Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2541,2,Mod(1,2541)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2541, 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("2541.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2541 = 3 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2541.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(20.2899871536\) |
Analytic rank: | \(1\) |
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 | 1.4 | ||
Root | \(-0.477260\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2541.1 |
$q$-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 | \(-0.284456\pi\) | ||||
0.626575 | + | 0.779361i | \(0.284456\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.14077 | 0.570387 | ||||||||
\(5\) | 0.589926 | 0.263823 | 0.131911 | − | 0.991262i | \(-0.457889\pi\) | ||||
0.131911 | + | 0.991262i | \(0.457889\pi\) | |||||||
\(6\) | −1.77222 | −0.723507 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −1.52274 | −0.538370 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.04548 | 0.330610 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −1.14077 | −0.329313 | ||||||||
\(13\) | −1.54445 | −0.428352 | −0.214176 | − | 0.976795i | \(-0.568707\pi\) | ||||
−0.214176 | + | 0.976795i | \(0.568707\pi\) | |||||||
\(14\) | −1.77222 | −0.473646 | ||||||||
\(15\) | −0.589926 | −0.152318 | ||||||||
\(16\) | −4.98018 | −1.24505 | ||||||||
\(17\) | 7.14511 | 1.73294 | 0.866472 | − | 0.499226i | \(-0.166382\pi\) | ||||
0.866472 | + | 0.499226i | \(0.166382\pi\) | |||||||
\(18\) | 1.77222 | 0.417717 | ||||||||
\(19\) | −6.19059 | −1.42022 | −0.710109 | − | 0.704092i | \(-0.751354\pi\) | ||||
−0.710109 | + | 0.704092i | \(0.751354\pi\) | |||||||
\(20\) | 0.672972 | 0.150481 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.76314 | 0.784669 | 0.392335 | − | 0.919823i | \(-0.371668\pi\) | ||||
0.392335 | + | 0.919823i | \(0.371668\pi\) | |||||||
\(24\) | 1.52274 | 0.310828 | ||||||||
\(25\) | −4.65199 | −0.930398 | ||||||||
\(26\) | −2.73710 | −0.536790 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.14077 | −0.215586 | ||||||||
\(29\) | 0.607298 | 0.112772 | 0.0563862 | − | 0.998409i | \(-0.482042\pi\) | ||||
0.0563862 | + | 0.998409i | \(0.482042\pi\) | |||||||
\(30\) | −1.04548 | −0.190878 | ||||||||
\(31\) | −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 | ||||||||
\(36\) | 1.14077 | 0.190129 | ||||||||
\(37\) | −7.70693 | −1.26701 | −0.633505 | − | 0.773738i | \(-0.718385\pi\) | ||||
−0.633505 | + | 0.773738i | \(0.718385\pi\) | |||||||
\(38\) | −10.9711 | −1.77975 | ||||||||
\(39\) | 1.54445 | 0.247309 | ||||||||
\(40\) | −0.898304 | −0.142034 | ||||||||
\(41\) | 7.48287 | 1.16863 | 0.584314 | − | 0.811528i | \(-0.301364\pi\) | ||||
0.584314 | + | 0.811528i | \(0.301364\pi\) | |||||||
\(42\) | 1.77222 | 0.273460 | ||||||||
\(43\) | −10.9537 | −1.67043 | −0.835214 | − | 0.549925i | \(-0.814656\pi\) | ||||
−0.835214 | + | 0.549925i | \(0.814656\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.589926 | 0.0879409 | ||||||||
\(46\) | 6.66913 | 0.983309 | ||||||||
\(47\) | −10.2072 | −1.48887 | −0.744434 | − | 0.667696i | \(-0.767281\pi\) | ||||
−0.744434 | + | 0.667696i | \(0.767281\pi\) | |||||||
\(48\) | 4.98018 | 0.718827 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −8.24436 | −1.16593 | ||||||||
\(51\) | −7.14511 | −1.00052 | ||||||||
\(52\) | −1.76186 | −0.244327 | ||||||||
\(53\) | 7.04469 | 0.967663 | 0.483831 | − | 0.875161i | \(-0.339245\pi\) | ||||
0.483831 | + | 0.875161i | \(0.339245\pi\) | |||||||
\(54\) | −1.77222 | −0.241169 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.52274 | 0.203485 | ||||||||
\(57\) | 6.19059 | 0.819963 | ||||||||
\(58\) | 1.07627 | 0.141321 | ||||||||
\(59\) | −3.35386 | −0.436635 | −0.218318 | − | 0.975878i | \(-0.570057\pi\) | ||||
−0.218318 | + | 0.975878i | \(0.570057\pi\) | |||||||
\(60\) | −0.672972 | −0.0868803 | ||||||||
\(61\) | −3.37044 | −0.431541 | −0.215770 | − | 0.976444i | \(-0.569226\pi\) | ||||
−0.215770 | + | 0.976444i | \(0.569226\pi\) | |||||||
\(62\) | −12.1778 | −1.54658 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | −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 | ||||||||
\(69\) | −3.76314 | −0.453029 | ||||||||
\(70\) | −1.04548 | −0.124959 | ||||||||
\(71\) | −13.9430 | −1.65473 | −0.827364 | − | 0.561665i | \(-0.810161\pi\) | ||||
−0.827364 | + | 0.561665i | \(0.810161\pi\) | |||||||
\(72\) | −1.52274 | −0.179457 | ||||||||
\(73\) | −2.58993 | −0.303128 | −0.151564 | − | 0.988447i | \(-0.548431\pi\) | ||||
−0.151564 | + | 0.988447i | \(0.548431\pi\) | |||||||
\(74\) | −13.6584 | −1.58776 | ||||||||
\(75\) | 4.65199 | 0.537165 | ||||||||
\(76\) | −7.06206 | −0.810074 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 2.73710 | 0.309916 | ||||||||
\(79\) | −4.66351 | −0.524686 | −0.262343 | − | 0.964975i | \(-0.584495\pi\) | ||||
−0.262343 | + | 0.964975i | \(0.584495\pi\) | |||||||
\(80\) | −2.93794 | −0.328471 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 13.2613 | 1.46447 | ||||||||
\(83\) | −3.50970 | −0.385240 | −0.192620 | − | 0.981273i | \(-0.561698\pi\) | ||||
−0.192620 | + | 0.981273i | \(0.561698\pi\) | |||||||
\(84\) | 1.14077 | 0.124469 | ||||||||
\(85\) | 4.21508 | 0.457190 | ||||||||
\(86\) | −19.4125 | −2.09330 | ||||||||
\(87\) | −0.607298 | −0.0651091 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.15095 | 0.863999 | 0.432000 | − | 0.901874i | \(-0.357808\pi\) | ||||
0.432000 | + | 0.901874i | \(0.357808\pi\) | |||||||
\(90\) | 1.04548 | 0.110203 | ||||||||
\(91\) | 1.54445 | 0.161902 | ||||||||
\(92\) | 4.29289 | 0.447565 | ||||||||
\(93\) | 6.87147 | 0.712539 | ||||||||
\(94\) | −18.0894 | −1.86578 | ||||||||
\(95\) | −3.65199 | −0.374686 | ||||||||
\(96\) | 5.78051 | 0.589971 | ||||||||
\(97\) | −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 | \(-0.522612\pi\) | ||||
−0.0709788 | + | 0.997478i | \(0.522612\pi\) | |||||||
\(102\) | −12.6627 | −1.25380 | ||||||||
\(103\) | 17.6172 | 1.73588 | 0.867939 | − | 0.496670i | \(-0.165444\pi\) | ||||
0.867939 | + | 0.496670i | \(0.165444\pi\) | |||||||
\(104\) | 2.35179 | 0.230612 | ||||||||
\(105\) | 0.589926 | 0.0575709 | ||||||||
\(106\) | 12.4848 | 1.21263 | ||||||||
\(107\) | −7.20005 | −0.696055 | −0.348027 | − | 0.937484i | \(-0.613148\pi\) | ||||
−0.348027 | + | 0.937484i | \(0.613148\pi\) | |||||||
\(108\) | −1.14077 | −0.109771 | ||||||||
\(109\) | −8.88678 | −0.851199 | −0.425599 | − | 0.904912i | \(-0.639937\pi\) | ||||
−0.425599 | + | 0.904912i | \(0.639937\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.70693 | 0.731509 | ||||||||
\(112\) | 4.98018 | 0.470583 | ||||||||
\(113\) | −7.80862 | −0.734573 | −0.367287 | − | 0.930108i | \(-0.619713\pi\) | ||||
−0.367287 | + | 0.930108i | \(0.619713\pi\) | |||||||
\(114\) | 10.9711 | 1.02754 | ||||||||
\(115\) | 2.21997 | 0.207014 | ||||||||
\(116\) | 0.692789 | 0.0643239 | ||||||||
\(117\) | −1.54445 | −0.142784 | ||||||||
\(118\) | −5.94378 | −0.547170 | ||||||||
\(119\) | −7.14511 | −0.654991 | ||||||||
\(120\) | 0.898304 | 0.0820035 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −5.97317 | −0.540785 | ||||||||
\(123\) | −7.48287 | −0.674708 | ||||||||
\(124\) | −7.83880 | −0.703945 | ||||||||
\(125\) | −5.69396 | −0.509283 | ||||||||
\(126\) | −1.77222 | −0.157882 | ||||||||
\(127\) | 8.25186 | 0.732234 | 0.366117 | − | 0.930569i | \(-0.380687\pi\) | ||||
0.366117 | + | 0.930569i | \(0.380687\pi\) | |||||||
\(128\) | 11.0577 | 0.977374 | ||||||||
\(129\) | 10.9537 | 0.964422 | ||||||||
\(130\) | −1.61469 | −0.141617 | ||||||||
\(131\) | 12.1162 | 1.05860 | 0.529299 | − | 0.848435i | \(-0.322455\pi\) | ||||
0.529299 | + | 0.848435i | \(0.322455\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.19059 | 0.536792 | ||||||||
\(134\) | −3.88361 | −0.335493 | ||||||||
\(135\) | −0.589926 | −0.0507727 | ||||||||
\(136\) | −10.8801 | −0.932964 | ||||||||
\(137\) | −17.4548 | −1.49126 | −0.745631 | − | 0.666360i | \(-0.767852\pi\) | ||||
−0.745631 | + | 0.666360i | \(0.767852\pi\) | |||||||
\(138\) | −6.66913 | −0.567714 | ||||||||
\(139\) | 14.7624 | 1.25213 | 0.626063 | − | 0.779772i | \(-0.284665\pi\) | ||||
0.626063 | + | 0.779772i | \(0.284665\pi\) | |||||||
\(140\) | −0.672972 | −0.0568765 | ||||||||
\(141\) | 10.2072 | 0.859599 | ||||||||
\(142\) | −24.7101 | −2.07362 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −4.98018 | −0.415015 | ||||||||
\(145\) | 0.358261 | 0.0297519 | ||||||||
\(146\) | −4.58993 | −0.379865 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | −8.79186 | −0.722686 | ||||||||
\(149\) | 12.5258 | 1.02615 | 0.513077 | − | 0.858343i | \(-0.328506\pi\) | ||||
0.513077 | + | 0.858343i | \(0.328506\pi\) | |||||||
\(150\) | 8.24436 | 0.673149 | ||||||||
\(151\) | 0.328572 | 0.0267388 | 0.0133694 | − | 0.999911i | \(-0.495744\pi\) | ||||
0.0133694 | + | 0.999911i | \(0.495744\pi\) | |||||||
\(152\) | 9.42666 | 0.764603 | ||||||||
\(153\) | 7.14511 | 0.577648 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.05366 | −0.325598 | ||||||||
\(156\) | 1.76186 | 0.141062 | ||||||||
\(157\) | −2.68089 | −0.213958 | −0.106979 | − | 0.994261i | \(-0.534118\pi\) | ||||
−0.106979 | + | 0.994261i | \(0.534118\pi\) | |||||||
\(158\) | −8.26479 | −0.657511 | ||||||||
\(159\) | −7.04469 | −0.558680 | ||||||||
\(160\) | −3.41007 | −0.269590 | ||||||||
\(161\) | −3.76314 | −0.296577 | ||||||||
\(162\) | 1.77222 | 0.139239 | ||||||||
\(163\) | −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 | \(-0.352382\pi\) | ||||
0.447310 | + | 0.894379i | \(0.352382\pi\) | |||||||
\(168\) | −1.52274 | −0.117482 | ||||||||
\(169\) | −10.6147 | −0.816514 | ||||||||
\(170\) | 7.47007 | 0.572928 | ||||||||
\(171\) | −6.19059 | −0.473406 | ||||||||
\(172\) | −12.4957 | −0.952790 | ||||||||
\(173\) | 8.98926 | 0.683441 | 0.341721 | − | 0.939802i | \(-0.388990\pi\) | ||||
0.341721 | + | 0.939802i | \(0.388990\pi\) | |||||||
\(174\) | −1.07627 | −0.0815916 | ||||||||
\(175\) | 4.65199 | 0.351657 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.35386 | 0.252091 | ||||||||
\(178\) | 14.4453 | 1.08272 | ||||||||
\(179\) | −6.14590 | −0.459366 | −0.229683 | − | 0.973265i | \(-0.573769\pi\) | ||||
−0.229683 | + | 0.973265i | \(0.573769\pi\) | |||||||
\(180\) | 0.672972 | 0.0501604 | ||||||||
\(181\) | 14.9662 | 1.11243 | 0.556215 | − | 0.831039i | \(-0.312253\pi\) | ||||
0.556215 | + | 0.831039i | \(0.312253\pi\) | |||||||
\(182\) | 2.73710 | 0.202888 | ||||||||
\(183\) | 3.37044 | 0.249150 | ||||||||
\(184\) | −5.73029 | −0.422442 | ||||||||
\(185\) | −4.54651 | −0.334266 | ||||||||
\(186\) | 12.1778 | 0.892918 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −11.6441 | −0.849231 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | −6.47214 | −0.469538 | ||||||||
\(191\) | 9.87351 | 0.714422 | 0.357211 | − | 0.934024i | \(-0.383728\pi\) | ||||
0.357211 | + | 0.934024i | \(0.383728\pi\) | |||||||
\(192\) | 0.283993 | 0.0204955 | ||||||||
\(193\) | −6.18113 | −0.444927 | −0.222464 | − | 0.974941i | \(-0.571410\pi\) | ||||
−0.222464 | + | 0.974941i | \(0.571410\pi\) | |||||||
\(194\) | −8.50152 | −0.610374 | ||||||||
\(195\) | 0.911108 | 0.0652458 | ||||||||
\(196\) | 1.14077 | 0.0814839 | ||||||||
\(197\) | −19.0720 | −1.35882 | −0.679412 | − | 0.733757i | \(-0.737765\pi\) | ||||
−0.679412 | + | 0.733757i | \(0.737765\pi\) | |||||||
\(198\) | 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 | ||||||||
\(201\) | 2.19138 | 0.154568 | ||||||||
\(202\) | −2.52835 | −0.177894 | ||||||||
\(203\) | −0.607298 | −0.0426239 | ||||||||
\(204\) | −8.15095 | −0.570681 | ||||||||
\(205\) | 4.41434 | 0.308311 | ||||||||
\(206\) | 31.2217 | 2.17532 | ||||||||
\(207\) | 3.76314 | 0.261556 | ||||||||
\(208\) | 7.69162 | 0.533318 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 1.04548 | 0.0721450 | ||||||||
\(211\) | −20.9810 | −1.44439 | −0.722197 | − | 0.691687i | \(-0.756868\pi\) | ||||
−0.722197 | + | 0.691687i | \(0.756868\pi\) | |||||||
\(212\) | 8.03640 | 0.551942 | ||||||||
\(213\) | 13.9430 | 0.955358 | ||||||||
\(214\) | −12.7601 | −0.872262 | ||||||||
\(215\) | −6.46189 | −0.440697 | ||||||||
\(216\) | 1.52274 | 0.103609 | ||||||||
\(217\) | 6.87147 | 0.466466 | ||||||||
\(218\) | −15.7493 | −1.06668 | ||||||||
\(219\) | 2.58993 | 0.175011 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −11.0352 | −0.742310 | ||||||||
\(222\) | 13.6584 | 0.916691 | ||||||||
\(223\) | 3.38860 | 0.226918 | 0.113459 | − | 0.993543i | \(-0.463807\pi\) | ||||
0.113459 | + | 0.993543i | \(0.463807\pi\) | |||||||
\(224\) | 5.78051 | 0.386227 | ||||||||
\(225\) | −4.65199 | −0.310133 | ||||||||
\(226\) | −13.8386 | −0.920531 | ||||||||
\(227\) | 19.3973 | 1.28744 | 0.643721 | − | 0.765260i | \(-0.277390\pi\) | ||||
0.643721 | + | 0.765260i | \(0.277390\pi\) | |||||||
\(228\) | 7.06206 | 0.467696 | ||||||||
\(229\) | −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 | \(-0.425006\pi\) | ||||
0.233426 | + | 0.972375i | \(0.425006\pi\) | |||||||
\(234\) | −2.73710 | −0.178930 | ||||||||
\(235\) | −6.02147 | −0.392798 | ||||||||
\(236\) | −3.82599 | −0.249051 | ||||||||
\(237\) | 4.66351 | 0.302928 | ||||||||
\(238\) | −12.6627 | −0.820802 | ||||||||
\(239\) | 22.2894 | 1.44178 | 0.720892 | − | 0.693048i | \(-0.243733\pi\) | ||||
0.720892 | + | 0.693048i | \(0.243733\pi\) | |||||||
\(240\) | 2.93794 | 0.189643 | ||||||||
\(241\) | 14.8753 | 0.958199 | 0.479100 | − | 0.877761i | \(-0.340963\pi\) | ||||
0.479100 | + | 0.877761i | \(0.340963\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −3.84491 | −0.246145 | ||||||||
\(245\) | 0.589926 | 0.0376890 | ||||||||
\(246\) | −13.2613 | −0.845511 | ||||||||
\(247\) | 9.56103 | 0.608354 | ||||||||
\(248\) | 10.4635 | 0.664431 | ||||||||
\(249\) | 3.50970 | 0.222418 | ||||||||
\(250\) | −10.0910 | −0.638208 | ||||||||
\(251\) | −25.9233 | −1.63626 | −0.818132 | − | 0.575031i | \(-0.804990\pi\) | ||||
−0.818132 | + | 0.575031i | \(0.804990\pi\) | |||||||
\(252\) | −1.14077 | −0.0718620 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 14.6241 | 0.917600 | ||||||||
\(255\) | −4.21508 | −0.263959 | ||||||||
\(256\) | 20.1647 | 1.26030 | ||||||||
\(257\) | 0.871474 | 0.0543610 | 0.0271805 | − | 0.999631i | \(-0.491347\pi\) | ||||
0.0271805 | + | 0.999631i | \(0.491347\pi\) | |||||||
\(258\) | 19.4125 | 1.20857 | ||||||||
\(259\) | 7.70693 | 0.478885 | ||||||||
\(260\) | −1.03937 | −0.0644589 | ||||||||
\(261\) | 0.607298 | 0.0375908 | ||||||||
\(262\) | 21.4726 | 1.32658 | ||||||||
\(263\) | 26.8873 | 1.65794 | 0.828970 | − | 0.559293i | \(-0.188927\pi\) | ||||
0.828970 | + | 0.559293i | \(0.188927\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.15584 | 0.255291 | ||||||||
\(266\) | 10.9711 | 0.672681 | ||||||||
\(267\) | −8.15095 | −0.498830 | ||||||||
\(268\) | −2.49987 | −0.152704 | ||||||||
\(269\) | −0.992574 | −0.0605183 | −0.0302592 | − | 0.999542i | \(-0.509633\pi\) | ||||
−0.0302592 | + | 0.999542i | \(0.509633\pi\) | |||||||
\(270\) | −1.04548 | −0.0636259 | ||||||||
\(271\) | 26.8650 | 1.63193 | 0.815966 | − | 0.578099i | \(-0.196205\pi\) | ||||
0.815966 | + | 0.578099i | \(0.196205\pi\) | |||||||
\(272\) | −35.5839 | −2.15759 | ||||||||
\(273\) | −1.54445 | −0.0934741 | ||||||||
\(274\) | −30.9337 | −1.86878 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −4.29289 | −0.258402 | ||||||||
\(277\) | −27.6302 | −1.66014 | −0.830069 | − | 0.557660i | \(-0.811699\pi\) | ||||
−0.830069 | + | 0.557660i | \(0.811699\pi\) | |||||||
\(278\) | 26.1622 | 1.56910 | ||||||||
\(279\) | −6.87147 | −0.411384 | ||||||||
\(280\) | 0.898304 | 0.0536839 | ||||||||
\(281\) | 23.8418 | 1.42228 | 0.711141 | − | 0.703050i | \(-0.248179\pi\) | ||||
0.711141 | + | 0.703050i | \(0.248179\pi\) | |||||||
\(282\) | 18.0894 | 1.07721 | ||||||||
\(283\) | 8.74735 | 0.519976 | 0.259988 | − | 0.965612i | \(-0.416281\pi\) | ||||
0.259988 | + | 0.965612i | \(0.416281\pi\) | |||||||
\(284\) | −15.9058 | −0.943836 | ||||||||
\(285\) | 3.65199 | 0.216325 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.48287 | −0.441700 | ||||||||
\(288\) | −5.78051 | −0.340620 | ||||||||
\(289\) | 34.0526 | 2.00309 | ||||||||
\(290\) | 0.634918 | 0.0372836 | ||||||||
\(291\) | 4.79710 | 0.281211 | ||||||||
\(292\) | −2.95452 | −0.172900 | ||||||||
\(293\) | −19.6252 | −1.14651 | −0.573257 | − | 0.819376i | \(-0.694320\pi\) | ||||
−0.573257 | + | 0.819376i | \(0.694320\pi\) | |||||||
\(294\) | −1.77222 | −0.103358 | ||||||||
\(295\) | −1.97853 | −0.115194 | ||||||||
\(296\) | 11.7356 | 0.682120 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 22.1985 | 1.28592 | ||||||||
\(299\) | −5.81197 | −0.336115 | ||||||||
\(300\) | 5.30687 | 0.306392 | ||||||||
\(301\) | 10.9537 | 0.631362 | ||||||||
\(302\) | 0.582303 | 0.0335078 | ||||||||
\(303\) | 1.42666 | 0.0819592 | ||||||||
\(304\) | 30.8303 | 1.76824 | ||||||||
\(305\) | −1.98831 | −0.113850 | ||||||||
\(306\) | 12.6627 | 0.723880 | ||||||||
\(307\) | −17.0835 | −0.975009 | −0.487504 | − | 0.873121i | \(-0.662093\pi\) | ||||
−0.487504 | + | 0.873121i | \(0.662093\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −17.6172 | −1.00221 | ||||||||
\(310\) | −7.18399 | −0.408023 | ||||||||
\(311\) | −7.23351 | −0.410175 | −0.205087 | − | 0.978744i | \(-0.565748\pi\) | ||||
−0.205087 | + | 0.978744i | \(0.565748\pi\) | |||||||
\(312\) | −2.35179 | −0.133144 | ||||||||
\(313\) | 13.7784 | 0.778804 | 0.389402 | − | 0.921068i | \(-0.372682\pi\) | ||||
0.389402 | + | 0.921068i | \(0.372682\pi\) | |||||||
\(314\) | −4.75113 | −0.268122 | ||||||||
\(315\) | −0.589926 | −0.0332386 | ||||||||
\(316\) | −5.32002 | −0.299274 | ||||||||
\(317\) | −6.95629 | −0.390704 | −0.195352 | − | 0.980733i | \(-0.562585\pi\) | ||||
−0.195352 | + | 0.980733i | \(0.562585\pi\) | |||||||
\(318\) | −12.4848 | −0.700111 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −0.167535 | −0.00936550 | ||||||||
\(321\) | 7.20005 | 0.401867 | ||||||||
\(322\) | −6.66913 | −0.371656 | ||||||||
\(323\) | −44.2324 | −2.46116 | ||||||||
\(324\) | 1.14077 | 0.0633763 | ||||||||
\(325\) | 7.18474 | 0.398538 | ||||||||
\(326\) | −1.58023 | −0.0875211 | ||||||||
\(327\) | 8.88678 | 0.491440 | ||||||||
\(328\) | −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 | ||||||||
\(333\) | −7.70693 | −0.422337 | ||||||||
\(334\) | 20.4887 | 1.12109 | ||||||||
\(335\) | −1.29275 | −0.0706305 | ||||||||
\(336\) | −4.98018 | −0.271691 | ||||||||
\(337\) | 19.5714 | 1.06612 | 0.533062 | − | 0.846076i | \(-0.321041\pi\) | ||||
0.533062 | + | 0.846076i | \(0.321041\pi\) | |||||||
\(338\) | −18.8116 | −1.02322 | ||||||||
\(339\) | 7.80862 | 0.424106 | ||||||||
\(340\) | 4.80846 | 0.260775 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −10.9711 | −0.593249 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 16.6797 | 0.899308 | ||||||||
\(345\) | −2.21997 | −0.119519 | ||||||||
\(346\) | 15.9310 | 0.856455 | ||||||||
\(347\) | −6.49184 | −0.348500 | −0.174250 | − | 0.984701i | \(-0.555750\pi\) | ||||
−0.174250 | + | 0.984701i | \(0.555750\pi\) | |||||||
\(348\) | −0.692789 | −0.0371374 | ||||||||
\(349\) | 7.87965 | 0.421788 | 0.210894 | − | 0.977509i | \(-0.432362\pi\) | ||||
0.210894 | + | 0.977509i | \(0.432362\pi\) | |||||||
\(350\) | 8.24436 | 0.440680 | ||||||||
\(351\) | 1.54445 | 0.0824364 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.34594 | −0.284536 | −0.142268 | − | 0.989828i | \(-0.545439\pi\) | ||||
−0.142268 | + | 0.989828i | \(0.545439\pi\) | |||||||
\(354\) | 5.94378 | 0.315909 | ||||||||
\(355\) | −8.22533 | −0.436555 | ||||||||
\(356\) | 9.29840 | 0.492814 | ||||||||
\(357\) | 7.14511 | 0.378159 | ||||||||
\(358\) | −10.8919 | −0.575655 | ||||||||
\(359\) | −17.8515 | −0.942169 | −0.471084 | − | 0.882088i | \(-0.656137\pi\) | ||||
−0.471084 | + | 0.882088i | \(0.656137\pi\) | |||||||
\(360\) | −0.898304 | −0.0473448 | ||||||||
\(361\) | 19.3234 | 1.01702 | ||||||||
\(362\) | 26.5235 | 1.39404 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.76186 | 0.0923467 | ||||||||
\(365\) | −1.52786 | −0.0799721 | ||||||||
\(366\) | 5.97317 | 0.312223 | ||||||||
\(367\) | −29.9357 | −1.56263 | −0.781316 | − | 0.624135i | \(-0.785451\pi\) | ||||
−0.781316 | + | 0.624135i | \(0.785451\pi\) | |||||||
\(368\) | −18.7411 | −0.976949 | ||||||||
\(369\) | 7.48287 | 0.389543 | ||||||||
\(370\) | −8.05744 | −0.418886 | ||||||||
\(371\) | −7.04469 | −0.365742 | ||||||||
\(372\) | 7.83880 | 0.406423 | ||||||||
\(373\) | 23.4915 | 1.21635 | 0.608173 | − | 0.793805i | \(-0.291903\pi\) | ||||
0.608173 | + | 0.793805i | \(0.291903\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5.69396 | 0.294035 | ||||||||
\(376\) | 15.5429 | 0.801562 | ||||||||
\(377\) | −0.937938 | −0.0483063 | ||||||||
\(378\) | 1.77222 | 0.0911533 | ||||||||
\(379\) | −31.4532 | −1.61564 | −0.807821 | − | 0.589428i | \(-0.799353\pi\) | ||||
−0.807821 | + | 0.589428i | \(0.799353\pi\) | |||||||
\(380\) | −4.16609 | −0.213716 | ||||||||
\(381\) | −8.25186 | −0.422756 | ||||||||
\(382\) | 17.4981 | 0.895278 | ||||||||
\(383\) | −5.62749 | −0.287551 | −0.143776 | − | 0.989610i | \(-0.545924\pi\) | ||||
−0.143776 | + | 0.989610i | \(0.545924\pi\) | |||||||
\(384\) | −11.0577 | −0.564287 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −10.9543 | −0.557561 | ||||||||
\(387\) | −10.9537 | −0.556809 | ||||||||
\(388\) | −5.47240 | −0.277819 | ||||||||
\(389\) | 26.1072 | 1.32369 | 0.661845 | − | 0.749641i | \(-0.269774\pi\) | ||||
0.661845 | + | 0.749641i | \(0.269774\pi\) | |||||||
\(390\) | 1.61469 | 0.0817629 | ||||||||
\(391\) | 26.8881 | 1.35979 | ||||||||
\(392\) | −1.52274 | −0.0769100 | ||||||||
\(393\) | −12.1162 | −0.611182 | ||||||||
\(394\) | −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 | ||||||||
\(399\) | −6.19059 | −0.309917 | ||||||||
\(400\) | 23.1677 | 1.15839 | ||||||||
\(401\) | 3.68876 | 0.184208 | 0.0921040 | − | 0.995749i | \(-0.470641\pi\) | ||||
0.0921040 | + | 0.995749i | \(0.470641\pi\) | |||||||
\(402\) | 3.88361 | 0.193697 | ||||||||
\(403\) | 10.6126 | 0.528652 | ||||||||
\(404\) | −1.62749 | −0.0809708 | ||||||||
\(405\) | 0.589926 | 0.0293136 | ||||||||
\(406\) | −1.07627 | −0.0534142 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 10.8801 | 0.538647 | ||||||||
\(409\) | 1.08022 | 0.0534136 | 0.0267068 | − | 0.999643i | \(-0.491498\pi\) | ||||
0.0267068 | + | 0.999643i | \(0.491498\pi\) | |||||||
\(410\) | 7.82319 | 0.386360 | ||||||||
\(411\) | 17.4548 | 0.860980 | ||||||||
\(412\) | 20.0973 | 0.990123 | ||||||||
\(413\) | 3.35386 | 0.165033 | ||||||||
\(414\) | 6.66913 | 0.327770 | ||||||||
\(415\) | −2.07046 | −0.101635 | ||||||||
\(416\) | 8.92769 | 0.437716 | ||||||||
\(417\) | −14.7624 | −0.722915 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.0766 | 0.492273 | 0.246136 | − | 0.969235i | \(-0.420839\pi\) | ||||
0.246136 | + | 0.969235i | \(0.420839\pi\) | |||||||
\(420\) | 0.672972 | 0.0328377 | ||||||||
\(421\) | 11.9757 | 0.583658 | 0.291829 | − | 0.956470i | \(-0.405736\pi\) | ||||
0.291829 | + | 0.956470i | \(0.405736\pi\) | |||||||
\(422\) | −37.1831 | −1.81004 | ||||||||
\(423\) | −10.2072 | −0.496290 | ||||||||
\(424\) | −10.7272 | −0.520960 | ||||||||
\(425\) | −33.2390 | −1.61233 | ||||||||
\(426\) | 24.7101 | 1.19721 | ||||||||
\(427\) | 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 | \(-0.504205\pi\) | ||||
−0.0132113 | + | 0.999913i | \(0.504205\pi\) | |||||||
\(432\) | 4.98018 | 0.239609 | ||||||||
\(433\) | 19.5879 | 0.941332 | 0.470666 | − | 0.882311i | \(-0.344014\pi\) | ||||
0.470666 | + | 0.882311i | \(0.344014\pi\) | |||||||
\(434\) | 12.1778 | 0.584552 | ||||||||
\(435\) | −0.358261 | −0.0171773 | ||||||||
\(436\) | −10.1378 | −0.485513 | ||||||||
\(437\) | −23.2961 | −1.11440 | ||||||||
\(438\) | 4.58993 | 0.219315 | ||||||||
\(439\) | 37.4069 | 1.78533 | 0.892667 | − | 0.450716i | \(-0.148831\pi\) | ||||
0.892667 | + | 0.450716i | \(0.148831\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | −19.5569 | −0.930226 | ||||||||
\(443\) | 21.4478 | 1.01902 | 0.509508 | − | 0.860466i | \(-0.329827\pi\) | ||||
0.509508 | + | 0.860466i | \(0.329827\pi\) | |||||||
\(444\) | 8.79186 | 0.417243 | ||||||||
\(445\) | 4.80846 | 0.227943 | ||||||||
\(446\) | 6.00536 | 0.284362 | ||||||||
\(447\) | −12.5258 | −0.592450 | ||||||||
\(448\) | 0.283993 | 0.0134174 | ||||||||
\(449\) | 6.39904 | 0.301989 | 0.150995 | − | 0.988535i | \(-0.451752\pi\) | ||||
0.150995 | + | 0.988535i | \(0.451752\pi\) | |||||||
\(450\) | −8.24436 | −0.388643 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −8.90787 | −0.418991 | ||||||||
\(453\) | −0.328572 | −0.0154377 | ||||||||
\(454\) | 34.3763 | 1.61336 | ||||||||
\(455\) | 0.911108 | 0.0427134 | ||||||||
\(456\) | −9.42666 | −0.441444 | ||||||||
\(457\) | −36.9430 | −1.72812 | −0.864060 | − | 0.503389i | \(-0.832086\pi\) | ||||
−0.864060 | + | 0.503389i | \(0.832086\pi\) | |||||||
\(458\) | −17.4813 | −0.816847 | ||||||||
\(459\) | −7.14511 | −0.333505 | ||||||||
\(460\) | 2.53249 | 0.118078 | ||||||||
\(461\) | 7.39825 | 0.344571 | 0.172285 | − | 0.985047i | \(-0.444885\pi\) | ||||
0.172285 | + | 0.985047i | \(0.444885\pi\) | |||||||
\(462\) | 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 | ||||||||
\(465\) | 4.05366 | 0.187984 | ||||||||
\(466\) | 12.6292 | 0.585036 | ||||||||
\(467\) | 36.1626 | 1.67341 | 0.836704 | − | 0.547656i | \(-0.184480\pi\) | ||||
0.836704 | + | 0.547656i | \(0.184480\pi\) | |||||||
\(468\) | −1.76186 | −0.0814422 | ||||||||
\(469\) | 2.19138 | 0.101188 | ||||||||
\(470\) | −10.6714 | −0.492235 | ||||||||
\(471\) | 2.68089 | 0.123529 | ||||||||
\(472\) | 5.10705 | 0.235071 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 8.26479 | 0.379614 | ||||||||
\(475\) | 28.7985 | 1.32137 | ||||||||
\(476\) | −8.15095 | −0.373598 | ||||||||
\(477\) | 7.04469 | 0.322554 | ||||||||
\(478\) | 39.5018 | 1.80677 | ||||||||
\(479\) | 16.0252 | 0.732212 | 0.366106 | − | 0.930573i | \(-0.380691\pi\) | ||||
0.366106 | + | 0.930573i | \(0.380691\pi\) | |||||||
\(480\) | 3.41007 | 0.155648 | ||||||||
\(481\) | 11.9029 | 0.542727 | ||||||||
\(482\) | 26.3623 | 1.20077 | ||||||||
\(483\) | 3.76314 | 0.171229 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.82993 | −0.128501 | ||||||||
\(486\) | −1.77222 | −0.0803897 | ||||||||
\(487\) | 1.55059 | 0.0702641 | 0.0351320 | − | 0.999383i | \(-0.488815\pi\) | ||||
0.0351320 | + | 0.999383i | \(0.488815\pi\) | |||||||
\(488\) | 5.13230 | 0.232328 | ||||||||
\(489\) | 0.891668 | 0.0403226 | ||||||||
\(490\) | 1.04548 | 0.0472300 | ||||||||
\(491\) | −0.0331635 | −0.00149665 | −0.000748324 | − | 1.00000i | \(-0.500238\pi\) | ||||
−0.000748324 | 1.00000i | \(0.500238\pi\) | ||||||||
\(492\) | −8.53627 | −0.384845 | ||||||||
\(493\) | 4.33921 | 0.195428 | ||||||||
\(494\) | 16.9443 | 0.762359 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 34.2212 | 1.53658 | ||||||||
\(497\) | 13.9430 | 0.625429 | ||||||||
\(498\) | 6.21997 | 0.278724 | ||||||||
\(499\) | −27.0314 | −1.21009 | −0.605046 | − | 0.796190i | \(-0.706845\pi\) | ||||
−0.605046 | + | 0.796190i | \(0.706845\pi\) | |||||||
\(500\) | −6.49552 | −0.290488 | ||||||||
\(501\) | −11.5610 | −0.516509 | ||||||||
\(502\) | −45.9418 | −2.05048 | ||||||||
\(503\) | −29.3341 | −1.30794 | −0.653972 | − | 0.756519i | \(-0.726899\pi\) | ||||
−0.653972 | + | 0.756519i | \(0.726899\pi\) | |||||||
\(504\) | 1.52274 | 0.0678282 | ||||||||
\(505\) | −0.841621 | −0.0374516 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 10.6147 | 0.471415 | ||||||||
\(508\) | 9.41351 | 0.417657 | ||||||||
\(509\) | −16.6329 | −0.737239 | −0.368620 | − | 0.929580i | \(-0.620169\pi\) | ||||
−0.368620 | + | 0.929580i | \(0.620169\pi\) | |||||||
\(510\) | −7.47007 | −0.330780 | ||||||||
\(511\) | 2.58993 | 0.114572 | ||||||||
\(512\) | 13.6210 | 0.601967 | ||||||||
\(513\) | 6.19059 | 0.273321 | ||||||||
\(514\) | 1.54445 | 0.0681226 | ||||||||
\(515\) | 10.3929 | 0.457964 | ||||||||
\(516\) | 12.4957 | 0.550094 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 13.6584 | 0.600115 | ||||||||
\(519\) | −8.98926 | −0.394585 | ||||||||
\(520\) | 1.38738 | 0.0608407 | ||||||||
\(521\) | 35.8923 | 1.57247 | 0.786236 | − | 0.617927i | \(-0.212027\pi\) | ||||
0.786236 | + | 0.617927i | \(0.212027\pi\) | |||||||
\(522\) | 1.07627 | 0.0471069 | ||||||||
\(523\) | 7.27873 | 0.318276 | 0.159138 | − | 0.987256i | \(-0.449128\pi\) | ||||
0.159138 | + | 0.987256i | \(0.449128\pi\) | |||||||
\(524\) | 13.8219 | 0.603811 | ||||||||
\(525\) | −4.65199 | −0.203029 | ||||||||
\(526\) | 47.6502 | 2.07765 | ||||||||
\(527\) | −49.0974 | −2.13872 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.83876 | −0.384294 | ||||||||
\(530\) | 7.36508 | 0.319919 | ||||||||
\(531\) | −3.35386 | −0.145545 | ||||||||
\(532\) | 7.06206 | 0.306179 | ||||||||
\(533\) | −11.5569 | −0.500585 | ||||||||
\(534\) | −14.4453 | −0.625110 | ||||||||
\(535\) | −4.24749 | −0.183635 | ||||||||
\(536\) | 3.33690 | 0.144132 | ||||||||
\(537\) | 6.14590 | 0.265215 | ||||||||
\(538\) | −1.75906 | −0.0758386 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −0.672972 | −0.0289601 | ||||||||
\(541\) | −10.4709 | −0.450177 | −0.225089 | − | 0.974338i | \(-0.572267\pi\) | ||||
−0.225089 | + | 0.974338i | \(0.572267\pi\) | |||||||
\(542\) | 47.6108 | 2.04506 | ||||||||
\(543\) | −14.9662 | −0.642262 | ||||||||
\(544\) | −41.3024 | −1.77083 | ||||||||
\(545\) | −5.24254 | −0.224566 | ||||||||
\(546\) | −2.73710 | −0.117137 | ||||||||
\(547\) | 8.16609 | 0.349157 | 0.174578 | − | 0.984643i | \(-0.444144\pi\) | ||||
0.174578 | + | 0.984643i | \(0.444144\pi\) | |||||||
\(548\) | −19.9119 | −0.850596 | ||||||||
\(549\) | −3.37044 | −0.143847 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.75953 | −0.160161 | ||||||||
\(552\) | 5.73029 | 0.243897 | ||||||||
\(553\) | 4.66351 | 0.198313 | ||||||||
\(554\) | −48.9669 | −2.08040 | ||||||||
\(555\) | 4.54651 | 0.192989 | ||||||||
\(556\) | 16.8405 | 0.714197 | ||||||||
\(557\) | 11.8765 | 0.503225 | 0.251612 | − | 0.967828i | \(-0.419039\pi\) | ||||
0.251612 | + | 0.967828i | \(0.419039\pi\) | |||||||
\(558\) | −12.1778 | −0.515527 | ||||||||
\(559\) | 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 | \(-0.467484\pi\) | ||||
0.101976 | + | 0.994787i | \(0.467484\pi\) | |||||||
\(564\) | 11.6441 | 0.490304 | ||||||||
\(565\) | −4.60651 | −0.193797 | ||||||||
\(566\) | 15.5023 | 0.651608 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | 21.2316 | 0.890856 | ||||||||
\(569\) | 6.52993 | 0.273749 | 0.136875 | − | 0.990588i | \(-0.456294\pi\) | ||||
0.136875 | + | 0.990588i | \(0.456294\pi\) | |||||||
\(570\) | 6.47214 | 0.271088 | ||||||||
\(571\) | −33.8691 | −1.41738 | −0.708689 | − | 0.705521i | \(-0.750713\pi\) | ||||
−0.708689 | + | 0.705521i | \(0.750713\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9.87351 | −0.412472 | ||||||||
\(574\) | −13.2613 | −0.553517 | ||||||||
\(575\) | −17.5061 | −0.730054 | ||||||||
\(576\) | −0.283993 | −0.0118331 | ||||||||
\(577\) | −37.3609 | −1.55536 | −0.777678 | − | 0.628662i | \(-0.783603\pi\) | ||||
−0.777678 | + | 0.628662i | \(0.783603\pi\) | |||||||
\(578\) | 60.3487 | 2.51018 | ||||||||
\(579\) | 6.18113 | 0.256879 | ||||||||
\(580\) | 0.408694 | 0.0169701 | ||||||||
\(581\) | 3.50970 | 0.145607 | ||||||||
\(582\) | 8.50152 | 0.352399 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 3.94378 | 0.163195 | ||||||||
\(585\) | −0.911108 | −0.0376697 | ||||||||
\(586\) | −34.7802 | −1.43675 | ||||||||
\(587\) | −2.07974 | −0.0858399 | −0.0429199 | − | 0.999079i | \(-0.513666\pi\) | ||||
−0.0429199 | + | 0.999079i | \(0.513666\pi\) | |||||||
\(588\) | −1.14077 | −0.0470447 | ||||||||
\(589\) | 42.5385 | 1.75277 | ||||||||
\(590\) | −3.50639 | −0.144356 | ||||||||
\(591\) | 19.0720 | 0.784518 | ||||||||
\(592\) | 38.3819 | 1.57749 | ||||||||
\(593\) | 6.54983 | 0.268969 | 0.134485 | − | 0.990916i | \(-0.457062\pi\) | ||||
0.134485 | + | 0.990916i | \(0.457062\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.21508 | −0.172802 | ||||||||
\(596\) | 14.2891 | 0.585304 | ||||||||
\(597\) | 11.8479 | 0.484904 | ||||||||
\(598\) | −10.3001 | −0.421203 | ||||||||
\(599\) | −4.98187 | −0.203554 | −0.101777 | − | 0.994807i | \(-0.532453\pi\) | ||||
−0.101777 | + | 0.994807i | \(0.532453\pi\) | |||||||
\(600\) | −7.08377 | −0.289194 | ||||||||
\(601\) | −32.4713 | −1.32453 | −0.662266 | − | 0.749269i | \(-0.730405\pi\) | ||||
−0.662266 | + | 0.749269i | \(0.730405\pi\) | |||||||
\(602\) | 19.4125 | 0.791192 | ||||||||
\(603\) | −2.19138 | −0.0892398 | ||||||||
\(604\) | 0.374827 | 0.0152515 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 2.52835 | 0.102707 | ||||||||
\(607\) | 3.13388 | 0.127200 | 0.0636002 | − | 0.997975i | \(-0.479742\pi\) | ||||
0.0636002 | + | 0.997975i | \(0.479742\pi\) | |||||||
\(608\) | 35.7848 | 1.45126 | ||||||||
\(609\) | 0.607298 | 0.0246089 | ||||||||
\(610\) | −3.52373 | −0.142672 | ||||||||
\(611\) | 15.7644 | 0.637760 | ||||||||
\(612\) | 8.15095 | 0.329483 | ||||||||
\(613\) | 46.8484 | 1.89219 | 0.946094 | − | 0.323892i | \(-0.104991\pi\) | ||||
0.946094 | + | 0.323892i | \(0.104991\pi\) | |||||||
\(614\) | −30.2758 | −1.22183 | ||||||||
\(615\) | −4.41434 | −0.178003 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 26.5924 | 1.07057 | 0.535286 | − | 0.844671i | \(-0.320204\pi\) | ||||
0.535286 | + | 0.844671i | \(0.320204\pi\) | |||||||
\(618\) | −31.2217 | −1.25592 | ||||||||
\(619\) | −32.9765 | −1.32544 | −0.662718 | − | 0.748869i | \(-0.730597\pi\) | ||||
−0.662718 | + | 0.748869i | \(0.730597\pi\) | |||||||
\(620\) | −4.62431 | −0.185717 | ||||||||
\(621\) | −3.76314 | −0.151010 | ||||||||
\(622\) | −12.8194 | −0.514011 | ||||||||
\(623\) | −8.15095 | −0.326561 | ||||||||
\(624\) | −7.69162 | −0.307911 | ||||||||
\(625\) | 19.9009 | 0.796037 | ||||||||
\(626\) | 24.4185 | 0.975959 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3.05828 | −0.122039 | ||||||||
\(629\) | −55.0668 | −2.19566 | ||||||||
\(630\) | −1.04548 | −0.0416529 | ||||||||
\(631\) | 11.1721 | 0.444754 | 0.222377 | − | 0.974961i | \(-0.428618\pi\) | ||||
0.222377 | + | 0.974961i | \(0.428618\pi\) | |||||||
\(632\) | 7.10132 | 0.282475 | ||||||||
\(633\) | 20.9810 | 0.833922 | ||||||||
\(634\) | −12.3281 | −0.489611 | ||||||||
\(635\) | 4.86798 | 0.193180 | ||||||||
\(636\) | −8.03640 | −0.318664 | ||||||||
\(637\) | −1.54445 | −0.0611932 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −13.9430 | −0.551576 | ||||||||
\(640\) | 6.52324 | 0.257854 | ||||||||
\(641\) | −41.9153 | −1.65556 | −0.827778 | − | 0.561056i | \(-0.810395\pi\) | ||||
−0.827778 | + | 0.561056i | \(0.810395\pi\) | |||||||
\(642\) | 12.7601 | 0.503600 | ||||||||
\(643\) | 29.0873 | 1.14709 | 0.573546 | − | 0.819173i | \(-0.305567\pi\) | ||||
0.573546 | + | 0.819173i | \(0.305567\pi\) | |||||||
\(644\) | −4.29289 | −0.169164 | ||||||||
\(645\) | 6.46189 | 0.254437 | ||||||||
\(646\) | −78.3897 | −3.08420 | ||||||||
\(647\) | 1.89804 | 0.0746196 | 0.0373098 | − | 0.999304i | \(-0.488121\pi\) | ||||
0.0373098 | + | 0.999304i | \(0.488121\pi\) | |||||||
\(648\) | −1.52274 | −0.0598189 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 12.7330 | 0.499428 | ||||||||
\(651\) | −6.87147 | −0.269314 | ||||||||
\(652\) | −1.01719 | −0.0398363 | ||||||||
\(653\) | 20.2519 | 0.792517 | 0.396258 | − | 0.918139i | \(-0.370308\pi\) | ||||
0.396258 | + | 0.918139i | \(0.370308\pi\) | |||||||
\(654\) | 15.7493 | 0.615848 | ||||||||
\(655\) | 7.14766 | 0.279282 | ||||||||
\(656\) | −37.2661 | −1.45500 | ||||||||
\(657\) | −2.58993 | −0.101043 | ||||||||
\(658\) | 18.0894 | 0.705197 | ||||||||
\(659\) | −11.5620 | −0.450392 | −0.225196 | − | 0.974314i | \(-0.572302\pi\) | ||||
−0.225196 | + | 0.974314i | \(0.572302\pi\) | |||||||
\(660\) | 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 | ||||||||
\(663\) | 11.0352 | 0.428573 | ||||||||
\(664\) | 5.34436 | 0.207402 | ||||||||
\(665\) | 3.65199 | 0.141618 | ||||||||
\(666\) | −13.6584 | −0.529252 | ||||||||
\(667\) | 2.28535 | 0.0884890 | ||||||||
\(668\) | 13.1885 | 0.510279 | ||||||||
\(669\) | −3.38860 | −0.131011 | ||||||||
\(670\) | −2.29104 | −0.0885107 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −5.78051 | −0.222988 | ||||||||
\(673\) | −20.1249 | −0.775758 | −0.387879 | − | 0.921710i | \(-0.626792\pi\) | ||||
−0.387879 | + | 0.921710i | \(0.626792\pi\) | |||||||
\(674\) | 34.6850 | 1.33601 | ||||||||
\(675\) | 4.65199 | 0.179055 | ||||||||
\(676\) | −12.1090 | −0.465729 | ||||||||
\(677\) | 23.5746 | 0.906045 | 0.453022 | − | 0.891499i | \(-0.350346\pi\) | ||||
0.453022 | + | 0.891499i | \(0.350346\pi\) | |||||||
\(678\) | 13.8386 | 0.531469 | ||||||||
\(679\) | 4.79710 | 0.184096 | ||||||||
\(680\) | −6.41848 | −0.246137 | ||||||||
\(681\) | −19.3973 | −0.743305 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 11.5812 | 0.443143 | 0.221572 | − | 0.975144i | \(-0.428881\pi\) | ||||
0.221572 | + | 0.975144i | \(0.428881\pi\) | |||||||
\(684\) | −7.06206 | −0.270025 | ||||||||
\(685\) | −10.2970 | −0.393429 | ||||||||
\(686\) | −1.77222 | −0.0676638 | ||||||||
\(687\) | 9.86405 | 0.376337 | ||||||||
\(688\) | 54.5516 | 2.07976 | ||||||||
\(689\) | −10.8801 | −0.414500 | ||||||||
\(690\) | −3.93429 | −0.149776 | ||||||||
\(691\) | 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 | ||||||||
\(696\) | 0.924756 | 0.0350528 | ||||||||
\(697\) | 53.4659 | 2.02517 | ||||||||
\(698\) | 13.9645 | 0.528564 | ||||||||
\(699\) | −7.12619 | −0.269537 | ||||||||
\(700\) | 5.30687 | 0.200581 | ||||||||
\(701\) | −22.8165 | −0.861769 | −0.430884 | − | 0.902407i | \(-0.641798\pi\) | ||||
−0.430884 | + | 0.902407i | \(0.641798\pi\) | |||||||
\(702\) | 2.73710 | 0.103305 | ||||||||
\(703\) | 47.7104 | 1.79943 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6.02147 | 0.226782 | ||||||||
\(706\) | −9.47420 | −0.356566 | ||||||||
\(707\) | 1.42666 | 0.0536549 | ||||||||
\(708\) | 3.82599 | 0.143790 | ||||||||
\(709\) | 39.9746 | 1.50128 | 0.750638 | − | 0.660713i | \(-0.229746\pi\) | ||||
0.750638 | + | 0.660713i | \(0.229746\pi\) | |||||||
\(710\) | −14.5771 | −0.547070 | ||||||||
\(711\) | −4.66351 | −0.174895 | ||||||||
\(712\) | −12.4118 | −0.465151 | ||||||||
\(713\) | −25.8583 | −0.968402 | ||||||||
\(714\) | 12.6627 | 0.473891 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −7.01108 | −0.262016 | ||||||||
\(717\) | −22.2894 | −0.832414 | ||||||||
\(718\) | −31.6369 | −1.18068 | ||||||||
\(719\) | −26.2200 | −0.977840 | −0.488920 | − | 0.872329i | \(-0.662609\pi\) | ||||
−0.488920 | + | 0.872329i | \(0.662609\pi\) | |||||||
\(720\) | −2.93794 | −0.109490 | ||||||||
\(721\) | −17.6172 | −0.656100 | ||||||||
\(722\) | 34.2453 | 1.27448 | ||||||||
\(723\) | −14.8753 | −0.553217 | ||||||||
\(724\) | 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 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −2.70772 | −0.100217 | ||||||||
\(731\) | −78.2656 | −2.89476 | ||||||||
\(732\) | 3.84491 | 0.142112 | ||||||||
\(733\) | −21.1284 | −0.780395 | −0.390197 | − | 0.920731i | \(-0.627593\pi\) | ||||
−0.390197 | + | 0.920731i | \(0.627593\pi\) | |||||||
\(734\) | −53.0528 | −1.95821 | ||||||||
\(735\) | −0.589926 | −0.0217597 | ||||||||
\(736\) | −21.7529 | −0.801822 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 13.2613 | 0.488156 | ||||||||
\(739\) | 37.5036 | 1.37959 | 0.689795 | − | 0.724004i | \(-0.257701\pi\) | ||||
0.689795 | + | 0.724004i | \(0.257701\pi\) | |||||||
\(740\) | −5.18655 | −0.190661 | ||||||||
\(741\) | −9.56103 | −0.351233 | ||||||||
\(742\) | −12.4848 | −0.458330 | ||||||||
\(743\) | −36.1464 | −1.32608 | −0.663041 | − | 0.748583i | \(-0.730735\pi\) | ||||
−0.663041 | + | 0.748583i | \(0.730735\pi\) | |||||||
\(744\) | −10.4635 | −0.383609 | ||||||||
\(745\) | 7.38929 | 0.270723 | ||||||||
\(746\) | 41.6322 | 1.52426 | ||||||||
\(747\) | −3.50970 | −0.128413 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.20005 | 0.263084 | ||||||||
\(750\) | 10.0910 | 0.368470 | ||||||||
\(751\) | −43.5533 | −1.58928 | −0.794641 | − | 0.607080i | \(-0.792341\pi\) | ||||
−0.794641 | + | 0.607080i | \(0.792341\pi\) | |||||||
\(752\) | 50.8336 | 1.85371 | ||||||||
\(753\) | 25.9233 | 0.944697 | ||||||||
\(754\) | −1.66224 | −0.0605351 | ||||||||
\(755\) | 0.193833 | 0.00705431 | ||||||||
\(756\) | 1.14077 | 0.0414895 | ||||||||
\(757\) | −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 | \(-0.593422\pi\) | ||||
−0.289299 | + | 0.957239i | \(0.593422\pi\) | |||||||
\(762\) | −14.6241 | −0.529777 | ||||||||
\(763\) | 8.88678 | 0.321723 | ||||||||
\(764\) | 11.2634 | 0.407497 | ||||||||
\(765\) | 4.21508 | 0.152397 | ||||||||
\(766\) | −9.97317 | −0.360345 | ||||||||
\(767\) | 5.17985 | 0.187034 | ||||||||
\(768\) | −20.1647 | −0.727633 | ||||||||
\(769\) | 5.19899 | 0.187480 | 0.0937402 | − | 0.995597i | \(-0.470118\pi\) | ||||
0.0937402 | + | 0.995597i | \(0.470118\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.871474 | −0.0313854 | ||||||||
\(772\) | −7.05127 | −0.253781 | ||||||||
\(773\) | −12.1614 | −0.437416 | −0.218708 | − | 0.975790i | \(-0.570184\pi\) | ||||
−0.218708 | + | 0.975790i | \(0.570184\pi\) | |||||||
\(774\) | −19.4125 | −0.697766 | ||||||||
\(775\) | 31.9660 | 1.14825 | ||||||||
\(776\) | 7.30473 | 0.262224 | ||||||||
\(777\) | −7.70693 | −0.276484 | ||||||||
\(778\) | 46.2678 | 1.65878 | ||||||||
\(779\) | −46.3234 | −1.65971 | ||||||||
\(780\) | 1.03937 | 0.0372154 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 47.6516 | 1.70402 | ||||||||
\(783\) | −0.607298 | −0.0217030 | ||||||||
\(784\) | −4.98018 | −0.177864 | ||||||||
\(785\) | −1.58152 | −0.0564470 | ||||||||
\(786\) | −21.4726 | −0.765903 | ||||||||
\(787\) | −39.6430 | −1.41312 | −0.706559 | − | 0.707654i | \(-0.749754\pi\) | ||||
−0.706559 | + | 0.707654i | \(0.749754\pi\) | |||||||
\(788\) | −21.7569 | −0.775056 | ||||||||
\(789\) | −26.8873 | −0.957212 | ||||||||
\(790\) | −4.87561 | −0.173466 | ||||||||
\(791\) | 7.80862 | 0.277643 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.20546 | 0.184851 | ||||||||
\(794\) | 18.4006 | 0.653011 | ||||||||
\(795\) | −4.15584 | −0.147393 | ||||||||
\(796\) | −13.5158 | −0.479055 | ||||||||
\(797\) | −35.1118 | −1.24372 | −0.621862 | − | 0.783127i | \(-0.713624\pi\) | ||||
−0.621862 | + | 0.783127i | \(0.713624\pi\) | |||||||
\(798\) | −10.9711 | −0.388373 | ||||||||
\(799\) | −72.9313 | −2.58012 | ||||||||
\(800\) | 26.8909 | 0.950736 | ||||||||
\(801\) | 8.15095 | 0.288000 | ||||||||
\(802\) | 6.53731 | 0.230840 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 2.49987 | 0.0881635 | ||||||||
\(805\) | −2.21997 | −0.0782438 | ||||||||
\(806\) | 18.8079 | 0.662481 | ||||||||
\(807\) | 0.992574 | 0.0349403 | ||||||||
\(808\) | 2.17243 | 0.0764257 | ||||||||
\(809\) | −41.7873 | −1.46916 | −0.734581 | − | 0.678521i | \(-0.762621\pi\) | ||||
−0.734581 | + | 0.678521i | \(0.762621\pi\) | |||||||
\(810\) | 1.04548 | 0.0367344 | ||||||||
\(811\) | −9.89879 | −0.347594 | −0.173797 | − | 0.984782i | \(-0.555604\pi\) | ||||
−0.173797 | + | 0.984782i | \(0.555604\pi\) | |||||||
\(812\) | −0.692789 | −0.0243121 | ||||||||
\(813\) | −26.8650 | −0.942197 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.526018 | −0.0184256 | ||||||||
\(816\) | 35.5839 | 1.24569 | ||||||||
\(817\) | 67.8100 | 2.37237 | ||||||||
\(818\) | 1.91440 | 0.0669353 | ||||||||
\(819\) | 1.54445 | 0.0539673 | ||||||||
\(820\) | 5.03576 | 0.175856 | ||||||||
\(821\) | 16.1936 | 0.565161 | 0.282580 | − | 0.959244i | \(-0.408810\pi\) | ||||
0.282580 | + | 0.959244i | \(0.408810\pi\) | |||||||
\(822\) | 30.9337 | 1.07894 | ||||||||
\(823\) | −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 | \(-0.802720\pi\) | ||||
−0.814009 | + | 0.580852i | \(0.802720\pi\) | |||||||
\(828\) | 4.29289 | 0.149188 | ||||||||
\(829\) | −41.5599 | −1.44344 | −0.721718 | − | 0.692187i | \(-0.756647\pi\) | ||||
−0.721718 | + | 0.692187i | \(0.756647\pi\) | |||||||
\(830\) | −3.66932 | −0.127364 | ||||||||
\(831\) | 27.6302 | 0.958481 | ||||||||
\(832\) | 0.438613 | 0.0152062 | ||||||||
\(833\) | 7.14511 | 0.247563 | ||||||||
\(834\) | −26.1622 | −0.905922 | ||||||||
\(835\) | 6.82015 | 0.236021 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.87147 | 0.237513 | ||||||||
\(838\) | 17.8579 | 0.616892 | ||||||||
\(839\) | 5.14119 | 0.177494 | 0.0887469 | − | 0.996054i | \(-0.471714\pi\) | ||||
0.0887469 | + | 0.996054i | \(0.471714\pi\) | |||||||
\(840\) | −0.898304 | −0.0309944 | ||||||||
\(841\) | −28.6312 | −0.987282 | ||||||||
\(842\) | 21.2236 | 0.731412 | ||||||||
\(843\) | −23.8418 | −0.821155 | ||||||||
\(844\) | −23.9346 | −0.823864 | ||||||||
\(845\) | −6.26188 | −0.215415 | ||||||||
\(846\) | −18.0894 | −0.621926 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −35.0838 | −1.20478 | ||||||||
\(849\) | −8.74735 | −0.300208 | ||||||||
\(850\) | −58.9068 | −2.02049 | ||||||||
\(851\) | −29.0023 | −0.994184 | ||||||||
\(852\) | 15.9058 | 0.544924 | ||||||||
\(853\) | 6.69649 | 0.229283 | 0.114642 | − | 0.993407i | \(-0.463428\pi\) | ||||
0.114642 | + | 0.993407i | \(0.463428\pi\) | |||||||
\(854\) | 5.97317 | 0.204398 | ||||||||
\(855\) | −3.65199 | −0.124895 | ||||||||
\(856\) | 10.9638 | 0.374735 | ||||||||
\(857\) | −36.1064 | −1.23337 | −0.616686 | − | 0.787209i | \(-0.711525\pi\) | ||||
−0.616686 | + | 0.787209i | \(0.711525\pi\) | |||||||
\(858\) | 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 | ||||||||
\(861\) | 7.48287 | 0.255016 | ||||||||
\(862\) | −0.972147 | −0.0331115 | ||||||||
\(863\) | 38.3724 | 1.30621 | 0.653105 | − | 0.757267i | \(-0.273466\pi\) | ||||
0.653105 | + | 0.757267i | \(0.273466\pi\) | |||||||
\(864\) | 5.78051 | 0.196657 | ||||||||
\(865\) | 5.30300 | 0.180307 | ||||||||
\(866\) | 34.7140 | 1.17963 | ||||||||
\(867\) | −34.0526 | −1.15649 | ||||||||
\(868\) | 7.83880 | 0.266066 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −0.634918 | −0.0215257 | ||||||||
\(871\) | 3.38446 | 0.114678 | ||||||||
\(872\) | 13.5323 | 0.458260 | ||||||||
\(873\) | −4.79710 | −0.162357 | ||||||||
\(874\) | −41.2858 | −1.39651 | ||||||||
\(875\) | 5.69396 | 0.192491 | ||||||||
\(876\) | 2.95452 | 0.0998240 | ||||||||
\(877\) | −0.811156 | −0.0273908 | −0.0136954 | − | 0.999906i | \(-0.504360\pi\) | ||||
−0.0136954 | + | 0.999906i | \(0.504360\pi\) | |||||||
\(878\) | 66.2934 | 2.23729 | ||||||||
\(879\) | 19.6252 | 0.661940 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −32.5076 | −1.09521 | −0.547605 | − | 0.836737i | \(-0.684460\pi\) | ||||
−0.547605 | + | 0.836737i | \(0.684460\pi\) | |||||||
\(882\) | 1.77222 | 0.0596738 | ||||||||
\(883\) | 48.0995 | 1.61868 | 0.809338 | − | 0.587343i | \(-0.199826\pi\) | ||||
0.809338 | + | 0.587343i | \(0.199826\pi\) | |||||||
\(884\) | −12.5887 | −0.423404 | ||||||||
\(885\) | 1.97853 | 0.0665075 | ||||||||
\(886\) | 38.0103 | 1.27698 | ||||||||
\(887\) | 11.3847 | 0.382260 | 0.191130 | − | 0.981565i | \(-0.438785\pi\) | ||||
0.191130 | + | 0.981565i | \(0.438785\pi\) | |||||||
\(888\) | −11.7356 | −0.393822 | ||||||||
\(889\) | −8.25186 | −0.276758 | ||||||||
\(890\) | 8.52166 | 0.285647 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3.86563 | 0.129431 | ||||||||
\(893\) | 63.1884 | 2.11452 | ||||||||
\(894\) | −22.1985 | −0.742429 | ||||||||
\(895\) | −3.62562 | −0.121191 | ||||||||
\(896\) | −11.0577 | −0.369413 | ||||||||
\(897\) | 5.81197 | 0.194056 | ||||||||
\(898\) | 11.3405 | 0.378438 | ||||||||
\(899\) | −4.17303 | −0.139178 | ||||||||
\(900\) | −5.30687 | −0.176896 | ||||||||
\(901\) | 50.3351 | 1.67690 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −10.9537 | −0.364517 | ||||||||
\(904\) | 11.8905 | 0.395472 | ||||||||
\(905\) | 8.82895 | 0.293484 | ||||||||
\(906\) | −0.582303 | −0.0193457 | ||||||||
\(907\) | 13.4259 | 0.445799 | 0.222899 | − | 0.974841i | \(-0.428448\pi\) | ||||
0.222899 | + | 0.974841i | \(0.428448\pi\) | |||||||
\(908\) | 22.1279 | 0.734340 | ||||||||
\(909\) | −1.42666 | −0.0473192 | ||||||||
\(910\) | 1.61469 | 0.0535264 | ||||||||
\(911\) | 3.39303 | 0.112416 | 0.0562080 | − | 0.998419i | \(-0.482099\pi\) | ||||
0.0562080 | + | 0.998419i | \(0.482099\pi\) | |||||||
\(912\) | −30.8303 | −1.02089 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −65.4712 | −2.16560 | ||||||||
\(915\) | 1.98831 | 0.0657315 | ||||||||
\(916\) | −11.2526 | −0.371798 | ||||||||
\(917\) | −12.1162 | −0.400112 | ||||||||
\(918\) | −12.6627 | −0.417932 | ||||||||
\(919\) | −44.5668 | −1.47012 | −0.735062 | − | 0.678000i | \(-0.762847\pi\) | ||||
−0.735062 | + | 0.678000i | \(0.762847\pi\) | |||||||
\(920\) | −3.38044 | −0.111450 | ||||||||
\(921\) | 17.0835 | 0.562922 | ||||||||
\(922\) | 13.1113 | 0.431799 | ||||||||
\(923\) | 21.5342 | 0.708807 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 35.8525 | 1.17882 | ||||||||
\(926\) | −25.4699 | −0.836992 | ||||||||
\(927\) | 17.6172 | 0.578626 | ||||||||
\(928\) | −3.51049 | −0.115238 | ||||||||
\(929\) | −7.15205 | −0.234651 | −0.117325 | − | 0.993094i | \(-0.537432\pi\) | ||||
−0.117325 | + | 0.993094i | \(0.537432\pi\) | |||||||
\(930\) | 7.18399 | 0.235572 | ||||||||
\(931\) | −6.19059 | −0.202888 | ||||||||
\(932\) | 8.12937 | 0.266287 | ||||||||
\(933\) | 7.23351 | 0.236815 | ||||||||
\(934\) | 64.0883 | 2.09703 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.35179 | 0.0768706 | ||||||||
\(937\) | −1.30811 | −0.0427342 | −0.0213671 | − | 0.999772i | \(-0.506802\pi\) | ||||
−0.0213671 | + | 0.999772i | \(0.506802\pi\) | |||||||
\(938\) | 3.88361 | 0.126804 | ||||||||
\(939\) | −13.7784 | −0.449643 | ||||||||
\(940\) | −6.86914 | −0.224047 | ||||||||
\(941\) | −22.1225 | −0.721174 | −0.360587 | − | 0.932726i | \(-0.617424\pi\) | ||||
−0.360587 | + | 0.932726i | \(0.617424\pi\) | |||||||
\(942\) | 4.75113 | 0.154800 | ||||||||
\(943\) | 28.1591 | 0.916987 | ||||||||
\(944\) | 16.7028 | 0.543631 | ||||||||
\(945\) | 0.589926 | 0.0191903 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −17.6842 | −0.574658 | −0.287329 | − | 0.957832i | \(-0.592767\pi\) | ||||
−0.287329 | + | 0.957832i | \(0.592767\pi\) | |||||||
\(948\) | 5.32002 | 0.172786 | ||||||||
\(949\) | 4.00000 | 0.129845 | ||||||||
\(950\) | 51.0374 | 1.65587 | ||||||||
\(951\) | 6.95629 | 0.225573 | ||||||||
\(952\) | 10.8801 | 0.352627 | ||||||||
\(953\) | −23.7741 | −0.770118 | −0.385059 | − | 0.922892i | \(-0.625819\pi\) | ||||
−0.385059 | + | 0.922892i | \(0.625819\pi\) | |||||||
\(954\) | 12.4848 | 0.404209 | ||||||||
\(955\) | 5.82464 | 0.188481 | ||||||||
\(956\) | 25.4272 | 0.822374 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 28.4003 | 0.917573 | ||||||||
\(959\) | 17.4548 | 0.563644 | ||||||||
\(960\) | 0.167535 | 0.00540717 | ||||||||
\(961\) | 16.2172 | 0.523134 | ||||||||
\(962\) | 21.0946 | 0.680119 | ||||||||
\(963\) | −7.20005 | −0.232018 | ||||||||
\(964\) | 16.9693 | 0.546544 | ||||||||
\(965\) | −3.64641 | −0.117382 | ||||||||
\(966\) | 6.66913 | 0.214576 | ||||||||
\(967\) | 21.1829 | 0.681195 | 0.340597 | − | 0.940209i | \(-0.389371\pi\) | ||||
0.340597 | + | 0.940209i | \(0.389371\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 44.2324 | 1.42095 | ||||||||
\(970\) | −5.01527 | −0.161031 | ||||||||
\(971\) | −47.4360 | −1.52229 | −0.761147 | − | 0.648579i | \(-0.775363\pi\) | ||||
−0.761147 | + | 0.648579i | \(0.775363\pi\) | |||||||
\(972\) | −1.14077 | −0.0365903 | ||||||||
\(973\) | −14.7624 | −0.473259 | ||||||||
\(974\) | 2.74800 | 0.0880515 | ||||||||
\(975\) | −7.18474 | −0.230096 | ||||||||
\(976\) | 16.7854 | 0.537288 | ||||||||
\(977\) | −13.1860 | −0.421858 | −0.210929 | − | 0.977501i | \(-0.567649\pi\) | ||||
−0.210929 | + | 0.977501i | \(0.567649\pi\) | |||||||
\(978\) | 1.58023 | 0.0505303 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0.672972 | 0.0214973 | ||||||||
\(981\) | −8.88678 | −0.283733 | ||||||||
\(982\) | −0.0587731 | −0.00187553 | ||||||||
\(983\) | −4.07740 | −0.130049 | −0.0650244 | − | 0.997884i | \(-0.520713\pi\) | ||||
−0.0650244 | + | 0.997884i | \(0.520713\pi\) | |||||||
\(984\) | 11.3945 | 0.363242 | ||||||||
\(985\) | −11.2511 | −0.358489 | ||||||||
\(986\) | 7.69004 | 0.244901 | ||||||||
\(987\) | −10.2072 | −0.324898 | ||||||||
\(988\) | 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 | ||||||||
\(993\) | 29.6698 | 0.941544 | ||||||||
\(994\) | 24.7101 | 0.783757 | ||||||||
\(995\) | −6.98940 | −0.221579 | ||||||||
\(996\) | 4.00378 | 0.126865 | ||||||||
\(997\) | 22.9725 | 0.727548 | 0.363774 | − | 0.931487i | \(-0.381488\pi\) | ||||
0.363774 | + | 0.931487i | \(0.381488\pi\) | |||||||
\(998\) | −47.9057 | −1.51643 | ||||||||
\(999\) | 7.70693 | 0.243836 |
(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 | 2541.2.a.bn.1.4 | 4 | ||
3.2 | odd | 2 | 7623.2.a.ci.1.1 | 4 | |||
11.5 | even | 5 | 231.2.j.f.190.1 | yes | 8 | ||
11.9 | even | 5 | 231.2.j.f.169.1 | ✓ | 8 | ||
11.10 | odd | 2 | 2541.2.a.bm.1.1 | 4 | |||
33.5 | odd | 10 | 693.2.m.f.190.2 | 8 | |||
33.20 | odd | 10 | 693.2.m.f.631.2 | 8 | |||
33.32 | even | 2 | 7623.2.a.cl.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
231.2.j.f.169.1 | ✓ | 8 | 11.9 | even | 5 | ||
231.2.j.f.190.1 | yes | 8 | 11.5 | even | 5 | ||
693.2.m.f.190.2 | 8 | 33.5 | odd | 10 | |||
693.2.m.f.631.2 | 8 | 33.20 | odd | 10 | |||
2541.2.a.bm.1.1 | 4 | 11.10 | odd | 2 | |||
2541.2.a.bn.1.4 | 4 | 1.1 | even | 1 | trivial | ||
7623.2.a.ci.1.1 | 4 | 3.2 | odd | 2 | |||
7623.2.a.cl.1.4 | 4 | 33.32 | even | 2 |