Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6025,2,Mod(1,6025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6025, 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("6025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6025 = 5^{2} \cdot 241 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6025.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: | \(48.1098672178\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 6025.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.44334 | −1.02060 | −0.510299 | − | 0.859997i | \(-0.670465\pi\) | ||||
−0.510299 | + | 0.859997i | \(0.670465\pi\) | |||||||
\(3\) | −2.75896 | −1.59289 | −0.796444 | − | 0.604712i | \(-0.793288\pi\) | ||||
−0.796444 | + | 0.604712i | \(0.793288\pi\) | |||||||
\(4\) | 0.0832441 | 0.0416220 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 3.98213 | 1.62570 | ||||||||
\(7\) | 1.64702 | 0.622516 | 0.311258 | − | 0.950325i | \(-0.399250\pi\) | ||||
0.311258 | + | 0.950325i | \(0.399250\pi\) | |||||||
\(8\) | 2.76654 | 0.978119 | ||||||||
\(9\) | 4.61187 | 1.53729 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.45824 | −0.741188 | −0.370594 | − | 0.928795i | \(-0.620846\pi\) | ||||
−0.370594 | + | 0.928795i | \(0.620846\pi\) | |||||||
\(12\) | −0.229667 | −0.0662992 | ||||||||
\(13\) | 0.225525 | 0.0625494 | 0.0312747 | − | 0.999511i | \(-0.490043\pi\) | ||||
0.0312747 | + | 0.999511i | \(0.490043\pi\) | |||||||
\(14\) | −2.37722 | −0.635339 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.15956 | −1.03989 | ||||||||
\(17\) | 5.45215 | 1.32234 | 0.661171 | − | 0.750236i | \(-0.270060\pi\) | ||||
0.661171 | + | 0.750236i | \(0.270060\pi\) | |||||||
\(18\) | −6.65652 | −1.56896 | ||||||||
\(19\) | 4.16394 | 0.955273 | 0.477637 | − | 0.878557i | \(-0.341494\pi\) | ||||
0.477637 | + | 0.878557i | \(0.341494\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.54407 | −0.991598 | ||||||||
\(22\) | 3.54809 | 0.756456 | ||||||||
\(23\) | 1.41953 | 0.295993 | 0.147997 | − | 0.988988i | \(-0.452717\pi\) | ||||
0.147997 | + | 0.988988i | \(0.452717\pi\) | |||||||
\(24\) | −7.63278 | −1.55803 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.325510 | −0.0638378 | ||||||||
\(27\) | −4.44710 | −0.855845 | ||||||||
\(28\) | 0.137105 | 0.0259104 | ||||||||
\(29\) | −0.147625 | −0.0274134 | −0.0137067 | − | 0.999906i | \(-0.504363\pi\) | ||||
−0.0137067 | + | 0.999906i | \(0.504363\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.53138 | 0.275043 | 0.137522 | − | 0.990499i | \(-0.456086\pi\) | ||||
0.137522 | + | 0.990499i | \(0.456086\pi\) | |||||||
\(32\) | 0.470598 | 0.0831907 | ||||||||
\(33\) | 6.78220 | 1.18063 | ||||||||
\(34\) | −7.86934 | −1.34958 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.383911 | 0.0639852 | ||||||||
\(37\) | 11.1762 | 1.83735 | 0.918675 | − | 0.395015i | \(-0.129261\pi\) | ||||
0.918675 | + | 0.395015i | \(0.129261\pi\) | |||||||
\(38\) | −6.01000 | −0.974951 | ||||||||
\(39\) | −0.622215 | −0.0996342 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.94197 | −0.459458 | −0.229729 | − | 0.973255i | \(-0.573784\pi\) | ||||
−0.229729 | + | 0.973255i | \(0.573784\pi\) | |||||||
\(42\) | 6.55866 | 1.01202 | ||||||||
\(43\) | 10.1529 | 1.54830 | 0.774149 | − | 0.633003i | \(-0.218178\pi\) | ||||
0.774149 | + | 0.633003i | \(0.218178\pi\) | |||||||
\(44\) | −0.204634 | −0.0308498 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.04888 | −0.302091 | ||||||||
\(47\) | 7.51645 | 1.09639 | 0.548194 | − | 0.836352i | \(-0.315316\pi\) | ||||
0.548194 | + | 0.836352i | \(0.315316\pi\) | |||||||
\(48\) | 11.4761 | 1.65643 | ||||||||
\(49\) | −4.28732 | −0.612474 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −15.0423 | −2.10634 | ||||||||
\(52\) | 0.0187736 | 0.00260343 | ||||||||
\(53\) | 14.4535 | 1.98534 | 0.992672 | − | 0.120836i | \(-0.0385576\pi\) | ||||
0.992672 | + | 0.120836i | \(0.0385576\pi\) | |||||||
\(54\) | 6.41870 | 0.873474 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.55655 | 0.608895 | ||||||||
\(57\) | −11.4882 | −1.52164 | ||||||||
\(58\) | 0.213074 | 0.0279780 | ||||||||
\(59\) | 4.70568 | 0.612627 | 0.306314 | − | 0.951931i | \(-0.400904\pi\) | ||||
0.306314 | + | 0.951931i | \(0.400904\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.54627 | 0.326017 | 0.163008 | − | 0.986625i | \(-0.447880\pi\) | ||||
0.163008 | + | 0.986625i | \(0.447880\pi\) | |||||||
\(62\) | −2.21031 | −0.280709 | ||||||||
\(63\) | 7.59586 | 0.956988 | ||||||||
\(64\) | 7.63988 | 0.954985 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −9.78905 | −1.20495 | ||||||||
\(67\) | −9.13811 | −1.11640 | −0.558199 | − | 0.829707i | \(-0.688507\pi\) | ||||
−0.558199 | + | 0.829707i | \(0.688507\pi\) | |||||||
\(68\) | 0.453859 | 0.0550385 | ||||||||
\(69\) | −3.91644 | −0.471484 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.9420 | 1.77329 | 0.886647 | − | 0.462448i | \(-0.153029\pi\) | ||||
0.886647 | + | 0.462448i | \(0.153029\pi\) | |||||||
\(72\) | 12.7589 | 1.50365 | ||||||||
\(73\) | −5.54388 | −0.648862 | −0.324431 | − | 0.945909i | \(-0.605173\pi\) | ||||
−0.324431 | + | 0.945909i | \(0.605173\pi\) | |||||||
\(74\) | −16.1310 | −1.87520 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.346623 | 0.0397604 | ||||||||
\(77\) | −4.04878 | −0.461401 | ||||||||
\(78\) | 0.898071 | 0.101687 | ||||||||
\(79\) | 15.2219 | 1.71260 | 0.856301 | − | 0.516476i | \(-0.172757\pi\) | ||||
0.856301 | + | 0.516476i | \(0.172757\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.56624 | −0.174027 | ||||||||
\(82\) | 4.24627 | 0.468922 | ||||||||
\(83\) | 8.01520 | 0.879782 | 0.439891 | − | 0.898051i | \(-0.355017\pi\) | ||||
0.439891 | + | 0.898051i | \(0.355017\pi\) | |||||||
\(84\) | −0.378267 | −0.0412723 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −14.6541 | −1.58019 | ||||||||
\(87\) | 0.407293 | 0.0436664 | ||||||||
\(88\) | −6.80083 | −0.724971 | ||||||||
\(89\) | 14.7136 | 1.55964 | 0.779821 | − | 0.626002i | \(-0.215310\pi\) | ||||
0.779821 | + | 0.626002i | \(0.215310\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.371445 | 0.0389380 | ||||||||
\(92\) | 0.118168 | 0.0123199 | ||||||||
\(93\) | −4.22501 | −0.438113 | ||||||||
\(94\) | −10.8488 | −1.11897 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.29836 | −0.132514 | ||||||||
\(97\) | −11.9794 | −1.21633 | −0.608164 | − | 0.793811i | \(-0.708094\pi\) | ||||
−0.608164 | + | 0.793811i | \(0.708094\pi\) | |||||||
\(98\) | 6.18808 | 0.625090 | ||||||||
\(99\) | −11.3371 | −1.13942 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −17.3352 | −1.72492 | −0.862459 | − | 0.506126i | \(-0.831077\pi\) | ||||
−0.862459 | + | 0.506126i | \(0.831077\pi\) | |||||||
\(102\) | 21.7112 | 2.14973 | ||||||||
\(103\) | 0.781262 | 0.0769800 | 0.0384900 | − | 0.999259i | \(-0.487745\pi\) | ||||
0.0384900 | + | 0.999259i | \(0.487745\pi\) | |||||||
\(104\) | 0.623924 | 0.0611808 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −20.8614 | −2.02624 | ||||||||
\(107\) | −9.08155 | −0.877946 | −0.438973 | − | 0.898500i | \(-0.644658\pi\) | ||||
−0.438973 | + | 0.898500i | \(0.644658\pi\) | |||||||
\(108\) | −0.370195 | −0.0356220 | ||||||||
\(109\) | −1.64207 | −0.157282 | −0.0786408 | − | 0.996903i | \(-0.525058\pi\) | ||||
−0.0786408 | + | 0.996903i | \(0.525058\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −30.8346 | −2.92669 | ||||||||
\(112\) | −6.85088 | −0.647348 | ||||||||
\(113\) | 14.2820 | 1.34354 | 0.671771 | − | 0.740759i | \(-0.265534\pi\) | ||||
0.671771 | + | 0.740759i | \(0.265534\pi\) | |||||||
\(114\) | 16.5814 | 1.55299 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.0122889 | −0.00114100 | ||||||||
\(117\) | 1.04009 | 0.0961566 | ||||||||
\(118\) | −6.79192 | −0.625247 | ||||||||
\(119\) | 8.97981 | 0.823178 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.95704 | −0.450640 | ||||||||
\(122\) | −3.67515 | −0.332732 | ||||||||
\(123\) | 8.11677 | 0.731865 | ||||||||
\(124\) | 0.127478 | 0.0114479 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −10.9634 | −0.976701 | ||||||||
\(127\) | 11.8480 | 1.05134 | 0.525668 | − | 0.850690i | \(-0.323815\pi\) | ||||
0.525668 | + | 0.850690i | \(0.323815\pi\) | |||||||
\(128\) | −11.9682 | −1.05785 | ||||||||
\(129\) | −28.0114 | −2.46627 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.67360 | −0.670445 | −0.335223 | − | 0.942139i | \(-0.608812\pi\) | ||||
−0.335223 | + | 0.942139i | \(0.608812\pi\) | |||||||
\(132\) | 0.564578 | 0.0491402 | ||||||||
\(133\) | 6.85810 | 0.594673 | ||||||||
\(134\) | 13.1894 | 1.13939 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 15.0836 | 1.29341 | ||||||||
\(137\) | −7.37050 | −0.629705 | −0.314852 | − | 0.949141i | \(-0.601955\pi\) | ||||
−0.314852 | + | 0.949141i | \(0.601955\pi\) | |||||||
\(138\) | 5.65278 | 0.481196 | ||||||||
\(139\) | −5.61434 | −0.476202 | −0.238101 | − | 0.971240i | \(-0.576525\pi\) | ||||
−0.238101 | + | 0.971240i | \(0.576525\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −20.7376 | −1.74642 | ||||||||
\(142\) | −21.5665 | −1.80982 | ||||||||
\(143\) | −0.554395 | −0.0463609 | ||||||||
\(144\) | −19.1834 | −1.59861 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 8.00173 | 0.662228 | ||||||||
\(147\) | 11.8286 | 0.975603 | ||||||||
\(148\) | 0.930349 | 0.0764742 | ||||||||
\(149\) | −0.264724 | −0.0216870 | −0.0108435 | − | 0.999941i | \(-0.503452\pi\) | ||||
−0.0108435 | + | 0.999941i | \(0.503452\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.15925 | −0.0943386 | −0.0471693 | − | 0.998887i | \(-0.515020\pi\) | ||||
−0.0471693 | + | 0.998887i | \(0.515020\pi\) | |||||||
\(152\) | 11.5197 | 0.934371 | ||||||||
\(153\) | 25.1446 | 2.03282 | ||||||||
\(154\) | 5.84378 | 0.470906 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.0517957 | −0.00414698 | ||||||||
\(157\) | 6.80215 | 0.542870 | 0.271435 | − | 0.962457i | \(-0.412502\pi\) | ||||
0.271435 | + | 0.962457i | \(0.412502\pi\) | |||||||
\(158\) | −21.9705 | −1.74788 | ||||||||
\(159\) | −39.8767 | −3.16243 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.33800 | 0.184261 | ||||||||
\(162\) | 2.26062 | 0.177611 | ||||||||
\(163\) | −0.874753 | −0.0685160 | −0.0342580 | − | 0.999413i | \(-0.510907\pi\) | ||||
−0.0342580 | + | 0.999413i | \(0.510907\pi\) | |||||||
\(164\) | −0.244901 | −0.0191236 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −11.5687 | −0.897905 | ||||||||
\(167\) | −7.64858 | −0.591865 | −0.295932 | − | 0.955209i | \(-0.595630\pi\) | ||||
−0.295932 | + | 0.955209i | \(0.595630\pi\) | |||||||
\(168\) | −12.5714 | −0.969901 | ||||||||
\(169\) | −12.9491 | −0.996088 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 19.2036 | 1.46853 | ||||||||
\(172\) | 0.845166 | 0.0644433 | ||||||||
\(173\) | −15.1779 | −1.15396 | −0.576978 | − | 0.816760i | \(-0.695768\pi\) | ||||
−0.576978 | + | 0.816760i | \(0.695768\pi\) | |||||||
\(174\) | −0.587864 | −0.0445659 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 10.2252 | 0.770754 | ||||||||
\(177\) | −12.9828 | −0.975846 | ||||||||
\(178\) | −21.2369 | −1.59177 | ||||||||
\(179\) | 3.91906 | 0.292924 | 0.146462 | − | 0.989216i | \(-0.453211\pi\) | ||||
0.146462 | + | 0.989216i | \(0.453211\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −21.0049 | −1.56128 | −0.780640 | − | 0.624981i | \(-0.785107\pi\) | ||||
−0.780640 | + | 0.624981i | \(0.785107\pi\) | |||||||
\(182\) | −0.536123 | −0.0397401 | ||||||||
\(183\) | −7.02507 | −0.519308 | ||||||||
\(184\) | 3.92720 | 0.289517 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 6.09815 | 0.447138 | ||||||||
\(187\) | −13.4027 | −0.980104 | ||||||||
\(188\) | 0.625700 | 0.0456339 | ||||||||
\(189\) | −7.32447 | −0.532777 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.93234 | −0.429249 | −0.214624 | − | 0.976697i | \(-0.568853\pi\) | ||||
−0.214624 | + | 0.976697i | \(0.568853\pi\) | |||||||
\(192\) | −21.0781 | −1.52118 | ||||||||
\(193\) | 6.26083 | 0.450664 | 0.225332 | − | 0.974282i | \(-0.427653\pi\) | ||||
0.225332 | + | 0.974282i | \(0.427653\pi\) | |||||||
\(194\) | 17.2905 | 1.24138 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.356894 | −0.0254924 | ||||||||
\(197\) | 3.71334 | 0.264565 | 0.132282 | − | 0.991212i | \(-0.457769\pi\) | ||||
0.132282 | + | 0.991212i | \(0.457769\pi\) | |||||||
\(198\) | 16.3634 | 1.16289 | ||||||||
\(199\) | 17.2066 | 1.21974 | 0.609871 | − | 0.792501i | \(-0.291221\pi\) | ||||
0.609871 | + | 0.792501i | \(0.291221\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 25.2117 | 1.77830 | ||||||||
\(202\) | 25.0207 | 1.76045 | ||||||||
\(203\) | −0.243142 | −0.0170652 | ||||||||
\(204\) | −1.25218 | −0.0876702 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1.12763 | −0.0785657 | ||||||||
\(207\) | 6.54672 | 0.455028 | ||||||||
\(208\) | −0.938085 | −0.0650445 | ||||||||
\(209\) | −10.2360 | −0.708037 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.22632 | 0.290952 | 0.145476 | − | 0.989362i | \(-0.453529\pi\) | ||||
0.145476 | + | 0.989362i | \(0.453529\pi\) | |||||||
\(212\) | 1.20317 | 0.0826341 | ||||||||
\(213\) | −41.2245 | −2.82466 | ||||||||
\(214\) | 13.1078 | 0.896031 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −12.3031 | −0.837118 | ||||||||
\(217\) | 2.52221 | 0.171219 | ||||||||
\(218\) | 2.37007 | 0.160521 | ||||||||
\(219\) | 15.2953 | 1.03356 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.22960 | 0.0827116 | ||||||||
\(222\) | 44.5050 | 2.98698 | ||||||||
\(223\) | −0.761791 | −0.0510133 | −0.0255066 | − | 0.999675i | \(-0.508120\pi\) | ||||
−0.0255066 | + | 0.999675i | \(0.508120\pi\) | |||||||
\(224\) | 0.775085 | 0.0517875 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −20.6139 | −1.37122 | ||||||||
\(227\) | −6.91558 | −0.459003 | −0.229502 | − | 0.973308i | \(-0.573710\pi\) | ||||
−0.229502 | + | 0.973308i | \(0.573710\pi\) | |||||||
\(228\) | −0.956321 | −0.0633339 | ||||||||
\(229\) | 1.84311 | 0.121796 | 0.0608980 | − | 0.998144i | \(-0.480604\pi\) | ||||
0.0608980 | + | 0.998144i | \(0.480604\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 11.1704 | 0.734960 | ||||||||
\(232\) | −0.408412 | −0.0268135 | ||||||||
\(233\) | 24.9350 | 1.63355 | 0.816775 | − | 0.576957i | \(-0.195760\pi\) | ||||
0.816775 | + | 0.576957i | \(0.195760\pi\) | |||||||
\(234\) | −1.50121 | −0.0981373 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0.391720 | 0.0254988 | ||||||||
\(237\) | −41.9968 | −2.72798 | ||||||||
\(238\) | −12.9610 | −0.840135 | ||||||||
\(239\) | −6.11414 | −0.395491 | −0.197746 | − | 0.980253i | \(-0.563362\pi\) | ||||
−0.197746 | + | 0.980253i | \(0.563362\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.00000 | −0.0644157 | ||||||||
\(242\) | 7.15472 | 0.459923 | ||||||||
\(243\) | 17.6625 | 1.13305 | ||||||||
\(244\) | 0.211962 | 0.0135695 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −11.7153 | −0.746940 | ||||||||
\(247\) | 0.939073 | 0.0597518 | ||||||||
\(248\) | 4.23662 | 0.269025 | ||||||||
\(249\) | −22.1136 | −1.40139 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.17822 | 0.326846 | 0.163423 | − | 0.986556i | \(-0.447746\pi\) | ||||
0.163423 | + | 0.986556i | \(0.447746\pi\) | |||||||
\(252\) | 0.632310 | 0.0398318 | ||||||||
\(253\) | −3.48956 | −0.219387 | ||||||||
\(254\) | −17.1007 | −1.07299 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.99444 | 0.124653 | ||||||||
\(257\) | 28.1570 | 1.75639 | 0.878193 | − | 0.478306i | \(-0.158749\pi\) | ||||
0.878193 | + | 0.478306i | \(0.158749\pi\) | |||||||
\(258\) | 40.4301 | 2.51707 | ||||||||
\(259\) | 18.4074 | 1.14378 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.680830 | −0.0421423 | ||||||||
\(262\) | 11.0756 | 0.684256 | ||||||||
\(263\) | −11.3044 | −0.697060 | −0.348530 | − | 0.937298i | \(-0.613319\pi\) | ||||
−0.348530 | + | 0.937298i | \(0.613319\pi\) | |||||||
\(264\) | 18.7632 | 1.15480 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −9.89860 | −0.606922 | ||||||||
\(267\) | −40.5944 | −2.48434 | ||||||||
\(268\) | −0.760694 | −0.0464668 | ||||||||
\(269\) | −17.7202 | −1.08042 | −0.540210 | − | 0.841530i | \(-0.681655\pi\) | ||||
−0.540210 | + | 0.841530i | \(0.681655\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.44509 | 0.391511 | 0.195756 | − | 0.980653i | \(-0.437284\pi\) | ||||
0.195756 | + | 0.980653i | \(0.437284\pi\) | |||||||
\(272\) | −22.6785 | −1.37509 | ||||||||
\(273\) | −1.02480 | −0.0620238 | ||||||||
\(274\) | 10.6382 | 0.642676 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.326021 | −0.0196241 | ||||||||
\(277\) | −23.9729 | −1.44039 | −0.720195 | − | 0.693772i | \(-0.755948\pi\) | ||||
−0.720195 | + | 0.693772i | \(0.755948\pi\) | |||||||
\(278\) | 8.10342 | 0.486011 | ||||||||
\(279\) | 7.06252 | 0.422822 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −29.3389 | −1.75021 | −0.875105 | − | 0.483933i | \(-0.839208\pi\) | ||||
−0.875105 | + | 0.483933i | \(0.839208\pi\) | |||||||
\(282\) | 29.9315 | 1.78240 | ||||||||
\(283\) | −15.6157 | −0.928255 | −0.464127 | − | 0.885768i | \(-0.653632\pi\) | ||||
−0.464127 | + | 0.885768i | \(0.653632\pi\) | |||||||
\(284\) | 1.24384 | 0.0738081 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.800184 | 0.0473158 | ||||||||
\(287\) | −4.84548 | −0.286020 | ||||||||
\(288\) | 2.17034 | 0.127888 | ||||||||
\(289\) | 12.7260 | 0.748586 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 33.0508 | 1.93747 | ||||||||
\(292\) | −0.461495 | −0.0270069 | ||||||||
\(293\) | 6.05757 | 0.353887 | 0.176944 | − | 0.984221i | \(-0.443379\pi\) | ||||
0.176944 | + | 0.984221i | \(0.443379\pi\) | |||||||
\(294\) | −17.0727 | −0.995699 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 30.9193 | 1.79715 | ||||||||
\(297\) | 10.9321 | 0.634342 | ||||||||
\(298\) | 0.382087 | 0.0221337 | ||||||||
\(299\) | 0.320141 | 0.0185142 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 16.7220 | 0.963840 | ||||||||
\(302\) | 1.67320 | 0.0962819 | ||||||||
\(303\) | 47.8272 | 2.74760 | ||||||||
\(304\) | −17.3202 | −0.993379 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −36.2924 | −2.07470 | ||||||||
\(307\) | −15.6112 | −0.890976 | −0.445488 | − | 0.895288i | \(-0.646970\pi\) | ||||
−0.445488 | + | 0.895288i | \(0.646970\pi\) | |||||||
\(308\) | −0.337037 | −0.0192045 | ||||||||
\(309\) | −2.15547 | −0.122621 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.77861 | −0.157561 | −0.0787803 | − | 0.996892i | \(-0.525103\pi\) | ||||
−0.0787803 | + | 0.996892i | \(0.525103\pi\) | |||||||
\(312\) | −1.72138 | −0.0974541 | ||||||||
\(313\) | −11.2889 | −0.638086 | −0.319043 | − | 0.947740i | \(-0.603361\pi\) | ||||
−0.319043 | + | 0.947740i | \(0.603361\pi\) | |||||||
\(314\) | −9.81784 | −0.554053 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.26714 | 0.0712820 | ||||||||
\(317\) | −28.8984 | −1.62310 | −0.811548 | − | 0.584286i | \(-0.801375\pi\) | ||||
−0.811548 | + | 0.584286i | \(0.801375\pi\) | |||||||
\(318\) | 57.5559 | 3.22757 | ||||||||
\(319\) | 0.362899 | 0.0203185 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 25.0557 | 1.39847 | ||||||||
\(322\) | −3.37455 | −0.188056 | ||||||||
\(323\) | 22.7024 | 1.26320 | ||||||||
\(324\) | −0.130380 | −0.00724335 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1.26257 | 0.0699273 | ||||||||
\(327\) | 4.53040 | 0.250532 | ||||||||
\(328\) | −8.13906 | −0.449405 | ||||||||
\(329\) | 12.3798 | 0.682518 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.6833 | 0.587206 | 0.293603 | − | 0.955927i | \(-0.405146\pi\) | ||||
0.293603 | + | 0.955927i | \(0.405146\pi\) | |||||||
\(332\) | 0.667218 | 0.0366183 | ||||||||
\(333\) | 51.5430 | 2.82454 | ||||||||
\(334\) | 11.0395 | 0.604057 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 18.9013 | 1.03115 | ||||||||
\(337\) | −14.7605 | −0.804054 | −0.402027 | − | 0.915628i | \(-0.631694\pi\) | ||||
−0.402027 | + | 0.915628i | \(0.631694\pi\) | |||||||
\(338\) | 18.6901 | 1.01661 | ||||||||
\(339\) | −39.4036 | −2.14011 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.76450 | −0.203859 | ||||||||
\(342\) | −27.7174 | −1.49878 | ||||||||
\(343\) | −18.5905 | −1.00379 | ||||||||
\(344\) | 28.0883 | 1.51442 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 21.9070 | 1.17773 | ||||||||
\(347\) | 8.25614 | 0.443213 | 0.221606 | − | 0.975136i | \(-0.428870\pi\) | ||||
0.221606 | + | 0.975136i | \(0.428870\pi\) | |||||||
\(348\) | 0.0339047 | 0.00181748 | ||||||||
\(349\) | −0.275027 | −0.0147219 | −0.00736093 | − | 0.999973i | \(-0.502343\pi\) | ||||
−0.00736093 | + | 0.999973i | \(0.502343\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.00293 | −0.0535326 | ||||||||
\(352\) | −1.15684 | −0.0616600 | ||||||||
\(353\) | −0.217232 | −0.0115621 | −0.00578105 | − | 0.999983i | \(-0.501840\pi\) | ||||
−0.00578105 | + | 0.999983i | \(0.501840\pi\) | |||||||
\(354\) | 18.7386 | 0.995948 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.22482 | 0.0649155 | ||||||||
\(357\) | −24.7750 | −1.31123 | ||||||||
\(358\) | −5.65656 | −0.298958 | ||||||||
\(359\) | −29.2946 | −1.54611 | −0.773055 | − | 0.634339i | \(-0.781273\pi\) | ||||
−0.773055 | + | 0.634339i | \(0.781273\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.66161 | −0.0874531 | ||||||||
\(362\) | 30.3173 | 1.59344 | ||||||||
\(363\) | 13.6763 | 0.717819 | ||||||||
\(364\) | 0.0309206 | 0.00162068 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 10.1396 | 0.530005 | ||||||||
\(367\) | 29.2016 | 1.52431 | 0.762157 | − | 0.647392i | \(-0.224140\pi\) | ||||
0.762157 | + | 0.647392i | \(0.224140\pi\) | |||||||
\(368\) | −5.90464 | −0.307801 | ||||||||
\(369\) | −13.5680 | −0.706321 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 23.8053 | 1.23591 | ||||||||
\(372\) | −0.351707 | −0.0182352 | ||||||||
\(373\) | −33.0815 | −1.71289 | −0.856447 | − | 0.516235i | \(-0.827333\pi\) | ||||
−0.856447 | + | 0.516235i | \(0.827333\pi\) | |||||||
\(374\) | 19.3447 | 1.00029 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 20.7946 | 1.07240 | ||||||||
\(377\) | −0.0332932 | −0.00171469 | ||||||||
\(378\) | 10.5717 | 0.543751 | ||||||||
\(379\) | 24.1530 | 1.24066 | 0.620328 | − | 0.784343i | \(-0.287000\pi\) | ||||
0.620328 | + | 0.784343i | \(0.287000\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −32.6881 | −1.67466 | ||||||||
\(382\) | 8.56241 | 0.438091 | ||||||||
\(383\) | 37.9978 | 1.94159 | 0.970797 | − | 0.239901i | \(-0.0771150\pi\) | ||||
0.970797 | + | 0.239901i | \(0.0771150\pi\) | |||||||
\(384\) | 33.0198 | 1.68503 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −9.03653 | −0.459947 | ||||||||
\(387\) | 46.8238 | 2.38019 | ||||||||
\(388\) | −0.997218 | −0.0506261 | ||||||||
\(389\) | 30.7749 | 1.56035 | 0.780176 | − | 0.625561i | \(-0.215130\pi\) | ||||
0.780176 | + | 0.625561i | \(0.215130\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.73952 | 0.391404 | ||||||||
\(392\) | −11.8610 | −0.599073 | ||||||||
\(393\) | 21.1712 | 1.06794 | ||||||||
\(394\) | −5.35963 | −0.270014 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.943747 | −0.0474251 | ||||||||
\(397\) | 33.3421 | 1.67339 | 0.836696 | − | 0.547667i | \(-0.184484\pi\) | ||||
0.836696 | + | 0.547667i | \(0.184484\pi\) | |||||||
\(398\) | −24.8350 | −1.24487 | ||||||||
\(399\) | −18.9212 | −0.947247 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 25.3102 | 1.26393 | 0.631965 | − | 0.774997i | \(-0.282249\pi\) | ||||
0.631965 | + | 0.774997i | \(0.282249\pi\) | |||||||
\(402\) | −36.3892 | −1.81493 | ||||||||
\(403\) | 0.345364 | 0.0172038 | ||||||||
\(404\) | −1.44305 | −0.0717946 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.350938 | 0.0174168 | ||||||||
\(407\) | −27.4737 | −1.36182 | ||||||||
\(408\) | −41.6151 | −2.06025 | ||||||||
\(409\) | 28.5752 | 1.41295 | 0.706477 | − | 0.707736i | \(-0.250284\pi\) | ||||
0.706477 | + | 0.707736i | \(0.250284\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 20.3349 | 1.00305 | ||||||||
\(412\) | 0.0650354 | 0.00320407 | ||||||||
\(413\) | 7.75035 | 0.381370 | ||||||||
\(414\) | −9.44917 | −0.464401 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0.106132 | 0.00520353 | ||||||||
\(417\) | 15.4897 | 0.758536 | ||||||||
\(418\) | 14.7740 | 0.722622 | ||||||||
\(419\) | 40.7895 | 1.99270 | 0.996349 | − | 0.0853741i | \(-0.0272085\pi\) | ||||
0.996349 | + | 0.0853741i | \(0.0272085\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.35946 | 0.163730 | 0.0818650 | − | 0.996643i | \(-0.473912\pi\) | ||||
0.0818650 | + | 0.996643i | \(0.473912\pi\) | |||||||
\(422\) | −6.10004 | −0.296945 | ||||||||
\(423\) | 34.6649 | 1.68547 | ||||||||
\(424\) | 39.9863 | 1.94190 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 59.5012 | 2.88284 | ||||||||
\(427\) | 4.19376 | 0.202950 | ||||||||
\(428\) | −0.755985 | −0.0365419 | ||||||||
\(429\) | 1.52956 | 0.0738476 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.87111 | 0.234633 | 0.117317 | − | 0.993095i | \(-0.462571\pi\) | ||||
0.117317 | + | 0.993095i | \(0.462571\pi\) | |||||||
\(432\) | 18.4980 | 0.889984 | ||||||||
\(433\) | −12.6736 | −0.609054 | −0.304527 | − | 0.952504i | \(-0.598498\pi\) | ||||
−0.304527 | + | 0.952504i | \(0.598498\pi\) | |||||||
\(434\) | −3.64042 | −0.174746 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.136692 | −0.00654638 | ||||||||
\(437\) | 5.91086 | 0.282755 | ||||||||
\(438\) | −22.0765 | −1.05485 | ||||||||
\(439\) | 9.86326 | 0.470748 | 0.235374 | − | 0.971905i | \(-0.424369\pi\) | ||||
0.235374 | + | 0.971905i | \(0.424369\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −19.7726 | −0.941551 | ||||||||
\(442\) | −1.77473 | −0.0844154 | ||||||||
\(443\) | 22.4789 | 1.06801 | 0.534003 | − | 0.845483i | \(-0.320687\pi\) | ||||
0.534003 | + | 0.845483i | \(0.320687\pi\) | |||||||
\(444\) | −2.56680 | −0.121815 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1.09953 | 0.0520641 | ||||||||
\(447\) | 0.730362 | 0.0345450 | ||||||||
\(448\) | 12.5831 | 0.594493 | ||||||||
\(449\) | 29.9519 | 1.41352 | 0.706760 | − | 0.707454i | \(-0.250156\pi\) | ||||
0.706760 | + | 0.707454i | \(0.250156\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.23207 | 0.340545 | ||||||||
\(452\) | 1.18890 | 0.0559210 | ||||||||
\(453\) | 3.19833 | 0.150271 | ||||||||
\(454\) | 9.98157 | 0.468458 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −31.7824 | −1.48835 | ||||||||
\(457\) | −12.3781 | −0.579022 | −0.289511 | − | 0.957175i | \(-0.593493\pi\) | ||||
−0.289511 | + | 0.957175i | \(0.593493\pi\) | |||||||
\(458\) | −2.66024 | −0.124305 | ||||||||
\(459\) | −24.2463 | −1.13172 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −25.7753 | −1.20048 | −0.600238 | − | 0.799821i | \(-0.704928\pi\) | ||||
−0.600238 | + | 0.799821i | \(0.704928\pi\) | |||||||
\(462\) | −16.1228 | −0.750100 | ||||||||
\(463\) | 3.05091 | 0.141788 | 0.0708938 | − | 0.997484i | \(-0.477415\pi\) | ||||
0.0708938 | + | 0.997484i | \(0.477415\pi\) | |||||||
\(464\) | 0.614057 | 0.0285069 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −35.9899 | −1.66720 | ||||||||
\(467\) | 10.8914 | 0.503994 | 0.251997 | − | 0.967728i | \(-0.418913\pi\) | ||||
0.251997 | + | 0.967728i | \(0.418913\pi\) | |||||||
\(468\) | 0.0865816 | 0.00400224 | ||||||||
\(469\) | −15.0507 | −0.694975 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −18.7669 | −0.864732 | ||||||||
\(472\) | 13.0184 | 0.599223 | ||||||||
\(473\) | −24.9582 | −1.14758 | ||||||||
\(474\) | 60.6158 | 2.78418 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0.747516 | 0.0342624 | ||||||||
\(477\) | 66.6579 | 3.05205 | ||||||||
\(478\) | 8.82482 | 0.403638 | ||||||||
\(479\) | −24.7057 | −1.12883 | −0.564416 | − | 0.825490i | \(-0.690899\pi\) | ||||
−0.564416 | + | 0.825490i | \(0.690899\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.52050 | 0.114925 | ||||||||
\(482\) | 1.44334 | 0.0657426 | ||||||||
\(483\) | −6.45047 | −0.293506 | ||||||||
\(484\) | −0.412644 | −0.0187566 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −25.4931 | −1.15639 | ||||||||
\(487\) | 14.6482 | 0.663775 | 0.331887 | − | 0.943319i | \(-0.392315\pi\) | ||||
0.331887 | + | 0.943319i | \(0.392315\pi\) | |||||||
\(488\) | 7.04436 | 0.318883 | ||||||||
\(489\) | 2.41341 | 0.109138 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 30.4629 | 1.37477 | 0.687386 | − | 0.726292i | \(-0.258758\pi\) | ||||
0.687386 | + | 0.726292i | \(0.258758\pi\) | |||||||
\(492\) | 0.675673 | 0.0304617 | ||||||||
\(493\) | −0.804877 | −0.0362498 | ||||||||
\(494\) | −1.35541 | −0.0609826 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6.36985 | −0.286015 | ||||||||
\(497\) | 24.6099 | 1.10390 | ||||||||
\(498\) | 31.9176 | 1.43026 | ||||||||
\(499\) | 15.7174 | 0.703608 | 0.351804 | − | 0.936074i | \(-0.385568\pi\) | ||||
0.351804 | + | 0.936074i | \(0.385568\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 21.1021 | 0.942774 | ||||||||
\(502\) | −7.47396 | −0.333579 | ||||||||
\(503\) | 23.5099 | 1.04825 | 0.524126 | − | 0.851641i | \(-0.324392\pi\) | ||||
0.524126 | + | 0.851641i | \(0.324392\pi\) | |||||||
\(504\) | 21.0142 | 0.936049 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 5.03664 | 0.223906 | ||||||||
\(507\) | 35.7262 | 1.58666 | ||||||||
\(508\) | 0.986273 | 0.0437588 | ||||||||
\(509\) | −14.2914 | −0.633454 | −0.316727 | − | 0.948517i | \(-0.602584\pi\) | ||||
−0.316727 | + | 0.948517i | \(0.602584\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.13089 | −0.403927 | ||||||||
\(512\) | 21.0577 | 0.930627 | ||||||||
\(513\) | −18.5175 | −0.817566 | ||||||||
\(514\) | −40.6403 | −1.79257 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −2.33178 | −0.102651 | ||||||||
\(517\) | −18.4773 | −0.812629 | ||||||||
\(518\) | −26.5682 | −1.16734 | ||||||||
\(519\) | 41.8753 | 1.83812 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 19.7643 | 0.865888 | 0.432944 | − | 0.901421i | \(-0.357475\pi\) | ||||
0.432944 | + | 0.901421i | \(0.357475\pi\) | |||||||
\(522\) | 0.982672 | 0.0430104 | ||||||||
\(523\) | −11.6148 | −0.507882 | −0.253941 | − | 0.967220i | \(-0.581727\pi\) | ||||
−0.253941 | + | 0.967220i | \(0.581727\pi\) | |||||||
\(524\) | −0.638781 | −0.0279053 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 16.3162 | 0.711418 | ||||||||
\(527\) | 8.34930 | 0.363701 | ||||||||
\(528\) | −28.2110 | −1.22772 | ||||||||
\(529\) | −20.9849 | −0.912388 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 21.7020 | 0.941786 | ||||||||
\(532\) | 0.570896 | 0.0247515 | ||||||||
\(533\) | −0.663487 | −0.0287388 | ||||||||
\(534\) | 58.5917 | 2.53551 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −25.2810 | −1.09197 | ||||||||
\(537\) | −10.8125 | −0.466596 | ||||||||
\(538\) | 25.5764 | 1.10268 | ||||||||
\(539\) | 10.5393 | 0.453959 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.3419 | −0.573613 | −0.286807 | − | 0.957989i | \(-0.592594\pi\) | ||||
−0.286807 | + | 0.957989i | \(0.592594\pi\) | |||||||
\(542\) | −9.30248 | −0.399576 | ||||||||
\(543\) | 57.9517 | 2.48694 | ||||||||
\(544\) | 2.56577 | 0.110007 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1.47914 | 0.0633014 | ||||||||
\(547\) | −13.4875 | −0.576685 | −0.288343 | − | 0.957527i | \(-0.593104\pi\) | ||||
−0.288343 | + | 0.957527i | \(0.593104\pi\) | |||||||
\(548\) | −0.613551 | −0.0262096 | ||||||||
\(549\) | 11.7431 | 0.501182 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.614704 | −0.0261872 | ||||||||
\(552\) | −10.8350 | −0.461168 | ||||||||
\(553\) | 25.0709 | 1.06612 | ||||||||
\(554\) | 34.6011 | 1.47006 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.467360 | −0.0198205 | ||||||||
\(557\) | −6.61321 | −0.280211 | −0.140105 | − | 0.990137i | \(-0.544744\pi\) | ||||
−0.140105 | + | 0.990137i | \(0.544744\pi\) | |||||||
\(558\) | −10.1936 | −0.431532 | ||||||||
\(559\) | 2.28973 | 0.0968451 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 36.9776 | 1.56119 | ||||||||
\(562\) | 42.3461 | 1.78626 | ||||||||
\(563\) | −6.33895 | −0.267155 | −0.133577 | − | 0.991038i | \(-0.542646\pi\) | ||||
−0.133577 | + | 0.991038i | \(0.542646\pi\) | |||||||
\(564\) | −1.72628 | −0.0726896 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 22.5388 | 0.947376 | ||||||||
\(567\) | −2.57963 | −0.108334 | ||||||||
\(568\) | 41.3377 | 1.73449 | ||||||||
\(569\) | −17.3303 | −0.726525 | −0.363263 | − | 0.931687i | \(-0.618337\pi\) | ||||
−0.363263 | + | 0.931687i | \(0.618337\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −26.3909 | −1.10442 | −0.552211 | − | 0.833704i | \(-0.686216\pi\) | ||||
−0.552211 | + | 0.833704i | \(0.686216\pi\) | |||||||
\(572\) | −0.0461501 | −0.00192963 | ||||||||
\(573\) | 16.3671 | 0.683745 | ||||||||
\(574\) | 6.99370 | 0.291911 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 35.2342 | 1.46809 | ||||||||
\(577\) | 36.1007 | 1.50289 | 0.751446 | − | 0.659795i | \(-0.229357\pi\) | ||||
0.751446 | + | 0.659795i | \(0.229357\pi\) | |||||||
\(578\) | −18.3680 | −0.764006 | ||||||||
\(579\) | −17.2734 | −0.717858 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13.2012 | 0.547678 | ||||||||
\(582\) | −47.7037 | −1.97738 | ||||||||
\(583\) | −35.5303 | −1.47151 | ||||||||
\(584\) | −15.3374 | −0.634664 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −8.74317 | −0.361177 | ||||||||
\(587\) | 8.80044 | 0.363233 | 0.181617 | − | 0.983369i | \(-0.441867\pi\) | ||||
0.181617 | + | 0.983369i | \(0.441867\pi\) | |||||||
\(588\) | 0.984657 | 0.0406066 | ||||||||
\(589\) | 6.37656 | 0.262742 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −10.2450 | −0.421422 | ||||||||
\(592\) | −46.4879 | −1.91064 | ||||||||
\(593\) | −8.41291 | −0.345477 | −0.172738 | − | 0.984968i | \(-0.555261\pi\) | ||||
−0.172738 | + | 0.984968i | \(0.555261\pi\) | |||||||
\(594\) | −15.7787 | −0.647409 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −0.0220367 | −0.000902657 0 | ||||||||
\(597\) | −47.4723 | −1.94291 | ||||||||
\(598\) | −0.462073 | −0.0188956 | ||||||||
\(599\) | −36.9523 | −1.50983 | −0.754915 | − | 0.655822i | \(-0.772322\pi\) | ||||
−0.754915 | + | 0.655822i | \(0.772322\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.16858 | 0.0884583 | 0.0442291 | − | 0.999021i | \(-0.485917\pi\) | ||||
0.0442291 | + | 0.999021i | \(0.485917\pi\) | |||||||
\(602\) | −24.1356 | −0.983694 | ||||||||
\(603\) | −42.1438 | −1.71623 | ||||||||
\(604\) | −0.0965009 | −0.00392657 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −69.0312 | −2.80420 | ||||||||
\(607\) | −37.1254 | −1.50687 | −0.753437 | − | 0.657520i | \(-0.771605\pi\) | ||||
−0.753437 | + | 0.657520i | \(0.771605\pi\) | |||||||
\(608\) | 1.95954 | 0.0794699 | ||||||||
\(609\) | 0.670821 | 0.0271830 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.69515 | 0.0685783 | ||||||||
\(612\) | 2.09314 | 0.0846103 | ||||||||
\(613\) | −6.76953 | −0.273419 | −0.136709 | − | 0.990611i | \(-0.543653\pi\) | ||||
−0.136709 | + | 0.990611i | \(0.543653\pi\) | |||||||
\(614\) | 22.5323 | 0.909329 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −11.2011 | −0.451306 | ||||||||
\(617\) | 23.6341 | 0.951473 | 0.475737 | − | 0.879588i | \(-0.342182\pi\) | ||||
0.475737 | + | 0.879588i | \(0.342182\pi\) | |||||||
\(618\) | 3.11109 | 0.125146 | ||||||||
\(619\) | 16.7010 | 0.671270 | 0.335635 | − | 0.941992i | \(-0.391049\pi\) | ||||
0.335635 | + | 0.941992i | \(0.391049\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.31281 | −0.253324 | ||||||||
\(622\) | 4.01049 | 0.160806 | ||||||||
\(623\) | 24.2337 | 0.970902 | ||||||||
\(624\) | 2.58814 | 0.103609 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 16.2938 | 0.651229 | ||||||||
\(627\) | 28.2407 | 1.12782 | ||||||||
\(628\) | 0.566238 | 0.0225954 | ||||||||
\(629\) | 60.9341 | 2.42960 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −32.0618 | −1.27636 | −0.638181 | − | 0.769887i | \(-0.720313\pi\) | ||||
−0.638181 | + | 0.769887i | \(0.720313\pi\) | |||||||
\(632\) | 42.1121 | 1.67513 | ||||||||
\(633\) | −11.6603 | −0.463454 | ||||||||
\(634\) | 41.7104 | 1.65653 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −3.31950 | −0.131627 | ||||||||
\(637\) | −0.966898 | −0.0383099 | ||||||||
\(638\) | −0.523789 | −0.0207370 | ||||||||
\(639\) | 68.9108 | 2.72607 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 39.4981 | 1.56008 | 0.780041 | − | 0.625728i | \(-0.215198\pi\) | ||||
0.780041 | + | 0.625728i | \(0.215198\pi\) | |||||||
\(642\) | −36.1639 | −1.42728 | ||||||||
\(643\) | −18.3883 | −0.725164 | −0.362582 | − | 0.931952i | \(-0.618105\pi\) | ||||
−0.362582 | + | 0.931952i | \(0.618105\pi\) | |||||||
\(644\) | 0.194625 | 0.00766930 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −32.7674 | −1.28922 | ||||||||
\(647\) | −30.4542 | −1.19728 | −0.598639 | − | 0.801019i | \(-0.704291\pi\) | ||||
−0.598639 | + | 0.801019i | \(0.704291\pi\) | |||||||
\(648\) | −4.33307 | −0.170219 | ||||||||
\(649\) | −11.5677 | −0.454072 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.95869 | −0.272732 | ||||||||
\(652\) | −0.0728180 | −0.00285177 | ||||||||
\(653\) | −4.69509 | −0.183733 | −0.0918665 | − | 0.995771i | \(-0.529283\pi\) | ||||
−0.0918665 | + | 0.995771i | \(0.529283\pi\) | |||||||
\(654\) | −6.53893 | −0.255693 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 12.2373 | 0.477785 | ||||||||
\(657\) | −25.5677 | −0.997490 | ||||||||
\(658\) | −17.8683 | −0.696577 | ||||||||
\(659\) | −11.5156 | −0.448585 | −0.224292 | − | 0.974522i | \(-0.572007\pi\) | ||||
−0.224292 | + | 0.974522i | \(0.572007\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20.7745 | −0.808036 | −0.404018 | − | 0.914751i | \(-0.632387\pi\) | ||||
−0.404018 | + | 0.914751i | \(0.632387\pi\) | |||||||
\(662\) | −15.4196 | −0.599301 | ||||||||
\(663\) | −3.39241 | −0.131750 | ||||||||
\(664\) | 22.1744 | 0.860532 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −74.3944 | −2.88272 | ||||||||
\(667\) | −0.209559 | −0.00811418 | ||||||||
\(668\) | −0.636699 | −0.0246346 | ||||||||
\(669\) | 2.10175 | 0.0812584 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.25935 | −0.241640 | ||||||||
\(672\) | −2.13843 | −0.0824917 | ||||||||
\(673\) | −2.21790 | −0.0854937 | −0.0427468 | − | 0.999086i | \(-0.513611\pi\) | ||||
−0.0427468 | + | 0.999086i | \(0.513611\pi\) | |||||||
\(674\) | 21.3045 | 0.820617 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.07794 | −0.0414592 | ||||||||
\(677\) | −6.92193 | −0.266032 | −0.133016 | − | 0.991114i | \(-0.542466\pi\) | ||||
−0.133016 | + | 0.991114i | \(0.542466\pi\) | |||||||
\(678\) | 56.8730 | 2.18420 | ||||||||
\(679\) | −19.7304 | −0.757183 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 19.0798 | 0.731141 | ||||||||
\(682\) | 5.43347 | 0.208058 | ||||||||
\(683\) | −17.5298 | −0.670757 | −0.335379 | − | 0.942083i | \(-0.608864\pi\) | ||||
−0.335379 | + | 0.942083i | \(0.608864\pi\) | |||||||
\(684\) | 1.59858 | 0.0611234 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 26.8324 | 1.02447 | ||||||||
\(687\) | −5.08507 | −0.194007 | ||||||||
\(688\) | −42.2315 | −1.61006 | ||||||||
\(689\) | 3.25963 | 0.124182 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15.5684 | −0.592248 | −0.296124 | − | 0.955149i | \(-0.595694\pi\) | ||||
−0.296124 | + | 0.955149i | \(0.595694\pi\) | |||||||
\(692\) | −1.26347 | −0.0480300 | ||||||||
\(693\) | −18.6725 | −0.709308 | ||||||||
\(694\) | −11.9165 | −0.452343 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.12679 | 0.0427110 | ||||||||
\(697\) | −16.0400 | −0.607560 | ||||||||
\(698\) | 0.396959 | 0.0150251 | ||||||||
\(699\) | −68.7949 | −2.60206 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −30.5535 | −1.15399 | −0.576994 | − | 0.816748i | \(-0.695775\pi\) | ||||
−0.576994 | + | 0.816748i | \(0.695775\pi\) | |||||||
\(702\) | 1.44758 | 0.0546353 | ||||||||
\(703\) | 46.5368 | 1.75517 | ||||||||
\(704\) | −18.7807 | −0.707824 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.313541 | 0.0118003 | ||||||||
\(707\) | −28.5515 | −1.07379 | ||||||||
\(708\) | −1.08074 | −0.0406167 | ||||||||
\(709\) | 17.8130 | 0.668983 | 0.334492 | − | 0.942399i | \(-0.391435\pi\) | ||||
0.334492 | + | 0.942399i | \(0.391435\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 70.2017 | 2.63277 | ||||||||
\(712\) | 40.7059 | 1.52552 | ||||||||
\(713\) | 2.17384 | 0.0814111 | ||||||||
\(714\) | 35.7588 | 1.33824 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0.326239 | 0.0121921 | ||||||||
\(717\) | 16.8687 | 0.629973 | ||||||||
\(718\) | 42.2822 | 1.57796 | ||||||||
\(719\) | −2.19390 | −0.0818185 | −0.0409093 | − | 0.999163i | \(-0.513025\pi\) | ||||
−0.0409093 | + | 0.999163i | \(0.513025\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.28676 | 0.0479213 | ||||||||
\(722\) | 2.39827 | 0.0892545 | ||||||||
\(723\) | 2.75896 | 0.102607 | ||||||||
\(724\) | −1.74853 | −0.0649837 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −19.7396 | −0.732605 | ||||||||
\(727\) | 17.5138 | 0.649552 | 0.324776 | − | 0.945791i | \(-0.394711\pi\) | ||||
0.324776 | + | 0.945791i | \(0.394711\pi\) | |||||||
\(728\) | 1.02762 | 0.0380860 | ||||||||
\(729\) | −44.0314 | −1.63079 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 55.3550 | 2.04738 | ||||||||
\(732\) | −0.584795 | −0.0216147 | ||||||||
\(733\) | −50.4547 | −1.86359 | −0.931794 | − | 0.362987i | \(-0.881757\pi\) | ||||
−0.931794 | + | 0.362987i | \(0.881757\pi\) | |||||||
\(734\) | −42.1480 | −1.55571 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.668030 | 0.0246239 | ||||||||
\(737\) | 22.4637 | 0.827461 | ||||||||
\(738\) | 19.5833 | 0.720870 | ||||||||
\(739\) | −25.6051 | −0.941898 | −0.470949 | − | 0.882160i | \(-0.656088\pi\) | ||||
−0.470949 | + | 0.882160i | \(0.656088\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.59087 | −0.0951778 | ||||||||
\(742\) | −34.3592 | −1.26137 | ||||||||
\(743\) | −22.6764 | −0.831916 | −0.415958 | − | 0.909384i | \(-0.636554\pi\) | ||||
−0.415958 | + | 0.909384i | \(0.636554\pi\) | |||||||
\(744\) | −11.6887 | −0.428527 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 47.7480 | 1.74818 | ||||||||
\(747\) | 36.9651 | 1.35248 | ||||||||
\(748\) | −1.11570 | −0.0407939 | ||||||||
\(749\) | −14.9575 | −0.546535 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22.5865 | 0.824192 | 0.412096 | − | 0.911140i | \(-0.364797\pi\) | ||||
0.412096 | + | 0.911140i | \(0.364797\pi\) | |||||||
\(752\) | −31.2651 | −1.14012 | ||||||||
\(753\) | −14.2865 | −0.520630 | ||||||||
\(754\) | 0.0480536 | 0.00175001 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −0.609719 | −0.0221753 | ||||||||
\(757\) | 9.50982 | 0.345640 | 0.172820 | − | 0.984953i | \(-0.444712\pi\) | ||||
0.172820 | + | 0.984953i | \(0.444712\pi\) | |||||||
\(758\) | −34.8611 | −1.26621 | ||||||||
\(759\) | 9.62757 | 0.349459 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 21.2805 | 0.771417 | 0.385708 | − | 0.922621i | \(-0.373957\pi\) | ||||
0.385708 | + | 0.922621i | \(0.373957\pi\) | |||||||
\(762\) | 47.1802 | 1.70916 | ||||||||
\(763\) | −2.70452 | −0.0979102 | ||||||||
\(764\) | −0.493832 | −0.0178662 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −54.8439 | −1.98159 | ||||||||
\(767\) | 1.06125 | 0.0383195 | ||||||||
\(768\) | −5.50260 | −0.198558 | ||||||||
\(769\) | −4.82925 | −0.174147 | −0.0870736 | − | 0.996202i | \(-0.527752\pi\) | ||||
−0.0870736 | + | 0.996202i | \(0.527752\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −77.6841 | −2.79773 | ||||||||
\(772\) | 0.521177 | 0.0187576 | ||||||||
\(773\) | −35.0577 | −1.26094 | −0.630468 | − | 0.776215i | \(-0.717137\pi\) | ||||
−0.630468 | + | 0.776215i | \(0.717137\pi\) | |||||||
\(774\) | −67.5828 | −2.42921 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −33.1416 | −1.18971 | ||||||||
\(777\) | −50.7853 | −1.82191 | ||||||||
\(778\) | −44.4188 | −1.59249 | ||||||||
\(779\) | −12.2502 | −0.438908 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −36.7311 | −1.31434 | ||||||||
\(782\) | −11.1708 | −0.399467 | ||||||||
\(783\) | 0.656505 | 0.0234616 | ||||||||
\(784\) | 17.8334 | 0.636906 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −30.5573 | −1.08994 | ||||||||
\(787\) | 6.28899 | 0.224178 | 0.112089 | − | 0.993698i | \(-0.464246\pi\) | ||||
0.112089 | + | 0.993698i | \(0.464246\pi\) | |||||||
\(788\) | 0.309114 | 0.0110117 | ||||||||
\(789\) | 31.1884 | 1.11034 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 23.5228 | 0.836376 | ||||||||
\(792\) | −31.3646 | −1.11449 | ||||||||
\(793\) | 0.574248 | 0.0203921 | ||||||||
\(794\) | −48.1242 | −1.70786 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.43234 | 0.0507681 | ||||||||
\(797\) | 49.4271 | 1.75080 | 0.875400 | − | 0.483400i | \(-0.160598\pi\) | ||||
0.875400 | + | 0.483400i | \(0.160598\pi\) | |||||||
\(798\) | 27.3099 | 0.966759 | ||||||||
\(799\) | 40.9808 | 1.44980 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 67.8574 | 2.39762 | ||||||||
\(802\) | −36.5313 | −1.28996 | ||||||||
\(803\) | 13.6282 | 0.480929 | ||||||||
\(804\) | 2.09873 | 0.0740164 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.498479 | −0.0175582 | ||||||||
\(807\) | 48.8894 | 1.72099 | ||||||||
\(808\) | −47.9586 | −1.68718 | ||||||||
\(809\) | 55.5426 | 1.95277 | 0.976386 | − | 0.216031i | \(-0.0693113\pi\) | ||||
0.976386 | + | 0.216031i | \(0.0693113\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −49.9380 | −1.75356 | −0.876781 | − | 0.480890i | \(-0.840314\pi\) | ||||
−0.876781 | + | 0.480890i | \(0.840314\pi\) | |||||||
\(812\) | −0.0202402 | −0.000710290 0 | ||||||||
\(813\) | −17.7817 | −0.623633 | ||||||||
\(814\) | 39.6540 | 1.38987 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 62.5693 | 2.19036 | ||||||||
\(817\) | 42.2759 | 1.47905 | ||||||||
\(818\) | −41.2439 | −1.44206 | ||||||||
\(819\) | 1.71306 | 0.0598590 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.33524 | −0.221101 | −0.110551 | − | 0.993870i | \(-0.535261\pi\) | ||||
−0.110551 | + | 0.993870i | \(0.535261\pi\) | |||||||
\(822\) | −29.3503 | −1.02371 | ||||||||
\(823\) | 46.0306 | 1.60453 | 0.802263 | − | 0.596971i | \(-0.203629\pi\) | ||||
0.802263 | + | 0.596971i | \(0.203629\pi\) | |||||||
\(824\) | 2.16139 | 0.0752957 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −11.1864 | −0.389226 | ||||||||
\(827\) | −25.5389 | −0.888073 | −0.444037 | − | 0.896009i | \(-0.646454\pi\) | ||||
−0.444037 | + | 0.896009i | \(0.646454\pi\) | |||||||
\(828\) | 0.544975 | 0.0189392 | ||||||||
\(829\) | −27.6145 | −0.959093 | −0.479546 | − | 0.877517i | \(-0.659199\pi\) | ||||
−0.479546 | + | 0.877517i | \(0.659199\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 66.1402 | 2.29438 | ||||||||
\(832\) | 1.72298 | 0.0597337 | ||||||||
\(833\) | −23.3751 | −0.809900 | ||||||||
\(834\) | −22.3570 | −0.774161 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −0.852084 | −0.0294700 | ||||||||
\(837\) | −6.81019 | −0.235395 | ||||||||
\(838\) | −58.8733 | −2.03375 | ||||||||
\(839\) | 11.9619 | 0.412972 | 0.206486 | − | 0.978450i | \(-0.433797\pi\) | ||||
0.206486 | + | 0.978450i | \(0.433797\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9782 | −0.999249 | ||||||||
\(842\) | −4.84886 | −0.167103 | ||||||||
\(843\) | 80.9449 | 2.78789 | ||||||||
\(844\) | 0.351816 | 0.0121100 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −50.0334 | −1.72019 | ||||||||
\(847\) | −8.16436 | −0.280531 | ||||||||
\(848\) | −60.1203 | −2.06454 | ||||||||
\(849\) | 43.0830 | 1.47861 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 15.8649 | 0.543843 | ||||||||
\(852\) | −3.43170 | −0.117568 | ||||||||
\(853\) | −18.4156 | −0.630539 | −0.315269 | − | 0.949002i | \(-0.602095\pi\) | ||||
−0.315269 | + | 0.949002i | \(0.602095\pi\) | |||||||
\(854\) | −6.05305 | −0.207131 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −25.1245 | −0.858737 | ||||||||
\(857\) | 22.3682 | 0.764083 | 0.382041 | − | 0.924145i | \(-0.375221\pi\) | ||||
0.382041 | + | 0.924145i | \(0.375221\pi\) | |||||||
\(858\) | −2.20768 | −0.0753688 | ||||||||
\(859\) | −41.6353 | −1.42058 | −0.710288 | − | 0.703911i | \(-0.751435\pi\) | ||||
−0.710288 | + | 0.703911i | \(0.751435\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 13.3685 | 0.455597 | ||||||||
\(862\) | −7.03069 | −0.239466 | ||||||||
\(863\) | 40.0019 | 1.36168 | 0.680840 | − | 0.732432i | \(-0.261615\pi\) | ||||
0.680840 | + | 0.732432i | \(0.261615\pi\) | |||||||
\(864\) | −2.09280 | −0.0711984 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 18.2924 | 0.621600 | ||||||||
\(867\) | −35.1105 | −1.19241 | ||||||||
\(868\) | 0.209959 | 0.00712648 | ||||||||
\(869\) | −37.4192 | −1.26936 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.06087 | −0.0698300 | ||||||||
\(872\) | −4.54285 | −0.153840 | ||||||||
\(873\) | −55.2477 | −1.86985 | ||||||||
\(874\) | −8.53140 | −0.288579 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.27325 | 0.0430190 | ||||||||
\(877\) | −1.09857 | −0.0370960 | −0.0185480 | − | 0.999828i | \(-0.505904\pi\) | ||||
−0.0185480 | + | 0.999828i | \(0.505904\pi\) | |||||||
\(878\) | −14.2361 | −0.480445 | ||||||||
\(879\) | −16.7126 | −0.563703 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.25152 | 0.109546 | 0.0547732 | − | 0.998499i | \(-0.482556\pi\) | ||||
0.0547732 | + | 0.998499i | \(0.482556\pi\) | |||||||
\(882\) | 28.5386 | 0.960946 | ||||||||
\(883\) | 24.8297 | 0.835588 | 0.417794 | − | 0.908542i | \(-0.362803\pi\) | ||||
0.417794 | + | 0.908542i | \(0.362803\pi\) | |||||||
\(884\) | 0.102357 | 0.00344263 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −32.4448 | −1.09001 | ||||||||
\(887\) | 18.7378 | 0.629155 | 0.314577 | − | 0.949232i | \(-0.398137\pi\) | ||||
0.314577 | + | 0.949232i | \(0.398137\pi\) | |||||||
\(888\) | −85.3051 | −2.86265 | ||||||||
\(889\) | 19.5139 | 0.654474 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.85020 | 0.128987 | ||||||||
\(892\) | −0.0634146 | −0.00212328 | ||||||||
\(893\) | 31.2980 | 1.04735 | ||||||||
\(894\) | −1.05416 | −0.0352565 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −19.7119 | −0.658527 | ||||||||
\(897\) | −0.883256 | −0.0294911 | ||||||||
\(898\) | −43.2310 | −1.44264 | ||||||||
\(899\) | −0.226070 | −0.00753987 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 78.8028 | 2.62530 | ||||||||
\(902\) | −10.4384 | −0.347560 | ||||||||
\(903\) | −46.1354 | −1.53529 | ||||||||
\(904\) | 39.5119 | 1.31414 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −4.61630 | −0.153366 | ||||||||
\(907\) | −2.97151 | −0.0986675 | −0.0493337 | − | 0.998782i | \(-0.515710\pi\) | ||||
−0.0493337 | + | 0.998782i | \(0.515710\pi\) | |||||||
\(908\) | −0.575681 | −0.0191047 | ||||||||
\(909\) | −79.9478 | −2.65170 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.36696 | 0.0452893 | 0.0226447 | − | 0.999744i | \(-0.492791\pi\) | ||||
0.0226447 | + | 0.999744i | \(0.492791\pi\) | |||||||
\(912\) | 47.7856 | 1.58234 | ||||||||
\(913\) | −19.7033 | −0.652084 | ||||||||
\(914\) | 17.8658 | 0.590950 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.153428 | 0.00506940 | ||||||||
\(917\) | −12.6386 | −0.417363 | ||||||||
\(918\) | 34.9957 | 1.15503 | ||||||||
\(919\) | −30.7514 | −1.01440 | −0.507198 | − | 0.861830i | \(-0.669319\pi\) | ||||
−0.507198 | + | 0.861830i | \(0.669319\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 43.0706 | 1.41922 | ||||||||
\(922\) | 37.2027 | 1.22521 | ||||||||
\(923\) | 3.36980 | 0.110918 | ||||||||
\(924\) | 0.929872 | 0.0305905 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −4.40351 | −0.144708 | ||||||||
\(927\) | 3.60308 | 0.118341 | ||||||||
\(928\) | −0.0694722 | −0.00228054 | ||||||||
\(929\) | 20.7909 | 0.682126 | 0.341063 | − | 0.940040i | \(-0.389213\pi\) | ||||
0.341063 | + | 0.940040i | \(0.389213\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −17.8521 | −0.585080 | ||||||||
\(932\) | 2.07569 | 0.0679916 | ||||||||
\(933\) | 7.66608 | 0.250976 | ||||||||
\(934\) | −15.7200 | −0.514375 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.87746 | 0.0940527 | ||||||||
\(937\) | 28.3485 | 0.926105 | 0.463052 | − | 0.886331i | \(-0.346754\pi\) | ||||
0.463052 | + | 0.886331i | \(0.346754\pi\) | |||||||
\(938\) | 21.7233 | 0.709291 | ||||||||
\(939\) | 31.1456 | 1.01640 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −24.4494 | −0.797028 | −0.398514 | − | 0.917162i | \(-0.630474\pi\) | ||||
−0.398514 | + | 0.917162i | \(0.630474\pi\) | |||||||
\(942\) | 27.0871 | 0.882544 | ||||||||
\(943\) | −4.17622 | −0.135997 | ||||||||
\(944\) | −19.5735 | −0.637065 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 36.0233 | 1.17122 | ||||||||
\(947\) | 41.9342 | 1.36268 | 0.681340 | − | 0.731967i | \(-0.261398\pi\) | ||||
0.681340 | + | 0.731967i | \(0.261398\pi\) | |||||||
\(948\) | −3.49598 | −0.113544 | ||||||||
\(949\) | −1.25028 | −0.0405859 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 79.7296 | 2.58541 | ||||||||
\(952\) | 24.8430 | 0.805167 | ||||||||
\(953\) | −14.0181 | −0.454091 | −0.227045 | − | 0.973884i | \(-0.572907\pi\) | ||||
−0.227045 | + | 0.973884i | \(0.572907\pi\) | |||||||
\(954\) | −96.2103 | −3.11492 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −0.508966 | −0.0164611 | ||||||||
\(957\) | −1.00123 | −0.0323650 | ||||||||
\(958\) | 35.6588 | 1.15209 | ||||||||
\(959\) | −12.1394 | −0.392001 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.6549 | −0.924351 | ||||||||
\(962\) | −3.63796 | −0.117292 | ||||||||
\(963\) | −41.8830 | −1.34966 | ||||||||
\(964\) | −0.0832441 | −0.00268111 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 9.31025 | 0.299552 | ||||||||
\(967\) | −17.3691 | −0.558551 | −0.279276 | − | 0.960211i | \(-0.590094\pi\) | ||||
−0.279276 | + | 0.960211i | \(0.590094\pi\) | |||||||
\(968\) | −13.7139 | −0.440780 | ||||||||
\(969\) | −62.6352 | −2.01213 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 46.9881 | 1.50792 | 0.753961 | − | 0.656920i | \(-0.228141\pi\) | ||||
0.753961 | + | 0.656920i | \(0.228141\pi\) | |||||||
\(972\) | 1.47030 | 0.0471598 | ||||||||
\(973\) | −9.24693 | −0.296443 | ||||||||
\(974\) | −21.1424 | −0.677448 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −10.5914 | −0.339021 | ||||||||
\(977\) | 16.7488 | 0.535843 | 0.267921 | − | 0.963441i | \(-0.413663\pi\) | ||||
0.267921 | + | 0.963441i | \(0.413663\pi\) | |||||||
\(978\) | −3.48339 | −0.111386 | ||||||||
\(979\) | −36.1697 | −1.15599 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.57301 | −0.241788 | ||||||||
\(982\) | −43.9685 | −1.40309 | ||||||||
\(983\) | 6.05195 | 0.193027 | 0.0965136 | − | 0.995332i | \(-0.469231\pi\) | ||||
0.0965136 | + | 0.995332i | \(0.469231\pi\) | |||||||
\(984\) | 22.4554 | 0.715851 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1.16171 | 0.0369965 | ||||||||
\(987\) | −34.1553 | −1.08717 | ||||||||
\(988\) | 0.0781722 | 0.00248699 | ||||||||
\(989\) | 14.4124 | 0.458286 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18.5883 | −0.590476 | −0.295238 | − | 0.955424i | \(-0.595399\pi\) | ||||
−0.295238 | + | 0.955424i | \(0.595399\pi\) | |||||||
\(992\) | 0.720663 | 0.0228811 | ||||||||
\(993\) | −29.4747 | −0.935353 | ||||||||
\(994\) | −35.5205 | −1.12664 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1.84083 | −0.0583289 | ||||||||
\(997\) | 28.6039 | 0.905894 | 0.452947 | − | 0.891537i | \(-0.350373\pi\) | ||||
0.452947 | + | 0.891537i | \(0.350373\pi\) | |||||||
\(998\) | −22.6856 | −0.718101 | ||||||||
\(999\) | −49.7015 | −1.57249 |
(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 | 6025.2.a.o.1.8 | yes | 40 | |
5.4 | even | 2 | 6025.2.a.l.1.33 | ✓ | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6025.2.a.l.1.33 | ✓ | 40 | 5.4 | even | 2 | ||
6025.2.a.o.1.8 | yes | 40 | 1.1 | even | 1 | trivial |