||
\(329\) | 9.85744 | 0.543458 | ||||||||
\(330\) | 1.52317 | 0.0838475 | ||||||||
\(331\) | −24.3030 | −1.33581 | −0.667906 | − | 0.744246i | \(-0.732809\pi\) | ||||
−0.667906 | + | 0.744246i | \(0.732809\pi\) | |||||||
\(332\) | −6.12707 | −0.336267 | ||||||||
\(333\) | −0.634484 | −0.0347695 | ||||||||
\(334\) | −13.2964 | −0.727544 | ||||||||
\(335\) | 4.85522 | 0.265269 | ||||||||
\(336\) | −3.56072 | −0.194253 | ||||||||
\(337\) | −33.2534 | −1.81143 | −0.905715 | − | 0.423886i | \(-0.860666\pi\) | ||||
−0.905715 | + | 0.423886i | \(0.860666\pi\) | |||||||
\(338\) | −72.6893 | −3.95378 | ||||||||
\(339\) | −3.28563 | −0.178451 | ||||||||
\(340\) | −5.00588 | −0.271482 | ||||||||
\(341\) | 9.92986 | 0.537732 | ||||||||
\(342\) | 8.31718 | 0.449742 | ||||||||
\(343\) | 10.4644 | 0.565025 | ||||||||
\(344\) | −10.0533 | −0.542039 | ||||||||
\(345\) | −0.0678196 | −0.00365129 | ||||||||
\(346\) | 35.9897 | 1.93482 | ||||||||
\(347\) | 33.3486 | 1.79025 | 0.895124 | − | 0.445817i | \(-0.147087\pi\) | ||||
0.895124 | + | 0.445817i | \(0.147087\pi\) | |||||||
\(348\) | −25.6608 | −1.37556 | ||||||||
\(349\) | 30.1214 | 1.61236 | 0.806181 | − | 0.591670i | \(-0.201531\pi\) | ||||
0.806181 | + | 0.591670i | \(0.201531\pi\) | |||||||
\(350\) | −7.87854 | −0.421126 | ||||||||
\(351\) | −38.3769 | −2.04841 | ||||||||
\(352\) | −8.02095 | −0.427518 | ||||||||
\(353\) | 5.82745 | 0.310164 | 0.155082 | − | 0.987902i | \(-0.450436\pi\) | ||||
0.155082 | + | 0.987902i | \(0.450436\pi\) | |||||||
\(354\) | −3.20244 | −0.170208 | ||||||||
\(355\) | 1.00117 | 0.0531365 | ||||||||
\(356\) | 6.81157 | 0.361012 | ||||||||
\(357\) | 5.37282 | 0.284360 | ||||||||
\(358\) | 45.1281 | 2.38510 | ||||||||
\(359\) | −23.3824 | −1.23408 | −0.617038 | − | 0.786933i | \(-0.711668\pi\) | ||||
−0.617038 | + | 0.786933i | \(0.711668\pi\) | |||||||
\(360\) | −0.248739 | −0.0131097 | ||||||||
\(361\) | 27.6228 | 1.45383 | ||||||||
\(362\) | 29.8791 | 1.57041 | ||||||||
\(363\) | −1.55624 | −0.0816817 | ||||||||
\(364\) | 13.1408 | 0.688765 | ||||||||
\(365\) | −1.39131 | −0.0728243 | ||||||||
\(366\) | −11.7391 | −0.613613 | ||||||||
\(367\) | 8.32041 | 0.434322 | 0.217161 | − | 0.976136i | \(-0.430320\pi\) | ||||
0.217161 | + | 0.976136i | \(0.430320\pi\) | |||||||
\(368\) | 0.274650 | 0.0143171 | ||||||||
\(369\) | 5.80405 | 0.302147 | ||||||||
\(370\) | 1.07420 | 0.0558451 | ||||||||
\(371\) | −2.97730 | −0.154574 | ||||||||
\(372\) | 37.7000 | 1.95466 | ||||||||
\(373\) | 32.5387 | 1.68479 | 0.842396 | − | 0.538860i | \(-0.181145\pi\) | ||||
0.842396 | + | 0.538860i | \(0.181145\pi\) | |||||||
\(374\) | 9.30755 | 0.481282 | ||||||||
\(375\) | −7.07296 | −0.365246 | ||||||||
\(376\) | 11.6828 | 0.602493 | ||||||||
\(377\) | −46.5812 | −2.39905 | ||||||||
\(378\) | 9.16990 | 0.471649 | ||||||||
\(379\) | 34.7857 | 1.78682 | 0.893411 | − | 0.449239i | \(-0.148305\pi\) | ||||
0.893411 | + | 0.449239i | \(0.148305\pi\) | |||||||
\(380\) | −7.73779 | −0.396940 | ||||||||
\(381\) | 17.8858 | 0.916315 | ||||||||
\(382\) | 15.2083 | 0.778123 | ||||||||
\(383\) | 17.7180 | 0.905347 | 0.452673 | − | 0.891676i | \(-0.350470\pi\) | ||||
0.452673 | + | 0.891676i | \(0.350470\pi\) | |||||||
\(384\) | −11.2536 | −0.574282 | ||||||||
\(385\) | −0.363043 | −0.0185024 | ||||||||
\(386\) | 15.0351 | 0.765266 | ||||||||
\(387\) | −6.27439 | −0.318945 | ||||||||
\(388\) | −4.42594 | −0.224693 | ||||||||
\(389\) | −14.9057 | −0.755749 | −0.377875 | − | 0.925857i | \(-0.623345\pi\) | ||||
−0.377875 | + | 0.925857i | \(0.623345\pi\) | |||||||
\(390\) | 10.4975 | 0.531562 | ||||||||
\(391\) | −0.414423 | −0.0209583 | ||||||||
\(392\) | 5.91817 | 0.298913 | ||||||||
\(393\) | 0.742661 | 0.0374623 | ||||||||
\(394\) | −1.78006 | −0.0896782 | ||||||||
\(395\) | −2.02790 | −0.102035 | ||||||||
\(396\) | 1.41034 | 0.0708725 | ||||||||
\(397\) | 9.74094 | 0.488884 | 0.244442 | − | 0.969664i | \(-0.421395\pi\) | ||||
0.244442 | + | 0.969664i | \(0.421395\pi\) | |||||||
\(398\) | 25.0774 | 1.25702 | ||||||||
\(399\) | 8.30498 | 0.415769 | ||||||||
\(400\) | 14.0059 | 0.700295 | ||||||||
\(401\) | −5.39741 | −0.269534 | −0.134767 | − | 0.990877i | \(-0.543029\pi\) | ||||
−0.134767 | + | 0.990877i | \(0.543029\pi\) | |||||||
\(402\) | −34.2738 | −1.70942 | ||||||||
\(403\) | 68.4356 | 3.40902 | ||||||||
\(404\) | 35.1410 | 1.74833 | ||||||||
\(405\) | 3.21976 | 0.159991 | ||||||||
\(406\) | 11.1303 | 0.552385 | ||||||||
\(407\) | −1.09753 | −0.0544026 | ||||||||
\(408\) | 6.36772 | 0.315249 | ||||||||
\(409\) | 12.9682 | 0.641235 | 0.320618 | − | 0.947209i | \(-0.396110\pi\) | ||||
0.320618 | + | 0.947209i | \(0.396110\pi\) | |||||||
\(410\) | −9.82643 | −0.485293 | ||||||||
\(411\) | 14.0416 | 0.692620 | ||||||||
\(412\) | −3.55668 | −0.175225 | ||||||||
\(413\) | 0.763295 | 0.0375593 | ||||||||
\(414\) | −0.114277 | −0.00561640 | ||||||||
\(415\) | 1.16662 | 0.0572670 | ||||||||
\(416\) | −55.2796 | −2.71031 | ||||||||
\(417\) | 30.5948 | 1.49823 | ||||||||
\(418\) | 14.3871 | 0.703694 | ||||||||
\(419\) | 38.7312 | 1.89214 | 0.946070 | − | 0.323961i | \(-0.105015\pi\) | ||||
0.946070 | + | 0.323961i | \(0.105015\pi\) | |||||||
\(420\) | −1.37834 | −0.0672562 | ||||||||
\(421\) | −7.34889 | −0.358163 | −0.179081 | − | 0.983834i | \(-0.557313\pi\) | ||||
−0.179081 | + | 0.983834i | \(0.557313\pi\) | |||||||
\(422\) | 36.6546 | 1.78432 | ||||||||
\(423\) | 7.29134 | 0.354517 | ||||||||
\(424\) | −3.52862 | −0.171365 | ||||||||
\(425\) | −21.1337 | −1.02513 | ||||||||
\(426\) | −7.06742 | −0.342418 | ||||||||
\(427\) | 2.79799 | 0.135404 | ||||||||
\(428\) | −31.8056 | −1.53738 | ||||||||
\(429\) | −10.7255 | −0.517831 | ||||||||
\(430\) | 10.6227 | 0.512273 | ||||||||
\(431\) | 27.3475 | 1.31728 | 0.658640 | − | 0.752458i | \(-0.271132\pi\) | ||||
0.658640 | + | 0.752458i | \(0.271132\pi\) | |||||||
\(432\) | −16.3016 | −0.784310 | ||||||||
\(433\) | −8.25871 | −0.396888 | −0.198444 | − | 0.980112i | \(-0.563589\pi\) | ||||
−0.198444 | + | 0.980112i | \(0.563589\pi\) | |||||||
\(434\) | −16.3522 | −0.784932 | ||||||||
\(435\) | 4.88591 | 0.234262 | ||||||||
\(436\) | 29.6683 | 1.42085 | ||||||||
\(437\) | −0.640590 | −0.0306436 | ||||||||
\(438\) | 9.82147 | 0.469288 | ||||||||
\(439\) | −2.96070 | −0.141307 | −0.0706533 | − | 0.997501i | \(-0.522508\pi\) | ||||
−0.0706533 | + | 0.997501i | \(0.522508\pi\) | |||||||
\(440\) | −0.430269 | −0.0205123 | ||||||||
\(441\) | 3.69359 | 0.175885 | ||||||||
\(442\) | 64.1467 | 3.05115 | ||||||||
\(443\) | 2.03486 | 0.0966791 | 0.0483395 | − | 0.998831i | \(-0.484607\pi\) | ||||
0.0483395 | + | 0.998831i | \(0.484607\pi\) | |||||||
\(444\) | −4.16692 | −0.197753 | ||||||||
\(445\) | −1.29695 | −0.0614813 | ||||||||
\(446\) | −51.7098 | −2.44853 | ||||||||
\(447\) | 29.6493 | 1.40237 | ||||||||
\(448\) | 8.63264 | 0.407854 | ||||||||
\(449\) | 7.46400 | 0.352248 | 0.176124 | − | 0.984368i | \(-0.443644\pi\) | ||||
0.176124 | + | 0.984368i | \(0.443644\pi\) | |||||||
\(450\) | −5.82759 | −0.274715 | ||||||||
\(451\) | 10.0398 | 0.472758 | ||||||||
\(452\) | 5.15064 | 0.242266 | ||||||||
\(453\) | 16.5086 | 0.775643 | ||||||||
\(454\) | −13.6096 | −0.638729 | ||||||||
\(455\) | −2.50206 | −0.117298 | ||||||||
\(456\) | 9.84284 | 0.460933 | ||||||||
\(457\) | −15.0131 | −0.702284 | −0.351142 | − | 0.936322i | \(-0.614207\pi\) | ||||
−0.351142 | + | 0.936322i | \(0.614207\pi\) | |||||||
\(458\) | −45.4971 | −2.12594 | ||||||||
\(459\) | 24.5976 | 1.14812 | ||||||||
\(460\) | 0.106316 | 0.00495701 | ||||||||
\(461\) | −1.46451 | −0.0682089 | −0.0341044 | − | 0.999418i | \(-0.510858\pi\) | ||||
−0.0341044 | + | 0.999418i | \(0.510858\pi\) | |||||||
\(462\) | 2.56278 | 0.119231 | ||||||||
\(463\) | 11.5876 | 0.538522 | 0.269261 | − | 0.963067i | \(-0.413221\pi\) | ||||
0.269261 | + | 0.963067i | \(0.413221\pi\) | |||||||
\(464\) | −19.7866 | −0.918568 | ||||||||
\(465\) | −7.17823 | −0.332882 | ||||||||
\(466\) | 11.9540 | 0.553759 | ||||||||
\(467\) | −35.7088 | −1.65241 | −0.826204 | − | 0.563372i | \(-0.809504\pi\) | ||||
−0.826204 | + | 0.563372i | \(0.809504\pi\) | |||||||
\(468\) | 9.71996 | 0.449305 | ||||||||
\(469\) | 8.16909 | 0.377213 | ||||||||
\(470\) | −12.3445 | −0.569407 | ||||||||
\(471\) | −26.2081 | −1.20761 | ||||||||
\(472\) | 0.904636 | 0.0416393 | ||||||||
\(473\) | −10.8534 | −0.499041 | ||||||||
\(474\) | 14.3153 | 0.657524 | ||||||||
\(475\) | −32.6672 | −1.49887 | ||||||||
\(476\) | −8.42258 | −0.386048 | ||||||||
\(477\) | −2.20225 | −0.100834 | ||||||||
\(478\) | 42.9966 | 1.96662 | ||||||||
\(479\) | 21.5204 | 0.983291 | 0.491646 | − | 0.870795i | \(-0.336396\pi\) | ||||
0.491646 | + | 0.870795i | \(0.336396\pi\) | |||||||
\(480\) | 5.79829 | 0.264655 | ||||||||
\(481\) | −7.56407 | −0.344892 | ||||||||
\(482\) | 34.8933 | 1.58935 | ||||||||
\(483\) | −0.114109 | −0.00519215 | ||||||||
\(484\) | 2.43961 | 0.110892 | ||||||||
\(485\) | 0.842716 | 0.0382658 | ||||||||
\(486\) | 12.4697 | 0.565636 | ||||||||
\(487\) | 26.6710 | 1.20858 | 0.604289 | − | 0.796766i | \(-0.293457\pi\) | ||||
0.604289 | + | 0.796766i | \(0.293457\pi\) | |||||||
\(488\) | 3.31610 | 0.150113 | ||||||||
\(489\) | −21.2027 | −0.958821 | ||||||||
\(490\) | −6.25336 | −0.282498 | ||||||||
\(491\) | −12.2152 | −0.551266 | −0.275633 | − | 0.961263i | \(-0.588888\pi\) | ||||
−0.275633 | + | 0.961263i | \(0.588888\pi\) | |||||||
\(492\) | 38.1176 | 1.71847 | ||||||||
\(493\) | 29.8562 | 1.34465 | ||||||||
\(494\) | 99.1542 | 4.46116 | ||||||||
\(495\) | −0.268535 | −0.0120697 | ||||||||
\(496\) | 29.0698 | 1.30527 | ||||||||
\(497\) | 1.68450 | 0.0755603 | ||||||||
\(498\) | −8.23536 | −0.369035 | ||||||||
\(499\) | 29.7420 | 1.33144 | 0.665718 | − | 0.746203i | \(-0.268125\pi\) | ||||
0.665718 | + | 0.746203i | \(0.268125\pi\) | |||||||
\(500\) | 11.0878 | 0.495860 | ||||||||
\(501\) | −9.82060 | −0.438752 | ||||||||
\(502\) | 0.465863 | 0.0207925 | ||||||||
\(503\) | 24.2720 | 1.08224 | 0.541119 | − | 0.840946i | \(-0.318001\pi\) | ||||
0.541119 | + | 0.840946i | \(0.318001\pi\) | |||||||
\(504\) | −0.418513 | −0.0186420 | ||||||||
\(505\) | −6.69097 | −0.297744 | ||||||||
\(506\) | −0.197676 | −0.00878776 | ||||||||
\(507\) | −53.6878 | −2.38436 | ||||||||
\(508\) | −28.0382 | −1.24399 | ||||||||
\(509\) | 5.90079 | 0.261548 | 0.130774 | − | 0.991412i | \(-0.458254\pi\) | ||||
0.130774 | + | 0.991412i | \(0.458254\pi\) | |||||||
\(510\) | −6.72837 | −0.297937 | ||||||||
\(511\) | −2.34093 | −0.103556 | ||||||||
\(512\) | −28.9049 | −1.27743 | ||||||||
\(513\) | 38.0216 | 1.67869 | ||||||||
\(514\) | −54.7933 | −2.41683 | ||||||||
\(515\) | 0.677205 | 0.0298412 | ||||||||
\(516\) | −41.2065 | −1.81402 | ||||||||
\(517\) | 12.6125 | 0.554699 | ||||||||
\(518\) | 1.80738 | 0.0794119 | ||||||||
\(519\) | 26.5817 | 1.16681 | ||||||||
\(520\) | −2.96537 | −0.130040 | ||||||||
\(521\) | −39.2608 | −1.72005 | −0.860024 | − | 0.510253i | \(-0.829552\pi\) | ||||
−0.860024 | + | 0.510253i | \(0.829552\pi\) | |||||||
\(522\) | 8.23281 | 0.360340 | ||||||||
\(523\) | 40.9889 | 1.79232 | 0.896160 | − | 0.443731i | \(-0.146345\pi\) | ||||
0.896160 | + | 0.443731i | \(0.146345\pi\) | |||||||
\(524\) | −1.16422 | −0.0508590 | ||||||||
\(525\) | −5.81904 | −0.253964 | ||||||||
\(526\) | −36.1494 | −1.57619 | ||||||||
\(527\) | −43.8638 | −1.91074 | ||||||||
\(528\) | −4.55593 | −0.198271 | ||||||||
\(529\) | −22.9912 | −0.999617 | ||||||||
\(530\) | 3.72847 | 0.161954 | ||||||||
\(531\) | 0.564593 | 0.0245012 | ||||||||
\(532\) | −13.0191 | −0.564451 | ||||||||
\(533\) | 69.1936 | 2.99711 | ||||||||
\(534\) | 9.15539 | 0.396192 | ||||||||
\(535\) | 6.05590 | 0.261819 | ||||||||
\(536\) | 9.68179 | 0.418189 | ||||||||
\(537\) | 33.3313 | 1.43835 | ||||||||
\(538\) | 34.7742 | 1.49922 | ||||||||
\(539\) | 6.38917 | 0.275201 | ||||||||
\(540\) | −6.31027 | −0.271551 | ||||||||
\(541\) | 31.8812 | 1.37068 | 0.685340 | − | 0.728224i | \(-0.259654\pi\) | ||||
0.685340 | + | 0.728224i | \(0.259654\pi\) | |||||||
\(542\) | −54.2652 | −2.33089 | ||||||||
\(543\) | 22.0685 | 0.947050 | ||||||||
\(544\) | 35.4314 | 1.51911 | ||||||||
\(545\) | −5.64896 | −0.241975 | ||||||||
\(546\) | 17.6625 | 0.755883 | ||||||||
\(547\) | 1.00000 | 0.0427569 | ||||||||
\(548\) | −22.0120 | −0.940305 | ||||||||
\(549\) | 2.06961 | 0.0883290 | ||||||||
\(550\) | −10.0806 | −0.429836 | ||||||||
\(551\) | 46.1499 | 1.96605 | ||||||||
\(552\) | −0.135239 | −0.00575616 | ||||||||
\(553\) | −3.41202 | −0.145094 | ||||||||
\(554\) | 46.9579 | 1.99505 | ||||||||
\(555\) | 0.793398 | 0.0336779 | ||||||||
\(556\) | −47.9612 | −2.03401 | ||||||||
\(557\) | −23.6530 | −1.00221 | −0.501104 | − | 0.865387i | \(-0.667073\pi\) | ||||
−0.501104 | + | 0.865387i | \(0.667073\pi\) | |||||||
\(558\) | −12.0954 | −0.512039 | ||||||||
\(559\) | −74.8008 | −3.16373 | ||||||||
\(560\) | −1.06281 | −0.0449120 | ||||||||
\(561\) | 6.87450 | 0.290241 | ||||||||
\(562\) | 3.44997 | 0.145528 | ||||||||
\(563\) | −20.9677 | −0.883681 | −0.441841 | − | 0.897094i | \(-0.645674\pi\) | ||||
−0.441841 | + | 0.897094i | \(0.645674\pi\) | |||||||
\(564\) | 47.8853 | 2.01633 | ||||||||
\(565\) | −0.980701 | −0.0412584 | ||||||||
\(566\) | −25.5175 | −1.07258 | ||||||||
\(567\) | 5.41737 | 0.227508 | ||||||||
\(568\) | 1.99643 | 0.0837683 | ||||||||
\(569\) | −27.5476 | −1.15485 | −0.577427 | − | 0.816442i | \(-0.695943\pi\) | ||||
−0.577427 | + | 0.816442i | \(0.695943\pi\) | |||||||
\(570\) | −10.4003 | −0.435621 | ||||||||
\(571\) | −29.0532 | −1.21584 | −0.607920 | − | 0.793999i | \(-0.707996\pi\) | ||||
−0.607920 | + | 0.793999i | \(0.707996\pi\) | |||||||
\(572\) | 16.8136 | 0.703011 | ||||||||
\(573\) | 11.2327 | 0.469254 | ||||||||
\(574\) | −16.5333 | −0.690088 | ||||||||
\(575\) | 0.448842 | 0.0187180 | ||||||||
\(576\) | 6.38538 | 0.266058 | ||||||||
\(577\) | 12.7582 | 0.531131 | 0.265565 | − | 0.964093i | \(-0.414441\pi\) | ||||
0.265565 | + | 0.964093i | \(0.414441\pi\) | |||||||
\(578\) | −5.29517 | −0.220250 | ||||||||
\(579\) | 11.1048 | 0.461501 | ||||||||
\(580\) | −7.65929 | −0.318035 | ||||||||
\(581\) | 1.96288 | 0.0814339 | ||||||||
\(582\) | −5.94888 | −0.246589 | ||||||||
\(583\) | −3.80944 | −0.157771 | ||||||||
\(584\) | −2.77440 | −0.114806 | ||||||||
\(585\) | −1.85072 | −0.0765177 | ||||||||
\(586\) | 22.8870 | 0.945454 | ||||||||
\(587\) | 2.22645 | 0.0918954 | 0.0459477 | − | 0.998944i | \(-0.485369\pi\) | ||||
0.0459477 | + | 0.998944i | \(0.485369\pi\) | |||||||
\(588\) | 24.2573 | 1.00036 | ||||||||
\(589\) | −67.8020 | −2.79373 | ||||||||
\(590\) | −0.955872 | −0.0393526 | ||||||||
\(591\) | −1.31474 | −0.0540812 | ||||||||
\(592\) | −3.21304 | −0.132055 | ||||||||
\(593\) | −28.6928 | −1.17827 | −0.589136 | − | 0.808034i | \(-0.700532\pi\) | ||||
−0.589136 | + | 0.808034i | \(0.700532\pi\) | |||||||
\(594\) | 11.7328 | 0.481404 | ||||||||
\(595\) | 1.60369 | 0.0657449 | ||||||||
\(596\) | −46.4791 | −1.90386 | ||||||||
\(597\) | 18.5220 | 0.758056 | ||||||||
\(598\) | −1.36236 | −0.0557112 | ||||||||
\(599\) | 19.1236 | 0.781371 | 0.390685 | − | 0.920524i | \(-0.372238\pi\) | ||||
0.390685 | + | 0.920524i | \(0.372238\pi\) | |||||||
\(600\) | −6.89657 | −0.281551 | ||||||||
\(601\) | 15.6066 | 0.636607 | 0.318303 | − | 0.947989i | \(-0.396887\pi\) | ||||
0.318303 | + | 0.947989i | \(0.396887\pi\) | |||||||
\(602\) | 17.8731 | 0.728455 | ||||||||
\(603\) | 6.04250 | 0.246070 | ||||||||
\(604\) | −25.8794 | −1.05302 | ||||||||
\(605\) | −0.464512 | −0.0188851 | ||||||||
\(606\) | 47.2328 | 1.91870 | ||||||||
\(607\) | 36.9665 | 1.50042 | 0.750212 | − | 0.661197i | \(-0.229951\pi\) | ||||
0.750212 | + | 0.661197i | \(0.229951\pi\) | |||||||
\(608\) | 54.7678 | 2.22113 | ||||||||
\(609\) | 8.22074 | 0.333121 | ||||||||
\(610\) | −3.50392 | −0.141870 | ||||||||
\(611\) | 86.9245 | 3.51659 | ||||||||
\(612\) | −6.23000 | −0.251833 | ||||||||
\(613\) | −8.44792 | −0.341208 | −0.170604 | − | 0.985340i | \(-0.554572\pi\) | ||||
−0.170604 | + | 0.985340i | \(0.554572\pi\) | |||||||
\(614\) | −62.3013 | −2.51428 | ||||||||
\(615\) | −7.25774 | −0.292660 | ||||||||
\(616\) | −0.723943 | −0.0291685 | ||||||||
\(617\) | −19.2430 | −0.774694 | −0.387347 | − | 0.921934i | \(-0.626609\pi\) | ||||
−0.387347 | + | 0.921934i | \(0.626609\pi\) | |||||||
\(618\) | −4.78051 | −0.192300 | ||||||||
\(619\) | −21.6280 | −0.869302 | −0.434651 | − | 0.900599i | \(-0.643128\pi\) | ||||
−0.434651 | + | 0.900599i | \(0.643128\pi\) | |||||||
\(620\) | 11.2528 | 0.451923 | ||||||||
\(621\) | −0.522410 | −0.0209636 | ||||||||
\(622\) | 63.8465 | 2.56001 | ||||||||
\(623\) | −2.18217 | −0.0874266 | ||||||||
\(624\) | −31.3990 | −1.25697 | ||||||||
\(625\) | 21.8100 | 0.872400 | ||||||||
\(626\) | 44.1438 | 1.76434 | ||||||||
\(627\) | 10.6262 | 0.424369 | ||||||||
\(628\) | 41.0846 | 1.63945 | ||||||||
\(629\) | 4.84819 | 0.193310 | ||||||||
\(630\) | 0.442216 | 0.0176183 | ||||||||
\(631\) | 32.1437 | 1.27962 | 0.639810 | − | 0.768533i | \(-0.279013\pi\) | ||||
0.639810 | + | 0.768533i | \(0.279013\pi\) | |||||||
\(632\) | −4.04384 | −0.160855 | ||||||||
\(633\) | 27.0728 | 1.07605 | ||||||||
\(634\) | −0.741585 | −0.0294521 | ||||||||
\(635\) | 5.33858 | 0.211855 | ||||||||
\(636\) | −14.4631 | −0.573498 | ||||||||
\(637\) | 44.0335 | 1.74467 | ||||||||
\(638\) | 14.2411 | 0.563811 | ||||||||
\(639\) | 1.24599 | 0.0492906 | ||||||||
\(640\) | −3.35900 | −0.132776 | ||||||||
\(641\) | 21.9280 | 0.866105 | 0.433052 | − | 0.901369i | \(-0.357437\pi\) | ||||
0.433052 | + | 0.901369i | \(0.357437\pi\) | |||||||
\(642\) | −42.7496 | −1.68719 | ||||||||
\(643\) | 27.2923 | 1.07630 | 0.538151 | − | 0.842848i | \(-0.319123\pi\) | ||||
0.538151 | + | 0.842848i | \(0.319123\pi\) | |||||||
\(644\) | 0.178881 | 0.00704889 | ||||||||
\(645\) | 7.84587 | 0.308931 | ||||||||
\(646\) | −63.5528 | −2.50045 | ||||||||
\(647\) | 30.0400 | 1.18099 | 0.590497 | − | 0.807040i | \(-0.298932\pi\) | ||||
0.590497 | + | 0.807040i | \(0.298932\pi\) | |||||||
\(648\) | 6.42052 | 0.252222 | ||||||||
\(649\) | 0.976632 | 0.0383362 | ||||||||
\(650\) | −69.4742 | −2.72500 | ||||||||
\(651\) | −12.0776 | −0.473360 | ||||||||
\(652\) | 33.2380 | 1.30170 | ||||||||
\(653\) | −18.4555 | −0.722219 | −0.361109 | − | 0.932523i | \(-0.617602\pi\) | ||||
−0.361109 | + | 0.932523i | \(0.617602\pi\) | |||||||
\(654\) | 39.8770 | 1.55931 | ||||||||
\(655\) | 0.221671 | 0.00866141 | ||||||||
\(656\) | 29.3918 | 1.14756 | ||||||||
\(657\) | −1.73153 | −0.0675535 | ||||||||
\(658\) | −20.7700 | −0.809700 | ||||||||
\(659\) | 11.9488 | 0.465461 | 0.232730 | − | 0.972541i | \(-0.425234\pi\) | ||||
0.232730 | + | 0.972541i | \(0.425234\pi\) | |||||||
\(660\) | −1.76358 | −0.0686473 | ||||||||
\(661\) | 23.3109 | 0.906688 | 0.453344 | − | 0.891336i | \(-0.350231\pi\) | ||||
0.453344 | + | 0.891336i | \(0.350231\pi\) | |||||||
\(662\) | 51.2073 | 1.99023 | ||||||||
\(663\) | 47.3784 | 1.84002 | ||||||||
\(664\) | 2.32635 | 0.0902799 | ||||||||
\(665\) | 2.47889 | 0.0961272 | ||||||||
\(666\) | 1.33688 | 0.0518032 | ||||||||
\(667\) | −0.634092 | −0.0245521 | ||||||||
\(668\) | 15.3950 | 0.595652 | ||||||||
\(669\) | −38.1925 | −1.47661 | ||||||||
\(670\) | −10.2301 | −0.395225 | ||||||||
\(671\) | 3.58002 | 0.138205 | ||||||||
\(672\) | 9.75585 | 0.376340 | ||||||||
\(673\) | −23.8973 | −0.921173 | −0.460586 | − | 0.887615i | \(-0.652361\pi\) | ||||
−0.460586 | + | 0.887615i | \(0.652361\pi\) | |||||||
\(674\) | 70.0663 | 2.69885 | ||||||||
\(675\) | −26.6405 | −1.02539 | ||||||||
\(676\) | 84.1625 | 3.23702 | ||||||||
\(677\) | −16.1862 | −0.622084 | −0.311042 | − | 0.950396i | \(-0.600678\pi\) | ||||
−0.311042 | + | 0.950396i | \(0.600678\pi\) | |||||||
\(678\) | 6.92294 | 0.265874 | ||||||||
\(679\) | 1.41790 | 0.0544141 | ||||||||
\(680\) | 1.90065 | 0.0728867 | ||||||||
\(681\) | −10.0519 | −0.385191 | ||||||||
\(682\) | −20.9226 | −0.801168 | ||||||||
\(683\) | −20.6285 | −0.789328 | −0.394664 | − | 0.918826i | \(-0.629139\pi\) | ||||
−0.394664 | + | 0.918826i | \(0.629139\pi\) | |||||||
\(684\) | −9.62996 | −0.368211 | ||||||||
\(685\) | 4.19116 | 0.160136 | ||||||||
\(686\) | −22.0489 | −0.841832 | ||||||||
\(687\) | −33.6038 | −1.28207 | ||||||||
\(688\) | −31.7736 | −1.21136 | ||||||||
\(689\) | −26.2543 | −1.00021 | ||||||||
\(690\) | 0.142899 | 0.00544006 | ||||||||
\(691\) | −21.6319 | −0.822915 | −0.411457 | − | 0.911429i | \(-0.634980\pi\) | ||||
−0.411457 | + | 0.911429i | \(0.634980\pi\) | |||||||
\(692\) | −41.6703 | −1.58407 | ||||||||
\(693\) | −0.451820 | −0.0171632 | ||||||||
\(694\) | −70.2669 | −2.66729 | ||||||||
\(695\) | 9.13199 | 0.346396 | ||||||||
\(696\) | 9.74299 | 0.369307 | ||||||||
\(697\) | −44.3496 | −1.67986 | ||||||||
\(698\) | −63.4669 | −2.40226 | ||||||||
\(699\) | 8.82916 | 0.333949 | ||||||||
\(700\) | 9.12209 | 0.344783 | ||||||||
\(701\) | 6.73632 | 0.254427 | 0.127214 | − | 0.991875i | \(-0.459397\pi\) | ||||
0.127214 | + | 0.991875i | \(0.459397\pi\) | |||||||
\(702\) | 80.8616 | 3.05192 | ||||||||
\(703\) | 7.49404 | 0.282643 | ||||||||
\(704\) | 11.0454 | 0.416290 | ||||||||
\(705\) | −9.11753 | −0.343386 | ||||||||
\(706\) | −12.2787 | −0.462113 | ||||||||
\(707\) | −11.2578 | −0.423394 | ||||||||
\(708\) | 3.70792 | 0.139352 | ||||||||
\(709\) | 2.95332 | 0.110914 | 0.0554571 | − | 0.998461i | \(-0.482338\pi\) | ||||
0.0554571 | + | 0.998461i | \(0.482338\pi\) | |||||||
\(710\) | −2.10950 | −0.0791681 | ||||||||
\(711\) | −2.52380 | −0.0946499 | ||||||||
\(712\) | −2.58624 | −0.0969236 | ||||||||
\(713\) | 0.931588 | 0.0348883 | ||||||||
\(714\) | −11.3207 | −0.423668 | ||||||||
\(715\) | −3.20137 | −0.119724 | ||||||||
\(716\) | −52.2511 | −1.95272 | ||||||||
\(717\) | 31.7570 | 1.18599 | ||||||||
\(718\) | 49.2677 | 1.83865 | ||||||||
\(719\) | −4.80117 | −0.179053 | −0.0895267 | − | 0.995984i | \(-0.528535\pi\) | ||||
−0.0895267 | + | 0.995984i | \(0.528535\pi\) | |||||||
\(720\) | −0.786140 | −0.0292977 | ||||||||
\(721\) | 1.13942 | 0.0424343 | ||||||||
\(722\) | −58.2024 | −2.16607 | ||||||||
\(723\) | 25.7720 | 0.958471 | ||||||||
\(724\) | −34.5952 | −1.28572 | ||||||||
\(725\) | −32.3358 | −1.20092 | ||||||||
\(726\) | 3.27907 | 0.121698 | ||||||||
\(727\) | 35.2737 | 1.30823 | 0.654115 | − | 0.756395i | \(-0.273041\pi\) | ||||
0.654115 | + | 0.756395i | \(0.273041\pi\) | |||||||
\(728\) | −4.98935 | −0.184917 | ||||||||
\(729\) | 30.0045 | 1.11128 | ||||||||
\(730\) | 2.93154 | 0.108501 | ||||||||
\(731\) | 47.9435 | 1.77325 | ||||||||
\(732\) | 13.5920 | 0.502375 | ||||||||
\(733\) | 32.5383 | 1.20183 | 0.600915 | − | 0.799313i | \(-0.294803\pi\) | ||||
0.600915 | + | 0.799313i | \(0.294803\pi\) | |||||||
\(734\) | −17.5314 | −0.647097 | ||||||||
\(735\) | −4.61869 | −0.170363 | ||||||||
\(736\) | −0.752501 | −0.0277375 | ||||||||
\(737\) | 10.4523 | 0.385016 | ||||||||
\(738\) | −12.2294 | −0.450169 | ||||||||
\(739\) | −23.1591 | −0.851922 | −0.425961 | − | 0.904741i | \(-0.640064\pi\) | ||||
−0.425961 | + | 0.904741i | \(0.640064\pi\) | |||||||
\(740\) | −1.24375 | −0.0457213 | ||||||||
\(741\) | 73.2346 | 2.69034 | ||||||||
\(742\) | 6.27329 | 0.230300 | ||||||||
\(743\) | 48.0380 | 1.76235 | 0.881173 | − | 0.472795i | \(-0.156755\pi\) | ||||
0.881173 | + | 0.472795i | \(0.156755\pi\) | |||||||
\(744\) | −14.3141 | −0.524780 | ||||||||
\(745\) | 8.84980 | 0.324232 | ||||||||
\(746\) | −68.5603 | −2.51017 | ||||||||
\(747\) | 1.45190 | 0.0531222 | ||||||||
\(748\) | −10.7767 | −0.394033 | ||||||||
\(749\) | 10.1893 | 0.372308 | ||||||||
\(750\) | 14.9030 | 0.544180 | ||||||||
\(751\) | −26.7033 | −0.974416 | −0.487208 | − | 0.873286i | \(-0.661985\pi\) | ||||
−0.487208 | + | 0.873286i | \(0.661985\pi\) | |||||||
\(752\) | 36.9234 | 1.34646 | ||||||||
\(753\) | 0.344083 | 0.0125391 | ||||||||
\(754\) | 98.1483 | 3.57435 | ||||||||
\(755\) | 4.92754 | 0.179331 | ||||||||
\(756\) | −10.6173 | −0.386146 | ||||||||
\(757\) | 19.3461 | 0.703145 | 0.351573 | − | 0.936161i | \(-0.385647\pi\) | ||||
0.351573 | + | 0.936161i | \(0.385647\pi\) | |||||||
\(758\) | −73.2949 | −2.66219 | ||||||||
\(759\) | −0.146002 | −0.00529954 | ||||||||
\(760\) | 2.93791 | 0.106569 | ||||||||
\(761\) | 3.47525 | 0.125978 | 0.0629888 | − | 0.998014i | \(-0.479937\pi\) | ||||
0.0629888 | + | 0.998014i | \(0.479937\pi\) | |||||||
\(762\) | −37.6860 | −1.36522 | ||||||||
\(763\) | −9.50458 | −0.344089 | ||||||||
\(764\) | −17.6088 | −0.637062 | ||||||||
\(765\) | 1.18622 | 0.0428877 | ||||||||
\(766\) | −37.3325 | −1.34888 | ||||||||
\(767\) | 6.73085 | 0.243037 | ||||||||
\(768\) | −10.6670 | −0.384913 | ||||||||
\(769\) | −14.3148 | −0.516207 | −0.258103 | − | 0.966117i | \(-0.583097\pi\) | ||||
−0.258103 | + | 0.966117i | \(0.583097\pi\) | |||||||
\(770\) | 0.764945 | 0.0275667 | ||||||||
\(771\) | −40.4699 | −1.45749 | ||||||||
\(772\) | −17.4082 | −0.626536 | ||||||||
\(773\) | 35.2376 | 1.26741 | 0.633705 | − | 0.773575i | \(-0.281533\pi\) | ||||
0.633705 | + | 0.773575i | \(0.281533\pi\) | |||||||
\(774\) | 13.2204 | 0.475197 | ||||||||
\(775\) | 47.5067 | 1.70649 | ||||||||
\(776\) | 1.68046 | 0.0603250 | ||||||||
\(777\) | 1.33492 | 0.0478901 | ||||||||
\(778\) | 31.4069 | 1.12599 | ||||||||
\(779\) | −68.5529 | −2.45616 | ||||||||
\(780\) | −12.1544 | −0.435198 | ||||||||
\(781\) | 2.15531 | 0.0771232 | ||||||||
\(782\) | 0.873206 | 0.0312258 | ||||||||
\(783\) | 37.6359 | 1.34500 | ||||||||
\(784\) | 18.7044 | 0.668013 | ||||||||
\(785\) | −7.82266 | −0.279203 | ||||||||
\(786\) | −1.56482 | −0.0558151 | ||||||||
\(787\) | 22.2012 | 0.791386 | 0.395693 | − | 0.918383i | \(-0.370505\pi\) | ||||
0.395693 | + | 0.918383i | \(0.370505\pi\) | |||||||
\(788\) | 2.06103 | 0.0734210 | ||||||||
\(789\) | −26.6997 | −0.950534 | ||||||||
\(790\) | 4.27287 | 0.152022 | ||||||||
\(791\) | −1.65007 | −0.0586696 | ||||||||
\(792\) | −0.535485 | −0.0190276 | ||||||||
\(793\) | 24.6731 | 0.876168 | ||||||||
\(794\) | −20.5245 | −0.728389 | ||||||||
\(795\) | 2.75382 | 0.0976680 | ||||||||
\(796\) | −29.0356 | −1.02914 | ||||||||
\(797\) | 16.1029 | 0.570395 | 0.285197 | − | 0.958469i | \(-0.407941\pi\) | ||||
0.285197 | + | 0.958469i | \(0.407941\pi\) | |||||||
\(798\) | −17.4989 | −0.619455 | ||||||||
\(799\) | −55.7142 | −1.97103 | ||||||||
\(800\) | −38.3741 | −1.35673 | ||||||||
\(801\) | −1.61410 | −0.0570314 | ||||||||
\(802\) | 11.3726 | 0.401579 | ||||||||
\(803\) | −2.99520 | −0.105698 | ||||||||
\(804\) | 39.6836 | 1.39953 | ||||||||
\(805\) | −0.0340596 | −0.00120044 | ||||||||
\(806\) | −144.196 | −5.07910 | ||||||||
\(807\) | 25.6840 | 0.904120 | ||||||||
\(808\) | −13.3425 | −0.469386 | ||||||||
\(809\) | 14.6650 | 0.515593 | 0.257796 | − | 0.966199i | \(-0.417004\pi\) | ||||
0.257796 | + | 0.966199i | \(0.417004\pi\) | |||||||
\(810\) | −6.78416 | −0.238371 | ||||||||
\(811\) | −16.3449 | −0.573948 | −0.286974 | − | 0.957938i | \(-0.592649\pi\) | ||||
−0.286974 | + | 0.957938i | \(0.592649\pi\) | |||||||
\(812\) | −12.8871 | −0.452247 | ||||||||
\(813\) | −40.0800 | −1.40567 | ||||||||
\(814\) | 2.31254 | 0.0810545 | ||||||||
\(815\) | −6.32864 | −0.221683 | ||||||||
\(816\) | 20.1252 | 0.704522 | ||||||||
\(817\) | 74.1082 | 2.59272 | ||||||||
\(818\) | −27.3245 | −0.955377 | ||||||||
\(819\) | −3.11390 | −0.108809 | ||||||||
\(820\) | 11.3774 | 0.397317 | ||||||||
\(821\) | 26.5610 | 0.926986 | 0.463493 | − | 0.886101i | \(-0.346596\pi\) | ||||
0.463493 | + | 0.886101i | \(0.346596\pi\) | |||||||
\(822\) | −29.5861 | −1.03194 | ||||||||
\(823\) | −9.25481 | −0.322602 | −0.161301 | − | 0.986905i | \(-0.551569\pi\) | ||||
−0.161301 | + | 0.986905i | \(0.551569\pi\) | |||||||
\(824\) | 1.35041 | 0.0470439 | ||||||||
\(825\) | −7.44543 | −0.259217 | ||||||||
\(826\) | −1.60829 | −0.0559596 | ||||||||
\(827\) | 28.1400 | 0.978524 | 0.489262 | − | 0.872137i | \(-0.337266\pi\) | ||||
0.489262 | + | 0.872137i | \(0.337266\pi\) | |||||||
\(828\) | 0.132314 | 0.00459824 | ||||||||
\(829\) | 46.1754 | 1.60374 | 0.801868 | − | 0.597501i | \(-0.203839\pi\) | ||||
0.801868 | + | 0.597501i | \(0.203839\pi\) | |||||||
\(830\) | −2.45811 | −0.0853222 | ||||||||
\(831\) | 34.6828 | 1.20313 | ||||||||
\(832\) | 76.1240 | 2.63912 | ||||||||
\(833\) | −28.2233 | −0.977878 | ||||||||
\(834\) | −64.4643 | −2.23222 | ||||||||
\(835\) | −2.93127 | −0.101441 | ||||||||
\(836\) | −16.6579 | −0.576126 | ||||||||
\(837\) | −55.2934 | −1.91122 | ||||||||
\(838\) | −81.6081 | −2.81910 | ||||||||
\(839\) | −16.3322 | −0.563850 | −0.281925 | − | 0.959436i | \(-0.590973\pi\) | ||||
−0.281925 | + | 0.959436i | \(0.590973\pi\) | |||||||
\(840\) | 0.523334 | 0.0180567 | ||||||||
\(841\) | 16.6817 | 0.575232 | ||||||||
\(842\) | 15.4844 | 0.533627 | ||||||||
\(843\) | 2.54813 | 0.0877622 | ||||||||
\(844\) | −42.4401 | −1.46085 | ||||||||
\(845\) | −16.0249 | −0.551272 | ||||||||
\(846\) | −15.3631 | −0.528195 | ||||||||
\(847\) | −0.781558 | −0.0268547 | ||||||||
\(848\) | −11.1522 | −0.382968 | ||||||||
\(849\) | −18.8470 | −0.646828 | ||||||||
\(850\) | 44.5295 | 1.52735 | ||||||||
\(851\) | −0.102967 | −0.00352966 | ||||||||
\(852\) | 8.18294 | 0.280343 | ||||||||
\(853\) | −38.3110 | −1.31174 | −0.655872 | − | 0.754872i | \(-0.727699\pi\) | ||||
−0.655872 | + | 0.754872i | \(0.727699\pi\) | |||||||
\(854\) | −5.89548 | −0.201739 | ||||||||
\(855\) | 1.83358 | 0.0627072 | ||||||||
\(856\) | 12.0761 | 0.412751 | ||||||||
\(857\) | 8.80332 | 0.300716 | 0.150358 | − | 0.988632i | \(-0.451957\pi\) | ||||
0.150358 | + | 0.988632i | \(0.451957\pi\) | |||||||
\(858\) | 22.5990 | 0.771518 | ||||||||
\(859\) | 39.2768 | 1.34011 | 0.670053 | − | 0.742313i | \(-0.266271\pi\) | ||||
0.670053 | + | 0.742313i | \(0.266271\pi\) | |||||||
\(860\) | −12.2994 | −0.419406 | ||||||||
\(861\) | −12.2114 | −0.416164 | ||||||||
\(862\) | −57.6221 | −1.96262 | ||||||||
\(863\) | 25.6138 | 0.871905 | 0.435952 | − | 0.899970i | \(-0.356412\pi\) | ||||
0.435952 | + | 0.899970i | \(0.356412\pi\) | |||||||
\(864\) | 44.6639 | 1.51950 | ||||||||
\(865\) | 7.93418 | 0.269770 | ||||||||
\(866\) | 17.4014 | 0.591325 | ||||||||
\(867\) | −3.91097 | −0.132824 | ||||||||
\(868\) | 18.9333 | 0.642637 | ||||||||
\(869\) | −4.36567 | −0.148095 | ||||||||
\(870\) | −10.2948 | −0.349027 | ||||||||
\(871\) | 72.0363 | 2.44086 | ||||||||
\(872\) | −11.2646 | −0.381467 | ||||||||
\(873\) | 1.04879 | 0.0354962 | ||||||||
\(874\) | 1.34975 | 0.0456559 | ||||||||
\(875\) | −3.55209 | −0.120083 | ||||||||
\(876\) | −11.3717 | −0.384214 | ||||||||
\(877\) | −10.1716 | −0.343470 | −0.171735 | − | 0.985143i | \(-0.554937\pi\) | ||||
−0.171735 | + | 0.985143i | \(0.554937\pi\) | |||||||
\(878\) | 6.23832 | 0.210533 | ||||||||
\(879\) | 16.9042 | 0.570165 | ||||||||
\(880\) | −1.35986 | −0.0458410 | ||||||||
\(881\) | −37.9802 | −1.27959 | −0.639793 | − | 0.768547i | \(-0.720980\pi\) | ||||
−0.639793 | + | 0.768547i | \(0.720980\pi\) | |||||||
\(882\) | −7.78254 | −0.262052 | ||||||||
\(883\) | −4.78415 | −0.160999 | −0.0804997 | − | 0.996755i | \(-0.525652\pi\) | ||||
−0.0804997 | + | 0.996755i | \(0.525652\pi\) | |||||||
\(884\) | −74.2716 | −2.49803 | ||||||||
\(885\) | −0.706001 | −0.0237320 | ||||||||
\(886\) | −4.28753 | −0.144042 | ||||||||
\(887\) | 40.6272 | 1.36413 | 0.682064 | − | 0.731293i | \(-0.261083\pi\) | ||||
0.682064 | + | 0.731293i | \(0.261083\pi\) | |||||||
\(888\) | 1.58211 | 0.0530923 | ||||||||
\(889\) | 8.98236 | 0.301259 | ||||||||
\(890\) | 2.73272 | 0.0916010 | ||||||||
\(891\) | 6.93149 | 0.232214 | ||||||||
\(892\) | 59.8716 | 2.00465 | ||||||||
\(893\) | −86.1196 | −2.88188 | ||||||||
\(894\) | −62.4723 | −2.08939 | ||||||||
\(895\) | 9.94881 | 0.332552 | ||||||||
\(896\) | −5.65164 | −0.188808 | ||||||||
\(897\) | −1.00623 | −0.0335971 | ||||||||
\(898\) | −15.7269 | −0.524815 | ||||||||
\(899\) | −67.1142 | −2.23838 | ||||||||
\(900\) | 6.74741 | 0.224914 | ||||||||
\(901\) | 16.8277 | 0.560611 | ||||||||
\(902\) | −21.1543 | −0.704362 | ||||||||
\(903\) | 13.2010 | 0.439301 | ||||||||
\(904\) | −1.95561 | −0.0650428 | ||||||||
\(905\) | 6.58705 | 0.218961 | ||||||||
\(906\) | −34.7843 | −1.15563 | ||||||||
\(907\) | −0.368797 | −0.0122457 | −0.00612285 | − | 0.999981i | \(-0.501949\pi\) | ||||
−0.00612285 | + | 0.999981i | \(0.501949\pi\) | |||||||
\(908\) | 15.7577 | 0.522938 | ||||||||
\(909\) | −8.32717 | −0.276195 | ||||||||
\(910\) | 5.27193 | 0.174763 | ||||||||
\(911\) | 13.6707 | 0.452931 | 0.226466 | − | 0.974019i | \(-0.427283\pi\) | ||||
0.226466 | + | 0.974019i | \(0.427283\pi\) | |||||||
\(912\) | 31.1083 | 1.03010 | ||||||||
\(913\) | 2.51149 | 0.0831183 | ||||||||
\(914\) | 31.6332 | 1.04633 | ||||||||
\(915\) | −2.58797 | −0.0855557 | ||||||||
\(916\) | 52.6783 | 1.74054 | ||||||||
\(917\) | 0.372970 | 0.0123166 | ||||||||
\(918\) | −51.8282 | −1.71059 | ||||||||
\(919\) | 10.9742 | 0.362006 | 0.181003 | − | 0.983483i | \(-0.442066\pi\) | ||||
0.181003 | + | 0.983483i | \(0.442066\pi\) | |||||||
\(920\) | −0.0403665 | −0.00133084 | ||||||||
\(921\) | −46.0153 | −1.51626 | ||||||||
\(922\) | 3.08577 | 0.101624 | ||||||||
\(923\) | 14.8542 | 0.488932 | ||||||||
\(924\) | −2.96729 | −0.0976167 | ||||||||
\(925\) | −5.25084 | −0.172646 | ||||||||
\(926\) | −24.4155 | −0.802344 | ||||||||
\(927\) | 0.842807 | 0.0276814 | ||||||||
\(928\) | 54.2122 | 1.77960 | ||||||||
\(929\) | −3.09566 | −0.101565 | −0.0507827 | − | 0.998710i | \(-0.516172\pi\) | ||||
−0.0507827 | + | 0.998710i | \(0.516172\pi\) | |||||||
\(930\) | 15.1248 | 0.495962 | ||||||||
\(931\) | −43.6258 | −1.42978 | ||||||||
\(932\) | −13.8408 | −0.453372 | ||||||||
\(933\) | 47.1566 | 1.54384 | ||||||||
\(934\) | 75.2399 | 2.46192 | ||||||||
\(935\) | 2.05192 | 0.0671048 | ||||||||
\(936\) | −3.69051 | −0.120628 | ||||||||
\(937\) | −5.44538 | −0.177893 | −0.0889463 | − | 0.996036i | \(-0.528350\pi\) | ||||
−0.0889463 | + | 0.996036i | \(0.528350\pi\) | |||||||
\(938\) | −17.2126 | −0.562011 | ||||||||
\(939\) | 32.6043 | 1.06400 | ||||||||
\(940\) | 14.2929 | 0.466183 | ||||||||
\(941\) | −3.08325 | −0.100511 | −0.0502556 | − | 0.998736i | \(-0.516004\pi\) | ||||
−0.0502556 | + | 0.998736i | \(0.516004\pi\) | |||||||
\(942\) | 55.2215 | 1.79921 | ||||||||
\(943\) | 0.941907 | 0.0306727 | ||||||||
\(944\) | 2.85910 | 0.0930559 | ||||||||
\(945\) | 2.02157 | 0.0657616 | ||||||||
\(946\) | 22.8686 | 0.743522 | ||||||||
\(947\) | −7.41852 | −0.241070 | −0.120535 | − | 0.992709i | \(-0.538461\pi\) | ||||
−0.120535 | + | 0.992709i | \(0.538461\pi\) | |||||||
\(948\) | −16.5748 | −0.538326 | ||||||||
\(949\) | −20.6426 | −0.670088 | ||||||||
\(950\) | 68.8310 | 2.23317 | ||||||||
\(951\) | −0.547730 | −0.0177614 | ||||||||
\(952\) | 3.19792 | 0.103645 | ||||||||
\(953\) | 33.8231 | 1.09564 | 0.547819 | − | 0.836597i | \(-0.315458\pi\) | ||||
0.547819 | + | 0.836597i | \(0.315458\pi\) | |||||||
\(954\) | 4.64022 | 0.150233 | ||||||||
\(955\) | 3.35277 | 0.108493 | ||||||||
\(956\) | −49.7831 | −1.61010 | ||||||||
\(957\) | 10.5184 | 0.340011 | ||||||||
\(958\) | −45.3443 | −1.46501 | ||||||||
\(959\) | 7.05179 | 0.227714 | ||||||||
\(960\) | −7.98467 | −0.257704 | ||||||||
\(961\) | 67.6020 | 2.18071 | ||||||||
\(962\) | 15.9378 | 0.513855 | ||||||||
\(963\) | 7.53679 | 0.242870 | ||||||||
\(964\) | −40.4009 | −1.30123 | ||||||||
\(965\) | 3.31459 | 0.106700 | ||||||||
\(966\) | 0.240432 | 0.00773579 | ||||||||
\(967\) | 48.6831 | 1.56554 | 0.782771 | − | 0.622310i | \(-0.213806\pi\) | ||||
0.782771 | + | 0.622310i | \(0.213806\pi\) | |||||||
\(968\) | −0.926282 | −0.0297718 | ||||||||
\(969\) | −46.9397 | −1.50792 | ||||||||
\(970\) | −1.77564 | −0.0570122 | ||||||||
\(971\) | −13.0405 | −0.418488 | −0.209244 | − | 0.977863i | \(-0.567100\pi\) | ||||
−0.209244 | + | 0.977863i | \(0.567100\pi\) | |||||||
\(972\) | −14.4379 | −0.463096 | ||||||||
\(973\) | 15.3649 | 0.492577 | ||||||||
\(974\) | −56.1968 | −1.80066 | ||||||||
\(975\) | −51.3132 | −1.64334 | ||||||||
\(976\) | 10.4805 | 0.335474 | ||||||||
\(977\) | 17.1476 | 0.548599 | 0.274299 | − | 0.961644i | \(-0.411554\pi\) | ||||
0.274299 | + | 0.961644i | \(0.411554\pi\) | |||||||
\(978\) | 44.6750 | 1.42855 | ||||||||
\(979\) | −2.79207 | −0.0892349 | ||||||||
\(980\) | 7.24038 | 0.231286 | ||||||||
\(981\) | −7.03034 | −0.224461 | ||||||||
\(982\) | 25.7380 | 0.821333 | ||||||||
\(983\) | 51.9784 | 1.65785 | 0.828926 | − | 0.559358i | \(-0.188952\pi\) | ||||
0.828926 | + | 0.559358i | \(0.188952\pi\) | |||||||
\(984\) | −14.4726 | −0.461371 | ||||||||
\(985\) | −0.392427 | −0.0125038 | ||||||||
\(986\) | −62.9081 | −2.00340 | ||||||||
\(987\) | −15.3406 | −0.488297 | ||||||||
\(988\) | −114.805 | −3.65242 | ||||||||
\(989\) | −1.01823 | −0.0323780 | ||||||||
\(990\) | 0.565814 | 0.0179827 | ||||||||
\(991\) | −7.57921 | −0.240761 | −0.120381 | − | 0.992728i | \(-0.538412\pi\) | ||||
−0.120381 | + | 0.992728i | \(0.538412\pi\) | |||||||
\(992\) | −79.6469 | −2.52879 | ||||||||
\(993\) | 37.8214 | 1.20022 | ||||||||
\(994\) | −3.54931 | −0.112577 | ||||||||
\(995\) | 5.52849 | 0.175265 | ||||||||
\(996\) | 9.53522 | 0.302135 | ||||||||
\(997\) | −14.3053 | −0.453053 | −0.226526 | − | 0.974005i | \(-0.572737\pi\) | ||||
−0.226526 | + | 0.974005i | \(0.572737\pi\) | |||||||
\(998\) | −62.6677 | −1.98371 | ||||||||
\(999\) | 6.11149 | 0.193359 |
(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 | 6017.2.a.f.1.20 | ✓ | 121 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6017.2.a.f.1.20 | ✓ | 121 | 1.1 | even | 1 | trivial |