Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8018,2,Mod(1,8018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8018, 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("8018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8018 = 2 \cdot 19 \cdot 211 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8018.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.0240523407\) |
Analytic rank: | \(1\) |
Dimension: | \(34\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Character | \(\chi\) | \(=\) | 8018.1 |
$q$-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 | ||||||||
\(3\) | −2.56521 | −1.48103 | −0.740513 | − | 0.672042i | \(-0.765417\pi\) | ||||
−0.740513 | + | 0.672042i | \(0.765417\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.62382 | 1.62062 | 0.810311 | − | 0.586001i | \(-0.199298\pi\) | ||||
0.810311 | + | 0.586001i | \(0.199298\pi\) | |||||||
\(6\) | 2.56521 | 1.04724 | ||||||||
\(7\) | 4.81473 | 1.81980 | 0.909898 | − | 0.414833i | \(-0.136160\pi\) | ||||
0.909898 | + | 0.414833i | \(0.136160\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 3.58031 | 1.19344 | ||||||||
\(10\) | −3.62382 | −1.14595 | ||||||||
\(11\) | 0.483333 | 0.145730 | 0.0728651 | − | 0.997342i | \(-0.476786\pi\) | ||||
0.0728651 | + | 0.997342i | \(0.476786\pi\) | |||||||
\(12\) | −2.56521 | −0.740513 | ||||||||
\(13\) | −5.40690 | −1.49960 | −0.749802 | − | 0.661662i | \(-0.769851\pi\) | ||||
−0.749802 | + | 0.661662i | \(0.769851\pi\) | |||||||
\(14\) | −4.81473 | −1.28679 | ||||||||
\(15\) | −9.29586 | −2.40018 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.64515 | −1.36915 | −0.684575 | − | 0.728943i | \(-0.740012\pi\) | ||||
−0.684575 | + | 0.728943i | \(0.740012\pi\) | |||||||
\(18\) | −3.58031 | −0.843888 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 3.62382 | 0.810311 | ||||||||
\(21\) | −12.3508 | −2.69516 | ||||||||
\(22\) | −0.483333 | −0.103047 | ||||||||
\(23\) | −3.29287 | −0.686611 | −0.343306 | − | 0.939224i | \(-0.611547\pi\) | ||||
−0.343306 | + | 0.939224i | \(0.611547\pi\) | |||||||
\(24\) | 2.56521 | 0.523622 | ||||||||
\(25\) | 8.13206 | 1.62641 | ||||||||
\(26\) | 5.40690 | 1.06038 | ||||||||
\(27\) | −1.48862 | −0.286486 | ||||||||
\(28\) | 4.81473 | 0.909898 | ||||||||
\(29\) | 7.39723 | 1.37363 | 0.686816 | − | 0.726832i | \(-0.259008\pi\) | ||||
0.686816 | + | 0.726832i | \(0.259008\pi\) | |||||||
\(30\) | 9.29586 | 1.69718 | ||||||||
\(31\) | −3.65660 | −0.656745 | −0.328373 | − | 0.944548i | \(-0.606500\pi\) | ||||
−0.328373 | + | 0.944548i | \(0.606500\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −1.23985 | −0.215830 | ||||||||
\(34\) | 5.64515 | 0.968135 | ||||||||
\(35\) | 17.4477 | 2.94920 | ||||||||
\(36\) | 3.58031 | 0.596719 | ||||||||
\(37\) | −4.09678 | −0.673507 | −0.336754 | − | 0.941593i | \(-0.609329\pi\) | ||||
−0.336754 | + | 0.941593i | \(0.609329\pi\) | |||||||
\(38\) | 1.00000 | 0.162221 | ||||||||
\(39\) | 13.8698 | 2.22095 | ||||||||
\(40\) | −3.62382 | −0.572976 | ||||||||
\(41\) | 3.25360 | 0.508126 | 0.254063 | − | 0.967188i | \(-0.418233\pi\) | ||||
0.254063 | + | 0.967188i | \(0.418233\pi\) | |||||||
\(42\) | 12.3508 | 1.90577 | ||||||||
\(43\) | −9.51322 | −1.45075 | −0.725376 | − | 0.688353i | \(-0.758334\pi\) | ||||
−0.725376 | + | 0.688353i | \(0.758334\pi\) | |||||||
\(44\) | 0.483333 | 0.0728651 | ||||||||
\(45\) | 12.9744 | 1.93411 | ||||||||
\(46\) | 3.29287 | 0.485508 | ||||||||
\(47\) | −1.74149 | −0.254023 | −0.127012 | − | 0.991901i | \(-0.540539\pi\) | ||||
−0.127012 | + | 0.991901i | \(0.540539\pi\) | |||||||
\(48\) | −2.56521 | −0.370256 | ||||||||
\(49\) | 16.1816 | 2.31165 | ||||||||
\(50\) | −8.13206 | −1.15005 | ||||||||
\(51\) | 14.4810 | 2.02775 | ||||||||
\(52\) | −5.40690 | −0.749802 | ||||||||
\(53\) | −10.5836 | −1.45377 | −0.726887 | − | 0.686757i | \(-0.759034\pi\) | ||||
−0.726887 | + | 0.686757i | \(0.759034\pi\) | |||||||
\(54\) | 1.48862 | 0.202576 | ||||||||
\(55\) | 1.75151 | 0.236174 | ||||||||
\(56\) | −4.81473 | −0.643395 | ||||||||
\(57\) | 2.56521 | 0.339771 | ||||||||
\(58\) | −7.39723 | −0.971304 | ||||||||
\(59\) | 3.36884 | 0.438586 | 0.219293 | − | 0.975659i | \(-0.429625\pi\) | ||||
0.219293 | + | 0.975659i | \(0.429625\pi\) | |||||||
\(60\) | −9.29586 | −1.20009 | ||||||||
\(61\) | 0.239416 | 0.0306541 | 0.0153271 | − | 0.999883i | \(-0.495121\pi\) | ||||
0.0153271 | + | 0.999883i | \(0.495121\pi\) | |||||||
\(62\) | 3.65660 | 0.464389 | ||||||||
\(63\) | 17.2382 | 2.17181 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −19.5936 | −2.43029 | ||||||||
\(66\) | 1.23985 | 0.152615 | ||||||||
\(67\) | −2.95102 | −0.360525 | −0.180262 | − | 0.983619i | \(-0.557695\pi\) | ||||
−0.180262 | + | 0.983619i | \(0.557695\pi\) | |||||||
\(68\) | −5.64515 | −0.684575 | ||||||||
\(69\) | 8.44691 | 1.01689 | ||||||||
\(70\) | −17.4477 | −2.08540 | ||||||||
\(71\) | 0.0139607 | 0.00165683 | 0.000828416 | − | 1.00000i | \(-0.499736\pi\) | ||||
0.000828416 | 1.00000i | \(0.499736\pi\) | ||||||||
\(72\) | −3.58031 | −0.421944 | ||||||||
\(73\) | 8.52837 | 0.998170 | 0.499085 | − | 0.866553i | \(-0.333669\pi\) | ||||
0.499085 | + | 0.866553i | \(0.333669\pi\) | |||||||
\(74\) | 4.09678 | 0.476241 | ||||||||
\(75\) | −20.8605 | −2.40876 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | 2.32711 | 0.265199 | ||||||||
\(78\) | −13.8698 | −1.57045 | ||||||||
\(79\) | 4.43438 | 0.498907 | 0.249454 | − | 0.968387i | \(-0.419749\pi\) | ||||
0.249454 | + | 0.968387i | \(0.419749\pi\) | |||||||
\(80\) | 3.62382 | 0.405155 | ||||||||
\(81\) | −6.92230 | −0.769145 | ||||||||
\(82\) | −3.25360 | −0.359299 | ||||||||
\(83\) | −3.63352 | −0.398831 | −0.199415 | − | 0.979915i | \(-0.563904\pi\) | ||||
−0.199415 | + | 0.979915i | \(0.563904\pi\) | |||||||
\(84\) | −12.3508 | −1.34758 | ||||||||
\(85\) | −20.4570 | −2.21887 | ||||||||
\(86\) | 9.51322 | 1.02584 | ||||||||
\(87\) | −18.9755 | −2.03438 | ||||||||
\(88\) | −0.483333 | −0.0515234 | ||||||||
\(89\) | −13.1060 | −1.38924 | −0.694618 | − | 0.719378i | \(-0.744427\pi\) | ||||
−0.694618 | + | 0.719378i | \(0.744427\pi\) | |||||||
\(90\) | −12.9744 | −1.36762 | ||||||||
\(91\) | −26.0327 | −2.72897 | ||||||||
\(92\) | −3.29287 | −0.343306 | ||||||||
\(93\) | 9.37996 | 0.972657 | ||||||||
\(94\) | 1.74149 | 0.179621 | ||||||||
\(95\) | −3.62382 | −0.371796 | ||||||||
\(96\) | 2.56521 | 0.261811 | ||||||||
\(97\) | −7.06235 | −0.717073 | −0.358536 | − | 0.933516i | \(-0.616724\pi\) | ||||
−0.358536 | + | 0.933516i | \(0.616724\pi\) | |||||||
\(98\) | −16.1816 | −1.63459 | ||||||||
\(99\) | 1.73048 | 0.173920 | ||||||||
\(100\) | 8.13206 | 0.813206 | ||||||||
\(101\) | 17.3847 | 1.72984 | 0.864921 | − | 0.501907i | \(-0.167368\pi\) | ||||
0.864921 | + | 0.501907i | \(0.167368\pi\) | |||||||
\(102\) | −14.4810 | −1.43383 | ||||||||
\(103\) | 1.16071 | 0.114368 | 0.0571839 | − | 0.998364i | \(-0.481788\pi\) | ||||
0.0571839 | + | 0.998364i | \(0.481788\pi\) | |||||||
\(104\) | 5.40690 | 0.530190 | ||||||||
\(105\) | −44.7570 | −4.36784 | ||||||||
\(106\) | 10.5836 | 1.02797 | ||||||||
\(107\) | −1.98841 | −0.192227 | −0.0961135 | − | 0.995370i | \(-0.530641\pi\) | ||||
−0.0961135 | + | 0.995370i | \(0.530641\pi\) | |||||||
\(108\) | −1.48862 | −0.143243 | ||||||||
\(109\) | 6.13451 | 0.587580 | 0.293790 | − | 0.955870i | \(-0.405083\pi\) | ||||
0.293790 | + | 0.955870i | \(0.405083\pi\) | |||||||
\(110\) | −1.75151 | −0.167000 | ||||||||
\(111\) | 10.5091 | 0.997481 | ||||||||
\(112\) | 4.81473 | 0.454949 | ||||||||
\(113\) | −14.2125 | −1.33700 | −0.668500 | − | 0.743712i | \(-0.733063\pi\) | ||||
−0.668500 | + | 0.743712i | \(0.733063\pi\) | |||||||
\(114\) | −2.56521 | −0.240254 | ||||||||
\(115\) | −11.9328 | −1.11274 | ||||||||
\(116\) | 7.39723 | 0.686816 | ||||||||
\(117\) | −19.3584 | −1.78968 | ||||||||
\(118\) | −3.36884 | −0.310127 | ||||||||
\(119\) | −27.1798 | −2.49157 | ||||||||
\(120\) | 9.29586 | 0.848592 | ||||||||
\(121\) | −10.7664 | −0.978763 | ||||||||
\(122\) | −0.239416 | −0.0216757 | ||||||||
\(123\) | −8.34616 | −0.752548 | ||||||||
\(124\) | −3.65660 | −0.328373 | ||||||||
\(125\) | 11.3500 | 1.01518 | ||||||||
\(126\) | −17.2382 | −1.53570 | ||||||||
\(127\) | −0.471433 | −0.0418329 | −0.0209165 | − | 0.999781i | \(-0.506658\pi\) | ||||
−0.0209165 | + | 0.999781i | \(0.506658\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 24.4034 | 2.14860 | ||||||||
\(130\) | 19.5936 | 1.71847 | ||||||||
\(131\) | −19.0185 | −1.66165 | −0.830825 | − | 0.556533i | \(-0.812131\pi\) | ||||
−0.830825 | + | 0.556533i | \(0.812131\pi\) | |||||||
\(132\) | −1.23985 | −0.107915 | ||||||||
\(133\) | −4.81473 | −0.417490 | ||||||||
\(134\) | 2.95102 | 0.254929 | ||||||||
\(135\) | −5.39450 | −0.464285 | ||||||||
\(136\) | 5.64515 | 0.484067 | ||||||||
\(137\) | −3.39468 | −0.290027 | −0.145013 | − | 0.989430i | \(-0.546323\pi\) | ||||
−0.145013 | + | 0.989430i | \(0.546323\pi\) | |||||||
\(138\) | −8.44691 | −0.719049 | ||||||||
\(139\) | 4.92798 | 0.417986 | 0.208993 | − | 0.977917i | \(-0.432981\pi\) | ||||
0.208993 | + | 0.977917i | \(0.432981\pi\) | |||||||
\(140\) | 17.4477 | 1.47460 | ||||||||
\(141\) | 4.46730 | 0.376215 | ||||||||
\(142\) | −0.0139607 | −0.00117156 | ||||||||
\(143\) | −2.61333 | −0.218538 | ||||||||
\(144\) | 3.58031 | 0.298359 | ||||||||
\(145\) | 26.8062 | 2.22614 | ||||||||
\(146\) | −8.52837 | −0.705813 | ||||||||
\(147\) | −41.5092 | −3.42362 | ||||||||
\(148\) | −4.09678 | −0.336754 | ||||||||
\(149\) | −12.9917 | −1.06432 | −0.532160 | − | 0.846644i | \(-0.678620\pi\) | ||||
−0.532160 | + | 0.846644i | \(0.678620\pi\) | |||||||
\(150\) | 20.8605 | 1.70325 | ||||||||
\(151\) | −18.6205 | −1.51532 | −0.757659 | − | 0.652651i | \(-0.773657\pi\) | ||||
−0.757659 | + | 0.652651i | \(0.773657\pi\) | |||||||
\(152\) | 1.00000 | 0.0811107 | ||||||||
\(153\) | −20.2114 | −1.63399 | ||||||||
\(154\) | −2.32711 | −0.187524 | ||||||||
\(155\) | −13.2509 | −1.06434 | ||||||||
\(156\) | 13.8698 | 1.11048 | ||||||||
\(157\) | 4.81982 | 0.384664 | 0.192332 | − | 0.981330i | \(-0.438395\pi\) | ||||
0.192332 | + | 0.981330i | \(0.438395\pi\) | |||||||
\(158\) | −4.43438 | −0.352781 | ||||||||
\(159\) | 27.1493 | 2.15308 | ||||||||
\(160\) | −3.62382 | −0.286488 | ||||||||
\(161\) | −15.8543 | −1.24949 | ||||||||
\(162\) | 6.92230 | 0.543867 | ||||||||
\(163\) | 10.5352 | 0.825179 | 0.412590 | − | 0.910917i | \(-0.364624\pi\) | ||||
0.412590 | + | 0.910917i | \(0.364624\pi\) | |||||||
\(164\) | 3.25360 | 0.254063 | ||||||||
\(165\) | −4.49299 | −0.349779 | ||||||||
\(166\) | 3.63352 | 0.282016 | ||||||||
\(167\) | −9.47281 | −0.733028 | −0.366514 | − | 0.930413i | \(-0.619449\pi\) | ||||
−0.366514 | + | 0.930413i | \(0.619449\pi\) | |||||||
\(168\) | 12.3508 | 0.952884 | ||||||||
\(169\) | 16.2346 | 1.24881 | ||||||||
\(170\) | 20.4570 | 1.56898 | ||||||||
\(171\) | −3.58031 | −0.273793 | ||||||||
\(172\) | −9.51322 | −0.725376 | ||||||||
\(173\) | −17.6072 | −1.33865 | −0.669326 | − | 0.742969i | \(-0.733417\pi\) | ||||
−0.669326 | + | 0.742969i | \(0.733417\pi\) | |||||||
\(174\) | 18.9755 | 1.43853 | ||||||||
\(175\) | 39.1536 | 2.95974 | ||||||||
\(176\) | 0.483333 | 0.0364326 | ||||||||
\(177\) | −8.64179 | −0.649557 | ||||||||
\(178\) | 13.1060 | 0.982339 | ||||||||
\(179\) | 16.1982 | 1.21071 | 0.605355 | − | 0.795956i | \(-0.293031\pi\) | ||||
0.605355 | + | 0.795956i | \(0.293031\pi\) | |||||||
\(180\) | 12.9744 | 0.967055 | ||||||||
\(181\) | −14.9491 | −1.11116 | −0.555578 | − | 0.831464i | \(-0.687503\pi\) | ||||
−0.555578 | + | 0.831464i | \(0.687503\pi\) | |||||||
\(182\) | 26.0327 | 1.92967 | ||||||||
\(183\) | −0.614154 | −0.0453996 | ||||||||
\(184\) | 3.29287 | 0.242754 | ||||||||
\(185\) | −14.8460 | −1.09150 | ||||||||
\(186\) | −9.37996 | −0.687772 | ||||||||
\(187\) | −2.72848 | −0.199526 | ||||||||
\(188\) | −1.74149 | −0.127012 | ||||||||
\(189\) | −7.16731 | −0.521345 | ||||||||
\(190\) | 3.62382 | 0.262899 | ||||||||
\(191\) | 16.5906 | 1.20045 | 0.600226 | − | 0.799831i | \(-0.295077\pi\) | ||||
0.600226 | + | 0.799831i | \(0.295077\pi\) | |||||||
\(192\) | −2.56521 | −0.185128 | ||||||||
\(193\) | −19.7455 | −1.42131 | −0.710656 | − | 0.703540i | \(-0.751602\pi\) | ||||
−0.710656 | + | 0.703540i | \(0.751602\pi\) | |||||||
\(194\) | 7.06235 | 0.507047 | ||||||||
\(195\) | 50.2618 | 3.59932 | ||||||||
\(196\) | 16.1816 | 1.15583 | ||||||||
\(197\) | 18.8208 | 1.34093 | 0.670465 | − | 0.741941i | \(-0.266095\pi\) | ||||
0.670465 | + | 0.741941i | \(0.266095\pi\) | |||||||
\(198\) | −1.73048 | −0.122980 | ||||||||
\(199\) | −11.5459 | −0.818464 | −0.409232 | − | 0.912430i | \(-0.634203\pi\) | ||||
−0.409232 | + | 0.912430i | \(0.634203\pi\) | |||||||
\(200\) | −8.13206 | −0.575024 | ||||||||
\(201\) | 7.57000 | 0.533946 | ||||||||
\(202\) | −17.3847 | −1.22318 | ||||||||
\(203\) | 35.6156 | 2.49973 | ||||||||
\(204\) | 14.4810 | 1.01387 | ||||||||
\(205\) | 11.7904 | 0.823480 | ||||||||
\(206\) | −1.16071 | −0.0808702 | ||||||||
\(207\) | −11.7895 | −0.819428 | ||||||||
\(208\) | −5.40690 | −0.374901 | ||||||||
\(209\) | −0.483333 | −0.0334328 | ||||||||
\(210\) | 44.7570 | 3.08853 | ||||||||
\(211\) | −1.00000 | −0.0688428 | ||||||||
\(212\) | −10.5836 | −0.726887 | ||||||||
\(213\) | −0.0358122 | −0.00245381 | ||||||||
\(214\) | 1.98841 | 0.135925 | ||||||||
\(215\) | −34.4742 | −2.35112 | ||||||||
\(216\) | 1.48862 | 0.101288 | ||||||||
\(217\) | −17.6055 | −1.19514 | ||||||||
\(218\) | −6.13451 | −0.415482 | ||||||||
\(219\) | −21.8771 | −1.47832 | ||||||||
\(220\) | 1.75151 | 0.118087 | ||||||||
\(221\) | 30.5227 | 2.05318 | ||||||||
\(222\) | −10.5091 | −0.705326 | ||||||||
\(223\) | −23.0712 | −1.54496 | −0.772479 | − | 0.635040i | \(-0.780984\pi\) | ||||
−0.772479 | + | 0.635040i | \(0.780984\pi\) | |||||||
\(224\) | −4.81473 | −0.321697 | ||||||||
\(225\) | 29.1153 | 1.94102 | ||||||||
\(226\) | 14.2125 | 0.945402 | ||||||||
\(227\) | 16.5721 | 1.09993 | 0.549963 | − | 0.835189i | \(-0.314642\pi\) | ||||
0.549963 | + | 0.835189i | \(0.314642\pi\) | |||||||
\(228\) | 2.56521 | 0.169885 | ||||||||
\(229\) | 3.42397 | 0.226263 | 0.113131 | − | 0.993580i | \(-0.463912\pi\) | ||||
0.113131 | + | 0.993580i | \(0.463912\pi\) | |||||||
\(230\) | 11.9328 | 0.786824 | ||||||||
\(231\) | −5.96954 | −0.392767 | ||||||||
\(232\) | −7.39723 | −0.485652 | ||||||||
\(233\) | 5.79695 | 0.379770 | 0.189885 | − | 0.981806i | \(-0.439188\pi\) | ||||
0.189885 | + | 0.981806i | \(0.439188\pi\) | |||||||
\(234\) | 19.3584 | 1.26550 | ||||||||
\(235\) | −6.31086 | −0.411675 | ||||||||
\(236\) | 3.36884 | 0.219293 | ||||||||
\(237\) | −11.3751 | −0.738894 | ||||||||
\(238\) | 27.1798 | 1.76181 | ||||||||
\(239\) | −0.233983 | −0.0151351 | −0.00756755 | − | 0.999971i | \(-0.502409\pi\) | ||||
−0.00756755 | + | 0.999971i | \(0.502409\pi\) | |||||||
\(240\) | −9.29586 | −0.600045 | ||||||||
\(241\) | 9.45390 | 0.608980 | 0.304490 | − | 0.952516i | \(-0.401514\pi\) | ||||
0.304490 | + | 0.952516i | \(0.401514\pi\) | |||||||
\(242\) | 10.7664 | 0.692090 | ||||||||
\(243\) | 22.2230 | 1.42561 | ||||||||
\(244\) | 0.239416 | 0.0153271 | ||||||||
\(245\) | 58.6391 | 3.74631 | ||||||||
\(246\) | 8.34616 | 0.532132 | ||||||||
\(247\) | 5.40690 | 0.344033 | ||||||||
\(248\) | 3.65660 | 0.232195 | ||||||||
\(249\) | 9.32075 | 0.590679 | ||||||||
\(250\) | −11.3500 | −0.717839 | ||||||||
\(251\) | −14.1920 | −0.895788 | −0.447894 | − | 0.894087i | \(-0.647826\pi\) | ||||
−0.447894 | + | 0.894087i | \(0.647826\pi\) | |||||||
\(252\) | 17.2382 | 1.08591 | ||||||||
\(253\) | −1.59155 | −0.100060 | ||||||||
\(254\) | 0.471433 | 0.0295803 | ||||||||
\(255\) | 52.4765 | 3.28621 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 25.7696 | 1.60746 | 0.803731 | − | 0.594992i | \(-0.202845\pi\) | ||||
0.803731 | + | 0.594992i | \(0.202845\pi\) | |||||||
\(258\) | −24.4034 | −1.51929 | ||||||||
\(259\) | −19.7249 | −1.22564 | ||||||||
\(260\) | −19.5936 | −1.21515 | ||||||||
\(261\) | 26.4844 | 1.63934 | ||||||||
\(262\) | 19.0185 | 1.17496 | ||||||||
\(263\) | −26.3234 | −1.62317 | −0.811586 | − | 0.584233i | \(-0.801395\pi\) | ||||
−0.811586 | + | 0.584233i | \(0.801395\pi\) | |||||||
\(264\) | 1.23985 | 0.0763075 | ||||||||
\(265\) | −38.3532 | −2.35602 | ||||||||
\(266\) | 4.81473 | 0.295210 | ||||||||
\(267\) | 33.6197 | 2.05750 | ||||||||
\(268\) | −2.95102 | −0.180262 | ||||||||
\(269\) | 24.6133 | 1.50070 | 0.750349 | − | 0.661042i | \(-0.229886\pi\) | ||||
0.750349 | + | 0.661042i | \(0.229886\pi\) | |||||||
\(270\) | 5.39450 | 0.328299 | ||||||||
\(271\) | −14.8630 | −0.902862 | −0.451431 | − | 0.892306i | \(-0.649086\pi\) | ||||
−0.451431 | + | 0.892306i | \(0.649086\pi\) | |||||||
\(272\) | −5.64515 | −0.342287 | ||||||||
\(273\) | 66.7795 | 4.04168 | ||||||||
\(274\) | 3.39468 | 0.205080 | ||||||||
\(275\) | 3.93049 | 0.237018 | ||||||||
\(276\) | 8.44691 | 0.508445 | ||||||||
\(277\) | 3.58959 | 0.215678 | 0.107839 | − | 0.994168i | \(-0.465607\pi\) | ||||
0.107839 | + | 0.994168i | \(0.465607\pi\) | |||||||
\(278\) | −4.92798 | −0.295560 | ||||||||
\(279\) | −13.0918 | −0.783785 | ||||||||
\(280\) | −17.4477 | −1.04270 | ||||||||
\(281\) | 26.4608 | 1.57852 | 0.789261 | − | 0.614059i | \(-0.210464\pi\) | ||||
0.789261 | + | 0.614059i | \(0.210464\pi\) | |||||||
\(282\) | −4.46730 | −0.266024 | ||||||||
\(283\) | 14.6346 | 0.869937 | 0.434969 | − | 0.900446i | \(-0.356759\pi\) | ||||
0.434969 | + | 0.900446i | \(0.356759\pi\) | |||||||
\(284\) | 0.0139607 | 0.000828416 0 | ||||||||
\(285\) | 9.29586 | 0.550639 | ||||||||
\(286\) | 2.61333 | 0.154530 | ||||||||
\(287\) | 15.6652 | 0.924686 | ||||||||
\(288\) | −3.58031 | −0.210972 | ||||||||
\(289\) | 14.8677 | 0.874570 | ||||||||
\(290\) | −26.8062 | −1.57412 | ||||||||
\(291\) | 18.1164 | 1.06200 | ||||||||
\(292\) | 8.52837 | 0.499085 | ||||||||
\(293\) | 19.7157 | 1.15180 | 0.575901 | − | 0.817520i | \(-0.304652\pi\) | ||||
0.575901 | + | 0.817520i | \(0.304652\pi\) | |||||||
\(294\) | 41.5092 | 2.42086 | ||||||||
\(295\) | 12.2081 | 0.710782 | ||||||||
\(296\) | 4.09678 | 0.238121 | ||||||||
\(297\) | −0.719500 | −0.0417496 | ||||||||
\(298\) | 12.9917 | 0.752588 | ||||||||
\(299\) | 17.8042 | 1.02965 | ||||||||
\(300\) | −20.8605 | −1.20438 | ||||||||
\(301\) | −45.8035 | −2.64007 | ||||||||
\(302\) | 18.6205 | 1.07149 | ||||||||
\(303\) | −44.5955 | −2.56194 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | 0.867602 | 0.0496787 | ||||||||
\(306\) | 20.2114 | 1.15541 | ||||||||
\(307\) | −30.0320 | −1.71402 | −0.857008 | − | 0.515303i | \(-0.827679\pi\) | ||||
−0.857008 | + | 0.515303i | \(0.827679\pi\) | |||||||
\(308\) | 2.32711 | 0.132600 | ||||||||
\(309\) | −2.97746 | −0.169382 | ||||||||
\(310\) | 13.2509 | 0.752599 | ||||||||
\(311\) | −33.1178 | −1.87794 | −0.938968 | − | 0.344003i | \(-0.888217\pi\) | ||||
−0.938968 | + | 0.344003i | \(0.888217\pi\) | |||||||
\(312\) | −13.8698 | −0.785225 | ||||||||
\(313\) | 0.709517 | 0.0401043 | 0.0200521 | − | 0.999799i | \(-0.493617\pi\) | ||||
0.0200521 | + | 0.999799i | \(0.493617\pi\) | |||||||
\(314\) | −4.81982 | −0.271998 | ||||||||
\(315\) | 62.4682 | 3.51968 | ||||||||
\(316\) | 4.43438 | 0.249454 | ||||||||
\(317\) | 2.38483 | 0.133946 | 0.0669728 | − | 0.997755i | \(-0.478666\pi\) | ||||
0.0669728 | + | 0.997755i | \(0.478666\pi\) | |||||||
\(318\) | −27.1493 | −1.52246 | ||||||||
\(319\) | 3.57532 | 0.200180 | ||||||||
\(320\) | 3.62382 | 0.202578 | ||||||||
\(321\) | 5.10070 | 0.284693 | ||||||||
\(322\) | 15.8543 | 0.883524 | ||||||||
\(323\) | 5.64515 | 0.314104 | ||||||||
\(324\) | −6.92230 | −0.384572 | ||||||||
\(325\) | −43.9692 | −2.43897 | ||||||||
\(326\) | −10.5352 | −0.583490 | ||||||||
\(327\) | −15.7363 | −0.870221 | ||||||||
\(328\) | −3.25360 | −0.179650 | ||||||||
\(329\) | −8.38482 | −0.462270 | ||||||||
\(330\) | 4.49299 | 0.247331 | ||||||||
\(331\) | −29.5601 | −1.62477 | −0.812386 | − | 0.583120i | \(-0.801832\pi\) | ||||
−0.812386 | + | 0.583120i | \(0.801832\pi\) | |||||||
\(332\) | −3.63352 | −0.199415 | ||||||||
\(333\) | −14.6678 | −0.803789 | ||||||||
\(334\) | 9.47281 | 0.518329 | ||||||||
\(335\) | −10.6940 | −0.584274 | ||||||||
\(336\) | −12.3508 | −0.673791 | ||||||||
\(337\) | −11.6149 | −0.632705 | −0.316352 | − | 0.948642i | \(-0.602458\pi\) | ||||
−0.316352 | + | 0.948642i | \(0.602458\pi\) | |||||||
\(338\) | −16.2346 | −0.883044 | ||||||||
\(339\) | 36.4581 | 1.98013 | ||||||||
\(340\) | −20.4570 | −1.10944 | ||||||||
\(341\) | −1.76736 | −0.0957077 | ||||||||
\(342\) | 3.58031 | 0.193601 | ||||||||
\(343\) | 44.2068 | 2.38694 | ||||||||
\(344\) | 9.51322 | 0.512918 | ||||||||
\(345\) | 30.6101 | 1.64799 | ||||||||
\(346\) | 17.6072 | 0.946570 | ||||||||
\(347\) | 1.42388 | 0.0764377 | 0.0382189 | − | 0.999269i | \(-0.487832\pi\) | ||||
0.0382189 | + | 0.999269i | \(0.487832\pi\) | |||||||
\(348\) | −18.9755 | −1.01719 | ||||||||
\(349\) | −6.02755 | −0.322647 | −0.161324 | − | 0.986902i | \(-0.551576\pi\) | ||||
−0.161324 | + | 0.986902i | \(0.551576\pi\) | |||||||
\(350\) | −39.1536 | −2.09285 | ||||||||
\(351\) | 8.04883 | 0.429615 | ||||||||
\(352\) | −0.483333 | −0.0257617 | ||||||||
\(353\) | −1.61861 | −0.0861499 | −0.0430750 | − | 0.999072i | \(-0.513715\pi\) | ||||
−0.0430750 | + | 0.999072i | \(0.513715\pi\) | |||||||
\(354\) | 8.64179 | 0.459306 | ||||||||
\(355\) | 0.0505911 | 0.00268510 | ||||||||
\(356\) | −13.1060 | −0.694618 | ||||||||
\(357\) | 69.7220 | 3.69008 | ||||||||
\(358\) | −16.1982 | −0.856101 | ||||||||
\(359\) | −20.7395 | −1.09459 | −0.547294 | − | 0.836940i | \(-0.684342\pi\) | ||||
−0.547294 | + | 0.836940i | \(0.684342\pi\) | |||||||
\(360\) | −12.9744 | −0.683811 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 14.9491 | 0.785706 | ||||||||
\(363\) | 27.6181 | 1.44957 | ||||||||
\(364\) | −26.0327 | −1.36449 | ||||||||
\(365\) | 30.9053 | 1.61766 | ||||||||
\(366\) | 0.614154 | 0.0321023 | ||||||||
\(367\) | −7.59985 | −0.396709 | −0.198355 | − | 0.980130i | \(-0.563560\pi\) | ||||
−0.198355 | + | 0.980130i | \(0.563560\pi\) | |||||||
\(368\) | −3.29287 | −0.171653 | ||||||||
\(369\) | 11.6489 | 0.606417 | ||||||||
\(370\) | 14.8460 | 0.771807 | ||||||||
\(371\) | −50.9573 | −2.64557 | ||||||||
\(372\) | 9.37996 | 0.486328 | ||||||||
\(373\) | 24.5031 | 1.26872 | 0.634362 | − | 0.773036i | \(-0.281263\pi\) | ||||
0.634362 | + | 0.773036i | \(0.281263\pi\) | |||||||
\(374\) | 2.72848 | 0.141087 | ||||||||
\(375\) | −29.1152 | −1.50350 | ||||||||
\(376\) | 1.74149 | 0.0898107 | ||||||||
\(377\) | −39.9961 | −2.05990 | ||||||||
\(378\) | 7.16731 | 0.368647 | ||||||||
\(379\) | −8.53571 | −0.438450 | −0.219225 | − | 0.975674i | \(-0.570353\pi\) | ||||
−0.219225 | + | 0.975674i | \(0.570353\pi\) | |||||||
\(380\) | −3.62382 | −0.185898 | ||||||||
\(381\) | 1.20933 | 0.0619556 | ||||||||
\(382\) | −16.5906 | −0.848848 | ||||||||
\(383\) | −11.7009 | −0.597889 | −0.298945 | − | 0.954270i | \(-0.596635\pi\) | ||||
−0.298945 | + | 0.954270i | \(0.596635\pi\) | |||||||
\(384\) | 2.56521 | 0.130905 | ||||||||
\(385\) | 8.43304 | 0.429787 | ||||||||
\(386\) | 19.7455 | 1.00502 | ||||||||
\(387\) | −34.0603 | −1.73138 | ||||||||
\(388\) | −7.06235 | −0.358536 | ||||||||
\(389\) | 24.3028 | 1.23220 | 0.616100 | − | 0.787668i | \(-0.288712\pi\) | ||||
0.616100 | + | 0.787668i | \(0.288712\pi\) | |||||||
\(390\) | −50.2618 | −2.54511 | ||||||||
\(391\) | 18.5887 | 0.940073 | ||||||||
\(392\) | −16.1816 | −0.817293 | ||||||||
\(393\) | 48.7864 | 2.46095 | ||||||||
\(394\) | −18.8208 | −0.948180 | ||||||||
\(395\) | 16.0694 | 0.808540 | ||||||||
\(396\) | 1.73048 | 0.0869600 | ||||||||
\(397\) | −27.2367 | −1.36697 | −0.683486 | − | 0.729964i | \(-0.739537\pi\) | ||||
−0.683486 | + | 0.729964i | \(0.739537\pi\) | |||||||
\(398\) | 11.5459 | 0.578741 | ||||||||
\(399\) | 12.3508 | 0.618313 | ||||||||
\(400\) | 8.13206 | 0.406603 | ||||||||
\(401\) | −18.5289 | −0.925287 | −0.462643 | − | 0.886544i | \(-0.653099\pi\) | ||||
−0.462643 | + | 0.886544i | \(0.653099\pi\) | |||||||
\(402\) | −7.57000 | −0.377557 | ||||||||
\(403\) | 19.7709 | 0.984858 | ||||||||
\(404\) | 17.3847 | 0.864921 | ||||||||
\(405\) | −25.0852 | −1.24649 | ||||||||
\(406\) | −35.6156 | −1.76757 | ||||||||
\(407\) | −1.98011 | −0.0981504 | ||||||||
\(408\) | −14.4810 | −0.716916 | ||||||||
\(409\) | −14.8965 | −0.736584 | −0.368292 | − | 0.929710i | \(-0.620057\pi\) | ||||
−0.368292 | + | 0.929710i | \(0.620057\pi\) | |||||||
\(410\) | −11.7904 | −0.582288 | ||||||||
\(411\) | 8.70806 | 0.429537 | ||||||||
\(412\) | 1.16071 | 0.0571839 | ||||||||
\(413\) | 16.2201 | 0.798137 | ||||||||
\(414\) | 11.7895 | 0.579423 | ||||||||
\(415\) | −13.1672 | −0.646354 | ||||||||
\(416\) | 5.40690 | 0.265095 | ||||||||
\(417\) | −12.6413 | −0.619047 | ||||||||
\(418\) | 0.483333 | 0.0236406 | ||||||||
\(419\) | 0.854101 | 0.0417256 | 0.0208628 | − | 0.999782i | \(-0.493359\pi\) | ||||
0.0208628 | + | 0.999782i | \(0.493359\pi\) | |||||||
\(420\) | −44.7570 | −2.18392 | ||||||||
\(421\) | −17.8339 | −0.869171 | −0.434585 | − | 0.900631i | \(-0.643105\pi\) | ||||
−0.434585 | + | 0.900631i | \(0.643105\pi\) | |||||||
\(422\) | 1.00000 | 0.0486792 | ||||||||
\(423\) | −6.23509 | −0.303161 | ||||||||
\(424\) | 10.5836 | 0.513987 | ||||||||
\(425\) | −45.9067 | −2.22680 | ||||||||
\(426\) | 0.0358122 | 0.00173511 | ||||||||
\(427\) | 1.15272 | 0.0557842 | ||||||||
\(428\) | −1.98841 | −0.0961135 | ||||||||
\(429\) | 6.70375 | 0.323660 | ||||||||
\(430\) | 34.4742 | 1.66249 | ||||||||
\(431\) | −28.9693 | −1.39540 | −0.697701 | − | 0.716389i | \(-0.745794\pi\) | ||||
−0.697701 | + | 0.716389i | \(0.745794\pi\) | |||||||
\(432\) | −1.48862 | −0.0716214 | ||||||||
\(433\) | 24.0138 | 1.15403 | 0.577015 | − | 0.816734i | \(-0.304217\pi\) | ||||
0.577015 | + | 0.816734i | \(0.304217\pi\) | |||||||
\(434\) | 17.6055 | 0.845093 | ||||||||
\(435\) | −68.7636 | −3.29696 | ||||||||
\(436\) | 6.13451 | 0.293790 | ||||||||
\(437\) | 3.29287 | 0.157519 | ||||||||
\(438\) | 21.8771 | 1.04533 | ||||||||
\(439\) | 13.1530 | 0.627758 | 0.313879 | − | 0.949463i | \(-0.398371\pi\) | ||||
0.313879 | + | 0.949463i | \(0.398371\pi\) | |||||||
\(440\) | −1.75151 | −0.0835000 | ||||||||
\(441\) | 57.9351 | 2.75881 | ||||||||
\(442\) | −30.5227 | −1.45182 | ||||||||
\(443\) | −8.78113 | −0.417204 | −0.208602 | − | 0.978001i | \(-0.566891\pi\) | ||||
−0.208602 | + | 0.978001i | \(0.566891\pi\) | |||||||
\(444\) | 10.5091 | 0.498741 | ||||||||
\(445\) | −47.4939 | −2.25143 | ||||||||
\(446\) | 23.0712 | 1.09245 | ||||||||
\(447\) | 33.3264 | 1.57629 | ||||||||
\(448\) | 4.81473 | 0.227474 | ||||||||
\(449\) | 17.6450 | 0.832719 | 0.416359 | − | 0.909200i | \(-0.363306\pi\) | ||||
0.416359 | + | 0.909200i | \(0.363306\pi\) | |||||||
\(450\) | −29.1153 | −1.37251 | ||||||||
\(451\) | 1.57257 | 0.0740494 | ||||||||
\(452\) | −14.2125 | −0.668500 | ||||||||
\(453\) | 47.7656 | 2.24422 | ||||||||
\(454\) | −16.5721 | −0.777765 | ||||||||
\(455\) | −94.3379 | −4.42263 | ||||||||
\(456\) | −2.56521 | −0.120127 | ||||||||
\(457\) | −21.8845 | −1.02371 | −0.511856 | − | 0.859071i | \(-0.671042\pi\) | ||||
−0.511856 | + | 0.859071i | \(0.671042\pi\) | |||||||
\(458\) | −3.42397 | −0.159992 | ||||||||
\(459\) | 8.40350 | 0.392242 | ||||||||
\(460\) | −11.9328 | −0.556368 | ||||||||
\(461\) | −4.83115 | −0.225009 | −0.112505 | − | 0.993651i | \(-0.535887\pi\) | ||||
−0.112505 | + | 0.993651i | \(0.535887\pi\) | |||||||
\(462\) | 5.96954 | 0.277728 | ||||||||
\(463\) | 5.95116 | 0.276574 | 0.138287 | − | 0.990392i | \(-0.455840\pi\) | ||||
0.138287 | + | 0.990392i | \(0.455840\pi\) | |||||||
\(464\) | 7.39723 | 0.343408 | ||||||||
\(465\) | 33.9913 | 1.57631 | ||||||||
\(466\) | −5.79695 | −0.268538 | ||||||||
\(467\) | −0.943463 | −0.0436583 | −0.0218291 | − | 0.999762i | \(-0.506949\pi\) | ||||
−0.0218291 | + | 0.999762i | \(0.506949\pi\) | |||||||
\(468\) | −19.3584 | −0.894842 | ||||||||
\(469\) | −14.2084 | −0.656081 | ||||||||
\(470\) | 6.31086 | 0.291098 | ||||||||
\(471\) | −12.3639 | −0.569697 | ||||||||
\(472\) | −3.36884 | −0.155064 | ||||||||
\(473\) | −4.59805 | −0.211418 | ||||||||
\(474\) | 11.3751 | 0.522477 | ||||||||
\(475\) | −8.13206 | −0.373125 | ||||||||
\(476\) | −27.1798 | −1.24579 | ||||||||
\(477\) | −37.8927 | −1.73499 | ||||||||
\(478\) | 0.233983 | 0.0107021 | ||||||||
\(479\) | −28.7216 | −1.31232 | −0.656162 | − | 0.754620i | \(-0.727821\pi\) | ||||
−0.656162 | + | 0.754620i | \(0.727821\pi\) | |||||||
\(480\) | 9.29586 | 0.424296 | ||||||||
\(481\) | 22.1509 | 1.00999 | ||||||||
\(482\) | −9.45390 | −0.430614 | ||||||||
\(483\) | 40.6696 | 1.85053 | ||||||||
\(484\) | −10.7664 | −0.489381 | ||||||||
\(485\) | −25.5927 | −1.16210 | ||||||||
\(486\) | −22.2230 | −1.00806 | ||||||||
\(487\) | 21.1829 | 0.959890 | 0.479945 | − | 0.877299i | \(-0.340657\pi\) | ||||
0.479945 | + | 0.877299i | \(0.340657\pi\) | |||||||
\(488\) | −0.239416 | −0.0108379 | ||||||||
\(489\) | −27.0250 | −1.22211 | ||||||||
\(490\) | −58.6391 | −2.64904 | ||||||||
\(491\) | −8.36445 | −0.377482 | −0.188741 | − | 0.982027i | \(-0.560441\pi\) | ||||
−0.188741 | + | 0.982027i | \(0.560441\pi\) | |||||||
\(492\) | −8.34616 | −0.376274 | ||||||||
\(493\) | −41.7585 | −1.88071 | ||||||||
\(494\) | −5.40690 | −0.243268 | ||||||||
\(495\) | 6.27095 | 0.281858 | ||||||||
\(496\) | −3.65660 | −0.164186 | ||||||||
\(497\) | 0.0672170 | 0.00301510 | ||||||||
\(498\) | −9.32075 | −0.417673 | ||||||||
\(499\) | 23.5808 | 1.05562 | 0.527810 | − | 0.849362i | \(-0.323013\pi\) | ||||
0.527810 | + | 0.849362i | \(0.323013\pi\) | |||||||
\(500\) | 11.3500 | 0.507589 | ||||||||
\(501\) | 24.2998 | 1.08563 | ||||||||
\(502\) | 14.1920 | 0.633418 | ||||||||
\(503\) | −21.0962 | −0.940635 | −0.470318 | − | 0.882497i | \(-0.655861\pi\) | ||||
−0.470318 | + | 0.882497i | \(0.655861\pi\) | |||||||
\(504\) | −17.2382 | −0.767851 | ||||||||
\(505\) | 62.9990 | 2.80342 | ||||||||
\(506\) | 1.59155 | 0.0707531 | ||||||||
\(507\) | −41.6451 | −1.84952 | ||||||||
\(508\) | −0.471433 | −0.0209165 | ||||||||
\(509\) | 7.33577 | 0.325152 | 0.162576 | − | 0.986696i | \(-0.448020\pi\) | ||||
0.162576 | + | 0.986696i | \(0.448020\pi\) | |||||||
\(510\) | −52.4765 | −2.32370 | ||||||||
\(511\) | 41.0618 | 1.81647 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 1.48862 | 0.0657243 | ||||||||
\(514\) | −25.7696 | −1.13665 | ||||||||
\(515\) | 4.20619 | 0.185347 | ||||||||
\(516\) | 24.4034 | 1.07430 | ||||||||
\(517\) | −0.841721 | −0.0370189 | ||||||||
\(518\) | 19.7249 | 0.866662 | ||||||||
\(519\) | 45.1662 | 1.98258 | ||||||||
\(520\) | 19.5936 | 0.859237 | ||||||||
\(521\) | 12.7746 | 0.559665 | 0.279833 | − | 0.960049i | \(-0.409721\pi\) | ||||
0.279833 | + | 0.960049i | \(0.409721\pi\) | |||||||
\(522\) | −26.4844 | −1.15919 | ||||||||
\(523\) | −26.6711 | −1.16624 | −0.583122 | − | 0.812384i | \(-0.698169\pi\) | ||||
−0.583122 | + | 0.812384i | \(0.698169\pi\) | |||||||
\(524\) | −19.0185 | −0.830825 | ||||||||
\(525\) | −100.437 | −4.38345 | ||||||||
\(526\) | 26.3234 | 1.14776 | ||||||||
\(527\) | 20.6421 | 0.899183 | ||||||||
\(528\) | −1.23985 | −0.0539576 | ||||||||
\(529\) | −12.1570 | −0.528565 | ||||||||
\(530\) | 38.3532 | 1.66596 | ||||||||
\(531\) | 12.0615 | 0.523425 | ||||||||
\(532\) | −4.81473 | −0.208745 | ||||||||
\(533\) | −17.5919 | −0.761988 | ||||||||
\(534\) | −33.6197 | −1.45487 | ||||||||
\(535\) | −7.20565 | −0.311527 | ||||||||
\(536\) | 2.95102 | 0.127465 | ||||||||
\(537\) | −41.5518 | −1.79309 | ||||||||
\(538\) | −24.6133 | −1.06115 | ||||||||
\(539\) | 7.82108 | 0.336878 | ||||||||
\(540\) | −5.39450 | −0.232142 | ||||||||
\(541\) | −7.48518 | −0.321813 | −0.160907 | − | 0.986970i | \(-0.551442\pi\) | ||||
−0.160907 | + | 0.986970i | \(0.551442\pi\) | |||||||
\(542\) | 14.8630 | 0.638420 | ||||||||
\(543\) | 38.3475 | 1.64565 | ||||||||
\(544\) | 5.64515 | 0.242034 | ||||||||
\(545\) | 22.2304 | 0.952244 | ||||||||
\(546\) | −66.7795 | −2.85790 | ||||||||
\(547\) | −25.8450 | −1.10505 | −0.552526 | − | 0.833496i | \(-0.686336\pi\) | ||||
−0.552526 | + | 0.833496i | \(0.686336\pi\) | |||||||
\(548\) | −3.39468 | −0.145013 | ||||||||
\(549\) | 0.857185 | 0.0365838 | ||||||||
\(550\) | −3.93049 | −0.167597 | ||||||||
\(551\) | −7.39723 | −0.315133 | ||||||||
\(552\) | −8.44691 | −0.359525 | ||||||||
\(553\) | 21.3503 | 0.907909 | ||||||||
\(554\) | −3.58959 | −0.152507 | ||||||||
\(555\) | 38.0831 | 1.61654 | ||||||||
\(556\) | 4.92798 | 0.208993 | ||||||||
\(557\) | −29.4861 | −1.24937 | −0.624684 | − | 0.780878i | \(-0.714772\pi\) | ||||
−0.624684 | + | 0.780878i | \(0.714772\pi\) | |||||||
\(558\) | 13.0918 | 0.554219 | ||||||||
\(559\) | 51.4370 | 2.17555 | ||||||||
\(560\) | 17.4477 | 0.737300 | ||||||||
\(561\) | 6.99914 | 0.295504 | ||||||||
\(562\) | −26.4608 | −1.11618 | ||||||||
\(563\) | 1.73847 | 0.0732676 | 0.0366338 | − | 0.999329i | \(-0.488336\pi\) | ||||
0.0366338 | + | 0.999329i | \(0.488336\pi\) | |||||||
\(564\) | 4.46730 | 0.188107 | ||||||||
\(565\) | −51.5036 | −2.16677 | ||||||||
\(566\) | −14.6346 | −0.615138 | ||||||||
\(567\) | −33.3290 | −1.39969 | ||||||||
\(568\) | −0.0139607 | −0.000585779 0 | ||||||||
\(569\) | 36.4497 | 1.52805 | 0.764025 | − | 0.645186i | \(-0.223220\pi\) | ||||
0.764025 | + | 0.645186i | \(0.223220\pi\) | |||||||
\(570\) | −9.29586 | −0.389361 | ||||||||
\(571\) | 2.10049 | 0.0879028 | 0.0439514 | − | 0.999034i | \(-0.486005\pi\) | ||||
0.0439514 | + | 0.999034i | \(0.486005\pi\) | |||||||
\(572\) | −2.61333 | −0.109269 | ||||||||
\(573\) | −42.5583 | −1.77790 | ||||||||
\(574\) | −15.6652 | −0.653851 | ||||||||
\(575\) | −26.7778 | −1.11671 | ||||||||
\(576\) | 3.58031 | 0.149180 | ||||||||
\(577\) | 35.9192 | 1.49534 | 0.747668 | − | 0.664073i | \(-0.231174\pi\) | ||||
0.747668 | + | 0.664073i | \(0.231174\pi\) | |||||||
\(578\) | −14.8677 | −0.618414 | ||||||||
\(579\) | 50.6514 | 2.10500 | ||||||||
\(580\) | 26.8062 | 1.11307 | ||||||||
\(581\) | −17.4944 | −0.725790 | ||||||||
\(582\) | −18.1164 | −0.750949 | ||||||||
\(583\) | −5.11542 | −0.211859 | ||||||||
\(584\) | −8.52837 | −0.352907 | ||||||||
\(585\) | −70.1513 | −2.90040 | ||||||||
\(586\) | −19.7157 | −0.814446 | ||||||||
\(587\) | 42.6923 | 1.76210 | 0.881049 | − | 0.473025i | \(-0.156838\pi\) | ||||
0.881049 | + | 0.473025i | \(0.156838\pi\) | |||||||
\(588\) | −41.5092 | −1.71181 | ||||||||
\(589\) | 3.65660 | 0.150668 | ||||||||
\(590\) | −12.2081 | −0.502598 | ||||||||
\(591\) | −48.2794 | −1.98595 | ||||||||
\(592\) | −4.09678 | −0.168377 | ||||||||
\(593\) | 16.6590 | 0.684105 | 0.342052 | − | 0.939681i | \(-0.388878\pi\) | ||||
0.342052 | + | 0.939681i | \(0.388878\pi\) | |||||||
\(594\) | 0.719500 | 0.0295214 | ||||||||
\(595\) | −98.4948 | −4.03789 | ||||||||
\(596\) | −12.9917 | −0.532160 | ||||||||
\(597\) | 29.6176 | 1.21217 | ||||||||
\(598\) | −17.8042 | −0.728069 | ||||||||
\(599\) | −19.6946 | −0.804702 | −0.402351 | − | 0.915486i | \(-0.631807\pi\) | ||||
−0.402351 | + | 0.915486i | \(0.631807\pi\) | |||||||
\(600\) | 20.8605 | 0.851625 | ||||||||
\(601\) | 21.3739 | 0.871859 | 0.435930 | − | 0.899981i | \(-0.356420\pi\) | ||||
0.435930 | + | 0.899981i | \(0.356420\pi\) | |||||||
\(602\) | 45.8035 | 1.86681 | ||||||||
\(603\) | −10.5656 | −0.430264 | ||||||||
\(604\) | −18.6205 | −0.757659 | ||||||||
\(605\) | −39.0154 | −1.58620 | ||||||||
\(606\) | 44.5955 | 1.81157 | ||||||||
\(607\) | 16.5595 | 0.672131 | 0.336066 | − | 0.941839i | \(-0.390904\pi\) | ||||
0.336066 | + | 0.941839i | \(0.390904\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | −91.3616 | −3.70216 | ||||||||
\(610\) | −0.867602 | −0.0351282 | ||||||||
\(611\) | 9.41609 | 0.380934 | ||||||||
\(612\) | −20.2114 | −0.816997 | ||||||||
\(613\) | −20.0082 | −0.808125 | −0.404062 | − | 0.914731i | \(-0.632402\pi\) | ||||
−0.404062 | + | 0.914731i | \(0.632402\pi\) | |||||||
\(614\) | 30.0320 | 1.21199 | ||||||||
\(615\) | −30.2450 | −1.21960 | ||||||||
\(616\) | −2.32711 | −0.0937621 | ||||||||
\(617\) | −1.54570 | −0.0622274 | −0.0311137 | − | 0.999516i | \(-0.509905\pi\) | ||||
−0.0311137 | + | 0.999516i | \(0.509905\pi\) | |||||||
\(618\) | 2.97746 | 0.119771 | ||||||||
\(619\) | −28.7093 | −1.15392 | −0.576962 | − | 0.816771i | \(-0.695762\pi\) | ||||
−0.576962 | + | 0.816771i | \(0.695762\pi\) | |||||||
\(620\) | −13.2509 | −0.532168 | ||||||||
\(621\) | 4.90184 | 0.196704 | ||||||||
\(622\) | 33.1178 | 1.32790 | ||||||||
\(623\) | −63.1019 | −2.52813 | ||||||||
\(624\) | 13.8698 | 0.555238 | ||||||||
\(625\) | 0.470126 | 0.0188050 | ||||||||
\(626\) | −0.709517 | −0.0283580 | ||||||||
\(627\) | 1.23985 | 0.0495149 | ||||||||
\(628\) | 4.81982 | 0.192332 | ||||||||
\(629\) | 23.1269 | 0.922132 | ||||||||
\(630\) | −62.4682 | −2.48879 | ||||||||
\(631\) | −32.6313 | −1.29903 | −0.649516 | − | 0.760348i | \(-0.725028\pi\) | ||||
−0.649516 | + | 0.760348i | \(0.725028\pi\) | |||||||
\(632\) | −4.43438 | −0.176390 | ||||||||
\(633\) | 2.56521 | 0.101958 | ||||||||
\(634\) | −2.38483 | −0.0947139 | ||||||||
\(635\) | −1.70839 | −0.0677953 | ||||||||
\(636\) | 27.1493 | 1.07654 | ||||||||
\(637\) | −87.4922 | −3.46657 | ||||||||
\(638\) | −3.57532 | −0.141548 | ||||||||
\(639\) | 0.0499837 | 0.00197733 | ||||||||
\(640\) | −3.62382 | −0.143244 | ||||||||
\(641\) | 29.4825 | 1.16449 | 0.582245 | − | 0.813014i | \(-0.302175\pi\) | ||||
0.582245 | + | 0.813014i | \(0.302175\pi\) | |||||||
\(642\) | −5.10070 | −0.201309 | ||||||||
\(643\) | 26.1111 | 1.02972 | 0.514861 | − | 0.857274i | \(-0.327844\pi\) | ||||
0.514861 | + | 0.857274i | \(0.327844\pi\) | |||||||
\(644\) | −15.8543 | −0.624746 | ||||||||
\(645\) | 88.4335 | 3.48207 | ||||||||
\(646\) | −5.64515 | −0.222105 | ||||||||
\(647\) | 34.3605 | 1.35085 | 0.675425 | − | 0.737428i | \(-0.263960\pi\) | ||||
0.675425 | + | 0.737428i | \(0.263960\pi\) | |||||||
\(648\) | 6.92230 | 0.271934 | ||||||||
\(649\) | 1.62827 | 0.0639152 | ||||||||
\(650\) | 43.9692 | 1.72462 | ||||||||
\(651\) | 45.1619 | 1.77004 | ||||||||
\(652\) | 10.5352 | 0.412590 | ||||||||
\(653\) | −40.3342 | −1.57840 | −0.789200 | − | 0.614137i | \(-0.789504\pi\) | ||||
−0.789200 | + | 0.614137i | \(0.789504\pi\) | |||||||
\(654\) | 15.7363 | 0.615339 | ||||||||
\(655\) | −68.9195 | −2.69291 | ||||||||
\(656\) | 3.25360 | 0.127032 | ||||||||
\(657\) | 30.5342 | 1.19125 | ||||||||
\(658\) | 8.38482 | 0.326874 | ||||||||
\(659\) | 17.7621 | 0.691915 | 0.345957 | − | 0.938250i | \(-0.387554\pi\) | ||||
0.345957 | + | 0.938250i | \(0.387554\pi\) | |||||||
\(660\) | −4.49299 | −0.174890 | ||||||||
\(661\) | 37.7222 | 1.46722 | 0.733612 | − | 0.679568i | \(-0.237833\pi\) | ||||
0.733612 | + | 0.679568i | \(0.237833\pi\) | |||||||
\(662\) | 29.5601 | 1.14889 | ||||||||
\(663\) | −78.2973 | −3.04082 | ||||||||
\(664\) | 3.63352 | 0.141008 | ||||||||
\(665\) | −17.4477 | −0.676592 | ||||||||
\(666\) | 14.6678 | 0.568364 | ||||||||
\(667\) | −24.3581 | −0.943151 | ||||||||
\(668\) | −9.47281 | −0.366514 | ||||||||
\(669\) | 59.1824 | 2.28812 | ||||||||
\(670\) | 10.6940 | 0.413144 | ||||||||
\(671\) | 0.115718 | 0.00446723 | ||||||||
\(672\) | 12.3508 | 0.476442 | ||||||||
\(673\) | 34.8916 | 1.34497 | 0.672486 | − | 0.740109i | \(-0.265226\pi\) | ||||
0.672486 | + | 0.740109i | \(0.265226\pi\) | |||||||
\(674\) | 11.6149 | 0.447390 | ||||||||
\(675\) | −12.1056 | −0.465944 | ||||||||
\(676\) | 16.2346 | 0.624406 | ||||||||
\(677\) | −30.7839 | −1.18312 | −0.591560 | − | 0.806261i | \(-0.701488\pi\) | ||||
−0.591560 | + | 0.806261i | \(0.701488\pi\) | |||||||
\(678\) | −36.4581 | −1.40016 | ||||||||
\(679\) | −34.0033 | −1.30493 | ||||||||
\(680\) | 20.4570 | 0.784490 | ||||||||
\(681\) | −42.5108 | −1.62902 | ||||||||
\(682\) | 1.76736 | 0.0676756 | ||||||||
\(683\) | 29.6790 | 1.13564 | 0.567819 | − | 0.823154i | \(-0.307788\pi\) | ||||
0.567819 | + | 0.823154i | \(0.307788\pi\) | |||||||
\(684\) | −3.58031 | −0.136897 | ||||||||
\(685\) | −12.3017 | −0.470023 | ||||||||
\(686\) | −44.2068 | −1.68782 | ||||||||
\(687\) | −8.78322 | −0.335101 | ||||||||
\(688\) | −9.51322 | −0.362688 | ||||||||
\(689\) | 57.2247 | 2.18009 | ||||||||
\(690\) | −30.6101 | −1.16531 | ||||||||
\(691\) | 5.38223 | 0.204750 | 0.102375 | − | 0.994746i | \(-0.467356\pi\) | ||||
0.102375 | + | 0.994746i | \(0.467356\pi\) | |||||||
\(692\) | −17.6072 | −0.669326 | ||||||||
\(693\) | 8.33179 | 0.316499 | ||||||||
\(694\) | −1.42388 | −0.0540496 | ||||||||
\(695\) | 17.8581 | 0.677396 | ||||||||
\(696\) | 18.9755 | 0.719263 | ||||||||
\(697\) | −18.3670 | −0.695701 | ||||||||
\(698\) | 6.02755 | 0.228146 | ||||||||
\(699\) | −14.8704 | −0.562450 | ||||||||
\(700\) | 39.1536 | 1.47987 | ||||||||
\(701\) | −0.881147 | −0.0332805 | −0.0166402 | − | 0.999862i | \(-0.505297\pi\) | ||||
−0.0166402 | + | 0.999862i | \(0.505297\pi\) | |||||||
\(702\) | −8.04883 | −0.303784 | ||||||||
\(703\) | 4.09678 | 0.154513 | ||||||||
\(704\) | 0.483333 | 0.0182163 | ||||||||
\(705\) | 16.1887 | 0.609702 | ||||||||
\(706\) | 1.61861 | 0.0609172 | ||||||||
\(707\) | 83.7026 | 3.14796 | ||||||||
\(708\) | −8.64179 | −0.324779 | ||||||||
\(709\) | 35.1686 | 1.32078 | 0.660391 | − | 0.750922i | \(-0.270390\pi\) | ||||
0.660391 | + | 0.750922i | \(0.270390\pi\) | |||||||
\(710\) | −0.0505911 | −0.00189865 | ||||||||
\(711\) | 15.8765 | 0.595415 | ||||||||
\(712\) | 13.1060 | 0.491169 | ||||||||
\(713\) | 12.0407 | 0.450929 | ||||||||
\(714\) | −69.7220 | −2.60928 | ||||||||
\(715\) | −9.47024 | −0.354167 | ||||||||
\(716\) | 16.1982 | 0.605355 | ||||||||
\(717\) | 0.600216 | 0.0224155 | ||||||||
\(718\) | 20.7395 | 0.773991 | ||||||||
\(719\) | −23.4978 | −0.876320 | −0.438160 | − | 0.898897i | \(-0.644370\pi\) | ||||
−0.438160 | + | 0.898897i | \(0.644370\pi\) | |||||||
\(720\) | 12.9744 | 0.483527 | ||||||||
\(721\) | 5.58848 | 0.208126 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | −24.2513 | −0.901914 | ||||||||
\(724\) | −14.9491 | −0.555578 | ||||||||
\(725\) | 60.1547 | 2.23409 | ||||||||
\(726\) | −27.6181 | −1.02500 | ||||||||
\(727\) | 31.7852 | 1.17885 | 0.589423 | − | 0.807824i | \(-0.299355\pi\) | ||||
0.589423 | + | 0.807824i | \(0.299355\pi\) | |||||||
\(728\) | 26.0327 | 0.964837 | ||||||||
\(729\) | −36.2399 | −1.34222 | ||||||||
\(730\) | −30.9053 | −1.14386 | ||||||||
\(731\) | 53.7035 | 1.98630 | ||||||||
\(732\) | −0.614154 | −0.0226998 | ||||||||
\(733\) | 47.8357 | 1.76685 | 0.883425 | − | 0.468572i | \(-0.155231\pi\) | ||||
0.883425 | + | 0.468572i | \(0.155231\pi\) | |||||||
\(734\) | 7.59985 | 0.280516 | ||||||||
\(735\) | −150.422 | −5.54839 | ||||||||
\(736\) | 3.29287 | 0.121377 | ||||||||
\(737\) | −1.42633 | −0.0525394 | ||||||||
\(738\) | −11.6489 | −0.428801 | ||||||||
\(739\) | −51.1768 | −1.88257 | −0.941284 | − | 0.337615i | \(-0.890380\pi\) | ||||
−0.941284 | + | 0.337615i | \(0.890380\pi\) | |||||||
\(740\) | −14.8460 | −0.545750 | ||||||||
\(741\) | −13.8698 | −0.509521 | ||||||||
\(742\) | 50.9573 | 1.87070 | ||||||||
\(743\) | −16.8041 | −0.616484 | −0.308242 | − | 0.951308i | \(-0.599741\pi\) | ||||
−0.308242 | + | 0.951308i | \(0.599741\pi\) | |||||||
\(744\) | −9.37996 | −0.343886 | ||||||||
\(745\) | −47.0795 | −1.72486 | ||||||||
\(746\) | −24.5031 | −0.897123 | ||||||||
\(747\) | −13.0091 | −0.475980 | ||||||||
\(748\) | −2.72848 | −0.0997632 | ||||||||
\(749\) | −9.57366 | −0.349814 | ||||||||
\(750\) | 29.1152 | 1.06314 | ||||||||
\(751\) | −23.7296 | −0.865905 | −0.432953 | − | 0.901417i | \(-0.642528\pi\) | ||||
−0.432953 | + | 0.901417i | \(0.642528\pi\) | |||||||
\(752\) | −1.74149 | −0.0635058 | ||||||||
\(753\) | 36.4054 | 1.32669 | ||||||||
\(754\) | 39.9961 | 1.45657 | ||||||||
\(755\) | −67.4775 | −2.45576 | ||||||||
\(756\) | −7.16731 | −0.260673 | ||||||||
\(757\) | −5.90532 | −0.214632 | −0.107316 | − | 0.994225i | \(-0.534226\pi\) | ||||
−0.107316 | + | 0.994225i | \(0.534226\pi\) | |||||||
\(758\) | 8.53571 | 0.310031 | ||||||||
\(759\) | 4.08267 | 0.148192 | ||||||||
\(760\) | 3.62382 | 0.131450 | ||||||||
\(761\) | 47.0067 | 1.70399 | 0.851997 | − | 0.523547i | \(-0.175392\pi\) | ||||
0.851997 | + | 0.523547i | \(0.175392\pi\) | |||||||
\(762\) | −1.20933 | −0.0438093 | ||||||||
\(763\) | 29.5360 | 1.06927 | ||||||||
\(764\) | 16.5906 | 0.600226 | ||||||||
\(765\) | −73.2424 | −2.64808 | ||||||||
\(766\) | 11.7009 | 0.422771 | ||||||||
\(767\) | −18.2150 | −0.657705 | ||||||||
\(768\) | −2.56521 | −0.0925641 | ||||||||
\(769\) | −23.1141 | −0.833517 | −0.416758 | − | 0.909017i | \(-0.636834\pi\) | ||||
−0.416758 | + | 0.909017i | \(0.636834\pi\) | |||||||
\(770\) | −8.43304 | −0.303906 | ||||||||
\(771\) | −66.1044 | −2.38069 | ||||||||
\(772\) | −19.7455 | −0.710656 | ||||||||
\(773\) | 24.5982 | 0.884734 | 0.442367 | − | 0.896834i | \(-0.354139\pi\) | ||||
0.442367 | + | 0.896834i | \(0.354139\pi\) | |||||||
\(774\) | 34.0603 | 1.22427 | ||||||||
\(775\) | −29.7357 | −1.06814 | ||||||||
\(776\) | 7.06235 | 0.253523 | ||||||||
\(777\) | 50.5985 | 1.81521 | ||||||||
\(778\) | −24.3028 | −0.871298 | ||||||||
\(779\) | −3.25360 | −0.116572 | ||||||||
\(780\) | 50.2618 | 1.79966 | ||||||||
\(781\) | 0.00674767 | 0.000241451 0 | ||||||||
\(782\) | −18.5887 | −0.664732 | ||||||||
\(783\) | −11.0117 | −0.393526 | ||||||||
\(784\) | 16.1816 | 0.577913 | ||||||||
\(785\) | 17.4662 | 0.623394 | ||||||||
\(786\) | −48.7864 | −1.74015 | ||||||||
\(787\) | −13.4320 | −0.478799 | −0.239400 | − | 0.970921i | \(-0.576951\pi\) | ||||
−0.239400 | + | 0.970921i | \(0.576951\pi\) | |||||||
\(788\) | 18.8208 | 0.670465 | ||||||||
\(789\) | 67.5252 | 2.40396 | ||||||||
\(790\) | −16.0694 | −0.571724 | ||||||||
\(791\) | −68.4293 | −2.43307 | ||||||||
\(792\) | −1.73048 | −0.0614900 | ||||||||
\(793\) | −1.29450 | −0.0459691 | ||||||||
\(794\) | 27.2367 | 0.966595 | ||||||||
\(795\) | 98.3841 | 3.48932 | ||||||||
\(796\) | −11.5459 | −0.409232 | ||||||||
\(797\) | 22.9776 | 0.813908 | 0.406954 | − | 0.913449i | \(-0.366591\pi\) | ||||
0.406954 | + | 0.913449i | \(0.366591\pi\) | |||||||
\(798\) | −12.3508 | −0.437213 | ||||||||
\(799\) | 9.83099 | 0.347796 | ||||||||
\(800\) | −8.13206 | −0.287512 | ||||||||
\(801\) | −46.9237 | −1.65797 | ||||||||
\(802\) | 18.5289 | 0.654277 | ||||||||
\(803\) | 4.12204 | 0.145464 | ||||||||
\(804\) | 7.57000 | 0.266973 | ||||||||
\(805\) | −57.4530 | −2.02495 | ||||||||
\(806\) | −19.7709 | −0.696400 | ||||||||
\(807\) | −63.1382 | −2.22257 | ||||||||
\(808\) | −17.3847 | −0.611592 | ||||||||
\(809\) | −39.7478 | −1.39746 | −0.698729 | − | 0.715386i | \(-0.746251\pi\) | ||||
−0.698729 | + | 0.715386i | \(0.746251\pi\) | |||||||
\(810\) | 25.0852 | 0.881403 | ||||||||
\(811\) | 21.6945 | 0.761797 | 0.380898 | − | 0.924617i | \(-0.375615\pi\) | ||||
0.380898 | + | 0.924617i | \(0.375615\pi\) | |||||||
\(812\) | 35.6156 | 1.24986 | ||||||||
\(813\) | 38.1267 | 1.33716 | ||||||||
\(814\) | 1.98011 | 0.0694028 | ||||||||
\(815\) | 38.1776 | 1.33730 | ||||||||
\(816\) | 14.4810 | 0.506936 | ||||||||
\(817\) | 9.51322 | 0.332825 | ||||||||
\(818\) | 14.8965 | 0.520844 | ||||||||
\(819\) | −93.2053 | −3.25686 | ||||||||
\(820\) | 11.7904 | 0.411740 | ||||||||
\(821\) | 0.906308 | 0.0316304 | 0.0158152 | − | 0.999875i | \(-0.494966\pi\) | ||||
0.0158152 | + | 0.999875i | \(0.494966\pi\) | |||||||
\(822\) | −8.70806 | −0.303729 | ||||||||
\(823\) | −33.4016 | −1.16431 | −0.582154 | − | 0.813079i | \(-0.697790\pi\) | ||||
−0.582154 | + | 0.813079i | \(0.697790\pi\) | |||||||
\(824\) | −1.16071 | −0.0404351 | ||||||||
\(825\) | −10.0825 | −0.351029 | ||||||||
\(826\) | −16.2201 | −0.564368 | ||||||||
\(827\) | −48.4821 | −1.68589 | −0.842944 | − | 0.538002i | \(-0.819179\pi\) | ||||
−0.842944 | + | 0.538002i | \(0.819179\pi\) | |||||||
\(828\) | −11.7895 | −0.409714 | ||||||||
\(829\) | 21.1802 | 0.735619 | 0.367810 | − | 0.929901i | \(-0.380108\pi\) | ||||
0.367810 | + | 0.929901i | \(0.380108\pi\) | |||||||
\(830\) | 13.1672 | 0.457041 | ||||||||
\(831\) | −9.20806 | −0.319424 | ||||||||
\(832\) | −5.40690 | −0.187451 | ||||||||
\(833\) | −91.3474 | −3.16500 | ||||||||
\(834\) | 12.6413 | 0.437733 | ||||||||
\(835\) | −34.3277 | −1.18796 | ||||||||
\(836\) | −0.483333 | −0.0167164 | ||||||||
\(837\) | 5.44330 | 0.188148 | ||||||||
\(838\) | −0.854101 | −0.0295044 | ||||||||
\(839\) | 55.3200 | 1.90986 | 0.954930 | − | 0.296831i | \(-0.0959299\pi\) | ||||
0.954930 | + | 0.296831i | \(0.0959299\pi\) | |||||||
\(840\) | 44.7570 | 1.54426 | ||||||||
\(841\) | 25.7190 | 0.886863 | ||||||||
\(842\) | 17.8339 | 0.614597 | ||||||||
\(843\) | −67.8776 | −2.33783 | ||||||||
\(844\) | −1.00000 | −0.0344214 | ||||||||
\(845\) | 58.8311 | 2.02385 | ||||||||
\(846\) | 6.23509 | 0.214367 | ||||||||
\(847\) | −51.8372 | −1.78115 | ||||||||
\(848\) | −10.5836 | −0.363444 | ||||||||
\(849\) | −37.5409 | −1.28840 | ||||||||
\(850\) | 45.9067 | 1.57459 | ||||||||
\(851\) | 13.4902 | 0.462438 | ||||||||
\(852\) | −0.0358122 | −0.00122691 | ||||||||
\(853\) | 46.8225 | 1.60317 | 0.801585 | − | 0.597880i | \(-0.203990\pi\) | ||||
0.801585 | + | 0.597880i | \(0.203990\pi\) | |||||||
\(854\) | −1.15272 | −0.0394454 | ||||||||
\(855\) | −12.9744 | −0.443715 | ||||||||
\(856\) | 1.98841 | 0.0679625 | ||||||||
\(857\) | −3.25186 | −0.111082 | −0.0555408 | − | 0.998456i | \(-0.517688\pi\) | ||||
−0.0555408 | + | 0.998456i | \(0.517688\pi\) | |||||||
\(858\) | −6.70375 | −0.228862 | ||||||||
\(859\) | −14.1103 | −0.481438 | −0.240719 | − | 0.970595i | \(-0.577383\pi\) | ||||
−0.240719 | + | 0.970595i | \(0.577383\pi\) | |||||||
\(860\) | −34.4742 | −1.17556 | ||||||||
\(861\) | −40.1845 | −1.36948 | ||||||||
\(862\) | 28.9693 | 0.986698 | ||||||||
\(863\) | 2.88423 | 0.0981804 | 0.0490902 | − | 0.998794i | \(-0.484368\pi\) | ||||
0.0490902 | + | 0.998794i | \(0.484368\pi\) | |||||||
\(864\) | 1.48862 | 0.0506440 | ||||||||
\(865\) | −63.8054 | −2.16945 | ||||||||
\(866\) | −24.0138 | −0.816022 | ||||||||
\(867\) | −38.1388 | −1.29526 | ||||||||
\(868\) | −17.6055 | −0.597571 | ||||||||
\(869\) | 2.14328 | 0.0727059 | ||||||||
\(870\) | 68.7636 | 2.33131 | ||||||||
\(871\) | 15.9559 | 0.540644 | ||||||||
\(872\) | −6.13451 | −0.207741 | ||||||||
\(873\) | −25.2854 | −0.855781 | ||||||||
\(874\) | −3.29287 | −0.111383 | ||||||||
\(875\) | 54.6473 | 1.84741 | ||||||||
\(876\) | −21.8771 | −0.739158 | ||||||||
\(877\) | 52.5613 | 1.77487 | 0.887435 | − | 0.460933i | \(-0.152485\pi\) | ||||
0.887435 | + | 0.460933i | \(0.152485\pi\) | |||||||
\(878\) | −13.1530 | −0.443892 | ||||||||
\(879\) | −50.5748 | −1.70585 | ||||||||
\(880\) | 1.75151 | 0.0590434 | ||||||||
\(881\) | −2.76352 | −0.0931054 | −0.0465527 | − | 0.998916i | \(-0.514824\pi\) | ||||
−0.0465527 | + | 0.998916i | \(0.514824\pi\) | |||||||
\(882\) | −57.9351 | −1.95078 | ||||||||
\(883\) | −18.1987 | −0.612434 | −0.306217 | − | 0.951962i | \(-0.599063\pi\) | ||||
−0.306217 | + | 0.951962i | \(0.599063\pi\) | |||||||
\(884\) | 30.5227 | 1.02659 | ||||||||
\(885\) | −31.3163 | −1.05269 | ||||||||
\(886\) | 8.78113 | 0.295008 | ||||||||
\(887\) | −31.3928 | −1.05407 | −0.527034 | − | 0.849844i | \(-0.676696\pi\) | ||||
−0.527034 | + | 0.849844i | \(0.676696\pi\) | |||||||
\(888\) | −10.5091 | −0.352663 | ||||||||
\(889\) | −2.26982 | −0.0761273 | ||||||||
\(890\) | 47.4939 | 1.59200 | ||||||||
\(891\) | −3.34577 | −0.112088 | ||||||||
\(892\) | −23.0712 | −0.772479 | ||||||||
\(893\) | 1.74149 | 0.0582769 | ||||||||
\(894\) | −33.3264 | −1.11460 | ||||||||
\(895\) | 58.6993 | 1.96210 | ||||||||
\(896\) | −4.81473 | −0.160849 | ||||||||
\(897\) | −45.6716 | −1.52493 | ||||||||
\(898\) | −17.6450 | −0.588821 | ||||||||
\(899\) | −27.0487 | −0.902126 | ||||||||
\(900\) | 29.1153 | 0.970511 | ||||||||
\(901\) | 59.7462 | 1.99043 | ||||||||
\(902\) | −1.57257 | −0.0523608 | ||||||||
\(903\) | 117.496 | 3.91001 | ||||||||
\(904\) | 14.2125 | 0.472701 | ||||||||
\(905\) | −54.1727 | −1.80076 | ||||||||
\(906\) | −47.7656 | −1.58691 | ||||||||
\(907\) | −0.694013 | −0.0230443 | −0.0115222 | − | 0.999934i | \(-0.503668\pi\) | ||||
−0.0115222 | + | 0.999934i | \(0.503668\pi\) | |||||||
\(908\) | 16.5721 | 0.549963 | ||||||||
\(909\) | 62.2427 | 2.06446 | ||||||||
\(910\) | 94.3379 | 3.12727 | ||||||||
\(911\) | 49.4228 | 1.63745 | 0.818726 | − | 0.574185i | \(-0.194681\pi\) | ||||
0.818726 | + | 0.574185i | \(0.194681\pi\) | |||||||
\(912\) | 2.56521 | 0.0849427 | ||||||||
\(913\) | −1.75620 | −0.0581217 | ||||||||
\(914\) | 21.8845 | 0.723874 | ||||||||
\(915\) | −2.22558 | −0.0735755 | ||||||||
\(916\) | 3.42397 | 0.113131 | ||||||||
\(917\) | −91.5687 | −3.02386 | ||||||||
\(918\) | −8.40350 | −0.277357 | ||||||||
\(919\) | −35.4504 | −1.16940 | −0.584700 | − | 0.811249i | \(-0.698788\pi\) | ||||
−0.584700 | + | 0.811249i | \(0.698788\pi\) | |||||||
\(920\) | 11.9328 | 0.393412 | ||||||||
\(921\) | 77.0384 | 2.53850 | ||||||||
\(922\) | 4.83115 | 0.159105 | ||||||||
\(923\) | −0.0754842 | −0.00248459 | ||||||||
\(924\) | −5.96954 | −0.196383 | ||||||||
\(925\) | −33.3153 | −1.09540 | ||||||||
\(926\) | −5.95116 | −0.195567 | ||||||||
\(927\) | 4.15569 | 0.136491 | ||||||||
\(928\) | −7.39723 | −0.242826 | ||||||||
\(929\) | −42.7113 | −1.40131 | −0.700657 | − | 0.713498i | \(-0.747110\pi\) | ||||
−0.700657 | + | 0.713498i | \(0.747110\pi\) | |||||||
\(930\) | −33.9913 | −1.11462 | ||||||||
\(931\) | −16.1816 | −0.530330 | ||||||||
\(932\) | 5.79695 | 0.189885 | ||||||||
\(933\) | 84.9541 | 2.78127 | ||||||||
\(934\) | 0.943463 | 0.0308710 | ||||||||
\(935\) | −9.88753 | −0.323357 | ||||||||
\(936\) | 19.3584 | 0.632749 | ||||||||
\(937\) | −37.5728 | −1.22745 | −0.613725 | − | 0.789520i | \(-0.710330\pi\) | ||||
−0.613725 | + | 0.789520i | \(0.710330\pi\) | |||||||
\(938\) | 14.2084 | 0.463919 | ||||||||
\(939\) | −1.82006 | −0.0593955 | ||||||||
\(940\) | −6.31086 | −0.205838 | ||||||||
\(941\) | −49.3760 | −1.60961 | −0.804805 | − | 0.593539i | \(-0.797730\pi\) | ||||
−0.804805 | + | 0.593539i | \(0.797730\pi\) | |||||||
\(942\) | 12.3639 | 0.402836 | ||||||||
\(943\) | −10.7137 | −0.348885 | ||||||||
\(944\) | 3.36884 | 0.109646 | ||||||||
\(945\) | −25.9730 | −0.844903 | ||||||||
\(946\) | 4.59805 | 0.149495 | ||||||||
\(947\) | 20.2355 | 0.657566 | 0.328783 | − | 0.944405i | \(-0.393361\pi\) | ||||
0.328783 | + | 0.944405i | \(0.393361\pi\) | |||||||
\(948\) | −11.3751 | −0.369447 | ||||||||
\(949\) | −46.1121 | −1.49686 | ||||||||
\(950\) | 8.13206 | 0.263839 | ||||||||
\(951\) | −6.11760 | −0.198377 | ||||||||
\(952\) | 27.1798 | 0.880903 | ||||||||
\(953\) | 37.6841 | 1.22071 | 0.610355 | − | 0.792128i | \(-0.291027\pi\) | ||||
0.610355 | + | 0.792128i | \(0.291027\pi\) | |||||||
\(954\) | 37.8927 | 1.22682 | ||||||||
\(955\) | 60.1212 | 1.94548 | ||||||||
\(956\) | −0.233983 | −0.00756755 | ||||||||
\(957\) | −9.17146 | −0.296471 | ||||||||
\(958\) | 28.7216 | 0.927953 | ||||||||
\(959\) | −16.3444 | −0.527789 | ||||||||
\(960\) | −9.29586 | −0.300023 | ||||||||
\(961\) | −17.6292 | −0.568685 | ||||||||
\(962\) | −22.1509 | −0.714174 | ||||||||
\(963\) | −7.11914 | −0.229411 | ||||||||
\(964\) | 9.45390 | 0.304490 | ||||||||
\(965\) | −71.5541 | −2.30341 | ||||||||
\(966\) | −40.6696 | −1.30852 | ||||||||
\(967\) | 25.1088 | 0.807445 | 0.403722 | − | 0.914882i | \(-0.367716\pi\) | ||||
0.403722 | + | 0.914882i | \(0.367716\pi\) | |||||||
\(968\) | 10.7664 | 0.346045 | ||||||||
\(969\) | −14.4810 | −0.465197 | ||||||||
\(970\) | 25.5927 | 0.821731 | ||||||||
\(971\) | 9.66498 | 0.310164 | 0.155082 | − | 0.987902i | \(-0.450436\pi\) | ||||
0.155082 | + | 0.987902i | \(0.450436\pi\) | |||||||
\(972\) | 22.2230 | 0.712804 | ||||||||
\(973\) | 23.7269 | 0.760648 | ||||||||
\(974\) | −21.1829 | −0.678745 | ||||||||
\(975\) | 112.790 | 3.61218 | ||||||||
\(976\) | 0.239416 | 0.00766353 | ||||||||
\(977\) | 41.3547 | 1.32305 | 0.661527 | − | 0.749921i | \(-0.269909\pi\) | ||||
0.661527 | + | 0.749921i | \(0.269909\pi\) | |||||||
\(978\) | 27.0250 | 0.864164 | ||||||||
\(979\) | −6.33457 | −0.202454 | ||||||||
\(980\) | 58.6391 | 1.87316 | ||||||||
\(981\) | 21.9635 | 0.701240 | ||||||||
\(982\) | 8.36445 | 0.266920 | ||||||||
\(983\) | 36.1878 | 1.15421 | 0.577105 | − | 0.816670i | \(-0.304182\pi\) | ||||
0.577105 | + | 0.816670i | \(0.304182\pi\) | |||||||
\(984\) | 8.34616 | 0.266066 | ||||||||
\(985\) | 68.2033 | 2.17314 | ||||||||
\(986\) | 41.7585 | 1.32986 | ||||||||
\(987\) | 21.5088 | 0.684634 | ||||||||
\(988\) | 5.40690 | 0.172016 | ||||||||
\(989\) | 31.3258 | 0.996103 | ||||||||
\(990\) | −6.27095 | −0.199304 | ||||||||
\(991\) | −50.1090 | −1.59176 | −0.795882 | − | 0.605452i | \(-0.792992\pi\) | ||||
−0.795882 | + | 0.605452i | \(0.792992\pi\) | |||||||
\(992\) | 3.65660 | 0.116097 | ||||||||
\(993\) | 75.8280 | 2.40633 | ||||||||
\(994\) | −0.0672170 | −0.00213199 | ||||||||
\(995\) | −41.8401 | −1.32642 | ||||||||
\(996\) | 9.32075 | 0.295339 | ||||||||
\(997\) | −46.9996 | −1.48849 | −0.744247 | − | 0.667905i | \(-0.767191\pi\) | ||||
−0.744247 | + | 0.667905i | \(0.767191\pi\) | |||||||
\(998\) | −23.5808 | −0.746436 | ||||||||
\(999\) | 6.09857 | 0.192950 |
(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 | 8018.2.a.f.1.5 | ✓ | 34 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8018.2.a.f.1.5 | ✓ | 34 | 1.1 | even | 1 | trivial |