Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8001,2,Mod(1,8001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8001, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8001 = 3^{2} \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8001.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: | \(63.8883066572\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} - 20 x^{14} + 38 x^{13} + 155 x^{12} - 275 x^{11} - 593 x^{10} + 957 x^{9} + 1177 x^{8} + \cdots + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 889) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Root | \(1.33134\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.33134 | 0.941403 | 0.470701 | − | 0.882293i | \(-0.344001\pi\) | ||||
0.470701 | + | 0.882293i | \(0.344001\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.227522 | −0.113761 | ||||||||
\(5\) | 2.92411 | 1.30770 | 0.653850 | − | 0.756624i | \(-0.273153\pi\) | ||||
0.653850 | + | 0.756624i | \(0.273153\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −2.96560 | −1.04850 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.89299 | 1.23107 | ||||||||
\(11\) | −6.16901 | −1.86003 | −0.930013 | − | 0.367526i | \(-0.880205\pi\) | ||||
−0.930013 | + | 0.367526i | \(0.880205\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.620036 | −0.171967 | −0.0859836 | − | 0.996297i | \(-0.527403\pi\) | ||||
−0.0859836 | + | 0.996297i | \(0.527403\pi\) | |||||||
\(14\) | −1.33134 | −0.355817 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.49319 | −0.873298 | ||||||||
\(17\) | −0.644462 | −0.156305 | −0.0781525 | − | 0.996941i | \(-0.524902\pi\) | ||||
−0.0781525 | + | 0.996941i | \(0.524902\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.75517 | 0.632080 | 0.316040 | − | 0.948746i | \(-0.397647\pi\) | ||||
0.316040 | + | 0.948746i | \(0.397647\pi\) | |||||||
\(20\) | −0.665298 | −0.148765 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −8.21308 | −1.75103 | ||||||||
\(23\) | −4.71184 | −0.982486 | −0.491243 | − | 0.871023i | \(-0.663457\pi\) | ||||
−0.491243 | + | 0.871023i | \(0.663457\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.55041 | 0.710081 | ||||||||
\(26\) | −0.825482 | −0.161890 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.227522 | 0.0429976 | ||||||||
\(29\) | 8.85381 | 1.64411 | 0.822056 | − | 0.569407i | \(-0.192827\pi\) | ||||
0.822056 | + | 0.569407i | \(0.192827\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.41753 | 0.434202 | 0.217101 | − | 0.976149i | \(-0.430340\pi\) | ||||
0.217101 | + | 0.976149i | \(0.430340\pi\) | |||||||
\(32\) | 1.28056 | 0.226373 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.858001 | −0.147146 | ||||||||
\(35\) | −2.92411 | −0.494264 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.07476 | −0.998685 | −0.499343 | − | 0.866405i | \(-0.666425\pi\) | ||||
−0.499343 | + | 0.866405i | \(0.666425\pi\) | |||||||
\(38\) | 3.66808 | 0.595042 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −8.67173 | −1.37112 | ||||||||
\(41\) | 2.70008 | 0.421681 | 0.210840 | − | 0.977520i | \(-0.432380\pi\) | ||||
0.210840 | + | 0.977520i | \(0.432380\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.3043 | 1.57140 | 0.785698 | − | 0.618611i | \(-0.212304\pi\) | ||||
0.785698 | + | 0.618611i | \(0.212304\pi\) | |||||||
\(44\) | 1.40358 | 0.211598 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.27308 | −0.924915 | ||||||||
\(47\) | 10.7764 | 1.57190 | 0.785950 | − | 0.618290i | \(-0.212174\pi\) | ||||
0.785950 | + | 0.618290i | \(0.212174\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 4.72681 | 0.668472 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.141072 | 0.0195631 | ||||||||
\(53\) | −6.17224 | −0.847822 | −0.423911 | − | 0.905704i | \(-0.639343\pi\) | ||||
−0.423911 | + | 0.905704i | \(0.639343\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −18.0388 | −2.43236 | ||||||||
\(56\) | 2.96560 | 0.396295 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 11.7875 | 1.54777 | ||||||||
\(59\) | 11.6075 | 1.51116 | 0.755581 | − | 0.655055i | \(-0.227355\pi\) | ||||
0.755581 | + | 0.655055i | \(0.227355\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.3316 | −1.57890 | −0.789448 | − | 0.613818i | \(-0.789633\pi\) | ||||
−0.789448 | + | 0.613818i | \(0.789633\pi\) | |||||||
\(62\) | 3.21857 | 0.408759 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.69124 | 1.08641 | ||||||||
\(65\) | −1.81305 | −0.224882 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.3886 | 1.51351 | 0.756753 | − | 0.653701i | \(-0.226785\pi\) | ||||
0.756753 | + | 0.653701i | \(0.226785\pi\) | |||||||
\(68\) | 0.146629 | 0.0177814 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.89299 | −0.465302 | ||||||||
\(71\) | 10.0499 | 1.19270 | 0.596351 | − | 0.802724i | \(-0.296617\pi\) | ||||
0.596351 | + | 0.802724i | \(0.296617\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.20886 | 0.960775 | 0.480387 | − | 0.877056i | \(-0.340496\pi\) | ||||
0.480387 | + | 0.877056i | \(0.340496\pi\) | |||||||
\(74\) | −8.08760 | −0.940165 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.626862 | −0.0719060 | ||||||||
\(77\) | 6.16901 | 0.703024 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.30230 | 0.259029 | 0.129515 | − | 0.991578i | \(-0.458658\pi\) | ||||
0.129515 | + | 0.991578i | \(0.458658\pi\) | |||||||
\(80\) | −10.2145 | −1.14201 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.59473 | 0.396972 | ||||||||
\(83\) | 1.22797 | 0.134787 | 0.0673936 | − | 0.997726i | \(-0.478532\pi\) | ||||
0.0673936 | + | 0.997726i | \(0.478532\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.88448 | −0.204400 | ||||||||
\(86\) | 13.7186 | 1.47932 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 18.2948 | 1.95023 | ||||||||
\(89\) | −11.7296 | −1.24334 | −0.621668 | − | 0.783281i | \(-0.713544\pi\) | ||||
−0.621668 | + | 0.783281i | \(0.713544\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.620036 | 0.0649975 | ||||||||
\(92\) | 1.07205 | 0.111768 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 14.3471 | 1.47979 | ||||||||
\(95\) | 8.05642 | 0.826571 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.19035 | 0.120862 | 0.0604309 | − | 0.998172i | \(-0.480753\pi\) | ||||
0.0604309 | + | 0.998172i | \(0.480753\pi\) | |||||||
\(98\) | 1.33134 | 0.134486 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.807795 | −0.0807795 | ||||||||
\(101\) | 19.3595 | 1.92635 | 0.963173 | − | 0.268882i | \(-0.0866542\pi\) | ||||
0.963173 | + | 0.268882i | \(0.0866542\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.2002 | −1.00506 | −0.502528 | − | 0.864561i | \(-0.667597\pi\) | ||||
−0.502528 | + | 0.864561i | \(0.667597\pi\) | |||||||
\(104\) | 1.83878 | 0.180307 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.21738 | −0.798142 | ||||||||
\(107\) | 15.3876 | 1.48758 | 0.743788 | − | 0.668415i | \(-0.233027\pi\) | ||||
0.743788 | + | 0.668415i | \(0.233027\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.40780 | −0.230626 | −0.115313 | − | 0.993329i | \(-0.536787\pi\) | ||||
−0.115313 | + | 0.993329i | \(0.536787\pi\) | |||||||
\(110\) | −24.0159 | −2.28983 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.49319 | 0.330075 | ||||||||
\(113\) | 2.71096 | 0.255026 | 0.127513 | − | 0.991837i | \(-0.459301\pi\) | ||||
0.127513 | + | 0.991837i | \(0.459301\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −13.7779 | −1.28480 | ||||||||
\(116\) | −2.01443 | −0.187036 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 15.4535 | 1.42261 | ||||||||
\(119\) | 0.644462 | 0.0590777 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 27.0567 | 2.45970 | ||||||||
\(122\) | −16.4176 | −1.48638 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.550041 | −0.0493952 | ||||||||
\(125\) | −4.23877 | −0.379127 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.00000 | −0.0887357 | ||||||||
\(128\) | 9.00992 | 0.796372 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.41380 | −0.211704 | ||||||||
\(131\) | 12.0134 | 1.04961 | 0.524807 | − | 0.851222i | \(-0.324138\pi\) | ||||
0.524807 | + | 0.851222i | \(0.324138\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.75517 | −0.238904 | ||||||||
\(134\) | 16.4935 | 1.42482 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.91122 | 0.163885 | ||||||||
\(137\) | 12.6214 | 1.07832 | 0.539161 | − | 0.842203i | \(-0.318742\pi\) | ||||
0.539161 | + | 0.842203i | \(0.318742\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −17.1553 | −1.45510 | −0.727548 | − | 0.686057i | \(-0.759340\pi\) | ||||
−0.727548 | + | 0.686057i | \(0.759340\pi\) | |||||||
\(140\) | 0.665298 | 0.0562280 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 13.3799 | 1.12281 | ||||||||
\(143\) | 3.82501 | 0.319863 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 25.8895 | 2.15001 | ||||||||
\(146\) | 10.9288 | 0.904476 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.38214 | 0.113611 | ||||||||
\(149\) | −5.64770 | −0.462677 | −0.231339 | − | 0.972873i | \(-0.574311\pi\) | ||||
−0.231339 | + | 0.972873i | \(0.574311\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.0571 | 1.06257 | 0.531287 | − | 0.847192i | \(-0.321709\pi\) | ||||
0.531287 | + | 0.847192i | \(0.321709\pi\) | |||||||
\(152\) | −8.17074 | −0.662734 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 8.21308 | 0.661829 | ||||||||
\(155\) | 7.06913 | 0.567806 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.53317 | −0.521404 | −0.260702 | − | 0.965419i | \(-0.583954\pi\) | ||||
−0.260702 | + | 0.965419i | \(0.583954\pi\) | |||||||
\(158\) | 3.06516 | 0.243851 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3.74449 | 0.296028 | ||||||||
\(161\) | 4.71184 | 0.371345 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.2598 | 1.03858 | 0.519292 | − | 0.854597i | \(-0.326196\pi\) | ||||
0.519292 | + | 0.854597i | \(0.326196\pi\) | |||||||
\(164\) | −0.614326 | −0.0479708 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.63485 | 0.126889 | ||||||||
\(167\) | 2.01803 | 0.156160 | 0.0780801 | − | 0.996947i | \(-0.475121\pi\) | ||||
0.0780801 | + | 0.996947i | \(0.475121\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.6156 | −0.970427 | ||||||||
\(170\) | −2.50889 | −0.192423 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.34446 | −0.178763 | ||||||||
\(173\) | −1.84088 | −0.139960 | −0.0699799 | − | 0.997548i | \(-0.522294\pi\) | ||||
−0.0699799 | + | 0.997548i | \(0.522294\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.55041 | −0.268385 | ||||||||
\(176\) | 21.5495 | 1.62436 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −15.6161 | −1.17048 | ||||||||
\(179\) | −18.7622 | −1.40235 | −0.701177 | − | 0.712987i | \(-0.747342\pi\) | ||||
−0.701177 | + | 0.712987i | \(0.747342\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 23.1779 | 1.72280 | 0.861399 | − | 0.507929i | \(-0.169589\pi\) | ||||
0.861399 | + | 0.507929i | \(0.169589\pi\) | |||||||
\(182\) | 0.825482 | 0.0611888 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 13.9734 | 1.03013 | ||||||||
\(185\) | −17.7633 | −1.30598 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.97569 | 0.290731 | ||||||||
\(188\) | −2.45187 | −0.178821 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 10.7259 | 0.778137 | ||||||||
\(191\) | 0.0673136 | 0.00487064 | 0.00243532 | − | 0.999997i | \(-0.499225\pi\) | ||||
0.00243532 | + | 0.999997i | \(0.499225\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −22.7803 | −1.63976 | −0.819879 | − | 0.572536i | \(-0.805960\pi\) | ||||
−0.819879 | + | 0.572536i | \(0.805960\pi\) | |||||||
\(194\) | 1.58477 | 0.113780 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.227522 | −0.0162516 | ||||||||
\(197\) | 20.6532 | 1.47148 | 0.735741 | − | 0.677263i | \(-0.236834\pi\) | ||||
0.735741 | + | 0.677263i | \(0.236834\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.546917 | 0.0387699 | 0.0193850 | − | 0.999812i | \(-0.493829\pi\) | ||||
0.0193850 | + | 0.999812i | \(0.493829\pi\) | |||||||
\(200\) | −10.5291 | −0.744518 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 25.7742 | 1.81347 | ||||||||
\(203\) | −8.85381 | −0.621416 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.89531 | 0.551432 | ||||||||
\(206\) | −13.5800 | −0.946162 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.16590 | 0.150178 | ||||||||
\(209\) | −16.9967 | −1.17569 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.86912 | −0.541733 | −0.270866 | − | 0.962617i | \(-0.587310\pi\) | ||||
−0.270866 | + | 0.962617i | \(0.587310\pi\) | |||||||
\(212\) | 1.40432 | 0.0964490 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 20.4862 | 1.40041 | ||||||||
\(215\) | 30.1310 | 2.05491 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.41753 | −0.164113 | ||||||||
\(218\) | −3.20561 | −0.217112 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 4.10423 | 0.276707 | ||||||||
\(221\) | 0.399590 | 0.0268793 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.641278 | 0.0429432 | 0.0214716 | − | 0.999769i | \(-0.493165\pi\) | ||||
0.0214716 | + | 0.999769i | \(0.493165\pi\) | |||||||
\(224\) | −1.28056 | −0.0855609 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.60923 | 0.240082 | ||||||||
\(227\) | −25.4329 | −1.68804 | −0.844021 | − | 0.536310i | \(-0.819818\pi\) | ||||
−0.844021 | + | 0.536310i | \(0.819818\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −17.2560 | −1.14031 | −0.570156 | − | 0.821537i | \(-0.693117\pi\) | ||||
−0.570156 | + | 0.821537i | \(0.693117\pi\) | |||||||
\(230\) | −18.3432 | −1.20951 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −26.2568 | −1.72385 | ||||||||
\(233\) | −17.2249 | −1.12844 | −0.564219 | − | 0.825625i | \(-0.690823\pi\) | ||||
−0.564219 | + | 0.825625i | \(0.690823\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 31.5114 | 2.05557 | ||||||||
\(236\) | −2.64095 | −0.171911 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.858001 | 0.0556159 | ||||||||
\(239\) | 5.48952 | 0.355088 | 0.177544 | − | 0.984113i | \(-0.443185\pi\) | ||||
0.177544 | + | 0.984113i | \(0.443185\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −26.9366 | −1.73514 | −0.867571 | − | 0.497314i | \(-0.834320\pi\) | ||||
−0.867571 | + | 0.497314i | \(0.834320\pi\) | |||||||
\(242\) | 36.0218 | 2.31557 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.80570 | 0.179617 | ||||||||
\(245\) | 2.92411 | 0.186814 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.70831 | −0.108697 | ||||||||
\(248\) | −7.16943 | −0.455259 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −5.64326 | −0.356911 | ||||||||
\(251\) | −0.302222 | −0.0190761 | −0.00953804 | − | 0.999955i | \(-0.503036\pi\) | ||||
−0.00953804 | + | 0.999955i | \(0.503036\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 29.0674 | 1.82745 | ||||||||
\(254\) | −1.33134 | −0.0835360 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −5.38718 | −0.336698 | ||||||||
\(257\) | 18.7785 | 1.17137 | 0.585685 | − | 0.810539i | \(-0.300826\pi\) | ||||
0.585685 | + | 0.810539i | \(0.300826\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.07476 | 0.377467 | ||||||||
\(260\) | 0.412509 | 0.0255827 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 15.9939 | 0.988109 | ||||||||
\(263\) | 4.41926 | 0.272503 | 0.136251 | − | 0.990674i | \(-0.456494\pi\) | ||||
0.136251 | + | 0.990674i | \(0.456494\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −18.0483 | −1.10870 | ||||||||
\(266\) | −3.66808 | −0.224905 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2.81867 | −0.172178 | ||||||||
\(269\) | 2.13768 | 0.130337 | 0.0651683 | − | 0.997874i | \(-0.479242\pi\) | ||||
0.0651683 | + | 0.997874i | \(0.479242\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.17538 | −0.192891 | −0.0964454 | − | 0.995338i | \(-0.530747\pi\) | ||||
−0.0964454 | + | 0.995338i | \(0.530747\pi\) | |||||||
\(272\) | 2.25123 | 0.136501 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 16.8035 | 1.01513 | ||||||||
\(275\) | −21.9025 | −1.32077 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 20.5642 | 1.23559 | 0.617793 | − | 0.786341i | \(-0.288027\pi\) | ||||
0.617793 | + | 0.786341i | \(0.288027\pi\) | |||||||
\(278\) | −22.8396 | −1.36983 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 8.67173 | 0.518235 | ||||||||
\(281\) | 18.9073 | 1.12791 | 0.563956 | − | 0.825805i | \(-0.309279\pi\) | ||||
0.563956 | + | 0.825805i | \(0.309279\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.0480 | −0.894513 | −0.447256 | − | 0.894406i | \(-0.647599\pi\) | ||||
−0.447256 | + | 0.894406i | \(0.647599\pi\) | |||||||
\(284\) | −2.28657 | −0.135683 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.09241 | 0.301120 | ||||||||
\(287\) | −2.70008 | −0.159380 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.5847 | −0.975569 | ||||||||
\(290\) | 34.4678 | 2.02402 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.86770 | −0.109299 | ||||||||
\(293\) | −12.4842 | −0.729334 | −0.364667 | − | 0.931138i | \(-0.618817\pi\) | ||||
−0.364667 | + | 0.931138i | \(0.618817\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 33.9414 | 1.97615 | ||||||||
\(296\) | 18.0153 | 1.04712 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −7.51903 | −0.435566 | ||||||||
\(299\) | 2.92151 | 0.168955 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.3043 | −0.593932 | ||||||||
\(302\) | 17.3835 | 1.00031 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −9.62434 | −0.551994 | ||||||||
\(305\) | −36.0588 | −2.06472 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 27.4111 | 1.56443 | 0.782216 | − | 0.623007i | \(-0.214089\pi\) | ||||
0.782216 | + | 0.623007i | \(0.214089\pi\) | |||||||
\(308\) | −1.40358 | −0.0799766 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 9.41144 | 0.534534 | ||||||||
\(311\) | 25.1878 | 1.42827 | 0.714135 | − | 0.700008i | \(-0.246820\pi\) | ||||
0.714135 | + | 0.700008i | \(0.246820\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.7164 | −0.662251 | −0.331125 | − | 0.943587i | \(-0.607428\pi\) | ||||
−0.331125 | + | 0.943587i | \(0.607428\pi\) | |||||||
\(314\) | −8.69790 | −0.490851 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.523824 | −0.0294674 | ||||||||
\(317\) | −18.0033 | −1.01117 | −0.505584 | − | 0.862777i | \(-0.668723\pi\) | ||||
−0.505584 | + | 0.862777i | \(0.668723\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −54.6192 | −3.05809 | ||||||||
\(320\) | 25.4141 | 1.42069 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 6.27308 | 0.349585 | ||||||||
\(323\) | −1.77560 | −0.0987973 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.20138 | −0.122111 | ||||||||
\(326\) | 17.6533 | 0.977726 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −8.00734 | −0.442131 | ||||||||
\(329\) | −10.7764 | −0.594122 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.0863 | −0.774254 | −0.387127 | − | 0.922026i | \(-0.626533\pi\) | ||||
−0.387127 | + | 0.922026i | \(0.626533\pi\) | |||||||
\(332\) | −0.279390 | −0.0153335 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 2.68670 | 0.147010 | ||||||||
\(335\) | 36.2255 | 1.97921 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.85642 | 0.373493 | 0.186747 | − | 0.982408i | \(-0.440206\pi\) | ||||
0.186747 | + | 0.982408i | \(0.440206\pi\) | |||||||
\(338\) | −16.7957 | −0.913563 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0.428759 | 0.0232527 | ||||||||
\(341\) | −14.9138 | −0.807627 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −30.5585 | −1.64760 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.45085 | −0.131759 | ||||||||
\(347\) | −15.2537 | −0.818860 | −0.409430 | − | 0.912342i | \(-0.634272\pi\) | ||||
−0.409430 | + | 0.912342i | \(0.634272\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.20325 | 0.385581 | 0.192791 | − | 0.981240i | \(-0.438246\pi\) | ||||
0.192791 | + | 0.981240i | \(0.438246\pi\) | |||||||
\(350\) | −4.72681 | −0.252659 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −7.89977 | −0.421059 | ||||||||
\(353\) | 4.26996 | 0.227267 | 0.113633 | − | 0.993523i | \(-0.463751\pi\) | ||||
0.113633 | + | 0.993523i | \(0.463751\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 29.3869 | 1.55970 | ||||||||
\(356\) | 2.66874 | 0.141443 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −24.9790 | −1.32018 | ||||||||
\(359\) | 31.0817 | 1.64043 | 0.820214 | − | 0.572057i | \(-0.193854\pi\) | ||||
0.820214 | + | 0.572057i | \(0.193854\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.4090 | −0.600475 | ||||||||
\(362\) | 30.8577 | 1.62185 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.141072 | −0.00739417 | ||||||||
\(365\) | 24.0036 | 1.25641 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −18.3623 | −0.958503 | −0.479251 | − | 0.877678i | \(-0.659092\pi\) | ||||
−0.479251 | + | 0.877678i | \(0.659092\pi\) | |||||||
\(368\) | 16.4593 | 0.858002 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −23.6490 | −1.22945 | ||||||||
\(371\) | 6.17224 | 0.320447 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −20.8539 | −1.07977 | −0.539886 | − | 0.841738i | \(-0.681533\pi\) | ||||
−0.539886 | + | 0.841738i | \(0.681533\pi\) | |||||||
\(374\) | 5.29302 | 0.273695 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −31.9585 | −1.64813 | ||||||||
\(377\) | −5.48968 | −0.282733 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.97802 | 0.358437 | 0.179218 | − | 0.983809i | \(-0.442643\pi\) | ||||
0.179218 | + | 0.983809i | \(0.442643\pi\) | |||||||
\(380\) | −1.83301 | −0.0940315 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0.0896176 | 0.00458524 | ||||||||
\(383\) | 0.0360913 | 0.00184418 | 0.000922089 | − | 1.00000i | \(-0.499706\pi\) | ||||
0.000922089 | 1.00000i | \(0.499706\pi\) | ||||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 18.0388 | 0.919345 | ||||||||
\(386\) | −30.3284 | −1.54367 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −0.270831 | −0.0137494 | ||||||||
\(389\) | 19.6007 | 0.993793 | 0.496897 | − | 0.867810i | \(-0.334473\pi\) | ||||
0.496897 | + | 0.867810i | \(0.334473\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.03660 | 0.153567 | ||||||||
\(392\) | −2.96560 | −0.149785 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 27.4966 | 1.38526 | ||||||||
\(395\) | 6.73218 | 0.338733 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 20.6792 | 1.03786 | 0.518930 | − | 0.854817i | \(-0.326331\pi\) | ||||
0.518930 | + | 0.854817i | \(0.326331\pi\) | |||||||
\(398\) | 0.728135 | 0.0364981 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −12.4022 | −0.620112 | ||||||||
\(401\) | 24.7687 | 1.23689 | 0.618444 | − | 0.785829i | \(-0.287763\pi\) | ||||
0.618444 | + | 0.785829i | \(0.287763\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.49896 | −0.0746684 | ||||||||
\(404\) | −4.40472 | −0.219143 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −11.7875 | −0.585002 | ||||||||
\(407\) | 37.4753 | 1.85758 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −37.2721 | −1.84299 | −0.921494 | − | 0.388392i | \(-0.873031\pi\) | ||||
−0.921494 | + | 0.388392i | \(0.873031\pi\) | |||||||
\(410\) | 10.5114 | 0.519120 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.32077 | 0.114336 | ||||||||
\(413\) | −11.6075 | −0.571165 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.59071 | 0.176261 | ||||||||
\(416\) | −0.793992 | −0.0389287 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −22.6284 | −1.10679 | ||||||||
\(419\) | 25.0016 | 1.22141 | 0.610705 | − | 0.791858i | \(-0.290886\pi\) | ||||
0.610705 | + | 0.791858i | \(0.290886\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.6102 | 0.517108 | 0.258554 | − | 0.965997i | \(-0.416754\pi\) | ||||
0.258554 | + | 0.965997i | \(0.416754\pi\) | |||||||
\(422\) | −10.4765 | −0.509989 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 18.3044 | 0.888940 | ||||||||
\(425\) | −2.28810 | −0.110989 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.3316 | 0.596766 | ||||||||
\(428\) | −3.50102 | −0.169228 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 40.1147 | 1.93450 | ||||||||
\(431\) | 33.4302 | 1.61028 | 0.805138 | − | 0.593088i | \(-0.202091\pi\) | ||||
0.805138 | + | 0.593088i | \(0.202091\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.82890 | 0.232062 | 0.116031 | − | 0.993246i | \(-0.462983\pi\) | ||||
0.116031 | + | 0.993246i | \(0.462983\pi\) | |||||||
\(434\) | −3.21857 | −0.154496 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.547827 | 0.0262362 | ||||||||
\(437\) | −12.9819 | −0.621009 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.44232 | 0.259748 | 0.129874 | − | 0.991531i | \(-0.458543\pi\) | ||||
0.129874 | + | 0.991531i | \(0.458543\pi\) | |||||||
\(440\) | 53.4960 | 2.55032 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.531992 | 0.0253043 | ||||||||
\(443\) | 23.6814 | 1.12514 | 0.562568 | − | 0.826751i | \(-0.309813\pi\) | ||||
0.562568 | + | 0.826751i | \(0.309813\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −34.2986 | −1.62591 | ||||||||
\(446\) | 0.853762 | 0.0404268 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −8.69124 | −0.410623 | ||||||||
\(449\) | 7.30490 | 0.344740 | 0.172370 | − | 0.985032i | \(-0.444858\pi\) | ||||
0.172370 | + | 0.985032i | \(0.444858\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −16.6568 | −0.784338 | ||||||||
\(452\) | −0.616803 | −0.0290120 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −33.8600 | −1.58913 | ||||||||
\(455\) | 1.81305 | 0.0849972 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.66805 | 0.218362 | 0.109181 | − | 0.994022i | \(-0.465177\pi\) | ||||
0.109181 | + | 0.994022i | \(0.465177\pi\) | |||||||
\(458\) | −22.9737 | −1.07349 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.13478 | 0.146160 | ||||||||
\(461\) | −26.9450 | −1.25495 | −0.627477 | − | 0.778635i | \(-0.715912\pi\) | ||||
−0.627477 | + | 0.778635i | \(0.715912\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.98472 | 0.464029 | 0.232015 | − | 0.972712i | \(-0.425468\pi\) | ||||
0.232015 | + | 0.972712i | \(0.425468\pi\) | |||||||
\(464\) | −30.9280 | −1.43580 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −22.9322 | −1.06231 | ||||||||
\(467\) | 37.0776 | 1.71575 | 0.857873 | − | 0.513861i | \(-0.171785\pi\) | ||||
0.857873 | + | 0.513861i | \(0.171785\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.3886 | −0.572052 | ||||||||
\(470\) | 41.9525 | 1.93512 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −34.4231 | −1.58445 | ||||||||
\(473\) | −63.5675 | −2.92284 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 9.78198 | 0.448828 | ||||||||
\(476\) | −0.146629 | −0.00672074 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 7.30845 | 0.334281 | ||||||||
\(479\) | 18.8165 | 0.859748 | 0.429874 | − | 0.902889i | \(-0.358558\pi\) | ||||
0.429874 | + | 0.902889i | \(0.358558\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.76657 | 0.171741 | ||||||||
\(482\) | −35.8619 | −1.63347 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6.15598 | −0.279817 | ||||||||
\(485\) | 3.48072 | 0.158051 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −26.1973 | −1.18711 | −0.593556 | − | 0.804793i | \(-0.702276\pi\) | ||||
−0.593556 | + | 0.804793i | \(0.702276\pi\) | |||||||
\(488\) | 36.5705 | 1.65547 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 3.89299 | 0.175868 | ||||||||
\(491\) | −18.9523 | −0.855306 | −0.427653 | − | 0.903943i | \(-0.640660\pi\) | ||||
−0.427653 | + | 0.903943i | \(0.640660\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.70594 | −0.256983 | ||||||||
\(494\) | −2.27434 | −0.102328 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −8.44490 | −0.379187 | ||||||||
\(497\) | −10.0499 | −0.450799 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 23.2998 | 1.04304 | 0.521520 | − | 0.853239i | \(-0.325365\pi\) | ||||
0.521520 | + | 0.853239i | \(0.325365\pi\) | |||||||
\(500\) | 0.964412 | 0.0431298 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −0.402361 | −0.0179583 | ||||||||
\(503\) | −6.11772 | −0.272775 | −0.136388 | − | 0.990656i | \(-0.543549\pi\) | ||||
−0.136388 | + | 0.990656i | \(0.543549\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 56.6094 | 2.51908 | ||||||||
\(506\) | 38.6987 | 1.72037 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.227522 | 0.0100946 | ||||||||
\(509\) | 3.73713 | 0.165646 | 0.0828228 | − | 0.996564i | \(-0.473606\pi\) | ||||
0.0828228 | + | 0.996564i | \(0.473606\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.20886 | −0.363139 | ||||||||
\(512\) | −25.1920 | −1.11334 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 25.0006 | 1.10273 | ||||||||
\(515\) | −29.8265 | −1.31431 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −66.4797 | −2.92378 | ||||||||
\(518\) | 8.08760 | 0.355349 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 5.37679 | 0.235788 | ||||||||
\(521\) | 21.0747 | 0.923299 | 0.461649 | − | 0.887062i | \(-0.347258\pi\) | ||||
0.461649 | + | 0.887062i | \(0.347258\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.26739 | −0.317781 | −0.158890 | − | 0.987296i | \(-0.550792\pi\) | ||||
−0.158890 | + | 0.987296i | \(0.550792\pi\) | |||||||
\(524\) | −2.73330 | −0.119405 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.88355 | 0.256535 | ||||||||
\(527\) | −1.55801 | −0.0678679 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.798603 | −0.0347219 | ||||||||
\(530\) | −24.0285 | −1.04373 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.626862 | 0.0271779 | ||||||||
\(533\) | −1.67414 | −0.0725152 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 44.9950 | 1.94531 | ||||||||
\(536\) | −36.7396 | −1.58691 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 2.84599 | 0.122699 | ||||||||
\(539\) | −6.16901 | −0.265718 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.77573 | 0.420291 | 0.210146 | − | 0.977670i | \(-0.432606\pi\) | ||||
0.210146 | + | 0.977670i | \(0.432606\pi\) | |||||||
\(542\) | −4.22753 | −0.181588 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −0.825271 | −0.0353832 | ||||||||
\(545\) | −7.04067 | −0.301589 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.6478 | 0.840078 | 0.420039 | − | 0.907506i | \(-0.362016\pi\) | ||||
0.420039 | + | 0.907506i | \(0.362016\pi\) | |||||||
\(548\) | −2.87165 | −0.122671 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −29.1598 | −1.24338 | ||||||||
\(551\) | 24.3938 | 1.03921 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.30230 | −0.0979038 | ||||||||
\(554\) | 27.3781 | 1.16318 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.90321 | 0.165533 | ||||||||
\(557\) | −23.3748 | −0.990423 | −0.495211 | − | 0.868773i | \(-0.664909\pi\) | ||||
−0.495211 | + | 0.868773i | \(0.664909\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.38906 | −0.270228 | ||||||||
\(560\) | 10.2145 | 0.431640 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 25.1721 | 1.06182 | ||||||||
\(563\) | 2.16432 | 0.0912152 | 0.0456076 | − | 0.998959i | \(-0.485478\pi\) | ||||
0.0456076 | + | 0.998959i | \(0.485478\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.92715 | 0.333498 | ||||||||
\(566\) | −20.0341 | −0.842097 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −29.8039 | −1.25054 | ||||||||
\(569\) | −4.40419 | −0.184633 | −0.0923165 | − | 0.995730i | \(-0.529427\pi\) | ||||
−0.0923165 | + | 0.995730i | \(0.529427\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.17029 | −0.0908239 | −0.0454120 | − | 0.998968i | \(-0.514460\pi\) | ||||
−0.0454120 | + | 0.998968i | \(0.514460\pi\) | |||||||
\(572\) | −0.870273 | −0.0363879 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −3.59473 | −0.150041 | ||||||||
\(575\) | −16.7289 | −0.697645 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18.3420 | −0.763587 | −0.381794 | − | 0.924248i | \(-0.624694\pi\) | ||||
−0.381794 | + | 0.924248i | \(0.624694\pi\) | |||||||
\(578\) | −22.0799 | −0.918403 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −5.89042 | −0.244586 | ||||||||
\(581\) | −1.22797 | −0.0509447 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 38.0766 | 1.57697 | ||||||||
\(584\) | −24.3442 | −1.00737 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −16.6208 | −0.686597 | ||||||||
\(587\) | 4.64632 | 0.191774 | 0.0958871 | − | 0.995392i | \(-0.469431\pi\) | ||||
0.0958871 | + | 0.995392i | \(0.469431\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.66072 | 0.274450 | ||||||||
\(590\) | 45.1878 | 1.86035 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 21.2203 | 0.872149 | ||||||||
\(593\) | −35.2665 | −1.44822 | −0.724110 | − | 0.689684i | \(-0.757749\pi\) | ||||
−0.724110 | + | 0.689684i | \(0.757749\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.88448 | 0.0772560 | ||||||||
\(596\) | 1.28497 | 0.0526346 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 3.88953 | 0.159055 | ||||||||
\(599\) | 11.1046 | 0.453720 | 0.226860 | − | 0.973927i | \(-0.427154\pi\) | ||||
0.226860 | + | 0.973927i | \(0.427154\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 27.6727 | 1.12879 | 0.564397 | − | 0.825504i | \(-0.309109\pi\) | ||||
0.564397 | + | 0.825504i | \(0.309109\pi\) | |||||||
\(602\) | −13.7186 | −0.559129 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −2.97078 | −0.120879 | ||||||||
\(605\) | 79.1166 | 3.21655 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 39.8271 | 1.61653 | 0.808266 | − | 0.588818i | \(-0.200406\pi\) | ||||
0.808266 | + | 0.588818i | \(0.200406\pi\) | |||||||
\(608\) | 3.52816 | 0.143086 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −48.0067 | −1.94374 | ||||||||
\(611\) | −6.68176 | −0.270315 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11.1909 | −0.451997 | −0.225999 | − | 0.974128i | \(-0.572564\pi\) | ||||
−0.225999 | + | 0.974128i | \(0.572564\pi\) | |||||||
\(614\) | 36.4936 | 1.47276 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −18.2948 | −0.737119 | ||||||||
\(617\) | 21.1289 | 0.850617 | 0.425308 | − | 0.905049i | \(-0.360166\pi\) | ||||
0.425308 | + | 0.905049i | \(0.360166\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.30389 | 0.253375 | 0.126687 | − | 0.991943i | \(-0.459566\pi\) | ||||
0.126687 | + | 0.991943i | \(0.459566\pi\) | |||||||
\(620\) | −1.60838 | −0.0645941 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 33.5337 | 1.34458 | ||||||||
\(623\) | 11.7296 | 0.469936 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.1466 | −1.20587 | ||||||||
\(626\) | −15.5986 | −0.623445 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.48644 | 0.0593153 | ||||||||
\(629\) | 3.91496 | 0.156099 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 36.4561 | 1.45130 | 0.725648 | − | 0.688066i | \(-0.241540\pi\) | ||||
0.725648 | + | 0.688066i | \(0.241540\pi\) | |||||||
\(632\) | −6.82770 | −0.271591 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −23.9687 | −0.951917 | ||||||||
\(635\) | −2.92411 | −0.116040 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.620036 | −0.0245667 | ||||||||
\(638\) | −72.7170 | −2.87889 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 26.3460 | 1.04142 | ||||||||
\(641\) | −23.4463 | −0.926073 | −0.463037 | − | 0.886339i | \(-0.653240\pi\) | ||||
−0.463037 | + | 0.886339i | \(0.653240\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12.6228 | −0.497796 | −0.248898 | − | 0.968530i | \(-0.580068\pi\) | ||||
−0.248898 | + | 0.968530i | \(0.580068\pi\) | |||||||
\(644\) | −1.07205 | −0.0422445 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.36394 | −0.0930080 | ||||||||
\(647\) | −25.2402 | −0.992294 | −0.496147 | − | 0.868238i | \(-0.665252\pi\) | ||||
−0.496147 | + | 0.868238i | \(0.665252\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −71.6065 | −2.81080 | ||||||||
\(650\) | −2.93080 | −0.114955 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3.01688 | −0.118150 | ||||||||
\(653\) | 3.66022 | 0.143236 | 0.0716178 | − | 0.997432i | \(-0.477184\pi\) | ||||
0.0716178 | + | 0.997432i | \(0.477184\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 35.1284 | 1.37258 | ||||||||
\(656\) | −9.43188 | −0.368253 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −14.3471 | −0.559308 | ||||||||
\(659\) | −9.14308 | −0.356164 | −0.178082 | − | 0.984016i | \(-0.556989\pi\) | ||||
−0.178082 | + | 0.984016i | \(0.556989\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16.9706 | 0.660078 | 0.330039 | − | 0.943967i | \(-0.392938\pi\) | ||||
0.330039 | + | 0.943967i | \(0.392938\pi\) | |||||||
\(662\) | −18.7537 | −0.728885 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3.64166 | −0.141324 | ||||||||
\(665\) | −8.05642 | −0.312415 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −41.7177 | −1.61532 | ||||||||
\(668\) | −0.459147 | −0.0177649 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 48.2287 | 1.86324 | ||||||||
\(671\) | 76.0736 | 2.93679 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.01062 | 0.0775038 | 0.0387519 | − | 0.999249i | \(-0.487662\pi\) | ||||
0.0387519 | + | 0.999249i | \(0.487662\pi\) | |||||||
\(674\) | 9.12826 | 0.351607 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.87031 | 0.110397 | ||||||||
\(677\) | −7.34704 | −0.282370 | −0.141185 | − | 0.989983i | \(-0.545091\pi\) | ||||
−0.141185 | + | 0.989983i | \(0.545091\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.19035 | −0.0456815 | ||||||||
\(680\) | 5.58860 | 0.214313 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −19.8554 | −0.760302 | ||||||||
\(683\) | 30.7252 | 1.17567 | 0.587833 | − | 0.808982i | \(-0.299981\pi\) | ||||
0.587833 | + | 0.808982i | \(0.299981\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 36.9064 | 1.41012 | ||||||||
\(686\) | −1.33134 | −0.0508310 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −35.9950 | −1.37230 | ||||||||
\(689\) | 3.82701 | 0.145798 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 41.4079 | 1.57523 | 0.787616 | − | 0.616166i | \(-0.211315\pi\) | ||||
0.787616 | + | 0.616166i | \(0.211315\pi\) | |||||||
\(692\) | 0.418841 | 0.0159220 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −20.3079 | −0.770877 | ||||||||
\(695\) | −50.1640 | −1.90283 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.74010 | −0.0659108 | ||||||||
\(698\) | 9.59001 | 0.362987 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.807795 | 0.0305318 | ||||||||
\(701\) | −5.45833 | −0.206158 | −0.103079 | − | 0.994673i | \(-0.532869\pi\) | ||||
−0.103079 | + | 0.994673i | \(0.532869\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −16.7370 | −0.631249 | ||||||||
\(704\) | −53.6164 | −2.02074 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 5.68479 | 0.213950 | ||||||||
\(707\) | −19.3595 | −0.728090 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.69396 | 0.176285 | 0.0881427 | − | 0.996108i | \(-0.471907\pi\) | ||||
0.0881427 | + | 0.996108i | \(0.471907\pi\) | |||||||
\(710\) | 39.1241 | 1.46830 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 34.7853 | 1.30363 | ||||||||
\(713\) | −11.3910 | −0.426597 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 11.1847 | 0.418286 | ||||||||
\(716\) | 4.26882 | 0.159533 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 41.3804 | 1.54430 | ||||||||
\(719\) | 32.7760 | 1.22234 | 0.611170 | − | 0.791499i | \(-0.290699\pi\) | ||||
0.611170 | + | 0.791499i | \(0.290699\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.2002 | 0.379875 | ||||||||
\(722\) | −15.1893 | −0.565289 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −5.27347 | −0.195987 | ||||||||
\(725\) | 31.4346 | 1.16745 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −16.3785 | −0.607445 | −0.303723 | − | 0.952760i | \(-0.598230\pi\) | ||||
−0.303723 | + | 0.952760i | \(0.598230\pi\) | |||||||
\(728\) | −1.83878 | −0.0681497 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 31.9571 | 1.18278 | ||||||||
\(731\) | −6.64075 | −0.245617 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10.7267 | 0.396199 | 0.198100 | − | 0.980182i | \(-0.436523\pi\) | ||||
0.198100 | + | 0.980182i | \(0.436523\pi\) | |||||||
\(734\) | −24.4465 | −0.902337 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.03378 | −0.222408 | ||||||||
\(737\) | −76.4253 | −2.81516 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11.9344 | 0.439014 | 0.219507 | − | 0.975611i | \(-0.429555\pi\) | ||||
0.219507 | + | 0.975611i | \(0.429555\pi\) | |||||||
\(740\) | 4.04153 | 0.148570 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 8.21738 | 0.301669 | ||||||||
\(743\) | −3.45152 | −0.126624 | −0.0633119 | − | 0.997994i | \(-0.520166\pi\) | ||||
−0.0633119 | + | 0.997994i | \(0.520166\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −16.5145 | −0.605043 | ||||||||
\(746\) | −27.7637 | −1.01650 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −0.904557 | −0.0330739 | ||||||||
\(749\) | −15.3876 | −0.562251 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.508332 | −0.0185493 | −0.00927465 | − | 0.999957i | \(-0.502952\pi\) | ||||
−0.00927465 | + | 0.999957i | \(0.502952\pi\) | |||||||
\(752\) | −37.6440 | −1.37274 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −7.30866 | −0.266166 | ||||||||
\(755\) | 38.1804 | 1.38953 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11.2937 | 0.410477 | 0.205238 | − | 0.978712i | \(-0.434203\pi\) | ||||
0.205238 | + | 0.978712i | \(0.434203\pi\) | |||||||
\(758\) | 9.29014 | 0.337433 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −23.8921 | −0.866658 | ||||||||
\(761\) | −27.6722 | −1.00312 | −0.501558 | − | 0.865124i | \(-0.667240\pi\) | ||||
−0.501558 | + | 0.865124i | \(0.667240\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.40780 | 0.0871683 | ||||||||
\(764\) | −0.0153153 | −0.000554089 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0.0480499 | 0.00173611 | ||||||||
\(767\) | −7.19704 | −0.259870 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 29.1720 | 1.05197 | 0.525984 | − | 0.850495i | \(-0.323697\pi\) | ||||
0.525984 | + | 0.850495i | \(0.323697\pi\) | |||||||
\(770\) | 24.0159 | 0.865474 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 5.18300 | 0.186540 | ||||||||
\(773\) | 19.2965 | 0.694046 | 0.347023 | − | 0.937857i | \(-0.387193\pi\) | ||||
0.347023 | + | 0.937857i | \(0.387193\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.58322 | 0.308318 | ||||||||
\(776\) | −3.53010 | −0.126723 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 26.0952 | 0.935560 | ||||||||
\(779\) | 7.43917 | 0.266536 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −61.9978 | −2.21846 | ||||||||
\(782\) | 4.04276 | 0.144569 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.49319 | −0.124757 | ||||||||
\(785\) | −19.1037 | −0.681840 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −18.6400 | −0.664446 | −0.332223 | − | 0.943201i | \(-0.607799\pi\) | ||||
−0.332223 | + | 0.943201i | \(0.607799\pi\) | |||||||
\(788\) | −4.69906 | −0.167397 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 8.96285 | 0.318884 | ||||||||
\(791\) | −2.71096 | −0.0963908 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.64602 | 0.271518 | ||||||||
\(794\) | 27.5311 | 0.977044 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.124436 | −0.00441050 | ||||||||
\(797\) | 12.4612 | 0.441399 | 0.220699 | − | 0.975342i | \(-0.429166\pi\) | ||||
0.220699 | + | 0.975342i | \(0.429166\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.94498 | −0.245696 | ||||||||
\(800\) | 4.54650 | 0.160743 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 32.9756 | 1.16441 | ||||||||
\(803\) | −50.6405 | −1.78707 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 13.7779 | 0.485608 | ||||||||
\(806\) | −1.99563 | −0.0702930 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −57.4126 | −2.01977 | ||||||||
\(809\) | 27.8109 | 0.977779 | 0.488890 | − | 0.872346i | \(-0.337402\pi\) | ||||
0.488890 | + | 0.872346i | \(0.337402\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −27.0417 | −0.949561 | −0.474781 | − | 0.880104i | \(-0.657473\pi\) | ||||
−0.474781 | + | 0.880104i | \(0.657473\pi\) | |||||||
\(812\) | 2.01443 | 0.0706928 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 49.8925 | 1.74873 | ||||||||
\(815\) | 38.7730 | 1.35816 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 28.3902 | 0.993247 | ||||||||
\(818\) | −49.6221 | −1.73499 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.79636 | −0.0627314 | ||||||||
\(821\) | 0.578331 | 0.0201839 | 0.0100920 | − | 0.999949i | \(-0.496788\pi\) | ||||
0.0100920 | + | 0.999949i | \(0.496788\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.69777 | 0.338043 | 0.169022 | − | 0.985612i | \(-0.445939\pi\) | ||||
0.169022 | + | 0.985612i | \(0.445939\pi\) | |||||||
\(824\) | 30.2497 | 1.05380 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −15.4535 | −0.537697 | ||||||||
\(827\) | −27.9922 | −0.973384 | −0.486692 | − | 0.873574i | \(-0.661797\pi\) | ||||
−0.486692 | + | 0.873574i | \(0.661797\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 26.5981 | 0.923791 | 0.461895 | − | 0.886934i | \(-0.347170\pi\) | ||||
0.461895 | + | 0.886934i | \(0.347170\pi\) | |||||||
\(830\) | 4.78048 | 0.165933 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −5.38889 | −0.186826 | ||||||||
\(833\) | −0.644462 | −0.0223293 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.90095 | 0.204211 | ||||||||
\(836\) | 3.86712 | 0.133747 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 33.2858 | 1.14984 | ||||||||
\(839\) | −4.90573 | −0.169365 | −0.0846823 | − | 0.996408i | \(-0.526988\pi\) | ||||
−0.0846823 | + | 0.996408i | \(0.526988\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 49.3899 | 1.70310 | ||||||||
\(842\) | 14.1258 | 0.486807 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.79040 | 0.0616280 | ||||||||
\(845\) | −36.8892 | −1.26903 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −27.0567 | −0.929678 | ||||||||
\(848\) | 21.5608 | 0.740401 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −3.04625 | −0.104486 | ||||||||
\(851\) | 28.6233 | 0.981194 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 44.0800 | 1.50927 | 0.754635 | − | 0.656145i | \(-0.227814\pi\) | ||||
0.754635 | + | 0.656145i | \(0.227814\pi\) | |||||||
\(854\) | 16.4176 | 0.561798 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −45.6335 | −1.55972 | ||||||||
\(857\) | −10.7388 | −0.366829 | −0.183415 | − | 0.983036i | \(-0.558715\pi\) | ||||
−0.183415 | + | 0.983036i | \(0.558715\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 51.5763 | 1.75976 | 0.879880 | − | 0.475197i | \(-0.157623\pi\) | ||||
0.879880 | + | 0.475197i | \(0.157623\pi\) | |||||||
\(860\) | −6.85545 | −0.233769 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 44.5071 | 1.51592 | ||||||||
\(863\) | 33.0290 | 1.12432 | 0.562160 | − | 0.827029i | \(-0.309971\pi\) | ||||
0.562160 | + | 0.827029i | \(0.309971\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.38294 | −0.183026 | ||||||||
\(866\) | 6.42894 | 0.218464 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0.550041 | 0.0186696 | ||||||||
\(869\) | −14.2029 | −0.481801 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.68137 | −0.260273 | ||||||||
\(872\) | 7.14058 | 0.241810 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −17.2834 | −0.584620 | ||||||||
\(875\) | 4.23877 | 0.143297 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 30.4104 | 1.02689 | 0.513443 | − | 0.858124i | \(-0.328370\pi\) | ||||
0.513443 | + | 0.858124i | \(0.328370\pi\) | |||||||
\(878\) | 7.24560 | 0.244527 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 63.0131 | 2.12417 | ||||||||
\(881\) | 2.70216 | 0.0910381 | 0.0455190 | − | 0.998963i | \(-0.485506\pi\) | ||||
0.0455190 | + | 0.998963i | \(0.485506\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 57.0235 | 1.91899 | 0.959497 | − | 0.281719i | \(-0.0909045\pi\) | ||||
0.959497 | + | 0.281719i | \(0.0909045\pi\) | |||||||
\(884\) | −0.0909154 | −0.00305782 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 31.5281 | 1.05921 | ||||||||
\(887\) | −19.5634 | −0.656876 | −0.328438 | − | 0.944525i | \(-0.606522\pi\) | ||||
−0.328438 | + | 0.944525i | \(0.606522\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.00000 | 0.0335389 | ||||||||
\(890\) | −45.6633 | −1.53064 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −0.145905 | −0.00488525 | ||||||||
\(893\) | 29.6909 | 0.993566 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −54.8628 | −1.83386 | ||||||||
\(896\) | −9.00992 | −0.301000 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 9.72534 | 0.324539 | ||||||||
\(899\) | 21.4044 | 0.713876 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.97777 | 0.132519 | ||||||||
\(902\) | −22.1759 | −0.738378 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −8.03963 | −0.267394 | ||||||||
\(905\) | 67.7746 | 2.25290 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −38.9478 | −1.29324 | −0.646620 | − | 0.762812i | \(-0.723818\pi\) | ||||
−0.646620 | + | 0.762812i | \(0.723818\pi\) | |||||||
\(908\) | 5.78654 | 0.192033 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2.41380 | 0.0800166 | ||||||||
\(911\) | −49.6820 | −1.64604 | −0.823020 | − | 0.568013i | \(-0.807712\pi\) | ||||
−0.823020 | + | 0.568013i | \(0.807712\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.57535 | −0.250708 | ||||||||
\(914\) | 6.21479 | 0.205567 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.92613 | 0.129723 | ||||||||
\(917\) | −12.0134 | −0.396716 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −17.4080 | −0.574238 | −0.287119 | − | 0.957895i | \(-0.592698\pi\) | ||||
−0.287119 | + | 0.957895i | \(0.592698\pi\) | |||||||
\(920\) | 40.8598 | 1.34711 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −35.8731 | −1.18142 | ||||||||
\(923\) | −6.23129 | −0.205105 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −21.5679 | −0.709148 | ||||||||
\(926\) | 13.2931 | 0.436838 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 11.3378 | 0.372182 | ||||||||
\(929\) | 13.5172 | 0.443486 | 0.221743 | − | 0.975105i | \(-0.428825\pi\) | ||||
0.221743 | + | 0.975105i | \(0.428825\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.75517 | 0.0902971 | ||||||||
\(932\) | 3.91903 | 0.128372 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 49.3631 | 1.61521 | ||||||||
\(935\) | 11.6254 | 0.380190 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 19.8645 | 0.648944 | 0.324472 | − | 0.945895i | \(-0.394813\pi\) | ||||
0.324472 | + | 0.945895i | \(0.394813\pi\) | |||||||
\(938\) | −16.4935 | −0.538531 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −7.16952 | −0.233844 | ||||||||
\(941\) | −2.52477 | −0.0823051 | −0.0411525 | − | 0.999153i | \(-0.513103\pi\) | ||||
−0.0411525 | + | 0.999153i | \(0.513103\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −12.7223 | −0.414295 | ||||||||
\(944\) | −40.5470 | −1.31969 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −84.6302 | −2.75157 | ||||||||
\(947\) | 13.3429 | 0.433586 | 0.216793 | − | 0.976218i | \(-0.430440\pi\) | ||||
0.216793 | + | 0.976218i | \(0.430440\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.08979 | −0.165222 | ||||||||
\(950\) | 13.0232 | 0.422528 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.91122 | −0.0619429 | ||||||||
\(953\) | 19.1650 | 0.620816 | 0.310408 | − | 0.950603i | \(-0.399534\pi\) | ||||
0.310408 | + | 0.950603i | \(0.399534\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.196832 | 0.00636934 | ||||||||
\(956\) | −1.24899 | −0.0403951 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 25.0513 | 0.809369 | ||||||||
\(959\) | −12.6214 | −0.407567 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.1555 | −0.811469 | ||||||||
\(962\) | 5.01461 | 0.161677 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 6.12867 | 0.197391 | ||||||||
\(965\) | −66.6119 | −2.14431 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −41.8133 | −1.34463 | −0.672313 | − | 0.740267i | \(-0.734699\pi\) | ||||
−0.672313 | + | 0.740267i | \(0.734699\pi\) | |||||||
\(968\) | −80.2392 | −2.57899 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 4.63403 | 0.148790 | ||||||||
\(971\) | −4.23069 | −0.135769 | −0.0678846 | − | 0.997693i | \(-0.521625\pi\) | ||||
−0.0678846 | + | 0.997693i | \(0.521625\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 17.1553 | 0.549974 | ||||||||
\(974\) | −34.8776 | −1.11755 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 43.0765 | 1.37885 | ||||||||
\(977\) | 2.61078 | 0.0835263 | 0.0417631 | − | 0.999128i | \(-0.486703\pi\) | ||||
0.0417631 | + | 0.999128i | \(0.486703\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 72.3600 | 2.31264 | ||||||||
\(980\) | −0.665298 | −0.0212522 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −25.2321 | −0.805188 | ||||||||
\(983\) | −41.6466 | −1.32832 | −0.664159 | − | 0.747591i | \(-0.731210\pi\) | ||||
−0.664159 | + | 0.747591i | \(0.731210\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 60.3923 | 1.92426 | ||||||||
\(986\) | −7.59658 | −0.241924 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.388677 | 0.0123655 | ||||||||
\(989\) | −48.5523 | −1.54387 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.195803 | 0.00621990 | 0.00310995 | − | 0.999995i | \(-0.499010\pi\) | ||||
0.00310995 | + | 0.999995i | \(0.499010\pi\) | |||||||
\(992\) | 3.09579 | 0.0982915 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −13.3799 | −0.424383 | ||||||||
\(995\) | 1.59925 | 0.0506995 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.840968 | −0.0266337 | −0.0133169 | − | 0.999911i | \(-0.504239\pi\) | ||||
−0.0133169 | + | 0.999911i | \(0.504239\pi\) | |||||||
\(998\) | 31.0200 | 0.981921 | ||||||||
\(999\) | 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 | 8001.2.a.t.1.12 | 16 | ||
3.2 | odd | 2 | 889.2.a.c.1.5 | ✓ | 16 | ||
21.20 | even | 2 | 6223.2.a.k.1.5 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
889.2.a.c.1.5 | ✓ | 16 | 3.2 | odd | 2 | ||
6223.2.a.k.1.5 | 16 | 21.20 | even | 2 | |||
8001.2.a.t.1.12 | 16 | 1.1 | even | 1 | trivial |