Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6026,2,Mod(1,6026)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6026, 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("6026.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6026 = 2 \cdot 23 \cdot 131 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6026.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: | \(48.1178522580\) |
Analytic rank: | \(1\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 6026.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0.562960 | 0.325025 | 0.162512 | − | 0.986706i | \(-0.448040\pi\) | ||||
0.162512 | + | 0.986706i | \(0.448040\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.89005 | −1.73968 | −0.869841 | − | 0.493332i | \(-0.835779\pi\) | ||||
−0.869841 | + | 0.493332i | \(0.835779\pi\) | |||||||
\(6\) | −0.562960 | −0.229827 | ||||||||
\(7\) | −0.867650 | −0.327941 | −0.163970 | − | 0.986465i | \(-0.552430\pi\) | ||||
−0.163970 | + | 0.986465i | \(0.552430\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.68308 | −0.894359 | ||||||||
\(10\) | 3.89005 | 1.23014 | ||||||||
\(11\) | 0.507376 | 0.152980 | 0.0764899 | − | 0.997070i | \(-0.475629\pi\) | ||||
0.0764899 | + | 0.997070i | \(0.475629\pi\) | |||||||
\(12\) | 0.562960 | 0.162512 | ||||||||
\(13\) | −2.74039 | −0.760049 | −0.380024 | − | 0.924976i | \(-0.624084\pi\) | ||||
−0.380024 | + | 0.924976i | \(0.624084\pi\) | |||||||
\(14\) | 0.867650 | 0.231889 | ||||||||
\(15\) | −2.18994 | −0.565440 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.74576 | 0.908480 | 0.454240 | − | 0.890879i | \(-0.349911\pi\) | ||||
0.454240 | + | 0.890879i | \(0.349911\pi\) | |||||||
\(18\) | 2.68308 | 0.632407 | ||||||||
\(19\) | 4.55822 | 1.04573 | 0.522864 | − | 0.852416i | \(-0.324864\pi\) | ||||
0.522864 | + | 0.852416i | \(0.324864\pi\) | |||||||
\(20\) | −3.89005 | −0.869841 | ||||||||
\(21\) | −0.488452 | −0.106589 | ||||||||
\(22\) | −0.507376 | −0.108173 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | −0.562960 | −0.114914 | ||||||||
\(25\) | 10.1325 | 2.02649 | ||||||||
\(26\) | 2.74039 | 0.537436 | ||||||||
\(27\) | −3.19934 | −0.615714 | ||||||||
\(28\) | −0.867650 | −0.163970 | ||||||||
\(29\) | 5.93286 | 1.10170 | 0.550852 | − | 0.834603i | \(-0.314303\pi\) | ||||
0.550852 | + | 0.834603i | \(0.314303\pi\) | |||||||
\(30\) | 2.18994 | 0.399827 | ||||||||
\(31\) | −1.85973 | −0.334018 | −0.167009 | − | 0.985955i | \(-0.553411\pi\) | ||||
−0.167009 | + | 0.985955i | \(0.553411\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0.285633 | 0.0497222 | ||||||||
\(34\) | −3.74576 | −0.642392 | ||||||||
\(35\) | 3.37520 | 0.570513 | ||||||||
\(36\) | −2.68308 | −0.447179 | ||||||||
\(37\) | −0.608639 | −0.100060 | −0.0500298 | − | 0.998748i | \(-0.515932\pi\) | ||||
−0.0500298 | + | 0.998748i | \(0.515932\pi\) | |||||||
\(38\) | −4.55822 | −0.739441 | ||||||||
\(39\) | −1.54273 | −0.247035 | ||||||||
\(40\) | 3.89005 | 0.615070 | ||||||||
\(41\) | −9.86356 | −1.54043 | −0.770214 | − | 0.637785i | \(-0.779851\pi\) | ||||
−0.770214 | + | 0.637785i | \(0.779851\pi\) | |||||||
\(42\) | 0.488452 | 0.0753698 | ||||||||
\(43\) | −1.26441 | −0.192821 | −0.0964104 | − | 0.995342i | \(-0.530736\pi\) | ||||
−0.0964104 | + | 0.995342i | \(0.530736\pi\) | |||||||
\(44\) | 0.507376 | 0.0764899 | ||||||||
\(45\) | 10.4373 | 1.55590 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | 8.01654 | 1.16933 | 0.584667 | − | 0.811274i | \(-0.301225\pi\) | ||||
0.584667 | + | 0.811274i | \(0.301225\pi\) | |||||||
\(48\) | 0.562960 | 0.0812562 | ||||||||
\(49\) | −6.24718 | −0.892455 | ||||||||
\(50\) | −10.1325 | −1.43295 | ||||||||
\(51\) | 2.10871 | 0.295279 | ||||||||
\(52\) | −2.74039 | −0.380024 | ||||||||
\(53\) | 4.96984 | 0.682660 | 0.341330 | − | 0.939944i | \(-0.389123\pi\) | ||||
0.341330 | + | 0.939944i | \(0.389123\pi\) | |||||||
\(54\) | 3.19934 | 0.435375 | ||||||||
\(55\) | −1.97372 | −0.266136 | ||||||||
\(56\) | 0.867650 | 0.115945 | ||||||||
\(57\) | 2.56609 | 0.339888 | ||||||||
\(58\) | −5.93286 | −0.779023 | ||||||||
\(59\) | 5.28644 | 0.688236 | 0.344118 | − | 0.938926i | \(-0.388178\pi\) | ||||
0.344118 | + | 0.938926i | \(0.388178\pi\) | |||||||
\(60\) | −2.18994 | −0.282720 | ||||||||
\(61\) | 13.9133 | 1.78142 | 0.890708 | − | 0.454576i | \(-0.150209\pi\) | ||||
0.890708 | + | 0.454576i | \(0.150209\pi\) | |||||||
\(62\) | 1.85973 | 0.236186 | ||||||||
\(63\) | 2.32797 | 0.293297 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 10.6603 | 1.32224 | ||||||||
\(66\) | −0.285633 | −0.0351589 | ||||||||
\(67\) | −3.14252 | −0.383919 | −0.191960 | − | 0.981403i | \(-0.561484\pi\) | ||||
−0.191960 | + | 0.981403i | \(0.561484\pi\) | |||||||
\(68\) | 3.74576 | 0.454240 | ||||||||
\(69\) | −0.562960 | −0.0677724 | ||||||||
\(70\) | −3.37520 | −0.403413 | ||||||||
\(71\) | 11.8409 | 1.40526 | 0.702631 | − | 0.711554i | \(-0.252008\pi\) | ||||
0.702631 | + | 0.711554i | \(0.252008\pi\) | |||||||
\(72\) | 2.68308 | 0.316204 | ||||||||
\(73\) | −9.43228 | −1.10397 | −0.551983 | − | 0.833856i | \(-0.686129\pi\) | ||||
−0.551983 | + | 0.833856i | \(0.686129\pi\) | |||||||
\(74\) | 0.608639 | 0.0707529 | ||||||||
\(75\) | 5.70417 | 0.658661 | ||||||||
\(76\) | 4.55822 | 0.522864 | ||||||||
\(77\) | −0.440225 | −0.0501683 | ||||||||
\(78\) | 1.54273 | 0.174680 | ||||||||
\(79\) | −9.73748 | −1.09555 | −0.547776 | − | 0.836625i | \(-0.684525\pi\) | ||||
−0.547776 | + | 0.836625i | \(0.684525\pi\) | |||||||
\(80\) | −3.89005 | −0.434920 | ||||||||
\(81\) | 6.24813 | 0.694236 | ||||||||
\(82\) | 9.86356 | 1.08925 | ||||||||
\(83\) | −3.20604 | −0.351909 | −0.175954 | − | 0.984398i | \(-0.556301\pi\) | ||||
−0.175954 | + | 0.984398i | \(0.556301\pi\) | |||||||
\(84\) | −0.488452 | −0.0532945 | ||||||||
\(85\) | −14.5712 | −1.58047 | ||||||||
\(86\) | 1.26441 | 0.136345 | ||||||||
\(87\) | 3.33996 | 0.358081 | ||||||||
\(88\) | −0.507376 | −0.0540865 | ||||||||
\(89\) | 2.82208 | 0.299140 | 0.149570 | − | 0.988751i | \(-0.452211\pi\) | ||||
0.149570 | + | 0.988751i | \(0.452211\pi\) | |||||||
\(90\) | −10.4373 | −1.10019 | ||||||||
\(91\) | 2.37770 | 0.249251 | ||||||||
\(92\) | −1.00000 | −0.104257 | ||||||||
\(93\) | −1.04696 | −0.108564 | ||||||||
\(94\) | −8.01654 | −0.826843 | ||||||||
\(95\) | −17.7317 | −1.81923 | ||||||||
\(96\) | −0.562960 | −0.0574568 | ||||||||
\(97\) | 5.75507 | 0.584339 | 0.292170 | − | 0.956367i | \(-0.405623\pi\) | ||||
0.292170 | + | 0.956367i | \(0.405623\pi\) | |||||||
\(98\) | 6.24718 | 0.631061 | ||||||||
\(99\) | −1.36133 | −0.136819 | ||||||||
\(100\) | 10.1325 | 1.01325 | ||||||||
\(101\) | 9.45619 | 0.940926 | 0.470463 | − | 0.882420i | \(-0.344087\pi\) | ||||
0.470463 | + | 0.882420i | \(0.344087\pi\) | |||||||
\(102\) | −2.10871 | −0.208794 | ||||||||
\(103\) | 6.08876 | 0.599943 | 0.299971 | − | 0.953948i | \(-0.403023\pi\) | ||||
0.299971 | + | 0.953948i | \(0.403023\pi\) | |||||||
\(104\) | 2.74039 | 0.268718 | ||||||||
\(105\) | 1.90010 | 0.185431 | ||||||||
\(106\) | −4.96984 | −0.482713 | ||||||||
\(107\) | 7.08845 | 0.685267 | 0.342633 | − | 0.939469i | \(-0.388681\pi\) | ||||
0.342633 | + | 0.939469i | \(0.388681\pi\) | |||||||
\(108\) | −3.19934 | −0.307857 | ||||||||
\(109\) | −12.7903 | −1.22509 | −0.612546 | − | 0.790435i | \(-0.709854\pi\) | ||||
−0.612546 | + | 0.790435i | \(0.709854\pi\) | |||||||
\(110\) | 1.97372 | 0.188187 | ||||||||
\(111\) | −0.342639 | −0.0325219 | ||||||||
\(112\) | −0.867650 | −0.0819852 | ||||||||
\(113\) | 18.5333 | 1.74347 | 0.871734 | − | 0.489979i | \(-0.162996\pi\) | ||||
0.871734 | + | 0.489979i | \(0.162996\pi\) | |||||||
\(114\) | −2.56609 | −0.240337 | ||||||||
\(115\) | 3.89005 | 0.362749 | ||||||||
\(116\) | 5.93286 | 0.550852 | ||||||||
\(117\) | 7.35269 | 0.679756 | ||||||||
\(118\) | −5.28644 | −0.486656 | ||||||||
\(119\) | −3.25001 | −0.297928 | ||||||||
\(120\) | 2.18994 | 0.199913 | ||||||||
\(121\) | −10.7426 | −0.976597 | ||||||||
\(122\) | −13.9133 | −1.25965 | ||||||||
\(123\) | −5.55279 | −0.500678 | ||||||||
\(124\) | −1.85973 | −0.167009 | ||||||||
\(125\) | −19.9655 | −1.78577 | ||||||||
\(126\) | −2.32797 | −0.207392 | ||||||||
\(127\) | 8.13209 | 0.721606 | 0.360803 | − | 0.932642i | \(-0.382503\pi\) | ||||
0.360803 | + | 0.932642i | \(0.382503\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −0.711812 | −0.0626716 | ||||||||
\(130\) | −10.6603 | −0.934967 | ||||||||
\(131\) | −1.00000 | −0.0873704 | ||||||||
\(132\) | 0.285633 | 0.0248611 | ||||||||
\(133\) | −3.95494 | −0.342937 | ||||||||
\(134\) | 3.14252 | 0.271472 | ||||||||
\(135\) | 12.4456 | 1.07115 | ||||||||
\(136\) | −3.74576 | −0.321196 | ||||||||
\(137\) | −6.54458 | −0.559141 | −0.279571 | − | 0.960125i | \(-0.590192\pi\) | ||||
−0.279571 | + | 0.960125i | \(0.590192\pi\) | |||||||
\(138\) | 0.562960 | 0.0479223 | ||||||||
\(139\) | −9.03391 | −0.766246 | −0.383123 | − | 0.923697i | \(-0.625151\pi\) | ||||
−0.383123 | + | 0.923697i | \(0.625151\pi\) | |||||||
\(140\) | 3.37520 | 0.285256 | ||||||||
\(141\) | 4.51299 | 0.380062 | ||||||||
\(142\) | −11.8409 | −0.993670 | ||||||||
\(143\) | −1.39041 | −0.116272 | ||||||||
\(144\) | −2.68308 | −0.223590 | ||||||||
\(145\) | −23.0791 | −1.91662 | ||||||||
\(146\) | 9.43228 | 0.780621 | ||||||||
\(147\) | −3.51691 | −0.290070 | ||||||||
\(148\) | −0.608639 | −0.0500298 | ||||||||
\(149\) | −8.90678 | −0.729672 | −0.364836 | − | 0.931072i | \(-0.618875\pi\) | ||||
−0.364836 | + | 0.931072i | \(0.618875\pi\) | |||||||
\(150\) | −5.70417 | −0.465744 | ||||||||
\(151\) | −10.9588 | −0.891813 | −0.445907 | − | 0.895080i | \(-0.647119\pi\) | ||||
−0.445907 | + | 0.895080i | \(0.647119\pi\) | |||||||
\(152\) | −4.55822 | −0.369721 | ||||||||
\(153\) | −10.0502 | −0.812507 | ||||||||
\(154\) | 0.440225 | 0.0354744 | ||||||||
\(155\) | 7.23445 | 0.581085 | ||||||||
\(156\) | −1.54273 | −0.123517 | ||||||||
\(157\) | −1.72106 | −0.137356 | −0.0686779 | − | 0.997639i | \(-0.521878\pi\) | ||||
−0.0686779 | + | 0.997639i | \(0.521878\pi\) | |||||||
\(158\) | 9.73748 | 0.774672 | ||||||||
\(159\) | 2.79782 | 0.221881 | ||||||||
\(160\) | 3.89005 | 0.307535 | ||||||||
\(161\) | 0.867650 | 0.0683804 | ||||||||
\(162\) | −6.24813 | −0.490899 | ||||||||
\(163\) | −16.0234 | −1.25505 | −0.627526 | − | 0.778596i | \(-0.715932\pi\) | ||||
−0.627526 | + | 0.778596i | \(0.715932\pi\) | |||||||
\(164\) | −9.86356 | −0.770214 | ||||||||
\(165\) | −1.11112 | −0.0865009 | ||||||||
\(166\) | 3.20604 | 0.248837 | ||||||||
\(167\) | 0.505553 | 0.0391209 | 0.0195604 | − | 0.999809i | \(-0.493773\pi\) | ||||
0.0195604 | + | 0.999809i | \(0.493773\pi\) | |||||||
\(168\) | 0.488452 | 0.0376849 | ||||||||
\(169\) | −5.49024 | −0.422326 | ||||||||
\(170\) | 14.5712 | 1.11756 | ||||||||
\(171\) | −12.2301 | −0.935256 | ||||||||
\(172\) | −1.26441 | −0.0964104 | ||||||||
\(173\) | −3.02549 | −0.230024 | −0.115012 | − | 0.993364i | \(-0.536691\pi\) | ||||
−0.115012 | + | 0.993364i | \(0.536691\pi\) | |||||||
\(174\) | −3.33996 | −0.253202 | ||||||||
\(175\) | −8.79143 | −0.664570 | ||||||||
\(176\) | 0.507376 | 0.0382449 | ||||||||
\(177\) | 2.97605 | 0.223694 | ||||||||
\(178\) | −2.82208 | −0.211524 | ||||||||
\(179\) | −15.7268 | −1.17548 | −0.587739 | − | 0.809050i | \(-0.699982\pi\) | ||||
−0.587739 | + | 0.809050i | \(0.699982\pi\) | |||||||
\(180\) | 10.4373 | 0.777950 | ||||||||
\(181\) | −15.5241 | −1.15390 | −0.576948 | − | 0.816781i | \(-0.695757\pi\) | ||||
−0.576948 | + | 0.816781i | \(0.695757\pi\) | |||||||
\(182\) | −2.37770 | −0.176247 | ||||||||
\(183\) | 7.83263 | 0.579005 | ||||||||
\(184\) | 1.00000 | 0.0737210 | ||||||||
\(185\) | 2.36763 | 0.174072 | ||||||||
\(186\) | 1.04696 | 0.0767665 | ||||||||
\(187\) | 1.90051 | 0.138979 | ||||||||
\(188\) | 8.01654 | 0.584667 | ||||||||
\(189\) | 2.77591 | 0.201918 | ||||||||
\(190\) | 17.7317 | 1.28639 | ||||||||
\(191\) | 0.403227 | 0.0291765 | 0.0145882 | − | 0.999894i | \(-0.495356\pi\) | ||||
0.0145882 | + | 0.999894i | \(0.495356\pi\) | |||||||
\(192\) | 0.562960 | 0.0406281 | ||||||||
\(193\) | −14.3644 | −1.03397 | −0.516985 | − | 0.855994i | \(-0.672946\pi\) | ||||
−0.516985 | + | 0.855994i | \(0.672946\pi\) | |||||||
\(194\) | −5.75507 | −0.413190 | ||||||||
\(195\) | 6.00130 | 0.429762 | ||||||||
\(196\) | −6.24718 | −0.446227 | ||||||||
\(197\) | 6.65067 | 0.473841 | 0.236920 | − | 0.971529i | \(-0.423862\pi\) | ||||
0.236920 | + | 0.971529i | \(0.423862\pi\) | |||||||
\(198\) | 1.36133 | 0.0967455 | ||||||||
\(199\) | 5.24685 | 0.371939 | 0.185970 | − | 0.982555i | \(-0.440457\pi\) | ||||
0.185970 | + | 0.982555i | \(0.440457\pi\) | |||||||
\(200\) | −10.1325 | −0.716474 | ||||||||
\(201\) | −1.76911 | −0.124783 | ||||||||
\(202\) | −9.45619 | −0.665335 | ||||||||
\(203\) | −5.14764 | −0.361294 | ||||||||
\(204\) | 2.10871 | 0.147639 | ||||||||
\(205\) | 38.3697 | 2.67986 | ||||||||
\(206\) | −6.08876 | −0.424224 | ||||||||
\(207\) | 2.68308 | 0.186487 | ||||||||
\(208\) | −2.74039 | −0.190012 | ||||||||
\(209\) | 2.31273 | 0.159975 | ||||||||
\(210\) | −1.90010 | −0.131119 | ||||||||
\(211\) | 3.59198 | 0.247282 | 0.123641 | − | 0.992327i | \(-0.460543\pi\) | ||||
0.123641 | + | 0.992327i | \(0.460543\pi\) | |||||||
\(212\) | 4.96984 | 0.341330 | ||||||||
\(213\) | 6.66598 | 0.456745 | ||||||||
\(214\) | −7.08845 | −0.484557 | ||||||||
\(215\) | 4.91862 | 0.335447 | ||||||||
\(216\) | 3.19934 | 0.217688 | ||||||||
\(217\) | 1.61360 | 0.109538 | ||||||||
\(218\) | 12.7903 | 0.866270 | ||||||||
\(219\) | −5.31000 | −0.358816 | ||||||||
\(220\) | −1.97372 | −0.133068 | ||||||||
\(221\) | −10.2649 | −0.690489 | ||||||||
\(222\) | 0.342639 | 0.0229964 | ||||||||
\(223\) | 24.9469 | 1.67057 | 0.835285 | − | 0.549817i | \(-0.185303\pi\) | ||||
0.835285 | + | 0.549817i | \(0.185303\pi\) | |||||||
\(224\) | 0.867650 | 0.0579723 | ||||||||
\(225\) | −27.1862 | −1.81241 | ||||||||
\(226\) | −18.5333 | −1.23282 | ||||||||
\(227\) | 3.87747 | 0.257357 | 0.128678 | − | 0.991686i | \(-0.458927\pi\) | ||||
0.128678 | + | 0.991686i | \(0.458927\pi\) | |||||||
\(228\) | 2.56609 | 0.169944 | ||||||||
\(229\) | 2.35944 | 0.155916 | 0.0779579 | − | 0.996957i | \(-0.475160\pi\) | ||||
0.0779579 | + | 0.996957i | \(0.475160\pi\) | |||||||
\(230\) | −3.89005 | −0.256502 | ||||||||
\(231\) | −0.247829 | −0.0163060 | ||||||||
\(232\) | −5.93286 | −0.389511 | ||||||||
\(233\) | 1.47211 | 0.0964414 | 0.0482207 | − | 0.998837i | \(-0.484645\pi\) | ||||
0.0482207 | + | 0.998837i | \(0.484645\pi\) | |||||||
\(234\) | −7.35269 | −0.480660 | ||||||||
\(235\) | −31.1847 | −2.03427 | ||||||||
\(236\) | 5.28644 | 0.344118 | ||||||||
\(237\) | −5.48181 | −0.356082 | ||||||||
\(238\) | 3.25001 | 0.210667 | ||||||||
\(239\) | 18.8116 | 1.21682 | 0.608409 | − | 0.793623i | \(-0.291808\pi\) | ||||
0.608409 | + | 0.793623i | \(0.291808\pi\) | |||||||
\(240\) | −2.18994 | −0.141360 | ||||||||
\(241\) | −26.1881 | −1.68692 | −0.843462 | − | 0.537188i | \(-0.819486\pi\) | ||||
−0.843462 | + | 0.537188i | \(0.819486\pi\) | |||||||
\(242\) | 10.7426 | 0.690558 | ||||||||
\(243\) | 13.1155 | 0.841358 | ||||||||
\(244\) | 13.9133 | 0.890708 | ||||||||
\(245\) | 24.3018 | 1.55259 | ||||||||
\(246\) | 5.55279 | 0.354033 | ||||||||
\(247\) | −12.4913 | −0.794804 | ||||||||
\(248\) | 1.85973 | 0.118093 | ||||||||
\(249\) | −1.80487 | −0.114379 | ||||||||
\(250\) | 19.9655 | 1.26273 | ||||||||
\(251\) | 1.24316 | 0.0784673 | 0.0392336 | − | 0.999230i | \(-0.487508\pi\) | ||||
0.0392336 | + | 0.999230i | \(0.487508\pi\) | |||||||
\(252\) | 2.32797 | 0.146648 | ||||||||
\(253\) | −0.507376 | −0.0318985 | ||||||||
\(254\) | −8.13209 | −0.510252 | ||||||||
\(255\) | −8.20299 | −0.513691 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −28.9058 | −1.80310 | −0.901548 | − | 0.432679i | \(-0.857568\pi\) | ||||
−0.901548 | + | 0.432679i | \(0.857568\pi\) | |||||||
\(258\) | 0.711812 | 0.0443155 | ||||||||
\(259\) | 0.528086 | 0.0328136 | ||||||||
\(260\) | 10.6603 | 0.661122 | ||||||||
\(261\) | −15.9183 | −0.985319 | ||||||||
\(262\) | 1.00000 | 0.0617802 | ||||||||
\(263\) | −19.0743 | −1.17617 | −0.588086 | − | 0.808798i | \(-0.700118\pi\) | ||||
−0.588086 | + | 0.808798i | \(0.700118\pi\) | |||||||
\(264\) | −0.285633 | −0.0175795 | ||||||||
\(265\) | −19.3329 | −1.18761 | ||||||||
\(266\) | 3.95494 | 0.242493 | ||||||||
\(267\) | 1.58872 | 0.0972281 | ||||||||
\(268\) | −3.14252 | −0.191960 | ||||||||
\(269\) | −29.5171 | −1.79969 | −0.899846 | − | 0.436208i | \(-0.856321\pi\) | ||||
−0.899846 | + | 0.436208i | \(0.856321\pi\) | |||||||
\(270\) | −12.4456 | −0.757415 | ||||||||
\(271\) | −15.0703 | −0.915453 | −0.457727 | − | 0.889093i | \(-0.651336\pi\) | ||||
−0.457727 | + | 0.889093i | \(0.651336\pi\) | |||||||
\(272\) | 3.74576 | 0.227120 | ||||||||
\(273\) | 1.33855 | 0.0810128 | ||||||||
\(274\) | 6.54458 | 0.395373 | ||||||||
\(275\) | 5.14098 | 0.310012 | ||||||||
\(276\) | −0.562960 | −0.0338862 | ||||||||
\(277\) | 7.02450 | 0.422061 | 0.211031 | − | 0.977479i | \(-0.432318\pi\) | ||||
0.211031 | + | 0.977479i | \(0.432318\pi\) | |||||||
\(278\) | 9.03391 | 0.541818 | ||||||||
\(279\) | 4.98981 | 0.298732 | ||||||||
\(280\) | −3.37520 | −0.201707 | ||||||||
\(281\) | −0.665447 | −0.0396972 | −0.0198486 | − | 0.999803i | \(-0.506318\pi\) | ||||
−0.0198486 | + | 0.999803i | \(0.506318\pi\) | |||||||
\(282\) | −4.51299 | −0.268745 | ||||||||
\(283\) | −6.65446 | −0.395567 | −0.197783 | − | 0.980246i | \(-0.563374\pi\) | ||||
−0.197783 | + | 0.980246i | \(0.563374\pi\) | |||||||
\(284\) | 11.8409 | 0.702631 | ||||||||
\(285\) | −9.98223 | −0.591296 | ||||||||
\(286\) | 1.39041 | 0.0822168 | ||||||||
\(287\) | 8.55811 | 0.505169 | ||||||||
\(288\) | 2.68308 | 0.158102 | ||||||||
\(289\) | −2.96930 | −0.174664 | ||||||||
\(290\) | 23.0791 | 1.35525 | ||||||||
\(291\) | 3.23988 | 0.189925 | ||||||||
\(292\) | −9.43228 | −0.551983 | ||||||||
\(293\) | −11.6228 | −0.679009 | −0.339504 | − | 0.940604i | \(-0.610259\pi\) | ||||
−0.339504 | + | 0.940604i | \(0.610259\pi\) | |||||||
\(294\) | 3.51691 | 0.205111 | ||||||||
\(295\) | −20.5645 | −1.19731 | ||||||||
\(296\) | 0.608639 | 0.0353764 | ||||||||
\(297\) | −1.62327 | −0.0941918 | ||||||||
\(298\) | 8.90678 | 0.515956 | ||||||||
\(299\) | 2.74039 | 0.158481 | ||||||||
\(300\) | 5.70417 | 0.329330 | ||||||||
\(301\) | 1.09707 | 0.0632338 | ||||||||
\(302\) | 10.9588 | 0.630607 | ||||||||
\(303\) | 5.32346 | 0.305825 | ||||||||
\(304\) | 4.55822 | 0.261432 | ||||||||
\(305\) | −54.1234 | −3.09910 | ||||||||
\(306\) | 10.0502 | 0.574529 | ||||||||
\(307\) | −22.6431 | −1.29231 | −0.646154 | − | 0.763207i | \(-0.723624\pi\) | ||||
−0.646154 | + | 0.763207i | \(0.723624\pi\) | |||||||
\(308\) | −0.440225 | −0.0250842 | ||||||||
\(309\) | 3.42772 | 0.194996 | ||||||||
\(310\) | −7.23445 | −0.410889 | ||||||||
\(311\) | −20.0523 | −1.13706 | −0.568531 | − | 0.822662i | \(-0.692488\pi\) | ||||
−0.568531 | + | 0.822662i | \(0.692488\pi\) | |||||||
\(312\) | 1.54273 | 0.0873400 | ||||||||
\(313\) | −0.443118 | −0.0250465 | −0.0125233 | − | 0.999922i | \(-0.503986\pi\) | ||||
−0.0125233 | + | 0.999922i | \(0.503986\pi\) | |||||||
\(314\) | 1.72106 | 0.0971253 | ||||||||
\(315\) | −9.05592 | −0.510243 | ||||||||
\(316\) | −9.73748 | −0.547776 | ||||||||
\(317\) | −6.21367 | −0.348995 | −0.174497 | − | 0.984658i | \(-0.555830\pi\) | ||||
−0.174497 | + | 0.984658i | \(0.555830\pi\) | |||||||
\(318\) | −2.79782 | −0.156894 | ||||||||
\(319\) | 3.01019 | 0.168538 | ||||||||
\(320\) | −3.89005 | −0.217460 | ||||||||
\(321\) | 3.99051 | 0.222729 | ||||||||
\(322\) | −0.867650 | −0.0483522 | ||||||||
\(323\) | 17.0740 | 0.950022 | ||||||||
\(324\) | 6.24813 | 0.347118 | ||||||||
\(325\) | −27.7670 | −1.54023 | ||||||||
\(326\) | 16.0234 | 0.887455 | ||||||||
\(327\) | −7.20044 | −0.398185 | ||||||||
\(328\) | 9.86356 | 0.544624 | ||||||||
\(329\) | −6.95555 | −0.383472 | ||||||||
\(330\) | 1.11112 | 0.0611654 | ||||||||
\(331\) | 32.4781 | 1.78516 | 0.892579 | − | 0.450891i | \(-0.148894\pi\) | ||||
0.892579 | + | 0.450891i | \(0.148894\pi\) | |||||||
\(332\) | −3.20604 | −0.175954 | ||||||||
\(333\) | 1.63303 | 0.0894892 | ||||||||
\(334\) | −0.505553 | −0.0276626 | ||||||||
\(335\) | 12.2245 | 0.667898 | ||||||||
\(336\) | −0.488452 | −0.0266472 | ||||||||
\(337\) | 2.43414 | 0.132596 | 0.0662979 | − | 0.997800i | \(-0.478881\pi\) | ||||
0.0662979 | + | 0.997800i | \(0.478881\pi\) | |||||||
\(338\) | 5.49024 | 0.298630 | ||||||||
\(339\) | 10.4335 | 0.566671 | ||||||||
\(340\) | −14.5712 | −0.790233 | ||||||||
\(341\) | −0.943585 | −0.0510980 | ||||||||
\(342\) | 12.2301 | 0.661326 | ||||||||
\(343\) | 11.4939 | 0.620613 | ||||||||
\(344\) | 1.26441 | 0.0681725 | ||||||||
\(345\) | 2.18994 | 0.117902 | ||||||||
\(346\) | 3.02549 | 0.162651 | ||||||||
\(347\) | −7.34369 | −0.394230 | −0.197115 | − | 0.980380i | \(-0.563157\pi\) | ||||
−0.197115 | + | 0.980380i | \(0.563157\pi\) | |||||||
\(348\) | 3.33996 | 0.179041 | ||||||||
\(349\) | 22.6977 | 1.21498 | 0.607491 | − | 0.794327i | \(-0.292176\pi\) | ||||
0.607491 | + | 0.794327i | \(0.292176\pi\) | |||||||
\(350\) | 8.79143 | 0.469922 | ||||||||
\(351\) | 8.76746 | 0.467973 | ||||||||
\(352\) | −0.507376 | −0.0270433 | ||||||||
\(353\) | 4.70965 | 0.250670 | 0.125335 | − | 0.992115i | \(-0.459999\pi\) | ||||
0.125335 | + | 0.992115i | \(0.459999\pi\) | |||||||
\(354\) | −2.97605 | −0.158175 | ||||||||
\(355\) | −46.0618 | −2.44471 | ||||||||
\(356\) | 2.82208 | 0.149570 | ||||||||
\(357\) | −1.82962 | −0.0968339 | ||||||||
\(358\) | 15.7268 | 0.831189 | ||||||||
\(359\) | −27.9901 | −1.47726 | −0.738630 | − | 0.674111i | \(-0.764527\pi\) | ||||
−0.738630 | + | 0.674111i | \(0.764527\pi\) | |||||||
\(360\) | −10.4373 | −0.550094 | ||||||||
\(361\) | 1.77738 | 0.0935462 | ||||||||
\(362\) | 15.5241 | 0.815928 | ||||||||
\(363\) | −6.04763 | −0.317418 | ||||||||
\(364\) | 2.37770 | 0.124626 | ||||||||
\(365\) | 36.6920 | 1.92055 | ||||||||
\(366\) | −7.83263 | −0.409418 | ||||||||
\(367\) | −10.5595 | −0.551199 | −0.275599 | − | 0.961273i | \(-0.588876\pi\) | ||||
−0.275599 | + | 0.961273i | \(0.588876\pi\) | |||||||
\(368\) | −1.00000 | −0.0521286 | ||||||||
\(369\) | 26.4647 | 1.37770 | ||||||||
\(370\) | −2.36763 | −0.123087 | ||||||||
\(371\) | −4.31208 | −0.223872 | ||||||||
\(372\) | −1.04696 | −0.0542821 | ||||||||
\(373\) | −20.6225 | −1.06779 | −0.533897 | − | 0.845550i | \(-0.679273\pi\) | ||||
−0.533897 | + | 0.845550i | \(0.679273\pi\) | |||||||
\(374\) | −1.90051 | −0.0982730 | ||||||||
\(375\) | −11.2398 | −0.580421 | ||||||||
\(376\) | −8.01654 | −0.413422 | ||||||||
\(377\) | −16.2584 | −0.837349 | ||||||||
\(378\) | −2.77591 | −0.142777 | ||||||||
\(379\) | −0.843533 | −0.0433294 | −0.0216647 | − | 0.999765i | \(-0.506897\pi\) | ||||
−0.0216647 | + | 0.999765i | \(0.506897\pi\) | |||||||
\(380\) | −17.7317 | −0.909617 | ||||||||
\(381\) | 4.57804 | 0.234540 | ||||||||
\(382\) | −0.403227 | −0.0206309 | ||||||||
\(383\) | 0.943042 | 0.0481872 | 0.0240936 | − | 0.999710i | \(-0.492330\pi\) | ||||
0.0240936 | + | 0.999710i | \(0.492330\pi\) | |||||||
\(384\) | −0.562960 | −0.0287284 | ||||||||
\(385\) | 1.71250 | 0.0872769 | ||||||||
\(386\) | 14.3644 | 0.731127 | ||||||||
\(387\) | 3.39251 | 0.172451 | ||||||||
\(388\) | 5.75507 | 0.292170 | ||||||||
\(389\) | 7.05035 | 0.357467 | 0.178733 | − | 0.983898i | \(-0.442800\pi\) | ||||
0.178733 | + | 0.983898i | \(0.442800\pi\) | |||||||
\(390\) | −6.00130 | −0.303888 | ||||||||
\(391\) | −3.74576 | −0.189431 | ||||||||
\(392\) | 6.24718 | 0.315530 | ||||||||
\(393\) | −0.562960 | −0.0283976 | ||||||||
\(394\) | −6.65067 | −0.335056 | ||||||||
\(395\) | 37.8792 | 1.90591 | ||||||||
\(396\) | −1.36133 | −0.0684094 | ||||||||
\(397\) | −3.30514 | −0.165880 | −0.0829402 | − | 0.996555i | \(-0.526431\pi\) | ||||
−0.0829402 | + | 0.996555i | \(0.526431\pi\) | |||||||
\(398\) | −5.24685 | −0.263001 | ||||||||
\(399\) | −2.22647 | −0.111463 | ||||||||
\(400\) | 10.1325 | 0.506623 | ||||||||
\(401\) | −17.5817 | −0.877988 | −0.438994 | − | 0.898490i | \(-0.644665\pi\) | ||||
−0.438994 | + | 0.898490i | \(0.644665\pi\) | |||||||
\(402\) | 1.76911 | 0.0882352 | ||||||||
\(403\) | 5.09640 | 0.253870 | ||||||||
\(404\) | 9.45619 | 0.470463 | ||||||||
\(405\) | −24.3055 | −1.20775 | ||||||||
\(406\) | 5.14764 | 0.255473 | ||||||||
\(407\) | −0.308809 | −0.0153071 | ||||||||
\(408\) | −2.10871 | −0.104397 | ||||||||
\(409\) | −6.48197 | −0.320513 | −0.160256 | − | 0.987075i | \(-0.551232\pi\) | ||||
−0.160256 | + | 0.987075i | \(0.551232\pi\) | |||||||
\(410\) | −38.3697 | −1.89494 | ||||||||
\(411\) | −3.68434 | −0.181735 | ||||||||
\(412\) | 6.08876 | 0.299971 | ||||||||
\(413\) | −4.58678 | −0.225701 | ||||||||
\(414\) | −2.68308 | −0.131866 | ||||||||
\(415\) | 12.4716 | 0.612209 | ||||||||
\(416\) | 2.74039 | 0.134359 | ||||||||
\(417\) | −5.08573 | −0.249049 | ||||||||
\(418\) | −2.31273 | −0.113120 | ||||||||
\(419\) | 21.0811 | 1.02988 | 0.514940 | − | 0.857226i | \(-0.327814\pi\) | ||||
0.514940 | + | 0.857226i | \(0.327814\pi\) | |||||||
\(420\) | 1.90010 | 0.0927154 | ||||||||
\(421\) | −3.48417 | −0.169808 | −0.0849041 | − | 0.996389i | \(-0.527058\pi\) | ||||
−0.0849041 | + | 0.996389i | \(0.527058\pi\) | |||||||
\(422\) | −3.59198 | −0.174855 | ||||||||
\(423\) | −21.5090 | −1.04580 | ||||||||
\(424\) | −4.96984 | −0.241357 | ||||||||
\(425\) | 37.9538 | 1.84103 | ||||||||
\(426\) | −6.66598 | −0.322968 | ||||||||
\(427\) | −12.0719 | −0.584199 | ||||||||
\(428\) | 7.08845 | 0.342633 | ||||||||
\(429\) | −0.782746 | −0.0377913 | ||||||||
\(430\) | −4.91862 | −0.237197 | ||||||||
\(431\) | −15.4716 | −0.745243 | −0.372621 | − | 0.927983i | \(-0.621541\pi\) | ||||
−0.372621 | + | 0.927983i | \(0.621541\pi\) | |||||||
\(432\) | −3.19934 | −0.153928 | ||||||||
\(433\) | −20.3427 | −0.977606 | −0.488803 | − | 0.872394i | \(-0.662566\pi\) | ||||
−0.488803 | + | 0.872394i | \(0.662566\pi\) | |||||||
\(434\) | −1.61360 | −0.0774552 | ||||||||
\(435\) | −12.9926 | −0.622948 | ||||||||
\(436\) | −12.7903 | −0.612546 | ||||||||
\(437\) | −4.55822 | −0.218049 | ||||||||
\(438\) | 5.31000 | 0.253721 | ||||||||
\(439\) | 17.6676 | 0.843229 | 0.421614 | − | 0.906775i | \(-0.361464\pi\) | ||||
0.421614 | + | 0.906775i | \(0.361464\pi\) | |||||||
\(440\) | 1.97372 | 0.0940933 | ||||||||
\(441\) | 16.7617 | 0.798175 | ||||||||
\(442\) | 10.2649 | 0.488249 | ||||||||
\(443\) | 20.9706 | 0.996346 | 0.498173 | − | 0.867078i | \(-0.334005\pi\) | ||||
0.498173 | + | 0.867078i | \(0.334005\pi\) | |||||||
\(444\) | −0.342639 | −0.0162609 | ||||||||
\(445\) | −10.9780 | −0.520409 | ||||||||
\(446\) | −24.9469 | −1.18127 | ||||||||
\(447\) | −5.01416 | −0.237162 | ||||||||
\(448\) | −0.867650 | −0.0409926 | ||||||||
\(449\) | 0.184554 | 0.00870963 | 0.00435482 | − | 0.999991i | \(-0.498614\pi\) | ||||
0.00435482 | + | 0.999991i | \(0.498614\pi\) | |||||||
\(450\) | 27.1862 | 1.28157 | ||||||||
\(451\) | −5.00454 | −0.235654 | ||||||||
\(452\) | 18.5333 | 0.871734 | ||||||||
\(453\) | −6.16935 | −0.289862 | ||||||||
\(454\) | −3.87747 | −0.181979 | ||||||||
\(455\) | −9.24938 | −0.433618 | ||||||||
\(456\) | −2.56609 | −0.120168 | ||||||||
\(457\) | 0.149083 | 0.00697381 | 0.00348691 | − | 0.999994i | \(-0.498890\pi\) | ||||
0.00348691 | + | 0.999994i | \(0.498890\pi\) | |||||||
\(458\) | −2.35944 | −0.110249 | ||||||||
\(459\) | −11.9840 | −0.559364 | ||||||||
\(460\) | 3.89005 | 0.181374 | ||||||||
\(461\) | −16.6132 | −0.773756 | −0.386878 | − | 0.922131i | \(-0.626446\pi\) | ||||
−0.386878 | + | 0.922131i | \(0.626446\pi\) | |||||||
\(462\) | 0.247829 | 0.0115300 | ||||||||
\(463\) | 31.6334 | 1.47013 | 0.735065 | − | 0.677996i | \(-0.237152\pi\) | ||||
0.735065 | + | 0.677996i | \(0.237152\pi\) | |||||||
\(464\) | 5.93286 | 0.275426 | ||||||||
\(465\) | 4.07271 | 0.188867 | ||||||||
\(466\) | −1.47211 | −0.0681944 | ||||||||
\(467\) | −7.99381 | −0.369909 | −0.184955 | − | 0.982747i | \(-0.559214\pi\) | ||||
−0.184955 | + | 0.982747i | \(0.559214\pi\) | |||||||
\(468\) | 7.35269 | 0.339878 | ||||||||
\(469\) | 2.72660 | 0.125903 | ||||||||
\(470\) | 31.1847 | 1.43844 | ||||||||
\(471\) | −0.968890 | −0.0446441 | ||||||||
\(472\) | −5.28644 | −0.243328 | ||||||||
\(473\) | −0.641532 | −0.0294977 | ||||||||
\(474\) | 5.48181 | 0.251788 | ||||||||
\(475\) | 46.1860 | 2.11916 | ||||||||
\(476\) | −3.25001 | −0.148964 | ||||||||
\(477\) | −13.3345 | −0.610543 | ||||||||
\(478\) | −18.8116 | −0.860421 | ||||||||
\(479\) | 25.9475 | 1.18557 | 0.592786 | − | 0.805360i | \(-0.298028\pi\) | ||||
0.592786 | + | 0.805360i | \(0.298028\pi\) | |||||||
\(480\) | 2.18994 | 0.0999566 | ||||||||
\(481\) | 1.66791 | 0.0760502 | ||||||||
\(482\) | 26.1881 | 1.19284 | ||||||||
\(483\) | 0.488452 | 0.0222253 | ||||||||
\(484\) | −10.7426 | −0.488299 | ||||||||
\(485\) | −22.3875 | −1.01656 | ||||||||
\(486\) | −13.1155 | −0.594930 | ||||||||
\(487\) | 29.3717 | 1.33096 | 0.665479 | − | 0.746417i | \(-0.268227\pi\) | ||||
0.665479 | + | 0.746417i | \(0.268227\pi\) | |||||||
\(488\) | −13.9133 | −0.629826 | ||||||||
\(489\) | −9.02054 | −0.407923 | ||||||||
\(490\) | −24.3018 | −1.09785 | ||||||||
\(491\) | 28.1115 | 1.26865 | 0.634327 | − | 0.773065i | \(-0.281277\pi\) | ||||
0.634327 | + | 0.773065i | \(0.281277\pi\) | |||||||
\(492\) | −5.55279 | −0.250339 | ||||||||
\(493\) | 22.2231 | 1.00088 | ||||||||
\(494\) | 12.4913 | 0.562011 | ||||||||
\(495\) | 5.29564 | 0.238021 | ||||||||
\(496\) | −1.85973 | −0.0835045 | ||||||||
\(497\) | −10.2738 | −0.460843 | ||||||||
\(498\) | 1.80487 | 0.0808782 | ||||||||
\(499\) | 14.3639 | 0.643015 | 0.321508 | − | 0.946907i | \(-0.395810\pi\) | ||||
0.321508 | + | 0.946907i | \(0.395810\pi\) | |||||||
\(500\) | −19.9655 | −0.892886 | ||||||||
\(501\) | 0.284606 | 0.0127153 | ||||||||
\(502\) | −1.24316 | −0.0554848 | ||||||||
\(503\) | 25.9961 | 1.15911 | 0.579554 | − | 0.814934i | \(-0.303227\pi\) | ||||
0.579554 | + | 0.814934i | \(0.303227\pi\) | |||||||
\(504\) | −2.32797 | −0.103696 | ||||||||
\(505\) | −36.7850 | −1.63691 | ||||||||
\(506\) | 0.507376 | 0.0225556 | ||||||||
\(507\) | −3.09078 | −0.137266 | ||||||||
\(508\) | 8.13209 | 0.360803 | ||||||||
\(509\) | 1.10438 | 0.0489506 | 0.0244753 | − | 0.999700i | \(-0.492208\pi\) | ||||
0.0244753 | + | 0.999700i | \(0.492208\pi\) | |||||||
\(510\) | 8.20299 | 0.363234 | ||||||||
\(511\) | 8.18392 | 0.362035 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −14.5833 | −0.643869 | ||||||||
\(514\) | 28.9058 | 1.27498 | ||||||||
\(515\) | −23.6855 | −1.04371 | ||||||||
\(516\) | −0.711812 | −0.0313358 | ||||||||
\(517\) | 4.06741 | 0.178884 | ||||||||
\(518\) | −0.528086 | −0.0232028 | ||||||||
\(519\) | −1.70323 | −0.0747634 | ||||||||
\(520\) | −10.6603 | −0.467484 | ||||||||
\(521\) | 31.3119 | 1.37180 | 0.685900 | − | 0.727695i | \(-0.259409\pi\) | ||||
0.685900 | + | 0.727695i | \(0.259409\pi\) | |||||||
\(522\) | 15.9183 | 0.696726 | ||||||||
\(523\) | −4.33176 | −0.189415 | −0.0947074 | − | 0.995505i | \(-0.530192\pi\) | ||||
−0.0947074 | + | 0.995505i | \(0.530192\pi\) | |||||||
\(524\) | −1.00000 | −0.0436852 | ||||||||
\(525\) | −4.94922 | −0.216002 | ||||||||
\(526\) | 19.0743 | 0.831680 | ||||||||
\(527\) | −6.96611 | −0.303449 | ||||||||
\(528\) | 0.285633 | 0.0124306 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 19.3329 | 0.839768 | ||||||||
\(531\) | −14.1839 | −0.615530 | ||||||||
\(532\) | −3.95494 | −0.171468 | ||||||||
\(533\) | 27.0300 | 1.17080 | ||||||||
\(534\) | −1.58872 | −0.0687506 | ||||||||
\(535\) | −27.5744 | −1.19215 | ||||||||
\(536\) | 3.14252 | 0.135736 | ||||||||
\(537\) | −8.85357 | −0.382060 | ||||||||
\(538\) | 29.5171 | 1.27257 | ||||||||
\(539\) | −3.16967 | −0.136528 | ||||||||
\(540\) | 12.4456 | 0.535573 | ||||||||
\(541\) | 38.7795 | 1.66726 | 0.833630 | − | 0.552323i | \(-0.186258\pi\) | ||||
0.833630 | + | 0.552323i | \(0.186258\pi\) | |||||||
\(542\) | 15.0703 | 0.647323 | ||||||||
\(543\) | −8.73944 | −0.375045 | ||||||||
\(544\) | −3.74576 | −0.160598 | ||||||||
\(545\) | 49.7550 | 2.13127 | ||||||||
\(546\) | −1.33855 | −0.0572847 | ||||||||
\(547\) | 33.5932 | 1.43634 | 0.718171 | − | 0.695866i | \(-0.244979\pi\) | ||||
0.718171 | + | 0.695866i | \(0.244979\pi\) | |||||||
\(548\) | −6.54458 | −0.279571 | ||||||||
\(549\) | −37.3304 | −1.59322 | ||||||||
\(550\) | −5.14098 | −0.219212 | ||||||||
\(551\) | 27.0433 | 1.15208 | ||||||||
\(552\) | 0.562960 | 0.0239612 | ||||||||
\(553\) | 8.44872 | 0.359276 | ||||||||
\(554\) | −7.02450 | −0.298443 | ||||||||
\(555\) | 1.33288 | 0.0565777 | ||||||||
\(556\) | −9.03391 | −0.383123 | ||||||||
\(557\) | −36.3397 | −1.53976 | −0.769881 | − | 0.638188i | \(-0.779684\pi\) | ||||
−0.769881 | + | 0.638188i | \(0.779684\pi\) | |||||||
\(558\) | −4.98981 | −0.211235 | ||||||||
\(559\) | 3.46499 | 0.146553 | ||||||||
\(560\) | 3.37520 | 0.142628 | ||||||||
\(561\) | 1.06991 | 0.0451716 | ||||||||
\(562\) | 0.665447 | 0.0280702 | ||||||||
\(563\) | −0.485090 | −0.0204441 | −0.0102220 | − | 0.999948i | \(-0.503254\pi\) | ||||
−0.0102220 | + | 0.999948i | \(0.503254\pi\) | |||||||
\(564\) | 4.51299 | 0.190031 | ||||||||
\(565\) | −72.0955 | −3.03308 | ||||||||
\(566\) | 6.65446 | 0.279708 | ||||||||
\(567\) | −5.42119 | −0.227668 | ||||||||
\(568\) | −11.8409 | −0.496835 | ||||||||
\(569\) | −6.11144 | −0.256205 | −0.128102 | − | 0.991761i | \(-0.540889\pi\) | ||||
−0.128102 | + | 0.991761i | \(0.540889\pi\) | |||||||
\(570\) | 9.98223 | 0.418110 | ||||||||
\(571\) | −12.3642 | −0.517427 | −0.258713 | − | 0.965954i | \(-0.583299\pi\) | ||||
−0.258713 | + | 0.965954i | \(0.583299\pi\) | |||||||
\(572\) | −1.39041 | −0.0581360 | ||||||||
\(573\) | 0.227001 | 0.00948308 | ||||||||
\(574\) | −8.55811 | −0.357209 | ||||||||
\(575\) | −10.1325 | −0.422553 | ||||||||
\(576\) | −2.68308 | −0.111795 | ||||||||
\(577\) | 9.10810 | 0.379175 | 0.189588 | − | 0.981864i | \(-0.439285\pi\) | ||||
0.189588 | + | 0.981864i | \(0.439285\pi\) | |||||||
\(578\) | 2.96930 | 0.123506 | ||||||||
\(579\) | −8.08656 | −0.336066 | ||||||||
\(580\) | −23.0791 | −0.958308 | ||||||||
\(581\) | 2.78172 | 0.115405 | ||||||||
\(582\) | −3.23988 | −0.134297 | ||||||||
\(583\) | 2.52158 | 0.104433 | ||||||||
\(584\) | 9.43228 | 0.390311 | ||||||||
\(585\) | −28.6023 | −1.18256 | ||||||||
\(586\) | 11.6228 | 0.480132 | ||||||||
\(587\) | −16.8302 | −0.694657 | −0.347328 | − | 0.937744i | \(-0.612911\pi\) | ||||
−0.347328 | + | 0.937744i | \(0.612911\pi\) | |||||||
\(588\) | −3.51691 | −0.145035 | ||||||||
\(589\) | −8.47708 | −0.349292 | ||||||||
\(590\) | 20.5645 | 0.846627 | ||||||||
\(591\) | 3.74406 | 0.154010 | ||||||||
\(592\) | −0.608639 | −0.0250149 | ||||||||
\(593\) | −23.4869 | −0.964490 | −0.482245 | − | 0.876036i | \(-0.660178\pi\) | ||||
−0.482245 | + | 0.876036i | \(0.660178\pi\) | |||||||
\(594\) | 1.62327 | 0.0666036 | ||||||||
\(595\) | 12.6427 | 0.518299 | ||||||||
\(596\) | −8.90678 | −0.364836 | ||||||||
\(597\) | 2.95376 | 0.120890 | ||||||||
\(598\) | −2.74039 | −0.112063 | ||||||||
\(599\) | −1.53838 | −0.0628567 | −0.0314284 | − | 0.999506i | \(-0.510006\pi\) | ||||
−0.0314284 | + | 0.999506i | \(0.510006\pi\) | |||||||
\(600\) | −5.70417 | −0.232872 | ||||||||
\(601\) | −36.9377 | −1.50672 | −0.753359 | − | 0.657609i | \(-0.771568\pi\) | ||||
−0.753359 | + | 0.657609i | \(0.771568\pi\) | |||||||
\(602\) | −1.09707 | −0.0447131 | ||||||||
\(603\) | 8.43161 | 0.343362 | ||||||||
\(604\) | −10.9588 | −0.445907 | ||||||||
\(605\) | 41.7891 | 1.69897 | ||||||||
\(606\) | −5.32346 | −0.216251 | ||||||||
\(607\) | 42.2010 | 1.71289 | 0.856444 | − | 0.516240i | \(-0.172669\pi\) | ||||
0.856444 | + | 0.516240i | \(0.172669\pi\) | |||||||
\(608\) | −4.55822 | −0.184860 | ||||||||
\(609\) | −2.89792 | −0.117430 | ||||||||
\(610\) | 54.1234 | 2.19139 | ||||||||
\(611\) | −21.9685 | −0.888750 | ||||||||
\(612\) | −10.0502 | −0.406253 | ||||||||
\(613\) | −11.0111 | −0.444734 | −0.222367 | − | 0.974963i | \(-0.571378\pi\) | ||||
−0.222367 | + | 0.974963i | \(0.571378\pi\) | |||||||
\(614\) | 22.6431 | 0.913799 | ||||||||
\(615\) | 21.6006 | 0.871020 | ||||||||
\(616\) | 0.440225 | 0.0177372 | ||||||||
\(617\) | −6.45232 | −0.259761 | −0.129880 | − | 0.991530i | \(-0.541459\pi\) | ||||
−0.129880 | + | 0.991530i | \(0.541459\pi\) | |||||||
\(618\) | −3.42772 | −0.137883 | ||||||||
\(619\) | −31.6631 | −1.27265 | −0.636323 | − | 0.771423i | \(-0.719545\pi\) | ||||
−0.636323 | + | 0.771423i | \(0.719545\pi\) | |||||||
\(620\) | 7.23445 | 0.290543 | ||||||||
\(621\) | 3.19934 | 0.128385 | ||||||||
\(622\) | 20.0523 | 0.804025 | ||||||||
\(623\) | −2.44858 | −0.0981003 | ||||||||
\(624\) | −1.54273 | −0.0617587 | ||||||||
\(625\) | 27.0046 | 1.08018 | ||||||||
\(626\) | 0.443118 | 0.0177106 | ||||||||
\(627\) | 1.30198 | 0.0519959 | ||||||||
\(628\) | −1.72106 | −0.0686779 | ||||||||
\(629\) | −2.27981 | −0.0909022 | ||||||||
\(630\) | 9.05592 | 0.360796 | ||||||||
\(631\) | 11.9404 | 0.475339 | 0.237669 | − | 0.971346i | \(-0.423617\pi\) | ||||
0.237669 | + | 0.971346i | \(0.423617\pi\) | |||||||
\(632\) | 9.73748 | 0.387336 | ||||||||
\(633\) | 2.02214 | 0.0803730 | ||||||||
\(634\) | 6.21367 | 0.246776 | ||||||||
\(635\) | −31.6342 | −1.25536 | ||||||||
\(636\) | 2.79782 | 0.110941 | ||||||||
\(637\) | 17.1197 | 0.678309 | ||||||||
\(638\) | −3.01019 | −0.119175 | ||||||||
\(639\) | −31.7702 | −1.25681 | ||||||||
\(640\) | 3.89005 | 0.153768 | ||||||||
\(641\) | −10.4927 | −0.414438 | −0.207219 | − | 0.978295i | \(-0.566441\pi\) | ||||
−0.207219 | + | 0.978295i | \(0.566441\pi\) | |||||||
\(642\) | −3.99051 | −0.157493 | ||||||||
\(643\) | −31.2591 | −1.23274 | −0.616370 | − | 0.787456i | \(-0.711398\pi\) | ||||
−0.616370 | + | 0.787456i | \(0.711398\pi\) | |||||||
\(644\) | 0.867650 | 0.0341902 | ||||||||
\(645\) | 2.76898 | 0.109029 | ||||||||
\(646\) | −17.0740 | −0.671767 | ||||||||
\(647\) | 20.3952 | 0.801816 | 0.400908 | − | 0.916118i | \(-0.368695\pi\) | ||||
0.400908 | + | 0.916118i | \(0.368695\pi\) | |||||||
\(648\) | −6.24813 | −0.245450 | ||||||||
\(649\) | 2.68222 | 0.105286 | ||||||||
\(650\) | 27.7670 | 1.08911 | ||||||||
\(651\) | 0.908391 | 0.0356026 | ||||||||
\(652\) | −16.0234 | −0.627526 | ||||||||
\(653\) | 13.1835 | 0.515911 | 0.257955 | − | 0.966157i | \(-0.416951\pi\) | ||||
0.257955 | + | 0.966157i | \(0.416951\pi\) | |||||||
\(654\) | 7.20044 | 0.281559 | ||||||||
\(655\) | 3.89005 | 0.151997 | ||||||||
\(656\) | −9.86356 | −0.385107 | ||||||||
\(657\) | 25.3075 | 0.987341 | ||||||||
\(658\) | 6.95555 | 0.271156 | ||||||||
\(659\) | −31.6090 | −1.23131 | −0.615656 | − | 0.788015i | \(-0.711109\pi\) | ||||
−0.615656 | + | 0.788015i | \(0.711109\pi\) | |||||||
\(660\) | −1.11112 | −0.0432504 | ||||||||
\(661\) | −43.5918 | −1.69552 | −0.847762 | − | 0.530377i | \(-0.822051\pi\) | ||||
−0.847762 | + | 0.530377i | \(0.822051\pi\) | |||||||
\(662\) | −32.4781 | −1.26230 | ||||||||
\(663\) | −5.77870 | −0.224426 | ||||||||
\(664\) | 3.20604 | 0.124418 | ||||||||
\(665\) | 15.3849 | 0.596601 | ||||||||
\(666\) | −1.63303 | −0.0632784 | ||||||||
\(667\) | −5.93286 | −0.229721 | ||||||||
\(668\) | 0.505553 | 0.0195604 | ||||||||
\(669\) | 14.0441 | 0.542977 | ||||||||
\(670\) | −12.2245 | −0.472275 | ||||||||
\(671\) | 7.05928 | 0.272521 | ||||||||
\(672\) | 0.488452 | 0.0188424 | ||||||||
\(673\) | −5.69159 | −0.219395 | −0.109697 | − | 0.993965i | \(-0.534988\pi\) | ||||
−0.109697 | + | 0.993965i | \(0.534988\pi\) | |||||||
\(674\) | −2.43414 | −0.0937595 | ||||||||
\(675\) | −32.4172 | −1.24774 | ||||||||
\(676\) | −5.49024 | −0.211163 | ||||||||
\(677\) | 27.7504 | 1.06653 | 0.533267 | − | 0.845947i | \(-0.320964\pi\) | ||||
0.533267 | + | 0.845947i | \(0.320964\pi\) | |||||||
\(678\) | −10.4335 | −0.400697 | ||||||||
\(679\) | −4.99339 | −0.191629 | ||||||||
\(680\) | 14.5712 | 0.558779 | ||||||||
\(681\) | 2.18286 | 0.0836473 | ||||||||
\(682\) | 0.943585 | 0.0361317 | ||||||||
\(683\) | −11.9064 | −0.455584 | −0.227792 | − | 0.973710i | \(-0.573151\pi\) | ||||
−0.227792 | + | 0.973710i | \(0.573151\pi\) | |||||||
\(684\) | −12.2301 | −0.467628 | ||||||||
\(685\) | 25.4587 | 0.972728 | ||||||||
\(686\) | −11.4939 | −0.438840 | ||||||||
\(687\) | 1.32827 | 0.0506766 | ||||||||
\(688\) | −1.26441 | −0.0482052 | ||||||||
\(689\) | −13.6193 | −0.518855 | ||||||||
\(690\) | −2.18994 | −0.0833696 | ||||||||
\(691\) | −36.9998 | −1.40754 | −0.703769 | − | 0.710429i | \(-0.748501\pi\) | ||||
−0.703769 | + | 0.710429i | \(0.748501\pi\) | |||||||
\(692\) | −3.02549 | −0.115012 | ||||||||
\(693\) | 1.18116 | 0.0448685 | ||||||||
\(694\) | 7.34369 | 0.278763 | ||||||||
\(695\) | 35.1423 | 1.33302 | ||||||||
\(696\) | −3.33996 | −0.126601 | ||||||||
\(697\) | −36.9465 | −1.39945 | ||||||||
\(698\) | −22.6977 | −0.859122 | ||||||||
\(699\) | 0.828741 | 0.0313459 | ||||||||
\(700\) | −8.79143 | −0.332285 | ||||||||
\(701\) | 16.4539 | 0.621456 | 0.310728 | − | 0.950499i | \(-0.399427\pi\) | ||||
0.310728 | + | 0.950499i | \(0.399427\pi\) | |||||||
\(702\) | −8.76746 | −0.330907 | ||||||||
\(703\) | −2.77431 | −0.104635 | ||||||||
\(704\) | 0.507376 | 0.0191225 | ||||||||
\(705\) | −17.5557 | −0.661188 | ||||||||
\(706\) | −4.70965 | −0.177250 | ||||||||
\(707\) | −8.20466 | −0.308568 | ||||||||
\(708\) | 2.97605 | 0.111847 | ||||||||
\(709\) | 1.27314 | 0.0478137 | 0.0239069 | − | 0.999714i | \(-0.492389\pi\) | ||||
0.0239069 | + | 0.999714i | \(0.492389\pi\) | |||||||
\(710\) | 46.0618 | 1.72867 | ||||||||
\(711\) | 26.1264 | 0.979816 | ||||||||
\(712\) | −2.82208 | −0.105762 | ||||||||
\(713\) | 1.85973 | 0.0696476 | ||||||||
\(714\) | 1.82962 | 0.0684719 | ||||||||
\(715\) | 5.40877 | 0.202276 | ||||||||
\(716\) | −15.7268 | −0.587739 | ||||||||
\(717\) | 10.5902 | 0.395496 | ||||||||
\(718\) | 27.9901 | 1.04458 | ||||||||
\(719\) | 25.9542 | 0.967929 | 0.483965 | − | 0.875088i | \(-0.339196\pi\) | ||||
0.483965 | + | 0.875088i | \(0.339196\pi\) | |||||||
\(720\) | 10.4373 | 0.388975 | ||||||||
\(721\) | −5.28291 | −0.196746 | ||||||||
\(722\) | −1.77738 | −0.0661471 | ||||||||
\(723\) | −14.7429 | −0.548293 | ||||||||
\(724\) | −15.5241 | −0.576948 | ||||||||
\(725\) | 60.1145 | 2.23260 | ||||||||
\(726\) | 6.04763 | 0.224449 | ||||||||
\(727\) | 35.5548 | 1.31866 | 0.659328 | − | 0.751856i | \(-0.270841\pi\) | ||||
0.659328 | + | 0.751856i | \(0.270841\pi\) | |||||||
\(728\) | −2.37770 | −0.0881235 | ||||||||
\(729\) | −11.3609 | −0.420774 | ||||||||
\(730\) | −36.6920 | −1.35803 | ||||||||
\(731\) | −4.73618 | −0.175174 | ||||||||
\(732\) | 7.83263 | 0.289502 | ||||||||
\(733\) | 14.2057 | 0.524699 | 0.262350 | − | 0.964973i | \(-0.415503\pi\) | ||||
0.262350 | + | 0.964973i | \(0.415503\pi\) | |||||||
\(734\) | 10.5595 | 0.389757 | ||||||||
\(735\) | 13.6810 | 0.504630 | ||||||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | −1.59444 | −0.0587319 | ||||||||
\(738\) | −26.4647 | −0.974178 | ||||||||
\(739\) | −15.6392 | −0.575296 | −0.287648 | − | 0.957736i | \(-0.592873\pi\) | ||||
−0.287648 | + | 0.957736i | \(0.592873\pi\) | |||||||
\(740\) | 2.36763 | 0.0870360 | ||||||||
\(741\) | −7.03211 | −0.258331 | ||||||||
\(742\) | 4.31208 | 0.158301 | ||||||||
\(743\) | −32.9894 | −1.21026 | −0.605132 | − | 0.796125i | \(-0.706880\pi\) | ||||
−0.605132 | + | 0.796125i | \(0.706880\pi\) | |||||||
\(744\) | 1.04696 | 0.0383832 | ||||||||
\(745\) | 34.6478 | 1.26940 | ||||||||
\(746\) | 20.6225 | 0.755044 | ||||||||
\(747\) | 8.60205 | 0.314733 | ||||||||
\(748\) | 1.90051 | 0.0694895 | ||||||||
\(749\) | −6.15030 | −0.224727 | ||||||||
\(750\) | 11.2398 | 0.410419 | ||||||||
\(751\) | −16.6382 | −0.607135 | −0.303568 | − | 0.952810i | \(-0.598178\pi\) | ||||
−0.303568 | + | 0.952810i | \(0.598178\pi\) | |||||||
\(752\) | 8.01654 | 0.292333 | ||||||||
\(753\) | 0.699847 | 0.0255038 | ||||||||
\(754\) | 16.2584 | 0.592095 | ||||||||
\(755\) | 42.6302 | 1.55147 | ||||||||
\(756\) | 2.77591 | 0.100959 | ||||||||
\(757\) | −48.4319 | −1.76029 | −0.880144 | − | 0.474707i | \(-0.842554\pi\) | ||||
−0.880144 | + | 0.474707i | \(0.842554\pi\) | |||||||
\(758\) | 0.843533 | 0.0306385 | ||||||||
\(759\) | −0.285633 | −0.0103678 | ||||||||
\(760\) | 17.7317 | 0.643196 | ||||||||
\(761\) | 0.666239 | 0.0241512 | 0.0120756 | − | 0.999927i | \(-0.496156\pi\) | ||||
0.0120756 | + | 0.999927i | \(0.496156\pi\) | |||||||
\(762\) | −4.57804 | −0.165845 | ||||||||
\(763\) | 11.0975 | 0.401757 | ||||||||
\(764\) | 0.403227 | 0.0145882 | ||||||||
\(765\) | 39.0956 | 1.41350 | ||||||||
\(766\) | −0.943042 | −0.0340735 | ||||||||
\(767\) | −14.4869 | −0.523093 | ||||||||
\(768\) | 0.562960 | 0.0203141 | ||||||||
\(769\) | −1.87216 | −0.0675117 | −0.0337558 | − | 0.999430i | \(-0.510747\pi\) | ||||
−0.0337558 | + | 0.999430i | \(0.510747\pi\) | |||||||
\(770\) | −1.71250 | −0.0617141 | ||||||||
\(771\) | −16.2728 | −0.586051 | ||||||||
\(772\) | −14.3644 | −0.516985 | ||||||||
\(773\) | 7.45580 | 0.268166 | 0.134083 | − | 0.990970i | \(-0.457191\pi\) | ||||
0.134083 | + | 0.990970i | \(0.457191\pi\) | |||||||
\(774\) | −3.39251 | −0.121941 | ||||||||
\(775\) | −18.8437 | −0.676885 | ||||||||
\(776\) | −5.75507 | −0.206595 | ||||||||
\(777\) | 0.297291 | 0.0106653 | ||||||||
\(778\) | −7.05035 | −0.252767 | ||||||||
\(779\) | −44.9603 | −1.61087 | ||||||||
\(780\) | 6.00130 | 0.214881 | ||||||||
\(781\) | 6.00782 | 0.214977 | ||||||||
\(782\) | 3.74576 | 0.133948 | ||||||||
\(783\) | −18.9813 | −0.678335 | ||||||||
\(784\) | −6.24718 | −0.223114 | ||||||||
\(785\) | 6.69502 | 0.238955 | ||||||||
\(786\) | 0.562960 | 0.0200801 | ||||||||
\(787\) | −42.1308 | −1.50180 | −0.750900 | − | 0.660416i | \(-0.770380\pi\) | ||||
−0.750900 | + | 0.660416i | \(0.770380\pi\) | |||||||
\(788\) | 6.65067 | 0.236920 | ||||||||
\(789\) | −10.7381 | −0.382285 | ||||||||
\(790\) | −37.8792 | −1.34768 | ||||||||
\(791\) | −16.0804 | −0.571754 | ||||||||
\(792\) | 1.36133 | 0.0483727 | ||||||||
\(793\) | −38.1279 | −1.35396 | ||||||||
\(794\) | 3.30514 | 0.117295 | ||||||||
\(795\) | −10.8836 | −0.386003 | ||||||||
\(796\) | 5.24685 | 0.185970 | ||||||||
\(797\) | 47.4254 | 1.67989 | 0.839947 | − | 0.542669i | \(-0.182586\pi\) | ||||
0.839947 | + | 0.542669i | \(0.182586\pi\) | |||||||
\(798\) | 2.22647 | 0.0788163 | ||||||||
\(799\) | 30.0280 | 1.06232 | ||||||||
\(800\) | −10.1325 | −0.358237 | ||||||||
\(801\) | −7.57187 | −0.267539 | ||||||||
\(802\) | 17.5817 | 0.620831 | ||||||||
\(803\) | −4.78572 | −0.168884 | ||||||||
\(804\) | −1.76911 | −0.0623917 | ||||||||
\(805\) | −3.37520 | −0.118960 | ||||||||
\(806\) | −5.09640 | −0.179513 | ||||||||
\(807\) | −16.6170 | −0.584945 | ||||||||
\(808\) | −9.45619 | −0.332668 | ||||||||
\(809\) | 39.7086 | 1.39608 | 0.698040 | − | 0.716059i | \(-0.254056\pi\) | ||||
0.698040 | + | 0.716059i | \(0.254056\pi\) | |||||||
\(810\) | 24.3055 | 0.854009 | ||||||||
\(811\) | 4.10548 | 0.144163 | 0.0720815 | − | 0.997399i | \(-0.477036\pi\) | ||||
0.0720815 | + | 0.997399i | \(0.477036\pi\) | |||||||
\(812\) | −5.14764 | −0.180647 | ||||||||
\(813\) | −8.48395 | −0.297545 | ||||||||
\(814\) | 0.308809 | 0.0108238 | ||||||||
\(815\) | 62.3319 | 2.18339 | ||||||||
\(816\) | 2.10871 | 0.0738197 | ||||||||
\(817\) | −5.76346 | −0.201638 | ||||||||
\(818\) | 6.48197 | 0.226637 | ||||||||
\(819\) | −6.37956 | −0.222920 | ||||||||
\(820\) | 38.3697 | 1.33993 | ||||||||
\(821\) | −33.9836 | −1.18604 | −0.593018 | − | 0.805189i | \(-0.702064\pi\) | ||||
−0.593018 | + | 0.805189i | \(0.702064\pi\) | |||||||
\(822\) | 3.68434 | 0.128506 | ||||||||
\(823\) | −3.06504 | −0.106840 | −0.0534202 | − | 0.998572i | \(-0.517012\pi\) | ||||
−0.0534202 | + | 0.998572i | \(0.517012\pi\) | |||||||
\(824\) | −6.08876 | −0.212112 | ||||||||
\(825\) | 2.89416 | 0.100762 | ||||||||
\(826\) | 4.58678 | 0.159594 | ||||||||
\(827\) | −20.9051 | −0.726942 | −0.363471 | − | 0.931606i | \(-0.618408\pi\) | ||||
−0.363471 | + | 0.931606i | \(0.618408\pi\) | |||||||
\(828\) | 2.68308 | 0.0932433 | ||||||||
\(829\) | −35.1154 | −1.21961 | −0.609803 | − | 0.792553i | \(-0.708752\pi\) | ||||
−0.609803 | + | 0.792553i | \(0.708752\pi\) | |||||||
\(830\) | −12.4716 | −0.432897 | ||||||||
\(831\) | 3.95451 | 0.137181 | ||||||||
\(832\) | −2.74039 | −0.0950061 | ||||||||
\(833\) | −23.4004 | −0.810777 | ||||||||
\(834\) | 5.08573 | 0.176104 | ||||||||
\(835\) | −1.96663 | −0.0680579 | ||||||||
\(836\) | 2.31273 | 0.0799876 | ||||||||
\(837\) | 5.94993 | 0.205660 | ||||||||
\(838\) | −21.0811 | −0.728235 | ||||||||
\(839\) | −35.6940 | −1.23229 | −0.616147 | − | 0.787632i | \(-0.711307\pi\) | ||||
−0.616147 | + | 0.787632i | \(0.711307\pi\) | |||||||
\(840\) | −1.90010 | −0.0655597 | ||||||||
\(841\) | 6.19881 | 0.213752 | ||||||||
\(842\) | 3.48417 | 0.120073 | ||||||||
\(843\) | −0.374620 | −0.0129026 | ||||||||
\(844\) | 3.59198 | 0.123641 | ||||||||
\(845\) | 21.3573 | 0.734713 | ||||||||
\(846\) | 21.5090 | 0.739495 | ||||||||
\(847\) | 9.32079 | 0.320266 | ||||||||
\(848\) | 4.96984 | 0.170665 | ||||||||
\(849\) | −3.74619 | −0.128569 | ||||||||
\(850\) | −37.9538 | −1.30180 | ||||||||
\(851\) | 0.608639 | 0.0208639 | ||||||||
\(852\) | 6.66598 | 0.228373 | ||||||||
\(853\) | −28.6844 | −0.982137 | −0.491068 | − | 0.871121i | \(-0.663393\pi\) | ||||
−0.491068 | + | 0.871121i | \(0.663393\pi\) | |||||||
\(854\) | 12.0719 | 0.413091 | ||||||||
\(855\) | 47.5755 | 1.62705 | ||||||||
\(856\) | −7.08845 | −0.242278 | ||||||||
\(857\) | 51.0458 | 1.74369 | 0.871845 | − | 0.489782i | \(-0.162924\pi\) | ||||
0.871845 | + | 0.489782i | \(0.162924\pi\) | |||||||
\(858\) | 0.782746 | 0.0267225 | ||||||||
\(859\) | −23.6436 | −0.806710 | −0.403355 | − | 0.915044i | \(-0.632156\pi\) | ||||
−0.403355 | + | 0.915044i | \(0.632156\pi\) | |||||||
\(860\) | 4.91862 | 0.167724 | ||||||||
\(861\) | 4.81787 | 0.164193 | ||||||||
\(862\) | 15.4716 | 0.526966 | ||||||||
\(863\) | −6.83113 | −0.232534 | −0.116267 | − | 0.993218i | \(-0.537093\pi\) | ||||
−0.116267 | + | 0.993218i | \(0.537093\pi\) | |||||||
\(864\) | 3.19934 | 0.108844 | ||||||||
\(865\) | 11.7693 | 0.400168 | ||||||||
\(866\) | 20.3427 | 0.691272 | ||||||||
\(867\) | −1.67159 | −0.0567703 | ||||||||
\(868\) | 1.61360 | 0.0547691 | ||||||||
\(869\) | −4.94057 | −0.167597 | ||||||||
\(870\) | 12.9926 | 0.440491 | ||||||||
\(871\) | 8.61173 | 0.291797 | ||||||||
\(872\) | 12.7903 | 0.433135 | ||||||||
\(873\) | −15.4413 | −0.522609 | ||||||||
\(874\) | 4.55822 | 0.154184 | ||||||||
\(875\) | 17.3231 | 0.585628 | ||||||||
\(876\) | −5.31000 | −0.179408 | ||||||||
\(877\) | 30.2626 | 1.02189 | 0.510947 | − | 0.859612i | \(-0.329295\pi\) | ||||
0.510947 | + | 0.859612i | \(0.329295\pi\) | |||||||
\(878\) | −17.6676 | −0.596253 | ||||||||
\(879\) | −6.54314 | −0.220695 | ||||||||
\(880\) | −1.97372 | −0.0665340 | ||||||||
\(881\) | 57.0660 | 1.92260 | 0.961302 | − | 0.275498i | \(-0.0888426\pi\) | ||||
0.961302 | + | 0.275498i | \(0.0888426\pi\) | |||||||
\(882\) | −16.7617 | −0.564395 | ||||||||
\(883\) | −7.54318 | −0.253848 | −0.126924 | − | 0.991912i | \(-0.540510\pi\) | ||||
−0.126924 | + | 0.991912i | \(0.540510\pi\) | |||||||
\(884\) | −10.2649 | −0.345244 | ||||||||
\(885\) | −11.5770 | −0.389156 | ||||||||
\(886\) | −20.9706 | −0.704523 | ||||||||
\(887\) | 38.0193 | 1.27656 | 0.638281 | − | 0.769804i | \(-0.279646\pi\) | ||||
0.638281 | + | 0.769804i | \(0.279646\pi\) | |||||||
\(888\) | 0.342639 | 0.0114982 | ||||||||
\(889\) | −7.05580 | −0.236644 | ||||||||
\(890\) | 10.9780 | 0.367985 | ||||||||
\(891\) | 3.17015 | 0.106204 | ||||||||
\(892\) | 24.9469 | 0.835285 | ||||||||
\(893\) | 36.5412 | 1.22280 | ||||||||
\(894\) | 5.01416 | 0.167699 | ||||||||
\(895\) | 61.1781 | 2.04496 | ||||||||
\(896\) | 0.867650 | 0.0289861 | ||||||||
\(897\) | 1.54273 | 0.0515103 | ||||||||
\(898\) | −0.184554 | −0.00615864 | ||||||||
\(899\) | −11.0335 | −0.367989 | ||||||||
\(900\) | −27.1862 | −0.906206 | ||||||||
\(901\) | 18.6158 | 0.620183 | ||||||||
\(902\) | 5.00454 | 0.166633 | ||||||||
\(903\) | 0.617604 | 0.0205526 | ||||||||
\(904\) | −18.5333 | −0.616409 | ||||||||
\(905\) | 60.3895 | 2.00741 | ||||||||
\(906\) | 6.16935 | 0.204963 | ||||||||
\(907\) | −23.1706 | −0.769366 | −0.384683 | − | 0.923049i | \(-0.625689\pi\) | ||||
−0.384683 | + | 0.923049i | \(0.625689\pi\) | |||||||
\(908\) | 3.87747 | 0.128678 | ||||||||
\(909\) | −25.3717 | −0.841526 | ||||||||
\(910\) | 9.24938 | 0.306614 | ||||||||
\(911\) | 7.49641 | 0.248367 | 0.124184 | − | 0.992259i | \(-0.460369\pi\) | ||||
0.124184 | + | 0.992259i | \(0.460369\pi\) | |||||||
\(912\) | 2.56609 | 0.0849719 | ||||||||
\(913\) | −1.62667 | −0.0538349 | ||||||||
\(914\) | −0.149083 | −0.00493123 | ||||||||
\(915\) | −30.4693 | −1.00728 | ||||||||
\(916\) | 2.35944 | 0.0779579 | ||||||||
\(917\) | 0.867650 | 0.0286523 | ||||||||
\(918\) | 11.9840 | 0.395530 | ||||||||
\(919\) | −39.5258 | −1.30384 | −0.651918 | − | 0.758289i | \(-0.726035\pi\) | ||||
−0.651918 | + | 0.758289i | \(0.726035\pi\) | |||||||
\(920\) | −3.89005 | −0.128251 | ||||||||
\(921\) | −12.7471 | −0.420032 | ||||||||
\(922\) | 16.6132 | 0.547128 | ||||||||
\(923\) | −32.4489 | −1.06807 | ||||||||
\(924\) | −0.247829 | −0.00815298 | ||||||||
\(925\) | −6.16702 | −0.202770 | ||||||||
\(926\) | −31.6334 | −1.03954 | ||||||||
\(927\) | −16.3366 | −0.536564 | ||||||||
\(928\) | −5.93286 | −0.194756 | ||||||||
\(929\) | −15.6701 | −0.514119 | −0.257059 | − | 0.966396i | \(-0.582754\pi\) | ||||
−0.257059 | + | 0.966396i | \(0.582754\pi\) | |||||||
\(930\) | −4.07271 | −0.133549 | ||||||||
\(931\) | −28.4760 | −0.933265 | ||||||||
\(932\) | 1.47211 | 0.0482207 | ||||||||
\(933\) | −11.2886 | −0.369574 | ||||||||
\(934\) | 7.99381 | 0.261565 | ||||||||
\(935\) | −7.39307 | −0.241779 | ||||||||
\(936\) | −7.35269 | −0.240330 | ||||||||
\(937\) | −36.0191 | −1.17669 | −0.588346 | − | 0.808609i | \(-0.700221\pi\) | ||||
−0.588346 | + | 0.808609i | \(0.700221\pi\) | |||||||
\(938\) | −2.72660 | −0.0890268 | ||||||||
\(939\) | −0.249458 | −0.00814074 | ||||||||
\(940\) | −31.1847 | −1.01713 | ||||||||
\(941\) | −11.5406 | −0.376213 | −0.188107 | − | 0.982149i | \(-0.560235\pi\) | ||||
−0.188107 | + | 0.982149i | \(0.560235\pi\) | |||||||
\(942\) | 0.968890 | 0.0315681 | ||||||||
\(943\) | 9.86356 | 0.321202 | ||||||||
\(944\) | 5.28644 | 0.172059 | ||||||||
\(945\) | −10.7984 | −0.351273 | ||||||||
\(946\) | 0.641532 | 0.0208580 | ||||||||
\(947\) | −19.4110 | −0.630773 | −0.315386 | − | 0.948963i | \(-0.602134\pi\) | ||||
−0.315386 | + | 0.948963i | \(0.602134\pi\) | |||||||
\(948\) | −5.48181 | −0.178041 | ||||||||
\(949\) | 25.8482 | 0.839067 | ||||||||
\(950\) | −46.1860 | −1.49847 | ||||||||
\(951\) | −3.49805 | −0.113432 | ||||||||
\(952\) | 3.25001 | 0.105333 | ||||||||
\(953\) | −20.4627 | −0.662852 | −0.331426 | − | 0.943481i | \(-0.607530\pi\) | ||||
−0.331426 | + | 0.943481i | \(0.607530\pi\) | |||||||
\(954\) | 13.3345 | 0.431719 | ||||||||
\(955\) | −1.56857 | −0.0507578 | ||||||||
\(956\) | 18.8116 | 0.608409 | ||||||||
\(957\) | 1.69462 | 0.0547792 | ||||||||
\(958\) | −25.9475 | −0.838326 | ||||||||
\(959\) | 5.67841 | 0.183365 | ||||||||
\(960\) | −2.18994 | −0.0706800 | ||||||||
\(961\) | −27.5414 | −0.888432 | ||||||||
\(962\) | −1.66791 | −0.0537756 | ||||||||
\(963\) | −19.0189 | −0.612874 | ||||||||
\(964\) | −26.1881 | −0.843462 | ||||||||
\(965\) | 55.8781 | 1.79878 | ||||||||
\(966\) | −0.488452 | −0.0157157 | ||||||||
\(967\) | −53.3379 | −1.71523 | −0.857616 | − | 0.514291i | \(-0.828055\pi\) | ||||
−0.857616 | + | 0.514291i | \(0.828055\pi\) | |||||||
\(968\) | 10.7426 | 0.345279 | ||||||||
\(969\) | 9.61197 | 0.308781 | ||||||||
\(970\) | 22.3875 | 0.718820 | ||||||||
\(971\) | −17.6470 | −0.566320 | −0.283160 | − | 0.959073i | \(-0.591383\pi\) | ||||
−0.283160 | + | 0.959073i | \(0.591383\pi\) | |||||||
\(972\) | 13.1155 | 0.420679 | ||||||||
\(973\) | 7.83827 | 0.251283 | ||||||||
\(974\) | −29.3717 | −0.941129 | ||||||||
\(975\) | −15.6317 | −0.500614 | ||||||||
\(976\) | 13.9133 | 0.445354 | ||||||||
\(977\) | −22.2704 | −0.712492 | −0.356246 | − | 0.934392i | \(-0.615943\pi\) | ||||
−0.356246 | + | 0.934392i | \(0.615943\pi\) | |||||||
\(978\) | 9.02054 | 0.288445 | ||||||||
\(979\) | 1.43186 | 0.0457624 | ||||||||
\(980\) | 24.3018 | 0.776294 | ||||||||
\(981\) | 34.3174 | 1.09567 | ||||||||
\(982\) | −28.1115 | −0.897073 | ||||||||
\(983\) | 6.23592 | 0.198895 | 0.0994474 | − | 0.995043i | \(-0.468292\pi\) | ||||
0.0994474 | + | 0.995043i | \(0.468292\pi\) | |||||||
\(984\) | 5.55279 | 0.177016 | ||||||||
\(985\) | −25.8714 | −0.824332 | ||||||||
\(986\) | −22.2231 | −0.707726 | ||||||||
\(987\) | −3.91570 | −0.124638 | ||||||||
\(988\) | −12.4913 | −0.397402 | ||||||||
\(989\) | 1.26441 | 0.0402059 | ||||||||
\(990\) | −5.29564 | −0.168306 | ||||||||
\(991\) | −27.1762 | −0.863280 | −0.431640 | − | 0.902046i | \(-0.642065\pi\) | ||||
−0.431640 | + | 0.902046i | \(0.642065\pi\) | |||||||
\(992\) | 1.85973 | 0.0590466 | ||||||||
\(993\) | 18.2839 | 0.580221 | ||||||||
\(994\) | 10.2738 | 0.325865 | ||||||||
\(995\) | −20.4105 | −0.647056 | ||||||||
\(996\) | −1.80487 | −0.0571895 | ||||||||
\(997\) | 9.21406 | 0.291812 | 0.145906 | − | 0.989298i | \(-0.453390\pi\) | ||||
0.145906 | + | 0.989298i | \(0.453390\pi\) | |||||||
\(998\) | −14.3639 | −0.454681 | ||||||||
\(999\) | 1.94725 | 0.0616081 |
(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 | 6026.2.a.h.1.14 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6026.2.a.h.1.14 | ✓ | 24 | 1.1 | even | 1 | trivial |