Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6004,2,Mod(1,6004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6004, 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("6004.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6004 = 2^{2} \cdot 19 \cdot 79 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6004.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: | \(47.9421813736\) |
Analytic rank: | \(1\) |
Dimension: | \(27\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.25 | ||
Character | \(\chi\) | \(=\) | 6004.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.48243 | 1.43323 | 0.716617 | − | 0.697467i | \(-0.245690\pi\) | ||||
0.716617 | + | 0.697467i | \(0.245690\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00873 | 0.451116 | 0.225558 | − | 0.974230i | \(-0.427579\pi\) | ||||
0.225558 | + | 0.974230i | \(0.427579\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.658321 | 0.248822 | 0.124411 | − | 0.992231i | \(-0.460296\pi\) | ||||
0.124411 | + | 0.992231i | \(0.460296\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.16248 | 1.05416 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.12660 | −1.54573 | −0.772864 | − | 0.634571i | \(-0.781177\pi\) | ||||
−0.772864 | + | 0.634571i | \(0.781177\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.19021 | −0.607454 | −0.303727 | − | 0.952759i | \(-0.598231\pi\) | ||||
−0.303727 | + | 0.952759i | \(0.598231\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.50410 | 0.646555 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.93027 | −1.19577 | −0.597884 | − | 0.801583i | \(-0.703992\pi\) | ||||
−0.597884 | + | 0.801583i | \(0.703992\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.63424 | 0.356620 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.25019 | 0.469197 | 0.234598 | − | 0.972092i | \(-0.424622\pi\) | ||||
0.234598 | + | 0.972092i | \(0.424622\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.98247 | −0.796494 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.403349 | 0.0776246 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.27576 | −0.608294 | −0.304147 | − | 0.952625i | \(-0.598371\pi\) | ||||
−0.304147 | + | 0.952625i | \(0.598371\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.68263 | −1.20024 | −0.600118 | − | 0.799911i | \(-0.704880\pi\) | ||||
−0.600118 | + | 0.799911i | \(0.704880\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −12.7265 | −2.21539 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.664065 | 0.112248 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.75479 | 0.781683 | 0.390842 | − | 0.920458i | \(-0.372184\pi\) | ||||
0.390842 | + | 0.920458i | \(0.372184\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.43704 | −0.870623 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.29737 | −0.983484 | −0.491742 | − | 0.870741i | \(-0.663640\pi\) | ||||
−0.491742 | + | 0.870741i | \(0.663640\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.36027 | −1.12243 | −0.561215 | − | 0.827670i | \(-0.689666\pi\) | ||||
−0.561215 | + | 0.827670i | \(0.689666\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.19008 | 0.475549 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.45612 | −1.23345 | −0.616726 | − | 0.787178i | \(-0.711541\pi\) | ||||
−0.616726 | + | 0.787178i | \(0.711541\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.56661 | −0.938088 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −12.2391 | −1.71381 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.21683 | 0.853947 | 0.426974 | − | 0.904264i | \(-0.359580\pi\) | ||||
0.426974 | + | 0.904264i | \(0.359580\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.17134 | −0.697303 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.48243 | 0.328806 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.76767 | 0.360320 | 0.180160 | − | 0.983637i | \(-0.442338\pi\) | ||||
0.180160 | + | 0.983637i | \(0.442338\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.82136 | 0.233202 | 0.116601 | − | 0.993179i | \(-0.462800\pi\) | ||||
0.116601 | + | 0.993179i | \(0.462800\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.08193 | 0.262298 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.20932 | −0.274032 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.94750 | 0.970941 | 0.485471 | − | 0.874253i | \(-0.338648\pi\) | ||||
0.485471 | + | 0.874253i | \(0.338648\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.58595 | 0.672469 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.7260 | 1.62898 | 0.814490 | − | 0.580177i | \(-0.197017\pi\) | ||||
0.814490 | + | 0.580177i | \(0.197017\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.62552 | −0.424335 | −0.212167 | − | 0.977233i | \(-0.568052\pi\) | ||||
−0.212167 | + | 0.977233i | \(0.568052\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −9.88622 | −1.14156 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.37495 | −0.384611 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.00000 | −0.112509 | ||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.48616 | −0.942906 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.7858 | −1.40342 | −0.701712 | − | 0.712461i | \(-0.747581\pi\) | ||||
−0.701712 | + | 0.712461i | \(0.747581\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.97330 | −0.539430 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −8.13186 | −0.871827 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.3744 | 1.09969 | 0.549844 | − | 0.835267i | \(-0.314687\pi\) | ||||
0.549844 | + | 0.835267i | \(0.314687\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.44186 | −0.151148 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −16.5892 | −1.72022 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.00873 | 0.103493 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.58998 | 0.872180 | 0.436090 | − | 0.899903i | \(-0.356363\pi\) | ||||
0.436090 | + | 0.899903i | \(0.356363\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −16.2128 | −1.62945 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.57318 | −0.853063 | −0.426531 | − | 0.904473i | \(-0.640265\pi\) | ||||
−0.426531 | + | 0.904473i | \(0.640265\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.43742 | 0.338699 | 0.169349 | − | 0.985556i | \(-0.445833\pi\) | ||||
0.169349 | + | 0.985556i | \(0.445833\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.64850 | 0.160877 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.52295 | 0.630597 | 0.315299 | − | 0.948992i | \(-0.397895\pi\) | ||||
0.315299 | + | 0.948992i | \(0.397895\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.73287 | 0.932239 | 0.466120 | − | 0.884722i | \(-0.345652\pi\) | ||||
0.466120 | + | 0.884722i | \(0.345652\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 11.8035 | 1.12034 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 15.0997 | 1.42046 | 0.710229 | − | 0.703971i | \(-0.248591\pi\) | ||||
0.710229 | + | 0.703971i | \(0.248591\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.26983 | 0.211662 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −6.92648 | −0.640354 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.24570 | −0.297533 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 15.2821 | 1.38928 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −15.6328 | −1.40956 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.06086 | −0.810428 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.4992 | −1.10913 | −0.554564 | − | 0.832141i | \(-0.687115\pi\) | ||||
−0.554564 | + | 0.832141i | \(0.687115\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −18.2714 | −1.60871 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.20572 | −0.629567 | −0.314784 | − | 0.949163i | \(-0.601932\pi\) | ||||
−0.314784 | + | 0.949163i | \(0.601932\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.658321 | 0.0570836 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.406869 | 0.0350177 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.01038 | −0.684373 | −0.342186 | − | 0.939632i | \(-0.611167\pi\) | ||||
−0.342186 | + | 0.939632i | \(0.611167\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.63706 | −0.393311 | −0.196655 | − | 0.980473i | \(-0.563008\pi\) | ||||
−0.196655 | + | 0.980473i | \(0.563008\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −20.9918 | −1.76783 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 11.2283 | 0.938959 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.30435 | −0.274411 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −16.3012 | −1.34450 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −15.7408 | −1.28953 | −0.644766 | − | 0.764380i | \(-0.723045\pi\) | ||||
−0.644766 | + | 0.764380i | \(0.723045\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.04777 | 0.166645 | 0.0833225 | − | 0.996523i | \(-0.473447\pi\) | ||||
0.0833225 | + | 0.996523i | \(0.473447\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −15.5919 | −1.26053 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.74095 | −0.541446 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.50123 | 0.199620 | 0.0998101 | − | 0.995007i | \(-0.468176\pi\) | ||||
0.0998101 | + | 0.995007i | \(0.468176\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 15.4329 | 1.22391 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.48135 | 0.116746 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.69880 | −0.133060 | −0.0665301 | − | 0.997784i | \(-0.521193\pi\) | ||||
−0.0665301 | + | 0.997784i | \(0.521193\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −12.8375 | −0.999399 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.70694 | 0.286852 | 0.143426 | − | 0.989661i | \(-0.454188\pi\) | ||||
0.143426 | + | 0.989661i | \(0.454188\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.20300 | −0.631000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.16248 | 0.241841 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −19.0688 | −1.44977 | −0.724887 | − | 0.688868i | \(-0.758108\pi\) | ||||
−0.724887 | + | 0.688868i | \(0.758108\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.62174 | −0.198185 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.87056 | 0.516423 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.66901 | −0.573209 | −0.286604 | − | 0.958049i | \(-0.592527\pi\) | ||||
−0.286604 | + | 0.958049i | \(0.592527\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.381147 | −0.0283304 | −0.0141652 | − | 0.999900i | \(-0.504509\pi\) | ||||
−0.0141652 | + | 0.999900i | \(0.504509\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.52142 | 0.334233 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.79629 | 0.352630 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 25.2756 | 1.84833 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.265533 | 0.0193147 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.4223 | −0.754134 | −0.377067 | − | 0.926186i | \(-0.623067\pi\) | ||||
−0.377067 | + | 0.926186i | \(0.623067\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.46346 | 0.537231 | 0.268616 | − | 0.963247i | \(-0.413434\pi\) | ||||
0.268616 | + | 0.963247i | \(0.413434\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.48449 | −0.392752 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 22.3967 | 1.59570 | 0.797850 | − | 0.602856i | \(-0.205971\pi\) | ||||
0.797850 | + | 0.602856i | \(0.205971\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 24.3863 | 1.72870 | 0.864348 | − | 0.502894i | \(-0.167731\pi\) | ||||
0.864348 | + | 0.502894i | \(0.167731\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 19.7291 | 1.39159 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.15650 | −0.151357 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.35232 | −0.443666 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.11618 | 0.494609 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.12660 | −0.354615 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.68729 | 0.666901 | 0.333450 | − | 0.942768i | \(-0.391787\pi\) | ||||
0.333450 | + | 0.942768i | \(0.391787\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 34.0740 | 2.33471 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −7.42449 | −0.506346 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.39931 | −0.298645 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −9.00011 | −0.608171 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10.7983 | 0.726373 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.7265 | 1.25402 | 0.627009 | − | 0.779012i | \(-0.284279\pi\) | ||||
0.627009 | + | 0.779012i | \(0.284279\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −12.5945 | −0.839633 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.30619 | −0.153067 | −0.0765337 | − | 0.997067i | \(-0.524385\pi\) | ||||
−0.0765337 | + | 0.997067i | \(0.524385\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 20.6903 | 1.36725 | 0.683625 | − | 0.729833i | \(-0.260402\pi\) | ||||
0.683625 | + | 0.729833i | \(0.260402\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.37809 | −0.551238 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −24.6222 | −1.61306 | −0.806528 | − | 0.591196i | \(-0.798656\pi\) | ||||
−0.806528 | + | 0.591196i | \(0.798656\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.52991 | −0.556430 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.48243 | −0.161251 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 23.9200 | 1.54726 | 0.773629 | − | 0.633638i | \(-0.218439\pi\) | ||||
0.773629 | + | 0.633638i | \(0.218439\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.80322 | 0.567065 | 0.283533 | − | 0.958963i | \(-0.408494\pi\) | ||||
0.283533 | + | 0.958963i | \(0.408494\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −22.2764 | −1.42903 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.62392 | −0.423187 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.19021 | −0.139359 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −31.7399 | −2.01144 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.6885 | 0.674651 | 0.337326 | − | 0.941388i | \(-0.390478\pi\) | ||||
0.337326 | + | 0.941388i | \(0.390478\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −11.5358 | −0.725251 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −12.3459 | −0.773129 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.6042 | 0.910983 | 0.455492 | − | 0.890240i | \(-0.349464\pi\) | ||||
0.455492 | + | 0.890240i | \(0.349464\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.13018 | 0.194500 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −10.3595 | −0.641239 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.2383 | 0.754645 | 0.377322 | − | 0.926082i | \(-0.376845\pi\) | ||||
0.377322 | + | 0.926082i | \(0.376845\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.27108 | 0.385229 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 25.7539 | 1.57611 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.76623 | −0.290602 | −0.145301 | − | 0.989387i | \(-0.546415\pi\) | ||||
−0.145301 | + | 0.989387i | \(0.546415\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.12888 | 0.372303 | 0.186151 | − | 0.982521i | \(-0.440399\pi\) | ||||
0.186151 | + | 0.982521i | \(0.440399\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.57932 | −0.216630 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 20.4165 | 1.23116 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −12.5312 | −0.752924 | −0.376462 | − | 0.926432i | \(-0.622860\pi\) | ||||
−0.376462 | + | 0.926432i | \(0.622860\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −21.1337 | −1.26524 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.2783 | −0.792115 | −0.396058 | − | 0.918226i | \(-0.629622\pi\) | ||||
−0.396058 | + | 0.918226i | \(0.629622\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −28.2298 | −1.67809 | −0.839044 | − | 0.544064i | \(-0.816885\pi\) | ||||
−0.839044 | + | 0.544064i | \(0.816885\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.50410 | 0.148330 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.14569 | −0.244712 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.30761 | 0.429859 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 21.3241 | 1.25004 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −9.45824 | −0.552557 | −0.276278 | − | 0.961078i | \(-0.589101\pi\) | ||||
−0.276278 | + | 0.961078i | \(0.589101\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.79182 | 0.162546 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.06781 | −0.119987 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.92838 | −0.285015 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.84541 | −0.279285 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −21.2823 | −1.22264 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.83726 | 0.105201 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.5716 | 0.717501 | 0.358750 | − | 0.933433i | \(-0.383203\pi\) | ||||
0.358750 | + | 0.933433i | \(0.383203\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.53316 | 0.485435 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.56292 | −0.315444 | −0.157722 | − | 0.987484i | \(-0.550415\pi\) | ||||
−0.157722 | + | 0.987484i | \(0.550415\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.74202 | −0.437605 | −0.218802 | − | 0.975769i | \(-0.570215\pi\) | ||||
−0.218802 | + | 0.975769i | \(0.570215\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.10009 | 0.118327 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −21.6671 | −1.21695 | −0.608474 | − | 0.793574i | \(-0.708218\pi\) | ||||
−0.608474 | + | 0.793574i | \(0.708218\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 16.7935 | 0.940257 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 16.1928 | 0.903794 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.93027 | −0.274328 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.72243 | 0.483833 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 24.1612 | 1.33612 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.56684 | −0.306910 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.7476 | −1.08543 | −0.542714 | − | 0.839918i | \(-0.682603\pi\) | ||||
−0.542714 | + | 0.839918i | \(0.682603\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 15.0369 | 0.824020 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8.01685 | 0.438007 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.89769 | −0.157847 | −0.0789237 | − | 0.996881i | \(-0.525148\pi\) | ||||
−0.0789237 | + | 0.996881i | \(0.525148\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 37.4840 | 2.03585 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 34.2592 | 1.85524 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.93118 | −0.482238 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5.63469 | 0.303362 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 15.4000 | 0.826717 | 0.413358 | − | 0.910568i | \(-0.364356\pi\) | ||||
0.413358 | + | 0.910568i | \(0.364356\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.82234 | −0.472249 | −0.236125 | − | 0.971723i | \(-0.575877\pi\) | ||||
−0.236125 | + | 0.971723i | \(0.575877\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.883417 | −0.0471533 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 18.8313 | 1.00229 | 0.501144 | − | 0.865364i | \(-0.332913\pi\) | ||||
0.501144 | + | 0.865364i | \(0.332913\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 13.8458 | 0.734860 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −8.05724 | −0.426434 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6.38897 | −0.337197 | −0.168598 | − | 0.985685i | \(-0.553924\pi\) | ||||
−0.168598 | + | 0.985685i | \(0.553924\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 37.9367 | 1.99116 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.65716 | −0.191424 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.70570 | 0.297835 | 0.148918 | − | 0.988850i | \(-0.452421\pi\) | ||||
0.148918 | + | 0.988850i | \(0.452421\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −19.9153 | −1.03675 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.09267 | 0.212481 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 17.1999 | 0.890579 | 0.445290 | − | 0.895387i | \(-0.353101\pi\) | ||||
0.445290 | + | 0.895387i | \(0.353101\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −22.4930 | −1.16153 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7.17459 | 0.369510 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 17.6285 | 0.905517 | 0.452758 | − | 0.891633i | \(-0.350440\pi\) | ||||
0.452758 | + | 0.891633i | \(0.350440\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −31.0285 | −1.58964 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −30.5078 | −1.55888 | −0.779438 | − | 0.626480i | \(-0.784495\pi\) | ||||
−0.779438 | + | 0.626480i | \(0.784495\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.40440 | −0.173504 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −23.2767 | −1.18322 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −22.4593 | −1.13873 | −0.569366 | − | 0.822084i | \(-0.692811\pi\) | ||||
−0.569366 | + | 0.822084i | \(0.692811\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11.0941 | −0.561050 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −17.8877 | −0.902317 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.00873 | −0.0507545 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.91050 | −0.296640 | −0.148320 | − | 0.988939i | \(-0.547386\pi\) | ||||
−0.148320 | + | 0.988939i | \(0.547386\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.63424 | 0.0818142 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9.45266 | −0.472043 | −0.236022 | − | 0.971748i | \(-0.575844\pi\) | ||||
−0.236022 | + | 0.971748i | \(0.575844\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 14.6363 | 0.729088 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −8.56021 | −0.425360 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −24.3759 | −1.20827 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.79901 | 0.237296 | 0.118648 | − | 0.992936i | \(-0.462144\pi\) | ||||
0.118648 | + | 0.992936i | \(0.462144\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −19.8852 | −0.980867 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.82201 | 0.0896555 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.8974 | −0.633107 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −11.5112 | −0.563706 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13.2479 | −0.647202 | −0.323601 | − | 0.946194i | \(-0.604894\pi\) | ||||
−0.323601 | + | 0.946194i | \(0.604894\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 29.4889 | 1.43720 | 0.718601 | − | 0.695422i | \(-0.244783\pi\) | ||||
0.718601 | + | 0.695422i | \(0.244783\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −26.7423 | −1.30026 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 19.6347 | 0.952422 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.19904 | 0.0580257 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 27.8736 | 1.34575 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −30.9365 | −1.49016 | −0.745079 | − | 0.666977i | \(-0.767588\pi\) | ||||
−0.745079 | + | 0.666977i | \(0.767588\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 21.2939 | 1.02332 | 0.511659 | − | 0.859188i | \(-0.329031\pi\) | ||||
0.511659 | + | 0.859188i | \(0.329031\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −8.20283 | −0.393295 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.25019 | 0.107641 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −19.7974 | −0.944881 | −0.472440 | − | 0.881363i | \(-0.656627\pi\) | ||||
−0.472440 | + | 0.881363i | \(0.656627\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −20.7668 | −0.988895 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −24.0702 | −1.14361 | −0.571806 | − | 0.820389i | \(-0.693757\pi\) | ||||
−0.571806 | + | 0.820389i | \(0.693757\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.4650 | 0.496087 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −39.0754 | −1.84820 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.00537 | 0.0946390 | 0.0473195 | − | 0.998880i | \(-0.484932\pi\) | ||||
0.0473195 | + | 0.998880i | \(0.484932\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 32.2841 | 1.52020 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.08345 | 0.238841 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.45444 | −0.0681852 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.8639 | −0.508193 | −0.254096 | − | 0.967179i | \(-0.581778\pi\) | ||||
−0.254096 | + | 0.967179i | \(0.581778\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.98862 | −0.0928209 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15.4497 | 0.719564 | 0.359782 | − | 0.933036i | \(-0.382851\pi\) | ||||
0.359782 | + | 0.933036i | \(0.382851\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −18.7008 | −0.869100 | −0.434550 | − | 0.900648i | \(-0.643092\pi\) | ||||
−0.434550 | + | 0.900648i | \(0.643092\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −16.7340 | −0.776019 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 22.0548 | 1.02057 | 0.510287 | − | 0.860004i | \(-0.329539\pi\) | ||||
0.510287 | + | 0.860004i | \(0.329539\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.23200 | 0.241591 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.20915 | 0.286103 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 37.7332 | 1.73497 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.98247 | −0.182728 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 19.6606 | 0.900197 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −12.6854 | −0.579611 | −0.289806 | − | 0.957085i | \(-0.593591\pi\) | ||||
−0.289806 | + | 0.957085i | \(0.593591\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.4140 | −0.474837 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.67734 | 0.167325 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.66494 | 0.393455 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −25.4984 | −1.15544 | −0.577722 | − | 0.816234i | \(-0.696058\pi\) | ||||
−0.577722 | + | 0.816234i | \(0.696058\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.21715 | −0.190706 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 24.9883 | 1.12771 | 0.563853 | − | 0.825875i | \(-0.309318\pi\) | ||||
0.563853 | + | 0.825875i | \(0.309318\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 16.1504 | 0.727378 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −16.3543 | −0.735069 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9.03613 | 0.405326 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −23.3219 | −1.04403 | −0.522016 | − | 0.852935i | \(-0.674820\pi\) | ||||
−0.522016 | + | 0.852935i | \(0.674820\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9.20223 | 0.411126 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −11.6957 | −0.521487 | −0.260744 | − | 0.965408i | \(-0.583968\pi\) | ||||
−0.260744 | + | 0.965408i | \(0.583968\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.64799 | −0.384830 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −20.3634 | −0.904371 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −14.9289 | −0.661710 | −0.330855 | − | 0.943682i | \(-0.607337\pi\) | ||||
−0.330855 | + | 0.943682i | \(0.607337\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.38675 | −0.105584 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.403349 | 0.0178083 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.46741 | 0.152792 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 43.3512 | 1.90658 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −47.3370 | −2.07786 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 28.4538 | 1.24658 | 0.623291 | − | 0.781990i | \(-0.285795\pi\) | ||||
0.623291 | + | 0.781990i | \(0.285795\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.27044 | 0.274187 | 0.137094 | − | 0.990558i | \(-0.456224\pi\) | ||||
0.137094 | + | 0.990558i | \(0.456224\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −6.50830 | −0.284046 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 32.9472 | 1.43520 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.9366 | −0.779854 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.75271 | 0.379835 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13.7925 | 0.597421 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.57987 | 0.284473 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −19.0378 | −0.821542 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 33.6644 | 1.45003 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.76648 | −0.204927 | −0.102464 | − | 0.994737i | \(-0.532672\pi\) | ||||
−0.102464 | + | 0.994737i | \(0.532672\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.946173 | −0.0406042 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9.81780 | 0.420548 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.37305 | −0.144221 | −0.0721106 | − | 0.997397i | \(-0.522973\pi\) | ||||
−0.0721106 | + | 0.997397i | \(0.522973\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.76003 | 0.245832 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.27576 | −0.139552 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.658321 | −0.0279946 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 11.9065 | 0.505401 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −45.3138 | −1.92001 | −0.960003 | − | 0.279990i | \(-0.909669\pi\) | ||||
−0.960003 | + | 0.279990i | \(0.909669\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 16.1205 | 0.681824 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 62.7449 | 2.64909 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.07491 | −0.213882 | −0.106941 | − | 0.994265i | \(-0.534106\pi\) | ||||
−0.106941 | + | 0.994265i | \(0.534106\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 15.2314 | 0.640791 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −5.58661 | −0.234616 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −21.8671 | −0.916718 | −0.458359 | − | 0.888767i | \(-0.651563\pi\) | ||||
−0.458359 | + | 0.888767i | \(0.651563\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 22.5429 | 0.943389 | 0.471695 | − | 0.881762i | \(-0.343642\pi\) | ||||
0.471695 | + | 0.881762i | \(0.343642\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −25.8728 | −1.08085 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.96131 | −0.373713 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −39.0368 | −1.62512 | −0.812562 | − | 0.582874i | \(-0.801928\pi\) | ||||
−0.812562 | + | 0.582874i | \(0.801928\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 18.5275 | 0.769978 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.41716 | −0.349203 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −31.8712 | −1.31997 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −6.98693 | −0.288874 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −12.5986 | −0.520002 | −0.260001 | − | 0.965608i | \(-0.583723\pi\) | ||||
−0.260001 | + | 0.965608i | \(0.583723\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.68263 | −0.275353 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 55.5984 | 2.28701 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 27.3483 | 1.12306 | 0.561530 | − | 0.827457i | \(-0.310213\pi\) | ||||
0.561530 | + | 0.827457i | \(0.310213\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.27402 | −0.134222 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 60.5373 | 2.47763 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −17.0298 | −0.695818 | −0.347909 | − | 0.937528i | \(-0.613108\pi\) | ||||
−0.347909 | + | 0.937528i | \(0.613108\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.57587 | 0.349817 | 0.174909 | − | 0.984585i | \(-0.444037\pi\) | ||||
0.174909 | + | 0.984585i | \(0.444037\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 25.1338 | 1.02353 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 15.4154 | 0.626726 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 41.0258 | 1.66519 | 0.832594 | − | 0.553884i | \(-0.186855\pi\) | ||||
0.832594 | + | 0.553884i | \(0.186855\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.35337 | −0.216930 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 18.5206 | 0.749265 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −33.2855 | −1.34439 | −0.672193 | − | 0.740376i | \(-0.734648\pi\) | ||||
−0.672193 | + | 0.740376i | \(0.734648\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −15.7692 | −0.635877 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 37.8994 | 1.52577 | 0.762887 | − | 0.646532i | \(-0.223781\pi\) | ||||
0.762887 | + | 0.646532i | \(0.223781\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.58989 | −0.0639029 | −0.0319515 | − | 0.999489i | \(-0.510172\pi\) | ||||
−0.0319515 | + | 0.999489i | \(0.510172\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.907612 | 0.0364212 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.82971 | 0.273627 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 10.7724 | 0.430897 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −12.7265 | −0.508246 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −23.4424 | −0.934711 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21.3500 | −0.849929 | −0.424965 | − | 0.905210i | \(-0.639713\pi\) | ||||
−0.424965 | + | 0.905210i | \(0.639713\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 24.0481 | 0.955825 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −12.6083 | −0.500345 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 14.3822 | 0.569845 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 43.4083 | 1.71721 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.25486 | −0.365545 | −0.182773 | − | 0.983155i | \(-0.558507\pi\) | ||||
−0.182773 | + | 0.983155i | \(0.558507\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 36.9308 | 1.45641 | 0.728204 | − | 0.685360i | \(-0.240355\pi\) | ||||
0.728204 | + | 0.685360i | \(0.240355\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −18.4308 | −0.725713 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.43717 | 0.174443 | 0.0872215 | − | 0.996189i | \(-0.472201\pi\) | ||||
0.0872215 | + | 0.996189i | \(0.472201\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −14.1887 | −0.556957 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −10.9210 | −0.428028 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −31.7716 | −1.24332 | −0.621660 | − | 0.783287i | \(-0.713541\pi\) | ||||
−0.621660 | + | 0.783287i | \(0.713541\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.26860 | −0.284008 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −11.4656 | −0.447317 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −18.8368 | −0.733778 | −0.366889 | − | 0.930265i | \(-0.619577\pi\) | ||||
−0.366889 | + | 0.930265i | \(0.619577\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.00428 | 0.0779576 | 0.0389788 | − | 0.999240i | \(-0.487590\pi\) | ||||
0.0389788 | + | 0.999240i | \(0.487590\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 26.8061 | 1.04106 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.664065 | 0.0257513 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.37108 | −0.285410 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 46.4873 | 1.79730 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.33741 | −0.360467 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17.5254 | 0.675555 | 0.337778 | − | 0.941226i | \(-0.390325\pi\) | ||||
0.337778 | + | 0.941226i | \(0.390325\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.60633 | −0.0618275 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −10.0753 | −0.387227 | −0.193614 | − | 0.981078i | \(-0.562021\pi\) | ||||
−0.193614 | + | 0.981078i | \(0.562021\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.65496 | 0.217017 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.72497 | −0.219382 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6.96926 | −0.266671 | −0.133336 | − | 0.991071i | \(-0.542569\pi\) | ||||
−0.133336 | + | 0.991071i | \(0.542569\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.08028 | −0.308732 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 51.3622 | 1.95959 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −13.6161 | −0.518733 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −36.3762 | −1.38382 | −0.691908 | − | 0.721985i | \(-0.743230\pi\) | ||||
−0.691908 | + | 0.721985i | \(0.743230\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −10.6732 | −0.405442 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.67753 | −0.177429 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 31.0478 | 1.17602 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −61.1230 | −2.31189 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 20.7487 | 0.783668 | 0.391834 | − | 0.920036i | \(-0.371841\pi\) | ||||
0.391834 | + | 0.920036i | \(0.371841\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.75479 | 0.179330 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −21.1749 | −0.797495 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −5.64390 | −0.212261 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16.7842 | 0.630345 | 0.315172 | − | 0.949034i | \(-0.397938\pi\) | ||||
0.315172 | + | 0.949034i | \(0.397938\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.16248 | −0.118602 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −15.0372 | −0.563147 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 11.3263 | 0.423579 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 59.3799 | 2.21758 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −12.4046 | −0.462615 | −0.231307 | − | 0.972881i | \(-0.574300\pi\) | ||||
−0.231307 | + | 0.972881i | \(0.574300\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.26292 | 0.0842756 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 21.8534 | 0.812738 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 13.0456 | 0.484502 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −44.4741 | −1.64945 | −0.824727 | − | 0.565530i | \(-0.808671\pi\) | ||||
−0.824727 | + | 0.565530i | \(0.808671\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −29.8412 | −1.10523 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 36.2881 | 1.34217 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −20.2150 | −0.746656 | −0.373328 | − | 0.927699i | \(-0.621783\pi\) | ||||
−0.373328 | + | 0.927699i | \(0.621783\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −16.4434 | −0.606525 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −40.7437 | −1.50081 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 40.0180 | 1.47209 | 0.736043 | − | 0.676935i | \(-0.236692\pi\) | ||||
0.736043 | + | 0.676935i | \(0.236692\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.43704 | −0.199735 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 13.4838 | 0.494673 | 0.247337 | − | 0.968930i | \(-0.420445\pi\) | ||||
0.247337 | + | 0.968930i | \(0.420445\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15.8781 | −0.581729 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −40.4349 | −1.47943 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.29419 | 0.156906 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −25.4034 | −0.926984 | −0.463492 | − | 0.886101i | \(-0.653404\pi\) | ||||
−0.463492 | + | 0.886101i | \(0.653404\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 26.5335 | 0.966933 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.06564 | 0.0751762 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −28.1858 | −1.02443 | −0.512215 | − | 0.858857i | \(-0.671175\pi\) | ||||
−0.512215 | + | 0.858857i | \(0.671175\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −28.6369 | −1.03945 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −28.9203 | −1.04836 | −0.524179 | − | 0.851608i | \(-0.675628\pi\) | ||||
−0.524179 | + | 0.851608i | \(0.675628\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.40734 | 0.231961 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −15.7280 | −0.568646 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6.06177 | −0.218878 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −24.2439 | −0.874256 | −0.437128 | − | 0.899399i | \(-0.644004\pi\) | ||||
−0.437128 | + | 0.899399i | \(0.644004\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 36.2539 | 1.30565 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 13.2842 | 0.477801 | 0.238901 | − | 0.971044i | \(-0.423213\pi\) | ||||
0.238901 | + | 0.971044i | \(0.423213\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 26.6134 | 0.955981 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7.77046 | 0.278764 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.29737 | −0.225627 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −70.3679 | −2.51796 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.32128 | −0.0472185 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.52306 | 0.0900519 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 51.9098 | 1.85038 | 0.925192 | − | 0.379498i | \(-0.123903\pi\) | ||||
0.925192 | + | 0.379498i | \(0.123903\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 30.3807 | 1.08158 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.94042 | 0.353441 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.98916 | −0.141659 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 15.5675 | 0.552124 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −19.9085 | −0.705197 | −0.352598 | − | 0.935775i | \(-0.614702\pi\) | ||||
−0.352598 | + | 0.935775i | \(0.614702\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 41.6910 | 1.47492 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 32.8090 | 1.15925 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 18.5866 | 0.655906 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.49427 | 0.0526662 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −11.8319 | −0.416501 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 7.23883 | 0.254504 | 0.127252 | − | 0.991870i | \(-0.459384\pi\) | ||||
0.127252 | + | 0.991870i | \(0.459384\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.70986 | 0.340959 | 0.170480 | − | 0.985361i | \(-0.445468\pi\) | ||||
0.170480 | + | 0.985361i | \(0.445468\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 15.2145 | 0.533597 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.71362 | −0.0600256 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.36027 | −0.257503 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.55985 | −0.159334 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −30.3133 | −1.05794 | −0.528970 | − | 0.848640i | \(-0.677422\pi\) | ||||
−0.528970 | + | 0.848640i | \(0.677422\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 22.4937 | 0.784083 | 0.392041 | − | 0.919948i | \(-0.371769\pi\) | ||||
0.392041 | + | 0.919948i | \(0.371769\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 50.6827 | 1.76455 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −31.3105 | −1.08877 | −0.544386 | − | 0.838835i | \(-0.683237\pi\) | ||||
−0.544386 | + | 0.838835i | \(0.683237\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −0.349214 | −0.0121287 | −0.00606435 | − | 0.999982i | \(-0.501930\pi\) | ||||
−0.00606435 | + | 0.999982i | \(0.501930\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −31.1078 | −1.07912 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 32.3752 | 1.12173 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.73929 | 0.129403 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.69543 | −0.0931678 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 27.1615 | 0.937720 | 0.468860 | − | 0.883273i | \(-0.344665\pi\) | ||||
0.468860 | + | 0.883273i | \(0.344665\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.2694 | −0.629979 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −32.9624 | −1.13529 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −8.27458 | −0.284654 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.0605 | 0.345683 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −70.0786 | −2.40509 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10.6992 | 0.366763 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.70825 | −0.263926 | −0.131963 | − | 0.991255i | \(-0.542128\pi\) | ||||
−0.131963 | + | 0.991255i | \(0.542128\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.19008 | 0.109098 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 44.6750 | 1.52607 | 0.763034 | − | 0.646358i | \(-0.223709\pi\) | ||||
0.763034 | + | 0.646358i | \(0.223709\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 29.2965 | 0.999583 | 0.499791 | − | 0.866146i | \(-0.333410\pi\) | ||||
0.499791 | + | 0.866146i | \(0.333410\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −10.2914 | −0.350730 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −32.3740 | −1.10202 | −0.551011 | − | 0.834498i | \(-0.685758\pi\) | ||||
−0.551011 | + | 0.834498i | \(0.685758\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −19.2352 | −0.654016 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 18.1407 | 0.616089 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.12660 | 0.173908 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −17.4067 | −0.589802 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 27.1656 | 0.919418 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5.96495 | −0.201652 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.26761 | 0.0765717 | 0.0382859 | − | 0.999267i | \(-0.487810\pi\) | ||||
0.0382859 | + | 0.999267i | \(0.487810\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −23.4795 | −0.791943 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.18348 | 0.107254 | 0.0536271 | − | 0.998561i | \(-0.482922\pi\) | ||||
0.0536271 | + | 0.998561i | \(0.482922\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16.1955 | −0.545021 | −0.272510 | − | 0.962153i | \(-0.587854\pi\) | ||||
−0.272510 | + | 0.962153i | \(0.587854\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.93052 | 0.232967 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −12.2848 | −0.412483 | −0.206241 | − | 0.978501i | \(-0.566123\pi\) | ||||
−0.206241 | + | 0.978501i | \(0.566123\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.22850 | −0.275975 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 43.5051 | 1.45748 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −8.45612 | −0.282973 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.73593 | −0.258584 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −12.2344 | −0.408494 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 21.8907 | 0.730096 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −30.6507 | −1.02112 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −12.0284 | −0.400281 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.384473 | −0.0127803 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 38.1373 | 1.26633 | 0.633164 | − | 0.774018i | \(-0.281756\pi\) | ||||
0.633164 | + | 0.774018i | \(0.281756\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −27.1125 | −0.899265 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 59.0466 | 1.95630 | 0.978150 | − | 0.207899i | \(-0.0666624\pi\) | ||||
0.978150 | + | 0.207899i | \(0.0666624\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 65.5477 | 2.16931 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 4.56087 | 0.150778 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.74368 | −0.156650 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 48.6032 | 1.60327 | 0.801635 | − | 0.597814i | \(-0.203964\pi\) | ||||
0.801635 | + | 0.597814i | \(0.203964\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 31.2083 | 1.02835 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −30.0628 | −0.989530 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −18.9358 | −0.622606 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 10.8708 | 0.357043 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −36.1498 | −1.18604 | −0.593018 | − | 0.805189i | \(-0.702064\pi\) | ||||
−0.593018 | + | 0.805189i | \(0.702064\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.56661 | −0.215212 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −13.8096 | −0.452105 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 25.4961 | 0.833812 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.54777 | 0.0505633 | 0.0252817 | − | 0.999680i | \(-0.491952\pi\) | ||||
0.0252817 | + | 0.999680i | \(0.491952\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −19.2191 | −0.627190 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −46.3173 | −1.50990 | −0.754950 | − | 0.655782i | \(-0.772339\pi\) | ||||
−0.754950 | + | 0.655782i | \(0.772339\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −14.1703 | −0.461448 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.267850 | 0.00871316 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −47.0761 | −1.52977 | −0.764884 | − | 0.644169i | \(-0.777204\pi\) | ||||
−0.764884 | + | 0.644169i | \(0.777204\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.94063 | 0.257764 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −53.7872 | −1.74417 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 12.7537 | 0.413134 | 0.206567 | − | 0.978432i | \(-0.433771\pi\) | ||||
0.206567 | + | 0.978432i | \(0.433771\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −10.5133 | −0.340202 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 41.6888 | 1.34761 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.27340 | −0.170287 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.6576 | 0.440567 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 20.6287 | 0.664751 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 7.52859 | 0.242354 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9.92906 | −0.319297 | −0.159649 | − | 0.987174i | \(-0.551036\pi\) | ||||
−0.159649 | + | 0.987174i | \(0.551036\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −12.2391 | −0.393176 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 36.8091 | 1.18126 | 0.590630 | − | 0.806943i | \(-0.298879\pi\) | ||||
0.590630 | + | 0.806943i | \(0.298879\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.05267 | −0.0978642 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 21.6529 | 0.693447 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −31.2825 | −1.00082 | −0.500408 | − | 0.865790i | \(-0.666817\pi\) | ||||
−0.500408 | + | 0.865790i | \(0.666817\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −53.1856 | −1.69982 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 30.7800 | 0.982730 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 28.0864 | 0.895816 | 0.447908 | − | 0.894080i | \(-0.352169\pi\) | ||||
0.447908 | + | 0.894080i | \(0.352169\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 22.5922 | 0.719846 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −13.8193 | −0.439873 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −16.5620 | −0.526641 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13.2215 | −0.419995 | −0.209997 | − | 0.977702i | \(-0.567346\pi\) | ||||
−0.209997 | + | 0.977702i | \(0.567346\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −49.0222 | −1.55567 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 24.5991 | 0.779843 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 40.5073 | 1.28288 | 0.641440 | − | 0.767173i | \(-0.278337\pi\) | ||||
0.641440 | + | 0.767173i | \(0.278337\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.91784 | 0.0606778 |
(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 | 6004.2.a.g.1.25 | ✓ | 27 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6004.2.a.g.1.25 | ✓ | 27 | 1.1 | even | 1 | trivial |