Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6037,2,Mod(1,6037)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6037, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6037.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6037 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6037.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: | \(48.2056877002\) |
Analytic rank: | \(0\) |
Dimension: | \(259\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Character | \(\chi\) | \(=\) | 6037.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.61164 | −1.84671 | −0.923353 | − | 0.383951i | \(-0.874563\pi\) | ||||
−0.923353 | + | 0.383951i | \(0.874563\pi\) | |||||||
\(3\) | 1.28286 | 0.740662 | 0.370331 | − | 0.928900i | \(-0.379244\pi\) | ||||
0.370331 | + | 0.928900i | \(0.379244\pi\) | |||||||
\(4\) | 4.82065 | 2.41033 | ||||||||
\(5\) | −1.11903 | −0.500445 | −0.250223 | − | 0.968188i | \(-0.580504\pi\) | ||||
−0.250223 | + | 0.968188i | \(0.580504\pi\) | |||||||
\(6\) | −3.35038 | −1.36779 | ||||||||
\(7\) | −4.20141 | −1.58798 | −0.793992 | − | 0.607929i | \(-0.792001\pi\) | ||||
−0.793992 | + | 0.607929i | \(0.792001\pi\) | |||||||
\(8\) | −7.36653 | −2.60446 | ||||||||
\(9\) | −1.35426 | −0.451419 | ||||||||
\(10\) | 2.92250 | 0.924176 | ||||||||
\(11\) | 2.82959 | 0.853153 | 0.426577 | − | 0.904451i | \(-0.359719\pi\) | ||||
0.426577 | + | 0.904451i | \(0.359719\pi\) | |||||||
\(12\) | 6.18425 | 1.78524 | ||||||||
\(13\) | 1.00728 | 0.279370 | 0.139685 | − | 0.990196i | \(-0.455391\pi\) | ||||
0.139685 | + | 0.990196i | \(0.455391\pi\) | |||||||
\(14\) | 10.9726 | 2.93254 | ||||||||
\(15\) | −1.43556 | −0.370661 | ||||||||
\(16\) | 9.59739 | 2.39935 | ||||||||
\(17\) | 1.46991 | 0.356505 | 0.178253 | − | 0.983985i | \(-0.442956\pi\) | ||||
0.178253 | + | 0.983985i | \(0.442956\pi\) | |||||||
\(18\) | 3.53683 | 0.833639 | ||||||||
\(19\) | −2.86394 | −0.657032 | −0.328516 | − | 0.944498i | \(-0.606549\pi\) | ||||
−0.328516 | + | 0.944498i | \(0.606549\pi\) | |||||||
\(20\) | −5.39446 | −1.20624 | ||||||||
\(21\) | −5.38984 | −1.17616 | ||||||||
\(22\) | −7.38986 | −1.57552 | ||||||||
\(23\) | −3.53074 | −0.736210 | −0.368105 | − | 0.929784i | \(-0.619993\pi\) | ||||
−0.368105 | + | 0.929784i | \(0.619993\pi\) | |||||||
\(24\) | −9.45026 | −1.92903 | ||||||||
\(25\) | −3.74777 | −0.749554 | ||||||||
\(26\) | −2.63066 | −0.515915 | ||||||||
\(27\) | −5.58592 | −1.07501 | ||||||||
\(28\) | −20.2535 | −3.82756 | ||||||||
\(29\) | −8.86395 | −1.64600 | −0.822998 | − | 0.568045i | \(-0.807700\pi\) | ||||
−0.822998 | + | 0.568045i | \(0.807700\pi\) | |||||||
\(30\) | 3.74917 | 0.684502 | ||||||||
\(31\) | −6.85343 | −1.23091 | −0.615457 | − | 0.788171i | \(-0.711028\pi\) | ||||
−0.615457 | + | 0.788171i | \(0.711028\pi\) | |||||||
\(32\) | −10.3319 | −1.82643 | ||||||||
\(33\) | 3.62998 | 0.631899 | ||||||||
\(34\) | −3.83887 | −0.658361 | ||||||||
\(35\) | 4.70150 | 0.794699 | ||||||||
\(36\) | −6.52841 | −1.08807 | ||||||||
\(37\) | −0.211479 | −0.0347670 | −0.0173835 | − | 0.999849i | \(-0.505534\pi\) | ||||
−0.0173835 | + | 0.999849i | \(0.505534\pi\) | |||||||
\(38\) | 7.47957 | 1.21335 | ||||||||
\(39\) | 1.29221 | 0.206919 | ||||||||
\(40\) | 8.24336 | 1.30339 | ||||||||
\(41\) | −7.52978 | −1.17595 | −0.587977 | − | 0.808878i | \(-0.700075\pi\) | ||||
−0.587977 | + | 0.808878i | \(0.700075\pi\) | |||||||
\(42\) | 14.0763 | 2.17202 | ||||||||
\(43\) | 11.1911 | 1.70663 | 0.853316 | − | 0.521394i | \(-0.174588\pi\) | ||||
0.853316 | + | 0.521394i | \(0.174588\pi\) | |||||||
\(44\) | 13.6405 | 2.05638 | ||||||||
\(45\) | 1.51546 | 0.225911 | ||||||||
\(46\) | 9.22102 | 1.35957 | ||||||||
\(47\) | −1.60481 | −0.234085 | −0.117043 | − | 0.993127i | \(-0.537341\pi\) | ||||
−0.117043 | + | 0.993127i | \(0.537341\pi\) | |||||||
\(48\) | 12.3122 | 1.77711 | ||||||||
\(49\) | 10.6518 | 1.52169 | ||||||||
\(50\) | 9.78782 | 1.38421 | ||||||||
\(51\) | 1.88569 | 0.264050 | ||||||||
\(52\) | 4.85577 | 0.673374 | ||||||||
\(53\) | −3.94279 | −0.541584 | −0.270792 | − | 0.962638i | \(-0.587286\pi\) | ||||
−0.270792 | + | 0.962638i | \(0.587286\pi\) | |||||||
\(54\) | 14.5884 | 1.98523 | ||||||||
\(55\) | −3.16640 | −0.426957 | ||||||||
\(56\) | 30.9498 | 4.13584 | ||||||||
\(57\) | −3.67404 | −0.486639 | ||||||||
\(58\) | 23.1494 | 3.03967 | ||||||||
\(59\) | 10.0715 | 1.31120 | 0.655599 | − | 0.755110i | \(-0.272416\pi\) | ||||
0.655599 | + | 0.755110i | \(0.272416\pi\) | |||||||
\(60\) | −6.92036 | −0.893414 | ||||||||
\(61\) | −4.38955 | −0.562024 | −0.281012 | − | 0.959704i | \(-0.590670\pi\) | ||||
−0.281012 | + | 0.959704i | \(0.590670\pi\) | |||||||
\(62\) | 17.8987 | 2.27314 | ||||||||
\(63\) | 5.68979 | 0.716846 | ||||||||
\(64\) | 7.78830 | 0.973537 | ||||||||
\(65\) | −1.12718 | −0.139810 | ||||||||
\(66\) | −9.48020 | −1.16693 | ||||||||
\(67\) | 3.36813 | 0.411483 | 0.205742 | − | 0.978606i | \(-0.434039\pi\) | ||||
0.205742 | + | 0.978606i | \(0.434039\pi\) | |||||||
\(68\) | 7.08592 | 0.859294 | ||||||||
\(69\) | −4.52946 | −0.545283 | ||||||||
\(70\) | −12.2786 | −1.46758 | ||||||||
\(71\) | 1.50833 | 0.179005 | 0.0895027 | − | 0.995987i | \(-0.471472\pi\) | ||||
0.0895027 | + | 0.995987i | \(0.471472\pi\) | |||||||
\(72\) | 9.97618 | 1.17570 | ||||||||
\(73\) | 6.72037 | 0.786559 | 0.393280 | − | 0.919419i | \(-0.371340\pi\) | ||||
0.393280 | + | 0.919419i | \(0.371340\pi\) | |||||||
\(74\) | 0.552308 | 0.0642045 | ||||||||
\(75\) | −4.80788 | −0.555167 | ||||||||
\(76\) | −13.8060 | −1.58366 | ||||||||
\(77\) | −11.8883 | −1.35479 | ||||||||
\(78\) | −3.37478 | −0.382119 | ||||||||
\(79\) | −3.72519 | −0.419116 | −0.209558 | − | 0.977796i | \(-0.567203\pi\) | ||||
−0.209558 | + | 0.977796i | \(0.567203\pi\) | |||||||
\(80\) | −10.7398 | −1.20074 | ||||||||
\(81\) | −3.10321 | −0.344801 | ||||||||
\(82\) | 19.6651 | 2.17164 | ||||||||
\(83\) | 1.48778 | 0.163305 | 0.0816526 | − | 0.996661i | \(-0.473980\pi\) | ||||
0.0816526 | + | 0.996661i | \(0.473980\pi\) | |||||||
\(84\) | −25.9825 | −2.83493 | ||||||||
\(85\) | −1.64487 | −0.178411 | ||||||||
\(86\) | −29.2272 | −3.15165 | ||||||||
\(87\) | −11.3713 | −1.21913 | ||||||||
\(88\) | −20.8442 | −2.22200 | ||||||||
\(89\) | 1.53772 | 0.162998 | 0.0814991 | − | 0.996673i | \(-0.474029\pi\) | ||||
0.0814991 | + | 0.996673i | \(0.474029\pi\) | |||||||
\(90\) | −3.95782 | −0.417191 | ||||||||
\(91\) | −4.23201 | −0.443635 | ||||||||
\(92\) | −17.0205 | −1.77451 | ||||||||
\(93\) | −8.79203 | −0.911691 | ||||||||
\(94\) | 4.19118 | 0.432287 | ||||||||
\(95\) | 3.20483 | 0.328809 | ||||||||
\(96\) | −13.2544 | −1.35277 | ||||||||
\(97\) | 1.89782 | 0.192694 | 0.0963470 | − | 0.995348i | \(-0.469284\pi\) | ||||
0.0963470 | + | 0.995348i | \(0.469284\pi\) | |||||||
\(98\) | −27.8187 | −2.81012 | ||||||||
\(99\) | −3.83200 | −0.385130 | ||||||||
\(100\) | −18.0667 | −1.80667 | ||||||||
\(101\) | 15.2431 | 1.51675 | 0.758373 | − | 0.651820i | \(-0.225994\pi\) | ||||
0.758373 | + | 0.651820i | \(0.225994\pi\) | |||||||
\(102\) | −4.92475 | −0.487623 | ||||||||
\(103\) | −18.8386 | −1.85622 | −0.928109 | − | 0.372309i | \(-0.878566\pi\) | ||||
−0.928109 | + | 0.372309i | \(0.878566\pi\) | |||||||
\(104\) | −7.42019 | −0.727609 | ||||||||
\(105\) | 6.03139 | 0.588603 | ||||||||
\(106\) | 10.2971 | 1.00015 | ||||||||
\(107\) | −6.64813 | −0.642699 | −0.321349 | − | 0.946961i | \(-0.604136\pi\) | ||||
−0.321349 | + | 0.946961i | \(0.604136\pi\) | |||||||
\(108\) | −26.9278 | −2.59113 | ||||||||
\(109\) | 6.57837 | 0.630093 | 0.315047 | − | 0.949076i | \(-0.397980\pi\) | ||||
0.315047 | + | 0.949076i | \(0.397980\pi\) | |||||||
\(110\) | 8.26948 | 0.788464 | ||||||||
\(111\) | −0.271300 | −0.0257506 | ||||||||
\(112\) | −40.3226 | −3.81012 | ||||||||
\(113\) | 15.7650 | 1.48304 | 0.741522 | − | 0.670928i | \(-0.234104\pi\) | ||||
0.741522 | + | 0.670928i | \(0.234104\pi\) | |||||||
\(114\) | 9.59527 | 0.898679 | ||||||||
\(115\) | 3.95101 | 0.368433 | ||||||||
\(116\) | −42.7301 | −3.96739 | ||||||||
\(117\) | −1.36412 | −0.126113 | ||||||||
\(118\) | −26.3031 | −2.42140 | ||||||||
\(119\) | −6.17569 | −0.566124 | ||||||||
\(120\) | 10.5751 | 0.965372 | ||||||||
\(121\) | −2.99342 | −0.272129 | ||||||||
\(122\) | 11.4639 | 1.03789 | ||||||||
\(123\) | −9.65969 | −0.870985 | ||||||||
\(124\) | −33.0380 | −2.96690 | ||||||||
\(125\) | 9.78902 | 0.875556 | ||||||||
\(126\) | −14.8597 | −1.32381 | ||||||||
\(127\) | 2.41873 | 0.214628 | 0.107314 | − | 0.994225i | \(-0.465775\pi\) | ||||
0.107314 | + | 0.994225i | \(0.465775\pi\) | |||||||
\(128\) | 0.323503 | 0.0285939 | ||||||||
\(129\) | 14.3567 | 1.26404 | ||||||||
\(130\) | 2.94379 | 0.258187 | ||||||||
\(131\) | −7.04690 | −0.615690 | −0.307845 | − | 0.951436i | \(-0.599608\pi\) | ||||
−0.307845 | + | 0.951436i | \(0.599608\pi\) | |||||||
\(132\) | 17.4989 | 1.52308 | ||||||||
\(133\) | 12.0326 | 1.04336 | ||||||||
\(134\) | −8.79635 | −0.759889 | ||||||||
\(135\) | 6.25082 | 0.537985 | ||||||||
\(136\) | −10.8281 | −0.928504 | ||||||||
\(137\) | −0.657384 | −0.0561641 | −0.0280821 | − | 0.999606i | \(-0.508940\pi\) | ||||
−0.0280821 | + | 0.999606i | \(0.508940\pi\) | |||||||
\(138\) | 11.8293 | 1.00698 | ||||||||
\(139\) | −9.85669 | −0.836033 | −0.418017 | − | 0.908439i | \(-0.637275\pi\) | ||||
−0.418017 | + | 0.908439i | \(0.637275\pi\) | |||||||
\(140\) | 22.6643 | 1.91548 | ||||||||
\(141\) | −2.05875 | −0.173378 | ||||||||
\(142\) | −3.93920 | −0.330571 | ||||||||
\(143\) | 2.85020 | 0.238346 | ||||||||
\(144\) | −12.9973 | −1.08311 | ||||||||
\(145\) | 9.91903 | 0.823731 | ||||||||
\(146\) | −17.5512 | −1.45254 | ||||||||
\(147\) | 13.6649 | 1.12706 | ||||||||
\(148\) | −1.01947 | −0.0837998 | ||||||||
\(149\) | 11.4641 | 0.939176 | 0.469588 | − | 0.882886i | \(-0.344402\pi\) | ||||
0.469588 | + | 0.882886i | \(0.344402\pi\) | |||||||
\(150\) | 12.5565 | 1.02523 | ||||||||
\(151\) | 6.56656 | 0.534379 | 0.267190 | − | 0.963644i | \(-0.413905\pi\) | ||||
0.267190 | + | 0.963644i | \(0.413905\pi\) | |||||||
\(152\) | 21.0973 | 1.71121 | ||||||||
\(153\) | −1.99064 | −0.160933 | ||||||||
\(154\) | 31.0478 | 2.50191 | ||||||||
\(155\) | 7.66920 | 0.616005 | ||||||||
\(156\) | 6.22929 | 0.498743 | ||||||||
\(157\) | −6.42856 | −0.513055 | −0.256527 | − | 0.966537i | \(-0.582578\pi\) | ||||
−0.256527 | + | 0.966537i | \(0.582578\pi\) | |||||||
\(158\) | 9.72884 | 0.773985 | ||||||||
\(159\) | −5.05807 | −0.401131 | ||||||||
\(160\) | 11.5617 | 0.914030 | ||||||||
\(161\) | 14.8341 | 1.16909 | ||||||||
\(162\) | 8.10446 | 0.636747 | ||||||||
\(163\) | −10.0848 | −0.789902 | −0.394951 | − | 0.918702i | \(-0.629238\pi\) | ||||
−0.394951 | + | 0.918702i | \(0.629238\pi\) | |||||||
\(164\) | −36.2985 | −2.83443 | ||||||||
\(165\) | −4.06206 | −0.316231 | ||||||||
\(166\) | −3.88555 | −0.301577 | ||||||||
\(167\) | 0.938901 | 0.0726543 | 0.0363272 | − | 0.999340i | \(-0.488434\pi\) | ||||
0.0363272 | + | 0.999340i | \(0.488434\pi\) | |||||||
\(168\) | 39.7044 | 3.06326 | ||||||||
\(169\) | −11.9854 | −0.921952 | ||||||||
\(170\) | 4.29581 | 0.329474 | ||||||||
\(171\) | 3.87851 | 0.296597 | ||||||||
\(172\) | 53.9486 | 4.11354 | ||||||||
\(173\) | −13.4312 | −1.02115 | −0.510577 | − | 0.859832i | \(-0.670568\pi\) | ||||
−0.510577 | + | 0.859832i | \(0.670568\pi\) | |||||||
\(174\) | 29.6976 | 2.25137 | ||||||||
\(175\) | 15.7459 | 1.19028 | ||||||||
\(176\) | 27.1567 | 2.04701 | ||||||||
\(177\) | 12.9204 | 0.971154 | ||||||||
\(178\) | −4.01597 | −0.301010 | ||||||||
\(179\) | 24.9757 | 1.86677 | 0.933385 | − | 0.358878i | \(-0.116840\pi\) | ||||
0.933385 | + | 0.358878i | \(0.116840\pi\) | |||||||
\(180\) | 7.30549 | 0.544519 | ||||||||
\(181\) | −16.7609 | −1.24583 | −0.622915 | − | 0.782290i | \(-0.714052\pi\) | ||||
−0.622915 | + | 0.782290i | \(0.714052\pi\) | |||||||
\(182\) | 11.0525 | 0.819265 | ||||||||
\(183\) | −5.63119 | −0.416270 | ||||||||
\(184\) | 26.0093 | 1.91743 | ||||||||
\(185\) | 0.236652 | 0.0173990 | ||||||||
\(186\) | 22.9616 | 1.68363 | ||||||||
\(187\) | 4.15924 | 0.304154 | ||||||||
\(188\) | −7.73622 | −0.564222 | ||||||||
\(189\) | 23.4687 | 1.70710 | ||||||||
\(190\) | −8.36986 | −0.607213 | ||||||||
\(191\) | 2.48542 | 0.179839 | 0.0899193 | − | 0.995949i | \(-0.471339\pi\) | ||||
0.0899193 | + | 0.995949i | \(0.471339\pi\) | |||||||
\(192\) | 9.99133 | 0.721062 | ||||||||
\(193\) | −0.139371 | −0.0100322 | −0.00501609 | − | 0.999987i | \(-0.501597\pi\) | ||||
−0.00501609 | + | 0.999987i | \(0.501597\pi\) | |||||||
\(194\) | −4.95641 | −0.355849 | ||||||||
\(195\) | −1.44602 | −0.103552 | ||||||||
\(196\) | 51.3488 | 3.66777 | ||||||||
\(197\) | −3.99492 | −0.284627 | −0.142313 | − | 0.989822i | \(-0.545454\pi\) | ||||
−0.142313 | + | 0.989822i | \(0.545454\pi\) | |||||||
\(198\) | 10.0078 | 0.711222 | ||||||||
\(199\) | −25.1577 | −1.78339 | −0.891693 | − | 0.452641i | \(-0.850482\pi\) | ||||
−0.891693 | + | 0.452641i | \(0.850482\pi\) | |||||||
\(200\) | 27.6081 | 1.95218 | ||||||||
\(201\) | 4.32086 | 0.304770 | ||||||||
\(202\) | −39.8095 | −2.80099 | ||||||||
\(203\) | 37.2411 | 2.61381 | ||||||||
\(204\) | 9.09028 | 0.636447 | ||||||||
\(205\) | 8.42605 | 0.588501 | ||||||||
\(206\) | 49.1995 | 3.42789 | ||||||||
\(207\) | 4.78154 | 0.332340 | ||||||||
\(208\) | 9.66730 | 0.670307 | ||||||||
\(209\) | −8.10377 | −0.560549 | ||||||||
\(210\) | −15.7518 | −1.08698 | ||||||||
\(211\) | −24.6337 | −1.69586 | −0.847928 | − | 0.530112i | \(-0.822150\pi\) | ||||
−0.847928 | + | 0.530112i | \(0.822150\pi\) | |||||||
\(212\) | −19.0068 | −1.30539 | ||||||||
\(213\) | 1.93498 | 0.132583 | ||||||||
\(214\) | 17.3625 | 1.18688 | ||||||||
\(215\) | −12.5232 | −0.854077 | ||||||||
\(216\) | 41.1489 | 2.79982 | ||||||||
\(217\) | 28.7941 | 1.95467 | ||||||||
\(218\) | −17.1803 | −1.16360 | ||||||||
\(219\) | 8.62132 | 0.582575 | ||||||||
\(220\) | −15.2641 | −1.02911 | ||||||||
\(221\) | 1.48062 | 0.0995970 | ||||||||
\(222\) | 0.708536 | 0.0475538 | ||||||||
\(223\) | −8.80877 | −0.589879 | −0.294940 | − | 0.955516i | \(-0.595300\pi\) | ||||
−0.294940 | + | 0.955516i | \(0.595300\pi\) | |||||||
\(224\) | 43.4084 | 2.90034 | ||||||||
\(225\) | 5.07545 | 0.338363 | ||||||||
\(226\) | −41.1724 | −2.73875 | ||||||||
\(227\) | −7.88235 | −0.523170 | −0.261585 | − | 0.965180i | \(-0.584245\pi\) | ||||
−0.261585 | + | 0.965180i | \(0.584245\pi\) | |||||||
\(228\) | −17.7113 | −1.17296 | ||||||||
\(229\) | 25.1134 | 1.65954 | 0.829769 | − | 0.558106i | \(-0.188472\pi\) | ||||
0.829769 | + | 0.558106i | \(0.188472\pi\) | |||||||
\(230\) | −10.3186 | −0.680388 | ||||||||
\(231\) | −15.2510 | −1.00344 | ||||||||
\(232\) | 65.2965 | 4.28693 | ||||||||
\(233\) | 10.2776 | 0.673309 | 0.336654 | − | 0.941628i | \(-0.390705\pi\) | ||||
0.336654 | + | 0.941628i | \(0.390705\pi\) | |||||||
\(234\) | 3.56260 | 0.232894 | ||||||||
\(235\) | 1.79583 | 0.117147 | ||||||||
\(236\) | 48.5512 | 3.16041 | ||||||||
\(237\) | −4.77891 | −0.310423 | ||||||||
\(238\) | 16.1287 | 1.04547 | ||||||||
\(239\) | −10.4434 | −0.675525 | −0.337763 | − | 0.941231i | \(-0.609670\pi\) | ||||
−0.337763 | + | 0.941231i | \(0.609670\pi\) | |||||||
\(240\) | −13.7777 | −0.889345 | ||||||||
\(241\) | −5.73788 | −0.369609 | −0.184805 | − | 0.982775i | \(-0.559165\pi\) | ||||
−0.184805 | + | 0.982775i | \(0.559165\pi\) | |||||||
\(242\) | 7.81773 | 0.502543 | ||||||||
\(243\) | 12.7768 | 0.819630 | ||||||||
\(244\) | −21.1605 | −1.35466 | ||||||||
\(245\) | −11.9197 | −0.761523 | ||||||||
\(246\) | 25.2276 | 1.60845 | ||||||||
\(247\) | −2.88480 | −0.183555 | ||||||||
\(248\) | 50.4860 | 3.20586 | ||||||||
\(249\) | 1.90862 | 0.120954 | ||||||||
\(250\) | −25.5654 | −1.61690 | ||||||||
\(251\) | −15.0816 | −0.951940 | −0.475970 | − | 0.879461i | \(-0.657903\pi\) | ||||
−0.475970 | + | 0.879461i | \(0.657903\pi\) | |||||||
\(252\) | 27.4285 | 1.72783 | ||||||||
\(253\) | −9.99055 | −0.628101 | ||||||||
\(254\) | −6.31686 | −0.396355 | ||||||||
\(255\) | −2.11015 | −0.132143 | ||||||||
\(256\) | −16.4215 | −1.02634 | ||||||||
\(257\) | −11.3195 | −0.706094 | −0.353047 | − | 0.935606i | \(-0.614854\pi\) | ||||
−0.353047 | + | 0.935606i | \(0.614854\pi\) | |||||||
\(258\) | −37.4945 | −2.33431 | ||||||||
\(259\) | 0.888511 | 0.0552094 | ||||||||
\(260\) | −5.43375 | −0.336987 | ||||||||
\(261\) | 12.0041 | 0.743034 | ||||||||
\(262\) | 18.4039 | 1.13700 | ||||||||
\(263\) | 30.9532 | 1.90865 | 0.954327 | − | 0.298764i | \(-0.0965743\pi\) | ||||
0.954327 | + | 0.298764i | \(0.0965743\pi\) | |||||||
\(264\) | −26.7403 | −1.64575 | ||||||||
\(265\) | 4.41210 | 0.271033 | ||||||||
\(266\) | −31.4247 | −1.92677 | ||||||||
\(267\) | 1.97269 | 0.120727 | ||||||||
\(268\) | 16.2366 | 0.991809 | ||||||||
\(269\) | 0.638812 | 0.0389490 | 0.0194745 | − | 0.999810i | \(-0.493801\pi\) | ||||
0.0194745 | + | 0.999810i | \(0.493801\pi\) | |||||||
\(270\) | −16.3249 | −0.993500 | ||||||||
\(271\) | 16.3560 | 0.993554 | 0.496777 | − | 0.867878i | \(-0.334517\pi\) | ||||
0.496777 | + | 0.867878i | \(0.334517\pi\) | |||||||
\(272\) | 14.1073 | 0.855380 | ||||||||
\(273\) | −5.42910 | −0.328584 | ||||||||
\(274\) | 1.71685 | 0.103719 | ||||||||
\(275\) | −10.6047 | −0.639485 | ||||||||
\(276\) | −21.8350 | −1.31431 | ||||||||
\(277\) | −9.64324 | −0.579406 | −0.289703 | − | 0.957117i | \(-0.593557\pi\) | ||||
−0.289703 | + | 0.957117i | \(0.593557\pi\) | |||||||
\(278\) | 25.7421 | 1.54391 | ||||||||
\(279\) | 9.28132 | 0.555658 | ||||||||
\(280\) | −34.6337 | −2.06976 | ||||||||
\(281\) | 18.2904 | 1.09111 | 0.545557 | − | 0.838074i | \(-0.316318\pi\) | ||||
0.545557 | + | 0.838074i | \(0.316318\pi\) | |||||||
\(282\) | 5.37671 | 0.320179 | ||||||||
\(283\) | 27.8422 | 1.65505 | 0.827524 | − | 0.561431i | \(-0.189749\pi\) | ||||
0.827524 | + | 0.561431i | \(0.189749\pi\) | |||||||
\(284\) | 7.27112 | 0.431462 | ||||||||
\(285\) | 4.11136 | 0.243536 | ||||||||
\(286\) | −7.44369 | −0.440155 | ||||||||
\(287\) | 31.6357 | 1.86740 | ||||||||
\(288\) | 13.9920 | 0.824487 | ||||||||
\(289\) | −14.8394 | −0.872904 | ||||||||
\(290\) | −25.9049 | −1.52119 | ||||||||
\(291\) | 2.43464 | 0.142721 | ||||||||
\(292\) | 32.3966 | 1.89586 | ||||||||
\(293\) | −7.24125 | −0.423038 | −0.211519 | − | 0.977374i | \(-0.567841\pi\) | ||||
−0.211519 | + | 0.977374i | \(0.567841\pi\) | |||||||
\(294\) | −35.6877 | −2.08135 | ||||||||
\(295\) | −11.2703 | −0.656183 | ||||||||
\(296\) | 1.55787 | 0.0905493 | ||||||||
\(297\) | −15.8059 | −0.917150 | ||||||||
\(298\) | −29.9401 | −1.73438 | ||||||||
\(299\) | −3.55646 | −0.205675 | ||||||||
\(300\) | −23.1771 | −1.33813 | ||||||||
\(301\) | −47.0185 | −2.71010 | ||||||||
\(302\) | −17.1495 | −0.986842 | ||||||||
\(303\) | 19.5549 | 1.12340 | ||||||||
\(304\) | −27.4863 | −1.57645 | ||||||||
\(305\) | 4.91203 | 0.281262 | ||||||||
\(306\) | 5.19882 | 0.297197 | ||||||||
\(307\) | 32.2779 | 1.84219 | 0.921097 | − | 0.389333i | \(-0.127294\pi\) | ||||
0.921097 | + | 0.389333i | \(0.127294\pi\) | |||||||
\(308\) | −57.3092 | −3.26549 | ||||||||
\(309\) | −24.1673 | −1.37483 | ||||||||
\(310\) | −20.0292 | −1.13758 | ||||||||
\(311\) | 14.1352 | 0.801535 | 0.400768 | − | 0.916180i | \(-0.368744\pi\) | ||||
0.400768 | + | 0.916180i | \(0.368744\pi\) | |||||||
\(312\) | −9.51909 | −0.538913 | ||||||||
\(313\) | 30.3998 | 1.71830 | 0.859148 | − | 0.511727i | \(-0.170994\pi\) | ||||
0.859148 | + | 0.511727i | \(0.170994\pi\) | |||||||
\(314\) | 16.7891 | 0.947462 | ||||||||
\(315\) | −6.36705 | −0.358742 | ||||||||
\(316\) | −17.9578 | −1.01021 | ||||||||
\(317\) | 21.3456 | 1.19889 | 0.599443 | − | 0.800417i | \(-0.295389\pi\) | ||||
0.599443 | + | 0.800417i | \(0.295389\pi\) | |||||||
\(318\) | 13.2098 | 0.740771 | ||||||||
\(319\) | −25.0814 | −1.40429 | ||||||||
\(320\) | −8.71534 | −0.487202 | ||||||||
\(321\) | −8.52864 | −0.476023 | ||||||||
\(322\) | −38.7413 | −2.15897 | ||||||||
\(323\) | −4.20973 | −0.234235 | ||||||||
\(324\) | −14.9595 | −0.831083 | ||||||||
\(325\) | −3.77507 | −0.209403 | ||||||||
\(326\) | 26.3378 | 1.45872 | ||||||||
\(327\) | 8.43915 | 0.466686 | ||||||||
\(328\) | 55.4683 | 3.06273 | ||||||||
\(329\) | 6.74245 | 0.371723 | ||||||||
\(330\) | 10.6086 | 0.583986 | ||||||||
\(331\) | −7.22501 | −0.397122 | −0.198561 | − | 0.980088i | \(-0.563627\pi\) | ||||
−0.198561 | + | 0.980088i | \(0.563627\pi\) | |||||||
\(332\) | 7.17208 | 0.393619 | ||||||||
\(333\) | 0.286398 | 0.0156945 | ||||||||
\(334\) | −2.45207 | −0.134171 | ||||||||
\(335\) | −3.76904 | −0.205925 | ||||||||
\(336\) | −51.7284 | −2.82201 | ||||||||
\(337\) | −22.4614 | −1.22355 | −0.611774 | − | 0.791032i | \(-0.709544\pi\) | ||||
−0.611774 | + | 0.791032i | \(0.709544\pi\) | |||||||
\(338\) | 31.3015 | 1.70258 | ||||||||
\(339\) | 20.2243 | 1.09844 | ||||||||
\(340\) | −7.92936 | −0.430030 | ||||||||
\(341\) | −19.3924 | −1.05016 | ||||||||
\(342\) | −10.1293 | −0.547728 | ||||||||
\(343\) | −15.3428 | −0.828435 | ||||||||
\(344\) | −82.4398 | −4.44486 | ||||||||
\(345\) | 5.06861 | 0.272885 | ||||||||
\(346\) | 35.0774 | 1.88577 | ||||||||
\(347\) | 14.7021 | 0.789249 | 0.394624 | − | 0.918843i | \(-0.370875\pi\) | ||||
0.394624 | + | 0.918843i | \(0.370875\pi\) | |||||||
\(348\) | −54.8169 | −2.93849 | ||||||||
\(349\) | −2.83163 | −0.151574 | −0.0757868 | − | 0.997124i | \(-0.524147\pi\) | ||||
−0.0757868 | + | 0.997124i | \(0.524147\pi\) | |||||||
\(350\) | −41.1226 | −2.19810 | ||||||||
\(351\) | −5.62661 | −0.300326 | ||||||||
\(352\) | −29.2349 | −1.55823 | ||||||||
\(353\) | 4.40691 | 0.234556 | 0.117278 | − | 0.993099i | \(-0.462583\pi\) | ||||
0.117278 | + | 0.993099i | \(0.462583\pi\) | |||||||
\(354\) | −33.7433 | −1.79344 | ||||||||
\(355\) | −1.68786 | −0.0895825 | ||||||||
\(356\) | 7.41282 | 0.392879 | ||||||||
\(357\) | −7.92257 | −0.419307 | ||||||||
\(358\) | −65.2274 | −3.44738 | ||||||||
\(359\) | 34.1871 | 1.80433 | 0.902164 | − | 0.431394i | \(-0.141978\pi\) | ||||
0.902164 | + | 0.431394i | \(0.141978\pi\) | |||||||
\(360\) | −11.1636 | −0.588376 | ||||||||
\(361\) | −10.7979 | −0.568309 | ||||||||
\(362\) | 43.7735 | 2.30068 | ||||||||
\(363\) | −3.84015 | −0.201556 | ||||||||
\(364\) | −20.4011 | −1.06931 | ||||||||
\(365\) | −7.52029 | −0.393630 | ||||||||
\(366\) | 14.7066 | 0.768728 | ||||||||
\(367\) | −8.41005 | −0.439001 | −0.219500 | − | 0.975612i | \(-0.570443\pi\) | ||||
−0.219500 | + | 0.975612i | \(0.570443\pi\) | |||||||
\(368\) | −33.8859 | −1.76643 | ||||||||
\(369\) | 10.1973 | 0.530848 | ||||||||
\(370\) | −0.618049 | −0.0321308 | ||||||||
\(371\) | 16.5653 | 0.860026 | ||||||||
\(372\) | −42.3833 | −2.19747 | ||||||||
\(373\) | 32.2263 | 1.66861 | 0.834306 | − | 0.551301i | \(-0.185868\pi\) | ||||
0.834306 | + | 0.551301i | \(0.185868\pi\) | |||||||
\(374\) | −10.8624 | −0.561683 | ||||||||
\(375\) | 12.5580 | 0.648492 | ||||||||
\(376\) | 11.8219 | 0.609666 | ||||||||
\(377\) | −8.92852 | −0.459842 | ||||||||
\(378\) | −61.2919 | −3.15251 | ||||||||
\(379\) | −4.86791 | −0.250048 | −0.125024 | − | 0.992154i | \(-0.539901\pi\) | ||||
−0.125024 | + | 0.992154i | \(0.539901\pi\) | |||||||
\(380\) | 15.4494 | 0.792536 | ||||||||
\(381\) | 3.10291 | 0.158967 | ||||||||
\(382\) | −6.49101 | −0.332109 | ||||||||
\(383\) | −36.9345 | −1.88727 | −0.943633 | − | 0.330994i | \(-0.892616\pi\) | ||||
−0.943633 | + | 0.330994i | \(0.892616\pi\) | |||||||
\(384\) | 0.415010 | 0.0211784 | ||||||||
\(385\) | 13.3033 | 0.678000 | ||||||||
\(386\) | 0.363988 | 0.0185265 | ||||||||
\(387\) | −15.1557 | −0.770407 | ||||||||
\(388\) | 9.14871 | 0.464456 | ||||||||
\(389\) | 6.60571 | 0.334923 | 0.167461 | − | 0.985879i | \(-0.446443\pi\) | ||||
0.167461 | + | 0.985879i | \(0.446443\pi\) | |||||||
\(390\) | 3.77648 | 0.191230 | ||||||||
\(391\) | −5.18987 | −0.262463 | ||||||||
\(392\) | −78.4670 | −3.96318 | ||||||||
\(393\) | −9.04022 | −0.456019 | ||||||||
\(394\) | 10.4333 | 0.525622 | ||||||||
\(395\) | 4.16859 | 0.209745 | ||||||||
\(396\) | −18.4727 | −0.928289 | ||||||||
\(397\) | 5.10326 | 0.256125 | 0.128063 | − | 0.991766i | \(-0.459124\pi\) | ||||
0.128063 | + | 0.991766i | \(0.459124\pi\) | |||||||
\(398\) | 65.7029 | 3.29339 | ||||||||
\(399\) | 15.4362 | 0.772774 | ||||||||
\(400\) | −35.9688 | −1.79844 | ||||||||
\(401\) | 32.4967 | 1.62281 | 0.811403 | − | 0.584487i | \(-0.198704\pi\) | ||||
0.811403 | + | 0.584487i | \(0.198704\pi\) | |||||||
\(402\) | −11.2845 | −0.562821 | ||||||||
\(403\) | −6.90336 | −0.343881 | ||||||||
\(404\) | 73.4818 | 3.65586 | ||||||||
\(405\) | 3.47258 | 0.172554 | ||||||||
\(406\) | −97.2603 | −4.82695 | ||||||||
\(407\) | −0.598400 | −0.0296616 | ||||||||
\(408\) | −13.8910 | −0.687708 | ||||||||
\(409\) | −38.6499 | −1.91111 | −0.955557 | − | 0.294806i | \(-0.904745\pi\) | ||||
−0.955557 | + | 0.294806i | \(0.904745\pi\) | |||||||
\(410\) | −22.0058 | −1.08679 | ||||||||
\(411\) | −0.843335 | −0.0415986 | ||||||||
\(412\) | −90.8141 | −4.47409 | ||||||||
\(413\) | −42.3145 | −2.08216 | ||||||||
\(414\) | −12.4876 | −0.613734 | ||||||||
\(415\) | −1.66487 | −0.0817253 | ||||||||
\(416\) | −10.4071 | −0.510251 | ||||||||
\(417\) | −12.6448 | −0.619218 | ||||||||
\(418\) | 21.1641 | 1.03517 | ||||||||
\(419\) | 37.0314 | 1.80910 | 0.904550 | − | 0.426367i | \(-0.140207\pi\) | ||||
0.904550 | + | 0.426367i | \(0.140207\pi\) | |||||||
\(420\) | 29.0752 | 1.41873 | ||||||||
\(421\) | −22.1194 | −1.07803 | −0.539016 | − | 0.842295i | \(-0.681204\pi\) | ||||
−0.539016 | + | 0.842295i | \(0.681204\pi\) | |||||||
\(422\) | 64.3344 | 3.13175 | ||||||||
\(423\) | 2.17332 | 0.105671 | ||||||||
\(424\) | 29.0447 | 1.41053 | ||||||||
\(425\) | −5.50888 | −0.267220 | ||||||||
\(426\) | −5.05347 | −0.244841 | ||||||||
\(427\) | 18.4423 | 0.892484 | ||||||||
\(428\) | −32.0483 | −1.54911 | ||||||||
\(429\) | 3.65642 | 0.176534 | ||||||||
\(430\) | 32.7061 | 1.57723 | ||||||||
\(431\) | −2.65193 | −0.127739 | −0.0638695 | − | 0.997958i | \(-0.520344\pi\) | ||||
−0.0638695 | + | 0.997958i | \(0.520344\pi\) | |||||||
\(432\) | −53.6103 | −2.57933 | ||||||||
\(433\) | 31.9800 | 1.53686 | 0.768429 | − | 0.639935i | \(-0.221039\pi\) | ||||
0.768429 | + | 0.639935i | \(0.221039\pi\) | |||||||
\(434\) | −75.1997 | −3.60970 | ||||||||
\(435\) | 12.7248 | 0.610106 | ||||||||
\(436\) | 31.7120 | 1.51873 | ||||||||
\(437\) | 10.1118 | 0.483714 | ||||||||
\(438\) | −22.5158 | −1.07584 | ||||||||
\(439\) | −14.4634 | −0.690300 | −0.345150 | − | 0.938548i | \(-0.612172\pi\) | ||||
−0.345150 | + | 0.938548i | \(0.612172\pi\) | |||||||
\(440\) | 23.3253 | 1.11199 | ||||||||
\(441\) | −14.4253 | −0.686920 | ||||||||
\(442\) | −3.86683 | −0.183927 | ||||||||
\(443\) | 38.2162 | 1.81571 | 0.907854 | − | 0.419287i | \(-0.137720\pi\) | ||||
0.907854 | + | 0.419287i | \(0.137720\pi\) | |||||||
\(444\) | −1.30784 | −0.0620674 | ||||||||
\(445\) | −1.72076 | −0.0815717 | ||||||||
\(446\) | 23.0053 | 1.08933 | ||||||||
\(447\) | 14.7069 | 0.695612 | ||||||||
\(448\) | −32.7218 | −1.54596 | ||||||||
\(449\) | 16.4348 | 0.775606 | 0.387803 | − | 0.921742i | \(-0.373234\pi\) | ||||
0.387803 | + | 0.921742i | \(0.373234\pi\) | |||||||
\(450\) | −13.2552 | −0.624858 | ||||||||
\(451\) | −21.3062 | −1.00327 | ||||||||
\(452\) | 75.9975 | 3.57462 | ||||||||
\(453\) | 8.42401 | 0.395795 | ||||||||
\(454\) | 20.5858 | 0.966141 | ||||||||
\(455\) | 4.73575 | 0.222015 | ||||||||
\(456\) | 27.0649 | 1.26743 | ||||||||
\(457\) | 14.6850 | 0.686935 | 0.343468 | − | 0.939164i | \(-0.388398\pi\) | ||||
0.343468 | + | 0.939164i | \(0.388398\pi\) | |||||||
\(458\) | −65.5871 | −3.06468 | ||||||||
\(459\) | −8.21080 | −0.383247 | ||||||||
\(460\) | 19.0464 | 0.888044 | ||||||||
\(461\) | 15.3975 | 0.717131 | 0.358565 | − | 0.933505i | \(-0.383266\pi\) | ||||
0.358565 | + | 0.933505i | \(0.383266\pi\) | |||||||
\(462\) | 39.8302 | 1.85307 | ||||||||
\(463\) | 27.0492 | 1.25708 | 0.628540 | − | 0.777777i | \(-0.283653\pi\) | ||||
0.628540 | + | 0.777777i | \(0.283653\pi\) | |||||||
\(464\) | −85.0708 | −3.94931 | ||||||||
\(465\) | 9.83854 | 0.456252 | ||||||||
\(466\) | −26.8414 | −1.24340 | ||||||||
\(467\) | −6.17382 | −0.285690 | −0.142845 | − | 0.989745i | \(-0.545625\pi\) | ||||
−0.142845 | + | 0.989745i | \(0.545625\pi\) | |||||||
\(468\) | −6.57596 | −0.303974 | ||||||||
\(469\) | −14.1509 | −0.653428 | ||||||||
\(470\) | −4.69005 | −0.216336 | ||||||||
\(471\) | −8.24697 | −0.380000 | ||||||||
\(472\) | −74.1919 | −3.41496 | ||||||||
\(473\) | 31.6663 | 1.45602 | ||||||||
\(474\) | 12.4808 | 0.573261 | ||||||||
\(475\) | 10.7334 | 0.492481 | ||||||||
\(476\) | −29.7709 | −1.36454 | ||||||||
\(477\) | 5.33956 | 0.244481 | ||||||||
\(478\) | 27.2743 | 1.24750 | ||||||||
\(479\) | 15.1701 | 0.693139 | 0.346570 | − | 0.938024i | \(-0.387346\pi\) | ||||
0.346570 | + | 0.938024i | \(0.387346\pi\) | |||||||
\(480\) | 14.8320 | 0.676987 | ||||||||
\(481\) | −0.213020 | −0.00971287 | ||||||||
\(482\) | 14.9853 | 0.682560 | ||||||||
\(483\) | 19.0301 | 0.865901 | ||||||||
\(484\) | −14.4302 | −0.655920 | ||||||||
\(485\) | −2.12371 | −0.0964329 | ||||||||
\(486\) | −33.3683 | −1.51362 | ||||||||
\(487\) | −0.567945 | −0.0257360 | −0.0128680 | − | 0.999917i | \(-0.504096\pi\) | ||||
−0.0128680 | + | 0.999917i | \(0.504096\pi\) | |||||||
\(488\) | 32.3357 | 1.46377 | ||||||||
\(489\) | −12.9374 | −0.585051 | ||||||||
\(490\) | 31.1300 | 1.40631 | ||||||||
\(491\) | 9.34795 | 0.421867 | 0.210934 | − | 0.977500i | \(-0.432350\pi\) | ||||
0.210934 | + | 0.977500i | \(0.432350\pi\) | |||||||
\(492\) | −46.5660 | −2.09936 | ||||||||
\(493\) | −13.0292 | −0.586806 | ||||||||
\(494\) | 7.53405 | 0.338973 | ||||||||
\(495\) | 4.28812 | 0.192737 | ||||||||
\(496\) | −65.7751 | −2.95339 | ||||||||
\(497\) | −6.33710 | −0.284258 | ||||||||
\(498\) | −4.98463 | −0.223367 | ||||||||
\(499\) | −8.37644 | −0.374981 | −0.187490 | − | 0.982266i | \(-0.560035\pi\) | ||||
−0.187490 | + | 0.982266i | \(0.560035\pi\) | |||||||
\(500\) | 47.1895 | 2.11038 | ||||||||
\(501\) | 1.20448 | 0.0538123 | ||||||||
\(502\) | 39.3876 | 1.75795 | ||||||||
\(503\) | 0.0103533 | 0.000461631 0 | 0.000230816 | − | 1.00000i | \(-0.499927\pi\) | ||||
0.000230816 | 1.00000i | \(0.499927\pi\) | ||||||||
\(504\) | −41.9140 | −1.86700 | ||||||||
\(505\) | −17.0575 | −0.759049 | ||||||||
\(506\) | 26.0917 | 1.15992 | ||||||||
\(507\) | −15.3756 | −0.682855 | ||||||||
\(508\) | 11.6599 | 0.517323 | ||||||||
\(509\) | −28.5771 | −1.26666 | −0.633328 | − | 0.773883i | \(-0.718312\pi\) | ||||
−0.633328 | + | 0.773883i | \(0.718312\pi\) | |||||||
\(510\) | 5.51094 | 0.244029 | ||||||||
\(511\) | −28.2350 | −1.24904 | ||||||||
\(512\) | 42.2399 | 1.86676 | ||||||||
\(513\) | 15.9977 | 0.706317 | ||||||||
\(514\) | 29.5626 | 1.30395 | ||||||||
\(515\) | 21.0809 | 0.928936 | ||||||||
\(516\) | 69.2088 | 3.04675 | ||||||||
\(517\) | −4.54095 | −0.199711 | ||||||||
\(518\) | −2.32047 | −0.101956 | ||||||||
\(519\) | −17.2304 | −0.756330 | ||||||||
\(520\) | 8.30341 | 0.364129 | ||||||||
\(521\) | −5.41399 | −0.237191 | −0.118596 | − | 0.992943i | \(-0.537839\pi\) | ||||
−0.118596 | + | 0.992943i | \(0.537839\pi\) | |||||||
\(522\) | −31.3503 | −1.37217 | ||||||||
\(523\) | 26.9182 | 1.17705 | 0.588526 | − | 0.808479i | \(-0.299709\pi\) | ||||
0.588526 | + | 0.808479i | \(0.299709\pi\) | |||||||
\(524\) | −33.9707 | −1.48401 | ||||||||
\(525\) | 20.1999 | 0.881595 | ||||||||
\(526\) | −80.8385 | −3.52472 | ||||||||
\(527\) | −10.0739 | −0.438827 | ||||||||
\(528\) | 34.8383 | 1.51614 | ||||||||
\(529\) | −10.5339 | −0.457994 | ||||||||
\(530\) | −11.5228 | −0.500519 | ||||||||
\(531\) | −13.6394 | −0.591900 | ||||||||
\(532\) | 58.0048 | 2.51483 | ||||||||
\(533\) | −7.58463 | −0.328527 | ||||||||
\(534\) | −5.15195 | −0.222947 | ||||||||
\(535\) | 7.43945 | 0.321636 | ||||||||
\(536\) | −24.8114 | −1.07169 | ||||||||
\(537\) | 32.0404 | 1.38265 | ||||||||
\(538\) | −1.66834 | −0.0719274 | ||||||||
\(539\) | 30.1403 | 1.29824 | ||||||||
\(540\) | 30.1330 | 1.29672 | ||||||||
\(541\) | −30.3367 | −1.30428 | −0.652138 | − | 0.758100i | \(-0.726128\pi\) | ||||
−0.652138 | + | 0.758100i | \(0.726128\pi\) | |||||||
\(542\) | −42.7158 | −1.83480 | ||||||||
\(543\) | −21.5020 | −0.922739 | ||||||||
\(544\) | −15.1869 | −0.651133 | ||||||||
\(545\) | −7.36139 | −0.315327 | ||||||||
\(546\) | 14.1788 | 0.606798 | ||||||||
\(547\) | −0.317784 | −0.0135875 | −0.00679374 | − | 0.999977i | \(-0.502163\pi\) | ||||
−0.00679374 | + | 0.999977i | \(0.502163\pi\) | |||||||
\(548\) | −3.16902 | −0.135374 | ||||||||
\(549\) | 5.94458 | 0.253708 | ||||||||
\(550\) | 27.6955 | 1.18094 | ||||||||
\(551\) | 25.3858 | 1.08147 | ||||||||
\(552\) | 33.3664 | 1.42017 | ||||||||
\(553\) | 15.6510 | 0.665549 | ||||||||
\(554\) | 25.1847 | 1.06999 | ||||||||
\(555\) | 0.303592 | 0.0128868 | ||||||||
\(556\) | −47.5157 | −2.01511 | ||||||||
\(557\) | 20.1990 | 0.855859 | 0.427929 | − | 0.903812i | \(-0.359243\pi\) | ||||
0.427929 | + | 0.903812i | \(0.359243\pi\) | |||||||
\(558\) | −24.2395 | −1.02614 | ||||||||
\(559\) | 11.2727 | 0.476783 | ||||||||
\(560\) | 45.1222 | 1.90676 | ||||||||
\(561\) | 5.33574 | 0.225275 | ||||||||
\(562\) | −47.7679 | −2.01497 | ||||||||
\(563\) | 26.6162 | 1.12174 | 0.560870 | − | 0.827904i | \(-0.310467\pi\) | ||||
0.560870 | + | 0.827904i | \(0.310467\pi\) | |||||||
\(564\) | −9.92453 | −0.417898 | ||||||||
\(565\) | −17.6415 | −0.742183 | ||||||||
\(566\) | −72.7138 | −3.05639 | ||||||||
\(567\) | 13.0379 | 0.547538 | ||||||||
\(568\) | −11.1111 | −0.466213 | ||||||||
\(569\) | 15.3123 | 0.641924 | 0.320962 | − | 0.947092i | \(-0.395994\pi\) | ||||
0.320962 | + | 0.947092i | \(0.395994\pi\) | |||||||
\(570\) | −10.7374 | −0.449740 | ||||||||
\(571\) | 14.4782 | 0.605892 | 0.302946 | − | 0.953008i | \(-0.402030\pi\) | ||||
0.302946 | + | 0.953008i | \(0.402030\pi\) | |||||||
\(572\) | 13.7398 | 0.574491 | ||||||||
\(573\) | 3.18846 | 0.133200 | ||||||||
\(574\) | −82.6209 | −3.44853 | ||||||||
\(575\) | 13.2324 | 0.551830 | ||||||||
\(576\) | −10.5474 | −0.439474 | ||||||||
\(577\) | 40.6537 | 1.69244 | 0.846218 | − | 0.532836i | \(-0.178874\pi\) | ||||
0.846218 | + | 0.532836i | \(0.178874\pi\) | |||||||
\(578\) | 38.7551 | 1.61200 | ||||||||
\(579\) | −0.178795 | −0.00743045 | ||||||||
\(580\) | 47.8162 | 1.98546 | ||||||||
\(581\) | −6.25078 | −0.259326 | ||||||||
\(582\) | −6.35840 | −0.263564 | ||||||||
\(583\) | −11.1565 | −0.462054 | ||||||||
\(584\) | −49.5057 | −2.04856 | ||||||||
\(585\) | 1.52649 | 0.0631128 | ||||||||
\(586\) | 18.9115 | 0.781228 | ||||||||
\(587\) | 2.43061 | 0.100322 | 0.0501611 | − | 0.998741i | \(-0.484027\pi\) | ||||
0.0501611 | + | 0.998741i | \(0.484027\pi\) | |||||||
\(588\) | 65.8735 | 2.71658 | ||||||||
\(589\) | 19.6278 | 0.808750 | ||||||||
\(590\) | 29.4340 | 1.21178 | ||||||||
\(591\) | −5.12495 | −0.210812 | ||||||||
\(592\) | −2.02965 | −0.0834181 | ||||||||
\(593\) | 23.2360 | 0.954188 | 0.477094 | − | 0.878852i | \(-0.341690\pi\) | ||||
0.477094 | + | 0.878852i | \(0.341690\pi\) | |||||||
\(594\) | 41.2792 | 1.69371 | ||||||||
\(595\) | 6.91078 | 0.283314 | ||||||||
\(596\) | 55.2645 | 2.26372 | ||||||||
\(597\) | −32.2740 | −1.32089 | ||||||||
\(598\) | 9.28819 | 0.379822 | ||||||||
\(599\) | 17.2938 | 0.706605 | 0.353302 | − | 0.935509i | \(-0.385059\pi\) | ||||
0.353302 | + | 0.935509i | \(0.385059\pi\) | |||||||
\(600\) | 35.4174 | 1.44591 | ||||||||
\(601\) | −14.5658 | −0.594151 | −0.297076 | − | 0.954854i | \(-0.596011\pi\) | ||||
−0.297076 | + | 0.954854i | \(0.596011\pi\) | |||||||
\(602\) | 122.795 | 5.00477 | ||||||||
\(603\) | −4.56132 | −0.185751 | ||||||||
\(604\) | 31.6551 | 1.28803 | ||||||||
\(605\) | 3.34973 | 0.136186 | ||||||||
\(606\) | −51.0702 | −2.07459 | ||||||||
\(607\) | 37.2638 | 1.51249 | 0.756246 | − | 0.654288i | \(-0.227031\pi\) | ||||
0.756246 | + | 0.654288i | \(0.227031\pi\) | |||||||
\(608\) | 29.5898 | 1.20002 | ||||||||
\(609\) | 47.7753 | 1.93595 | ||||||||
\(610\) | −12.8285 | −0.519409 | ||||||||
\(611\) | −1.61650 | −0.0653965 | ||||||||
\(612\) | −9.59617 | −0.387902 | ||||||||
\(613\) | 21.9268 | 0.885614 | 0.442807 | − | 0.896617i | \(-0.353983\pi\) | ||||
0.442807 | + | 0.896617i | \(0.353983\pi\) | |||||||
\(614\) | −84.2981 | −3.40199 | ||||||||
\(615\) | 10.8095 | 0.435880 | ||||||||
\(616\) | 87.5752 | 3.52850 | ||||||||
\(617\) | −26.1001 | −1.05075 | −0.525374 | − | 0.850871i | \(-0.676075\pi\) | ||||
−0.525374 | + | 0.850871i | \(0.676075\pi\) | |||||||
\(618\) | 63.1163 | 2.53891 | ||||||||
\(619\) | −2.43384 | −0.0978243 | −0.0489121 | − | 0.998803i | \(-0.515575\pi\) | ||||
−0.0489121 | + | 0.998803i | \(0.515575\pi\) | |||||||
\(620\) | 36.9706 | 1.48477 | ||||||||
\(621\) | 19.7225 | 0.791435 | ||||||||
\(622\) | −36.9161 | −1.48020 | ||||||||
\(623\) | −6.46059 | −0.258838 | ||||||||
\(624\) | 12.4018 | 0.496471 | ||||||||
\(625\) | 7.78465 | 0.311386 | ||||||||
\(626\) | −79.3932 | −3.17319 | ||||||||
\(627\) | −10.3960 | −0.415178 | ||||||||
\(628\) | −30.9898 | −1.23663 | ||||||||
\(629\) | −0.310856 | −0.0123946 | ||||||||
\(630\) | 16.6284 | 0.662492 | ||||||||
\(631\) | 2.18041 | 0.0868006 | 0.0434003 | − | 0.999058i | \(-0.486181\pi\) | ||||
0.0434003 | + | 0.999058i | \(0.486181\pi\) | |||||||
\(632\) | 27.4417 | 1.09157 | ||||||||
\(633\) | −31.6017 | −1.25606 | ||||||||
\(634\) | −55.7469 | −2.21399 | ||||||||
\(635\) | −2.70664 | −0.107410 | ||||||||
\(636\) | −24.3832 | −0.966856 | ||||||||
\(637\) | 10.7294 | 0.425115 | ||||||||
\(638\) | 65.5034 | 2.59331 | ||||||||
\(639\) | −2.04266 | −0.0808066 | ||||||||
\(640\) | −0.362009 | −0.0143097 | ||||||||
\(641\) | −36.1860 | −1.42926 | −0.714631 | − | 0.699502i | \(-0.753405\pi\) | ||||
−0.714631 | + | 0.699502i | \(0.753405\pi\) | |||||||
\(642\) | 22.2737 | 0.879074 | ||||||||
\(643\) | −13.1340 | −0.517954 | −0.258977 | − | 0.965884i | \(-0.583385\pi\) | ||||
−0.258977 | + | 0.965884i | \(0.583385\pi\) | |||||||
\(644\) | 71.5100 | 2.81789 | ||||||||
\(645\) | −16.0656 | −0.632582 | ||||||||
\(646\) | 10.9943 | 0.432564 | ||||||||
\(647\) | 24.8577 | 0.977256 | 0.488628 | − | 0.872492i | \(-0.337497\pi\) | ||||
0.488628 | + | 0.872492i | \(0.337497\pi\) | |||||||
\(648\) | 22.8599 | 0.898021 | ||||||||
\(649\) | 28.4982 | 1.11865 | ||||||||
\(650\) | 9.85912 | 0.386707 | ||||||||
\(651\) | 36.9389 | 1.44775 | ||||||||
\(652\) | −48.6153 | −1.90392 | ||||||||
\(653\) | −17.5499 | −0.686780 | −0.343390 | − | 0.939193i | \(-0.611575\pi\) | ||||
−0.343390 | + | 0.939193i | \(0.611575\pi\) | |||||||
\(654\) | −22.0400 | −0.861833 | ||||||||
\(655\) | 7.88569 | 0.308119 | ||||||||
\(656\) | −72.2662 | −2.82152 | ||||||||
\(657\) | −9.10111 | −0.355068 | ||||||||
\(658\) | −17.6088 | −0.686464 | ||||||||
\(659\) | −31.3329 | −1.22056 | −0.610279 | − | 0.792187i | \(-0.708943\pi\) | ||||
−0.610279 | + | 0.792187i | \(0.708943\pi\) | |||||||
\(660\) | −19.5818 | −0.762219 | ||||||||
\(661\) | 16.3526 | 0.636041 | 0.318021 | − | 0.948084i | \(-0.396982\pi\) | ||||
0.318021 | + | 0.948084i | \(0.396982\pi\) | |||||||
\(662\) | 18.8691 | 0.733369 | ||||||||
\(663\) | 1.89943 | 0.0737678 | ||||||||
\(664\) | −10.9598 | −0.425322 | ||||||||
\(665\) | −13.4648 | −0.522143 | ||||||||
\(666\) | −0.747967 | −0.0289831 | ||||||||
\(667\) | 31.2963 | 1.21180 | ||||||||
\(668\) | 4.52611 | 0.175121 | ||||||||
\(669\) | −11.3005 | −0.436901 | ||||||||
\(670\) | 9.84338 | 0.380283 | ||||||||
\(671\) | −12.4206 | −0.479493 | ||||||||
\(672\) | 55.6871 | 2.14818 | ||||||||
\(673\) | 31.7777 | 1.22494 | 0.612470 | − | 0.790494i | \(-0.290176\pi\) | ||||
0.612470 | + | 0.790494i | \(0.290176\pi\) | |||||||
\(674\) | 58.6610 | 2.25954 | ||||||||
\(675\) | 20.9348 | 0.805780 | ||||||||
\(676\) | −57.7774 | −2.22221 | ||||||||
\(677\) | −5.83035 | −0.224079 | −0.112039 | − | 0.993704i | \(-0.535738\pi\) | ||||
−0.112039 | + | 0.993704i | \(0.535738\pi\) | |||||||
\(678\) | −52.8187 | −2.02849 | ||||||||
\(679\) | −7.97350 | −0.305995 | ||||||||
\(680\) | 12.1170 | 0.464666 | ||||||||
\(681\) | −10.1120 | −0.387492 | ||||||||
\(682\) | 50.6460 | 1.93933 | ||||||||
\(683\) | 10.2312 | 0.391486 | 0.195743 | − | 0.980655i | \(-0.437288\pi\) | ||||
0.195743 | + | 0.980655i | \(0.437288\pi\) | |||||||
\(684\) | 18.6970 | 0.714896 | ||||||||
\(685\) | 0.735632 | 0.0281071 | ||||||||
\(686\) | 40.0699 | 1.52988 | ||||||||
\(687\) | 32.2171 | 1.22916 | ||||||||
\(688\) | 107.406 | 4.09481 | ||||||||
\(689\) | −3.97151 | −0.151302 | ||||||||
\(690\) | −13.2374 | −0.503938 | ||||||||
\(691\) | −40.8206 | −1.55289 | −0.776444 | − | 0.630186i | \(-0.782979\pi\) | ||||
−0.776444 | + | 0.630186i | \(0.782979\pi\) | |||||||
\(692\) | −64.7471 | −2.46132 | ||||||||
\(693\) | 16.0998 | 0.611580 | ||||||||
\(694\) | −38.3965 | −1.45751 | ||||||||
\(695\) | 11.0299 | 0.418389 | ||||||||
\(696\) | 83.7666 | 3.17517 | ||||||||
\(697\) | −11.0681 | −0.419234 | ||||||||
\(698\) | 7.39519 | 0.279912 | ||||||||
\(699\) | 13.1848 | 0.498694 | ||||||||
\(700\) | 75.9056 | 2.86896 | ||||||||
\(701\) | −41.3896 | −1.56326 | −0.781631 | − | 0.623741i | \(-0.785612\pi\) | ||||
−0.781631 | + | 0.623741i | \(0.785612\pi\) | |||||||
\(702\) | 14.6947 | 0.554615 | ||||||||
\(703\) | 0.605664 | 0.0228430 | ||||||||
\(704\) | 22.0377 | 0.830577 | ||||||||
\(705\) | 2.30380 | 0.0867663 | ||||||||
\(706\) | −11.5093 | −0.433157 | ||||||||
\(707\) | −64.0426 | −2.40857 | ||||||||
\(708\) | 62.2846 | 2.34080 | ||||||||
\(709\) | −0.863009 | −0.0324110 | −0.0162055 | − | 0.999869i | \(-0.505159\pi\) | ||||
−0.0162055 | + | 0.999869i | \(0.505159\pi\) | |||||||
\(710\) | 4.40809 | 0.165433 | ||||||||
\(711\) | 5.04486 | 0.189197 | ||||||||
\(712\) | −11.3277 | −0.424522 | ||||||||
\(713\) | 24.1977 | 0.906211 | ||||||||
\(714\) | 20.6909 | 0.774337 | ||||||||
\(715\) | −3.18946 | −0.119279 | ||||||||
\(716\) | 120.399 | 4.49952 | ||||||||
\(717\) | −13.3974 | −0.500336 | ||||||||
\(718\) | −89.2844 | −3.33206 | ||||||||
\(719\) | −7.00009 | −0.261059 | −0.130530 | − | 0.991444i | \(-0.541668\pi\) | ||||
−0.130530 | + | 0.991444i | \(0.541668\pi\) | |||||||
\(720\) | 14.5444 | 0.542039 | ||||||||
\(721\) | 79.1484 | 2.94764 | ||||||||
\(722\) | 28.2001 | 1.04950 | ||||||||
\(723\) | −7.36092 | −0.273756 | ||||||||
\(724\) | −80.7986 | −3.00286 | ||||||||
\(725\) | 33.2201 | 1.23376 | ||||||||
\(726\) | 10.0291 | 0.372214 | ||||||||
\(727\) | 6.73167 | 0.249664 | 0.124832 | − | 0.992178i | \(-0.460161\pi\) | ||||
0.124832 | + | 0.992178i | \(0.460161\pi\) | |||||||
\(728\) | 31.1752 | 1.15543 | ||||||||
\(729\) | 25.7005 | 0.951870 | ||||||||
\(730\) | 19.6403 | 0.726919 | ||||||||
\(731\) | 16.4500 | 0.608424 | ||||||||
\(732\) | −27.1460 | −1.00335 | ||||||||
\(733\) | 20.4679 | 0.755999 | 0.377999 | − | 0.925806i | \(-0.376612\pi\) | ||||
0.377999 | + | 0.925806i | \(0.376612\pi\) | |||||||
\(734\) | 21.9640 | 0.810706 | ||||||||
\(735\) | −15.2914 | −0.564031 | ||||||||
\(736\) | 36.4791 | 1.34464 | ||||||||
\(737\) | 9.53044 | 0.351058 | ||||||||
\(738\) | −26.6316 | −0.980322 | ||||||||
\(739\) | 45.8462 | 1.68648 | 0.843240 | − | 0.537538i | \(-0.180645\pi\) | ||||
0.843240 | + | 0.537538i | \(0.180645\pi\) | |||||||
\(740\) | 1.14082 | 0.0419372 | ||||||||
\(741\) | −3.70081 | −0.135953 | ||||||||
\(742\) | −43.2625 | −1.58822 | ||||||||
\(743\) | −14.0817 | −0.516608 | −0.258304 | − | 0.966064i | \(-0.583164\pi\) | ||||
−0.258304 | + | 0.966064i | \(0.583164\pi\) | |||||||
\(744\) | 64.7667 | 2.37446 | ||||||||
\(745\) | −12.8287 | −0.470006 | ||||||||
\(746\) | −84.1633 | −3.08144 | ||||||||
\(747\) | −2.01484 | −0.0737191 | ||||||||
\(748\) | 20.0503 | 0.733110 | ||||||||
\(749\) | 27.9315 | 1.02059 | ||||||||
\(750\) | −32.7969 | −1.19757 | ||||||||
\(751\) | −35.8379 | −1.30774 | −0.653872 | − | 0.756606i | \(-0.726856\pi\) | ||||
−0.653872 | + | 0.756606i | \(0.726856\pi\) | |||||||
\(752\) | −15.4020 | −0.561652 | ||||||||
\(753\) | −19.3476 | −0.705066 | ||||||||
\(754\) | 23.3181 | 0.849194 | ||||||||
\(755\) | −7.34818 | −0.267428 | ||||||||
\(756\) | 113.135 | 4.11467 | ||||||||
\(757\) | 9.88664 | 0.359336 | 0.179668 | − | 0.983727i | \(-0.442498\pi\) | ||||
0.179668 | + | 0.983727i | \(0.442498\pi\) | |||||||
\(758\) | 12.7132 | 0.461765 | ||||||||
\(759\) | −12.8165 | −0.465210 | ||||||||
\(760\) | −23.6085 | −0.856369 | ||||||||
\(761\) | −2.13679 | −0.0774586 | −0.0387293 | − | 0.999250i | \(-0.512331\pi\) | ||||
−0.0387293 | + | 0.999250i | \(0.512331\pi\) | |||||||
\(762\) | −8.10367 | −0.293565 | ||||||||
\(763\) | −27.6384 | −1.00058 | ||||||||
\(764\) | 11.9813 | 0.433470 | ||||||||
\(765\) | 2.22758 | 0.0805384 | ||||||||
\(766\) | 96.4596 | 3.48523 | ||||||||
\(767\) | 10.1449 | 0.366310 | ||||||||
\(768\) | −21.0665 | −0.760173 | ||||||||
\(769\) | 8.46265 | 0.305171 | 0.152586 | − | 0.988290i | \(-0.451240\pi\) | ||||
0.152586 | + | 0.988290i | \(0.451240\pi\) | |||||||
\(770\) | −34.7435 | −1.25207 | ||||||||
\(771\) | −14.5214 | −0.522977 | ||||||||
\(772\) | −0.671861 | −0.0241808 | ||||||||
\(773\) | −42.4446 | −1.52663 | −0.763313 | − | 0.646028i | \(-0.776429\pi\) | ||||
−0.763313 | + | 0.646028i | \(0.776429\pi\) | |||||||
\(774\) | 39.5812 | 1.42272 | ||||||||
\(775\) | 25.6851 | 0.922636 | ||||||||
\(776\) | −13.9803 | −0.501864 | ||||||||
\(777\) | 1.13984 | 0.0408915 | ||||||||
\(778\) | −17.2517 | −0.618504 | ||||||||
\(779\) | 21.5648 | 0.772640 | ||||||||
\(780\) | −6.97077 | −0.249593 | ||||||||
\(781\) | 4.26795 | 0.152719 | ||||||||
\(782\) | 13.5541 | 0.484692 | ||||||||
\(783\) | 49.5134 | 1.76946 | ||||||||
\(784\) | 102.230 | 3.65106 | ||||||||
\(785\) | 7.19375 | 0.256756 | ||||||||
\(786\) | 23.6098 | 0.842133 | ||||||||
\(787\) | −8.01789 | −0.285807 | −0.142903 | − | 0.989737i | \(-0.545644\pi\) | ||||
−0.142903 | + | 0.989737i | \(0.545644\pi\) | |||||||
\(788\) | −19.2581 | −0.686043 | ||||||||
\(789\) | 39.7087 | 1.41367 | ||||||||
\(790\) | −10.8869 | −0.387337 | ||||||||
\(791\) | −66.2351 | −2.35505 | ||||||||
\(792\) | 28.2285 | 1.00306 | ||||||||
\(793\) | −4.42152 | −0.157013 | ||||||||
\(794\) | −13.3279 | −0.472988 | ||||||||
\(795\) | 5.66013 | 0.200744 | ||||||||
\(796\) | −121.277 | −4.29854 | ||||||||
\(797\) | −21.9098 | −0.776085 | −0.388043 | − | 0.921641i | \(-0.626849\pi\) | ||||
−0.388043 | + | 0.921641i | \(0.626849\pi\) | |||||||
\(798\) | −40.3137 | −1.42709 | ||||||||
\(799\) | −2.35892 | −0.0834526 | ||||||||
\(800\) | 38.7215 | 1.36901 | ||||||||
\(801\) | −2.08247 | −0.0735805 | ||||||||
\(802\) | −84.8696 | −2.99685 | ||||||||
\(803\) | 19.0159 | 0.671056 | ||||||||
\(804\) | 20.8294 | 0.734595 | ||||||||
\(805\) | −16.5998 | −0.585066 | ||||||||
\(806\) | 18.0291 | 0.635047 | ||||||||
\(807\) | 0.819509 | 0.0288481 | ||||||||
\(808\) | −112.289 | −3.95031 | ||||||||
\(809\) | 10.5787 | 0.371927 | 0.185963 | − | 0.982557i | \(-0.440459\pi\) | ||||
0.185963 | + | 0.982557i | \(0.440459\pi\) | |||||||
\(810\) | −9.06914 | −0.318657 | ||||||||
\(811\) | 0.528482 | 0.0185575 | 0.00927876 | − | 0.999957i | \(-0.497046\pi\) | ||||
0.00927876 | + | 0.999957i | \(0.497046\pi\) | |||||||
\(812\) | 179.526 | 6.30014 | ||||||||
\(813\) | 20.9825 | 0.735888 | ||||||||
\(814\) | 1.56280 | 0.0547763 | ||||||||
\(815\) | 11.2852 | 0.395303 | ||||||||
\(816\) | 18.0977 | 0.633548 | ||||||||
\(817\) | −32.0507 | −1.12131 | ||||||||
\(818\) | 100.940 | 3.52927 | ||||||||
\(819\) | 5.73124 | 0.200266 | ||||||||
\(820\) | 40.6191 | 1.41848 | ||||||||
\(821\) | 18.0156 | 0.628748 | 0.314374 | − | 0.949299i | \(-0.398205\pi\) | ||||
0.314374 | + | 0.949299i | \(0.398205\pi\) | |||||||
\(822\) | 2.20248 | 0.0768205 | ||||||||
\(823\) | −21.5585 | −0.751481 | −0.375740 | − | 0.926725i | \(-0.622612\pi\) | ||||
−0.375740 | + | 0.926725i | \(0.622612\pi\) | |||||||
\(824\) | 138.775 | 4.83444 | ||||||||
\(825\) | −13.6043 | −0.473642 | ||||||||
\(826\) | 110.510 | 3.84514 | ||||||||
\(827\) | 19.2633 | 0.669850 | 0.334925 | − | 0.942245i | \(-0.391289\pi\) | ||||
0.334925 | + | 0.942245i | \(0.391289\pi\) | |||||||
\(828\) | 23.0501 | 0.801047 | ||||||||
\(829\) | −23.7503 | −0.824883 | −0.412442 | − | 0.910984i | \(-0.635324\pi\) | ||||
−0.412442 | + | 0.910984i | \(0.635324\pi\) | |||||||
\(830\) | 4.34804 | 0.150923 | ||||||||
\(831\) | −12.3710 | −0.429144 | ||||||||
\(832\) | 7.84503 | 0.271978 | ||||||||
\(833\) | 15.6572 | 0.542491 | ||||||||
\(834\) | 33.0236 | 1.14351 | ||||||||
\(835\) | −1.05066 | −0.0363595 | ||||||||
\(836\) | −39.0655 | −1.35111 | ||||||||
\(837\) | 38.2828 | 1.32325 | ||||||||
\(838\) | −96.7125 | −3.34088 | ||||||||
\(839\) | −13.3464 | −0.460770 | −0.230385 | − | 0.973100i | \(-0.573999\pi\) | ||||
−0.230385 | + | 0.973100i | \(0.573999\pi\) | |||||||
\(840\) | −44.4304 | −1.53299 | ||||||||
\(841\) | 49.5697 | 1.70930 | ||||||||
\(842\) | 57.7678 | 1.99081 | ||||||||
\(843\) | 23.4641 | 0.808147 | ||||||||
\(844\) | −118.751 | −4.08757 | ||||||||
\(845\) | 13.4120 | 0.461387 | ||||||||
\(846\) | −5.67594 | −0.195143 | ||||||||
\(847\) | 12.5766 | 0.432136 | ||||||||
\(848\) | −37.8405 | −1.29945 | ||||||||
\(849\) | 35.7178 | 1.22583 | ||||||||
\(850\) | 14.3872 | 0.493477 | ||||||||
\(851\) | 0.746679 | 0.0255958 | ||||||||
\(852\) | 9.32787 | 0.319567 | ||||||||
\(853\) | 16.6009 | 0.568402 | 0.284201 | − | 0.958765i | \(-0.408272\pi\) | ||||
0.284201 | + | 0.958765i | \(0.408272\pi\) | |||||||
\(854\) | −48.1646 | −1.64816 | ||||||||
\(855\) | −4.34017 | −0.148431 | ||||||||
\(856\) | 48.9736 | 1.67388 | ||||||||
\(857\) | −53.4256 | −1.82498 | −0.912492 | − | 0.409094i | \(-0.865845\pi\) | ||||
−0.912492 | + | 0.409094i | \(0.865845\pi\) | |||||||
\(858\) | −9.54925 | −0.326006 | ||||||||
\(859\) | 1.37622 | 0.0469559 | 0.0234780 | − | 0.999724i | \(-0.492526\pi\) | ||||
0.0234780 | + | 0.999724i | \(0.492526\pi\) | |||||||
\(860\) | −60.3701 | −2.05860 | ||||||||
\(861\) | 40.5843 | 1.38311 | ||||||||
\(862\) | 6.92589 | 0.235897 | ||||||||
\(863\) | 41.7353 | 1.42069 | 0.710343 | − | 0.703855i | \(-0.248540\pi\) | ||||
0.710343 | + | 0.703855i | \(0.248540\pi\) | |||||||
\(864\) | 57.7130 | 1.96344 | ||||||||
\(865\) | 15.0299 | 0.511032 | ||||||||
\(866\) | −83.5201 | −2.83813 | ||||||||
\(867\) | −19.0369 | −0.646527 | ||||||||
\(868\) | 138.806 | 4.71139 | ||||||||
\(869\) | −10.5407 | −0.357570 | ||||||||
\(870\) | −33.2325 | −1.12669 | ||||||||
\(871\) | 3.39267 | 0.114956 | ||||||||
\(872\) | −48.4597 | −1.64105 | ||||||||
\(873\) | −2.57013 | −0.0869858 | ||||||||
\(874\) | −26.4084 | −0.893278 | ||||||||
\(875\) | −41.1277 | −1.39037 | ||||||||
\(876\) | 41.5604 | 1.40420 | ||||||||
\(877\) | 53.1848 | 1.79592 | 0.897962 | − | 0.440074i | \(-0.145048\pi\) | ||||
0.897962 | + | 0.440074i | \(0.145048\pi\) | |||||||
\(878\) | 37.7731 | 1.27478 | ||||||||
\(879\) | −9.28955 | −0.313329 | ||||||||
\(880\) | −30.3891 | −1.02442 | ||||||||
\(881\) | 37.8932 | 1.27665 | 0.638327 | − | 0.769765i | \(-0.279627\pi\) | ||||
0.638327 | + | 0.769765i | \(0.279627\pi\) | |||||||
\(882\) | 37.6737 | 1.26854 | ||||||||
\(883\) | −44.3424 | −1.49224 | −0.746120 | − | 0.665811i | \(-0.768086\pi\) | ||||
−0.746120 | + | 0.665811i | \(0.768086\pi\) | |||||||
\(884\) | 7.13754 | 0.240061 | ||||||||
\(885\) | −14.4583 | −0.486010 | ||||||||
\(886\) | −99.8070 | −3.35308 | ||||||||
\(887\) | −41.0432 | −1.37810 | −0.689049 | − | 0.724715i | \(-0.741971\pi\) | ||||
−0.689049 | + | 0.724715i | \(0.741971\pi\) | |||||||
\(888\) | 1.99853 | 0.0670664 | ||||||||
\(889\) | −10.1621 | −0.340825 | ||||||||
\(890\) | 4.49399 | 0.150639 | ||||||||
\(891\) | −8.78081 | −0.294168 | ||||||||
\(892\) | −42.4640 | −1.42180 | ||||||||
\(893\) | 4.59607 | 0.153802 | ||||||||
\(894\) | −38.4091 | −1.28459 | ||||||||
\(895\) | −27.9485 | −0.934216 | ||||||||
\(896\) | −1.35917 | −0.0454066 | ||||||||
\(897\) | −4.56246 | −0.152336 | ||||||||
\(898\) | −42.9217 | −1.43232 | ||||||||
\(899\) | 60.7485 | 2.02608 | ||||||||
\(900\) | 24.4670 | 0.815566 | ||||||||
\(901\) | −5.79554 | −0.193078 | ||||||||
\(902\) | 55.6441 | 1.85274 | ||||||||
\(903\) | −60.3184 | −2.00727 | ||||||||
\(904\) | −116.133 | −3.86253 | ||||||||
\(905\) | 18.7560 | 0.623470 | ||||||||
\(906\) | −22.0005 | −0.730917 | ||||||||
\(907\) | −34.8391 | −1.15681 | −0.578407 | − | 0.815748i | \(-0.696325\pi\) | ||||
−0.578407 | + | 0.815748i | \(0.696325\pi\) | |||||||
\(908\) | −37.9981 | −1.26101 | ||||||||
\(909\) | −20.6431 | −0.684689 | ||||||||
\(910\) | −12.3681 | −0.409997 | ||||||||
\(911\) | −1.27351 | −0.0421932 | −0.0210966 | − | 0.999777i | \(-0.506716\pi\) | ||||
−0.0210966 | + | 0.999777i | \(0.506716\pi\) | |||||||
\(912\) | −35.2612 | −1.16762 | ||||||||
\(913\) | 4.20981 | 0.139324 | ||||||||
\(914\) | −38.3519 | −1.26857 | ||||||||
\(915\) | 6.30148 | 0.208320 | ||||||||
\(916\) | 121.063 | 4.00003 | ||||||||
\(917\) | 29.6069 | 0.977706 | ||||||||
\(918\) | 21.4436 | 0.707746 | ||||||||
\(919\) | −2.63002 | −0.0867565 | −0.0433782 | − | 0.999059i | \(-0.513812\pi\) | ||||
−0.0433782 | + | 0.999059i | \(0.513812\pi\) | |||||||
\(920\) | −29.1052 | −0.959569 | ||||||||
\(921\) | 41.4081 | 1.36444 | ||||||||
\(922\) | −40.2126 | −1.32433 | ||||||||
\(923\) | 1.51931 | 0.0500088 | ||||||||
\(924\) | −73.5199 | −2.41863 | ||||||||
\(925\) | 0.792577 | 0.0260598 | ||||||||
\(926\) | −70.6426 | −2.32146 | ||||||||
\(927\) | 25.5123 | 0.837933 | ||||||||
\(928\) | 91.5812 | 3.00630 | ||||||||
\(929\) | 3.62522 | 0.118940 | 0.0594698 | − | 0.998230i | \(-0.481059\pi\) | ||||
0.0594698 | + | 0.998230i | \(0.481059\pi\) | |||||||
\(930\) | −25.6947 | −0.842563 | ||||||||
\(931\) | −30.5062 | −0.999799 | ||||||||
\(932\) | 49.5448 | 1.62289 | ||||||||
\(933\) | 18.1336 | 0.593667 | ||||||||
\(934\) | 16.1238 | 0.527586 | ||||||||
\(935\) | −4.65431 | −0.152212 | ||||||||
\(936\) | 10.0488 | 0.328457 | ||||||||
\(937\) | 28.1103 | 0.918325 | 0.459162 | − | 0.888352i | \(-0.348150\pi\) | ||||
0.459162 | + | 0.888352i | \(0.348150\pi\) | |||||||
\(938\) | 36.9570 | 1.20669 | ||||||||
\(939\) | 38.9988 | 1.27268 | ||||||||
\(940\) | 8.65706 | 0.282362 | ||||||||
\(941\) | −13.5804 | −0.442707 | −0.221354 | − | 0.975194i | \(-0.571047\pi\) | ||||
−0.221354 | + | 0.975194i | \(0.571047\pi\) | |||||||
\(942\) | 21.5381 | 0.701749 | ||||||||
\(943\) | 26.5857 | 0.865750 | ||||||||
\(944\) | 96.6601 | 3.14602 | ||||||||
\(945\) | −26.2622 | −0.854310 | ||||||||
\(946\) | −82.7010 | −2.68884 | ||||||||
\(947\) | −12.1484 | −0.394769 | −0.197385 | − | 0.980326i | \(-0.563245\pi\) | ||||
−0.197385 | + | 0.980326i | \(0.563245\pi\) | |||||||
\(948\) | −23.0375 | −0.748222 | ||||||||
\(949\) | 6.76932 | 0.219741 | ||||||||
\(950\) | −28.0317 | −0.909469 | ||||||||
\(951\) | 27.3835 | 0.887970 | ||||||||
\(952\) | 45.4934 | 1.47445 | ||||||||
\(953\) | 31.1937 | 1.01046 | 0.505231 | − | 0.862984i | \(-0.331407\pi\) | ||||
0.505231 | + | 0.862984i | \(0.331407\pi\) | |||||||
\(954\) | −13.9450 | −0.451486 | ||||||||
\(955\) | −2.78126 | −0.0899994 | ||||||||
\(956\) | −50.3439 | −1.62824 | ||||||||
\(957\) | −32.1760 | −1.04010 | ||||||||
\(958\) | −39.6188 | −1.28002 | ||||||||
\(959\) | 2.76194 | 0.0891876 | ||||||||
\(960\) | −11.1806 | −0.360852 | ||||||||
\(961\) | 15.9696 | 0.515147 | ||||||||
\(962\) | 0.556331 | 0.0179368 | ||||||||
\(963\) | 9.00328 | 0.290127 | ||||||||
\(964\) | −27.6603 | −0.890879 | ||||||||
\(965\) | 0.155961 | 0.00502055 | ||||||||
\(966\) | −49.6998 | −1.59906 | ||||||||
\(967\) | −16.7440 | −0.538452 | −0.269226 | − | 0.963077i | \(-0.586768\pi\) | ||||
−0.269226 | + | 0.963077i | \(0.586768\pi\) | |||||||
\(968\) | 22.0511 | 0.708749 | ||||||||
\(969\) | −5.40051 | −0.173489 | ||||||||
\(970\) | 5.54637 | 0.178083 | ||||||||
\(971\) | −40.6364 | −1.30408 | −0.652041 | − | 0.758183i | \(-0.726087\pi\) | ||||
−0.652041 | + | 0.758183i | \(0.726087\pi\) | |||||||
\(972\) | 61.5924 | 1.97558 | ||||||||
\(973\) | 41.4120 | 1.32761 | ||||||||
\(974\) | 1.48327 | 0.0475269 | ||||||||
\(975\) | −4.84291 | −0.155097 | ||||||||
\(976\) | −42.1282 | −1.34849 | ||||||||
\(977\) | 52.4846 | 1.67913 | 0.839565 | − | 0.543259i | \(-0.182810\pi\) | ||||
0.839565 | + | 0.543259i | \(0.182810\pi\) | |||||||
\(978\) | 33.7879 | 1.08042 | ||||||||
\(979\) | 4.35112 | 0.139062 | ||||||||
\(980\) | −57.4608 | −1.83552 | ||||||||
\(981\) | −8.90881 | −0.284436 | ||||||||
\(982\) | −24.4135 | −0.779065 | ||||||||
\(983\) | 51.1398 | 1.63111 | 0.815553 | − | 0.578683i | \(-0.196433\pi\) | ||||
0.815553 | + | 0.578683i | \(0.196433\pi\) | |||||||
\(984\) | 71.1583 | 2.26845 | ||||||||
\(985\) | 4.47044 | 0.142440 | ||||||||
\(986\) | 34.0276 | 1.08366 | ||||||||
\(987\) | 8.64965 | 0.275322 | ||||||||
\(988\) | −13.9066 | −0.442428 | ||||||||
\(989\) | −39.5130 | −1.25644 | ||||||||
\(990\) | −11.1990 | −0.355928 | ||||||||
\(991\) | −24.2281 | −0.769631 | −0.384815 | − | 0.922994i | \(-0.625735\pi\) | ||||
−0.384815 | + | 0.922994i | \(0.625735\pi\) | |||||||
\(992\) | 70.8087 | 2.24818 | ||||||||
\(993\) | −9.26871 | −0.294134 | ||||||||
\(994\) | 16.5502 | 0.524941 | ||||||||
\(995\) | 28.1523 | 0.892487 | ||||||||
\(996\) | 9.20080 | 0.291539 | ||||||||
\(997\) | 18.2197 | 0.577025 | 0.288512 | − | 0.957476i | \(-0.406839\pi\) | ||||
0.288512 | + | 0.957476i | \(0.406839\pi\) | |||||||
\(998\) | 21.8762 | 0.692480 | ||||||||
\(999\) | 1.18131 | 0.0373749 |
(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 | 6037.2.a.b.1.6 | ✓ | 259 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6037.2.a.b.1.6 | ✓ | 259 | 1.1 | even | 1 | trivial |