Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8003,2,Mod(1,8003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8003, 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("8003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8003 = 53 \cdot 151 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8003.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: | \(63.9042767376\) |
Analytic rank: | \(1\) |
Dimension: | \(153\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Character | \(\chi\) | \(=\) | 8003.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.71996 | −1.92330 | −0.961651 | − | 0.274276i | \(-0.911562\pi\) | ||||
−0.961651 | + | 0.274276i | \(0.911562\pi\) | |||||||
\(3\) | −3.40952 | −1.96848 | −0.984242 | − | 0.176824i | \(-0.943418\pi\) | ||||
−0.984242 | + | 0.176824i | \(0.943418\pi\) | |||||||
\(4\) | 5.39818 | 2.69909 | ||||||||
\(5\) | 0.859174 | 0.384234 | 0.192117 | − | 0.981372i | \(-0.438465\pi\) | ||||
0.192117 | + | 0.981372i | \(0.438465\pi\) | |||||||
\(6\) | 9.27375 | 3.78599 | ||||||||
\(7\) | 3.37109 | 1.27415 | 0.637077 | − | 0.770800i | \(-0.280143\pi\) | ||||
0.637077 | + | 0.770800i | \(0.280143\pi\) | |||||||
\(8\) | −9.24292 | −3.26787 | ||||||||
\(9\) | 8.62480 | 2.87493 | ||||||||
\(10\) | −2.33692 | −0.738998 | ||||||||
\(11\) | 2.40541 | 0.725258 | 0.362629 | − | 0.931934i | \(-0.381879\pi\) | ||||
0.362629 | + | 0.931934i | \(0.381879\pi\) | |||||||
\(12\) | −18.4052 | −5.31312 | ||||||||
\(13\) | −3.48432 | −0.966376 | −0.483188 | − | 0.875517i | \(-0.660521\pi\) | ||||
−0.483188 | + | 0.875517i | \(0.660521\pi\) | |||||||
\(14\) | −9.16924 | −2.45058 | ||||||||
\(15\) | −2.92937 | −0.756359 | ||||||||
\(16\) | 14.3440 | 3.58600 | ||||||||
\(17\) | 0.684330 | 0.165974 | 0.0829872 | − | 0.996551i | \(-0.473554\pi\) | ||||
0.0829872 | + | 0.996551i | \(0.473554\pi\) | |||||||
\(18\) | −23.4591 | −5.52937 | ||||||||
\(19\) | −7.35748 | −1.68792 | −0.843960 | − | 0.536406i | \(-0.819782\pi\) | ||||
−0.843960 | + | 0.536406i | \(0.819782\pi\) | |||||||
\(20\) | 4.63798 | 1.03708 | ||||||||
\(21\) | −11.4938 | −2.50815 | ||||||||
\(22\) | −6.54262 | −1.39489 | ||||||||
\(23\) | −0.186673 | −0.0389240 | −0.0194620 | − | 0.999811i | \(-0.506195\pi\) | ||||
−0.0194620 | + | 0.999811i | \(0.506195\pi\) | |||||||
\(24\) | 31.5139 | 6.43275 | ||||||||
\(25\) | −4.26182 | −0.852364 | ||||||||
\(26\) | 9.47721 | 1.85863 | ||||||||
\(27\) | −19.1778 | −3.69078 | ||||||||
\(28\) | 18.1978 | 3.43906 | ||||||||
\(29\) | 1.47872 | 0.274591 | 0.137295 | − | 0.990530i | \(-0.456159\pi\) | ||||
0.137295 | + | 0.990530i | \(0.456159\pi\) | |||||||
\(30\) | 7.96776 | 1.45471 | ||||||||
\(31\) | 7.64661 | 1.37337 | 0.686686 | − | 0.726954i | \(-0.259065\pi\) | ||||
0.686686 | + | 0.726954i | \(0.259065\pi\) | |||||||
\(32\) | −20.5293 | −3.62910 | ||||||||
\(33\) | −8.20128 | −1.42766 | ||||||||
\(34\) | −1.86135 | −0.319219 | ||||||||
\(35\) | 2.89636 | 0.489574 | ||||||||
\(36\) | 46.5582 | 7.75971 | ||||||||
\(37\) | 3.39270 | 0.557757 | 0.278878 | − | 0.960326i | \(-0.410037\pi\) | ||||
0.278878 | + | 0.960326i | \(0.410037\pi\) | |||||||
\(38\) | 20.0120 | 3.24638 | ||||||||
\(39\) | 11.8798 | 1.90230 | ||||||||
\(40\) | −7.94128 | −1.25563 | ||||||||
\(41\) | 3.74770 | 0.585293 | 0.292646 | − | 0.956221i | \(-0.405464\pi\) | ||||
0.292646 | + | 0.956221i | \(0.405464\pi\) | |||||||
\(42\) | 31.2627 | 4.82394 | ||||||||
\(43\) | 5.35095 | 0.816012 | 0.408006 | − | 0.912979i | \(-0.366224\pi\) | ||||
0.408006 | + | 0.912979i | \(0.366224\pi\) | |||||||
\(44\) | 12.9848 | 1.95754 | ||||||||
\(45\) | 7.41020 | 1.10465 | ||||||||
\(46\) | 0.507743 | 0.0748626 | ||||||||
\(47\) | 5.09621 | 0.743359 | 0.371680 | − | 0.928361i | \(-0.378782\pi\) | ||||
0.371680 | + | 0.928361i | \(0.378782\pi\) | |||||||
\(48\) | −48.9061 | −7.05899 | ||||||||
\(49\) | 4.36428 | 0.623468 | ||||||||
\(50\) | 11.5920 | 1.63935 | ||||||||
\(51\) | −2.33323 | −0.326718 | ||||||||
\(52\) | −18.8090 | −2.60834 | ||||||||
\(53\) | −1.00000 | −0.137361 | ||||||||
\(54\) | 52.1630 | 7.09848 | ||||||||
\(55\) | 2.06666 | 0.278669 | ||||||||
\(56\) | −31.1588 | −4.16376 | ||||||||
\(57\) | 25.0854 | 3.32265 | ||||||||
\(58\) | −4.02205 | −0.528121 | ||||||||
\(59\) | −11.9157 | −1.55130 | −0.775648 | − | 0.631165i | \(-0.782577\pi\) | ||||
−0.775648 | + | 0.631165i | \(0.782577\pi\) | |||||||
\(60\) | −15.8133 | −2.04148 | ||||||||
\(61\) | −10.5630 | −1.35246 | −0.676228 | − | 0.736693i | \(-0.736386\pi\) | ||||
−0.676228 | + | 0.736693i | \(0.736386\pi\) | |||||||
\(62\) | −20.7985 | −2.64141 | ||||||||
\(63\) | 29.0750 | 3.66311 | ||||||||
\(64\) | 27.1508 | 3.39386 | ||||||||
\(65\) | −2.99363 | −0.371315 | ||||||||
\(66\) | 22.3072 | 2.74582 | ||||||||
\(67\) | −15.1682 | −1.85309 | −0.926545 | − | 0.376184i | \(-0.877236\pi\) | ||||
−0.926545 | + | 0.376184i | \(0.877236\pi\) | |||||||
\(68\) | 3.69414 | 0.447980 | ||||||||
\(69\) | 0.636464 | 0.0766213 | ||||||||
\(70\) | −7.87797 | −0.941598 | ||||||||
\(71\) | 7.11200 | 0.844039 | 0.422019 | − | 0.906587i | \(-0.361321\pi\) | ||||
0.422019 | + | 0.906587i | \(0.361321\pi\) | |||||||
\(72\) | −79.7183 | −9.39490 | ||||||||
\(73\) | −0.544635 | −0.0637448 | −0.0318724 | − | 0.999492i | \(-0.510147\pi\) | ||||
−0.0318724 | + | 0.999492i | \(0.510147\pi\) | |||||||
\(74\) | −9.22801 | −1.07273 | ||||||||
\(75\) | 14.5307 | 1.67787 | ||||||||
\(76\) | −39.7170 | −4.55585 | ||||||||
\(77\) | 8.10886 | 0.924090 | ||||||||
\(78\) | −32.3127 | −3.65869 | ||||||||
\(79\) | 14.5016 | 1.63155 | 0.815777 | − | 0.578366i | \(-0.196309\pi\) | ||||
0.815777 | + | 0.578366i | \(0.196309\pi\) | |||||||
\(80\) | 12.3240 | 1.37786 | ||||||||
\(81\) | 39.5128 | 4.39031 | ||||||||
\(82\) | −10.1936 | −1.12569 | ||||||||
\(83\) | 4.02419 | 0.441712 | 0.220856 | − | 0.975306i | \(-0.429115\pi\) | ||||
0.220856 | + | 0.975306i | \(0.429115\pi\) | |||||||
\(84\) | −62.0456 | −6.76973 | ||||||||
\(85\) | 0.587959 | 0.0637731 | ||||||||
\(86\) | −14.5544 | −1.56944 | ||||||||
\(87\) | −5.04170 | −0.540527 | ||||||||
\(88\) | −22.2330 | −2.37005 | ||||||||
\(89\) | 4.74919 | 0.503413 | 0.251707 | − | 0.967804i | \(-0.419008\pi\) | ||||
0.251707 | + | 0.967804i | \(0.419008\pi\) | |||||||
\(90\) | −20.1555 | −2.12457 | ||||||||
\(91\) | −11.7460 | −1.23131 | ||||||||
\(92\) | −1.00769 | −0.105059 | ||||||||
\(93\) | −26.0712 | −2.70346 | ||||||||
\(94\) | −13.8615 | −1.42970 | ||||||||
\(95\) | −6.32135 | −0.648557 | ||||||||
\(96\) | 69.9950 | 7.14383 | ||||||||
\(97\) | −8.94108 | −0.907829 | −0.453915 | − | 0.891045i | \(-0.649973\pi\) | ||||
−0.453915 | + | 0.891045i | \(0.649973\pi\) | |||||||
\(98\) | −11.8707 | −1.19912 | ||||||||
\(99\) | 20.7462 | 2.08507 | ||||||||
\(100\) | −23.0061 | −2.30061 | ||||||||
\(101\) | 16.0576 | 1.59779 | 0.798895 | − | 0.601470i | \(-0.205418\pi\) | ||||
0.798895 | + | 0.601470i | \(0.205418\pi\) | |||||||
\(102\) | 6.34631 | 0.628378 | ||||||||
\(103\) | −12.7114 | −1.25249 | −0.626246 | − | 0.779625i | \(-0.715410\pi\) | ||||
−0.626246 | + | 0.779625i | \(0.715410\pi\) | |||||||
\(104\) | 32.2053 | 3.15799 | ||||||||
\(105\) | −9.87517 | −0.963718 | ||||||||
\(106\) | 2.71996 | 0.264186 | ||||||||
\(107\) | −4.49200 | −0.434258 | −0.217129 | − | 0.976143i | \(-0.569669\pi\) | ||||
−0.217129 | + | 0.976143i | \(0.569669\pi\) | |||||||
\(108\) | −103.525 | −9.96175 | ||||||||
\(109\) | −6.19932 | −0.593787 | −0.296894 | − | 0.954911i | \(-0.595951\pi\) | ||||
−0.296894 | + | 0.954911i | \(0.595951\pi\) | |||||||
\(110\) | −5.62124 | −0.535965 | ||||||||
\(111\) | −11.5675 | −1.09794 | ||||||||
\(112\) | 48.3550 | 4.56912 | ||||||||
\(113\) | 0.212688 | 0.0200080 | 0.0100040 | − | 0.999950i | \(-0.496816\pi\) | ||||
0.0100040 | + | 0.999950i | \(0.496816\pi\) | |||||||
\(114\) | −68.2314 | −6.39045 | ||||||||
\(115\) | −0.160384 | −0.0149559 | ||||||||
\(116\) | 7.98238 | 0.741145 | ||||||||
\(117\) | −30.0515 | −2.77827 | ||||||||
\(118\) | 32.4103 | 2.98361 | ||||||||
\(119\) | 2.30694 | 0.211477 | ||||||||
\(120\) | 27.0759 | 2.47168 | ||||||||
\(121\) | −5.21401 | −0.474001 | ||||||||
\(122\) | 28.7310 | 2.60118 | ||||||||
\(123\) | −12.7778 | −1.15214 | ||||||||
\(124\) | 41.2778 | 3.70686 | ||||||||
\(125\) | −7.95751 | −0.711742 | ||||||||
\(126\) | −79.0829 | −7.04526 | ||||||||
\(127\) | −9.46172 | −0.839591 | −0.419796 | − | 0.907619i | \(-0.637898\pi\) | ||||
−0.419796 | + | 0.907619i | \(0.637898\pi\) | |||||||
\(128\) | −32.7906 | −2.89831 | ||||||||
\(129\) | −18.2442 | −1.60631 | ||||||||
\(130\) | 8.14257 | 0.714150 | ||||||||
\(131\) | 6.65768 | 0.581684 | 0.290842 | − | 0.956771i | \(-0.406065\pi\) | ||||
0.290842 | + | 0.956771i | \(0.406065\pi\) | |||||||
\(132\) | −44.2720 | −3.85338 | ||||||||
\(133\) | −24.8027 | −2.15067 | ||||||||
\(134\) | 41.2569 | 3.56405 | ||||||||
\(135\) | −16.4771 | −1.41812 | ||||||||
\(136\) | −6.32521 | −0.542382 | ||||||||
\(137\) | −8.51114 | −0.727155 | −0.363578 | − | 0.931564i | \(-0.618445\pi\) | ||||
−0.363578 | + | 0.931564i | \(0.618445\pi\) | |||||||
\(138\) | −1.73116 | −0.147366 | ||||||||
\(139\) | 6.61698 | 0.561245 | 0.280622 | − | 0.959818i | \(-0.409459\pi\) | ||||
0.280622 | + | 0.959818i | \(0.409459\pi\) | |||||||
\(140\) | 15.6351 | 1.32140 | ||||||||
\(141\) | −17.3756 | −1.46329 | ||||||||
\(142\) | −19.3443 | −1.62334 | ||||||||
\(143\) | −8.38121 | −0.700872 | ||||||||
\(144\) | 123.714 | 10.3095 | ||||||||
\(145\) | 1.27047 | 0.105507 | ||||||||
\(146\) | 1.48139 | 0.122600 | ||||||||
\(147\) | −14.8801 | −1.22729 | ||||||||
\(148\) | 18.3144 | 1.50544 | ||||||||
\(149\) | −6.99588 | −0.573125 | −0.286562 | − | 0.958062i | \(-0.592513\pi\) | ||||
−0.286562 | + | 0.958062i | \(0.592513\pi\) | |||||||
\(150\) | −39.5230 | −3.22704 | ||||||||
\(151\) | −1.00000 | −0.0813788 | ||||||||
\(152\) | 68.0046 | 5.51590 | ||||||||
\(153\) | 5.90221 | 0.477165 | ||||||||
\(154\) | −22.0558 | −1.77731 | ||||||||
\(155\) | 6.56977 | 0.527697 | ||||||||
\(156\) | 64.1295 | 5.13447 | ||||||||
\(157\) | 3.66105 | 0.292184 | 0.146092 | − | 0.989271i | \(-0.453331\pi\) | ||||
0.146092 | + | 0.989271i | \(0.453331\pi\) | |||||||
\(158\) | −39.4437 | −3.13797 | ||||||||
\(159\) | 3.40952 | 0.270392 | ||||||||
\(160\) | −17.6382 | −1.39442 | ||||||||
\(161\) | −0.629292 | −0.0495951 | ||||||||
\(162\) | −107.473 | −8.44389 | ||||||||
\(163\) | 5.11931 | 0.400975 | 0.200488 | − | 0.979696i | \(-0.435747\pi\) | ||||
0.200488 | + | 0.979696i | \(0.435747\pi\) | |||||||
\(164\) | 20.2308 | 1.57976 | ||||||||
\(165\) | −7.04632 | −0.548556 | ||||||||
\(166\) | −10.9456 | −0.849546 | ||||||||
\(167\) | −17.3096 | −1.33946 | −0.669729 | − | 0.742605i | \(-0.733590\pi\) | ||||
−0.669729 | + | 0.742605i | \(0.733590\pi\) | |||||||
\(168\) | 106.236 | 8.19631 | ||||||||
\(169\) | −0.859528 | −0.0661175 | ||||||||
\(170\) | −1.59922 | −0.122655 | ||||||||
\(171\) | −63.4568 | −4.85266 | ||||||||
\(172\) | 28.8854 | 2.20249 | ||||||||
\(173\) | 23.0478 | 1.75229 | 0.876147 | − | 0.482044i | \(-0.160106\pi\) | ||||
0.876147 | + | 0.482044i | \(0.160106\pi\) | |||||||
\(174\) | 13.7132 | 1.03960 | ||||||||
\(175\) | −14.3670 | −1.08604 | ||||||||
\(176\) | 34.5032 | 2.60078 | ||||||||
\(177\) | 40.6269 | 3.05370 | ||||||||
\(178\) | −12.9176 | −0.968216 | ||||||||
\(179\) | 13.1705 | 0.984411 | 0.492206 | − | 0.870479i | \(-0.336191\pi\) | ||||
0.492206 | + | 0.870479i | \(0.336191\pi\) | |||||||
\(180\) | 40.0016 | 2.98154 | ||||||||
\(181\) | −10.6927 | −0.794784 | −0.397392 | − | 0.917649i | \(-0.630085\pi\) | ||||
−0.397392 | + | 0.917649i | \(0.630085\pi\) | |||||||
\(182\) | 31.9486 | 2.36818 | ||||||||
\(183\) | 36.0148 | 2.66229 | ||||||||
\(184\) | 1.72540 | 0.127198 | ||||||||
\(185\) | 2.91492 | 0.214309 | ||||||||
\(186\) | 70.9128 | 5.19958 | ||||||||
\(187\) | 1.64609 | 0.120374 | ||||||||
\(188\) | 27.5103 | 2.00639 | ||||||||
\(189\) | −64.6503 | −4.70262 | ||||||||
\(190\) | 17.1938 | 1.24737 | ||||||||
\(191\) | 0.269105 | 0.0194718 | 0.00973588 | − | 0.999953i | \(-0.496901\pi\) | ||||
0.00973588 | + | 0.999953i | \(0.496901\pi\) | |||||||
\(192\) | −92.5712 | −6.68075 | ||||||||
\(193\) | −2.96112 | −0.213146 | −0.106573 | − | 0.994305i | \(-0.533988\pi\) | ||||
−0.106573 | + | 0.994305i | \(0.533988\pi\) | |||||||
\(194\) | 24.3194 | 1.74603 | ||||||||
\(195\) | 10.2068 | 0.730927 | ||||||||
\(196\) | 23.5592 | 1.68280 | ||||||||
\(197\) | −18.3527 | −1.30758 | −0.653788 | − | 0.756678i | \(-0.726821\pi\) | ||||
−0.653788 | + | 0.756678i | \(0.726821\pi\) | |||||||
\(198\) | −56.4287 | −4.01022 | ||||||||
\(199\) | 17.5054 | 1.24093 | 0.620463 | − | 0.784236i | \(-0.286945\pi\) | ||||
0.620463 | + | 0.784236i | \(0.286945\pi\) | |||||||
\(200\) | 39.3917 | 2.78541 | ||||||||
\(201\) | 51.7162 | 3.64778 | ||||||||
\(202\) | −43.6760 | −3.07303 | ||||||||
\(203\) | 4.98489 | 0.349871 | ||||||||
\(204\) | −12.5952 | −0.881842 | ||||||||
\(205\) | 3.21993 | 0.224889 | ||||||||
\(206\) | 34.5745 | 2.40892 | ||||||||
\(207\) | −1.61002 | −0.111904 | ||||||||
\(208\) | −49.9791 | −3.46543 | ||||||||
\(209\) | −17.6977 | −1.22418 | ||||||||
\(210\) | 26.8601 | 1.85352 | ||||||||
\(211\) | −9.20183 | −0.633480 | −0.316740 | − | 0.948512i | \(-0.602588\pi\) | ||||
−0.316740 | + | 0.948512i | \(0.602588\pi\) | |||||||
\(212\) | −5.39818 | −0.370749 | ||||||||
\(213\) | −24.2485 | −1.66148 | ||||||||
\(214\) | 12.2181 | 0.835210 | ||||||||
\(215\) | 4.59740 | 0.313540 | ||||||||
\(216\) | 177.259 | 12.0610 | ||||||||
\(217\) | 25.7775 | 1.74989 | ||||||||
\(218\) | 16.8619 | 1.14203 | ||||||||
\(219\) | 1.85694 | 0.125481 | ||||||||
\(220\) | 11.1562 | 0.752153 | ||||||||
\(221\) | −2.38442 | −0.160394 | ||||||||
\(222\) | 31.4631 | 2.11166 | ||||||||
\(223\) | 10.2206 | 0.684424 | 0.342212 | − | 0.939623i | \(-0.388824\pi\) | ||||
0.342212 | + | 0.939623i | \(0.388824\pi\) | |||||||
\(224\) | −69.2062 | −4.62403 | ||||||||
\(225\) | −36.7573 | −2.45049 | ||||||||
\(226\) | −0.578502 | −0.0384814 | ||||||||
\(227\) | 12.0987 | 0.803019 | 0.401510 | − | 0.915855i | \(-0.368486\pi\) | ||||
0.401510 | + | 0.915855i | \(0.368486\pi\) | |||||||
\(228\) | 135.416 | 8.96813 | ||||||||
\(229\) | −15.7994 | −1.04405 | −0.522026 | − | 0.852930i | \(-0.674824\pi\) | ||||
−0.522026 | + | 0.852930i | \(0.674824\pi\) | |||||||
\(230\) | 0.436239 | 0.0287648 | ||||||||
\(231\) | −27.6473 | −1.81906 | ||||||||
\(232\) | −13.6676 | −0.897325 | ||||||||
\(233\) | −12.1921 | −0.798733 | −0.399367 | − | 0.916791i | \(-0.630770\pi\) | ||||
−0.399367 | + | 0.916791i | \(0.630770\pi\) | |||||||
\(234\) | 81.7390 | 5.34345 | ||||||||
\(235\) | 4.37853 | 0.285624 | ||||||||
\(236\) | −64.3233 | −4.18709 | ||||||||
\(237\) | −49.4434 | −3.21169 | ||||||||
\(238\) | −6.27479 | −0.406734 | ||||||||
\(239\) | −22.7224 | −1.46979 | −0.734895 | − | 0.678181i | \(-0.762769\pi\) | ||||
−0.734895 | + | 0.678181i | \(0.762769\pi\) | |||||||
\(240\) | −42.0189 | −2.71231 | ||||||||
\(241\) | −14.2838 | −0.920099 | −0.460050 | − | 0.887893i | \(-0.652168\pi\) | ||||
−0.460050 | + | 0.887893i | \(0.652168\pi\) | |||||||
\(242\) | 14.1819 | 0.911647 | ||||||||
\(243\) | −77.1859 | −4.95148 | ||||||||
\(244\) | −57.0211 | −3.65040 | ||||||||
\(245\) | 3.74967 | 0.239558 | ||||||||
\(246\) | 34.7552 | 2.21591 | ||||||||
\(247\) | 25.6358 | 1.63117 | ||||||||
\(248\) | −70.6770 | −4.48800 | ||||||||
\(249\) | −13.7205 | −0.869504 | ||||||||
\(250\) | 21.6441 | 1.36889 | ||||||||
\(251\) | 7.10158 | 0.448248 | 0.224124 | − | 0.974561i | \(-0.428048\pi\) | ||||
0.224124 | + | 0.974561i | \(0.428048\pi\) | |||||||
\(252\) | 156.952 | 9.88706 | ||||||||
\(253\) | −0.449024 | −0.0282299 | ||||||||
\(254\) | 25.7355 | 1.61479 | ||||||||
\(255\) | −2.00465 | −0.125536 | ||||||||
\(256\) | 34.8875 | 2.18047 | ||||||||
\(257\) | −10.3109 | −0.643177 | −0.321589 | − | 0.946879i | \(-0.604217\pi\) | ||||
−0.321589 | + | 0.946879i | \(0.604217\pi\) | |||||||
\(258\) | 49.6234 | 3.08942 | ||||||||
\(259\) | 11.4371 | 0.710668 | ||||||||
\(260\) | −16.1602 | −1.00221 | ||||||||
\(261\) | 12.7536 | 0.789429 | ||||||||
\(262\) | −18.1086 | −1.11875 | ||||||||
\(263\) | 12.5525 | 0.774020 | 0.387010 | − | 0.922075i | \(-0.373508\pi\) | ||||
0.387010 | + | 0.922075i | \(0.373508\pi\) | |||||||
\(264\) | 75.8038 | 4.66540 | ||||||||
\(265\) | −0.859174 | −0.0527786 | ||||||||
\(266\) | 67.4625 | 4.13639 | ||||||||
\(267\) | −16.1924 | −0.990961 | ||||||||
\(268\) | −81.8807 | −5.00166 | ||||||||
\(269\) | 6.05135 | 0.368957 | 0.184479 | − | 0.982837i | \(-0.440940\pi\) | ||||
0.184479 | + | 0.982837i | \(0.440940\pi\) | |||||||
\(270\) | 44.8170 | 2.72748 | ||||||||
\(271\) | −30.1932 | −1.83411 | −0.917053 | − | 0.398766i | \(-0.869439\pi\) | ||||
−0.917053 | + | 0.398766i | \(0.869439\pi\) | |||||||
\(272\) | 9.81604 | 0.595185 | ||||||||
\(273\) | 40.0481 | 2.42382 | ||||||||
\(274\) | 23.1500 | 1.39854 | ||||||||
\(275\) | −10.2514 | −0.618184 | ||||||||
\(276\) | 3.43575 | 0.206808 | ||||||||
\(277\) | 13.3790 | 0.803869 | 0.401934 | − | 0.915668i | \(-0.368338\pi\) | ||||
0.401934 | + | 0.915668i | \(0.368338\pi\) | |||||||
\(278\) | −17.9979 | −1.07944 | ||||||||
\(279\) | 65.9505 | 3.94835 | ||||||||
\(280\) | −26.7708 | −1.59986 | ||||||||
\(281\) | 7.17552 | 0.428055 | 0.214028 | − | 0.976828i | \(-0.431342\pi\) | ||||
0.214028 | + | 0.976828i | \(0.431342\pi\) | |||||||
\(282\) | 47.2610 | 2.81435 | ||||||||
\(283\) | −3.36337 | −0.199932 | −0.0999658 | − | 0.994991i | \(-0.531873\pi\) | ||||
−0.0999658 | + | 0.994991i | \(0.531873\pi\) | |||||||
\(284\) | 38.3919 | 2.27814 | ||||||||
\(285\) | 21.5527 | 1.27667 | ||||||||
\(286\) | 22.7966 | 1.34799 | ||||||||
\(287\) | 12.6339 | 0.745753 | ||||||||
\(288\) | −177.061 | −10.4334 | ||||||||
\(289\) | −16.5317 | −0.972452 | ||||||||
\(290\) | −3.45564 | −0.202922 | ||||||||
\(291\) | 30.4848 | 1.78705 | ||||||||
\(292\) | −2.94004 | −0.172053 | ||||||||
\(293\) | −19.7736 | −1.15519 | −0.577594 | − | 0.816325i | \(-0.696008\pi\) | ||||
−0.577594 | + | 0.816325i | \(0.696008\pi\) | |||||||
\(294\) | 40.4732 | 2.36045 | ||||||||
\(295\) | −10.2377 | −0.596061 | ||||||||
\(296\) | −31.3585 | −1.82267 | ||||||||
\(297\) | −46.1305 | −2.67677 | ||||||||
\(298\) | 19.0285 | 1.10229 | ||||||||
\(299\) | 0.650427 | 0.0376152 | ||||||||
\(300\) | 78.4396 | 4.52871 | ||||||||
\(301\) | 18.0386 | 1.03973 | ||||||||
\(302\) | 2.71996 | 0.156516 | ||||||||
\(303\) | −54.7486 | −3.14523 | ||||||||
\(304\) | −105.536 | −6.05289 | ||||||||
\(305\) | −9.07546 | −0.519660 | ||||||||
\(306\) | −16.0538 | −0.917733 | ||||||||
\(307\) | 4.42509 | 0.252553 | 0.126277 | − | 0.991995i | \(-0.459697\pi\) | ||||
0.126277 | + | 0.991995i | \(0.459697\pi\) | |||||||
\(308\) | 43.7731 | 2.49420 | ||||||||
\(309\) | 43.3398 | 2.46551 | ||||||||
\(310\) | −17.8695 | −1.01492 | ||||||||
\(311\) | −5.60454 | −0.317804 | −0.158902 | − | 0.987294i | \(-0.550795\pi\) | ||||
−0.158902 | + | 0.987294i | \(0.550795\pi\) | |||||||
\(312\) | −109.804 | −6.21645 | ||||||||
\(313\) | 19.4179 | 1.09757 | 0.548783 | − | 0.835965i | \(-0.315091\pi\) | ||||
0.548783 | + | 0.835965i | \(0.315091\pi\) | |||||||
\(314\) | −9.95791 | −0.561957 | ||||||||
\(315\) | 24.9805 | 1.40749 | ||||||||
\(316\) | 78.2822 | 4.40372 | ||||||||
\(317\) | −17.4569 | −0.980476 | −0.490238 | − | 0.871589i | \(-0.663090\pi\) | ||||
−0.490238 | + | 0.871589i | \(0.663090\pi\) | |||||||
\(318\) | −9.27375 | −0.520046 | ||||||||
\(319\) | 3.55691 | 0.199149 | ||||||||
\(320\) | 23.3273 | 1.30404 | ||||||||
\(321\) | 15.3156 | 0.854831 | ||||||||
\(322\) | 1.71165 | 0.0953864 | ||||||||
\(323\) | −5.03494 | −0.280152 | ||||||||
\(324\) | 213.297 | 11.8498 | ||||||||
\(325\) | 14.8495 | 0.823704 | ||||||||
\(326\) | −13.9243 | −0.771197 | ||||||||
\(327\) | 21.1367 | 1.16886 | ||||||||
\(328\) | −34.6397 | −1.91266 | ||||||||
\(329\) | 17.1798 | 0.947154 | ||||||||
\(330\) | 19.1657 | 1.05504 | ||||||||
\(331\) | 18.2570 | 1.00349 | 0.501746 | − | 0.865015i | \(-0.332691\pi\) | ||||
0.501746 | + | 0.865015i | \(0.332691\pi\) | |||||||
\(332\) | 21.7233 | 1.19222 | ||||||||
\(333\) | 29.2614 | 1.60351 | ||||||||
\(334\) | 47.0815 | 2.57618 | ||||||||
\(335\) | −13.0321 | −0.712020 | ||||||||
\(336\) | −164.867 | −8.99424 | ||||||||
\(337\) | 34.6957 | 1.89000 | 0.944999 | − | 0.327075i | \(-0.106063\pi\) | ||||
0.944999 | + | 0.327075i | \(0.106063\pi\) | |||||||
\(338\) | 2.33788 | 0.127164 | ||||||||
\(339\) | −0.725162 | −0.0393854 | ||||||||
\(340\) | 3.17391 | 0.172129 | ||||||||
\(341\) | 18.3932 | 0.996049 | ||||||||
\(342\) | 172.600 | 9.33313 | ||||||||
\(343\) | −8.88527 | −0.479759 | ||||||||
\(344\) | −49.4584 | −2.66662 | ||||||||
\(345\) | 0.546833 | 0.0294405 | ||||||||
\(346\) | −62.6892 | −3.37019 | ||||||||
\(347\) | −16.4013 | −0.880469 | −0.440235 | − | 0.897883i | \(-0.645105\pi\) | ||||
−0.440235 | + | 0.897883i | \(0.645105\pi\) | |||||||
\(348\) | −27.2160 | −1.45893 | ||||||||
\(349\) | −10.9435 | −0.585794 | −0.292897 | − | 0.956144i | \(-0.594619\pi\) | ||||
−0.292897 | + | 0.956144i | \(0.594619\pi\) | |||||||
\(350\) | 39.0777 | 2.08879 | ||||||||
\(351\) | 66.8217 | 3.56668 | ||||||||
\(352\) | −49.3813 | −2.63203 | ||||||||
\(353\) | −28.0567 | −1.49331 | −0.746655 | − | 0.665212i | \(-0.768341\pi\) | ||||
−0.746655 | + | 0.665212i | \(0.768341\pi\) | |||||||
\(354\) | −110.504 | −5.87320 | ||||||||
\(355\) | 6.11044 | 0.324309 | ||||||||
\(356\) | 25.6370 | 1.35876 | ||||||||
\(357\) | −7.86555 | −0.416289 | ||||||||
\(358\) | −35.8233 | −1.89332 | ||||||||
\(359\) | 35.0882 | 1.85188 | 0.925942 | − | 0.377666i | \(-0.123273\pi\) | ||||
0.925942 | + | 0.377666i | \(0.123273\pi\) | |||||||
\(360\) | −68.4919 | −3.60984 | ||||||||
\(361\) | 35.1324 | 1.84908 | ||||||||
\(362\) | 29.0838 | 1.52861 | ||||||||
\(363\) | 17.7772 | 0.933063 | ||||||||
\(364\) | −63.4069 | −3.32342 | ||||||||
\(365\) | −0.467936 | −0.0244929 | ||||||||
\(366\) | −97.9587 | −5.12038 | ||||||||
\(367\) | −24.1359 | −1.25989 | −0.629943 | − | 0.776641i | \(-0.716922\pi\) | ||||
−0.629943 | + | 0.776641i | \(0.716922\pi\) | |||||||
\(368\) | −2.67764 | −0.139581 | ||||||||
\(369\) | 32.3232 | 1.68268 | ||||||||
\(370\) | −7.92846 | −0.412181 | ||||||||
\(371\) | −3.37109 | −0.175019 | ||||||||
\(372\) | −140.737 | −7.29689 | ||||||||
\(373\) | −17.9290 | −0.928327 | −0.464163 | − | 0.885750i | \(-0.653645\pi\) | ||||
−0.464163 | + | 0.885750i | \(0.653645\pi\) | |||||||
\(374\) | −4.47731 | −0.231516 | ||||||||
\(375\) | 27.1313 | 1.40105 | ||||||||
\(376\) | −47.1039 | −2.42920 | ||||||||
\(377\) | −5.15231 | −0.265358 | ||||||||
\(378\) | 175.846 | 9.04456 | ||||||||
\(379\) | 0.880119 | 0.0452087 | 0.0226043 | − | 0.999744i | \(-0.492804\pi\) | ||||
0.0226043 | + | 0.999744i | \(0.492804\pi\) | |||||||
\(380\) | −34.1238 | −1.75051 | ||||||||
\(381\) | 32.2599 | 1.65272 | ||||||||
\(382\) | −0.731955 | −0.0374501 | ||||||||
\(383\) | 36.2049 | 1.84998 | 0.924992 | − | 0.379986i | \(-0.124071\pi\) | ||||
0.924992 | + | 0.379986i | \(0.124071\pi\) | |||||||
\(384\) | 111.800 | 5.70528 | ||||||||
\(385\) | 6.96692 | 0.355067 | ||||||||
\(386\) | 8.05412 | 0.409944 | ||||||||
\(387\) | 46.1509 | 2.34598 | ||||||||
\(388\) | −48.2656 | −2.45031 | ||||||||
\(389\) | 11.4485 | 0.580462 | 0.290231 | − | 0.956957i | \(-0.406268\pi\) | ||||
0.290231 | + | 0.956957i | \(0.406268\pi\) | |||||||
\(390\) | −27.7622 | −1.40579 | ||||||||
\(391\) | −0.127746 | −0.00646038 | ||||||||
\(392\) | −40.3387 | −2.03741 | ||||||||
\(393\) | −22.6995 | −1.14504 | ||||||||
\(394\) | 49.9186 | 2.51486 | ||||||||
\(395\) | 12.4594 | 0.626899 | ||||||||
\(396\) | 111.992 | 5.62779 | ||||||||
\(397\) | −34.6323 | −1.73815 | −0.869073 | − | 0.494684i | \(-0.835284\pi\) | ||||
−0.869073 | + | 0.494684i | \(0.835284\pi\) | |||||||
\(398\) | −47.6140 | −2.38668 | ||||||||
\(399\) | 84.5654 | 4.23356 | ||||||||
\(400\) | −61.1316 | −3.05658 | ||||||||
\(401\) | 7.81705 | 0.390365 | 0.195182 | − | 0.980767i | \(-0.437470\pi\) | ||||
0.195182 | + | 0.980767i | \(0.437470\pi\) | |||||||
\(402\) | −140.666 | −7.01578 | ||||||||
\(403\) | −26.6432 | −1.32719 | ||||||||
\(404\) | 86.6818 | 4.31258 | ||||||||
\(405\) | 33.9483 | 1.68691 | ||||||||
\(406\) | −13.5587 | −0.672907 | ||||||||
\(407\) | 8.16083 | 0.404517 | ||||||||
\(408\) | 21.5659 | 1.06767 | ||||||||
\(409\) | 0.422897 | 0.0209109 | 0.0104555 | − | 0.999945i | \(-0.496672\pi\) | ||||
0.0104555 | + | 0.999945i | \(0.496672\pi\) | |||||||
\(410\) | −8.75807 | −0.432530 | ||||||||
\(411\) | 29.0189 | 1.43139 | ||||||||
\(412\) | −68.6185 | −3.38059 | ||||||||
\(413\) | −40.1691 | −1.97659 | ||||||||
\(414\) | 4.37918 | 0.215225 | ||||||||
\(415\) | 3.45748 | 0.169721 | ||||||||
\(416\) | 71.5306 | 3.50708 | ||||||||
\(417\) | −22.5607 | −1.10480 | ||||||||
\(418\) | 48.1371 | 2.35446 | ||||||||
\(419\) | 1.67102 | 0.0816349 | 0.0408174 | − | 0.999167i | \(-0.487004\pi\) | ||||
0.0408174 | + | 0.999167i | \(0.487004\pi\) | |||||||
\(420\) | −53.3080 | −2.60116 | ||||||||
\(421\) | −9.20988 | −0.448862 | −0.224431 | − | 0.974490i | \(-0.572052\pi\) | ||||
−0.224431 | + | 0.974490i | \(0.572052\pi\) | |||||||
\(422\) | 25.0286 | 1.21837 | ||||||||
\(423\) | 43.9538 | 2.13711 | ||||||||
\(424\) | 9.24292 | 0.448876 | ||||||||
\(425\) | −2.91649 | −0.141471 | ||||||||
\(426\) | 65.9549 | 3.19552 | ||||||||
\(427\) | −35.6089 | −1.72324 | ||||||||
\(428\) | −24.2486 | −1.17210 | ||||||||
\(429\) | 28.5759 | 1.37966 | ||||||||
\(430\) | −12.5047 | −0.603032 | ||||||||
\(431\) | 36.4356 | 1.75504 | 0.877521 | − | 0.479537i | \(-0.159196\pi\) | ||||
0.877521 | + | 0.479537i | \(0.159196\pi\) | |||||||
\(432\) | −275.087 | −13.2351 | ||||||||
\(433\) | −8.50000 | −0.408484 | −0.204242 | − | 0.978920i | \(-0.565473\pi\) | ||||
−0.204242 | + | 0.978920i | \(0.565473\pi\) | |||||||
\(434\) | −70.1136 | −3.36556 | ||||||||
\(435\) | −4.33170 | −0.207689 | ||||||||
\(436\) | −33.4651 | −1.60269 | ||||||||
\(437\) | 1.37344 | 0.0657006 | ||||||||
\(438\) | −5.05081 | −0.241337 | ||||||||
\(439\) | −22.9377 | −1.09476 | −0.547379 | − | 0.836885i | \(-0.684374\pi\) | ||||
−0.547379 | + | 0.836885i | \(0.684374\pi\) | |||||||
\(440\) | −19.1020 | −0.910653 | ||||||||
\(441\) | 37.6410 | 1.79243 | ||||||||
\(442\) | 6.48554 | 0.308486 | ||||||||
\(443\) | −4.54266 | −0.215829 | −0.107914 | − | 0.994160i | \(-0.534417\pi\) | ||||
−0.107914 | + | 0.994160i | \(0.534417\pi\) | |||||||
\(444\) | −62.4433 | −2.96343 | ||||||||
\(445\) | 4.08038 | 0.193429 | ||||||||
\(446\) | −27.7997 | −1.31635 | ||||||||
\(447\) | 23.8526 | 1.12819 | ||||||||
\(448\) | 91.5281 | 4.32429 | ||||||||
\(449\) | 28.7987 | 1.35909 | 0.679547 | − | 0.733632i | \(-0.262176\pi\) | ||||
0.679547 | + | 0.733632i | \(0.262176\pi\) | |||||||
\(450\) | 99.9785 | 4.71303 | ||||||||
\(451\) | 9.01475 | 0.424488 | ||||||||
\(452\) | 1.14813 | 0.0540034 | ||||||||
\(453\) | 3.40952 | 0.160193 | ||||||||
\(454\) | −32.9080 | −1.54445 | ||||||||
\(455\) | −10.0918 | −0.473112 | ||||||||
\(456\) | −231.863 | −10.8580 | ||||||||
\(457\) | 22.8788 | 1.07023 | 0.535113 | − | 0.844780i | \(-0.320269\pi\) | ||||
0.535113 | + | 0.844780i | \(0.320269\pi\) | |||||||
\(458\) | 42.9737 | 2.00803 | ||||||||
\(459\) | −13.1240 | −0.612575 | ||||||||
\(460\) | −0.865784 | −0.0403674 | ||||||||
\(461\) | 26.4983 | 1.23415 | 0.617074 | − | 0.786905i | \(-0.288318\pi\) | ||||
0.617074 | + | 0.786905i | \(0.288318\pi\) | |||||||
\(462\) | 75.1995 | 3.49860 | ||||||||
\(463\) | 7.85173 | 0.364901 | 0.182450 | − | 0.983215i | \(-0.441597\pi\) | ||||
0.182450 | + | 0.983215i | \(0.441597\pi\) | |||||||
\(464\) | 21.2107 | 0.984682 | ||||||||
\(465\) | −22.3997 | −1.03876 | ||||||||
\(466\) | 33.1621 | 1.53621 | ||||||||
\(467\) | −8.15815 | −0.377514 | −0.188757 | − | 0.982024i | \(-0.560446\pi\) | ||||
−0.188757 | + | 0.982024i | \(0.560446\pi\) | |||||||
\(468\) | −162.224 | −7.49879 | ||||||||
\(469\) | −51.1334 | −2.36112 | ||||||||
\(470\) | −11.9094 | −0.549341 | ||||||||
\(471\) | −12.4824 | −0.575159 | ||||||||
\(472\) | 110.136 | 5.06943 | ||||||||
\(473\) | 12.8712 | 0.591820 | ||||||||
\(474\) | 134.484 | 6.17705 | ||||||||
\(475\) | 31.3562 | 1.43872 | ||||||||
\(476\) | 12.4533 | 0.570796 | ||||||||
\(477\) | −8.62480 | −0.394902 | ||||||||
\(478\) | 61.8040 | 2.82685 | ||||||||
\(479\) | 5.83104 | 0.266427 | 0.133214 | − | 0.991087i | \(-0.457470\pi\) | ||||
0.133214 | + | 0.991087i | \(0.457470\pi\) | |||||||
\(480\) | 60.1378 | 2.74490 | ||||||||
\(481\) | −11.8212 | −0.539003 | ||||||||
\(482\) | 38.8513 | 1.76963 | ||||||||
\(483\) | 2.14558 | 0.0976273 | ||||||||
\(484\) | −28.1462 | −1.27937 | ||||||||
\(485\) | −7.68194 | −0.348819 | ||||||||
\(486\) | 209.942 | 9.52318 | ||||||||
\(487\) | 9.97499 | 0.452010 | 0.226005 | − | 0.974126i | \(-0.427433\pi\) | ||||
0.226005 | + | 0.974126i | \(0.427433\pi\) | |||||||
\(488\) | 97.6331 | 4.41964 | ||||||||
\(489\) | −17.4544 | −0.789314 | ||||||||
\(490\) | −10.1990 | −0.460742 | ||||||||
\(491\) | −13.0671 | −0.589712 | −0.294856 | − | 0.955542i | \(-0.595272\pi\) | ||||
−0.294856 | + | 0.955542i | \(0.595272\pi\) | |||||||
\(492\) | −68.9771 | −3.10973 | ||||||||
\(493\) | 1.01193 | 0.0455750 | ||||||||
\(494\) | −69.7283 | −3.13723 | ||||||||
\(495\) | 17.8246 | 0.801154 | ||||||||
\(496\) | 109.683 | 4.92492 | ||||||||
\(497\) | 23.9752 | 1.07544 | ||||||||
\(498\) | 37.3193 | 1.67232 | ||||||||
\(499\) | −41.2518 | −1.84668 | −0.923341 | − | 0.383981i | \(-0.874553\pi\) | ||||
−0.923341 | + | 0.383981i | \(0.874553\pi\) | |||||||
\(500\) | −42.9561 | −1.92106 | ||||||||
\(501\) | 59.0174 | 2.63670 | ||||||||
\(502\) | −19.3160 | −0.862116 | ||||||||
\(503\) | 38.9778 | 1.73793 | 0.868967 | − | 0.494871i | \(-0.164785\pi\) | ||||
0.868967 | + | 0.494871i | \(0.164785\pi\) | |||||||
\(504\) | −268.738 | −11.9705 | ||||||||
\(505\) | 13.7963 | 0.613926 | ||||||||
\(506\) | 1.22133 | 0.0542947 | ||||||||
\(507\) | 2.93057 | 0.130151 | ||||||||
\(508\) | −51.0761 | −2.26613 | ||||||||
\(509\) | −38.5306 | −1.70784 | −0.853920 | − | 0.520404i | \(-0.825781\pi\) | ||||
−0.853920 | + | 0.520404i | \(0.825781\pi\) | |||||||
\(510\) | 5.45258 | 0.241444 | ||||||||
\(511\) | −1.83602 | −0.0812206 | ||||||||
\(512\) | −29.3113 | −1.29539 | ||||||||
\(513\) | 141.101 | 6.22974 | ||||||||
\(514\) | 28.0453 | 1.23702 | ||||||||
\(515\) | −10.9213 | −0.481251 | ||||||||
\(516\) | −98.4853 | −4.33557 | ||||||||
\(517\) | 12.2585 | 0.539127 | ||||||||
\(518\) | −31.1085 | −1.36683 | ||||||||
\(519\) | −78.5819 | −3.44936 | ||||||||
\(520\) | 27.6699 | 1.21341 | ||||||||
\(521\) | 35.3738 | 1.54975 | 0.774877 | − | 0.632112i | \(-0.217812\pi\) | ||||
0.774877 | + | 0.632112i | \(0.217812\pi\) | |||||||
\(522\) | −34.6893 | −1.51831 | ||||||||
\(523\) | 28.4591 | 1.24443 | 0.622215 | − | 0.782847i | \(-0.286233\pi\) | ||||
0.622215 | + | 0.782847i | \(0.286233\pi\) | |||||||
\(524\) | 35.9394 | 1.57002 | ||||||||
\(525\) | 48.9845 | 2.13786 | ||||||||
\(526\) | −34.1423 | −1.48868 | ||||||||
\(527\) | 5.23281 | 0.227945 | ||||||||
\(528\) | −117.639 | −5.11959 | ||||||||
\(529\) | −22.9652 | −0.998485 | ||||||||
\(530\) | 2.33692 | 0.101509 | ||||||||
\(531\) | −102.771 | −4.45987 | ||||||||
\(532\) | −133.890 | −5.80486 | ||||||||
\(533\) | −13.0582 | −0.565613 | ||||||||
\(534\) | 44.0428 | 1.90592 | ||||||||
\(535\) | −3.85941 | −0.166857 | ||||||||
\(536\) | 140.198 | 6.05565 | ||||||||
\(537\) | −44.9051 | −1.93780 | ||||||||
\(538\) | −16.4594 | −0.709616 | ||||||||
\(539\) | 10.4979 | 0.452175 | ||||||||
\(540\) | −88.9464 | −3.82764 | ||||||||
\(541\) | −27.6006 | −1.18664 | −0.593321 | − | 0.804966i | \(-0.702184\pi\) | ||||
−0.593321 | + | 0.804966i | \(0.702184\pi\) | |||||||
\(542\) | 82.1243 | 3.52754 | ||||||||
\(543\) | 36.4570 | 1.56452 | ||||||||
\(544\) | −14.0488 | −0.602338 | ||||||||
\(545\) | −5.32629 | −0.228153 | ||||||||
\(546\) | −108.929 | −4.66174 | ||||||||
\(547\) | 9.98261 | 0.426826 | 0.213413 | − | 0.976962i | \(-0.431542\pi\) | ||||
0.213413 | + | 0.976962i | \(0.431542\pi\) | |||||||
\(548\) | −45.9447 | −1.96266 | ||||||||
\(549\) | −91.1039 | −3.88822 | ||||||||
\(550\) | 27.8835 | 1.18895 | ||||||||
\(551\) | −10.8796 | −0.463487 | ||||||||
\(552\) | −5.88279 | −0.250388 | ||||||||
\(553\) | 48.8862 | 2.07885 | ||||||||
\(554\) | −36.3905 | −1.54608 | ||||||||
\(555\) | −9.93846 | −0.421864 | ||||||||
\(556\) | 35.7197 | 1.51485 | ||||||||
\(557\) | 38.2056 | 1.61882 | 0.809411 | − | 0.587243i | \(-0.199787\pi\) | ||||
0.809411 | + | 0.587243i | \(0.199787\pi\) | |||||||
\(558\) | −179.383 | −7.59388 | ||||||||
\(559\) | −18.6444 | −0.788575 | ||||||||
\(560\) | 41.5454 | 1.75561 | ||||||||
\(561\) | −5.61238 | −0.236955 | ||||||||
\(562\) | −19.5171 | −0.823280 | ||||||||
\(563\) | −33.7961 | −1.42434 | −0.712168 | − | 0.702009i | \(-0.752287\pi\) | ||||
−0.712168 | + | 0.702009i | \(0.752287\pi\) | |||||||
\(564\) | −93.7968 | −3.94956 | ||||||||
\(565\) | 0.182736 | 0.00768775 | ||||||||
\(566\) | 9.14823 | 0.384529 | ||||||||
\(567\) | 133.201 | 5.59393 | ||||||||
\(568\) | −65.7356 | −2.75821 | ||||||||
\(569\) | −28.9499 | −1.21364 | −0.606822 | − | 0.794838i | \(-0.707556\pi\) | ||||
−0.606822 | + | 0.794838i | \(0.707556\pi\) | |||||||
\(570\) | −58.6226 | −2.45543 | ||||||||
\(571\) | −24.8670 | −1.04065 | −0.520326 | − | 0.853967i | \(-0.674190\pi\) | ||||
−0.520326 | + | 0.853967i | \(0.674190\pi\) | |||||||
\(572\) | −45.2433 | −1.89172 | ||||||||
\(573\) | −0.917518 | −0.0383299 | ||||||||
\(574\) | −34.3636 | −1.43431 | ||||||||
\(575\) | 0.795566 | 0.0331774 | ||||||||
\(576\) | 234.171 | 9.75711 | ||||||||
\(577\) | −36.2956 | −1.51101 | −0.755503 | − | 0.655145i | \(-0.772608\pi\) | ||||
−0.755503 | + | 0.655145i | \(0.772608\pi\) | |||||||
\(578\) | 44.9655 | 1.87032 | ||||||||
\(579\) | 10.0960 | 0.419575 | ||||||||
\(580\) | 6.85825 | 0.284773 | ||||||||
\(581\) | 13.5659 | 0.562810 | ||||||||
\(582\) | −82.9173 | −3.43703 | ||||||||
\(583\) | −2.40541 | −0.0996218 | ||||||||
\(584\) | 5.03402 | 0.208309 | ||||||||
\(585\) | −25.8195 | −1.06750 | ||||||||
\(586\) | 53.7835 | 2.22177 | ||||||||
\(587\) | −32.4294 | −1.33850 | −0.669252 | − | 0.743035i | \(-0.733385\pi\) | ||||
−0.669252 | + | 0.743035i | \(0.733385\pi\) | |||||||
\(588\) | −80.3254 | −3.31256 | ||||||||
\(589\) | −56.2598 | −2.31814 | ||||||||
\(590\) | 27.8461 | 1.14641 | ||||||||
\(591\) | 62.5738 | 2.57394 | ||||||||
\(592\) | 48.6649 | 2.00012 | ||||||||
\(593\) | −47.8197 | −1.96372 | −0.981859 | − | 0.189612i | \(-0.939277\pi\) | ||||
−0.981859 | + | 0.189612i | \(0.939277\pi\) | |||||||
\(594\) | 125.473 | 5.14823 | ||||||||
\(595\) | 1.98206 | 0.0812567 | ||||||||
\(596\) | −37.7650 | −1.54692 | ||||||||
\(597\) | −59.6850 | −2.44274 | ||||||||
\(598\) | −1.76914 | −0.0723454 | ||||||||
\(599\) | 3.77767 | 0.154352 | 0.0771758 | − | 0.997018i | \(-0.475410\pi\) | ||||
0.0771758 | + | 0.997018i | \(0.475410\pi\) | |||||||
\(600\) | −134.307 | −5.48304 | ||||||||
\(601\) | −45.0536 | −1.83778 | −0.918888 | − | 0.394519i | \(-0.870911\pi\) | ||||
−0.918888 | + | 0.394519i | \(0.870911\pi\) | |||||||
\(602\) | −49.0642 | −1.99971 | ||||||||
\(603\) | −130.823 | −5.32751 | ||||||||
\(604\) | −5.39818 | −0.219649 | ||||||||
\(605\) | −4.47974 | −0.182127 | ||||||||
\(606\) | 148.914 | 6.04922 | ||||||||
\(607\) | −15.5546 | −0.631340 | −0.315670 | − | 0.948869i | \(-0.602229\pi\) | ||||
−0.315670 | + | 0.948869i | \(0.602229\pi\) | |||||||
\(608\) | 151.044 | 6.12563 | ||||||||
\(609\) | −16.9961 | −0.688715 | ||||||||
\(610\) | 24.6849 | 0.999462 | ||||||||
\(611\) | −17.7568 | −0.718364 | ||||||||
\(612\) | 31.8612 | 1.28791 | ||||||||
\(613\) | 45.7279 | 1.84693 | 0.923467 | − | 0.383679i | \(-0.125343\pi\) | ||||
0.923467 | + | 0.383679i | \(0.125343\pi\) | |||||||
\(614\) | −12.0361 | −0.485736 | ||||||||
\(615\) | −10.9784 | −0.442691 | ||||||||
\(616\) | −74.9496 | −3.01980 | ||||||||
\(617\) | 8.23058 | 0.331351 | 0.165675 | − | 0.986180i | \(-0.447020\pi\) | ||||
0.165675 | + | 0.986180i | \(0.447020\pi\) | |||||||
\(618\) | −117.882 | −4.74193 | ||||||||
\(619\) | 9.06005 | 0.364154 | 0.182077 | − | 0.983284i | \(-0.441718\pi\) | ||||
0.182077 | + | 0.983284i | \(0.441718\pi\) | |||||||
\(620\) | 35.4648 | 1.42430 | ||||||||
\(621\) | 3.57998 | 0.143660 | ||||||||
\(622\) | 15.2441 | 0.611233 | ||||||||
\(623\) | 16.0100 | 0.641426 | ||||||||
\(624\) | 170.405 | 6.82164 | ||||||||
\(625\) | 14.4722 | 0.578889 | ||||||||
\(626\) | −52.8159 | −2.11095 | ||||||||
\(627\) | 60.3407 | 2.40978 | ||||||||
\(628\) | 19.7630 | 0.788630 | ||||||||
\(629\) | 2.32173 | 0.0925733 | ||||||||
\(630\) | −67.9459 | −2.70703 | ||||||||
\(631\) | −34.3981 | −1.36937 | −0.684683 | − | 0.728841i | \(-0.740059\pi\) | ||||
−0.684683 | + | 0.728841i | \(0.740059\pi\) | |||||||
\(632\) | −134.037 | −5.33170 | ||||||||
\(633\) | 31.3738 | 1.24700 | ||||||||
\(634\) | 47.4820 | 1.88575 | ||||||||
\(635\) | −8.12926 | −0.322600 | ||||||||
\(636\) | 18.4052 | 0.729813 | ||||||||
\(637\) | −15.2065 | −0.602505 | ||||||||
\(638\) | −9.67467 | −0.383024 | ||||||||
\(639\) | 61.3395 | 2.42655 | ||||||||
\(640\) | −28.1728 | −1.11363 | ||||||||
\(641\) | −20.0849 | −0.793305 | −0.396652 | − | 0.917969i | \(-0.629828\pi\) | ||||
−0.396652 | + | 0.917969i | \(0.629828\pi\) | |||||||
\(642\) | −41.6577 | −1.64410 | ||||||||
\(643\) | 6.79226 | 0.267861 | 0.133930 | − | 0.990991i | \(-0.457240\pi\) | ||||
0.133930 | + | 0.990991i | \(0.457240\pi\) | |||||||
\(644\) | −3.39703 | −0.133862 | ||||||||
\(645\) | −15.6749 | −0.617198 | ||||||||
\(646\) | 13.6948 | 0.538816 | ||||||||
\(647\) | 14.8431 | 0.583541 | 0.291770 | − | 0.956488i | \(-0.405756\pi\) | ||||
0.291770 | + | 0.956488i | \(0.405756\pi\) | |||||||
\(648\) | −365.213 | −14.3469 | ||||||||
\(649\) | −28.6622 | −1.12509 | ||||||||
\(650\) | −40.3902 | −1.58423 | ||||||||
\(651\) | −87.8886 | −3.44463 | ||||||||
\(652\) | 27.6350 | 1.08227 | ||||||||
\(653\) | 5.33362 | 0.208721 | 0.104360 | − | 0.994540i | \(-0.466720\pi\) | ||||
0.104360 | + | 0.994540i | \(0.466720\pi\) | |||||||
\(654\) | −57.4909 | −2.24807 | ||||||||
\(655\) | 5.72010 | 0.223503 | ||||||||
\(656\) | 53.7571 | 2.09886 | ||||||||
\(657\) | −4.69737 | −0.183262 | ||||||||
\(658\) | −46.7284 | −1.82166 | ||||||||
\(659\) | −37.1744 | −1.44811 | −0.724054 | − | 0.689743i | \(-0.757724\pi\) | ||||
−0.724054 | + | 0.689743i | \(0.757724\pi\) | |||||||
\(660\) | −38.0373 | −1.48060 | ||||||||
\(661\) | 14.7625 | 0.574197 | 0.287098 | − | 0.957901i | \(-0.407309\pi\) | ||||
0.287098 | + | 0.957901i | \(0.407309\pi\) | |||||||
\(662\) | −49.6582 | −1.93002 | ||||||||
\(663\) | 8.12973 | 0.315733 | ||||||||
\(664\) | −37.1953 | −1.44346 | ||||||||
\(665\) | −21.3099 | −0.826361 | ||||||||
\(666\) | −79.5897 | −3.08404 | ||||||||
\(667\) | −0.276036 | −0.0106882 | ||||||||
\(668\) | −93.4405 | −3.61532 | ||||||||
\(669\) | −34.8474 | −1.34728 | ||||||||
\(670\) | 35.4468 | 1.36943 | ||||||||
\(671\) | −25.4084 | −0.980879 | ||||||||
\(672\) | 235.960 | 9.10234 | ||||||||
\(673\) | −6.19593 | −0.238835 | −0.119418 | − | 0.992844i | \(-0.538103\pi\) | ||||
−0.119418 | + | 0.992844i | \(0.538103\pi\) | |||||||
\(674\) | −94.3710 | −3.63504 | ||||||||
\(675\) | 81.7325 | 3.14589 | ||||||||
\(676\) | −4.63989 | −0.178457 | ||||||||
\(677\) | −29.8898 | −1.14876 | −0.574379 | − | 0.818590i | \(-0.694756\pi\) | ||||
−0.574379 | + | 0.818590i | \(0.694756\pi\) | |||||||
\(678\) | 1.97241 | 0.0757500 | ||||||||
\(679\) | −30.1412 | −1.15671 | ||||||||
\(680\) | −5.43445 | −0.208402 | ||||||||
\(681\) | −41.2507 | −1.58073 | ||||||||
\(682\) | −50.0288 | −1.91570 | ||||||||
\(683\) | −5.88873 | −0.225326 | −0.112663 | − | 0.993633i | \(-0.535938\pi\) | ||||
−0.112663 | + | 0.993633i | \(0.535938\pi\) | |||||||
\(684\) | −342.551 | −13.0978 | ||||||||
\(685\) | −7.31255 | −0.279398 | ||||||||
\(686\) | 24.1676 | 0.922722 | ||||||||
\(687\) | 53.8682 | 2.05520 | ||||||||
\(688\) | 76.7541 | 2.92622 | ||||||||
\(689\) | 3.48432 | 0.132742 | ||||||||
\(690\) | −1.48736 | −0.0566230 | ||||||||
\(691\) | 21.0106 | 0.799280 | 0.399640 | − | 0.916672i | \(-0.369135\pi\) | ||||
0.399640 | + | 0.916672i | \(0.369135\pi\) | |||||||
\(692\) | 124.416 | 4.72960 | ||||||||
\(693\) | 69.9373 | 2.65670 | ||||||||
\(694\) | 44.6109 | 1.69341 | ||||||||
\(695\) | 5.68513 | 0.215649 | ||||||||
\(696\) | 46.6001 | 1.76637 | ||||||||
\(697\) | 2.56466 | 0.0971436 | ||||||||
\(698\) | 29.7660 | 1.12666 | ||||||||
\(699\) | 41.5693 | 1.57229 | ||||||||
\(700\) | −77.5557 | −2.93133 | ||||||||
\(701\) | −28.6485 | −1.08204 | −0.541020 | − | 0.841010i | \(-0.681961\pi\) | ||||
−0.541020 | + | 0.841010i | \(0.681961\pi\) | |||||||
\(702\) | −181.752 | −6.85980 | ||||||||
\(703\) | −24.9617 | −0.941449 | ||||||||
\(704\) | 65.3089 | 2.46142 | ||||||||
\(705\) | −14.9287 | −0.562247 | ||||||||
\(706\) | 76.3132 | 2.87209 | ||||||||
\(707\) | 54.1317 | 2.03583 | ||||||||
\(708\) | 219.311 | 8.24223 | ||||||||
\(709\) | 42.2511 | 1.58677 | 0.793387 | − | 0.608717i | \(-0.208316\pi\) | ||||
0.793387 | + | 0.608717i | \(0.208316\pi\) | |||||||
\(710\) | −16.6202 | −0.623743 | ||||||||
\(711\) | 125.073 | 4.69061 | ||||||||
\(712\) | −43.8964 | −1.64509 | ||||||||
\(713\) | −1.42741 | −0.0534571 | ||||||||
\(714\) | 21.3940 | 0.800650 | ||||||||
\(715\) | −7.20091 | −0.269299 | ||||||||
\(716\) | 71.0969 | 2.65702 | ||||||||
\(717\) | 77.4724 | 2.89326 | ||||||||
\(718\) | −95.4385 | −3.56173 | ||||||||
\(719\) | 34.0378 | 1.26940 | 0.634698 | − | 0.772760i | \(-0.281124\pi\) | ||||
0.634698 | + | 0.772760i | \(0.281124\pi\) | |||||||
\(720\) | 106.292 | 3.96127 | ||||||||
\(721\) | −42.8514 | −1.59587 | ||||||||
\(722\) | −95.5589 | −3.55633 | ||||||||
\(723\) | 48.7008 | 1.81120 | ||||||||
\(724\) | −57.7213 | −2.14520 | ||||||||
\(725\) | −6.30202 | −0.234051 | ||||||||
\(726\) | −48.3534 | −1.79456 | ||||||||
\(727\) | −3.52713 | −0.130814 | −0.0654069 | − | 0.997859i | \(-0.520835\pi\) | ||||
−0.0654069 | + | 0.997859i | \(0.520835\pi\) | |||||||
\(728\) | 108.567 | 4.02376 | ||||||||
\(729\) | 144.628 | 5.35660 | ||||||||
\(730\) | 1.27277 | 0.0471073 | ||||||||
\(731\) | 3.66182 | 0.135437 | ||||||||
\(732\) | 194.414 | 7.18576 | ||||||||
\(733\) | 12.6933 | 0.468839 | 0.234419 | − | 0.972136i | \(-0.424681\pi\) | ||||
0.234419 | + | 0.972136i | \(0.424681\pi\) | |||||||
\(734\) | 65.6488 | 2.42314 | ||||||||
\(735\) | −12.7846 | −0.471566 | ||||||||
\(736\) | 3.83226 | 0.141259 | ||||||||
\(737\) | −36.4857 | −1.34397 | ||||||||
\(738\) | −87.9177 | −3.23630 | ||||||||
\(739\) | −40.4664 | −1.48858 | −0.744290 | − | 0.667857i | \(-0.767212\pi\) | ||||
−0.744290 | + | 0.667857i | \(0.767212\pi\) | |||||||
\(740\) | 15.7353 | 0.578440 | ||||||||
\(741\) | −87.4056 | −3.21093 | ||||||||
\(742\) | 9.16924 | 0.336613 | ||||||||
\(743\) | 1.48947 | 0.0546434 | 0.0273217 | − | 0.999627i | \(-0.491302\pi\) | ||||
0.0273217 | + | 0.999627i | \(0.491302\pi\) | |||||||
\(744\) | 240.974 | 8.83455 | ||||||||
\(745\) | −6.01067 | −0.220214 | ||||||||
\(746\) | 48.7661 | 1.78545 | ||||||||
\(747\) | 34.7078 | 1.26989 | ||||||||
\(748\) | 8.88591 | 0.324901 | ||||||||
\(749\) | −15.1430 | −0.553312 | ||||||||
\(750\) | −73.7960 | −2.69465 | ||||||||
\(751\) | 31.4438 | 1.14740 | 0.573701 | − | 0.819065i | \(-0.305507\pi\) | ||||
0.573701 | + | 0.819065i | \(0.305507\pi\) | |||||||
\(752\) | 73.1001 | 2.66569 | ||||||||
\(753\) | −24.2129 | −0.882369 | ||||||||
\(754\) | 14.0141 | 0.510363 | ||||||||
\(755\) | −0.859174 | −0.0312685 | ||||||||
\(756\) | −348.994 | −12.6928 | ||||||||
\(757\) | 40.0089 | 1.45415 | 0.727073 | − | 0.686560i | \(-0.240880\pi\) | ||||
0.727073 | + | 0.686560i | \(0.240880\pi\) | |||||||
\(758\) | −2.39389 | −0.0869499 | ||||||||
\(759\) | 1.53096 | 0.0555702 | ||||||||
\(760\) | 58.4277 | 2.11940 | ||||||||
\(761\) | −3.03210 | −0.109914 | −0.0549569 | − | 0.998489i | \(-0.517502\pi\) | ||||
−0.0549569 | + | 0.998489i | \(0.517502\pi\) | |||||||
\(762\) | −87.7456 | −3.17869 | ||||||||
\(763\) | −20.8985 | −0.756576 | ||||||||
\(764\) | 1.45268 | 0.0525561 | ||||||||
\(765\) | 5.07102 | 0.183343 | ||||||||
\(766\) | −98.4759 | −3.55808 | ||||||||
\(767\) | 41.5182 | 1.49914 | ||||||||
\(768\) | −118.949 | −4.29222 | ||||||||
\(769\) | −12.6658 | −0.456739 | −0.228369 | − | 0.973575i | \(-0.573339\pi\) | ||||
−0.228369 | + | 0.973575i | \(0.573339\pi\) | |||||||
\(770\) | −18.9497 | −0.682901 | ||||||||
\(771\) | 35.1552 | 1.26609 | ||||||||
\(772\) | −15.9847 | −0.575300 | ||||||||
\(773\) | 30.7892 | 1.10741 | 0.553705 | − | 0.832713i | \(-0.313213\pi\) | ||||
0.553705 | + | 0.832713i | \(0.313213\pi\) | |||||||
\(774\) | −125.529 | −4.51203 | ||||||||
\(775\) | −32.5885 | −1.17061 | ||||||||
\(776\) | 82.6417 | 2.96666 | ||||||||
\(777\) | −38.9950 | −1.39894 | ||||||||
\(778\) | −31.1394 | −1.11640 | ||||||||
\(779\) | −27.5736 | −0.987927 | ||||||||
\(780\) | 55.0984 | 1.97284 | ||||||||
\(781\) | 17.1073 | 0.612146 | ||||||||
\(782\) | 0.347464 | 0.0124253 | ||||||||
\(783\) | −28.3586 | −1.01345 | ||||||||
\(784\) | 62.6013 | 2.23576 | ||||||||
\(785\) | 3.14548 | 0.112267 | ||||||||
\(786\) | 61.7416 | 2.20225 | ||||||||
\(787\) | −22.6530 | −0.807493 | −0.403747 | − | 0.914871i | \(-0.632292\pi\) | ||||
−0.403747 | + | 0.914871i | \(0.632292\pi\) | |||||||
\(788\) | −99.0712 | −3.52927 | ||||||||
\(789\) | −42.7980 | −1.52365 | ||||||||
\(790\) | −33.8890 | −1.20572 | ||||||||
\(791\) | 0.716990 | 0.0254932 | ||||||||
\(792\) | −191.755 | −6.81372 | ||||||||
\(793\) | 36.8049 | 1.30698 | ||||||||
\(794\) | 94.1985 | 3.34298 | ||||||||
\(795\) | 2.92937 | 0.103894 | ||||||||
\(796\) | 94.4975 | 3.34937 | ||||||||
\(797\) | −35.9331 | −1.27281 | −0.636407 | − | 0.771353i | \(-0.719580\pi\) | ||||
−0.636407 | + | 0.771353i | \(0.719580\pi\) | |||||||
\(798\) | −230.014 | −8.14242 | ||||||||
\(799\) | 3.48749 | 0.123379 | ||||||||
\(800\) | 87.4922 | 3.09332 | ||||||||
\(801\) | 40.9608 | 1.44728 | ||||||||
\(802\) | −21.2621 | −0.750789 | ||||||||
\(803\) | −1.31007 | −0.0462314 | ||||||||
\(804\) | 279.173 | 9.84569 | ||||||||
\(805\) | −0.540671 | −0.0190561 | ||||||||
\(806\) | 72.4685 | 2.55259 | ||||||||
\(807\) | −20.6322 | −0.726286 | ||||||||
\(808\) | −148.419 | −5.22136 | ||||||||
\(809\) | 23.6332 | 0.830901 | 0.415450 | − | 0.909616i | \(-0.363624\pi\) | ||||
0.415450 | + | 0.909616i | \(0.363624\pi\) | |||||||
\(810\) | −92.3381 | −3.24443 | ||||||||
\(811\) | 30.6084 | 1.07481 | 0.537403 | − | 0.843325i | \(-0.319405\pi\) | ||||
0.537403 | + | 0.843325i | \(0.319405\pi\) | |||||||
\(812\) | 26.9093 | 0.944333 | ||||||||
\(813\) | 102.944 | 3.61041 | ||||||||
\(814\) | −22.1971 | −0.778009 | ||||||||
\(815\) | 4.39838 | 0.154068 | ||||||||
\(816\) | −33.4679 | −1.17161 | ||||||||
\(817\) | −39.3695 | −1.37736 | ||||||||
\(818\) | −1.15026 | −0.0402180 | ||||||||
\(819\) | −101.307 | −3.53994 | ||||||||
\(820\) | 17.3817 | 0.606997 | ||||||||
\(821\) | 19.0320 | 0.664221 | 0.332111 | − | 0.943240i | \(-0.392239\pi\) | ||||
0.332111 | + | 0.943240i | \(0.392239\pi\) | |||||||
\(822\) | −78.9301 | −2.75300 | ||||||||
\(823\) | −26.1676 | −0.912146 | −0.456073 | − | 0.889942i | \(-0.650744\pi\) | ||||
−0.456073 | + | 0.889942i | \(0.650744\pi\) | |||||||
\(824\) | 117.491 | 4.09298 | ||||||||
\(825\) | 34.9524 | 1.21689 | ||||||||
\(826\) | 109.258 | 3.80158 | ||||||||
\(827\) | 34.4580 | 1.19822 | 0.599111 | − | 0.800666i | \(-0.295521\pi\) | ||||
0.599111 | + | 0.800666i | \(0.295521\pi\) | |||||||
\(828\) | −8.69116 | −0.302039 | ||||||||
\(829\) | −37.9197 | −1.31701 | −0.658503 | − | 0.752578i | \(-0.728810\pi\) | ||||
−0.658503 | + | 0.752578i | \(0.728810\pi\) | |||||||
\(830\) | −9.40420 | −0.326425 | ||||||||
\(831\) | −45.6161 | −1.58240 | ||||||||
\(832\) | −94.6022 | −3.27974 | ||||||||
\(833\) | 2.98661 | 0.103480 | ||||||||
\(834\) | 61.3642 | 2.12487 | ||||||||
\(835\) | −14.8720 | −0.514666 | ||||||||
\(836\) | −95.5356 | −3.30417 | ||||||||
\(837\) | −146.646 | −5.06881 | ||||||||
\(838\) | −4.54512 | −0.157009 | ||||||||
\(839\) | −29.9289 | −1.03326 | −0.516631 | − | 0.856208i | \(-0.672814\pi\) | ||||
−0.516631 | + | 0.856208i | \(0.672814\pi\) | |||||||
\(840\) | 91.2754 | 3.14930 | ||||||||
\(841\) | −26.8134 | −0.924600 | ||||||||
\(842\) | 25.0505 | 0.863297 | ||||||||
\(843\) | −24.4650 | −0.842621 | ||||||||
\(844\) | −49.6731 | −1.70982 | ||||||||
\(845\) | −0.738484 | −0.0254046 | ||||||||
\(846\) | −119.553 | −4.11030 | ||||||||
\(847\) | −17.5769 | −0.603950 | ||||||||
\(848\) | −14.3440 | −0.492575 | ||||||||
\(849\) | 11.4675 | 0.393562 | ||||||||
\(850\) | 7.93274 | 0.272091 | ||||||||
\(851\) | −0.633325 | −0.0217101 | ||||||||
\(852\) | −130.898 | −4.48448 | ||||||||
\(853\) | 0.637030 | 0.0218115 | 0.0109058 | − | 0.999941i | \(-0.496529\pi\) | ||||
0.0109058 | + | 0.999941i | \(0.496529\pi\) | |||||||
\(854\) | 96.8548 | 3.31430 | ||||||||
\(855\) | −54.5204 | −1.86456 | ||||||||
\(856\) | 41.5192 | 1.41910 | ||||||||
\(857\) | −35.2063 | −1.20262 | −0.601312 | − | 0.799014i | \(-0.705355\pi\) | ||||
−0.601312 | + | 0.799014i | \(0.705355\pi\) | |||||||
\(858\) | −77.7252 | −2.65349 | ||||||||
\(859\) | 9.86511 | 0.336593 | 0.168297 | − | 0.985736i | \(-0.446173\pi\) | ||||
0.168297 | + | 0.985736i | \(0.446173\pi\) | |||||||
\(860\) | 24.8176 | 0.846273 | ||||||||
\(861\) | −43.0753 | −1.46800 | ||||||||
\(862\) | −99.1035 | −3.37548 | ||||||||
\(863\) | 11.5832 | 0.394296 | 0.197148 | − | 0.980374i | \(-0.436832\pi\) | ||||
0.197148 | + | 0.980374i | \(0.436832\pi\) | |||||||
\(864\) | 393.708 | 13.3942 | ||||||||
\(865\) | 19.8021 | 0.673291 | ||||||||
\(866\) | 23.1197 | 0.785638 | ||||||||
\(867\) | 56.3651 | 1.91426 | ||||||||
\(868\) | 139.151 | 4.72311 | ||||||||
\(869\) | 34.8822 | 1.18330 | ||||||||
\(870\) | 11.7820 | 0.399449 | ||||||||
\(871\) | 52.8508 | 1.79078 | ||||||||
\(872\) | 57.2998 | 1.94042 | ||||||||
\(873\) | −77.1150 | −2.60995 | ||||||||
\(874\) | −3.73570 | −0.126362 | ||||||||
\(875\) | −26.8255 | −0.906868 | ||||||||
\(876\) | 10.0241 | 0.338684 | ||||||||
\(877\) | −28.9186 | −0.976511 | −0.488255 | − | 0.872701i | \(-0.662367\pi\) | ||||
−0.488255 | + | 0.872701i | \(0.662367\pi\) | |||||||
\(878\) | 62.3897 | 2.10555 | ||||||||
\(879\) | 67.4185 | 2.27397 | ||||||||
\(880\) | 29.6443 | 0.999307 | ||||||||
\(881\) | −22.1792 | −0.747237 | −0.373619 | − | 0.927582i | \(-0.621883\pi\) | ||||
−0.373619 | + | 0.927582i | \(0.621883\pi\) | |||||||
\(882\) | −102.382 | −3.44738 | ||||||||
\(883\) | 54.9090 | 1.84784 | 0.923918 | − | 0.382591i | \(-0.124968\pi\) | ||||
0.923918 | + | 0.382591i | \(0.124968\pi\) | |||||||
\(884\) | −12.8716 | −0.432917 | ||||||||
\(885\) | 34.9056 | 1.17334 | ||||||||
\(886\) | 12.3559 | 0.415103 | ||||||||
\(887\) | 34.2062 | 1.14853 | 0.574265 | − | 0.818669i | \(-0.305288\pi\) | ||||
0.574265 | + | 0.818669i | \(0.305288\pi\) | |||||||
\(888\) | 106.917 | 3.58791 | ||||||||
\(889\) | −31.8963 | −1.06977 | ||||||||
\(890\) | −11.0985 | −0.372022 | ||||||||
\(891\) | 95.0443 | 3.18411 | ||||||||
\(892\) | 55.1728 | 1.84732 | ||||||||
\(893\) | −37.4953 | −1.25473 | ||||||||
\(894\) | −64.8780 | −2.16984 | ||||||||
\(895\) | 11.3158 | 0.378244 | ||||||||
\(896\) | −110.540 | −3.69289 | ||||||||
\(897\) | −2.21764 | −0.0740449 | ||||||||
\(898\) | −78.3313 | −2.61395 | ||||||||
\(899\) | 11.3072 | 0.377115 | ||||||||
\(900\) | −198.423 | −6.61410 | ||||||||
\(901\) | −0.684330 | −0.0227983 | ||||||||
\(902\) | −24.5198 | −0.816419 | ||||||||
\(903\) | −61.5028 | −2.04668 | ||||||||
\(904\) | −1.96586 | −0.0653834 | ||||||||
\(905\) | −9.18691 | −0.305383 | ||||||||
\(906\) | −9.27375 | −0.308100 | ||||||||
\(907\) | −57.3282 | −1.90355 | −0.951776 | − | 0.306795i | \(-0.900744\pi\) | ||||
−0.951776 | + | 0.306795i | \(0.900744\pi\) | |||||||
\(908\) | 65.3110 | 2.16742 | ||||||||
\(909\) | 138.494 | 4.59354 | ||||||||
\(910\) | 27.4494 | 0.909937 | ||||||||
\(911\) | 16.3948 | 0.543185 | 0.271592 | − | 0.962412i | \(-0.412450\pi\) | ||||
0.271592 | + | 0.962412i | \(0.412450\pi\) | |||||||
\(912\) | 359.826 | 11.9150 | ||||||||
\(913\) | 9.67982 | 0.320355 | ||||||||
\(914\) | −62.2295 | −2.05837 | ||||||||
\(915\) | 30.9429 | 1.02294 | ||||||||
\(916\) | −85.2879 | −2.81799 | ||||||||
\(917\) | 22.4437 | 0.741155 | ||||||||
\(918\) | 35.6967 | 1.17817 | ||||||||
\(919\) | 50.1888 | 1.65558 | 0.827788 | − | 0.561040i | \(-0.189599\pi\) | ||||
0.827788 | + | 0.561040i | \(0.189599\pi\) | |||||||
\(920\) | 1.48242 | 0.0488739 | ||||||||
\(921\) | −15.0874 | −0.497147 | ||||||||
\(922\) | −72.0742 | −2.37364 | ||||||||
\(923\) | −24.7805 | −0.815659 | ||||||||
\(924\) | −149.245 | −4.90980 | ||||||||
\(925\) | −14.4591 | −0.475412 | ||||||||
\(926\) | −21.3564 | −0.701815 | ||||||||
\(927\) | −109.633 | −3.60083 | ||||||||
\(928\) | −30.3570 | −0.996517 | ||||||||
\(929\) | −38.1403 | −1.25134 | −0.625671 | − | 0.780087i | \(-0.715175\pi\) | ||||
−0.625671 | + | 0.780087i | \(0.715175\pi\) | |||||||
\(930\) | 60.9264 | 1.99785 | ||||||||
\(931\) | −32.1101 | −1.05237 | ||||||||
\(932\) | −65.8154 | −2.15585 | ||||||||
\(933\) | 19.1088 | 0.625593 | ||||||||
\(934\) | 22.1898 | 0.726074 | ||||||||
\(935\) | 1.41428 | 0.0462519 | ||||||||
\(936\) | 277.764 | 9.07900 | ||||||||
\(937\) | −1.77357 | −0.0579399 | −0.0289699 | − | 0.999580i | \(-0.509223\pi\) | ||||
−0.0289699 | + | 0.999580i | \(0.509223\pi\) | |||||||
\(938\) | 139.081 | 4.54115 | ||||||||
\(939\) | −66.2057 | −2.16054 | ||||||||
\(940\) | 23.6361 | 0.770925 | ||||||||
\(941\) | −20.5078 | −0.668536 | −0.334268 | − | 0.942478i | \(-0.608489\pi\) | ||||
−0.334268 | + | 0.942478i | \(0.608489\pi\) | |||||||
\(942\) | 33.9517 | 1.10620 | ||||||||
\(943\) | −0.699594 | −0.0227819 | ||||||||
\(944\) | −170.919 | −5.56295 | ||||||||
\(945\) | −55.5459 | −1.80691 | ||||||||
\(946\) | −35.0092 | −1.13825 | ||||||||
\(947\) | 25.6908 | 0.834838 | 0.417419 | − | 0.908714i | \(-0.362935\pi\) | ||||
0.417419 | + | 0.908714i | \(0.362935\pi\) | |||||||
\(948\) | −266.904 | −8.66865 | ||||||||
\(949\) | 1.89768 | 0.0616014 | ||||||||
\(950\) | −85.2877 | −2.76710 | ||||||||
\(951\) | 59.5195 | 1.93005 | ||||||||
\(952\) | −21.3229 | −0.691079 | ||||||||
\(953\) | 13.2486 | 0.429165 | 0.214583 | − | 0.976706i | \(-0.431161\pi\) | ||||
0.214583 | + | 0.976706i | \(0.431161\pi\) | |||||||
\(954\) | 23.4591 | 0.759517 | ||||||||
\(955\) | 0.231208 | 0.00748172 | ||||||||
\(956\) | −122.660 | −3.96710 | ||||||||
\(957\) | −12.1274 | −0.392022 | ||||||||
\(958\) | −15.8602 | −0.512420 | ||||||||
\(959\) | −28.6918 | −0.926508 | ||||||||
\(960\) | −79.5348 | −2.56697 | ||||||||
\(961\) | 27.4707 | 0.886151 | ||||||||
\(962\) | 32.1533 | 1.03666 | ||||||||
\(963\) | −38.7426 | −1.24846 | ||||||||
\(964\) | −77.1065 | −2.48343 | ||||||||
\(965\) | −2.54411 | −0.0818979 | ||||||||
\(966\) | −5.83589 | −0.187767 | ||||||||
\(967\) | 37.8743 | 1.21796 | 0.608978 | − | 0.793187i | \(-0.291580\pi\) | ||||
0.608978 | + | 0.793187i | \(0.291580\pi\) | |||||||
\(968\) | 48.1927 | 1.54897 | ||||||||
\(969\) | 17.1667 | 0.551474 | ||||||||
\(970\) | 20.8946 | 0.670884 | ||||||||
\(971\) | 7.53642 | 0.241855 | 0.120928 | − | 0.992661i | \(-0.461413\pi\) | ||||
0.120928 | + | 0.992661i | \(0.461413\pi\) | |||||||
\(972\) | −416.663 | −13.3645 | ||||||||
\(973\) | 22.3065 | 0.715112 | ||||||||
\(974\) | −27.1316 | −0.869352 | ||||||||
\(975\) | −50.6297 | −1.62145 | ||||||||
\(976\) | −151.516 | −4.84991 | ||||||||
\(977\) | −42.7960 | −1.36917 | −0.684583 | − | 0.728934i | \(-0.740016\pi\) | ||||
−0.684583 | + | 0.728934i | \(0.740016\pi\) | |||||||
\(978\) | 47.4752 | 1.51809 | ||||||||
\(979\) | 11.4237 | 0.365104 | ||||||||
\(980\) | 20.2414 | 0.646589 | ||||||||
\(981\) | −53.4679 | −1.70710 | ||||||||
\(982\) | 35.5421 | 1.13419 | ||||||||
\(983\) | 51.1788 | 1.63235 | 0.816176 | − | 0.577804i | \(-0.196090\pi\) | ||||
0.816176 | + | 0.577804i | \(0.196090\pi\) | |||||||
\(984\) | 118.105 | 3.76504 | ||||||||
\(985\) | −15.7682 | −0.502415 | ||||||||
\(986\) | −2.75241 | −0.0876545 | ||||||||
\(987\) | −58.5749 | −1.86446 | ||||||||
\(988\) | 138.387 | 4.40267 | ||||||||
\(989\) | −0.998877 | −0.0317624 | ||||||||
\(990\) | −48.4821 | −1.54086 | ||||||||
\(991\) | −53.5386 | −1.70071 | −0.850354 | − | 0.526210i | \(-0.823612\pi\) | ||||
−0.850354 | + | 0.526210i | \(0.823612\pi\) | |||||||
\(992\) | −156.980 | −4.98411 | ||||||||
\(993\) | −62.2474 | −1.97536 | ||||||||
\(994\) | −65.2116 | −2.06839 | ||||||||
\(995\) | 15.0402 | 0.476806 | ||||||||
\(996\) | −74.0660 | −2.34687 | ||||||||
\(997\) | −34.8352 | −1.10324 | −0.551621 | − | 0.834095i | \(-0.685991\pi\) | ||||
−0.551621 | + | 0.834095i | \(0.685991\pi\) | |||||||
\(998\) | 112.203 | 3.55173 | ||||||||
\(999\) | −65.0647 | −2.05856 |
(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 | 8003.2.a.b.1.4 | ✓ | 153 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8003.2.a.b.1.4 | ✓ | 153 | 1.1 | even | 1 | trivial |