Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6018,2,Mod(1,6018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6018, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("6018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6018.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: | \(48.0539719364\) |
Analytic rank: | \(0\) |
Dimension: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 4 x^{12} - 41 x^{11} + 179 x^{10} + 540 x^{9} - 2773 x^{8} - 2260 x^{7} + 17621 x^{6} - 838 x^{5} - 44478 x^{4} + 16472 x^{3} + 29944 x^{2} - 6856 x + 128 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Root | \(4.08702\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6018.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 4.08702 | 1.82777 | 0.913886 | − | 0.405971i | \(-0.133067\pi\) | ||||
0.913886 | + | 0.405971i | \(0.133067\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −2.27776 | −0.860911 | −0.430455 | − | 0.902612i | \(-0.641647\pi\) | ||||
−0.430455 | + | 0.902612i | \(0.641647\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 4.08702 | 1.29243 | ||||||||
\(11\) | −4.97741 | −1.50075 | −0.750373 | − | 0.661015i | \(-0.770126\pi\) | ||||
−0.750373 | + | 0.661015i | \(0.770126\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 3.14470 | 0.872184 | 0.436092 | − | 0.899902i | \(-0.356362\pi\) | ||||
0.436092 | + | 0.899902i | \(0.356362\pi\) | |||||||
\(14\) | −2.27776 | −0.608756 | ||||||||
\(15\) | 4.08702 | 1.05526 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −1.30689 | −0.299822 | −0.149911 | − | 0.988699i | \(-0.547899\pi\) | ||||
−0.149911 | + | 0.988699i | \(0.547899\pi\) | |||||||
\(20\) | 4.08702 | 0.913886 | ||||||||
\(21\) | −2.27776 | −0.497047 | ||||||||
\(22\) | −4.97741 | −1.06119 | ||||||||
\(23\) | 3.59338 | 0.749272 | 0.374636 | − | 0.927172i | \(-0.377768\pi\) | ||||
0.374636 | + | 0.927172i | \(0.377768\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 11.7038 | 2.34075 | ||||||||
\(26\) | 3.14470 | 0.616727 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −2.27776 | −0.430455 | ||||||||
\(29\) | 0.323318 | 0.0600386 | 0.0300193 | − | 0.999549i | \(-0.490443\pi\) | ||||
0.0300193 | + | 0.999549i | \(0.490443\pi\) | |||||||
\(30\) | 4.08702 | 0.746185 | ||||||||
\(31\) | −1.53298 | −0.275332 | −0.137666 | − | 0.990479i | \(-0.543960\pi\) | ||||
−0.137666 | + | 0.990479i | \(0.543960\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −4.97741 | −0.866456 | ||||||||
\(34\) | 1.00000 | 0.171499 | ||||||||
\(35\) | −9.30924 | −1.57355 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 6.77537 | 1.11386 | 0.556932 | − | 0.830558i | \(-0.311978\pi\) | ||||
0.556932 | + | 0.830558i | \(0.311978\pi\) | |||||||
\(38\) | −1.30689 | −0.212006 | ||||||||
\(39\) | 3.14470 | 0.503556 | ||||||||
\(40\) | 4.08702 | 0.646215 | ||||||||
\(41\) | 8.35887 | 1.30544 | 0.652718 | − | 0.757601i | \(-0.273629\pi\) | ||||
0.652718 | + | 0.757601i | \(0.273629\pi\) | |||||||
\(42\) | −2.27776 | −0.351465 | ||||||||
\(43\) | 5.11297 | 0.779720 | 0.389860 | − | 0.920874i | \(-0.372523\pi\) | ||||
0.389860 | + | 0.920874i | \(0.372523\pi\) | |||||||
\(44\) | −4.97741 | −0.750373 | ||||||||
\(45\) | 4.08702 | 0.609257 | ||||||||
\(46\) | 3.59338 | 0.529816 | ||||||||
\(47\) | 3.42062 | 0.498948 | 0.249474 | − | 0.968381i | \(-0.419742\pi\) | ||||
0.249474 | + | 0.968381i | \(0.419742\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −1.81183 | −0.258832 | ||||||||
\(50\) | 11.7038 | 1.65516 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | 3.14470 | 0.436092 | ||||||||
\(53\) | 2.94049 | 0.403907 | 0.201953 | − | 0.979395i | \(-0.435271\pi\) | ||||
0.201953 | + | 0.979395i | \(0.435271\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −20.3428 | −2.74302 | ||||||||
\(56\) | −2.27776 | −0.304378 | ||||||||
\(57\) | −1.30689 | −0.173102 | ||||||||
\(58\) | 0.323318 | 0.0424537 | ||||||||
\(59\) | −1.00000 | −0.130189 | ||||||||
\(60\) | 4.08702 | 0.527632 | ||||||||
\(61\) | −7.45651 | −0.954708 | −0.477354 | − | 0.878711i | \(-0.658404\pi\) | ||||
−0.477354 | + | 0.878711i | \(0.658404\pi\) | |||||||
\(62\) | −1.53298 | −0.194689 | ||||||||
\(63\) | −2.27776 | −0.286970 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 12.8525 | 1.59415 | ||||||||
\(66\) | −4.97741 | −0.612677 | ||||||||
\(67\) | −11.1237 | −1.35898 | −0.679488 | − | 0.733686i | \(-0.737798\pi\) | ||||
−0.679488 | + | 0.733686i | \(0.737798\pi\) | |||||||
\(68\) | 1.00000 | 0.121268 | ||||||||
\(69\) | 3.59338 | 0.432593 | ||||||||
\(70\) | −9.30924 | −1.11267 | ||||||||
\(71\) | 6.20001 | 0.735806 | 0.367903 | − | 0.929864i | \(-0.380076\pi\) | ||||
0.367903 | + | 0.929864i | \(0.380076\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 8.75380 | 1.02455 | 0.512277 | − | 0.858820i | \(-0.328802\pi\) | ||||
0.512277 | + | 0.858820i | \(0.328802\pi\) | |||||||
\(74\) | 6.77537 | 0.787621 | ||||||||
\(75\) | 11.7038 | 1.35143 | ||||||||
\(76\) | −1.30689 | −0.149911 | ||||||||
\(77\) | 11.3373 | 1.29201 | ||||||||
\(78\) | 3.14470 | 0.356068 | ||||||||
\(79\) | 9.24674 | 1.04034 | 0.520170 | − | 0.854063i | \(-0.325869\pi\) | ||||
0.520170 | + | 0.854063i | \(0.325869\pi\) | |||||||
\(80\) | 4.08702 | 0.456943 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 8.35887 | 0.923082 | ||||||||
\(83\) | 1.66129 | 0.182350 | 0.0911752 | − | 0.995835i | \(-0.470938\pi\) | ||||
0.0911752 | + | 0.995835i | \(0.470938\pi\) | |||||||
\(84\) | −2.27776 | −0.248524 | ||||||||
\(85\) | 4.08702 | 0.443300 | ||||||||
\(86\) | 5.11297 | 0.551345 | ||||||||
\(87\) | 0.323318 | 0.0346633 | ||||||||
\(88\) | −4.97741 | −0.530594 | ||||||||
\(89\) | −3.42829 | −0.363398 | −0.181699 | − | 0.983354i | \(-0.558160\pi\) | ||||
−0.181699 | + | 0.983354i | \(0.558160\pi\) | |||||||
\(90\) | 4.08702 | 0.430810 | ||||||||
\(91\) | −7.16287 | −0.750873 | ||||||||
\(92\) | 3.59338 | 0.374636 | ||||||||
\(93\) | −1.53298 | −0.158963 | ||||||||
\(94\) | 3.42062 | 0.352810 | ||||||||
\(95\) | −5.34130 | −0.548006 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −8.73640 | −0.887047 | −0.443524 | − | 0.896263i | \(-0.646272\pi\) | ||||
−0.443524 | + | 0.896263i | \(0.646272\pi\) | |||||||
\(98\) | −1.81183 | −0.183022 | ||||||||
\(99\) | −4.97741 | −0.500249 | ||||||||
\(100\) | 11.7038 | 1.17038 | ||||||||
\(101\) | 3.85469 | 0.383556 | 0.191778 | − | 0.981438i | \(-0.438575\pi\) | ||||
0.191778 | + | 0.981438i | \(0.438575\pi\) | |||||||
\(102\) | 1.00000 | 0.0990148 | ||||||||
\(103\) | −2.37041 | −0.233563 | −0.116782 | − | 0.993158i | \(-0.537258\pi\) | ||||
−0.116782 | + | 0.993158i | \(0.537258\pi\) | |||||||
\(104\) | 3.14470 | 0.308364 | ||||||||
\(105\) | −9.30924 | −0.908489 | ||||||||
\(106\) | 2.94049 | 0.285605 | ||||||||
\(107\) | 0.620217 | 0.0599587 | 0.0299793 | − | 0.999551i | \(-0.490456\pi\) | ||||
0.0299793 | + | 0.999551i | \(0.490456\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 16.0601 | 1.53827 | 0.769137 | − | 0.639084i | \(-0.220686\pi\) | ||||
0.769137 | + | 0.639084i | \(0.220686\pi\) | |||||||
\(110\) | −20.3428 | −1.93961 | ||||||||
\(111\) | 6.77537 | 0.643090 | ||||||||
\(112\) | −2.27776 | −0.215228 | ||||||||
\(113\) | −2.60248 | −0.244821 | −0.122411 | − | 0.992480i | \(-0.539062\pi\) | ||||
−0.122411 | + | 0.992480i | \(0.539062\pi\) | |||||||
\(114\) | −1.30689 | −0.122402 | ||||||||
\(115\) | 14.6862 | 1.36950 | ||||||||
\(116\) | 0.323318 | 0.0300193 | ||||||||
\(117\) | 3.14470 | 0.290728 | ||||||||
\(118\) | −1.00000 | −0.0920575 | ||||||||
\(119\) | −2.27776 | −0.208802 | ||||||||
\(120\) | 4.08702 | 0.373092 | ||||||||
\(121\) | 13.7746 | 1.25224 | ||||||||
\(122\) | −7.45651 | −0.675080 | ||||||||
\(123\) | 8.35887 | 0.753693 | ||||||||
\(124\) | −1.53298 | −0.137666 | ||||||||
\(125\) | 27.3984 | 2.45059 | ||||||||
\(126\) | −2.27776 | −0.202919 | ||||||||
\(127\) | 20.7461 | 1.84092 | 0.920458 | − | 0.390841i | \(-0.127816\pi\) | ||||
0.920458 | + | 0.390841i | \(0.127816\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 5.11297 | 0.450172 | ||||||||
\(130\) | 12.8525 | 1.12724 | ||||||||
\(131\) | −20.2666 | −1.77070 | −0.885349 | − | 0.464928i | \(-0.846080\pi\) | ||||
−0.885349 | + | 0.464928i | \(0.846080\pi\) | |||||||
\(132\) | −4.97741 | −0.433228 | ||||||||
\(133\) | 2.97679 | 0.258120 | ||||||||
\(134\) | −11.1237 | −0.960942 | ||||||||
\(135\) | 4.08702 | 0.351755 | ||||||||
\(136\) | 1.00000 | 0.0857493 | ||||||||
\(137\) | −11.6936 | −0.999053 | −0.499526 | − | 0.866299i | \(-0.666493\pi\) | ||||
−0.499526 | + | 0.866299i | \(0.666493\pi\) | |||||||
\(138\) | 3.59338 | 0.305889 | ||||||||
\(139\) | −6.48633 | −0.550163 | −0.275082 | − | 0.961421i | \(-0.588705\pi\) | ||||
−0.275082 | + | 0.961421i | \(0.588705\pi\) | |||||||
\(140\) | −9.30924 | −0.786774 | ||||||||
\(141\) | 3.42062 | 0.288068 | ||||||||
\(142\) | 6.20001 | 0.520293 | ||||||||
\(143\) | −15.6525 | −1.30893 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 1.32141 | 0.109737 | ||||||||
\(146\) | 8.75380 | 0.724469 | ||||||||
\(147\) | −1.81183 | −0.149437 | ||||||||
\(148\) | 6.77537 | 0.556932 | ||||||||
\(149\) | 0.843435 | 0.0690969 | 0.0345485 | − | 0.999403i | \(-0.489001\pi\) | ||||
0.0345485 | + | 0.999403i | \(0.489001\pi\) | |||||||
\(150\) | 11.7038 | 0.955607 | ||||||||
\(151\) | −4.52554 | −0.368284 | −0.184142 | − | 0.982900i | \(-0.558951\pi\) | ||||
−0.184142 | + | 0.982900i | \(0.558951\pi\) | |||||||
\(152\) | −1.30689 | −0.106003 | ||||||||
\(153\) | 1.00000 | 0.0808452 | ||||||||
\(154\) | 11.3373 | 0.913588 | ||||||||
\(155\) | −6.26534 | −0.503244 | ||||||||
\(156\) | 3.14470 | 0.251778 | ||||||||
\(157\) | −18.8717 | −1.50612 | −0.753061 | − | 0.657951i | \(-0.771423\pi\) | ||||
−0.753061 | + | 0.657951i | \(0.771423\pi\) | |||||||
\(158\) | 9.24674 | 0.735631 | ||||||||
\(159\) | 2.94049 | 0.233196 | ||||||||
\(160\) | 4.08702 | 0.323107 | ||||||||
\(161\) | −8.18485 | −0.645057 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 7.35972 | 0.576458 | 0.288229 | − | 0.957562i | \(-0.406934\pi\) | ||||
0.288229 | + | 0.957562i | \(0.406934\pi\) | |||||||
\(164\) | 8.35887 | 0.652718 | ||||||||
\(165\) | −20.3428 | −1.58368 | ||||||||
\(166\) | 1.66129 | 0.128941 | ||||||||
\(167\) | −7.07794 | −0.547708 | −0.273854 | − | 0.961771i | \(-0.588298\pi\) | ||||
−0.273854 | + | 0.961771i | \(0.588298\pi\) | |||||||
\(168\) | −2.27776 | −0.175733 | ||||||||
\(169\) | −3.11083 | −0.239295 | ||||||||
\(170\) | 4.08702 | 0.313460 | ||||||||
\(171\) | −1.30689 | −0.0999407 | ||||||||
\(172\) | 5.11297 | 0.389860 | ||||||||
\(173\) | −1.83515 | −0.139524 | −0.0697620 | − | 0.997564i | \(-0.522224\pi\) | ||||
−0.0697620 | + | 0.997564i | \(0.522224\pi\) | |||||||
\(174\) | 0.323318 | 0.0245107 | ||||||||
\(175\) | −26.6583 | −2.01518 | ||||||||
\(176\) | −4.97741 | −0.375186 | ||||||||
\(177\) | −1.00000 | −0.0751646 | ||||||||
\(178\) | −3.42829 | −0.256961 | ||||||||
\(179\) | 8.48650 | 0.634311 | 0.317155 | − | 0.948374i | \(-0.397272\pi\) | ||||
0.317155 | + | 0.948374i | \(0.397272\pi\) | |||||||
\(180\) | 4.08702 | 0.304629 | ||||||||
\(181\) | 18.8006 | 1.39744 | 0.698719 | − | 0.715396i | \(-0.253754\pi\) | ||||
0.698719 | + | 0.715396i | \(0.253754\pi\) | |||||||
\(182\) | −7.16287 | −0.530947 | ||||||||
\(183\) | −7.45651 | −0.551201 | ||||||||
\(184\) | 3.59338 | 0.264908 | ||||||||
\(185\) | 27.6911 | 2.03589 | ||||||||
\(186\) | −1.53298 | −0.112404 | ||||||||
\(187\) | −4.97741 | −0.363984 | ||||||||
\(188\) | 3.42062 | 0.249474 | ||||||||
\(189\) | −2.27776 | −0.165682 | ||||||||
\(190\) | −5.34130 | −0.387499 | ||||||||
\(191\) | 7.35714 | 0.532344 | 0.266172 | − | 0.963926i | \(-0.414241\pi\) | ||||
0.266172 | + | 0.963926i | \(0.414241\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −0.399035 | −0.0287232 | −0.0143616 | − | 0.999897i | \(-0.504572\pi\) | ||||
−0.0143616 | + | 0.999897i | \(0.504572\pi\) | |||||||
\(194\) | −8.73640 | −0.627237 | ||||||||
\(195\) | 12.8525 | 0.920385 | ||||||||
\(196\) | −1.81183 | −0.129416 | ||||||||
\(197\) | −23.3060 | −1.66048 | −0.830242 | − | 0.557403i | \(-0.811798\pi\) | ||||
−0.830242 | + | 0.557403i | \(0.811798\pi\) | |||||||
\(198\) | −4.97741 | −0.353729 | ||||||||
\(199\) | −23.2534 | −1.64839 | −0.824195 | − | 0.566307i | \(-0.808372\pi\) | ||||
−0.824195 | + | 0.566307i | \(0.808372\pi\) | |||||||
\(200\) | 11.7038 | 0.827580 | ||||||||
\(201\) | −11.1237 | −0.784606 | ||||||||
\(202\) | 3.85469 | 0.271215 | ||||||||
\(203\) | −0.736440 | −0.0516879 | ||||||||
\(204\) | 1.00000 | 0.0700140 | ||||||||
\(205\) | 34.1629 | 2.38604 | ||||||||
\(206\) | −2.37041 | −0.165154 | ||||||||
\(207\) | 3.59338 | 0.249757 | ||||||||
\(208\) | 3.14470 | 0.218046 | ||||||||
\(209\) | 6.50495 | 0.449957 | ||||||||
\(210\) | −9.30924 | −0.642399 | ||||||||
\(211\) | 20.0614 | 1.38109 | 0.690543 | − | 0.723291i | \(-0.257372\pi\) | ||||
0.690543 | + | 0.723291i | \(0.257372\pi\) | |||||||
\(212\) | 2.94049 | 0.201953 | ||||||||
\(213\) | 6.20001 | 0.424818 | ||||||||
\(214\) | 0.620217 | 0.0423972 | ||||||||
\(215\) | 20.8968 | 1.42515 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 3.49176 | 0.237036 | ||||||||
\(218\) | 16.0601 | 1.08772 | ||||||||
\(219\) | 8.75380 | 0.591527 | ||||||||
\(220\) | −20.3428 | −1.37151 | ||||||||
\(221\) | 3.14470 | 0.211536 | ||||||||
\(222\) | 6.77537 | 0.454733 | ||||||||
\(223\) | −10.2655 | −0.687425 | −0.343713 | − | 0.939075i | \(-0.611685\pi\) | ||||
−0.343713 | + | 0.939075i | \(0.611685\pi\) | |||||||
\(224\) | −2.27776 | −0.152189 | ||||||||
\(225\) | 11.7038 | 0.780250 | ||||||||
\(226\) | −2.60248 | −0.173115 | ||||||||
\(227\) | −23.0457 | −1.52960 | −0.764799 | − | 0.644269i | \(-0.777162\pi\) | ||||
−0.764799 | + | 0.644269i | \(0.777162\pi\) | |||||||
\(228\) | −1.30689 | −0.0865512 | ||||||||
\(229\) | −20.9627 | −1.38526 | −0.692628 | − | 0.721295i | \(-0.743547\pi\) | ||||
−0.692628 | + | 0.721295i | \(0.743547\pi\) | |||||||
\(230\) | 14.6862 | 0.968382 | ||||||||
\(231\) | 11.3373 | 0.745941 | ||||||||
\(232\) | 0.323318 | 0.0212269 | ||||||||
\(233\) | −17.8963 | −1.17242 | −0.586212 | − | 0.810158i | \(-0.699381\pi\) | ||||
−0.586212 | + | 0.810158i | \(0.699381\pi\) | |||||||
\(234\) | 3.14470 | 0.205576 | ||||||||
\(235\) | 13.9801 | 0.911964 | ||||||||
\(236\) | −1.00000 | −0.0650945 | ||||||||
\(237\) | 9.24674 | 0.600641 | ||||||||
\(238\) | −2.27776 | −0.147645 | ||||||||
\(239\) | 0.642085 | 0.0415331 | 0.0207665 | − | 0.999784i | \(-0.493389\pi\) | ||||
0.0207665 | + | 0.999784i | \(0.493389\pi\) | |||||||
\(240\) | 4.08702 | 0.263816 | ||||||||
\(241\) | −4.52390 | −0.291410 | −0.145705 | − | 0.989328i | \(-0.546545\pi\) | ||||
−0.145705 | + | 0.989328i | \(0.546545\pi\) | |||||||
\(242\) | 13.7746 | 0.885466 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −7.45651 | −0.477354 | ||||||||
\(245\) | −7.40498 | −0.473087 | ||||||||
\(246\) | 8.35887 | 0.532942 | ||||||||
\(247\) | −4.10980 | −0.261500 | ||||||||
\(248\) | −1.53298 | −0.0973446 | ||||||||
\(249\) | 1.66129 | 0.105280 | ||||||||
\(250\) | 27.3984 | 1.73283 | ||||||||
\(251\) | −23.0526 | −1.45507 | −0.727534 | − | 0.686072i | \(-0.759334\pi\) | ||||
−0.727534 | + | 0.686072i | \(0.759334\pi\) | |||||||
\(252\) | −2.27776 | −0.143485 | ||||||||
\(253\) | −17.8857 | −1.12447 | ||||||||
\(254\) | 20.7461 | 1.30172 | ||||||||
\(255\) | 4.08702 | 0.255939 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 14.5705 | 0.908882 | 0.454441 | − | 0.890777i | \(-0.349839\pi\) | ||||
0.454441 | + | 0.890777i | \(0.349839\pi\) | |||||||
\(258\) | 5.11297 | 0.318319 | ||||||||
\(259\) | −15.4326 | −0.958938 | ||||||||
\(260\) | 12.8525 | 0.797077 | ||||||||
\(261\) | 0.323318 | 0.0200129 | ||||||||
\(262\) | −20.2666 | −1.25207 | ||||||||
\(263\) | 8.13918 | 0.501883 | 0.250942 | − | 0.968002i | \(-0.419260\pi\) | ||||
0.250942 | + | 0.968002i | \(0.419260\pi\) | |||||||
\(264\) | −4.97741 | −0.306338 | ||||||||
\(265\) | 12.0178 | 0.738249 | ||||||||
\(266\) | 2.97679 | 0.182518 | ||||||||
\(267\) | −3.42829 | −0.209808 | ||||||||
\(268\) | −11.1237 | −0.679488 | ||||||||
\(269\) | 20.6899 | 1.26149 | 0.630744 | − | 0.775991i | \(-0.282750\pi\) | ||||
0.630744 | + | 0.775991i | \(0.282750\pi\) | |||||||
\(270\) | 4.08702 | 0.248728 | ||||||||
\(271\) | −9.74484 | −0.591957 | −0.295978 | − | 0.955195i | \(-0.595646\pi\) | ||||
−0.295978 | + | 0.955195i | \(0.595646\pi\) | |||||||
\(272\) | 1.00000 | 0.0606339 | ||||||||
\(273\) | −7.16287 | −0.433517 | ||||||||
\(274\) | −11.6936 | −0.706437 | ||||||||
\(275\) | −58.2544 | −3.51287 | ||||||||
\(276\) | 3.59338 | 0.216296 | ||||||||
\(277\) | 3.66544 | 0.220235 | 0.110117 | − | 0.993919i | \(-0.464877\pi\) | ||||
0.110117 | + | 0.993919i | \(0.464877\pi\) | |||||||
\(278\) | −6.48633 | −0.389024 | ||||||||
\(279\) | −1.53298 | −0.0917773 | ||||||||
\(280\) | −9.30924 | −0.556334 | ||||||||
\(281\) | −10.0881 | −0.601807 | −0.300904 | − | 0.953655i | \(-0.597288\pi\) | ||||
−0.300904 | + | 0.953655i | \(0.597288\pi\) | |||||||
\(282\) | 3.42062 | 0.203695 | ||||||||
\(283\) | −22.8465 | −1.35809 | −0.679043 | − | 0.734099i | \(-0.737605\pi\) | ||||
−0.679043 | + | 0.734099i | \(0.737605\pi\) | |||||||
\(284\) | 6.20001 | 0.367903 | ||||||||
\(285\) | −5.34130 | −0.316392 | ||||||||
\(286\) | −15.6525 | −0.925551 | ||||||||
\(287\) | −19.0395 | −1.12386 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 1.32141 | 0.0775957 | ||||||||
\(291\) | −8.73640 | −0.512137 | ||||||||
\(292\) | 8.75380 | 0.512277 | ||||||||
\(293\) | −16.9859 | −0.992329 | −0.496164 | − | 0.868229i | \(-0.665259\pi\) | ||||
−0.496164 | + | 0.868229i | \(0.665259\pi\) | |||||||
\(294\) | −1.81183 | −0.105668 | ||||||||
\(295\) | −4.08702 | −0.237956 | ||||||||
\(296\) | 6.77537 | 0.393810 | ||||||||
\(297\) | −4.97741 | −0.288819 | ||||||||
\(298\) | 0.843435 | 0.0488589 | ||||||||
\(299\) | 11.3001 | 0.653504 | ||||||||
\(300\) | 11.7038 | 0.675716 | ||||||||
\(301\) | −11.6461 | −0.671269 | ||||||||
\(302\) | −4.52554 | −0.260416 | ||||||||
\(303\) | 3.85469 | 0.221446 | ||||||||
\(304\) | −1.30689 | −0.0749555 | ||||||||
\(305\) | −30.4749 | −1.74499 | ||||||||
\(306\) | 1.00000 | 0.0571662 | ||||||||
\(307\) | 28.6640 | 1.63594 | 0.817970 | − | 0.575261i | \(-0.195100\pi\) | ||||
0.817970 | + | 0.575261i | \(0.195100\pi\) | |||||||
\(308\) | 11.3373 | 0.646004 | ||||||||
\(309\) | −2.37041 | −0.134848 | ||||||||
\(310\) | −6.26534 | −0.355847 | ||||||||
\(311\) | −12.3768 | −0.701826 | −0.350913 | − | 0.936408i | \(-0.614129\pi\) | ||||
−0.350913 | + | 0.936408i | \(0.614129\pi\) | |||||||
\(312\) | 3.14470 | 0.178034 | ||||||||
\(313\) | −21.1662 | −1.19638 | −0.598191 | − | 0.801353i | \(-0.704114\pi\) | ||||
−0.598191 | + | 0.801353i | \(0.704114\pi\) | |||||||
\(314\) | −18.8717 | −1.06499 | ||||||||
\(315\) | −9.30924 | −0.524516 | ||||||||
\(316\) | 9.24674 | 0.520170 | ||||||||
\(317\) | −20.5229 | −1.15268 | −0.576340 | − | 0.817210i | \(-0.695520\pi\) | ||||
−0.576340 | + | 0.817210i | \(0.695520\pi\) | |||||||
\(318\) | 2.94049 | 0.164894 | ||||||||
\(319\) | −1.60929 | −0.0901027 | ||||||||
\(320\) | 4.08702 | 0.228471 | ||||||||
\(321\) | 0.620217 | 0.0346172 | ||||||||
\(322\) | −8.18485 | −0.456124 | ||||||||
\(323\) | −1.30689 | −0.0727175 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 36.8048 | 2.04157 | ||||||||
\(326\) | 7.35972 | 0.407617 | ||||||||
\(327\) | 16.0601 | 0.888123 | ||||||||
\(328\) | 8.35887 | 0.461541 | ||||||||
\(329\) | −7.79133 | −0.429550 | ||||||||
\(330\) | −20.3428 | −1.11983 | ||||||||
\(331\) | −2.43796 | −0.134003 | −0.0670013 | − | 0.997753i | \(-0.521343\pi\) | ||||
−0.0670013 | + | 0.997753i | \(0.521343\pi\) | |||||||
\(332\) | 1.66129 | 0.0911752 | ||||||||
\(333\) | 6.77537 | 0.371288 | ||||||||
\(334\) | −7.07794 | −0.387288 | ||||||||
\(335\) | −45.4628 | −2.48390 | ||||||||
\(336\) | −2.27776 | −0.124262 | ||||||||
\(337\) | −13.2121 | −0.719708 | −0.359854 | − | 0.933009i | \(-0.617173\pi\) | ||||
−0.359854 | + | 0.933009i | \(0.617173\pi\) | |||||||
\(338\) | −3.11083 | −0.169207 | ||||||||
\(339\) | −2.60248 | −0.141348 | ||||||||
\(340\) | 4.08702 | 0.221650 | ||||||||
\(341\) | 7.63029 | 0.413203 | ||||||||
\(342\) | −1.30689 | −0.0706687 | ||||||||
\(343\) | 20.0712 | 1.08374 | ||||||||
\(344\) | 5.11297 | 0.275673 | ||||||||
\(345\) | 14.6862 | 0.790681 | ||||||||
\(346\) | −1.83515 | −0.0986583 | ||||||||
\(347\) | −20.3262 | −1.09117 | −0.545584 | − | 0.838056i | \(-0.683692\pi\) | ||||
−0.545584 | + | 0.838056i | \(0.683692\pi\) | |||||||
\(348\) | 0.323318 | 0.0173317 | ||||||||
\(349\) | 33.8846 | 1.81380 | 0.906901 | − | 0.421343i | \(-0.138441\pi\) | ||||
0.906901 | + | 0.421343i | \(0.138441\pi\) | |||||||
\(350\) | −26.6583 | −1.42495 | ||||||||
\(351\) | 3.14470 | 0.167852 | ||||||||
\(352\) | −4.97741 | −0.265297 | ||||||||
\(353\) | 22.9604 | 1.22206 | 0.611031 | − | 0.791607i | \(-0.290755\pi\) | ||||
0.611031 | + | 0.791607i | \(0.290755\pi\) | |||||||
\(354\) | −1.00000 | −0.0531494 | ||||||||
\(355\) | 25.3396 | 1.34488 | ||||||||
\(356\) | −3.42829 | −0.181699 | ||||||||
\(357\) | −2.27776 | −0.120552 | ||||||||
\(358\) | 8.48650 | 0.448525 | ||||||||
\(359\) | 0.852062 | 0.0449701 | 0.0224851 | − | 0.999747i | \(-0.492842\pi\) | ||||
0.0224851 | + | 0.999747i | \(0.492842\pi\) | |||||||
\(360\) | 4.08702 | 0.215405 | ||||||||
\(361\) | −17.2920 | −0.910107 | ||||||||
\(362\) | 18.8006 | 0.988138 | ||||||||
\(363\) | 13.7746 | 0.722980 | ||||||||
\(364\) | −7.16287 | −0.375436 | ||||||||
\(365\) | 35.7770 | 1.87265 | ||||||||
\(366\) | −7.45651 | −0.389758 | ||||||||
\(367\) | −20.1729 | −1.05301 | −0.526507 | − | 0.850171i | \(-0.676499\pi\) | ||||
−0.526507 | + | 0.850171i | \(0.676499\pi\) | |||||||
\(368\) | 3.59338 | 0.187318 | ||||||||
\(369\) | 8.35887 | 0.435145 | ||||||||
\(370\) | 27.6911 | 1.43959 | ||||||||
\(371\) | −6.69771 | −0.347728 | ||||||||
\(372\) | −1.53298 | −0.0794815 | ||||||||
\(373\) | 6.92011 | 0.358310 | 0.179155 | − | 0.983821i | \(-0.442664\pi\) | ||||
0.179155 | + | 0.983821i | \(0.442664\pi\) | |||||||
\(374\) | −4.97741 | −0.257376 | ||||||||
\(375\) | 27.3984 | 1.41485 | ||||||||
\(376\) | 3.42062 | 0.176405 | ||||||||
\(377\) | 1.01674 | 0.0523648 | ||||||||
\(378\) | −2.27776 | −0.117155 | ||||||||
\(379\) | 19.8059 | 1.01736 | 0.508679 | − | 0.860956i | \(-0.330134\pi\) | ||||
0.508679 | + | 0.860956i | \(0.330134\pi\) | |||||||
\(380\) | −5.34130 | −0.274003 | ||||||||
\(381\) | 20.7461 | 1.06285 | ||||||||
\(382\) | 7.35714 | 0.376424 | ||||||||
\(383\) | −3.88159 | −0.198340 | −0.0991700 | − | 0.995071i | \(-0.531619\pi\) | ||||
−0.0991700 | + | 0.995071i | \(0.531619\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 46.3359 | 2.36150 | ||||||||
\(386\) | −0.399035 | −0.0203104 | ||||||||
\(387\) | 5.11297 | 0.259907 | ||||||||
\(388\) | −8.73640 | −0.443524 | ||||||||
\(389\) | 29.4234 | 1.49182 | 0.745912 | − | 0.666044i | \(-0.232014\pi\) | ||||
0.745912 | + | 0.666044i | \(0.232014\pi\) | |||||||
\(390\) | 12.8525 | 0.650811 | ||||||||
\(391\) | 3.59338 | 0.181725 | ||||||||
\(392\) | −1.81183 | −0.0915111 | ||||||||
\(393\) | −20.2666 | −1.02231 | ||||||||
\(394\) | −23.3060 | −1.17414 | ||||||||
\(395\) | 37.7917 | 1.90150 | ||||||||
\(396\) | −4.97741 | −0.250124 | ||||||||
\(397\) | −25.6566 | −1.28767 | −0.643834 | − | 0.765165i | \(-0.722657\pi\) | ||||
−0.643834 | + | 0.765165i | \(0.722657\pi\) | |||||||
\(398\) | −23.2534 | −1.16559 | ||||||||
\(399\) | 2.97679 | 0.149026 | ||||||||
\(400\) | 11.7038 | 0.585188 | ||||||||
\(401\) | −18.3323 | −0.915472 | −0.457736 | − | 0.889088i | \(-0.651339\pi\) | ||||
−0.457736 | + | 0.889088i | \(0.651339\pi\) | |||||||
\(402\) | −11.1237 | −0.554800 | ||||||||
\(403\) | −4.82078 | −0.240140 | ||||||||
\(404\) | 3.85469 | 0.191778 | ||||||||
\(405\) | 4.08702 | 0.203086 | ||||||||
\(406\) | −0.736440 | −0.0365489 | ||||||||
\(407\) | −33.7238 | −1.67163 | ||||||||
\(408\) | 1.00000 | 0.0495074 | ||||||||
\(409\) | −19.2136 | −0.950053 | −0.475027 | − | 0.879971i | \(-0.657562\pi\) | ||||
−0.475027 | + | 0.879971i | \(0.657562\pi\) | |||||||
\(410\) | 34.1629 | 1.68718 | ||||||||
\(411\) | −11.6936 | −0.576803 | ||||||||
\(412\) | −2.37041 | −0.116782 | ||||||||
\(413\) | 2.27776 | 0.112081 | ||||||||
\(414\) | 3.59338 | 0.176605 | ||||||||
\(415\) | 6.78973 | 0.333295 | ||||||||
\(416\) | 3.14470 | 0.154182 | ||||||||
\(417\) | −6.48633 | −0.317637 | ||||||||
\(418\) | 6.50495 | 0.318167 | ||||||||
\(419\) | 9.40926 | 0.459672 | 0.229836 | − | 0.973229i | \(-0.426181\pi\) | ||||
0.229836 | + | 0.973229i | \(0.426181\pi\) | |||||||
\(420\) | −9.30924 | −0.454244 | ||||||||
\(421\) | 9.54620 | 0.465253 | 0.232627 | − | 0.972566i | \(-0.425268\pi\) | ||||
0.232627 | + | 0.972566i | \(0.425268\pi\) | |||||||
\(422\) | 20.0614 | 0.976575 | ||||||||
\(423\) | 3.42062 | 0.166316 | ||||||||
\(424\) | 2.94049 | 0.142803 | ||||||||
\(425\) | 11.7038 | 0.567715 | ||||||||
\(426\) | 6.20001 | 0.300391 | ||||||||
\(427\) | 16.9841 | 0.821918 | ||||||||
\(428\) | 0.620217 | 0.0299793 | ||||||||
\(429\) | −15.6525 | −0.755709 | ||||||||
\(430\) | 20.8968 | 1.00773 | ||||||||
\(431\) | −3.13096 | −0.150813 | −0.0754066 | − | 0.997153i | \(-0.524025\pi\) | ||||
−0.0754066 | + | 0.997153i | \(0.524025\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 16.1020 | 0.773812 | 0.386906 | − | 0.922119i | \(-0.373544\pi\) | ||||
0.386906 | + | 0.922119i | \(0.373544\pi\) | |||||||
\(434\) | 3.49176 | 0.167610 | ||||||||
\(435\) | 1.32141 | 0.0633567 | ||||||||
\(436\) | 16.0601 | 0.769137 | ||||||||
\(437\) | −4.69617 | −0.224648 | ||||||||
\(438\) | 8.75380 | 0.418273 | ||||||||
\(439\) | −35.1537 | −1.67779 | −0.838897 | − | 0.544291i | \(-0.816799\pi\) | ||||
−0.838897 | + | 0.544291i | \(0.816799\pi\) | |||||||
\(440\) | −20.3428 | −0.969804 | ||||||||
\(441\) | −1.81183 | −0.0862775 | ||||||||
\(442\) | 3.14470 | 0.149578 | ||||||||
\(443\) | 17.5708 | 0.834812 | 0.417406 | − | 0.908720i | \(-0.362939\pi\) | ||||
0.417406 | + | 0.908720i | \(0.362939\pi\) | |||||||
\(444\) | 6.77537 | 0.321545 | ||||||||
\(445\) | −14.0115 | −0.664209 | ||||||||
\(446\) | −10.2655 | −0.486083 | ||||||||
\(447\) | 0.843435 | 0.0398931 | ||||||||
\(448\) | −2.27776 | −0.107614 | ||||||||
\(449\) | −26.6121 | −1.25590 | −0.627951 | − | 0.778253i | \(-0.716106\pi\) | ||||
−0.627951 | + | 0.778253i | \(0.716106\pi\) | |||||||
\(450\) | 11.7038 | 0.551720 | ||||||||
\(451\) | −41.6055 | −1.95913 | ||||||||
\(452\) | −2.60248 | −0.122411 | ||||||||
\(453\) | −4.52554 | −0.212629 | ||||||||
\(454\) | −23.0457 | −1.08159 | ||||||||
\(455\) | −29.2748 | −1.37242 | ||||||||
\(456\) | −1.30689 | −0.0612009 | ||||||||
\(457\) | 7.42520 | 0.347336 | 0.173668 | − | 0.984804i | \(-0.444438\pi\) | ||||
0.173668 | + | 0.984804i | \(0.444438\pi\) | |||||||
\(458\) | −20.9627 | −0.979524 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | 14.6862 | 0.684750 | ||||||||
\(461\) | −5.40610 | −0.251787 | −0.125893 | − | 0.992044i | \(-0.540180\pi\) | ||||
−0.125893 | + | 0.992044i | \(0.540180\pi\) | |||||||
\(462\) | 11.3373 | 0.527460 | ||||||||
\(463\) | −15.3768 | −0.714619 | −0.357309 | − | 0.933986i | \(-0.616306\pi\) | ||||
−0.357309 | + | 0.933986i | \(0.616306\pi\) | |||||||
\(464\) | 0.323318 | 0.0150097 | ||||||||
\(465\) | −6.26534 | −0.290548 | ||||||||
\(466\) | −17.8963 | −0.829028 | ||||||||
\(467\) | −28.9318 | −1.33881 | −0.669403 | − | 0.742900i | \(-0.733450\pi\) | ||||
−0.669403 | + | 0.742900i | \(0.733450\pi\) | |||||||
\(468\) | 3.14470 | 0.145364 | ||||||||
\(469\) | 25.3371 | 1.16996 | ||||||||
\(470\) | 13.9801 | 0.644856 | ||||||||
\(471\) | −18.8717 | −0.869560 | ||||||||
\(472\) | −1.00000 | −0.0460287 | ||||||||
\(473\) | −25.4493 | −1.17016 | ||||||||
\(474\) | 9.24674 | 0.424717 | ||||||||
\(475\) | −15.2956 | −0.701809 | ||||||||
\(476\) | −2.27776 | −0.104401 | ||||||||
\(477\) | 2.94049 | 0.134636 | ||||||||
\(478\) | 0.642085 | 0.0293683 | ||||||||
\(479\) | −9.35258 | −0.427330 | −0.213665 | − | 0.976907i | \(-0.568540\pi\) | ||||
−0.213665 | + | 0.976907i | \(0.568540\pi\) | |||||||
\(480\) | 4.08702 | 0.186546 | ||||||||
\(481\) | 21.3065 | 0.971495 | ||||||||
\(482\) | −4.52390 | −0.206058 | ||||||||
\(483\) | −8.18485 | −0.372424 | ||||||||
\(484\) | 13.7746 | 0.626119 | ||||||||
\(485\) | −35.7059 | −1.62132 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −14.9865 | −0.679103 | −0.339551 | − | 0.940588i | \(-0.610275\pi\) | ||||
−0.339551 | + | 0.940588i | \(0.610275\pi\) | |||||||
\(488\) | −7.45651 | −0.337540 | ||||||||
\(489\) | 7.35972 | 0.332818 | ||||||||
\(490\) | −7.40498 | −0.334523 | ||||||||
\(491\) | 11.4391 | 0.516241 | 0.258121 | − | 0.966113i | \(-0.416897\pi\) | ||||
0.258121 | + | 0.966113i | \(0.416897\pi\) | |||||||
\(492\) | 8.35887 | 0.376847 | ||||||||
\(493\) | 0.323318 | 0.0145615 | ||||||||
\(494\) | −4.10980 | −0.184908 | ||||||||
\(495\) | −20.3428 | −0.914340 | ||||||||
\(496\) | −1.53298 | −0.0688330 | ||||||||
\(497\) | −14.1221 | −0.633463 | ||||||||
\(498\) | 1.66129 | 0.0744442 | ||||||||
\(499\) | −25.4224 | −1.13806 | −0.569031 | − | 0.822316i | \(-0.692681\pi\) | ||||
−0.569031 | + | 0.822316i | \(0.692681\pi\) | |||||||
\(500\) | 27.3984 | 1.22529 | ||||||||
\(501\) | −7.07794 | −0.316219 | ||||||||
\(502\) | −23.0526 | −1.02889 | ||||||||
\(503\) | −11.5767 | −0.516178 | −0.258089 | − | 0.966121i | \(-0.583093\pi\) | ||||
−0.258089 | + | 0.966121i | \(0.583093\pi\) | |||||||
\(504\) | −2.27776 | −0.101459 | ||||||||
\(505\) | 15.7542 | 0.701053 | ||||||||
\(506\) | −17.8857 | −0.795118 | ||||||||
\(507\) | −3.11083 | −0.138157 | ||||||||
\(508\) | 20.7461 | 0.920458 | ||||||||
\(509\) | 34.6216 | 1.53457 | 0.767287 | − | 0.641304i | \(-0.221606\pi\) | ||||
0.767287 | + | 0.641304i | \(0.221606\pi\) | |||||||
\(510\) | 4.08702 | 0.180976 | ||||||||
\(511\) | −19.9390 | −0.882050 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −1.30689 | −0.0577008 | ||||||||
\(514\) | 14.5705 | 0.642677 | ||||||||
\(515\) | −9.68791 | −0.426900 | ||||||||
\(516\) | 5.11297 | 0.225086 | ||||||||
\(517\) | −17.0258 | −0.748794 | ||||||||
\(518\) | −15.4326 | −0.678071 | ||||||||
\(519\) | −1.83515 | −0.0805542 | ||||||||
\(520\) | 12.8525 | 0.563618 | ||||||||
\(521\) | 26.1044 | 1.14366 | 0.571828 | − | 0.820374i | \(-0.306235\pi\) | ||||
0.571828 | + | 0.820374i | \(0.306235\pi\) | |||||||
\(522\) | 0.323318 | 0.0141512 | ||||||||
\(523\) | 18.1012 | 0.791510 | 0.395755 | − | 0.918356i | \(-0.370483\pi\) | ||||
0.395755 | + | 0.918356i | \(0.370483\pi\) | |||||||
\(524\) | −20.2666 | −0.885349 | ||||||||
\(525\) | −26.6583 | −1.16346 | ||||||||
\(526\) | 8.13918 | 0.354885 | ||||||||
\(527\) | −1.53298 | −0.0667778 | ||||||||
\(528\) | −4.97741 | −0.216614 | ||||||||
\(529\) | −10.0876 | −0.438591 | ||||||||
\(530\) | 12.0178 | 0.522021 | ||||||||
\(531\) | −1.00000 | −0.0433963 | ||||||||
\(532\) | 2.97679 | 0.129060 | ||||||||
\(533\) | 26.2862 | 1.13858 | ||||||||
\(534\) | −3.42829 | −0.148357 | ||||||||
\(535\) | 2.53484 | 0.109591 | ||||||||
\(536\) | −11.1237 | −0.480471 | ||||||||
\(537\) | 8.48650 | 0.366219 | ||||||||
\(538\) | 20.6899 | 0.892006 | ||||||||
\(539\) | 9.01821 | 0.388442 | ||||||||
\(540\) | 4.08702 | 0.175877 | ||||||||
\(541\) | 26.4961 | 1.13916 | 0.569578 | − | 0.821937i | \(-0.307107\pi\) | ||||
0.569578 | + | 0.821937i | \(0.307107\pi\) | |||||||
\(542\) | −9.74484 | −0.418577 | ||||||||
\(543\) | 18.8006 | 0.806812 | ||||||||
\(544\) | 1.00000 | 0.0428746 | ||||||||
\(545\) | 65.6378 | 2.81161 | ||||||||
\(546\) | −7.16287 | −0.306543 | ||||||||
\(547\) | 18.8129 | 0.804383 | 0.402191 | − | 0.915556i | \(-0.368249\pi\) | ||||
0.402191 | + | 0.915556i | \(0.368249\pi\) | |||||||
\(548\) | −11.6936 | −0.499526 | ||||||||
\(549\) | −7.45651 | −0.318236 | ||||||||
\(550\) | −58.2544 | −2.48397 | ||||||||
\(551\) | −0.422542 | −0.0180009 | ||||||||
\(552\) | 3.59338 | 0.152945 | ||||||||
\(553\) | −21.0618 | −0.895640 | ||||||||
\(554\) | 3.66544 | 0.155730 | ||||||||
\(555\) | 27.6911 | 1.17542 | ||||||||
\(556\) | −6.48633 | −0.275082 | ||||||||
\(557\) | 38.2073 | 1.61889 | 0.809447 | − | 0.587192i | \(-0.199767\pi\) | ||||
0.809447 | + | 0.587192i | \(0.199767\pi\) | |||||||
\(558\) | −1.53298 | −0.0648964 | ||||||||
\(559\) | 16.0788 | 0.680059 | ||||||||
\(560\) | −9.30924 | −0.393387 | ||||||||
\(561\) | −4.97741 | −0.210146 | ||||||||
\(562\) | −10.0881 | −0.425542 | ||||||||
\(563\) | −0.923939 | −0.0389394 | −0.0194697 | − | 0.999810i | \(-0.506198\pi\) | ||||
−0.0194697 | + | 0.999810i | \(0.506198\pi\) | |||||||
\(564\) | 3.42062 | 0.144034 | ||||||||
\(565\) | −10.6364 | −0.447477 | ||||||||
\(566\) | −22.8465 | −0.960311 | ||||||||
\(567\) | −2.27776 | −0.0956568 | ||||||||
\(568\) | 6.20001 | 0.260147 | ||||||||
\(569\) | −25.0704 | −1.05101 | −0.525503 | − | 0.850792i | \(-0.676123\pi\) | ||||
−0.525503 | + | 0.850792i | \(0.676123\pi\) | |||||||
\(570\) | −5.34130 | −0.223723 | ||||||||
\(571\) | 8.40864 | 0.351891 | 0.175945 | − | 0.984400i | \(-0.443702\pi\) | ||||
0.175945 | + | 0.984400i | \(0.443702\pi\) | |||||||
\(572\) | −15.6525 | −0.654463 | ||||||||
\(573\) | 7.35714 | 0.307349 | ||||||||
\(574\) | −19.0395 | −0.794692 | ||||||||
\(575\) | 42.0561 | 1.75386 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −21.7603 | −0.905893 | −0.452946 | − | 0.891538i | \(-0.649627\pi\) | ||||
−0.452946 | + | 0.891538i | \(0.649627\pi\) | |||||||
\(578\) | 1.00000 | 0.0415945 | ||||||||
\(579\) | −0.399035 | −0.0165833 | ||||||||
\(580\) | 1.32141 | 0.0548685 | ||||||||
\(581\) | −3.78401 | −0.156987 | ||||||||
\(582\) | −8.73640 | −0.362135 | ||||||||
\(583\) | −14.6360 | −0.606161 | ||||||||
\(584\) | 8.75380 | 0.362235 | ||||||||
\(585\) | 12.8525 | 0.531385 | ||||||||
\(586\) | −16.9859 | −0.701682 | ||||||||
\(587\) | −33.9917 | −1.40299 | −0.701495 | − | 0.712675i | \(-0.747484\pi\) | ||||
−0.701495 | + | 0.712675i | \(0.747484\pi\) | |||||||
\(588\) | −1.81183 | −0.0747185 | ||||||||
\(589\) | 2.00345 | 0.0825506 | ||||||||
\(590\) | −4.08702 | −0.168260 | ||||||||
\(591\) | −23.3060 | −0.958681 | ||||||||
\(592\) | 6.77537 | 0.278466 | ||||||||
\(593\) | 35.6982 | 1.46595 | 0.732975 | − | 0.680256i | \(-0.238131\pi\) | ||||
0.732975 | + | 0.680256i | \(0.238131\pi\) | |||||||
\(594\) | −4.97741 | −0.204226 | ||||||||
\(595\) | −9.30924 | −0.381642 | ||||||||
\(596\) | 0.843435 | 0.0345485 | ||||||||
\(597\) | −23.2534 | −0.951698 | ||||||||
\(598\) | 11.3001 | 0.462097 | ||||||||
\(599\) | 46.8489 | 1.91419 | 0.957097 | − | 0.289767i | \(-0.0935777\pi\) | ||||
0.957097 | + | 0.289767i | \(0.0935777\pi\) | |||||||
\(600\) | 11.7038 | 0.477804 | ||||||||
\(601\) | 2.25594 | 0.0920218 | 0.0460109 | − | 0.998941i | \(-0.485349\pi\) | ||||
0.0460109 | + | 0.998941i | \(0.485349\pi\) | |||||||
\(602\) | −11.6461 | −0.474659 | ||||||||
\(603\) | −11.1237 | −0.452992 | ||||||||
\(604\) | −4.52554 | −0.184142 | ||||||||
\(605\) | 56.2972 | 2.28880 | ||||||||
\(606\) | 3.85469 | 0.156586 | ||||||||
\(607\) | 11.6408 | 0.472487 | 0.236243 | − | 0.971694i | \(-0.424084\pi\) | ||||
0.236243 | + | 0.971694i | \(0.424084\pi\) | |||||||
\(608\) | −1.30689 | −0.0530015 | ||||||||
\(609\) | −0.736440 | −0.0298420 | ||||||||
\(610\) | −30.4749 | −1.23389 | ||||||||
\(611\) | 10.7568 | 0.435175 | ||||||||
\(612\) | 1.00000 | 0.0404226 | ||||||||
\(613\) | −23.4298 | −0.946322 | −0.473161 | − | 0.880976i | \(-0.656887\pi\) | ||||
−0.473161 | + | 0.880976i | \(0.656887\pi\) | |||||||
\(614\) | 28.6640 | 1.15678 | ||||||||
\(615\) | 34.1629 | 1.37758 | ||||||||
\(616\) | 11.3373 | 0.456794 | ||||||||
\(617\) | −33.3785 | −1.34377 | −0.671883 | − | 0.740657i | \(-0.734514\pi\) | ||||
−0.671883 | + | 0.740657i | \(0.734514\pi\) | |||||||
\(618\) | −2.37041 | −0.0953518 | ||||||||
\(619\) | −13.7098 | −0.551044 | −0.275522 | − | 0.961295i | \(-0.588851\pi\) | ||||
−0.275522 | + | 0.961295i | \(0.588851\pi\) | |||||||
\(620\) | −6.26534 | −0.251622 | ||||||||
\(621\) | 3.59338 | 0.144198 | ||||||||
\(622\) | −12.3768 | −0.496266 | ||||||||
\(623\) | 7.80881 | 0.312854 | ||||||||
\(624\) | 3.14470 | 0.125889 | ||||||||
\(625\) | 53.4591 | 2.13836 | ||||||||
\(626\) | −21.1662 | −0.845970 | ||||||||
\(627\) | 6.50495 | 0.259783 | ||||||||
\(628\) | −18.8717 | −0.753061 | ||||||||
\(629\) | 6.77537 | 0.270152 | ||||||||
\(630\) | −9.30924 | −0.370889 | ||||||||
\(631\) | 34.2957 | 1.36529 | 0.682645 | − | 0.730750i | \(-0.260829\pi\) | ||||
0.682645 | + | 0.730750i | \(0.260829\pi\) | |||||||
\(632\) | 9.24674 | 0.367816 | ||||||||
\(633\) | 20.0614 | 0.797370 | ||||||||
\(634\) | −20.5229 | −0.815068 | ||||||||
\(635\) | 84.7897 | 3.36478 | ||||||||
\(636\) | 2.94049 | 0.116598 | ||||||||
\(637\) | −5.69766 | −0.225750 | ||||||||
\(638\) | −1.60929 | −0.0637123 | ||||||||
\(639\) | 6.20001 | 0.245269 | ||||||||
\(640\) | 4.08702 | 0.161554 | ||||||||
\(641\) | −32.1423 | −1.26955 | −0.634773 | − | 0.772699i | \(-0.718906\pi\) | ||||
−0.634773 | + | 0.772699i | \(0.718906\pi\) | |||||||
\(642\) | 0.620217 | 0.0244780 | ||||||||
\(643\) | −20.6692 | −0.815112 | −0.407556 | − | 0.913180i | \(-0.633619\pi\) | ||||
−0.407556 | + | 0.913180i | \(0.633619\pi\) | |||||||
\(644\) | −8.18485 | −0.322528 | ||||||||
\(645\) | 20.8968 | 0.822811 | ||||||||
\(646\) | −1.30689 | −0.0514191 | ||||||||
\(647\) | 31.1376 | 1.22415 | 0.612073 | − | 0.790801i | \(-0.290336\pi\) | ||||
0.612073 | + | 0.790801i | \(0.290336\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 4.97741 | 0.195380 | ||||||||
\(650\) | 36.8048 | 1.44360 | ||||||||
\(651\) | 3.49176 | 0.136853 | ||||||||
\(652\) | 7.35972 | 0.288229 | ||||||||
\(653\) | 31.7537 | 1.24262 | 0.621310 | − | 0.783565i | \(-0.286601\pi\) | ||||
0.621310 | + | 0.783565i | \(0.286601\pi\) | |||||||
\(654\) | 16.0601 | 0.627998 | ||||||||
\(655\) | −82.8299 | −3.23643 | ||||||||
\(656\) | 8.35887 | 0.326359 | ||||||||
\(657\) | 8.75380 | 0.341518 | ||||||||
\(658\) | −7.79133 | −0.303738 | ||||||||
\(659\) | 7.07348 | 0.275544 | 0.137772 | − | 0.990464i | \(-0.456006\pi\) | ||||
0.137772 | + | 0.990464i | \(0.456006\pi\) | |||||||
\(660\) | −20.3428 | −0.791842 | ||||||||
\(661\) | 37.4356 | 1.45608 | 0.728038 | − | 0.685536i | \(-0.240432\pi\) | ||||
0.728038 | + | 0.685536i | \(0.240432\pi\) | |||||||
\(662\) | −2.43796 | −0.0947541 | ||||||||
\(663\) | 3.14470 | 0.122130 | ||||||||
\(664\) | 1.66129 | 0.0644706 | ||||||||
\(665\) | 12.1662 | 0.471785 | ||||||||
\(666\) | 6.77537 | 0.262540 | ||||||||
\(667\) | 1.16181 | 0.0449853 | ||||||||
\(668\) | −7.07794 | −0.273854 | ||||||||
\(669\) | −10.2655 | −0.396885 | ||||||||
\(670\) | −45.4628 | −1.75638 | ||||||||
\(671\) | 37.1141 | 1.43277 | ||||||||
\(672\) | −2.27776 | −0.0878664 | ||||||||
\(673\) | 35.5240 | 1.36935 | 0.684675 | − | 0.728848i | \(-0.259944\pi\) | ||||
0.684675 | + | 0.728848i | \(0.259944\pi\) | |||||||
\(674\) | −13.2121 | −0.508910 | ||||||||
\(675\) | 11.7038 | 0.450478 | ||||||||
\(676\) | −3.11083 | −0.119647 | ||||||||
\(677\) | −13.5173 | −0.519512 | −0.259756 | − | 0.965674i | \(-0.583642\pi\) | ||||
−0.259756 | + | 0.965674i | \(0.583642\pi\) | |||||||
\(678\) | −2.60248 | −0.0999478 | ||||||||
\(679\) | 19.8994 | 0.763669 | ||||||||
\(680\) | 4.08702 | 0.156730 | ||||||||
\(681\) | −23.0457 | −0.883114 | ||||||||
\(682\) | 7.63029 | 0.292179 | ||||||||
\(683\) | 35.3464 | 1.35249 | 0.676247 | − | 0.736675i | \(-0.263605\pi\) | ||||
0.676247 | + | 0.736675i | \(0.263605\pi\) | |||||||
\(684\) | −1.30689 | −0.0499703 | ||||||||
\(685\) | −47.7921 | −1.82604 | ||||||||
\(686\) | 20.0712 | 0.766322 | ||||||||
\(687\) | −20.9627 | −0.799778 | ||||||||
\(688\) | 5.11297 | 0.194930 | ||||||||
\(689\) | 9.24696 | 0.352281 | ||||||||
\(690\) | 14.6862 | 0.559096 | ||||||||
\(691\) | −17.5813 | −0.668825 | −0.334413 | − | 0.942427i | \(-0.608538\pi\) | ||||
−0.334413 | + | 0.942427i | \(0.608538\pi\) | |||||||
\(692\) | −1.83515 | −0.0697620 | ||||||||
\(693\) | 11.3373 | 0.430669 | ||||||||
\(694\) | −20.3262 | −0.771572 | ||||||||
\(695\) | −26.5098 | −1.00557 | ||||||||
\(696\) | 0.323318 | 0.0122553 | ||||||||
\(697\) | 8.35887 | 0.316615 | ||||||||
\(698\) | 33.8846 | 1.28255 | ||||||||
\(699\) | −17.8963 | −0.676899 | ||||||||
\(700\) | −26.6583 | −1.00759 | ||||||||
\(701\) | −23.5462 | −0.889328 | −0.444664 | − | 0.895697i | \(-0.646677\pi\) | ||||
−0.444664 | + | 0.895697i | \(0.646677\pi\) | |||||||
\(702\) | 3.14470 | 0.118689 | ||||||||
\(703\) | −8.85469 | −0.333961 | ||||||||
\(704\) | −4.97741 | −0.187593 | ||||||||
\(705\) | 13.9801 | 0.526522 | ||||||||
\(706\) | 22.9604 | 0.864128 | ||||||||
\(707\) | −8.78004 | −0.330207 | ||||||||
\(708\) | −1.00000 | −0.0375823 | ||||||||
\(709\) | −17.9998 | −0.675996 | −0.337998 | − | 0.941147i | \(-0.609750\pi\) | ||||
−0.337998 | + | 0.941147i | \(0.609750\pi\) | |||||||
\(710\) | 25.3396 | 0.950977 | ||||||||
\(711\) | 9.24674 | 0.346780 | ||||||||
\(712\) | −3.42829 | −0.128481 | ||||||||
\(713\) | −5.50860 | −0.206299 | ||||||||
\(714\) | −2.27776 | −0.0852429 | ||||||||
\(715\) | −63.9721 | −2.39242 | ||||||||
\(716\) | 8.48650 | 0.317155 | ||||||||
\(717\) | 0.642085 | 0.0239791 | ||||||||
\(718\) | 0.852062 | 0.0317987 | ||||||||
\(719\) | 40.7379 | 1.51927 | 0.759635 | − | 0.650350i | \(-0.225378\pi\) | ||||
0.759635 | + | 0.650350i | \(0.225378\pi\) | |||||||
\(720\) | 4.08702 | 0.152314 | ||||||||
\(721\) | 5.39921 | 0.201077 | ||||||||
\(722\) | −17.2920 | −0.643543 | ||||||||
\(723\) | −4.52390 | −0.168246 | ||||||||
\(724\) | 18.8006 | 0.698719 | ||||||||
\(725\) | 3.78403 | 0.140535 | ||||||||
\(726\) | 13.7746 | 0.511224 | ||||||||
\(727\) | −13.5112 | −0.501102 | −0.250551 | − | 0.968103i | \(-0.580612\pi\) | ||||
−0.250551 | + | 0.968103i | \(0.580612\pi\) | |||||||
\(728\) | −7.16287 | −0.265474 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 35.7770 | 1.32416 | ||||||||
\(731\) | 5.11297 | 0.189110 | ||||||||
\(732\) | −7.45651 | −0.275600 | ||||||||
\(733\) | −7.94022 | −0.293279 | −0.146639 | − | 0.989190i | \(-0.546846\pi\) | ||||
−0.146639 | + | 0.989190i | \(0.546846\pi\) | |||||||
\(734\) | −20.1729 | −0.744594 | ||||||||
\(735\) | −7.40498 | −0.273137 | ||||||||
\(736\) | 3.59338 | 0.132454 | ||||||||
\(737\) | 55.3672 | 2.03948 | ||||||||
\(738\) | 8.35887 | 0.307694 | ||||||||
\(739\) | −23.1235 | −0.850612 | −0.425306 | − | 0.905050i | \(-0.639833\pi\) | ||||
−0.425306 | + | 0.905050i | \(0.639833\pi\) | |||||||
\(740\) | 27.6911 | 1.01794 | ||||||||
\(741\) | −4.10980 | −0.150977 | ||||||||
\(742\) | −6.69771 | −0.245881 | ||||||||
\(743\) | 26.6774 | 0.978699 | 0.489349 | − | 0.872088i | \(-0.337234\pi\) | ||||
0.489349 | + | 0.872088i | \(0.337234\pi\) | |||||||
\(744\) | −1.53298 | −0.0562019 | ||||||||
\(745\) | 3.44714 | 0.126293 | ||||||||
\(746\) | 6.92011 | 0.253363 | ||||||||
\(747\) | 1.66129 | 0.0607834 | ||||||||
\(748\) | −4.97741 | −0.181992 | ||||||||
\(749\) | −1.41270 | −0.0516191 | ||||||||
\(750\) | 27.3984 | 1.00045 | ||||||||
\(751\) | 22.2657 | 0.812488 | 0.406244 | − | 0.913765i | \(-0.366838\pi\) | ||||
0.406244 | + | 0.913765i | \(0.366838\pi\) | |||||||
\(752\) | 3.42062 | 0.124737 | ||||||||
\(753\) | −23.0526 | −0.840084 | ||||||||
\(754\) | 1.01674 | 0.0370275 | ||||||||
\(755\) | −18.4960 | −0.673138 | ||||||||
\(756\) | −2.27776 | −0.0828412 | ||||||||
\(757\) | −15.3625 | −0.558359 | −0.279179 | − | 0.960239i | \(-0.590062\pi\) | ||||
−0.279179 | + | 0.960239i | \(0.590062\pi\) | |||||||
\(758\) | 19.8059 | 0.719381 | ||||||||
\(759\) | −17.8857 | −0.649212 | ||||||||
\(760\) | −5.34130 | −0.193749 | ||||||||
\(761\) | 20.4615 | 0.741729 | 0.370865 | − | 0.928687i | \(-0.379061\pi\) | ||||
0.370865 | + | 0.928687i | \(0.379061\pi\) | |||||||
\(762\) | 20.7461 | 0.751551 | ||||||||
\(763\) | −36.5809 | −1.32432 | ||||||||
\(764\) | 7.35714 | 0.266172 | ||||||||
\(765\) | 4.08702 | 0.147767 | ||||||||
\(766\) | −3.88159 | −0.140248 | ||||||||
\(767\) | −3.14470 | −0.113549 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −10.8477 | −0.391180 | −0.195590 | − | 0.980686i | \(-0.562662\pi\) | ||||
−0.195590 | + | 0.980686i | \(0.562662\pi\) | |||||||
\(770\) | 46.3359 | 1.66983 | ||||||||
\(771\) | 14.5705 | 0.524743 | ||||||||
\(772\) | −0.399035 | −0.0143616 | ||||||||
\(773\) | 12.2794 | 0.441661 | 0.220830 | − | 0.975312i | \(-0.429123\pi\) | ||||
0.220830 | + | 0.975312i | \(0.429123\pi\) | |||||||
\(774\) | 5.11297 | 0.183782 | ||||||||
\(775\) | −17.9417 | −0.644483 | ||||||||
\(776\) | −8.73640 | −0.313619 | ||||||||
\(777\) | −15.4326 | −0.553643 | ||||||||
\(778\) | 29.4234 | 1.05488 | ||||||||
\(779\) | −10.9242 | −0.391398 | ||||||||
\(780\) | 12.8525 | 0.460193 | ||||||||
\(781\) | −30.8600 | −1.10426 | ||||||||
\(782\) | 3.59338 | 0.128499 | ||||||||
\(783\) | 0.323318 | 0.0115544 | ||||||||
\(784\) | −1.81183 | −0.0647081 | ||||||||
\(785\) | −77.1289 | −2.75285 | ||||||||
\(786\) | −20.2666 | −0.722884 | ||||||||
\(787\) | −10.0093 | −0.356793 | −0.178397 | − | 0.983959i | \(-0.557091\pi\) | ||||
−0.178397 | + | 0.983959i | \(0.557091\pi\) | |||||||
\(788\) | −23.3060 | −0.830242 | ||||||||
\(789\) | 8.13918 | 0.289762 | ||||||||
\(790\) | 37.7917 | 1.34457 | ||||||||
\(791\) | 5.92782 | 0.210769 | ||||||||
\(792\) | −4.97741 | −0.176865 | ||||||||
\(793\) | −23.4485 | −0.832681 | ||||||||
\(794\) | −25.6566 | −0.910519 | ||||||||
\(795\) | 12.0178 | 0.426228 | ||||||||
\(796\) | −23.2534 | −0.824195 | ||||||||
\(797\) | 10.4321 | 0.369523 | 0.184761 | − | 0.982783i | \(-0.440849\pi\) | ||||
0.184761 | + | 0.982783i | \(0.440849\pi\) | |||||||
\(798\) | 2.97679 | 0.105377 | ||||||||
\(799\) | 3.42062 | 0.121013 | ||||||||
\(800\) | 11.7038 | 0.413790 | ||||||||
\(801\) | −3.42829 | −0.121133 | ||||||||
\(802\) | −18.3323 | −0.647336 | ||||||||
\(803\) | −43.5712 | −1.53760 | ||||||||
\(804\) | −11.1237 | −0.392303 | ||||||||
\(805\) | −33.4517 | −1.17902 | ||||||||
\(806\) | −4.82078 | −0.169805 | ||||||||
\(807\) | 20.6899 | 0.728320 | ||||||||
\(808\) | 3.85469 | 0.135607 | ||||||||
\(809\) | 47.4844 | 1.66946 | 0.834731 | − | 0.550657i | \(-0.185623\pi\) | ||||
0.834731 | + | 0.550657i | \(0.185623\pi\) | |||||||
\(810\) | 4.08702 | 0.143603 | ||||||||
\(811\) | 4.66901 | 0.163951 | 0.0819756 | − | 0.996634i | \(-0.473877\pi\) | ||||
0.0819756 | + | 0.996634i | \(0.473877\pi\) | |||||||
\(812\) | −0.736440 | −0.0258440 | ||||||||
\(813\) | −9.74484 | −0.341766 | ||||||||
\(814\) | −33.7238 | −1.18202 | ||||||||
\(815\) | 30.0793 | 1.05363 | ||||||||
\(816\) | 1.00000 | 0.0350070 | ||||||||
\(817\) | −6.68210 | −0.233777 | ||||||||
\(818\) | −19.2136 | −0.671789 | ||||||||
\(819\) | −7.16287 | −0.250291 | ||||||||
\(820\) | 34.1629 | 1.19302 | ||||||||
\(821\) | 12.4665 | 0.435085 | 0.217542 | − | 0.976051i | \(-0.430196\pi\) | ||||
0.217542 | + | 0.976051i | \(0.430196\pi\) | |||||||
\(822\) | −11.6936 | −0.407862 | ||||||||
\(823\) | −2.85465 | −0.0995069 | −0.0497535 | − | 0.998762i | \(-0.515844\pi\) | ||||
−0.0497535 | + | 0.998762i | \(0.515844\pi\) | |||||||
\(824\) | −2.37041 | −0.0825771 | ||||||||
\(825\) | −58.2544 | −2.02816 | ||||||||
\(826\) | 2.27776 | 0.0792533 | ||||||||
\(827\) | 37.7515 | 1.31275 | 0.656375 | − | 0.754435i | \(-0.272089\pi\) | ||||
0.656375 | + | 0.754435i | \(0.272089\pi\) | |||||||
\(828\) | 3.59338 | 0.124879 | ||||||||
\(829\) | −17.9797 | −0.624461 | −0.312231 | − | 0.950006i | \(-0.601076\pi\) | ||||
−0.312231 | + | 0.950006i | \(0.601076\pi\) | |||||||
\(830\) | 6.78973 | 0.235675 | ||||||||
\(831\) | 3.66544 | 0.127153 | ||||||||
\(832\) | 3.14470 | 0.109023 | ||||||||
\(833\) | −1.81183 | −0.0627761 | ||||||||
\(834\) | −6.48633 | −0.224603 | ||||||||
\(835\) | −28.9277 | −1.00108 | ||||||||
\(836\) | 6.50495 | 0.224978 | ||||||||
\(837\) | −1.53298 | −0.0529877 | ||||||||
\(838\) | 9.40926 | 0.325037 | ||||||||
\(839\) | 39.3767 | 1.35943 | 0.679717 | − | 0.733475i | \(-0.262103\pi\) | ||||
0.679717 | + | 0.733475i | \(0.262103\pi\) | |||||||
\(840\) | −9.30924 | −0.321199 | ||||||||
\(841\) | −28.8955 | −0.996395 | ||||||||
\(842\) | 9.54620 | 0.328984 | ||||||||
\(843\) | −10.0881 | −0.347453 | ||||||||
\(844\) | 20.0614 | 0.690543 | ||||||||
\(845\) | −12.7140 | −0.437376 | ||||||||
\(846\) | 3.42062 | 0.117603 | ||||||||
\(847\) | −31.3752 | −1.07807 | ||||||||
\(848\) | 2.94049 | 0.100977 | ||||||||
\(849\) | −22.8465 | −0.784091 | ||||||||
\(850\) | 11.7038 | 0.401435 | ||||||||
\(851\) | 24.3465 | 0.834588 | ||||||||
\(852\) | 6.20001 | 0.212409 | ||||||||
\(853\) | 32.6317 | 1.11729 | 0.558644 | − | 0.829407i | \(-0.311322\pi\) | ||||
0.558644 | + | 0.829407i | \(0.311322\pi\) | |||||||
\(854\) | 16.9841 | 0.581184 | ||||||||
\(855\) | −5.34130 | −0.182669 | ||||||||
\(856\) | 0.620217 | 0.0211986 | ||||||||
\(857\) | −5.78268 | −0.197533 | −0.0987663 | − | 0.995111i | \(-0.531490\pi\) | ||||
−0.0987663 | + | 0.995111i | \(0.531490\pi\) | |||||||
\(858\) | −15.6525 | −0.534367 | ||||||||
\(859\) | 43.7052 | 1.49120 | 0.745601 | − | 0.666393i | \(-0.232163\pi\) | ||||
0.745601 | + | 0.666393i | \(0.232163\pi\) | |||||||
\(860\) | 20.8968 | 0.712575 | ||||||||
\(861\) | −19.0395 | −0.648863 | ||||||||
\(862\) | −3.13096 | −0.106641 | ||||||||
\(863\) | 28.7751 | 0.979516 | 0.489758 | − | 0.871858i | \(-0.337085\pi\) | ||||
0.489758 | + | 0.871858i | \(0.337085\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −7.50030 | −0.255018 | ||||||||
\(866\) | 16.1020 | 0.547168 | ||||||||
\(867\) | 1.00000 | 0.0339618 | ||||||||
\(868\) | 3.49176 | 0.118518 | ||||||||
\(869\) | −46.0248 | −1.56129 | ||||||||
\(870\) | 1.32141 | 0.0447999 | ||||||||
\(871\) | −34.9808 | −1.18528 | ||||||||
\(872\) | 16.0601 | 0.543862 | ||||||||
\(873\) | −8.73640 | −0.295682 | ||||||||
\(874\) | −4.69617 | −0.158850 | ||||||||
\(875\) | −62.4068 | −2.10974 | ||||||||
\(876\) | 8.75380 | 0.295763 | ||||||||
\(877\) | 42.7561 | 1.44377 | 0.721885 | − | 0.692013i | \(-0.243276\pi\) | ||||
0.721885 | + | 0.692013i | \(0.243276\pi\) | |||||||
\(878\) | −35.1537 | −1.18638 | ||||||||
\(879\) | −16.9859 | −0.572921 | ||||||||
\(880\) | −20.3428 | −0.685755 | ||||||||
\(881\) | 5.44662 | 0.183501 | 0.0917506 | − | 0.995782i | \(-0.470754\pi\) | ||||
0.0917506 | + | 0.995782i | \(0.470754\pi\) | |||||||
\(882\) | −1.81183 | −0.0610074 | ||||||||
\(883\) | 8.28943 | 0.278961 | 0.139481 | − | 0.990225i | \(-0.455457\pi\) | ||||
0.139481 | + | 0.990225i | \(0.455457\pi\) | |||||||
\(884\) | 3.14470 | 0.105768 | ||||||||
\(885\) | −4.08702 | −0.137384 | ||||||||
\(886\) | 17.5708 | 0.590302 | ||||||||
\(887\) | −18.8214 | −0.631959 | −0.315980 | − | 0.948766i | \(-0.602333\pi\) | ||||
−0.315980 | + | 0.948766i | \(0.602333\pi\) | |||||||
\(888\) | 6.77537 | 0.227367 | ||||||||
\(889\) | −47.2545 | −1.58487 | ||||||||
\(890\) | −14.0115 | −0.469667 | ||||||||
\(891\) | −4.97741 | −0.166750 | ||||||||
\(892\) | −10.2655 | −0.343713 | ||||||||
\(893\) | −4.47038 | −0.149596 | ||||||||
\(894\) | 0.843435 | 0.0282087 | ||||||||
\(895\) | 34.6845 | 1.15938 | ||||||||
\(896\) | −2.27776 | −0.0760945 | ||||||||
\(897\) | 11.3001 | 0.377300 | ||||||||
\(898\) | −26.6121 | −0.888056 | ||||||||
\(899\) | −0.495641 | −0.0165306 | ||||||||
\(900\) | 11.7038 | 0.390125 | ||||||||
\(901\) | 2.94049 | 0.0979618 | ||||||||
\(902\) | −41.6055 | −1.38531 | ||||||||
\(903\) | −11.6461 | −0.387558 | ||||||||
\(904\) | −2.60248 | −0.0865573 | ||||||||
\(905\) | 76.8385 | 2.55420 | ||||||||
\(906\) | −4.52554 | −0.150351 | ||||||||
\(907\) | −36.0394 | −1.19667 | −0.598334 | − | 0.801247i | \(-0.704170\pi\) | ||||
−0.598334 | + | 0.801247i | \(0.704170\pi\) | |||||||
\(908\) | −23.0457 | −0.764799 | ||||||||
\(909\) | 3.85469 | 0.127852 | ||||||||
\(910\) | −29.2748 | −0.970451 | ||||||||
\(911\) | 41.8005 | 1.38491 | 0.692456 | − | 0.721460i | \(-0.256529\pi\) | ||||
0.692456 | + | 0.721460i | \(0.256529\pi\) | |||||||
\(912\) | −1.30689 | −0.0432756 | ||||||||
\(913\) | −8.26892 | −0.273661 | ||||||||
\(914\) | 7.42520 | 0.245604 | ||||||||
\(915\) | −30.4749 | −1.00747 | ||||||||
\(916\) | −20.9627 | −0.692628 | ||||||||
\(917\) | 46.1623 | 1.52441 | ||||||||
\(918\) | 1.00000 | 0.0330049 | ||||||||
\(919\) | −4.09329 | −0.135025 | −0.0675125 | − | 0.997718i | \(-0.521506\pi\) | ||||
−0.0675125 | + | 0.997718i | \(0.521506\pi\) | |||||||
\(920\) | 14.6862 | 0.484191 | ||||||||
\(921\) | 28.6640 | 0.944510 | ||||||||
\(922\) | −5.40610 | −0.178040 | ||||||||
\(923\) | 19.4972 | 0.641758 | ||||||||
\(924\) | 11.3373 | 0.372971 | ||||||||
\(925\) | 79.2973 | 2.60728 | ||||||||
\(926\) | −15.3768 | −0.505312 | ||||||||
\(927\) | −2.37041 | −0.0778544 | ||||||||
\(928\) | 0.323318 | 0.0106134 | ||||||||
\(929\) | −44.1156 | −1.44739 | −0.723694 | − | 0.690122i | \(-0.757557\pi\) | ||||
−0.723694 | + | 0.690122i | \(0.757557\pi\) | |||||||
\(930\) | −6.26534 | −0.205449 | ||||||||
\(931\) | 2.36787 | 0.0776037 | ||||||||
\(932\) | −17.8963 | −0.586212 | ||||||||
\(933\) | −12.3768 | −0.405199 | ||||||||
\(934\) | −28.9318 | −0.946678 | ||||||||
\(935\) | −20.3428 | −0.665280 | ||||||||
\(936\) | 3.14470 | 0.102788 | ||||||||
\(937\) | −38.7818 | −1.26695 | −0.633473 | − | 0.773764i | \(-0.718371\pi\) | ||||
−0.633473 | + | 0.773764i | \(0.718371\pi\) | |||||||
\(938\) | 25.3371 | 0.827285 | ||||||||
\(939\) | −21.1662 | −0.690732 | ||||||||
\(940\) | 13.9801 | 0.455982 | ||||||||
\(941\) | 18.1112 | 0.590408 | 0.295204 | − | 0.955434i | \(-0.404612\pi\) | ||||
0.295204 | + | 0.955434i | \(0.404612\pi\) | |||||||
\(942\) | −18.8717 | −0.614872 | ||||||||
\(943\) | 30.0366 | 0.978127 | ||||||||
\(944\) | −1.00000 | −0.0325472 | ||||||||
\(945\) | −9.30924 | −0.302830 | ||||||||
\(946\) | −25.4493 | −0.827429 | ||||||||
\(947\) | −36.1922 | −1.17609 | −0.588045 | − | 0.808828i | \(-0.700102\pi\) | ||||
−0.588045 | + | 0.808828i | \(0.700102\pi\) | |||||||
\(948\) | 9.24674 | 0.300320 | ||||||||
\(949\) | 27.5281 | 0.893600 | ||||||||
\(950\) | −15.2956 | −0.496254 | ||||||||
\(951\) | −20.5229 | −0.665500 | ||||||||
\(952\) | −2.27776 | −0.0738225 | ||||||||
\(953\) | −31.3283 | −1.01482 | −0.507411 | − | 0.861704i | \(-0.669397\pi\) | ||||
−0.507411 | + | 0.861704i | \(0.669397\pi\) | |||||||
\(954\) | 2.94049 | 0.0952017 | ||||||||
\(955\) | 30.0688 | 0.973003 | ||||||||
\(956\) | 0.642085 | 0.0207665 | ||||||||
\(957\) | −1.60929 | −0.0520208 | ||||||||
\(958\) | −9.35258 | −0.302168 | ||||||||
\(959\) | 26.6352 | 0.860095 | ||||||||
\(960\) | 4.08702 | 0.131908 | ||||||||
\(961\) | −28.6500 | −0.924192 | ||||||||
\(962\) | 21.3065 | 0.686950 | ||||||||
\(963\) | 0.620217 | 0.0199862 | ||||||||
\(964\) | −4.52390 | −0.145705 | ||||||||
\(965\) | −1.63087 | −0.0524994 | ||||||||
\(966\) | −8.18485 | −0.263343 | ||||||||
\(967\) | −39.5048 | −1.27039 | −0.635194 | − | 0.772353i | \(-0.719080\pi\) | ||||
−0.635194 | + | 0.772353i | \(0.719080\pi\) | |||||||
\(968\) | 13.7746 | 0.442733 | ||||||||
\(969\) | −1.30689 | −0.0419835 | ||||||||
\(970\) | −35.7059 | −1.14645 | ||||||||
\(971\) | −5.97866 | −0.191864 | −0.0959322 | − | 0.995388i | \(-0.530583\pi\) | ||||
−0.0959322 | + | 0.995388i | \(0.530583\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 14.7743 | 0.473642 | ||||||||
\(974\) | −14.9865 | −0.480198 | ||||||||
\(975\) | 36.8048 | 1.17870 | ||||||||
\(976\) | −7.45651 | −0.238677 | ||||||||
\(977\) | 7.40254 | 0.236828 | 0.118414 | − | 0.992964i | \(-0.462219\pi\) | ||||
0.118414 | + | 0.992964i | \(0.462219\pi\) | |||||||
\(978\) | 7.35972 | 0.235338 | ||||||||
\(979\) | 17.0640 | 0.545368 | ||||||||
\(980\) | −7.40498 | −0.236543 | ||||||||
\(981\) | 16.0601 | 0.512758 | ||||||||
\(982\) | 11.4391 | 0.365038 | ||||||||
\(983\) | −54.0107 | −1.72267 | −0.861337 | − | 0.508033i | \(-0.830373\pi\) | ||||
−0.861337 | + | 0.508033i | \(0.830373\pi\) | |||||||
\(984\) | 8.35887 | 0.266471 | ||||||||
\(985\) | −95.2522 | −3.03499 | ||||||||
\(986\) | 0.323318 | 0.0102965 | ||||||||
\(987\) | −7.79133 | −0.248001 | ||||||||
\(988\) | −4.10980 | −0.130750 | ||||||||
\(989\) | 18.3729 | 0.584223 | ||||||||
\(990\) | −20.3428 | −0.646536 | ||||||||
\(991\) | −7.86198 | −0.249744 | −0.124872 | − | 0.992173i | \(-0.539852\pi\) | ||||
−0.124872 | + | 0.992173i | \(0.539852\pi\) | |||||||
\(992\) | −1.53298 | −0.0486723 | ||||||||
\(993\) | −2.43796 | −0.0773664 | ||||||||
\(994\) | −14.1221 | −0.447926 | ||||||||
\(995\) | −95.0371 | −3.01288 | ||||||||
\(996\) | 1.66129 | 0.0526400 | ||||||||
\(997\) | 15.4399 | 0.488987 | 0.244493 | − | 0.969651i | \(-0.421378\pi\) | ||||
0.244493 | + | 0.969651i | \(0.421378\pi\) | |||||||
\(998\) | −25.4224 | −0.804731 | ||||||||
\(999\) | 6.77537 | 0.214363 |
(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 | 6018.2.a.bb.1.13 | ✓ | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6018.2.a.bb.1.13 | ✓ | 13 | 1.1 | even | 1 | trivial |