Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5994,2,Mod(1,5994)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5994, 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("5994.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5994 = 2 \cdot 3^{4} \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5994.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: | \(47.8623309716\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} - 26x^{8} + 49x^{7} + 236x^{6} - 420x^{5} - 860x^{4} + 1461x^{3} + 993x^{2} - 1638x + 99 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | no (minimal twist has level 666) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.15778\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5994.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.33861 | −1.49307 | −0.746536 | − | 0.665344i | \(-0.768285\pi\) | ||||
−0.746536 | + | 0.665344i | \(0.768285\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.195962 | 0.0740665 | 0.0370333 | − | 0.999314i | \(-0.488209\pi\) | ||||
0.0370333 | + | 0.999314i | \(0.488209\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3.33861 | −1.05576 | ||||||||
\(11\) | −5.08601 | −1.53349 | −0.766745 | − | 0.641952i | \(-0.778125\pi\) | ||||
−0.766745 | + | 0.641952i | \(0.778125\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.32840 | −1.47783 | −0.738917 | − | 0.673797i | \(-0.764662\pi\) | ||||
−0.738917 | + | 0.673797i | \(0.764662\pi\) | |||||||
\(14\) | 0.195962 | 0.0523729 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.739743 | 0.179414 | 0.0897070 | − | 0.995968i | \(-0.471407\pi\) | ||||
0.0897070 | + | 0.995968i | \(0.471407\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.26526 | 1.20793 | 0.603966 | − | 0.797010i | \(-0.293586\pi\) | ||||
0.603966 | + | 0.797010i | \(0.293586\pi\) | |||||||
\(20\) | −3.33861 | −0.746536 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.08601 | −1.08434 | ||||||||
\(23\) | 2.50863 | 0.523085 | 0.261543 | − | 0.965192i | \(-0.415769\pi\) | ||||
0.261543 | + | 0.965192i | \(0.415769\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.14633 | 1.22927 | ||||||||
\(26\) | −5.32840 | −1.04499 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.195962 | 0.0370333 | ||||||||
\(29\) | −6.13351 | −1.13896 | −0.569482 | − | 0.822004i | \(-0.692856\pi\) | ||||
−0.569482 | + | 0.822004i | \(0.692856\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.59981 | −0.287334 | −0.143667 | − | 0.989626i | \(-0.545889\pi\) | ||||
−0.143667 | + | 0.989626i | \(0.545889\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.739743 | 0.126865 | ||||||||
\(35\) | −0.654240 | −0.110587 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.00000 | −0.164399 | ||||||||
\(38\) | 5.26526 | 0.854137 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.33861 | −0.527881 | ||||||||
\(41\) | −5.25874 | −0.821277 | −0.410638 | − | 0.911798i | \(-0.634694\pi\) | ||||
−0.410638 | + | 0.911798i | \(0.634694\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.47515 | 0.682453 | 0.341227 | − | 0.939981i | \(-0.389158\pi\) | ||||
0.341227 | + | 0.939981i | \(0.389158\pi\) | |||||||
\(44\) | −5.08601 | −0.766745 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.50863 | 0.369877 | ||||||||
\(47\) | 13.4814 | 1.96647 | 0.983233 | − | 0.182352i | \(-0.0583709\pi\) | ||||
0.983233 | + | 0.182352i | \(0.0583709\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.96160 | −0.994514 | ||||||||
\(50\) | 6.14633 | 0.869223 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −5.32840 | −0.738917 | ||||||||
\(53\) | −9.76490 | −1.34131 | −0.670656 | − | 0.741768i | \(-0.733987\pi\) | ||||
−0.670656 | + | 0.741768i | \(0.733987\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 16.9802 | 2.28961 | ||||||||
\(56\) | 0.195962 | 0.0261865 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −6.13351 | −0.805369 | ||||||||
\(59\) | 0.821294 | 0.106923 | 0.0534617 | − | 0.998570i | \(-0.482974\pi\) | ||||
0.0534617 | + | 0.998570i | \(0.482974\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.12609 | 0.784366 | 0.392183 | − | 0.919887i | \(-0.371720\pi\) | ||||
0.392183 | + | 0.919887i | \(0.371720\pi\) | |||||||
\(62\) | −1.59981 | −0.203176 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 17.7895 | 2.20651 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.02877 | 0.858700 | 0.429350 | − | 0.903138i | \(-0.358743\pi\) | ||||
0.429350 | + | 0.903138i | \(0.358743\pi\) | |||||||
\(68\) | 0.739743 | 0.0897070 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.654240 | −0.0781966 | ||||||||
\(71\) | 10.4556 | 1.24085 | 0.620426 | − | 0.784265i | \(-0.286960\pi\) | ||||
0.620426 | + | 0.784265i | \(0.286960\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.73574 | 0.905400 | 0.452700 | − | 0.891663i | \(-0.350461\pi\) | ||||
0.452700 | + | 0.891663i | \(0.350461\pi\) | |||||||
\(74\) | −1.00000 | −0.116248 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.26526 | 0.603966 | ||||||||
\(77\) | −0.996662 | −0.113580 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.927623 | −0.104366 | −0.0521829 | − | 0.998638i | \(-0.516618\pi\) | ||||
−0.0521829 | + | 0.998638i | \(0.516618\pi\) | |||||||
\(80\) | −3.33861 | −0.373268 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −5.25874 | −0.580730 | ||||||||
\(83\) | −8.85942 | −0.972448 | −0.486224 | − | 0.873834i | \(-0.661626\pi\) | ||||
−0.486224 | + | 0.873834i | \(0.661626\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.46971 | −0.267878 | ||||||||
\(86\) | 4.47515 | 0.482567 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −5.08601 | −0.542170 | ||||||||
\(89\) | −10.6441 | −1.12827 | −0.564137 | − | 0.825682i | \(-0.690791\pi\) | ||||
−0.564137 | + | 0.825682i | \(0.690791\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.04416 | −0.109458 | ||||||||
\(92\) | 2.50863 | 0.261543 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 13.4814 | 1.39050 | ||||||||
\(95\) | −17.5787 | −1.80353 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.4087 | 1.05684 | 0.528422 | − | 0.848982i | \(-0.322784\pi\) | ||||
0.528422 | + | 0.848982i | \(0.322784\pi\) | |||||||
\(98\) | −6.96160 | −0.703228 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 6.14633 | 0.614633 | ||||||||
\(101\) | −2.91641 | −0.290193 | −0.145097 | − | 0.989417i | \(-0.546349\pi\) | ||||
−0.145097 | + | 0.989417i | \(0.546349\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.6134 | 1.24284 | 0.621419 | − | 0.783478i | \(-0.286557\pi\) | ||||
0.621419 | + | 0.783478i | \(0.286557\pi\) | |||||||
\(104\) | −5.32840 | −0.522493 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.76490 | −0.948451 | ||||||||
\(107\) | 3.87889 | 0.374987 | 0.187493 | − | 0.982266i | \(-0.439964\pi\) | ||||
0.187493 | + | 0.982266i | \(0.439964\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.536436 | 0.0513812 | 0.0256906 | − | 0.999670i | \(-0.491822\pi\) | ||||
0.0256906 | + | 0.999670i | \(0.491822\pi\) | |||||||
\(110\) | 16.9802 | 1.61900 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.195962 | 0.0185166 | ||||||||
\(113\) | 19.0344 | 1.79061 | 0.895304 | − | 0.445456i | \(-0.146959\pi\) | ||||
0.895304 | + | 0.445456i | \(0.146959\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.37534 | −0.781005 | ||||||||
\(116\) | −6.13351 | −0.569482 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.821294 | 0.0756063 | ||||||||
\(119\) | 0.144961 | 0.0132886 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14.8675 | 1.35159 | ||||||||
\(122\) | 6.12609 | 0.554630 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.59981 | −0.143667 | ||||||||
\(125\) | −3.82717 | −0.342312 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 20.0651 | 1.78049 | 0.890247 | − | 0.455479i | \(-0.150532\pi\) | ||||
0.890247 | + | 0.455479i | \(0.150532\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 17.7895 | 1.56024 | ||||||||
\(131\) | 8.42646 | 0.736223 | 0.368112 | − | 0.929782i | \(-0.380004\pi\) | ||||
0.368112 | + | 0.929782i | \(0.380004\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.03179 | 0.0894674 | ||||||||
\(134\) | 7.02877 | 0.607193 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.739743 | 0.0634324 | ||||||||
\(137\) | −20.8102 | −1.77794 | −0.888969 | − | 0.457968i | \(-0.848577\pi\) | ||||
−0.888969 | + | 0.457968i | \(0.848577\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.122437 | −0.0103849 | −0.00519246 | − | 0.999987i | \(-0.501653\pi\) | ||||
−0.00519246 | + | 0.999987i | \(0.501653\pi\) | |||||||
\(140\) | −0.654240 | −0.0552934 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 10.4556 | 0.877414 | ||||||||
\(143\) | 27.1003 | 2.26624 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 20.4774 | 1.70056 | ||||||||
\(146\) | 7.73574 | 0.640214 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.00000 | −0.0821995 | ||||||||
\(149\) | 6.84115 | 0.560449 | 0.280224 | − | 0.959935i | \(-0.409591\pi\) | ||||
0.280224 | + | 0.959935i | \(0.409591\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 21.8371 | 1.77708 | 0.888538 | − | 0.458803i | \(-0.151722\pi\) | ||||
0.888538 | + | 0.458803i | \(0.151722\pi\) | |||||||
\(152\) | 5.26526 | 0.427069 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.996662 | −0.0803133 | ||||||||
\(155\) | 5.34115 | 0.429011 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −19.8674 | −1.58559 | −0.792797 | − | 0.609486i | \(-0.791376\pi\) | ||||
−0.792797 | + | 0.609486i | \(0.791376\pi\) | |||||||
\(158\) | −0.927623 | −0.0737977 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3.33861 | −0.263941 | ||||||||
\(161\) | 0.491595 | 0.0387431 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.27443 | −0.334799 | −0.167399 | − | 0.985889i | \(-0.553537\pi\) | ||||
−0.167399 | + | 0.985889i | \(0.553537\pi\) | |||||||
\(164\) | −5.25874 | −0.410638 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.85942 | −0.687624 | ||||||||
\(167\) | 0.615260 | 0.0476102 | 0.0238051 | − | 0.999717i | \(-0.492422\pi\) | ||||
0.0238051 | + | 0.999717i | \(0.492422\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 15.3919 | 1.18399 | ||||||||
\(170\) | −2.46971 | −0.189418 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.47515 | 0.341227 | ||||||||
\(173\) | 20.9888 | 1.59575 | 0.797873 | − | 0.602826i | \(-0.205959\pi\) | ||||
0.797873 | + | 0.602826i | \(0.205959\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.20445 | 0.0910475 | ||||||||
\(176\) | −5.08601 | −0.383372 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −10.6441 | −0.797810 | ||||||||
\(179\) | −22.4414 | −1.67735 | −0.838673 | − | 0.544635i | \(-0.816668\pi\) | ||||
−0.838673 | + | 0.544635i | \(0.816668\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.60462 | 0.416588 | 0.208294 | − | 0.978066i | \(-0.433209\pi\) | ||||
0.208294 | + | 0.978066i | \(0.433209\pi\) | |||||||
\(182\) | −1.04416 | −0.0773985 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.50863 | 0.184939 | ||||||||
\(185\) | 3.33861 | 0.245460 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.76234 | −0.275129 | ||||||||
\(188\) | 13.4814 | 0.983233 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −17.5787 | −1.27529 | ||||||||
\(191\) | −4.12388 | −0.298393 | −0.149197 | − | 0.988808i | \(-0.547669\pi\) | ||||
−0.149197 | + | 0.988808i | \(0.547669\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.55099 | −0.615513 | −0.307757 | − | 0.951465i | \(-0.599578\pi\) | ||||
−0.307757 | + | 0.951465i | \(0.599578\pi\) | |||||||
\(194\) | 10.4087 | 0.747302 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.96160 | −0.497257 | ||||||||
\(197\) | 13.1755 | 0.938714 | 0.469357 | − | 0.883009i | \(-0.344486\pi\) | ||||
0.469357 | + | 0.883009i | \(0.344486\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.5811 | 1.31718 | 0.658589 | − | 0.752503i | \(-0.271154\pi\) | ||||
0.658589 | + | 0.752503i | \(0.271154\pi\) | |||||||
\(200\) | 6.14633 | 0.434611 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2.91641 | −0.205198 | ||||||||
\(203\) | −1.20193 | −0.0843591 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 17.5569 | 1.22623 | ||||||||
\(206\) | 12.6134 | 0.878819 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −5.32840 | −0.369458 | ||||||||
\(209\) | −26.7791 | −1.85235 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.80875 | −0.331048 | −0.165524 | − | 0.986206i | \(-0.552932\pi\) | ||||
−0.165524 | + | 0.986206i | \(0.552932\pi\) | |||||||
\(212\) | −9.76490 | −0.670656 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3.87889 | 0.265156 | ||||||||
\(215\) | −14.9408 | −1.01895 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.313501 | −0.0212819 | ||||||||
\(218\) | 0.536436 | 0.0363320 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 16.9802 | 1.14481 | ||||||||
\(221\) | −3.94165 | −0.265144 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.28621 | 0.353991 | 0.176995 | − | 0.984212i | \(-0.443362\pi\) | ||||
0.176995 | + | 0.984212i | \(0.443362\pi\) | |||||||
\(224\) | 0.195962 | 0.0130932 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 19.0344 | 1.26615 | ||||||||
\(227\) | 6.52175 | 0.432864 | 0.216432 | − | 0.976298i | \(-0.430558\pi\) | ||||
0.216432 | + | 0.976298i | \(0.430558\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.93818 | 0.392406 | 0.196203 | − | 0.980563i | \(-0.437139\pi\) | ||||
0.196203 | + | 0.980563i | \(0.437139\pi\) | |||||||
\(230\) | −8.37534 | −0.552254 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.13351 | −0.402685 | ||||||||
\(233\) | 18.4107 | 1.20613 | 0.603063 | − | 0.797693i | \(-0.293947\pi\) | ||||
0.603063 | + | 0.797693i | \(0.293947\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −45.0092 | −2.93608 | ||||||||
\(236\) | 0.821294 | 0.0534617 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.144961 | 0.00939644 | ||||||||
\(239\) | 24.0032 | 1.55264 | 0.776320 | − | 0.630339i | \(-0.217084\pi\) | ||||
0.776320 | + | 0.630339i | \(0.217084\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −17.2454 | −1.11087 | −0.555437 | − | 0.831559i | \(-0.687449\pi\) | ||||
−0.555437 | + | 0.831559i | \(0.687449\pi\) | |||||||
\(242\) | 14.8675 | 0.955717 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 6.12609 | 0.392183 | ||||||||
\(245\) | 23.2421 | 1.48488 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −28.0554 | −1.78512 | ||||||||
\(248\) | −1.59981 | −0.101588 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −3.82717 | −0.242051 | ||||||||
\(251\) | 5.56820 | 0.351462 | 0.175731 | − | 0.984438i | \(-0.443771\pi\) | ||||
0.175731 | + | 0.984438i | \(0.443771\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.7589 | −0.802146 | ||||||||
\(254\) | 20.0651 | 1.25900 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −12.8042 | −0.798705 | −0.399352 | − | 0.916798i | \(-0.630765\pi\) | ||||
−0.399352 | + | 0.916798i | \(0.630765\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.195962 | −0.0121765 | ||||||||
\(260\) | 17.7895 | 1.10326 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 8.42646 | 0.520588 | ||||||||
\(263\) | 3.24586 | 0.200149 | 0.100074 | − | 0.994980i | \(-0.468092\pi\) | ||||
0.100074 | + | 0.994980i | \(0.468092\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 32.6012 | 2.00268 | ||||||||
\(266\) | 1.03179 | 0.0632630 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 7.02877 | 0.429350 | ||||||||
\(269\) | −20.4388 | −1.24618 | −0.623089 | − | 0.782151i | \(-0.714122\pi\) | ||||
−0.623089 | + | 0.782151i | \(0.714122\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −18.6519 | −1.13303 | −0.566513 | − | 0.824053i | \(-0.691708\pi\) | ||||
−0.566513 | + | 0.824053i | \(0.691708\pi\) | |||||||
\(272\) | 0.739743 | 0.0448535 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −20.8102 | −1.25719 | ||||||||
\(275\) | −31.2603 | −1.88507 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.39476 | −0.384224 | −0.192112 | − | 0.981373i | \(-0.561534\pi\) | ||||
−0.192112 | + | 0.981373i | \(0.561534\pi\) | |||||||
\(278\) | −0.122437 | −0.00734325 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −0.654240 | −0.0390983 | ||||||||
\(281\) | −20.2860 | −1.21016 | −0.605081 | − | 0.796164i | \(-0.706859\pi\) | ||||
−0.605081 | + | 0.796164i | \(0.706859\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 21.7594 | 1.29346 | 0.646730 | − | 0.762719i | \(-0.276136\pi\) | ||||
0.646730 | + | 0.762719i | \(0.276136\pi\) | |||||||
\(284\) | 10.4556 | 0.620426 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 27.1003 | 1.60247 | ||||||||
\(287\) | −1.03051 | −0.0608291 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.4528 | −0.967811 | ||||||||
\(290\) | 20.4774 | 1.20248 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 7.73574 | 0.452700 | ||||||||
\(293\) | 29.9252 | 1.74825 | 0.874125 | − | 0.485700i | \(-0.161435\pi\) | ||||
0.874125 | + | 0.485700i | \(0.161435\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.74198 | −0.159644 | ||||||||
\(296\) | −1.00000 | −0.0581238 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6.84115 | 0.396297 | ||||||||
\(299\) | −13.3670 | −0.773033 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.876957 | 0.0505469 | ||||||||
\(302\) | 21.8371 | 1.25658 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 5.26526 | 0.301983 | ||||||||
\(305\) | −20.4527 | −1.17112 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −22.7730 | −1.29972 | −0.649861 | − | 0.760053i | \(-0.725173\pi\) | ||||
−0.649861 | + | 0.760053i | \(0.725173\pi\) | |||||||
\(308\) | −0.996662 | −0.0567901 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 5.34115 | 0.303357 | ||||||||
\(311\) | −31.3806 | −1.77943 | −0.889716 | − | 0.456513i | \(-0.849098\pi\) | ||||
−0.889716 | + | 0.456513i | \(0.849098\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.18723 | 0.236676 | 0.118338 | − | 0.992973i | \(-0.462243\pi\) | ||||
0.118338 | + | 0.992973i | \(0.462243\pi\) | |||||||
\(314\) | −19.8674 | −1.12118 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.927623 | −0.0521829 | ||||||||
\(317\) | −9.71753 | −0.545791 | −0.272895 | − | 0.962044i | \(-0.587981\pi\) | ||||
−0.272895 | + | 0.962044i | \(0.587981\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 31.1951 | 1.74659 | ||||||||
\(320\) | −3.33861 | −0.186634 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.491595 | 0.0273955 | ||||||||
\(323\) | 3.89493 | 0.216720 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −32.7502 | −1.81665 | ||||||||
\(326\) | −4.27443 | −0.236739 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −5.25874 | −0.290365 | ||||||||
\(329\) | 2.64184 | 0.145649 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.19467 | 0.230560 | 0.115280 | − | 0.993333i | \(-0.463223\pi\) | ||||
0.115280 | + | 0.993333i | \(0.463223\pi\) | |||||||
\(332\) | −8.85942 | −0.486224 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0.615260 | 0.0336655 | ||||||||
\(335\) | −23.4663 | −1.28210 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.3297 | 0.944010 | 0.472005 | − | 0.881596i | \(-0.343530\pi\) | ||||
0.472005 | + | 0.881596i | \(0.343530\pi\) | |||||||
\(338\) | 15.3919 | 0.837208 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2.46971 | −0.133939 | ||||||||
\(341\) | 8.13665 | 0.440624 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.73594 | −0.147727 | ||||||||
\(344\) | 4.47515 | 0.241284 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 20.9888 | 1.12836 | ||||||||
\(347\) | −0.604429 | −0.0324474 | −0.0162237 | − | 0.999868i | \(-0.505164\pi\) | ||||
−0.0162237 | + | 0.999868i | \(0.505164\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.8975 | 0.850971 | 0.425486 | − | 0.904965i | \(-0.360103\pi\) | ||||
0.425486 | + | 0.904965i | \(0.360103\pi\) | |||||||
\(350\) | 1.20445 | 0.0643803 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −5.08601 | −0.271085 | ||||||||
\(353\) | −5.98441 | −0.318518 | −0.159259 | − | 0.987237i | \(-0.550911\pi\) | ||||
−0.159259 | + | 0.987237i | \(0.550911\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −34.9072 | −1.85268 | ||||||||
\(356\) | −10.6441 | −0.564137 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −22.4414 | −1.18606 | ||||||||
\(359\) | 7.52687 | 0.397253 | 0.198627 | − | 0.980075i | \(-0.436352\pi\) | ||||
0.198627 | + | 0.980075i | \(0.436352\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.72292 | 0.459101 | ||||||||
\(362\) | 5.60462 | 0.294572 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.04416 | −0.0547290 | ||||||||
\(365\) | −25.8266 | −1.35183 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −18.5266 | −0.967080 | −0.483540 | − | 0.875322i | \(-0.660649\pi\) | ||||
−0.483540 | + | 0.875322i | \(0.660649\pi\) | |||||||
\(368\) | 2.50863 | 0.130771 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 3.33861 | 0.173566 | ||||||||
\(371\) | −1.91355 | −0.0993464 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −29.4102 | −1.52280 | −0.761401 | − | 0.648282i | \(-0.775488\pi\) | ||||
−0.761401 | + | 0.648282i | \(0.775488\pi\) | |||||||
\(374\) | −3.76234 | −0.194546 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 13.4814 | 0.695251 | ||||||||
\(377\) | 32.6818 | 1.68320 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.0742 | 0.517475 | 0.258738 | − | 0.965948i | \(-0.416694\pi\) | ||||
0.258738 | + | 0.965948i | \(0.416694\pi\) | |||||||
\(380\) | −17.5787 | −0.901766 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −4.12388 | −0.210996 | ||||||||
\(383\) | 15.6220 | 0.798248 | 0.399124 | − | 0.916897i | \(-0.369314\pi\) | ||||
0.399124 | + | 0.916897i | \(0.369314\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.32747 | 0.169584 | ||||||||
\(386\) | −8.55099 | −0.435234 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 10.4087 | 0.528422 | ||||||||
\(389\) | 16.6098 | 0.842151 | 0.421076 | − | 0.907026i | \(-0.361653\pi\) | ||||
0.421076 | + | 0.907026i | \(0.361653\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.85574 | 0.0938488 | ||||||||
\(392\) | −6.96160 | −0.351614 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 13.1755 | 0.663771 | ||||||||
\(395\) | 3.09697 | 0.155826 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 23.9512 | 1.20207 | 0.601037 | − | 0.799221i | \(-0.294754\pi\) | ||||
0.601037 | + | 0.799221i | \(0.294754\pi\) | |||||||
\(398\) | 18.5811 | 0.931385 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 6.14633 | 0.307317 | ||||||||
\(401\) | −28.2179 | −1.40913 | −0.704566 | − | 0.709638i | \(-0.748858\pi\) | ||||
−0.704566 | + | 0.709638i | \(0.748858\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.52443 | 0.424632 | ||||||||
\(404\) | −2.91641 | −0.145097 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.20193 | −0.0596509 | ||||||||
\(407\) | 5.08601 | 0.252104 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 20.8364 | 1.03029 | 0.515147 | − | 0.857102i | \(-0.327737\pi\) | ||||
0.515147 | + | 0.857102i | \(0.327737\pi\) | |||||||
\(410\) | 17.5569 | 0.867073 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 12.6134 | 0.621419 | ||||||||
\(413\) | 0.160942 | 0.00791945 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 29.5782 | 1.45194 | ||||||||
\(416\) | −5.32840 | −0.261246 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −26.7791 | −1.30981 | ||||||||
\(419\) | 23.4768 | 1.14691 | 0.573457 | − | 0.819235i | \(-0.305602\pi\) | ||||
0.573457 | + | 0.819235i | \(0.305602\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −26.6544 | −1.29905 | −0.649527 | − | 0.760338i | \(-0.725033\pi\) | ||||
−0.649527 | + | 0.760338i | \(0.725033\pi\) | |||||||
\(422\) | −4.80875 | −0.234086 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −9.76490 | −0.474226 | ||||||||
\(425\) | 4.54671 | 0.220548 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.20048 | 0.0580952 | ||||||||
\(428\) | 3.87889 | 0.187493 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −14.9408 | −0.720508 | ||||||||
\(431\) | 27.9472 | 1.34617 | 0.673085 | − | 0.739565i | \(-0.264969\pi\) | ||||
0.673085 | + | 0.739565i | \(0.264969\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.4980 | 0.696730 | 0.348365 | − | 0.937359i | \(-0.386737\pi\) | ||||
0.348365 | + | 0.937359i | \(0.386737\pi\) | |||||||
\(434\) | −0.313501 | −0.0150485 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.536436 | 0.0256906 | ||||||||
\(437\) | 13.2086 | 0.631852 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.2482 | 0.489122 | 0.244561 | − | 0.969634i | \(-0.421356\pi\) | ||||
0.244561 | + | 0.969634i | \(0.421356\pi\) | |||||||
\(440\) | 16.9802 | 0.809500 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.94165 | −0.187485 | ||||||||
\(443\) | 8.13881 | 0.386687 | 0.193343 | − | 0.981131i | \(-0.438067\pi\) | ||||
0.193343 | + | 0.981131i | \(0.438067\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 35.5365 | 1.68459 | ||||||||
\(446\) | 5.28621 | 0.250309 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.195962 | 0.00925832 | ||||||||
\(449\) | 1.81755 | 0.0857754 | 0.0428877 | − | 0.999080i | \(-0.486344\pi\) | ||||
0.0428877 | + | 0.999080i | \(0.486344\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 26.7460 | 1.25942 | ||||||||
\(452\) | 19.0344 | 0.895304 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 6.52175 | 0.306081 | ||||||||
\(455\) | 3.48605 | 0.163429 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −38.9876 | −1.82376 | −0.911880 | − | 0.410456i | \(-0.865370\pi\) | ||||
−0.911880 | + | 0.410456i | \(0.865370\pi\) | |||||||
\(458\) | 5.93818 | 0.277473 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −8.37534 | −0.390502 | ||||||||
\(461\) | −14.6527 | −0.682445 | −0.341223 | − | 0.939983i | \(-0.610841\pi\) | ||||
−0.341223 | + | 0.939983i | \(0.610841\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 25.3342 | 1.17738 | 0.588689 | − | 0.808359i | \(-0.299644\pi\) | ||||
0.588689 | + | 0.808359i | \(0.299644\pi\) | |||||||
\(464\) | −6.13351 | −0.284741 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 18.4107 | 0.852861 | ||||||||
\(467\) | −6.52767 | −0.302065 | −0.151032 | − | 0.988529i | \(-0.548260\pi\) | ||||
−0.151032 | + | 0.988529i | \(0.548260\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.37737 | 0.0636010 | ||||||||
\(470\) | −45.0092 | −2.07612 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0.821294 | 0.0378031 | ||||||||
\(473\) | −22.7606 | −1.04653 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 32.3620 | 1.48487 | ||||||||
\(476\) | 0.144961 | 0.00664428 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 24.0032 | 1.09788 | ||||||||
\(479\) | 19.4006 | 0.886438 | 0.443219 | − | 0.896413i | \(-0.353836\pi\) | ||||
0.443219 | + | 0.896413i | \(0.353836\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.32840 | 0.242954 | ||||||||
\(482\) | −17.2454 | −0.785506 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 14.8675 | 0.675794 | ||||||||
\(485\) | −34.7507 | −1.57795 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.5204 | −0.522040 | −0.261020 | − | 0.965333i | \(-0.584059\pi\) | ||||
−0.261020 | + | 0.965333i | \(0.584059\pi\) | |||||||
\(488\) | 6.12609 | 0.277315 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 23.2421 | 1.04997 | ||||||||
\(491\) | −30.0958 | −1.35821 | −0.679103 | − | 0.734043i | \(-0.737631\pi\) | ||||
−0.679103 | + | 0.734043i | \(0.737631\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.53722 | −0.204346 | ||||||||
\(494\) | −28.0554 | −1.26227 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.59981 | −0.0718336 | ||||||||
\(497\) | 2.04890 | 0.0919055 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 19.6116 | 0.877934 | 0.438967 | − | 0.898503i | \(-0.355345\pi\) | ||||
0.438967 | + | 0.898503i | \(0.355345\pi\) | |||||||
\(500\) | −3.82717 | −0.171156 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 5.56820 | 0.248521 | ||||||||
\(503\) | −19.1959 | −0.855903 | −0.427951 | − | 0.903802i | \(-0.640765\pi\) | ||||
−0.427951 | + | 0.903802i | \(0.640765\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.73675 | 0.433280 | ||||||||
\(506\) | −12.7589 | −0.567203 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 20.0651 | 0.890247 | ||||||||
\(509\) | 29.4055 | 1.30337 | 0.651687 | − | 0.758488i | \(-0.274062\pi\) | ||||
0.651687 | + | 0.758488i | \(0.274062\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.51591 | 0.0670598 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −12.8042 | −0.564769 | ||||||||
\(515\) | −42.1113 | −1.85565 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −68.5666 | −3.01556 | ||||||||
\(518\) | −0.195962 | −0.00861006 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 17.7895 | 0.780120 | ||||||||
\(521\) | −1.28738 | −0.0564013 | −0.0282006 | − | 0.999602i | \(-0.508978\pi\) | ||||
−0.0282006 | + | 0.999602i | \(0.508978\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.27752 | −0.187043 | −0.0935215 | − | 0.995617i | \(-0.529812\pi\) | ||||
−0.0935215 | + | 0.995617i | \(0.529812\pi\) | |||||||
\(524\) | 8.42646 | 0.368112 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.24586 | 0.141526 | ||||||||
\(527\) | −1.18345 | −0.0515518 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.7068 | −0.726382 | ||||||||
\(530\) | 32.6012 | 1.41611 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.03179 | 0.0447337 | ||||||||
\(533\) | 28.0207 | 1.21371 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12.9501 | −0.559882 | ||||||||
\(536\) | 7.02877 | 0.303596 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −20.4388 | −0.881180 | ||||||||
\(539\) | 35.4067 | 1.52508 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.96148 | 0.256304 | 0.128152 | − | 0.991755i | \(-0.459095\pi\) | ||||
0.128152 | + | 0.991755i | \(0.459095\pi\) | |||||||
\(542\) | −18.6519 | −0.801170 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.739743 | 0.0317162 | ||||||||
\(545\) | −1.79095 | −0.0767159 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 28.8625 | 1.23407 | 0.617036 | − | 0.786935i | \(-0.288333\pi\) | ||||
0.617036 | + | 0.786935i | \(0.288333\pi\) | |||||||
\(548\) | −20.8102 | −0.888969 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −31.2603 | −1.33294 | ||||||||
\(551\) | −32.2945 | −1.37579 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.181778 | −0.00773001 | ||||||||
\(554\) | −6.39476 | −0.271687 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.122437 | −0.00519246 | ||||||||
\(557\) | 27.3289 | 1.15796 | 0.578981 | − | 0.815341i | \(-0.303451\pi\) | ||||
0.578981 | + | 0.815341i | \(0.303451\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −23.8454 | −1.00855 | ||||||||
\(560\) | −0.654240 | −0.0276467 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −20.2860 | −0.855714 | ||||||||
\(563\) | 31.1305 | 1.31199 | 0.655996 | − | 0.754764i | \(-0.272249\pi\) | ||||
0.655996 | + | 0.754764i | \(0.272249\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −63.5485 | −2.67351 | ||||||||
\(566\) | 21.7594 | 0.914615 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 10.4556 | 0.438707 | ||||||||
\(569\) | −20.9407 | −0.877879 | −0.438939 | − | 0.898517i | \(-0.644646\pi\) | ||||
−0.438939 | + | 0.898517i | \(0.644646\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 37.5254 | 1.57039 | 0.785194 | − | 0.619250i | \(-0.212563\pi\) | ||||
0.785194 | + | 0.619250i | \(0.212563\pi\) | |||||||
\(572\) | 27.1003 | 1.13312 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.03051 | −0.0430127 | ||||||||
\(575\) | 15.4189 | 0.643012 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −17.9434 | −0.746993 | −0.373496 | − | 0.927632i | \(-0.621841\pi\) | ||||
−0.373496 | + | 0.927632i | \(0.621841\pi\) | |||||||
\(578\) | −16.4528 | −0.684345 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 20.4774 | 0.850278 | ||||||||
\(581\) | −1.73611 | −0.0720258 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 49.6644 | 2.05689 | ||||||||
\(584\) | 7.73574 | 0.320107 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 29.9252 | 1.23620 | ||||||||
\(587\) | −37.8461 | −1.56207 | −0.781037 | − | 0.624484i | \(-0.785309\pi\) | ||||
−0.781037 | + | 0.624484i | \(0.785309\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.42341 | −0.347081 | ||||||||
\(590\) | −2.74198 | −0.112886 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.00000 | −0.0410997 | ||||||||
\(593\) | −14.5823 | −0.598823 | −0.299412 | − | 0.954124i | \(-0.596790\pi\) | ||||
−0.299412 | + | 0.954124i | \(0.596790\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.483969 | −0.0198408 | ||||||||
\(596\) | 6.84115 | 0.280224 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −13.3670 | −0.546617 | ||||||||
\(599\) | 0.156940 | 0.00641241 | 0.00320620 | − | 0.999995i | \(-0.498979\pi\) | ||||
0.00320620 | + | 0.999995i | \(0.498979\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 36.9757 | 1.50827 | 0.754135 | − | 0.656720i | \(-0.228056\pi\) | ||||
0.754135 | + | 0.656720i | \(0.228056\pi\) | |||||||
\(602\) | 0.876957 | 0.0357421 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 21.8371 | 0.888538 | ||||||||
\(605\) | −49.6367 | −2.01802 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 40.9855 | 1.66355 | 0.831776 | − | 0.555112i | \(-0.187324\pi\) | ||||
0.831776 | + | 0.555112i | \(0.187324\pi\) | |||||||
\(608\) | 5.26526 | 0.213534 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −20.4527 | −0.828104 | ||||||||
\(611\) | −71.8344 | −2.90611 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.72829 | 0.150584 | 0.0752921 | − | 0.997162i | \(-0.476011\pi\) | ||||
0.0752921 | + | 0.997162i | \(0.476011\pi\) | |||||||
\(614\) | −22.7730 | −0.919042 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.996662 | −0.0401567 | ||||||||
\(617\) | −16.5328 | −0.665584 | −0.332792 | − | 0.943000i | \(-0.607991\pi\) | ||||
−0.332792 | + | 0.943000i | \(0.607991\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 24.5417 | 0.986415 | 0.493208 | − | 0.869912i | \(-0.335824\pi\) | ||||
0.493208 | + | 0.869912i | \(0.335824\pi\) | |||||||
\(620\) | 5.34115 | 0.214506 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −31.3806 | −1.25825 | ||||||||
\(623\) | −2.08584 | −0.0835673 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17.9542 | −0.718170 | ||||||||
\(626\) | 4.18723 | 0.167355 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −19.8674 | −0.792797 | ||||||||
\(629\) | −0.739743 | −0.0294955 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.74272 | 0.268423 | 0.134212 | − | 0.990953i | \(-0.457150\pi\) | ||||
0.134212 | + | 0.990953i | \(0.457150\pi\) | |||||||
\(632\) | −0.927623 | −0.0368989 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −9.71753 | −0.385932 | ||||||||
\(635\) | −66.9897 | −2.65841 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 37.0942 | 1.46973 | ||||||||
\(638\) | 31.1951 | 1.23502 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −3.33861 | −0.131970 | ||||||||
\(641\) | 33.4562 | 1.32144 | 0.660719 | − | 0.750633i | \(-0.270251\pi\) | ||||
0.660719 | + | 0.750633i | \(0.270251\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 44.9939 | 1.77439 | 0.887193 | − | 0.461398i | \(-0.152652\pi\) | ||||
0.887193 | + | 0.461398i | \(0.152652\pi\) | |||||||
\(644\) | 0.491595 | 0.0193716 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.89493 | 0.153244 | ||||||||
\(647\) | 4.93692 | 0.194090 | 0.0970451 | − | 0.995280i | \(-0.469061\pi\) | ||||
0.0970451 | + | 0.995280i | \(0.469061\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.17711 | −0.163966 | ||||||||
\(650\) | −32.7502 | −1.28457 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.27443 | −0.167399 | ||||||||
\(653\) | 36.7104 | 1.43659 | 0.718294 | − | 0.695740i | \(-0.244923\pi\) | ||||
0.718294 | + | 0.695740i | \(0.244923\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −28.1327 | −1.09923 | ||||||||
\(656\) | −5.25874 | −0.205319 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 2.64184 | 0.102990 | ||||||||
\(659\) | −43.6251 | −1.69939 | −0.849696 | − | 0.527273i | \(-0.823215\pi\) | ||||
−0.849696 | + | 0.527273i | \(0.823215\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13.6589 | −0.531268 | −0.265634 | − | 0.964074i | \(-0.585581\pi\) | ||||
−0.265634 | + | 0.964074i | \(0.585581\pi\) | |||||||
\(662\) | 4.19467 | 0.163031 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −8.85942 | −0.343812 | ||||||||
\(665\) | −3.44474 | −0.133581 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −15.3867 | −0.595776 | ||||||||
\(668\) | 0.615260 | 0.0238051 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −23.4663 | −0.906583 | ||||||||
\(671\) | −31.1574 | −1.20282 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −33.0580 | −1.27429 | −0.637146 | − | 0.770743i | \(-0.719885\pi\) | ||||
−0.637146 | + | 0.770743i | \(0.719885\pi\) | |||||||
\(674\) | 17.3297 | 0.667516 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 15.3919 | 0.591996 | ||||||||
\(677\) | −17.1146 | −0.657767 | −0.328884 | − | 0.944370i | \(-0.606672\pi\) | ||||
−0.328884 | + | 0.944370i | \(0.606672\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.03971 | 0.0782768 | ||||||||
\(680\) | −2.46971 | −0.0947092 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 8.13665 | 0.311568 | ||||||||
\(683\) | −0.957620 | −0.0366423 | −0.0183212 | − | 0.999832i | \(-0.505832\pi\) | ||||
−0.0183212 | + | 0.999832i | \(0.505832\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 69.4773 | 2.65459 | ||||||||
\(686\) | −2.73594 | −0.104459 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4.47515 | 0.170613 | ||||||||
\(689\) | 52.0314 | 1.98224 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.99795 | −0.380340 | −0.190170 | − | 0.981751i | \(-0.560904\pi\) | ||||
−0.190170 | + | 0.981751i | \(0.560904\pi\) | |||||||
\(692\) | 20.9888 | 0.797873 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −0.604429 | −0.0229438 | ||||||||
\(695\) | 0.408768 | 0.0155055 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.89011 | −0.147349 | ||||||||
\(698\) | 15.8975 | 0.601728 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.20445 | 0.0455238 | ||||||||
\(701\) | 3.05328 | 0.115321 | 0.0576604 | − | 0.998336i | \(-0.481636\pi\) | ||||
0.0576604 | + | 0.998336i | \(0.481636\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.26526 | −0.198583 | ||||||||
\(704\) | −5.08601 | −0.191686 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −5.98441 | −0.225226 | ||||||||
\(707\) | −0.571504 | −0.0214936 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −47.9650 | −1.80136 | −0.900682 | − | 0.434479i | \(-0.856933\pi\) | ||||
−0.900682 | + | 0.434479i | \(0.856933\pi\) | |||||||
\(710\) | −34.9072 | −1.31004 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −10.6441 | −0.398905 | ||||||||
\(713\) | −4.01333 | −0.150300 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −90.4774 | −3.38366 | ||||||||
\(716\) | −22.4414 | −0.838673 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 7.52687 | 0.280900 | ||||||||
\(719\) | 32.0932 | 1.19687 | 0.598437 | − | 0.801170i | \(-0.295789\pi\) | ||||
0.598437 | + | 0.801170i | \(0.295789\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.47175 | 0.0920527 | ||||||||
\(722\) | 8.72292 | 0.324633 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 5.60462 | 0.208294 | ||||||||
\(725\) | −37.6986 | −1.40009 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 23.7998 | 0.882686 | 0.441343 | − | 0.897339i | \(-0.354502\pi\) | ||||
0.441343 | + | 0.897339i | \(0.354502\pi\) | |||||||
\(728\) | −1.04416 | −0.0386992 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −25.8266 | −0.955887 | ||||||||
\(731\) | 3.31046 | 0.122442 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.63216 | 0.244964 | 0.122482 | − | 0.992471i | \(-0.460915\pi\) | ||||
0.122482 | + | 0.992471i | \(0.460915\pi\) | |||||||
\(734\) | −18.5266 | −0.683829 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.50863 | 0.0924693 | ||||||||
\(737\) | −35.7484 | −1.31681 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −42.4986 | −1.56334 | −0.781669 | − | 0.623694i | \(-0.785631\pi\) | ||||
−0.781669 | + | 0.623694i | \(0.785631\pi\) | |||||||
\(740\) | 3.33861 | 0.122730 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.91355 | −0.0702485 | ||||||||
\(743\) | −43.9188 | −1.61122 | −0.805612 | − | 0.592443i | \(-0.798164\pi\) | ||||
−0.805612 | + | 0.592443i | \(0.798164\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −22.8399 | −0.836791 | ||||||||
\(746\) | −29.4102 | −1.07678 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −3.76234 | −0.137565 | ||||||||
\(749\) | 0.760114 | 0.0277740 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.6148 | 0.387340 | 0.193670 | − | 0.981067i | \(-0.437961\pi\) | ||||
0.193670 | + | 0.981067i | \(0.437961\pi\) | |||||||
\(752\) | 13.4814 | 0.491617 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 32.6818 | 1.19020 | ||||||||
\(755\) | −72.9055 | −2.65330 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 40.1639 | 1.45978 | 0.729892 | − | 0.683563i | \(-0.239570\pi\) | ||||
0.729892 | + | 0.683563i | \(0.239570\pi\) | |||||||
\(758\) | 10.0742 | 0.365910 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −17.5787 | −0.637645 | ||||||||
\(761\) | 17.1467 | 0.621568 | 0.310784 | − | 0.950481i | \(-0.399408\pi\) | ||||
0.310784 | + | 0.950481i | \(0.399408\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.105121 | 0.00380563 | ||||||||
\(764\) | −4.12388 | −0.149197 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 15.6220 | 0.564446 | ||||||||
\(767\) | −4.37619 | −0.158015 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11.9471 | 0.430824 | 0.215412 | − | 0.976523i | \(-0.430891\pi\) | ||||
0.215412 | + | 0.976523i | \(0.430891\pi\) | |||||||
\(770\) | 3.32747 | 0.119914 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −8.55099 | −0.307757 | ||||||||
\(773\) | −50.8932 | −1.83050 | −0.915250 | − | 0.402886i | \(-0.868007\pi\) | ||||
−0.915250 | + | 0.402886i | \(0.868007\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.83297 | −0.353211 | ||||||||
\(776\) | 10.4087 | 0.373651 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 16.6098 | 0.595491 | ||||||||
\(779\) | −27.6886 | −0.992047 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −53.1773 | −1.90283 | ||||||||
\(782\) | 1.85574 | 0.0663611 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.96160 | −0.248629 | ||||||||
\(785\) | 66.3297 | 2.36741 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12.0089 | −0.428071 | −0.214036 | − | 0.976826i | \(-0.568661\pi\) | ||||
−0.214036 | + | 0.976826i | \(0.568661\pi\) | |||||||
\(788\) | 13.1755 | 0.469357 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 3.09697 | 0.110185 | ||||||||
\(791\) | 3.73001 | 0.132624 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −32.6423 | −1.15916 | ||||||||
\(794\) | 23.9512 | 0.849995 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 18.5811 | 0.658589 | ||||||||
\(797\) | −1.21781 | −0.0431372 | −0.0215686 | − | 0.999767i | \(-0.506866\pi\) | ||||
−0.0215686 | + | 0.999767i | \(0.506866\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.97278 | 0.352812 | ||||||||
\(800\) | 6.14633 | 0.217306 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −28.2179 | −0.996407 | ||||||||
\(803\) | −39.3440 | −1.38842 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.64125 | −0.0578463 | ||||||||
\(806\) | 8.52443 | 0.300260 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −2.91641 | −0.102599 | ||||||||
\(809\) | −31.5509 | −1.10927 | −0.554635 | − | 0.832094i | \(-0.687142\pi\) | ||||
−0.554635 | + | 0.832094i | \(0.687142\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11.0562 | −0.388235 | −0.194118 | − | 0.980978i | \(-0.562184\pi\) | ||||
−0.194118 | + | 0.980978i | \(0.562184\pi\) | |||||||
\(812\) | −1.20193 | −0.0421796 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 5.08601 | 0.178264 | ||||||||
\(815\) | 14.2707 | 0.499879 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 23.5628 | 0.824358 | ||||||||
\(818\) | 20.8364 | 0.728527 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 17.5569 | 0.613113 | ||||||||
\(821\) | 19.6171 | 0.684642 | 0.342321 | − | 0.939583i | \(-0.388787\pi\) | ||||
0.342321 | + | 0.939583i | \(0.388787\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −40.3719 | −1.40728 | −0.703638 | − | 0.710559i | \(-0.748442\pi\) | ||||
−0.703638 | + | 0.710559i | \(0.748442\pi\) | |||||||
\(824\) | 12.6134 | 0.439410 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.160942 | 0.00559989 | ||||||||
\(827\) | −44.3183 | −1.54110 | −0.770549 | − | 0.637381i | \(-0.780018\pi\) | ||||
−0.770549 | + | 0.637381i | \(0.780018\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14.1163 | −0.490279 | −0.245139 | − | 0.969488i | \(-0.578834\pi\) | ||||
−0.245139 | + | 0.969488i | \(0.578834\pi\) | |||||||
\(830\) | 29.5782 | 1.02667 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −5.32840 | −0.184729 | ||||||||
\(833\) | −5.14979 | −0.178430 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.05411 | −0.0710855 | ||||||||
\(836\) | −26.7791 | −0.926176 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 23.4768 | 0.810991 | ||||||||
\(839\) | −4.20041 | −0.145014 | −0.0725071 | − | 0.997368i | \(-0.523100\pi\) | ||||
−0.0725071 | + | 0.997368i | \(0.523100\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.61994 | 0.297239 | ||||||||
\(842\) | −26.6544 | −0.918570 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −4.80875 | −0.165524 | ||||||||
\(845\) | −51.3876 | −1.76779 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.91345 | 0.100107 | ||||||||
\(848\) | −9.76490 | −0.335328 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 4.54671 | 0.155951 | ||||||||
\(851\) | −2.50863 | −0.0859947 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −15.9537 | −0.546243 | −0.273121 | − | 0.961980i | \(-0.588056\pi\) | ||||
−0.273121 | + | 0.961980i | \(0.588056\pi\) | |||||||
\(854\) | 1.20048 | 0.0410795 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3.87889 | 0.132578 | ||||||||
\(857\) | −0.986693 | −0.0337048 | −0.0168524 | − | 0.999858i | \(-0.505365\pi\) | ||||
−0.0168524 | + | 0.999858i | \(0.505365\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.41493 | 0.218874 | 0.109437 | − | 0.993994i | \(-0.465095\pi\) | ||||
0.109437 | + | 0.993994i | \(0.465095\pi\) | |||||||
\(860\) | −14.9408 | −0.509476 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 27.9472 | 0.951886 | ||||||||
\(863\) | −19.6447 | −0.668714 | −0.334357 | − | 0.942446i | \(-0.608519\pi\) | ||||
−0.334357 | + | 0.942446i | \(0.608519\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −70.0733 | −2.38257 | ||||||||
\(866\) | 14.4980 | 0.492663 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −0.313501 | −0.0106409 | ||||||||
\(869\) | 4.71790 | 0.160044 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −37.4521 | −1.26902 | ||||||||
\(872\) | 0.536436 | 0.0181660 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 13.2086 | 0.446787 | ||||||||
\(875\) | −0.749978 | −0.0253539 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −25.0212 | −0.844905 | −0.422452 | − | 0.906385i | \(-0.638831\pi\) | ||||
−0.422452 | + | 0.906385i | \(0.638831\pi\) | |||||||
\(878\) | 10.2482 | 0.345861 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 16.9802 | 0.572403 | ||||||||
\(881\) | 20.0574 | 0.675751 | 0.337875 | − | 0.941191i | \(-0.390292\pi\) | ||||
0.337875 | + | 0.941191i | \(0.390292\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −10.4184 | −0.350608 | −0.175304 | − | 0.984514i | \(-0.556091\pi\) | ||||
−0.175304 | + | 0.984514i | \(0.556091\pi\) | |||||||
\(884\) | −3.94165 | −0.132572 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 8.13881 | 0.273429 | ||||||||
\(887\) | −28.0688 | −0.942459 | −0.471229 | − | 0.882011i | \(-0.656190\pi\) | ||||
−0.471229 | + | 0.882011i | \(0.656190\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.93200 | 0.131875 | ||||||||
\(890\) | 35.5365 | 1.19119 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 5.28621 | 0.176995 | ||||||||
\(893\) | 70.9831 | 2.37536 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 74.9230 | 2.50440 | ||||||||
\(896\) | 0.195962 | 0.00654662 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.81755 | 0.0606524 | ||||||||
\(899\) | 9.81245 | 0.327264 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.22352 | −0.240650 | ||||||||
\(902\) | 26.7460 | 0.890544 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 19.0344 | 0.633075 | ||||||||
\(905\) | −18.7116 | −0.621996 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6.81634 | −0.226333 | −0.113166 | − | 0.993576i | \(-0.536099\pi\) | ||||
−0.113166 | + | 0.993576i | \(0.536099\pi\) | |||||||
\(908\) | 6.52175 | 0.216432 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 3.48605 | 0.115562 | ||||||||
\(911\) | 46.1659 | 1.52954 | 0.764772 | − | 0.644301i | \(-0.222851\pi\) | ||||
0.764772 | + | 0.644301i | \(0.222851\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 45.0591 | 1.49124 | ||||||||
\(914\) | −38.9876 | −1.28959 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5.93818 | 0.196203 | ||||||||
\(917\) | 1.65126 | 0.0545295 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 26.8038 | 0.884175 | 0.442087 | − | 0.896972i | \(-0.354238\pi\) | ||||
0.442087 | + | 0.896972i | \(0.354238\pi\) | |||||||
\(920\) | −8.37534 | −0.276127 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −14.6527 | −0.482562 | ||||||||
\(923\) | −55.7117 | −1.83377 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.14633 | −0.202090 | ||||||||
\(926\) | 25.3342 | 0.832533 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −6.13351 | −0.201342 | ||||||||
\(929\) | 25.9178 | 0.850334 | 0.425167 | − | 0.905115i | \(-0.360215\pi\) | ||||
0.425167 | + | 0.905115i | \(0.360215\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −36.6546 | −1.20131 | ||||||||
\(932\) | 18.4107 | 0.603063 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −6.52767 | −0.213592 | ||||||||
\(935\) | 12.5610 | 0.410788 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8.04348 | 0.262769 | 0.131384 | − | 0.991331i | \(-0.458058\pi\) | ||||
0.131384 | + | 0.991331i | \(0.458058\pi\) | |||||||
\(938\) | 1.37737 | 0.0449727 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −45.0092 | −1.46804 | ||||||||
\(941\) | 57.0300 | 1.85913 | 0.929563 | − | 0.368664i | \(-0.120185\pi\) | ||||
0.929563 | + | 0.368664i | \(0.120185\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −13.1922 | −0.429598 | ||||||||
\(944\) | 0.821294 | 0.0267309 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −22.7606 | −0.740012 | ||||||||
\(947\) | −11.9823 | −0.389372 | −0.194686 | − | 0.980866i | \(-0.562369\pi\) | ||||
−0.194686 | + | 0.980866i | \(0.562369\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −41.2191 | −1.33803 | ||||||||
\(950\) | 32.3620 | 1.04996 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0.144961 | 0.00469822 | ||||||||
\(953\) | 53.7478 | 1.74106 | 0.870532 | − | 0.492112i | \(-0.163775\pi\) | ||||
0.870532 | + | 0.492112i | \(0.163775\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 13.7680 | 0.445523 | ||||||||
\(956\) | 24.0032 | 0.776320 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 19.4006 | 0.626806 | ||||||||
\(959\) | −4.07800 | −0.131686 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.4406 | −0.917439 | ||||||||
\(962\) | 5.32840 | 0.171795 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −17.2454 | −0.555437 | ||||||||
\(965\) | 28.5484 | 0.919006 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −54.0756 | −1.73895 | −0.869476 | − | 0.493975i | \(-0.835544\pi\) | ||||
−0.869476 | + | 0.493975i | \(0.835544\pi\) | |||||||
\(968\) | 14.8675 | 0.477859 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −34.7507 | −1.11578 | ||||||||
\(971\) | −16.9965 | −0.545442 | −0.272721 | − | 0.962093i | \(-0.587924\pi\) | ||||
−0.272721 | + | 0.962093i | \(0.587924\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.0239929 | −0.000769176 0 | ||||||||
\(974\) | −11.5204 | −0.369138 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6.12609 | 0.196091 | ||||||||
\(977\) | −14.3965 | −0.460585 | −0.230293 | − | 0.973121i | \(-0.573968\pi\) | ||||
−0.230293 | + | 0.973121i | \(0.573968\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 54.1360 | 1.73019 | ||||||||
\(980\) | 23.2421 | 0.742441 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −30.0958 | −0.960397 | ||||||||
\(983\) | −46.2710 | −1.47582 | −0.737908 | − | 0.674901i | \(-0.764186\pi\) | ||||
−0.737908 | + | 0.674901i | \(0.764186\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −43.9878 | −1.40157 | ||||||||
\(986\) | −4.53722 | −0.144494 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −28.0554 | −0.892561 | ||||||||
\(989\) | 11.2265 | 0.356981 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 50.4576 | 1.60284 | 0.801419 | − | 0.598103i | \(-0.204079\pi\) | ||||
0.801419 | + | 0.598103i | \(0.204079\pi\) | |||||||
\(992\) | −1.59981 | −0.0507940 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2.04890 | 0.0649870 | ||||||||
\(995\) | −62.0350 | −1.96664 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 51.1368 | 1.61952 | 0.809759 | − | 0.586762i | \(-0.199598\pi\) | ||||
0.809759 | + | 0.586762i | \(0.199598\pi\) | |||||||
\(998\) | 19.6116 | 0.620793 | ||||||||
\(999\) | 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 | 5994.2.a.bb.1.2 | 10 | ||
3.2 | odd | 2 | 5994.2.a.ba.1.9 | 10 | |||
9.2 | odd | 6 | 1998.2.e.e.1333.2 | 20 | |||
9.4 | even | 3 | 666.2.e.e.223.1 | ✓ | 20 | ||
9.5 | odd | 6 | 1998.2.e.e.667.2 | 20 | |||
9.7 | even | 3 | 666.2.e.e.445.1 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
666.2.e.e.223.1 | ✓ | 20 | 9.4 | even | 3 | ||
666.2.e.e.445.1 | yes | 20 | 9.7 | even | 3 | ||
1998.2.e.e.667.2 | 20 | 9.5 | odd | 6 | |||
1998.2.e.e.1333.2 | 20 | 9.2 | odd | 6 | |||
5994.2.a.ba.1.9 | 10 | 3.2 | odd | 2 | |||
5994.2.a.bb.1.2 | 10 | 1.1 | even | 1 | trivial |