Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7623,2,Mod(1,7623)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7623, 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("7623.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7623 = 3^{2} \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7623.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: | \(60.8699614608\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.725.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 3x^{2} + x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 231) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-0.477260\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7623.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.77222 | −1.25315 | −0.626575 | − | 0.779361i | \(-0.715544\pi\) | ||||
−0.626575 | + | 0.779361i | \(0.715544\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.14077 | 0.570387 | ||||||||
\(5\) | −0.589926 | −0.263823 | −0.131911 | − | 0.991262i | \(-0.542111\pi\) | ||||
−0.131911 | + | 0.991262i | \(0.542111\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 1.52274 | 0.538370 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.04548 | 0.330610 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.54445 | −0.428352 | −0.214176 | − | 0.976795i | \(-0.568707\pi\) | ||||
−0.214176 | + | 0.976795i | \(0.568707\pi\) | |||||||
\(14\) | 1.77222 | 0.473646 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.98018 | −1.24505 | ||||||||
\(17\) | −7.14511 | −1.73294 | −0.866472 | − | 0.499226i | \(-0.833618\pi\) | ||||
−0.866472 | + | 0.499226i | \(0.833618\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.19059 | −1.42022 | −0.710109 | − | 0.704092i | \(-0.751354\pi\) | ||||
−0.710109 | + | 0.704092i | \(0.751354\pi\) | |||||||
\(20\) | −0.672972 | −0.150481 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.76314 | −0.784669 | −0.392335 | − | 0.919823i | \(-0.628332\pi\) | ||||
−0.392335 | + | 0.919823i | \(0.628332\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.65199 | −0.930398 | ||||||||
\(26\) | 2.73710 | 0.536790 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.14077 | −0.215586 | ||||||||
\(29\) | −0.607298 | −0.112772 | −0.0563862 | − | 0.998409i | \(-0.517958\pi\) | ||||
−0.0563862 | + | 0.998409i | \(0.517958\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.87147 | −1.23415 | −0.617077 | − | 0.786903i | \(-0.711683\pi\) | ||||
−0.617077 | + | 0.786903i | \(0.711683\pi\) | |||||||
\(32\) | 5.78051 | 1.02186 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 12.6627 | 2.17164 | ||||||||
\(35\) | 0.589926 | 0.0997157 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.70693 | −1.26701 | −0.633505 | − | 0.773738i | \(-0.718385\pi\) | ||||
−0.633505 | + | 0.773738i | \(0.718385\pi\) | |||||||
\(38\) | 10.9711 | 1.77975 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.898304 | −0.142034 | ||||||||
\(41\) | −7.48287 | −1.16863 | −0.584314 | − | 0.811528i | \(-0.698636\pi\) | ||||
−0.584314 | + | 0.811528i | \(0.698636\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.9537 | −1.67043 | −0.835214 | − | 0.549925i | \(-0.814656\pi\) | ||||
−0.835214 | + | 0.549925i | \(0.814656\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.66913 | 0.983309 | ||||||||
\(47\) | 10.2072 | 1.48887 | 0.744434 | − | 0.667696i | \(-0.232719\pi\) | ||||
0.744434 | + | 0.667696i | \(0.232719\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 8.24436 | 1.16593 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.76186 | −0.244327 | ||||||||
\(53\) | −7.04469 | −0.967663 | −0.483831 | − | 0.875161i | \(-0.660755\pi\) | ||||
−0.483831 | + | 0.875161i | \(0.660755\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.52274 | −0.203485 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.07627 | 0.141321 | ||||||||
\(59\) | 3.35386 | 0.436635 | 0.218318 | − | 0.975878i | \(-0.429943\pi\) | ||||
0.218318 | + | 0.975878i | \(0.429943\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.37044 | −0.431541 | −0.215770 | − | 0.976444i | \(-0.569226\pi\) | ||||
−0.215770 | + | 0.976444i | \(0.569226\pi\) | |||||||
\(62\) | 12.1778 | 1.54658 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.283993 | −0.0354992 | ||||||||
\(65\) | 0.911108 | 0.113009 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.19138 | −0.267719 | −0.133860 | − | 0.991000i | \(-0.542737\pi\) | ||||
−0.133860 | + | 0.991000i | \(0.542737\pi\) | |||||||
\(68\) | −8.15095 | −0.988448 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.04548 | −0.124959 | ||||||||
\(71\) | 13.9430 | 1.65473 | 0.827364 | − | 0.561665i | \(-0.189839\pi\) | ||||
0.827364 | + | 0.561665i | \(0.189839\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.58993 | −0.303128 | −0.151564 | − | 0.988447i | \(-0.548431\pi\) | ||||
−0.151564 | + | 0.988447i | \(0.548431\pi\) | |||||||
\(74\) | 13.6584 | 1.58776 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −7.06206 | −0.810074 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.66351 | −0.524686 | −0.262343 | − | 0.964975i | \(-0.584495\pi\) | ||||
−0.262343 | + | 0.964975i | \(0.584495\pi\) | |||||||
\(80\) | 2.93794 | 0.328471 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 13.2613 | 1.46447 | ||||||||
\(83\) | 3.50970 | 0.385240 | 0.192620 | − | 0.981273i | \(-0.438302\pi\) | ||||
0.192620 | + | 0.981273i | \(0.438302\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.21508 | 0.457190 | ||||||||
\(86\) | 19.4125 | 2.09330 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.15095 | −0.863999 | −0.432000 | − | 0.901874i | \(-0.642192\pi\) | ||||
−0.432000 | + | 0.901874i | \(0.642192\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.54445 | 0.161902 | ||||||||
\(92\) | −4.29289 | −0.447565 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −18.0894 | −1.86578 | ||||||||
\(95\) | 3.65199 | 0.374686 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.79710 | −0.487071 | −0.243536 | − | 0.969892i | \(-0.578307\pi\) | ||||
−0.243536 | + | 0.969892i | \(0.578307\pi\) | |||||||
\(98\) | −1.77222 | −0.179022 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −5.30687 | −0.530687 | ||||||||
\(101\) | 1.42666 | 0.141958 | 0.0709788 | − | 0.997478i | \(-0.477388\pi\) | ||||
0.0709788 | + | 0.997478i | \(0.477388\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17.6172 | 1.73588 | 0.867939 | − | 0.496670i | \(-0.165444\pi\) | ||||
0.867939 | + | 0.496670i | \(0.165444\pi\) | |||||||
\(104\) | −2.35179 | −0.230612 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 12.4848 | 1.21263 | ||||||||
\(107\) | 7.20005 | 0.696055 | 0.348027 | − | 0.937484i | \(-0.386852\pi\) | ||||
0.348027 | + | 0.937484i | \(0.386852\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.88678 | −0.851199 | −0.425599 | − | 0.904912i | \(-0.639937\pi\) | ||||
−0.425599 | + | 0.904912i | \(0.639937\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.98018 | 0.470583 | ||||||||
\(113\) | 7.80862 | 0.734573 | 0.367287 | − | 0.930108i | \(-0.380287\pi\) | ||||
0.367287 | + | 0.930108i | \(0.380287\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.21997 | 0.207014 | ||||||||
\(116\) | −0.692789 | −0.0643239 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −5.94378 | −0.547170 | ||||||||
\(119\) | 7.14511 | 0.654991 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 5.97317 | 0.540785 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −7.83880 | −0.703945 | ||||||||
\(125\) | 5.69396 | 0.509283 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.25186 | 0.732234 | 0.366117 | − | 0.930569i | \(-0.380687\pi\) | ||||
0.366117 | + | 0.930569i | \(0.380687\pi\) | |||||||
\(128\) | −11.0577 | −0.977374 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.61469 | −0.141617 | ||||||||
\(131\) | −12.1162 | −1.05860 | −0.529299 | − | 0.848435i | \(-0.677545\pi\) | ||||
−0.529299 | + | 0.848435i | \(0.677545\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.19059 | 0.536792 | ||||||||
\(134\) | 3.88361 | 0.335493 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −10.8801 | −0.932964 | ||||||||
\(137\) | 17.4548 | 1.49126 | 0.745631 | − | 0.666360i | \(-0.232148\pi\) | ||||
0.745631 | + | 0.666360i | \(0.232148\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.7624 | 1.25213 | 0.626063 | − | 0.779772i | \(-0.284665\pi\) | ||||
0.626063 | + | 0.779772i | \(0.284665\pi\) | |||||||
\(140\) | 0.672972 | 0.0568765 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −24.7101 | −2.07362 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.358261 | 0.0297519 | ||||||||
\(146\) | 4.58993 | 0.379865 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −8.79186 | −0.722686 | ||||||||
\(149\) | −12.5258 | −1.02615 | −0.513077 | − | 0.858343i | \(-0.671494\pi\) | ||||
−0.513077 | + | 0.858343i | \(0.671494\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.328572 | 0.0267388 | 0.0133694 | − | 0.999911i | \(-0.495744\pi\) | ||||
0.0133694 | + | 0.999911i | \(0.495744\pi\) | |||||||
\(152\) | −9.42666 | −0.764603 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.05366 | 0.325598 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.68089 | −0.213958 | −0.106979 | − | 0.994261i | \(-0.534118\pi\) | ||||
−0.106979 | + | 0.994261i | \(0.534118\pi\) | |||||||
\(158\) | 8.26479 | 0.657511 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3.41007 | −0.269590 | ||||||||
\(161\) | 3.76314 | 0.296577 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.891668 | −0.0698408 | −0.0349204 | − | 0.999390i | \(-0.511118\pi\) | ||||
−0.0349204 | + | 0.999390i | \(0.511118\pi\) | |||||||
\(164\) | −8.53627 | −0.666570 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.21997 | −0.482764 | ||||||||
\(167\) | −11.5610 | −0.894619 | −0.447310 | − | 0.894379i | \(-0.647618\pi\) | ||||
−0.447310 | + | 0.894379i | \(0.647618\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.6147 | −0.816514 | ||||||||
\(170\) | −7.47007 | −0.572928 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −12.4957 | −0.952790 | ||||||||
\(173\) | −8.98926 | −0.683441 | −0.341721 | − | 0.939802i | \(-0.611010\pi\) | ||||
−0.341721 | + | 0.939802i | \(0.611010\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.65199 | 0.351657 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 14.4453 | 1.08272 | ||||||||
\(179\) | 6.14590 | 0.459366 | 0.229683 | − | 0.973265i | \(-0.426231\pi\) | ||||
0.229683 | + | 0.973265i | \(0.426231\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.9662 | 1.11243 | 0.556215 | − | 0.831039i | \(-0.312253\pi\) | ||||
0.556215 | + | 0.831039i | \(0.312253\pi\) | |||||||
\(182\) | −2.73710 | −0.202888 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −5.73029 | −0.422442 | ||||||||
\(185\) | 4.54651 | 0.334266 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 11.6441 | 0.849231 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −6.47214 | −0.469538 | ||||||||
\(191\) | −9.87351 | −0.714422 | −0.357211 | − | 0.934024i | \(-0.616272\pi\) | ||||
−0.357211 | + | 0.934024i | \(0.616272\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.18113 | −0.444927 | −0.222464 | − | 0.974941i | \(-0.571410\pi\) | ||||
−0.222464 | + | 0.974941i | \(0.571410\pi\) | |||||||
\(194\) | 8.50152 | 0.610374 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.14077 | 0.0814839 | ||||||||
\(197\) | 19.0720 | 1.35882 | 0.679412 | − | 0.733757i | \(-0.262235\pi\) | ||||
0.679412 | + | 0.733757i | \(0.262235\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.8479 | −0.839878 | −0.419939 | − | 0.907552i | \(-0.637948\pi\) | ||||
−0.419939 | + | 0.907552i | \(0.637948\pi\) | |||||||
\(200\) | −7.08377 | −0.500898 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2.52835 | −0.177894 | ||||||||
\(203\) | 0.607298 | 0.0426239 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.41434 | 0.308311 | ||||||||
\(206\) | −31.2217 | −2.17532 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 7.69162 | 0.533318 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −20.9810 | −1.44439 | −0.722197 | − | 0.691687i | \(-0.756868\pi\) | ||||
−0.722197 | + | 0.691687i | \(0.756868\pi\) | |||||||
\(212\) | −8.03640 | −0.551942 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −12.7601 | −0.872262 | ||||||||
\(215\) | 6.46189 | 0.440697 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.87147 | 0.466466 | ||||||||
\(218\) | 15.7493 | 1.06668 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 11.0352 | 0.742310 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.38860 | 0.226918 | 0.113459 | − | 0.993543i | \(-0.463807\pi\) | ||||
0.113459 | + | 0.993543i | \(0.463807\pi\) | |||||||
\(224\) | −5.78051 | −0.386227 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −13.8386 | −0.920531 | ||||||||
\(227\) | −19.3973 | −1.28744 | −0.643721 | − | 0.765260i | \(-0.722610\pi\) | ||||
−0.643721 | + | 0.765260i | \(0.722610\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.86405 | −0.651835 | −0.325917 | − | 0.945398i | \(-0.605673\pi\) | ||||
−0.325917 | + | 0.945398i | \(0.605673\pi\) | |||||||
\(230\) | −3.93429 | −0.259419 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.924756 | −0.0607132 | ||||||||
\(233\) | −7.12619 | −0.466852 | −0.233426 | − | 0.972375i | \(-0.574994\pi\) | ||||
−0.233426 | + | 0.972375i | \(0.574994\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.02147 | −0.392798 | ||||||||
\(236\) | 3.82599 | 0.249051 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −12.6627 | −0.820802 | ||||||||
\(239\) | −22.2894 | −1.44178 | −0.720892 | − | 0.693048i | \(-0.756267\pi\) | ||||
−0.720892 | + | 0.693048i | \(0.756267\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.8753 | 0.958199 | 0.479100 | − | 0.877761i | \(-0.340963\pi\) | ||||
0.479100 | + | 0.877761i | \(0.340963\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −3.84491 | −0.246145 | ||||||||
\(245\) | −0.589926 | −0.0376890 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.56103 | 0.608354 | ||||||||
\(248\) | −10.4635 | −0.664431 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −10.0910 | −0.638208 | ||||||||
\(251\) | 25.9233 | 1.63626 | 0.818132 | − | 0.575031i | \(-0.195010\pi\) | ||||
0.818132 | + | 0.575031i | \(0.195010\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −14.6241 | −0.917600 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 20.1647 | 1.26030 | ||||||||
\(257\) | −0.871474 | −0.0543610 | −0.0271805 | − | 0.999631i | \(-0.508653\pi\) | ||||
−0.0271805 | + | 0.999631i | \(0.508653\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.70693 | 0.478885 | ||||||||
\(260\) | 1.03937 | 0.0644589 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 21.4726 | 1.32658 | ||||||||
\(263\) | −26.8873 | −1.65794 | −0.828970 | − | 0.559293i | \(-0.811073\pi\) | ||||
−0.828970 | + | 0.559293i | \(0.811073\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.15584 | 0.255291 | ||||||||
\(266\) | −10.9711 | −0.672681 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2.49987 | −0.152704 | ||||||||
\(269\) | 0.992574 | 0.0605183 | 0.0302592 | − | 0.999542i | \(-0.490367\pi\) | ||||
0.0302592 | + | 0.999542i | \(0.490367\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 26.8650 | 1.63193 | 0.815966 | − | 0.578099i | \(-0.196205\pi\) | ||||
0.815966 | + | 0.578099i | \(0.196205\pi\) | |||||||
\(272\) | 35.5839 | 2.15759 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −30.9337 | −1.86878 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −27.6302 | −1.66014 | −0.830069 | − | 0.557660i | \(-0.811699\pi\) | ||||
−0.830069 | + | 0.557660i | \(0.811699\pi\) | |||||||
\(278\) | −26.1622 | −1.56910 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.898304 | 0.0536839 | ||||||||
\(281\) | −23.8418 | −1.42228 | −0.711141 | − | 0.703050i | \(-0.751821\pi\) | ||||
−0.711141 | + | 0.703050i | \(0.751821\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.74735 | 0.519976 | 0.259988 | − | 0.965612i | \(-0.416281\pi\) | ||||
0.259988 | + | 0.965612i | \(0.416281\pi\) | |||||||
\(284\) | 15.9058 | 0.943836 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.48287 | 0.441700 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 34.0526 | 2.00309 | ||||||||
\(290\) | −0.634918 | −0.0372836 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2.95452 | −0.172900 | ||||||||
\(293\) | 19.6252 | 1.14651 | 0.573257 | − | 0.819376i | \(-0.305680\pi\) | ||||
0.573257 | + | 0.819376i | \(0.305680\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.97853 | −0.115194 | ||||||||
\(296\) | −11.7356 | −0.682120 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 22.1985 | 1.28592 | ||||||||
\(299\) | 5.81197 | 0.336115 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.9537 | 0.631362 | ||||||||
\(302\) | −0.582303 | −0.0335078 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 30.8303 | 1.76824 | ||||||||
\(305\) | 1.98831 | 0.113850 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −17.0835 | −0.975009 | −0.487504 | − | 0.873121i | \(-0.662093\pi\) | ||||
−0.487504 | + | 0.873121i | \(0.662093\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −7.18399 | −0.408023 | ||||||||
\(311\) | 7.23351 | 0.410175 | 0.205087 | − | 0.978744i | \(-0.434252\pi\) | ||||
0.205087 | + | 0.978744i | \(0.434252\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.7784 | 0.778804 | 0.389402 | − | 0.921068i | \(-0.372682\pi\) | ||||
0.389402 | + | 0.921068i | \(0.372682\pi\) | |||||||
\(314\) | 4.75113 | 0.268122 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.32002 | −0.299274 | ||||||||
\(317\) | 6.95629 | 0.390704 | 0.195352 | − | 0.980733i | \(-0.437415\pi\) | ||||
0.195352 | + | 0.980733i | \(0.437415\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0.167535 | 0.00936550 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −6.66913 | −0.371656 | ||||||||
\(323\) | 44.2324 | 2.46116 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.18474 | 0.398538 | ||||||||
\(326\) | 1.58023 | 0.0875211 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −11.3945 | −0.629154 | ||||||||
\(329\) | −10.2072 | −0.562739 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −29.6698 | −1.63080 | −0.815401 | − | 0.578896i | \(-0.803484\pi\) | ||||
−0.815401 | + | 0.578896i | \(0.803484\pi\) | |||||||
\(332\) | 4.00378 | 0.219736 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 20.4887 | 1.12109 | ||||||||
\(335\) | 1.29275 | 0.0706305 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 19.5714 | 1.06612 | 0.533062 | − | 0.846076i | \(-0.321041\pi\) | ||||
0.533062 | + | 0.846076i | \(0.321041\pi\) | |||||||
\(338\) | 18.8116 | 1.02322 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 4.80846 | 0.260775 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −16.6797 | −0.899308 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 15.9310 | 0.856455 | ||||||||
\(347\) | 6.49184 | 0.348500 | 0.174250 | − | 0.984701i | \(-0.444250\pi\) | ||||
0.174250 | + | 0.984701i | \(0.444250\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.87965 | 0.421788 | 0.210894 | − | 0.977509i | \(-0.432362\pi\) | ||||
0.210894 | + | 0.977509i | \(0.432362\pi\) | |||||||
\(350\) | −8.24436 | −0.440680 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.34594 | 0.284536 | 0.142268 | − | 0.989828i | \(-0.454561\pi\) | ||||
0.142268 | + | 0.989828i | \(0.454561\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.22533 | −0.436555 | ||||||||
\(356\) | −9.29840 | −0.492814 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −10.8919 | −0.575655 | ||||||||
\(359\) | 17.8515 | 0.942169 | 0.471084 | − | 0.882088i | \(-0.343863\pi\) | ||||
0.471084 | + | 0.882088i | \(0.343863\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 19.3234 | 1.01702 | ||||||||
\(362\) | −26.5235 | −1.39404 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.76186 | 0.0923467 | ||||||||
\(365\) | 1.52786 | 0.0799721 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −29.9357 | −1.56263 | −0.781316 | − | 0.624135i | \(-0.785451\pi\) | ||||
−0.781316 | + | 0.624135i | \(0.785451\pi\) | |||||||
\(368\) | 18.7411 | 0.976949 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −8.05744 | −0.418886 | ||||||||
\(371\) | 7.04469 | 0.365742 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 23.4915 | 1.21635 | 0.608173 | − | 0.793805i | \(-0.291903\pi\) | ||||
0.608173 | + | 0.793805i | \(0.291903\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 15.5429 | 0.801562 | ||||||||
\(377\) | 0.937938 | 0.0483063 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −31.4532 | −1.61564 | −0.807821 | − | 0.589428i | \(-0.799353\pi\) | ||||
−0.807821 | + | 0.589428i | \(0.799353\pi\) | |||||||
\(380\) | 4.16609 | 0.213716 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 17.4981 | 0.895278 | ||||||||
\(383\) | 5.62749 | 0.287551 | 0.143776 | − | 0.989610i | \(-0.454076\pi\) | ||||
0.143776 | + | 0.989610i | \(0.454076\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 10.9543 | 0.557561 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −5.47240 | −0.277819 | ||||||||
\(389\) | −26.1072 | −1.32369 | −0.661845 | − | 0.749641i | \(-0.730226\pi\) | ||||
−0.661845 | + | 0.749641i | \(0.730226\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 26.8881 | 1.35979 | ||||||||
\(392\) | 1.52274 | 0.0769100 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −33.7998 | −1.70281 | ||||||||
\(395\) | 2.75113 | 0.138424 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.3828 | 0.521096 | 0.260548 | − | 0.965461i | \(-0.416097\pi\) | ||||
0.260548 | + | 0.965461i | \(0.416097\pi\) | |||||||
\(398\) | 20.9972 | 1.05249 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 23.1677 | 1.15839 | ||||||||
\(401\) | −3.68876 | −0.184208 | −0.0921040 | − | 0.995749i | \(-0.529359\pi\) | ||||
−0.0921040 | + | 0.995749i | \(0.529359\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.6126 | 0.528652 | ||||||||
\(404\) | 1.62749 | 0.0809708 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.07627 | −0.0534142 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.08022 | 0.0534136 | 0.0267068 | − | 0.999643i | \(-0.491498\pi\) | ||||
0.0267068 | + | 0.999643i | \(0.491498\pi\) | |||||||
\(410\) | −7.82319 | −0.386360 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 20.0973 | 0.990123 | ||||||||
\(413\) | −3.35386 | −0.165033 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.07046 | −0.101635 | ||||||||
\(416\) | −8.92769 | −0.437716 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10.0766 | −0.492273 | −0.246136 | − | 0.969235i | \(-0.579161\pi\) | ||||
−0.246136 | + | 0.969235i | \(0.579161\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.9757 | 0.583658 | 0.291829 | − | 0.956470i | \(-0.405736\pi\) | ||||
0.291829 | + | 0.956470i | \(0.405736\pi\) | |||||||
\(422\) | 37.1831 | 1.81004 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −10.7272 | −0.520960 | ||||||||
\(425\) | 33.2390 | 1.61233 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.37044 | 0.163107 | ||||||||
\(428\) | 8.21363 | 0.397021 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −11.4519 | −0.552260 | ||||||||
\(431\) | 0.548547 | 0.0264226 | 0.0132113 | − | 0.999913i | \(-0.495795\pi\) | ||||
0.0132113 | + | 0.999913i | \(0.495795\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 19.5879 | 0.941332 | 0.470666 | − | 0.882311i | \(-0.344014\pi\) | ||||
0.470666 | + | 0.882311i | \(0.344014\pi\) | |||||||
\(434\) | −12.1778 | −0.584552 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −10.1378 | −0.485513 | ||||||||
\(437\) | 23.2961 | 1.11440 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 37.4069 | 1.78533 | 0.892667 | − | 0.450716i | \(-0.148831\pi\) | ||||
0.892667 | + | 0.450716i | \(0.148831\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −19.5569 | −0.930226 | ||||||||
\(443\) | −21.4478 | −1.01902 | −0.509508 | − | 0.860466i | \(-0.670173\pi\) | ||||
−0.509508 | + | 0.860466i | \(0.670173\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.80846 | 0.227943 | ||||||||
\(446\) | −6.00536 | −0.284362 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.283993 | 0.0134174 | ||||||||
\(449\) | −6.39904 | −0.301989 | −0.150995 | − | 0.988535i | \(-0.548248\pi\) | ||||
−0.150995 | + | 0.988535i | \(0.548248\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 8.90787 | 0.418991 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 34.3763 | 1.61336 | ||||||||
\(455\) | −0.911108 | −0.0427134 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −36.9430 | −1.72812 | −0.864060 | − | 0.503389i | \(-0.832086\pi\) | ||||
−0.864060 | + | 0.503389i | \(0.832086\pi\) | |||||||
\(458\) | 17.4813 | 0.816847 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2.53249 | 0.118078 | ||||||||
\(461\) | −7.39825 | −0.344571 | −0.172285 | − | 0.985047i | \(-0.555115\pi\) | ||||
−0.172285 | + | 0.985047i | \(0.555115\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.3717 | −0.667910 | −0.333955 | − | 0.942589i | \(-0.608383\pi\) | ||||
−0.333955 | + | 0.942589i | \(0.608383\pi\) | |||||||
\(464\) | 3.02445 | 0.140407 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 12.6292 | 0.585036 | ||||||||
\(467\) | −36.1626 | −1.67341 | −0.836704 | − | 0.547656i | \(-0.815520\pi\) | ||||
−0.836704 | + | 0.547656i | \(0.815520\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.19138 | 0.101188 | ||||||||
\(470\) | 10.6714 | 0.492235 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 5.10705 | 0.235071 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 28.7985 | 1.32137 | ||||||||
\(476\) | 8.15095 | 0.373598 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 39.5018 | 1.80677 | ||||||||
\(479\) | −16.0252 | −0.732212 | −0.366106 | − | 0.930573i | \(-0.619309\pi\) | ||||
−0.366106 | + | 0.930573i | \(0.619309\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11.9029 | 0.542727 | ||||||||
\(482\) | −26.3623 | −1.20077 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.82993 | 0.128501 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.55059 | 0.0702641 | 0.0351320 | − | 0.999383i | \(-0.488815\pi\) | ||||
0.0351320 | + | 0.999383i | \(0.488815\pi\) | |||||||
\(488\) | −5.13230 | −0.232328 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.04548 | 0.0472300 | ||||||||
\(491\) | 0.0331635 | 0.00149665 | 0.000748324 | − | 1.00000i | \(-0.499762\pi\) | ||||
0.000748324 | 1.00000i | \(0.499762\pi\) | ||||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.33921 | 0.195428 | ||||||||
\(494\) | −16.9443 | −0.762359 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 34.2212 | 1.53658 | ||||||||
\(497\) | −13.9430 | −0.625429 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −27.0314 | −1.21009 | −0.605046 | − | 0.796190i | \(-0.706845\pi\) | ||||
−0.605046 | + | 0.796190i | \(0.706845\pi\) | |||||||
\(500\) | 6.49552 | 0.290488 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −45.9418 | −2.05048 | ||||||||
\(503\) | 29.3341 | 1.30794 | 0.653972 | − | 0.756519i | \(-0.273101\pi\) | ||||
0.653972 | + | 0.756519i | \(0.273101\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.841621 | −0.0374516 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 9.41351 | 0.417657 | ||||||||
\(509\) | 16.6329 | 0.737239 | 0.368620 | − | 0.929580i | \(-0.379831\pi\) | ||||
0.368620 | + | 0.929580i | \(0.379831\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.58993 | 0.114572 | ||||||||
\(512\) | −13.6210 | −0.601967 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1.54445 | 0.0681226 | ||||||||
\(515\) | −10.3929 | −0.457964 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −13.6584 | −0.600115 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.38738 | 0.0608407 | ||||||||
\(521\) | −35.8923 | −1.57247 | −0.786236 | − | 0.617927i | \(-0.787973\pi\) | ||||
−0.786236 | + | 0.617927i | \(0.787973\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.27873 | 0.318276 | 0.159138 | − | 0.987256i | \(-0.449128\pi\) | ||||
0.159138 | + | 0.987256i | \(0.449128\pi\) | |||||||
\(524\) | −13.8219 | −0.603811 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 47.6502 | 2.07765 | ||||||||
\(527\) | 49.0974 | 2.13872 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.83876 | −0.384294 | ||||||||
\(530\) | −7.36508 | −0.319919 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 7.06206 | 0.306179 | ||||||||
\(533\) | 11.5569 | 0.500585 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.24749 | −0.183635 | ||||||||
\(536\) | −3.33690 | −0.144132 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −1.75906 | −0.0758386 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.4709 | −0.450177 | −0.225089 | − | 0.974338i | \(-0.572267\pi\) | ||||
−0.225089 | + | 0.974338i | \(0.572267\pi\) | |||||||
\(542\) | −47.6108 | −2.04506 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −41.3024 | −1.77083 | ||||||||
\(545\) | 5.24254 | 0.224566 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.16609 | 0.349157 | 0.174578 | − | 0.984643i | \(-0.444144\pi\) | ||||
0.174578 | + | 0.984643i | \(0.444144\pi\) | |||||||
\(548\) | 19.9119 | 0.850596 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.75953 | 0.160161 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.66351 | 0.198313 | ||||||||
\(554\) | 48.9669 | 2.08040 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 16.8405 | 0.714197 | ||||||||
\(557\) | −11.8765 | −0.503225 | −0.251612 | − | 0.967828i | \(-0.580961\pi\) | ||||
−0.251612 | + | 0.967828i | \(0.580961\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 16.9174 | 0.715532 | ||||||||
\(560\) | −2.93794 | −0.124151 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 42.2530 | 1.78233 | ||||||||
\(563\) | −4.83929 | −0.203952 | −0.101976 | − | 0.994787i | \(-0.532516\pi\) | ||||
−0.101976 | + | 0.994787i | \(0.532516\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.60651 | −0.193797 | ||||||||
\(566\) | −15.5023 | −0.651608 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 21.2316 | 0.890856 | ||||||||
\(569\) | −6.52993 | −0.273749 | −0.136875 | − | 0.990588i | \(-0.543706\pi\) | ||||
−0.136875 | + | 0.990588i | \(0.543706\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −33.8691 | −1.41738 | −0.708689 | − | 0.705521i | \(-0.750713\pi\) | ||||
−0.708689 | + | 0.705521i | \(0.750713\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −13.2613 | −0.553517 | ||||||||
\(575\) | 17.5061 | 0.730054 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −37.3609 | −1.55536 | −0.777678 | − | 0.628662i | \(-0.783603\pi\) | ||||
−0.777678 | + | 0.628662i | \(0.783603\pi\) | |||||||
\(578\) | −60.3487 | −2.51018 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.408694 | 0.0169701 | ||||||||
\(581\) | −3.50970 | −0.145607 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −3.94378 | −0.163195 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −34.7802 | −1.43675 | ||||||||
\(587\) | 2.07974 | 0.0858399 | 0.0429199 | − | 0.999079i | \(-0.486334\pi\) | ||||
0.0429199 | + | 0.999079i | \(0.486334\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 42.5385 | 1.75277 | ||||||||
\(590\) | 3.50639 | 0.144356 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 38.3819 | 1.57749 | ||||||||
\(593\) | −6.54983 | −0.268969 | −0.134485 | − | 0.990916i | \(-0.542938\pi\) | ||||
−0.134485 | + | 0.990916i | \(0.542938\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.21508 | −0.172802 | ||||||||
\(596\) | −14.2891 | −0.585304 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −10.3001 | −0.421203 | ||||||||
\(599\) | 4.98187 | 0.203554 | 0.101777 | − | 0.994807i | \(-0.467547\pi\) | ||||
0.101777 | + | 0.994807i | \(0.467547\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −32.4713 | −1.32453 | −0.662266 | − | 0.749269i | \(-0.730405\pi\) | ||||
−0.662266 | + | 0.749269i | \(0.730405\pi\) | |||||||
\(602\) | −19.4125 | −0.791192 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0.374827 | 0.0152515 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.13388 | 0.127200 | 0.0636002 | − | 0.997975i | \(-0.479742\pi\) | ||||
0.0636002 | + | 0.997975i | \(0.479742\pi\) | |||||||
\(608\) | −35.7848 | −1.45126 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3.52373 | −0.142672 | ||||||||
\(611\) | −15.7644 | −0.637760 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 46.8484 | 1.89219 | 0.946094 | − | 0.323892i | \(-0.104991\pi\) | ||||
0.946094 | + | 0.323892i | \(0.104991\pi\) | |||||||
\(614\) | 30.2758 | 1.22183 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −26.5924 | −1.07057 | −0.535286 | − | 0.844671i | \(-0.679796\pi\) | ||||
−0.535286 | + | 0.844671i | \(0.679796\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −32.9765 | −1.32544 | −0.662718 | − | 0.748869i | \(-0.730597\pi\) | ||||
−0.662718 | + | 0.748869i | \(0.730597\pi\) | |||||||
\(620\) | 4.62431 | 0.185717 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −12.8194 | −0.514011 | ||||||||
\(623\) | 8.15095 | 0.326561 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.9009 | 0.796037 | ||||||||
\(626\) | −24.4185 | −0.975959 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3.05828 | −0.122039 | ||||||||
\(629\) | 55.0668 | 2.19566 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11.1721 | 0.444754 | 0.222377 | − | 0.974961i | \(-0.428618\pi\) | ||||
0.222377 | + | 0.974961i | \(0.428618\pi\) | |||||||
\(632\) | −7.10132 | −0.282475 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −12.3281 | −0.489611 | ||||||||
\(635\) | −4.86798 | −0.193180 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.54445 | −0.0611932 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 6.52324 | 0.257854 | ||||||||
\(641\) | 41.9153 | 1.65556 | 0.827778 | − | 0.561056i | \(-0.189605\pi\) | ||||
0.827778 | + | 0.561056i | \(0.189605\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 29.0873 | 1.14709 | 0.573546 | − | 0.819173i | \(-0.305567\pi\) | ||||
0.573546 | + | 0.819173i | \(0.305567\pi\) | |||||||
\(644\) | 4.29289 | 0.169164 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −78.3897 | −3.08420 | ||||||||
\(647\) | −1.89804 | −0.0746196 | −0.0373098 | − | 0.999304i | \(-0.511879\pi\) | ||||
−0.0373098 | + | 0.999304i | \(0.511879\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −12.7330 | −0.499428 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.01719 | −0.0398363 | ||||||||
\(653\) | −20.2519 | −0.792517 | −0.396258 | − | 0.918139i | \(-0.629692\pi\) | ||||
−0.396258 | + | 0.918139i | \(0.629692\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.14766 | 0.279282 | ||||||||
\(656\) | 37.2661 | 1.45500 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 18.0894 | 0.705197 | ||||||||
\(659\) | 11.5620 | 0.450392 | 0.225196 | − | 0.974314i | \(-0.427698\pi\) | ||||
0.225196 | + | 0.974314i | \(0.427698\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −32.6894 | −1.27147 | −0.635735 | − | 0.771907i | \(-0.719303\pi\) | ||||
−0.635735 | + | 0.771907i | \(0.719303\pi\) | |||||||
\(662\) | 52.5816 | 2.04364 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5.34436 | 0.207402 | ||||||||
\(665\) | −3.65199 | −0.141618 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.28535 | 0.0884890 | ||||||||
\(668\) | −13.1885 | −0.510279 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2.29104 | −0.0885107 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −20.1249 | −0.775758 | −0.387879 | − | 0.921710i | \(-0.626792\pi\) | ||||
−0.387879 | + | 0.921710i | \(0.626792\pi\) | |||||||
\(674\) | −34.6850 | −1.33601 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.1090 | −0.465729 | ||||||||
\(677\) | −23.5746 | −0.906045 | −0.453022 | − | 0.891499i | \(-0.649654\pi\) | ||||
−0.453022 | + | 0.891499i | \(0.649654\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.79710 | 0.184096 | ||||||||
\(680\) | 6.41848 | 0.246137 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −11.5812 | −0.443143 | −0.221572 | − | 0.975144i | \(-0.571119\pi\) | ||||
−0.221572 | + | 0.975144i | \(0.571119\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10.2970 | −0.393429 | ||||||||
\(686\) | 1.77222 | 0.0676638 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 54.5516 | 2.07976 | ||||||||
\(689\) | 10.8801 | 0.414500 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 43.8164 | 1.66685 | 0.833426 | − | 0.552630i | \(-0.186376\pi\) | ||||
0.833426 | + | 0.552630i | \(0.186376\pi\) | |||||||
\(692\) | −10.2547 | −0.389826 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −11.5050 | −0.436723 | ||||||||
\(695\) | −8.70869 | −0.330340 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 53.4659 | 2.02517 | ||||||||
\(698\) | −13.9645 | −0.528564 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 5.30687 | 0.200581 | ||||||||
\(701\) | 22.8165 | 0.861769 | 0.430884 | − | 0.902407i | \(-0.358202\pi\) | ||||
0.430884 | + | 0.902407i | \(0.358202\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 47.7104 | 1.79943 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −9.47420 | −0.356566 | ||||||||
\(707\) | −1.42666 | −0.0536549 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 39.9746 | 1.50128 | 0.750638 | − | 0.660713i | \(-0.229746\pi\) | ||||
0.750638 | + | 0.660713i | \(0.229746\pi\) | |||||||
\(710\) | 14.5771 | 0.547070 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −12.4118 | −0.465151 | ||||||||
\(713\) | 25.8583 | 0.968402 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 7.01108 | 0.262016 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −31.6369 | −1.18068 | ||||||||
\(719\) | 26.2200 | 0.977840 | 0.488920 | − | 0.872329i | \(-0.337391\pi\) | ||||
0.488920 | + | 0.872329i | \(0.337391\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −17.6172 | −0.656100 | ||||||||
\(722\) | −34.2453 | −1.27448 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 17.0731 | 0.634515 | ||||||||
\(725\) | 2.82514 | 0.104923 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −22.2366 | −0.824708 | −0.412354 | − | 0.911024i | \(-0.635293\pi\) | ||||
−0.412354 | + | 0.911024i | \(0.635293\pi\) | |||||||
\(728\) | 2.35179 | 0.0871631 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2.70772 | −0.100217 | ||||||||
\(731\) | 78.2656 | 2.89476 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −21.1284 | −0.780395 | −0.390197 | − | 0.920731i | \(-0.627593\pi\) | ||||
−0.390197 | + | 0.920731i | \(0.627593\pi\) | |||||||
\(734\) | 53.0528 | 1.95821 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −21.7529 | −0.801822 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 37.5036 | 1.37959 | 0.689795 | − | 0.724004i | \(-0.257701\pi\) | ||||
0.689795 | + | 0.724004i | \(0.257701\pi\) | |||||||
\(740\) | 5.18655 | 0.190661 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −12.4848 | −0.458330 | ||||||||
\(743\) | 36.1464 | 1.32608 | 0.663041 | − | 0.748583i | \(-0.269265\pi\) | ||||
0.663041 | + | 0.748583i | \(0.269265\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.38929 | 0.270723 | ||||||||
\(746\) | −41.6322 | −1.52426 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −7.20005 | −0.263084 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −43.5533 | −1.58928 | −0.794641 | − | 0.607080i | \(-0.792341\pi\) | ||||
−0.794641 | + | 0.607080i | \(0.792341\pi\) | |||||||
\(752\) | −50.8336 | −1.85371 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.66224 | −0.0605351 | ||||||||
\(755\) | −0.193833 | −0.00705431 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −44.4442 | −1.61535 | −0.807675 | − | 0.589628i | \(-0.799274\pi\) | ||||
−0.807675 | + | 0.589628i | \(0.799274\pi\) | |||||||
\(758\) | 55.7421 | 2.02464 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 5.56103 | 0.201720 | ||||||||
\(761\) | 15.9613 | 0.578598 | 0.289299 | − | 0.957239i | \(-0.406578\pi\) | ||||
0.289299 | + | 0.957239i | \(0.406578\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.88678 | 0.321723 | ||||||||
\(764\) | −11.2634 | −0.407497 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −9.97317 | −0.360345 | ||||||||
\(767\) | −5.17985 | −0.187034 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.19899 | 0.187480 | 0.0937402 | − | 0.995597i | \(-0.470118\pi\) | ||||
0.0937402 | + | 0.995597i | \(0.470118\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −7.05127 | −0.253781 | ||||||||
\(773\) | 12.1614 | 0.437416 | 0.218708 | − | 0.975790i | \(-0.429816\pi\) | ||||
0.218708 | + | 0.975790i | \(0.429816\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 31.9660 | 1.14825 | ||||||||
\(776\) | −7.30473 | −0.262224 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 46.2678 | 1.65878 | ||||||||
\(779\) | 46.3234 | 1.65971 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −47.6516 | −1.70402 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4.98018 | −0.177864 | ||||||||
\(785\) | 1.58152 | 0.0564470 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −39.6430 | −1.41312 | −0.706559 | − | 0.707654i | \(-0.749754\pi\) | ||||
−0.706559 | + | 0.707654i | \(0.749754\pi\) | |||||||
\(788\) | 21.7569 | 0.775056 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −4.87561 | −0.173466 | ||||||||
\(791\) | −7.80862 | −0.277643 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.20546 | 0.184851 | ||||||||
\(794\) | −18.4006 | −0.653011 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −13.5158 | −0.479055 | ||||||||
\(797\) | 35.1118 | 1.24372 | 0.621862 | − | 0.783127i | \(-0.286376\pi\) | ||||
0.621862 | + | 0.783127i | \(0.286376\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −72.9313 | −2.58012 | ||||||||
\(800\) | −26.8909 | −0.950736 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 6.53731 | 0.230840 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.21997 | −0.0782438 | ||||||||
\(806\) | −18.8079 | −0.662481 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2.17243 | 0.0764257 | ||||||||
\(809\) | 41.7873 | 1.46916 | 0.734581 | − | 0.678521i | \(-0.237379\pi\) | ||||
0.734581 | + | 0.678521i | \(0.237379\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9.89879 | −0.347594 | −0.173797 | − | 0.984782i | \(-0.555604\pi\) | ||||
−0.173797 | + | 0.984782i | \(0.555604\pi\) | |||||||
\(812\) | 0.692789 | 0.0243121 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.526018 | 0.0184256 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 67.8100 | 2.37237 | ||||||||
\(818\) | −1.91440 | −0.0669353 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 5.03576 | 0.175856 | ||||||||
\(821\) | −16.1936 | −0.565161 | −0.282580 | − | 0.959244i | \(-0.591190\pi\) | ||||
−0.282580 | + | 0.959244i | \(0.591190\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.86642 | −0.134775 | −0.0673874 | − | 0.997727i | \(-0.521466\pi\) | ||||
−0.0673874 | + | 0.997727i | \(0.521466\pi\) | |||||||
\(824\) | 26.8265 | 0.934545 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 5.94378 | 0.206811 | ||||||||
\(827\) | 46.8179 | 1.62802 | 0.814009 | − | 0.580852i | \(-0.197280\pi\) | ||||
0.814009 | + | 0.580852i | \(0.197280\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −41.5599 | −1.44344 | −0.721718 | − | 0.692187i | \(-0.756647\pi\) | ||||
−0.721718 | + | 0.692187i | \(0.756647\pi\) | |||||||
\(830\) | 3.66932 | 0.127364 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.438613 | 0.0152062 | ||||||||
\(833\) | −7.14511 | −0.247563 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.82015 | 0.236021 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 17.8579 | 0.616892 | ||||||||
\(839\) | −5.14119 | −0.177494 | −0.0887469 | − | 0.996054i | \(-0.528286\pi\) | ||||
−0.0887469 | + | 0.996054i | \(0.528286\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.6312 | −0.987282 | ||||||||
\(842\) | −21.2236 | −0.731412 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −23.9346 | −0.823864 | ||||||||
\(845\) | 6.26188 | 0.215415 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 35.0838 | 1.20478 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −58.9068 | −2.02049 | ||||||||
\(851\) | 29.0023 | 0.994184 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.69649 | 0.229283 | 0.114642 | − | 0.993407i | \(-0.463428\pi\) | ||||
0.114642 | + | 0.993407i | \(0.463428\pi\) | |||||||
\(854\) | −5.97317 | −0.204398 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 10.9638 | 0.374735 | ||||||||
\(857\) | 36.1064 | 1.23337 | 0.616686 | − | 0.787209i | \(-0.288475\pi\) | ||||
0.616686 | + | 0.787209i | \(0.288475\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −37.1034 | −1.26595 | −0.632976 | − | 0.774171i | \(-0.718167\pi\) | ||||
−0.632976 | + | 0.774171i | \(0.718167\pi\) | |||||||
\(860\) | 7.37155 | 0.251368 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −0.972147 | −0.0331115 | ||||||||
\(863\) | −38.3724 | −1.30621 | −0.653105 | − | 0.757267i | \(-0.726534\pi\) | ||||
−0.653105 | + | 0.757267i | \(0.726534\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.30300 | 0.180307 | ||||||||
\(866\) | −34.7140 | −1.17963 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 7.83880 | 0.266066 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.38446 | 0.114678 | ||||||||
\(872\) | −13.5323 | −0.458260 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −41.2858 | −1.39651 | ||||||||
\(875\) | −5.69396 | −0.192491 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.811156 | −0.0273908 | −0.0136954 | − | 0.999906i | \(-0.504360\pi\) | ||||
−0.0136954 | + | 0.999906i | \(0.504360\pi\) | |||||||
\(878\) | −66.2934 | −2.23729 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 32.5076 | 1.09521 | 0.547605 | − | 0.836737i | \(-0.315540\pi\) | ||||
0.547605 | + | 0.836737i | \(0.315540\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 48.0995 | 1.61868 | 0.809338 | − | 0.587343i | \(-0.199826\pi\) | ||||
0.809338 | + | 0.587343i | \(0.199826\pi\) | |||||||
\(884\) | 12.5887 | 0.423404 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 38.0103 | 1.27698 | ||||||||
\(887\) | −11.3847 | −0.382260 | −0.191130 | − | 0.981565i | \(-0.561215\pi\) | ||||
−0.191130 | + | 0.981565i | \(0.561215\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.25186 | −0.276758 | ||||||||
\(890\) | −8.52166 | −0.285647 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3.86563 | 0.129431 | ||||||||
\(893\) | −63.1884 | −2.11452 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.62562 | −0.121191 | ||||||||
\(896\) | 11.0577 | 0.369413 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 11.3405 | 0.378438 | ||||||||
\(899\) | 4.17303 | 0.139178 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 50.3351 | 1.67690 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 11.8905 | 0.395472 | ||||||||
\(905\) | −8.82895 | −0.293484 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 13.4259 | 0.445799 | 0.222899 | − | 0.974841i | \(-0.428448\pi\) | ||||
0.222899 | + | 0.974841i | \(0.428448\pi\) | |||||||
\(908\) | −22.1279 | −0.734340 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.61469 | 0.0535264 | ||||||||
\(911\) | −3.39303 | −0.112416 | −0.0562080 | − | 0.998419i | \(-0.517901\pi\) | ||||
−0.0562080 | + | 0.998419i | \(0.517901\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 65.4712 | 2.16560 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −11.2526 | −0.371798 | ||||||||
\(917\) | 12.1162 | 0.400112 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −44.5668 | −1.47012 | −0.735062 | − | 0.678000i | \(-0.762847\pi\) | ||||
−0.735062 | + | 0.678000i | \(0.762847\pi\) | |||||||
\(920\) | 3.38044 | 0.111450 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 13.1113 | 0.431799 | ||||||||
\(923\) | −21.5342 | −0.708807 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 35.8525 | 1.17882 | ||||||||
\(926\) | 25.4699 | 0.836992 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3.51049 | −0.115238 | ||||||||
\(929\) | 7.15205 | 0.234651 | 0.117325 | − | 0.993094i | \(-0.462568\pi\) | ||||
0.117325 | + | 0.993094i | \(0.462568\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.19059 | −0.202888 | ||||||||
\(932\) | −8.12937 | −0.266287 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 64.0883 | 2.09703 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.30811 | −0.0427342 | −0.0213671 | − | 0.999772i | \(-0.506802\pi\) | ||||
−0.0213671 | + | 0.999772i | \(0.506802\pi\) | |||||||
\(938\) | −3.88361 | −0.126804 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −6.86914 | −0.224047 | ||||||||
\(941\) | 22.1225 | 0.721174 | 0.360587 | − | 0.932726i | \(-0.382576\pi\) | ||||
0.360587 | + | 0.932726i | \(0.382576\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 28.1591 | 0.916987 | ||||||||
\(944\) | −16.7028 | −0.543631 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 17.6842 | 0.574658 | 0.287329 | − | 0.957832i | \(-0.407233\pi\) | ||||
0.287329 | + | 0.957832i | \(0.407233\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.00000 | 0.129845 | ||||||||
\(950\) | −51.0374 | −1.65587 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 10.8801 | 0.352627 | ||||||||
\(953\) | 23.7741 | 0.770118 | 0.385059 | − | 0.922892i | \(-0.374181\pi\) | ||||
0.385059 | + | 0.922892i | \(0.374181\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.82464 | 0.188481 | ||||||||
\(956\) | −25.4272 | −0.822374 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 28.4003 | 0.917573 | ||||||||
\(959\) | −17.4548 | −0.563644 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 16.2172 | 0.523134 | ||||||||
\(962\) | −21.0946 | −0.680119 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 16.9693 | 0.546544 | ||||||||
\(965\) | 3.64641 | 0.117382 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 21.1829 | 0.681195 | 0.340597 | − | 0.940209i | \(-0.389371\pi\) | ||||
0.340597 | + | 0.940209i | \(0.389371\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −5.01527 | −0.161031 | ||||||||
\(971\) | 47.4360 | 1.52229 | 0.761147 | − | 0.648579i | \(-0.224637\pi\) | ||||
0.761147 | + | 0.648579i | \(0.224637\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −14.7624 | −0.473259 | ||||||||
\(974\) | −2.74800 | −0.0880515 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 16.7854 | 0.537288 | ||||||||
\(977\) | 13.1860 | 0.421858 | 0.210929 | − | 0.977501i | \(-0.432351\pi\) | ||||
0.210929 | + | 0.977501i | \(0.432351\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −0.672972 | −0.0214973 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −0.0587731 | −0.00187553 | ||||||||
\(983\) | 4.07740 | 0.130049 | 0.0650244 | − | 0.997884i | \(-0.479287\pi\) | ||||
0.0650244 | + | 0.997884i | \(0.479287\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11.2511 | −0.358489 | ||||||||
\(986\) | −7.69004 | −0.244901 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 10.9070 | 0.346997 | ||||||||
\(989\) | 41.2204 | 1.31073 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.49154 | −0.174445 | −0.0872223 | − | 0.996189i | \(-0.527799\pi\) | ||||
−0.0872223 | + | 0.996189i | \(0.527799\pi\) | |||||||
\(992\) | −39.7206 | −1.26113 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 24.7101 | 0.783757 | ||||||||
\(995\) | 6.98940 | 0.221579 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 22.9725 | 0.727548 | 0.363774 | − | 0.931487i | \(-0.381488\pi\) | ||||
0.363774 | + | 0.931487i | \(0.381488\pi\) | |||||||
\(998\) | 47.9057 | 1.51643 | ||||||||
\(999\) | 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 | 7623.2.a.ci.1.1 | 4 | ||
3.2 | odd | 2 | 2541.2.a.bn.1.4 | 4 | |||
11.5 | even | 5 | 693.2.m.f.190.2 | 8 | |||
11.9 | even | 5 | 693.2.m.f.631.2 | 8 | |||
11.10 | odd | 2 | 7623.2.a.cl.1.4 | 4 | |||
33.5 | odd | 10 | 231.2.j.f.190.1 | yes | 8 | ||
33.20 | odd | 10 | 231.2.j.f.169.1 | ✓ | 8 | ||
33.32 | even | 2 | 2541.2.a.bm.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
231.2.j.f.169.1 | ✓ | 8 | 33.20 | odd | 10 | ||
231.2.j.f.190.1 | yes | 8 | 33.5 | odd | 10 | ||
693.2.m.f.190.2 | 8 | 11.5 | even | 5 | |||
693.2.m.f.631.2 | 8 | 11.9 | even | 5 | |||
2541.2.a.bm.1.1 | 4 | 33.32 | even | 2 | |||
2541.2.a.bn.1.4 | 4 | 3.2 | odd | 2 | |||
7623.2.a.ci.1.1 | 4 | 1.1 | even | 1 | trivial | ||
7623.2.a.cl.1.4 | 4 | 11.10 | odd | 2 |