Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2601,2,Mod(1,2601)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2601, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2601.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2601 = 3^{2} \cdot 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2601.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: | \(20.7690895657\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.8.4848615424.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 8x^{6} + 16x^{4} - 8x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 153) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(0.437573\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2601.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.72291 | −1.92538 | −0.962692 | − | 0.270598i | \(-0.912779\pi\) | ||||
−0.962692 | + | 0.270598i | \(0.912779\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 5.41421 | 2.70711 | ||||||||
\(5\) | −1.47363 | −0.659025 | −0.329513 | − | 0.944151i | \(-0.606884\pi\) | ||||
−0.329513 | + | 0.944151i | \(0.606884\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.37849 | −1.27695 | −0.638475 | − | 0.769642i | \(-0.720434\pi\) | ||||
−0.638475 | + | 0.769642i | \(0.720434\pi\) | |||||||
\(8\) | −9.29658 | −3.28684 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 4.01254 | 1.26888 | ||||||||
\(11\) | −3.55765 | −1.07267 | −0.536336 | − | 0.844005i | \(-0.680192\pi\) | ||||
−0.536336 | + | 0.844005i | \(0.680192\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.58579 | 0.439818 | 0.219909 | − | 0.975520i | \(-0.429424\pi\) | ||||
0.219909 | + | 0.975520i | \(0.429424\pi\) | |||||||
\(14\) | 9.19932 | 2.45862 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 14.4853 | 3.62132 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.58579 | 0.822636 | 0.411318 | − | 0.911492i | \(-0.365069\pi\) | ||||
0.411318 | + | 0.911492i | \(0.365069\pi\) | |||||||
\(20\) | −7.97852 | −1.78405 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 9.68714 | 2.06530 | ||||||||
\(23\) | 1.47363 | 0.307272 | 0.153636 | − | 0.988127i | \(-0.450902\pi\) | ||||
0.153636 | + | 0.988127i | \(0.450902\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.82843 | −0.565685 | ||||||||
\(26\) | −4.31795 | −0.846819 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −18.2919 | −3.45684 | ||||||||
\(29\) | 0.863230 | 0.160298 | 0.0801489 | − | 0.996783i | \(-0.474460\pi\) | ||||
0.0801489 | + | 0.996783i | \(0.474460\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.24718 | −0.583210 | −0.291605 | − | 0.956539i | \(-0.594189\pi\) | ||||
−0.291605 | + | 0.956539i | \(0.594189\pi\) | |||||||
\(32\) | −20.8489 | −3.68560 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.97863 | 0.841543 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.07401 | −1.16296 | −0.581480 | − | 0.813561i | \(-0.697526\pi\) | ||||
−0.581480 | + | 0.813561i | \(0.697526\pi\) | |||||||
\(38\) | −9.76376 | −1.58389 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 13.6997 | 2.16611 | ||||||||
\(41\) | −8.58892 | −1.34136 | −0.670682 | − | 0.741745i | \(-0.733998\pi\) | ||||
−0.670682 | + | 0.741745i | \(0.733998\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.07107 | −0.925829 | −0.462915 | − | 0.886403i | \(-0.653196\pi\) | ||||
−0.462915 | + | 0.886403i | \(0.653196\pi\) | |||||||
\(44\) | −19.2619 | −2.90383 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.01254 | −0.591617 | ||||||||
\(47\) | −7.70154 | −1.12338 | −0.561692 | − | 0.827346i | \(-0.689850\pi\) | ||||
−0.561692 | + | 0.827346i | \(0.689850\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.41421 | 0.630602 | ||||||||
\(50\) | 7.70154 | 1.08916 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 8.58579 | 1.19063 | ||||||||
\(53\) | 2.25573 | 0.309848 | 0.154924 | − | 0.987926i | \(-0.450487\pi\) | ||||
0.154924 | + | 0.987926i | \(0.450487\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.24264 | 0.706918 | ||||||||
\(56\) | 31.4084 | 4.19713 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.35049 | −0.308635 | ||||||||
\(59\) | 8.16872 | 1.06348 | 0.531738 | − | 0.846909i | \(-0.321539\pi\) | ||||
0.531738 | + | 0.846909i | \(0.321539\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.84776 | −0.236581 | −0.118291 | − | 0.992979i | \(-0.537741\pi\) | ||||
−0.118291 | + | 0.992979i | \(0.537741\pi\) | |||||||
\(62\) | 8.84175 | 1.12290 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 27.7990 | 3.47487 | ||||||||
\(65\) | −2.33686 | −0.289851 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.41421 | 0.417113 | 0.208556 | − | 0.978010i | \(-0.433124\pi\) | ||||
0.208556 | + | 0.978010i | \(0.433124\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −13.5563 | −1.62029 | ||||||||
\(71\) | −10.9258 | −1.29665 | −0.648326 | − | 0.761363i | \(-0.724530\pi\) | ||||
−0.648326 | + | 0.761363i | \(0.724530\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.02509 | −0.939265 | −0.469633 | − | 0.882862i | \(-0.655614\pi\) | ||||
−0.469633 | + | 0.882862i | \(0.655614\pi\) | |||||||
\(74\) | 19.2619 | 2.23915 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 19.4142 | 2.22696 | ||||||||
\(77\) | 12.0195 | 1.36975 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.68714 | 1.08989 | 0.544944 | − | 0.838472i | \(-0.316551\pi\) | ||||
0.544944 | + | 0.838472i | \(0.316551\pi\) | |||||||
\(80\) | −21.3459 | −2.38654 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 23.3868 | 2.58264 | ||||||||
\(83\) | 2.25573 | 0.247598 | 0.123799 | − | 0.992307i | \(-0.460492\pi\) | ||||
0.123799 | + | 0.992307i | \(0.460492\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 16.5309 | 1.78258 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 33.0740 | 3.52570 | ||||||||
\(89\) | −8.82940 | −0.935915 | −0.467957 | − | 0.883751i | \(-0.655010\pi\) | ||||
−0.467957 | + | 0.883751i | \(0.655010\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.35757 | −0.561626 | ||||||||
\(92\) | 7.97852 | 0.831819 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 20.9706 | 2.16295 | ||||||||
\(95\) | −5.28411 | −0.542138 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.448342 | −0.0455222 | −0.0227611 | − | 0.999741i | \(-0.507246\pi\) | ||||
−0.0227611 | + | 0.999741i | \(0.507246\pi\) | |||||||
\(98\) | −12.0195 | −1.21415 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −15.3137 | −1.53137 | ||||||||
\(101\) | 9.29658 | 0.925044 | 0.462522 | − | 0.886608i | \(-0.346945\pi\) | ||||
0.462522 | + | 0.886608i | \(0.346945\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.00000 | 0.0985329 | 0.0492665 | − | 0.998786i | \(-0.484312\pi\) | ||||
0.0492665 | + | 0.998786i | \(0.484312\pi\) | |||||||
\(104\) | −14.7424 | −1.44561 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.14214 | −0.596577 | ||||||||
\(107\) | −5.64167 | −0.545401 | −0.272700 | − | 0.962099i | \(-0.587917\pi\) | ||||
−0.272700 | + | 0.962099i | \(0.587917\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.6997 | 1.31219 | 0.656096 | − | 0.754678i | \(-0.272207\pi\) | ||||
0.656096 | + | 0.754678i | \(0.272207\pi\) | |||||||
\(110\) | −14.2752 | −1.36109 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −48.9384 | −4.62425 | ||||||||
\(113\) | 13.6202 | 1.28128 | 0.640640 | − | 0.767841i | \(-0.278669\pi\) | ||||
0.640640 | + | 0.767841i | \(0.278669\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.17157 | −0.202500 | ||||||||
\(116\) | 4.67371 | 0.433943 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −22.2426 | −2.04760 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.65685 | 0.150623 | ||||||||
\(122\) | 5.03127 | 0.455510 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −17.5809 | −1.57881 | ||||||||
\(125\) | 11.5362 | 1.03183 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.8995 | −1.14465 | −0.572323 | − | 0.820029i | \(-0.693957\pi\) | ||||
−0.572323 | + | 0.820029i | \(0.693957\pi\) | |||||||
\(128\) | −33.9962 | −3.00487 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 6.36304 | 0.558075 | ||||||||
\(131\) | 20.7355 | 1.81167 | 0.905834 | − | 0.423633i | \(-0.139245\pi\) | ||||
0.905834 | + | 0.423633i | \(0.139245\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −12.1146 | −1.05047 | ||||||||
\(134\) | −9.29658 | −0.803102 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.57368 | −0.561627 | −0.280813 | − | 0.959762i | \(-0.590604\pi\) | ||||
−0.280813 | + | 0.959762i | \(0.590604\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.7486 | 1.08132 | 0.540661 | − | 0.841240i | \(-0.318174\pi\) | ||||
0.540661 | + | 0.841240i | \(0.318174\pi\) | |||||||
\(140\) | 26.9554 | 2.27815 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 29.7499 | 2.49655 | ||||||||
\(143\) | −5.64167 | −0.471780 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.27208 | −0.105640 | ||||||||
\(146\) | 21.8516 | 1.80845 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −38.3002 | −3.14826 | ||||||||
\(149\) | 19.7210 | 1.61561 | 0.807805 | − | 0.589450i | \(-0.200656\pi\) | ||||
0.807805 | + | 0.589450i | \(0.200656\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.58579 | 0.210428 | 0.105214 | − | 0.994450i | \(-0.466447\pi\) | ||||
0.105214 | + | 0.994450i | \(0.466447\pi\) | |||||||
\(152\) | −33.3356 | −2.70387 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −32.7279 | −2.63729 | ||||||||
\(155\) | 4.78512 | 0.384350 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −20.7990 | −1.65994 | −0.829970 | − | 0.557808i | \(-0.811643\pi\) | ||||
−0.829970 | + | 0.557808i | \(0.811643\pi\) | |||||||
\(158\) | −26.3772 | −2.09845 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 30.7235 | 2.42890 | ||||||||
\(161\) | −4.97863 | −0.392371 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.67459 | −0.444468 | −0.222234 | − | 0.974993i | \(-0.571335\pi\) | ||||
−0.222234 | + | 0.974993i | \(0.571335\pi\) | |||||||
\(164\) | −46.5022 | −3.63122 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.14214 | −0.476722 | ||||||||
\(167\) | 17.7882 | 1.37650 | 0.688248 | − | 0.725476i | \(-0.258380\pi\) | ||||
0.688248 | + | 0.725476i | \(0.258380\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.4853 | −0.806560 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −32.8701 | −2.50632 | ||||||||
\(173\) | −24.0403 | −1.82775 | −0.913875 | − | 0.405995i | \(-0.866925\pi\) | ||||
−0.913875 | + | 0.405995i | \(0.866925\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9.55582 | 0.722352 | ||||||||
\(176\) | −51.5335 | −3.88449 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 24.0416 | 1.80200 | ||||||||
\(179\) | 23.1046 | 1.72692 | 0.863460 | − | 0.504417i | \(-0.168293\pi\) | ||||
0.863460 | + | 0.504417i | \(0.168293\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.09494 | −0.378704 | −0.189352 | − | 0.981909i | \(-0.560639\pi\) | ||||
−0.189352 | + | 0.981909i | \(0.560639\pi\) | |||||||
\(182\) | 14.5882 | 1.08135 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −13.6997 | −1.00995 | ||||||||
\(185\) | 10.4244 | 0.766420 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −41.6978 | −3.04112 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 14.3881 | 1.04382 | ||||||||
\(191\) | −1.78855 | −0.129415 | −0.0647075 | − | 0.997904i | \(-0.520611\pi\) | ||||
−0.0647075 | + | 0.997904i | \(0.520611\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −15.6788 | −1.12858 | −0.564291 | − | 0.825576i | \(-0.690850\pi\) | ||||
−0.564291 | + | 0.825576i | \(0.690850\pi\) | |||||||
\(194\) | 1.22079 | 0.0876477 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 23.8995 | 1.70711 | ||||||||
\(197\) | 6.86246 | 0.488930 | 0.244465 | − | 0.969658i | \(-0.421388\pi\) | ||||
0.244465 | + | 0.969658i | \(0.421388\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 25.0489 | 1.77567 | 0.887834 | − | 0.460165i | \(-0.152210\pi\) | ||||
0.887834 | + | 0.460165i | \(0.152210\pi\) | |||||||
\(200\) | 26.2947 | 1.85932 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −25.3137 | −1.78107 | ||||||||
\(203\) | −2.91642 | −0.204692 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 12.6569 | 0.883993 | ||||||||
\(206\) | −2.72291 | −0.189714 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 22.9706 | 1.59272 | ||||||||
\(209\) | −12.7570 | −0.882418 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.634051 | −0.0436498 | −0.0218249 | − | 0.999762i | \(-0.506948\pi\) | ||||
−0.0218249 | + | 0.999762i | \(0.506948\pi\) | |||||||
\(212\) | 12.2130 | 0.838792 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 15.3617 | 1.05011 | ||||||||
\(215\) | 8.94648 | 0.610145 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.9706 | 0.744730 | ||||||||
\(218\) | −37.3029 | −2.52647 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 28.3848 | 1.91370 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.07107 | 0.540479 | 0.270239 | − | 0.962793i | \(-0.412897\pi\) | ||||
0.270239 | + | 0.962793i | \(0.412897\pi\) | |||||||
\(224\) | 70.4378 | 4.70632 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −37.0865 | −2.46696 | ||||||||
\(227\) | 13.9778 | 0.927736 | 0.463868 | − | 0.885904i | \(-0.346461\pi\) | ||||
0.463868 | + | 0.885904i | \(0.346461\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.4142 | 1.15076 | 0.575382 | − | 0.817885i | \(-0.304853\pi\) | ||||
0.575382 | + | 0.817885i | \(0.304853\pi\) | |||||||
\(230\) | 5.91299 | 0.389891 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −8.02509 | −0.526873 | ||||||||
\(233\) | 19.5147 | 1.27845 | 0.639225 | − | 0.769020i | \(-0.279255\pi\) | ||||
0.639225 | + | 0.769020i | \(0.279255\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.3492 | 0.740339 | ||||||||
\(236\) | 44.2272 | 2.87894 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14.0817 | 0.910870 | 0.455435 | − | 0.890269i | \(-0.349484\pi\) | ||||
0.455435 | + | 0.890269i | \(0.349484\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −17.7122 | −1.14094 | −0.570472 | − | 0.821317i | \(-0.693240\pi\) | ||||
−0.570472 | + | 0.821317i | \(0.693240\pi\) | |||||||
\(242\) | −4.51146 | −0.290007 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −10.0042 | −0.640451 | ||||||||
\(245\) | −6.50490 | −0.415583 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.68629 | 0.361810 | ||||||||
\(248\) | 30.1876 | 1.91692 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −31.4119 | −1.98666 | ||||||||
\(251\) | −19.7210 | −1.24478 | −0.622390 | − | 0.782707i | \(-0.713838\pi\) | ||||
−0.622390 | + | 0.782707i | \(0.713838\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.24264 | −0.329602 | ||||||||
\(254\) | 35.1241 | 2.20388 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 36.9706 | 2.31066 | ||||||||
\(257\) | 13.6145 | 0.849251 | 0.424625 | − | 0.905369i | \(-0.360406\pi\) | ||||
0.424625 | + | 0.905369i | \(0.360406\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 23.8995 | 1.48504 | ||||||||
\(260\) | −12.6522 | −0.784658 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −56.4608 | −3.48816 | ||||||||
\(263\) | 18.1260 | 1.11770 | 0.558848 | − | 0.829270i | \(-0.311244\pi\) | ||||
0.558848 | + | 0.829270i | \(0.311244\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.32410 | −0.204198 | ||||||||
\(266\) | 32.9868 | 2.02255 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 18.4853 | 1.12917 | ||||||||
\(269\) | −9.80971 | −0.598109 | −0.299054 | − | 0.954236i | \(-0.596671\pi\) | ||||
−0.299054 | + | 0.954236i | \(0.596671\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 17.9289 | 1.08911 | 0.544553 | − | 0.838727i | \(-0.316699\pi\) | ||||
0.544553 | + | 0.838727i | \(0.316699\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 17.8995 | 1.08135 | ||||||||
\(275\) | 10.0625 | 0.606794 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 23.2555 | 1.39729 | 0.698644 | − | 0.715470i | \(-0.253787\pi\) | ||||
0.698644 | + | 0.715470i | \(0.253787\pi\) | |||||||
\(278\) | −34.7132 | −2.08196 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −46.2843 | −2.76601 | ||||||||
\(281\) | 18.3996 | 1.09763 | 0.548816 | − | 0.835943i | \(-0.315079\pi\) | ||||
0.548816 | + | 0.835943i | \(0.315079\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.93015 | 0.174179 | 0.0870897 | − | 0.996200i | \(-0.472243\pi\) | ||||
0.0870897 | + | 0.996200i | \(0.472243\pi\) | |||||||
\(284\) | −59.1545 | −3.51017 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 15.3617 | 0.908358 | ||||||||
\(287\) | 29.0176 | 1.71286 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | 3.46375 | 0.203398 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −43.4495 | −2.54269 | ||||||||
\(293\) | −12.6802 | −0.740784 | −0.370392 | − | 0.928876i | \(-0.620777\pi\) | ||||
−0.370392 | + | 0.928876i | \(0.620777\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.0376 | −0.700858 | ||||||||
\(296\) | 65.7641 | 3.82246 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −53.6985 | −3.11067 | ||||||||
\(299\) | 2.33686 | 0.135144 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 20.5111 | 1.18224 | ||||||||
\(302\) | −7.04085 | −0.405155 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 51.9411 | 2.97903 | ||||||||
\(305\) | 2.72291 | 0.155913 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 15.8995 | 0.907432 | 0.453716 | − | 0.891146i | \(-0.350098\pi\) | ||||
0.453716 | + | 0.891146i | \(0.350098\pi\) | |||||||
\(308\) | 65.0761 | 3.70805 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −13.0294 | −0.740022 | ||||||||
\(311\) | −10.4201 | −0.590870 | −0.295435 | − | 0.955363i | \(-0.595465\pi\) | ||||
−0.295435 | + | 0.955363i | \(0.595465\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 23.4412 | 1.32498 | 0.662488 | − | 0.749073i | \(-0.269501\pi\) | ||||
0.662488 | + | 0.749073i | \(0.269501\pi\) | |||||||
\(314\) | 56.6337 | 3.19602 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 52.4482 | 2.95044 | ||||||||
\(317\) | −0.863230 | −0.0484838 | −0.0242419 | − | 0.999706i | \(-0.507717\pi\) | ||||
−0.0242419 | + | 0.999706i | \(0.507717\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.07107 | −0.171947 | ||||||||
\(320\) | −40.9653 | −2.29003 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 13.5563 | 0.755466 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.48528 | −0.248799 | ||||||||
\(326\) | 15.4514 | 0.855773 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 79.8476 | 4.40885 | ||||||||
\(329\) | 26.0196 | 1.43451 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.14214 | −0.0627775 | −0.0313887 | − | 0.999507i | \(-0.509993\pi\) | ||||
−0.0313887 | + | 0.999507i | \(0.509993\pi\) | |||||||
\(332\) | 12.2130 | 0.670275 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −48.4357 | −2.65028 | ||||||||
\(335\) | −5.03127 | −0.274888 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −17.7122 | −0.964846 | −0.482423 | − | 0.875938i | \(-0.660243\pi\) | ||||
−0.482423 | + | 0.875938i | \(0.660243\pi\) | |||||||
\(338\) | 28.5504 | 1.55294 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 11.5523 | 0.625593 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.73606 | 0.471703 | ||||||||
\(344\) | 56.4402 | 3.04305 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 65.4595 | 3.51912 | ||||||||
\(347\) | −19.7675 | −1.06118 | −0.530588 | − | 0.847630i | \(-0.678029\pi\) | ||||
−0.530588 | + | 0.847630i | \(0.678029\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.72792 | −0.520724 | −0.260362 | − | 0.965511i | \(-0.583842\pi\) | ||||
−0.260362 | + | 0.965511i | \(0.583842\pi\) | |||||||
\(350\) | −26.0196 | −1.39081 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 74.1730 | 3.95343 | ||||||||
\(353\) | −16.5309 | −0.879853 | −0.439927 | − | 0.898034i | \(-0.644996\pi\) | ||||
−0.439927 | + | 0.898034i | \(0.644996\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 16.1005 | 0.854526 | ||||||||
\(356\) | −47.8043 | −2.53362 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −62.9117 | −3.32499 | ||||||||
\(359\) | −8.82940 | −0.465998 | −0.232999 | − | 0.972477i | \(-0.574854\pi\) | ||||
−0.232999 | + | 0.972477i | \(0.574854\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.14214 | −0.323270 | ||||||||
\(362\) | 13.8730 | 0.729150 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −29.0070 | −1.52038 | ||||||||
\(365\) | 11.8260 | 0.619000 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.84776 | 0.0964522 | 0.0482261 | − | 0.998836i | \(-0.484643\pi\) | ||||
0.0482261 | + | 0.998836i | \(0.484643\pi\) | |||||||
\(368\) | 21.3459 | 1.11273 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −28.3848 | −1.47565 | ||||||||
\(371\) | −7.62096 | −0.395661 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.0416 | 0.830604 | 0.415302 | − | 0.909684i | \(-0.363676\pi\) | ||||
0.415302 | + | 0.909684i | \(0.363676\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 71.5980 | 3.69238 | ||||||||
\(377\) | 1.36890 | 0.0705019 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.80591 | 0.298230 | 0.149115 | − | 0.988820i | \(-0.452358\pi\) | ||||
0.149115 | + | 0.988820i | \(0.452358\pi\) | |||||||
\(380\) | −28.6093 | −1.46763 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 4.87006 | 0.249174 | ||||||||
\(383\) | −3.19008 | −0.163006 | −0.0815028 | − | 0.996673i | \(-0.525972\pi\) | ||||
−0.0815028 | + | 0.996673i | \(0.525972\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −17.7122 | −0.902699 | ||||||||
\(386\) | 42.6918 | 2.17295 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2.42742 | −0.123233 | ||||||||
\(389\) | 2.72291 | 0.138057 | 0.0690284 | − | 0.997615i | \(-0.478010\pi\) | ||||
0.0690284 | + | 0.997615i | \(0.478010\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −41.0371 | −2.07269 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −18.6858 | −0.941379 | ||||||||
\(395\) | −14.2752 | −0.718264 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.35049 | −0.117968 | −0.0589839 | − | 0.998259i | \(-0.518786\pi\) | ||||
−0.0589839 | + | 0.998259i | \(0.518786\pi\) | |||||||
\(398\) | −68.2057 | −3.41884 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −40.9706 | −2.04853 | ||||||||
\(401\) | −13.9778 | −0.698016 | −0.349008 | − | 0.937120i | \(-0.613481\pi\) | ||||
−0.349008 | + | 0.937120i | \(0.613481\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.14933 | −0.256506 | ||||||||
\(404\) | 50.3337 | 2.50419 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 7.94113 | 0.394111 | ||||||||
\(407\) | 25.1668 | 1.24747 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 36.7990 | 1.81959 | 0.909796 | − | 0.415055i | \(-0.136238\pi\) | ||||
0.909796 | + | 0.415055i | \(0.136238\pi\) | |||||||
\(410\) | −34.4634 | −1.70203 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 5.41421 | 0.266739 | ||||||||
\(413\) | −27.5979 | −1.35801 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.32410 | −0.163174 | ||||||||
\(416\) | −33.0619 | −1.62099 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 34.7360 | 1.69899 | ||||||||
\(419\) | −38.8813 | −1.89948 | −0.949738 | − | 0.313047i | \(-0.898650\pi\) | ||||
−0.949738 | + | 0.313047i | \(0.898650\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.1716 | 0.495732 | 0.247866 | − | 0.968794i | \(-0.420271\pi\) | ||||
0.247866 | + | 0.968794i | \(0.420271\pi\) | |||||||
\(422\) | 1.72646 | 0.0840428 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −20.9706 | −1.01842 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.24264 | 0.302103 | ||||||||
\(428\) | −30.5452 | −1.47646 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −24.3604 | −1.17476 | ||||||||
\(431\) | −19.2619 | −0.927811 | −0.463906 | − | 0.885885i | \(-0.653552\pi\) | ||||
−0.463906 | + | 0.885885i | \(0.653552\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −40.7990 | −1.96067 | −0.980337 | − | 0.197330i | \(-0.936773\pi\) | ||||
−0.980337 | + | 0.197330i | \(0.936773\pi\) | |||||||
\(434\) | −29.8718 | −1.43389 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 74.1730 | 3.55224 | ||||||||
\(437\) | 5.28411 | 0.252773 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11.2723 | 0.537996 | 0.268998 | − | 0.963141i | \(-0.413308\pi\) | ||||
0.268998 | + | 0.963141i | \(0.413308\pi\) | |||||||
\(440\) | −48.7386 | −2.32352 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 15.4031 | 0.731822 | 0.365911 | − | 0.930650i | \(-0.380757\pi\) | ||||
0.365911 | + | 0.930650i | \(0.380757\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.0112 | 0.616792 | ||||||||
\(446\) | −21.9768 | −1.04063 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −93.9187 | −4.43724 | ||||||||
\(449\) | 14.2306 | 0.671583 | 0.335792 | − | 0.941936i | \(-0.390996\pi\) | ||||
0.335792 | + | 0.941936i | \(0.390996\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 30.5563 | 1.43884 | ||||||||
\(452\) | 73.7426 | 3.46856 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −38.0601 | −1.78625 | ||||||||
\(455\) | 7.89505 | 0.370126 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16.5563 | 0.774473 | 0.387237 | − | 0.921980i | \(-0.373430\pi\) | ||||
0.387237 | + | 0.921980i | \(0.373430\pi\) | |||||||
\(458\) | −47.4173 | −2.21566 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −11.7574 | −0.548190 | ||||||||
\(461\) | −12.6802 | −0.590575 | −0.295287 | − | 0.955409i | \(-0.595415\pi\) | ||||
−0.295287 | + | 0.955409i | \(0.595415\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 36.5269 | 1.69755 | 0.848775 | − | 0.528755i | \(-0.177341\pi\) | ||||
0.848775 | + | 0.528755i | \(0.177341\pi\) | |||||||
\(464\) | 12.5041 | 0.580490 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −53.1367 | −2.46151 | ||||||||
\(467\) | −19.0603 | −0.882007 | −0.441004 | − | 0.897505i | \(-0.645377\pi\) | ||||
−0.441004 | + | 0.897505i | \(0.645377\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −11.5349 | −0.532632 | ||||||||
\(470\) | −30.9028 | −1.42544 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −75.9411 | −3.49547 | ||||||||
\(473\) | 21.5987 | 0.993110 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −10.1421 | −0.465353 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −38.3431 | −1.75377 | ||||||||
\(479\) | −10.6729 | −0.487659 | −0.243830 | − | 0.969818i | \(-0.578404\pi\) | ||||
−0.243830 | + | 0.969818i | \(0.578404\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11.2179 | −0.511491 | ||||||||
\(482\) | 48.2287 | 2.19676 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 8.97056 | 0.407753 | ||||||||
\(485\) | 0.660688 | 0.0300003 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 25.6285 | 1.16134 | 0.580670 | − | 0.814139i | \(-0.302791\pi\) | ||||
0.580670 | + | 0.814139i | \(0.302791\pi\) | |||||||
\(488\) | 17.1778 | 0.777604 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 17.7122 | 0.800157 | ||||||||
\(491\) | 7.04085 | 0.317749 | 0.158875 | − | 0.987299i | \(-0.449213\pi\) | ||||
0.158875 | + | 0.987299i | \(0.449213\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −15.4832 | −0.696624 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −47.0363 | −2.11199 | ||||||||
\(497\) | 36.9127 | 1.65576 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.6942 | −0.568271 | −0.284135 | − | 0.958784i | \(-0.591707\pi\) | ||||
−0.284135 | + | 0.958784i | \(0.591707\pi\) | |||||||
\(500\) | 62.4593 | 2.79326 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 53.6985 | 2.39668 | ||||||||
\(503\) | 27.3451 | 1.21926 | 0.609629 | − | 0.792687i | \(-0.291318\pi\) | ||||
0.609629 | + | 0.792687i | \(0.291318\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −13.6997 | −0.609628 | ||||||||
\(506\) | 14.2752 | 0.634611 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −69.8406 | −3.09868 | ||||||||
\(509\) | 8.36223 | 0.370649 | 0.185325 | − | 0.982677i | \(-0.440666\pi\) | ||||
0.185325 | + | 0.982677i | \(0.440666\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 27.1127 | 1.19940 | ||||||||
\(512\) | −32.6749 | −1.44404 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −37.0711 | −1.63513 | ||||||||
\(515\) | −1.47363 | −0.0649357 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 27.3994 | 1.20502 | ||||||||
\(518\) | −65.0761 | −2.85928 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 21.7248 | 0.952694 | ||||||||
\(521\) | 24.0403 | 1.05322 | 0.526612 | − | 0.850106i | \(-0.323462\pi\) | ||||
0.526612 | + | 0.850106i | \(0.323462\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 31.5563 | 1.37986 | 0.689931 | − | 0.723875i | \(-0.257641\pi\) | ||||
0.689931 | + | 0.723875i | \(0.257641\pi\) | |||||||
\(524\) | 112.266 | 4.90438 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −49.3553 | −2.15200 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.8284 | −0.905584 | ||||||||
\(530\) | 9.05121 | 0.393159 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −65.5908 | −2.84372 | ||||||||
\(533\) | −13.6202 | −0.589956 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.31371 | 0.359433 | ||||||||
\(536\) | −31.7405 | −1.37098 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 26.7109 | 1.15159 | ||||||||
\(539\) | −15.7042 | −0.676428 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −20.0627 | −0.862564 | −0.431282 | − | 0.902217i | \(-0.641939\pi\) | ||||
−0.431282 | + | 0.902217i | \(0.641939\pi\) | |||||||
\(542\) | −48.8188 | −2.09695 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −20.1882 | −0.864768 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.6508 | 0.626421 | 0.313211 | − | 0.949684i | \(-0.398595\pi\) | ||||
0.313211 | + | 0.949684i | \(0.398595\pi\) | |||||||
\(548\) | −35.5913 | −1.52038 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −27.3994 | −1.16831 | ||||||||
\(551\) | 3.09536 | 0.131867 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −32.7279 | −1.39173 | ||||||||
\(554\) | −63.3225 | −2.69032 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 69.0237 | 2.92726 | ||||||||
\(557\) | −31.2733 | −1.32509 | −0.662547 | − | 0.749020i | \(-0.730524\pi\) | ||||
−0.662547 | + | 0.749020i | \(0.730524\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9.62742 | −0.407196 | ||||||||
\(560\) | 72.1169 | 3.04750 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −50.1005 | −2.11336 | ||||||||
\(563\) | −12.4867 | −0.526250 | −0.263125 | − | 0.964762i | \(-0.584753\pi\) | ||||
−0.263125 | + | 0.964762i | \(0.584753\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −20.0711 | −0.844396 | ||||||||
\(566\) | −7.97852 | −0.335362 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 101.572 | 4.26188 | ||||||||
\(569\) | −13.8080 | −0.578863 | −0.289432 | − | 0.957199i | \(-0.593466\pi\) | ||||
−0.289432 | + | 0.957199i | \(0.593466\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −39.9397 | −1.67143 | −0.835713 | − | 0.549167i | \(-0.814945\pi\) | ||||
−0.835713 | + | 0.549167i | \(0.814945\pi\) | |||||||
\(572\) | −30.5452 | −1.27716 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −79.0122 | −3.29791 | ||||||||
\(575\) | −4.16804 | −0.173819 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −12.3137 | −0.512626 | −0.256313 | − | 0.966594i | \(-0.582508\pi\) | ||||
−0.256313 | + | 0.966594i | \(0.582508\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −6.88730 | −0.285980 | ||||||||
\(581\) | −7.62096 | −0.316171 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.02509 | −0.332365 | ||||||||
\(584\) | 74.6059 | 3.08721 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 34.5269 | 1.42629 | ||||||||
\(587\) | 3.85077 | 0.158938 | 0.0794691 | − | 0.996837i | \(-0.474677\pi\) | ||||
0.0794691 | + | 0.996837i | \(0.474677\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −11.6437 | −0.479770 | ||||||||
\(590\) | 32.7773 | 1.34942 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −102.469 | −4.21145 | ||||||||
\(593\) | −19.2538 | −0.790661 | −0.395330 | − | 0.918539i | \(-0.629370\pi\) | ||||
−0.395330 | + | 0.918539i | \(0.629370\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 106.774 | 4.37363 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −6.36304 | −0.260204 | ||||||||
\(599\) | −26.7619 | −1.09346 | −0.546730 | − | 0.837309i | \(-0.684128\pi\) | ||||
−0.546730 | + | 0.837309i | \(0.684128\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23.0698 | 0.941036 | 0.470518 | − | 0.882390i | \(-0.344067\pi\) | ||||
0.470518 | + | 0.882390i | \(0.344067\pi\) | |||||||
\(602\) | −55.8497 | −2.27626 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 14.0000 | 0.569652 | ||||||||
\(605\) | −2.44158 | −0.0992645 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −12.5629 | −0.509912 | −0.254956 | − | 0.966953i | \(-0.582061\pi\) | ||||
−0.254956 | + | 0.966953i | \(0.582061\pi\) | |||||||
\(608\) | −74.7597 | −3.03190 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −7.41421 | −0.300193 | ||||||||
\(611\) | −12.2130 | −0.494085 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −26.3137 | −1.06280 | −0.531400 | − | 0.847121i | \(-0.678334\pi\) | ||||
−0.531400 | + | 0.847121i | \(0.678334\pi\) | |||||||
\(614\) | −43.2928 | −1.74716 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −111.740 | −4.50214 | ||||||||
\(617\) | 43.5550 | 1.75346 | 0.876729 | − | 0.480985i | \(-0.159721\pi\) | ||||
0.876729 | + | 0.480985i | \(0.159721\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.68714 | 0.389359 | 0.194679 | − | 0.980867i | \(-0.437633\pi\) | ||||
0.194679 | + | 0.980867i | \(0.437633\pi\) | |||||||
\(620\) | 25.9077 | 1.04048 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 28.3730 | 1.13765 | ||||||||
\(623\) | 29.8301 | 1.19512 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.85786 | −0.114315 | ||||||||
\(626\) | −63.8282 | −2.55109 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −112.610 | −4.49364 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.1421 | 0.682418 | 0.341209 | − | 0.939988i | \(-0.389164\pi\) | ||||
0.341209 | + | 0.939988i | \(0.389164\pi\) | |||||||
\(632\) | −90.0572 | −3.58228 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 2.35049 | 0.0933500 | ||||||||
\(635\) | 19.0090 | 0.754350 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7.00000 | 0.277350 | ||||||||
\(638\) | 8.36223 | 0.331064 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 50.0977 | 1.98029 | ||||||||
\(641\) | −3.55765 | −0.140519 | −0.0702593 | − | 0.997529i | \(-0.522383\pi\) | ||||
−0.0702593 | + | 0.997529i | \(0.522383\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.45381 | 0.0573327 | 0.0286663 | − | 0.999589i | \(-0.490874\pi\) | ||||
0.0286663 | + | 0.999589i | \(0.490874\pi\) | |||||||
\(644\) | −26.9554 | −1.06219 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −33.8027 | −1.32892 | −0.664461 | − | 0.747323i | \(-0.731339\pi\) | ||||
−0.664461 | + | 0.747323i | \(0.731339\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −29.0614 | −1.14076 | ||||||||
\(650\) | 12.2130 | 0.479033 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −30.7235 | −1.20322 | ||||||||
\(653\) | 39.1341 | 1.53144 | 0.765718 | − | 0.643176i | \(-0.222384\pi\) | ||||
0.765718 | + | 0.643176i | \(0.222384\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −30.5563 | −1.19394 | ||||||||
\(656\) | −124.413 | −4.85751 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −70.8489 | −2.76198 | ||||||||
\(659\) | 29.2913 | 1.14103 | 0.570513 | − | 0.821289i | \(-0.306744\pi\) | ||||
0.570513 | + | 0.821289i | \(0.306744\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16.2132 | 0.630621 | 0.315310 | − | 0.948989i | \(-0.397891\pi\) | ||||
0.315310 | + | 0.948989i | \(0.397891\pi\) | |||||||
\(662\) | 3.10993 | 0.120871 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −20.9706 | −0.813816 | ||||||||
\(665\) | 17.8523 | 0.692283 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.27208 | 0.0492551 | ||||||||
\(668\) | 96.3093 | 3.72632 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 13.6997 | 0.529265 | ||||||||
\(671\) | 6.57368 | 0.253774 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −39.9079 | −1.53834 | −0.769168 | − | 0.639047i | \(-0.779329\pi\) | ||||
−0.769168 | + | 0.639047i | \(0.779329\pi\) | |||||||
\(674\) | 48.2287 | 1.85770 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −56.7696 | −2.18344 | ||||||||
\(677\) | 0.967957 | 0.0372016 | 0.0186008 | − | 0.999827i | \(-0.494079\pi\) | ||||
0.0186008 | + | 0.999827i | \(0.494079\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.51472 | 0.0581296 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −31.4558 | −1.20451 | ||||||||
\(683\) | −9.09459 | −0.347995 | −0.173997 | − | 0.984746i | \(-0.555668\pi\) | ||||
−0.173997 | + | 0.984746i | \(0.555668\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.68714 | 0.370126 | ||||||||
\(686\) | −23.7875 | −0.908210 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −87.9411 | −3.35272 | ||||||||
\(689\) | 3.57710 | 0.136277 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28.4818 | 1.08350 | 0.541748 | − | 0.840541i | \(-0.317763\pi\) | ||||
0.541748 | + | 0.840541i | \(0.317763\pi\) | |||||||
\(692\) | −130.159 | −4.94792 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 53.8251 | 2.04317 | ||||||||
\(695\) | −18.7867 | −0.712619 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 26.4882 | 1.00259 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 51.7373 | 1.95548 | ||||||||
\(701\) | 8.36223 | 0.315837 | 0.157918 | − | 0.987452i | \(-0.449522\pi\) | ||||
0.157918 | + | 0.987452i | \(0.449522\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −25.3659 | −0.956693 | ||||||||
\(704\) | −98.8990 | −3.72740 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 45.0122 | 1.69406 | ||||||||
\(707\) | −31.4084 | −1.18124 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 24.5236 | 0.921003 | 0.460502 | − | 0.887659i | \(-0.347670\pi\) | ||||
0.460502 | + | 0.887659i | \(0.347670\pi\) | |||||||
\(710\) | −43.8402 | −1.64529 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 82.0833 | 3.07620 | ||||||||
\(713\) | −4.78512 | −0.179204 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.31371 | 0.310915 | ||||||||
\(716\) | 125.093 | 4.67496 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 24.0416 | 0.897226 | ||||||||
\(719\) | 18.6515 | 0.695582 | 0.347791 | − | 0.937572i | \(-0.386932\pi\) | ||||
0.347791 | + | 0.937572i | \(0.386932\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.37849 | −0.125822 | ||||||||
\(722\) | 16.7245 | 0.622420 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −27.5851 | −1.02519 | ||||||||
\(725\) | −2.44158 | −0.0906781 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32.1421 | 1.19209 | 0.596043 | − | 0.802953i | \(-0.296739\pi\) | ||||
0.596043 | + | 0.802953i | \(0.296739\pi\) | |||||||
\(728\) | 49.8071 | 1.84597 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −32.2010 | −1.19181 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 32.8701 | 1.21408 | 0.607042 | − | 0.794670i | \(-0.292356\pi\) | ||||
0.607042 | + | 0.794670i | \(0.292356\pi\) | |||||||
\(734\) | −5.03127 | −0.185708 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −30.7235 | −1.13248 | ||||||||
\(737\) | −12.1466 | −0.447425 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12.8995 | 0.474516 | 0.237258 | − | 0.971447i | \(-0.423751\pi\) | ||||
0.237258 | + | 0.971447i | \(0.423751\pi\) | |||||||
\(740\) | 56.4402 | 2.07478 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 20.7512 | 0.761799 | ||||||||
\(743\) | −24.2931 | −0.891229 | −0.445614 | − | 0.895225i | \(-0.647015\pi\) | ||||
−0.445614 | + | 0.895225i | \(0.647015\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −29.0614 | −1.06473 | ||||||||
\(746\) | −43.6798 | −1.59923 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 19.0603 | 0.696450 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.0866 | −0.404554 | −0.202277 | − | 0.979328i | \(-0.564834\pi\) | ||||
−0.202277 | + | 0.979328i | \(0.564834\pi\) | |||||||
\(752\) | −111.559 | −4.06814 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −3.72738 | −0.135743 | ||||||||
\(755\) | −3.81048 | −0.138678 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 23.9706 | 0.871225 | 0.435612 | − | 0.900134i | \(-0.356532\pi\) | ||||
0.435612 | + | 0.900134i | \(0.356532\pi\) | |||||||
\(758\) | −15.8089 | −0.574207 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 49.1241 | 1.78192 | ||||||||
\(761\) | 36.2520 | 1.31413 | 0.657066 | − | 0.753833i | \(-0.271797\pi\) | ||||
0.657066 | + | 0.753833i | \(0.271797\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −46.2843 | −1.67560 | ||||||||
\(764\) | −9.68360 | −0.350340 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 8.68629 | 0.313848 | ||||||||
\(767\) | 12.9538 | 0.467736 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.24264 | 0.0448108 | 0.0224054 | − | 0.999749i | \(-0.492868\pi\) | ||||
0.0224054 | + | 0.999749i | \(0.492868\pi\) | |||||||
\(770\) | 48.2287 | 1.73804 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −84.8881 | −3.05519 | ||||||||
\(773\) | −5.71948 | −0.205715 | −0.102858 | − | 0.994696i | \(-0.532799\pi\) | ||||
−0.102858 | + | 0.994696i | \(0.532799\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9.18440 | 0.329913 | ||||||||
\(776\) | 4.16804 | 0.149624 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −7.41421 | −0.265812 | ||||||||
\(779\) | −30.7980 | −1.10345 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 38.8701 | 1.39088 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 63.9411 | 2.28361 | ||||||||
\(785\) | 30.6499 | 1.09394 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −50.9175 | −1.81501 | −0.907506 | − | 0.420038i | \(-0.862017\pi\) | ||||
−0.907506 | + | 0.420038i | \(0.862017\pi\) | |||||||
\(788\) | 37.1548 | 1.32359 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 38.8701 | 1.38293 | ||||||||
\(791\) | −46.0157 | −1.63613 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.93015 | −0.104053 | ||||||||
\(794\) | 6.40017 | 0.227134 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 135.620 | 4.80692 | ||||||||
\(797\) | −42.6321 | −1.51011 | −0.755054 | − | 0.655663i | \(-0.772389\pi\) | ||||
−0.755054 | + | 0.655663i | \(0.772389\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 58.9696 | 2.08489 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 38.0601 | 1.34395 | ||||||||
\(803\) | 28.5504 | 1.00752 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.33664 | 0.258583 | ||||||||
\(806\) | 14.0211 | 0.493873 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −86.4264 | −3.04047 | ||||||||
\(809\) | 14.8410 | 0.521781 | 0.260891 | − | 0.965368i | \(-0.415984\pi\) | ||||
0.260891 | + | 0.965368i | \(0.415984\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15.6018 | 0.547854 | 0.273927 | − | 0.961750i | \(-0.411677\pi\) | ||||
0.273927 | + | 0.961750i | \(0.411677\pi\) | |||||||
\(812\) | −15.7901 | −0.554124 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −68.5269 | −2.40187 | ||||||||
\(815\) | 8.36223 | 0.292916 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −21.7696 | −0.761620 | ||||||||
\(818\) | −100.200 | −3.50342 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 68.5269 | 2.39306 | ||||||||
\(821\) | 23.5346 | 0.821364 | 0.410682 | − | 0.911779i | \(-0.365291\pi\) | ||||
0.410682 | + | 0.911779i | \(0.365291\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −31.7515 | −1.10679 | −0.553393 | − | 0.832920i | \(-0.686667\pi\) | ||||
−0.553393 | + | 0.832920i | \(0.686667\pi\) | |||||||
\(824\) | −9.29658 | −0.323862 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 75.1466 | 2.61468 | ||||||||
\(827\) | 16.5674 | 0.576107 | 0.288053 | − | 0.957614i | \(-0.406992\pi\) | ||||
0.288053 | + | 0.957614i | \(0.406992\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.75736 | 0.130498 | 0.0652492 | − | 0.997869i | \(-0.479216\pi\) | ||||
0.0652492 | + | 0.997869i | \(0.479216\pi\) | |||||||
\(830\) | 9.05121 | 0.314172 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 44.0833 | 1.52831 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −26.2132 | −0.907145 | ||||||||
\(836\) | −69.0689 | −2.38880 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 105.870 | 3.65722 | ||||||||
\(839\) | 6.50490 | 0.224574 | 0.112287 | − | 0.993676i | \(-0.464182\pi\) | ||||
0.112287 | + | 0.993676i | \(0.464182\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.2548 | −0.974305 | ||||||||
\(842\) | −27.6962 | −0.954475 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −3.43289 | −0.118165 | ||||||||
\(845\) | 15.4514 | 0.531544 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.59767 | −0.192338 | ||||||||
\(848\) | 32.6749 | 1.12206 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −10.4244 | −0.357345 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 28.7988 | 0.986051 | 0.493026 | − | 0.870015i | \(-0.335891\pi\) | ||||
0.493026 | + | 0.870015i | \(0.335891\pi\) | |||||||
\(854\) | −16.9981 | −0.581664 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 52.4482 | 1.79264 | ||||||||
\(857\) | −13.8730 | −0.473894 | −0.236947 | − | 0.971523i | \(-0.576147\pi\) | ||||
−0.236947 | + | 0.971523i | \(0.576147\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12.7279 | 0.434271 | 0.217136 | − | 0.976141i | \(-0.430329\pi\) | ||||
0.217136 | + | 0.976141i | \(0.430329\pi\) | |||||||
\(860\) | 48.4382 | 1.65173 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 52.4482 | 1.78639 | ||||||||
\(863\) | −3.65726 | −0.124495 | −0.0622473 | − | 0.998061i | \(-0.519827\pi\) | ||||
−0.0622473 | + | 0.998061i | \(0.519827\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 35.4264 | 1.20453 | ||||||||
\(866\) | 111.092 | 3.77505 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 59.3970 | 2.01606 | ||||||||
\(869\) | −34.4634 | −1.16909 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.41421 | 0.183454 | ||||||||
\(872\) | −127.360 | −4.31296 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −14.3881 | −0.486686 | ||||||||
\(875\) | −38.9749 | −1.31759 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 28.0878 | 0.948458 | 0.474229 | − | 0.880402i | \(-0.342727\pi\) | ||||
0.474229 | + | 0.880402i | \(0.342727\pi\) | |||||||
\(878\) | −30.6933 | −1.03585 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 75.9411 | 2.55997 | ||||||||
\(881\) | 8.84175 | 0.297886 | 0.148943 | − | 0.988846i | \(-0.452413\pi\) | ||||
0.148943 | + | 0.988846i | \(0.452413\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 25.0000 | 0.841317 | 0.420658 | − | 0.907219i | \(-0.361799\pi\) | ||||
0.420658 | + | 0.907219i | \(0.361799\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −41.9411 | −1.40904 | ||||||||
\(887\) | 58.0384 | 1.94874 | 0.974370 | − | 0.224953i | \(-0.0722227\pi\) | ||||
0.974370 | + | 0.224953i | \(0.0722227\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 43.5809 | 1.46165 | ||||||||
\(890\) | −35.4284 | −1.18756 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 43.6985 | 1.46313 | ||||||||
\(893\) | −27.6161 | −0.924137 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −34.0476 | −1.13808 | ||||||||
\(896\) | 114.856 | 3.83707 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −38.7485 | −1.29306 | ||||||||
\(899\) | −2.80306 | −0.0934873 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −83.2020 | −2.77033 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −126.621 | −4.21136 | ||||||||
\(905\) | 7.50803 | 0.249575 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −14.3563 | −0.476692 | −0.238346 | − | 0.971180i | \(-0.576605\pi\) | ||||
−0.238346 | + | 0.971180i | \(0.576605\pi\) | |||||||
\(908\) | 75.6786 | 2.51148 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −21.4975 | −0.712634 | ||||||||
\(911\) | −5.99923 | −0.198763 | −0.0993817 | − | 0.995049i | \(-0.531686\pi\) | ||||
−0.0993817 | + | 0.995049i | \(0.531686\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.02509 | −0.265592 | ||||||||
\(914\) | −45.0814 | −1.49116 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 94.2843 | 3.11524 | ||||||||
\(917\) | −70.0547 | −2.31341 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 38.1716 | 1.25916 | 0.629582 | − | 0.776934i | \(-0.283226\pi\) | ||||
0.629582 | + | 0.776934i | \(0.283226\pi\) | |||||||
\(920\) | 20.1882 | 0.665585 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 34.5269 | 1.13708 | ||||||||
\(923\) | −17.3259 | −0.570291 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 20.0083 | 0.657870 | ||||||||
\(926\) | −99.4593 | −3.26844 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −17.9974 | −0.590793 | ||||||||
\(929\) | −56.8176 | −1.86413 | −0.932063 | − | 0.362296i | \(-0.881993\pi\) | ||||
−0.932063 | + | 0.362296i | \(0.881993\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 15.8284 | 0.518756 | ||||||||
\(932\) | 105.657 | 3.46090 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 51.8995 | 1.69820 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 52.2843 | 1.70805 | 0.854026 | − | 0.520230i | \(-0.174154\pi\) | ||||
0.854026 | + | 0.520230i | \(0.174154\pi\) | |||||||
\(938\) | 31.4084 | 1.02552 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 61.4469 | 2.00418 | ||||||||
\(941\) | −31.7660 | −1.03554 | −0.517771 | − | 0.855519i | \(-0.673238\pi\) | ||||
−0.517771 | + | 0.855519i | \(0.673238\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −12.6569 | −0.412164 | ||||||||
\(944\) | 118.326 | 3.85119 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −58.8113 | −1.91212 | ||||||||
\(947\) | −4.31615 | −0.140256 | −0.0701280 | − | 0.997538i | \(-0.522341\pi\) | ||||
−0.0701280 | + | 0.997538i | \(0.522341\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.7261 | −0.413106 | ||||||||
\(950\) | 27.6161 | 0.895984 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 8.36223 | 0.270879 | 0.135440 | − | 0.990786i | \(-0.456755\pi\) | ||||
0.135440 | + | 0.990786i | \(0.456755\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.63566 | 0.0852878 | ||||||||
\(956\) | 76.2413 | 2.46582 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 29.0614 | 0.938932 | ||||||||
\(959\) | 22.2091 | 0.717170 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.4558 | −0.659866 | ||||||||
\(962\) | 30.5452 | 0.984817 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −95.8978 | −3.08866 | ||||||||
\(965\) | 23.1046 | 0.743764 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 31.3848 | 1.00927 | 0.504633 | − | 0.863334i | \(-0.331628\pi\) | ||||
0.504633 | + | 0.863334i | \(0.331628\pi\) | |||||||
\(968\) | −15.4031 | −0.495074 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1.79899 | −0.0577621 | ||||||||
\(971\) | 9.68360 | 0.310762 | 0.155381 | − | 0.987855i | \(-0.450340\pi\) | ||||
0.155381 | + | 0.987855i | \(0.450340\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −43.0711 | −1.38080 | ||||||||
\(974\) | −69.7840 | −2.23603 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −26.7653 | −0.856737 | ||||||||
\(977\) | 6.30001 | 0.201555 | 0.100778 | − | 0.994909i | \(-0.467867\pi\) | ||||
0.100778 | + | 0.994909i | \(0.467867\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 31.4119 | 1.00393 | ||||||||
\(980\) | −35.2189 | −1.12503 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −19.1716 | −0.611789 | ||||||||
\(983\) | 22.1044 | 0.705020 | 0.352510 | − | 0.935808i | \(-0.385328\pi\) | ||||
0.352510 | + | 0.935808i | \(0.385328\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −10.1127 | −0.322217 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 30.7868 | 0.979458 | ||||||||
\(989\) | −8.94648 | −0.284482 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.64820 | −0.211187 | −0.105594 | − | 0.994409i | \(-0.533674\pi\) | ||||
−0.105594 | + | 0.994409i | \(0.533674\pi\) | |||||||
\(992\) | 67.7000 | 2.14948 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −100.510 | −3.18797 | ||||||||
\(995\) | −36.9127 | −1.17021 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −46.3797 | −1.46886 | −0.734430 | − | 0.678685i | \(-0.762550\pi\) | ||||
−0.734430 | + | 0.678685i | \(0.762550\pi\) | |||||||
\(998\) | 34.5651 | 1.09414 | ||||||||
\(999\) | 0 | 0 |
(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 | 2601.2.a.bl.1.1 | 8 | ||
3.2 | odd | 2 | inner | 2601.2.a.bl.1.8 | 8 | ||
17.3 | odd | 16 | 153.2.l.d.145.1 | yes | 8 | ||
17.6 | odd | 16 | 153.2.l.d.19.1 | ✓ | 8 | ||
17.16 | even | 2 | inner | 2601.2.a.bl.1.2 | 8 | ||
51.20 | even | 16 | 153.2.l.d.145.2 | yes | 8 | ||
51.23 | even | 16 | 153.2.l.d.19.2 | yes | 8 | ||
51.50 | odd | 2 | inner | 2601.2.a.bl.1.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
153.2.l.d.19.1 | ✓ | 8 | 17.6 | odd | 16 | ||
153.2.l.d.19.2 | yes | 8 | 51.23 | even | 16 | ||
153.2.l.d.145.1 | yes | 8 | 17.3 | odd | 16 | ||
153.2.l.d.145.2 | yes | 8 | 51.20 | even | 16 | ||
2601.2.a.bl.1.1 | 8 | 1.1 | even | 1 | trivial | ||
2601.2.a.bl.1.2 | 8 | 17.16 | even | 2 | inner | ||
2601.2.a.bl.1.7 | 8 | 51.50 | odd | 2 | inner | ||
2601.2.a.bl.1.8 | 8 | 3.2 | odd | 2 | inner |