Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [77,4,Mod(1,77)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(77, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("77.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 77 = 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 77.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: | \(4.54314707044\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.522072.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 12x^{2} + 5x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(3.79597\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 77.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.53253 | 0.541832 | 0.270916 | − | 0.962603i | \(-0.412673\pi\) | ||||
0.270916 | + | 0.962603i | \(0.412673\pi\) | |||||||
\(3\) | 10.1459 | 1.95259 | 0.976294 | − | 0.216448i | \(-0.0694472\pi\) | ||||
0.976294 | + | 0.216448i | \(0.0694472\pi\) | |||||||
\(4\) | −5.65135 | −0.706418 | ||||||||
\(5\) | 8.69995 | 0.778148 | 0.389074 | − | 0.921207i | \(-0.372795\pi\) | ||||
0.389074 | + | 0.921207i | \(0.372795\pi\) | |||||||
\(6\) | 15.5490 | 1.05797 | ||||||||
\(7\) | −7.00000 | −0.377964 | ||||||||
\(8\) | −20.9211 | −0.924592 | ||||||||
\(9\) | 75.9402 | 2.81260 | ||||||||
\(10\) | 13.3330 | 0.421625 | ||||||||
\(11\) | −11.0000 | −0.301511 | ||||||||
\(12\) | −57.3382 | −1.37934 | ||||||||
\(13\) | −76.3572 | −1.62905 | −0.814526 | − | 0.580127i | \(-0.803003\pi\) | ||||
−0.814526 | + | 0.580127i | \(0.803003\pi\) | |||||||
\(14\) | −10.7277 | −0.204793 | ||||||||
\(15\) | 88.2693 | 1.51940 | ||||||||
\(16\) | 13.1485 | 0.205445 | ||||||||
\(17\) | 39.7278 | 0.566789 | 0.283395 | − | 0.959003i | \(-0.408539\pi\) | ||||
0.283395 | + | 0.959003i | \(0.408539\pi\) | |||||||
\(18\) | 116.381 | 1.52396 | ||||||||
\(19\) | −27.9876 | −0.337937 | −0.168968 | − | 0.985621i | \(-0.554044\pi\) | ||||
−0.168968 | + | 0.985621i | \(0.554044\pi\) | |||||||
\(20\) | −49.1664 | −0.549698 | ||||||||
\(21\) | −71.0216 | −0.738009 | ||||||||
\(22\) | −16.8579 | −0.163368 | ||||||||
\(23\) | 87.2055 | 0.790592 | 0.395296 | − | 0.918554i | \(-0.370642\pi\) | ||||
0.395296 | + | 0.918554i | \(0.370642\pi\) | |||||||
\(24\) | −212.265 | −1.80535 | ||||||||
\(25\) | −49.3108 | −0.394486 | ||||||||
\(26\) | −117.020 | −0.882673 | ||||||||
\(27\) | 496.545 | 3.53926 | ||||||||
\(28\) | 39.5594 | 0.267001 | ||||||||
\(29\) | −38.3019 | −0.245258 | −0.122629 | − | 0.992453i | \(-0.539133\pi\) | ||||
−0.122629 | + | 0.992453i | \(0.539133\pi\) | |||||||
\(30\) | 135.275 | 0.823260 | ||||||||
\(31\) | −186.071 | −1.07804 | −0.539021 | − | 0.842292i | \(-0.681206\pi\) | ||||
−0.539021 | + | 0.842292i | \(0.681206\pi\) | |||||||
\(32\) | 187.519 | 1.03591 | ||||||||
\(33\) | −111.605 | −0.588728 | ||||||||
\(34\) | 60.8842 | 0.307105 | ||||||||
\(35\) | −60.8997 | −0.294112 | ||||||||
\(36\) | −429.164 | −1.98687 | ||||||||
\(37\) | −218.781 | −0.972090 | −0.486045 | − | 0.873934i | \(-0.661561\pi\) | ||||
−0.486045 | + | 0.873934i | \(0.661561\pi\) | |||||||
\(38\) | −42.8919 | −0.183105 | ||||||||
\(39\) | −774.716 | −3.18087 | ||||||||
\(40\) | −182.013 | −0.719469 | ||||||||
\(41\) | 80.1687 | 0.305372 | 0.152686 | − | 0.988275i | \(-0.451208\pi\) | ||||
0.152686 | + | 0.988275i | \(0.451208\pi\) | |||||||
\(42\) | −108.843 | −0.399877 | ||||||||
\(43\) | −35.1155 | −0.124536 | −0.0622681 | − | 0.998059i | \(-0.519833\pi\) | ||||
−0.0622681 | + | 0.998059i | \(0.519833\pi\) | |||||||
\(44\) | 62.1648 | 0.212993 | ||||||||
\(45\) | 660.676 | 2.18862 | ||||||||
\(46\) | 133.645 | 0.428368 | ||||||||
\(47\) | −282.620 | −0.877116 | −0.438558 | − | 0.898703i | \(-0.644511\pi\) | ||||
−0.438558 | + | 0.898703i | \(0.644511\pi\) | |||||||
\(48\) | 133.404 | 0.401149 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | −75.5704 | −0.213745 | ||||||||
\(51\) | 403.077 | 1.10671 | ||||||||
\(52\) | 431.521 | 1.15079 | ||||||||
\(53\) | 145.296 | 0.376566 | 0.188283 | − | 0.982115i | \(-0.439708\pi\) | ||||
0.188283 | + | 0.982115i | \(0.439708\pi\) | |||||||
\(54\) | 760.971 | 1.91769 | ||||||||
\(55\) | −95.6995 | −0.234620 | ||||||||
\(56\) | 146.448 | 0.349463 | ||||||||
\(57\) | −283.961 | −0.659851 | ||||||||
\(58\) | −58.6989 | −0.132889 | ||||||||
\(59\) | 91.0461 | 0.200901 | 0.100451 | − | 0.994942i | \(-0.467972\pi\) | ||||
0.100451 | + | 0.994942i | \(0.467972\pi\) | |||||||
\(60\) | −498.840 | −1.07333 | ||||||||
\(61\) | 808.142 | 1.69626 | 0.848131 | − | 0.529787i | \(-0.177728\pi\) | ||||
0.848131 | + | 0.529787i | \(0.177728\pi\) | |||||||
\(62\) | −285.160 | −0.584118 | ||||||||
\(63\) | −531.582 | −1.06306 | ||||||||
\(64\) | 182.192 | 0.355843 | ||||||||
\(65\) | −664.304 | −1.26764 | ||||||||
\(66\) | −171.039 | −0.318991 | ||||||||
\(67\) | 794.222 | 1.44820 | 0.724102 | − | 0.689693i | \(-0.242255\pi\) | ||||
0.724102 | + | 0.689693i | \(0.242255\pi\) | |||||||
\(68\) | −224.516 | −0.400390 | ||||||||
\(69\) | 884.783 | 1.54370 | ||||||||
\(70\) | −93.3307 | −0.159359 | ||||||||
\(71\) | 946.901 | 1.58277 | 0.791384 | − | 0.611319i | \(-0.209361\pi\) | ||||
0.791384 | + | 0.611319i | \(0.209361\pi\) | |||||||
\(72\) | −1588.75 | −2.60051 | ||||||||
\(73\) | 801.324 | 1.28477 | 0.642383 | − | 0.766384i | \(-0.277946\pi\) | ||||
0.642383 | + | 0.766384i | \(0.277946\pi\) | |||||||
\(74\) | −335.288 | −0.526709 | ||||||||
\(75\) | −500.305 | −0.770270 | ||||||||
\(76\) | 158.168 | 0.238725 | ||||||||
\(77\) | 77.0000 | 0.113961 | ||||||||
\(78\) | −1187.28 | −1.72350 | ||||||||
\(79\) | −890.737 | −1.26855 | −0.634277 | − | 0.773106i | \(-0.718702\pi\) | ||||
−0.634277 | + | 0.773106i | \(0.718702\pi\) | |||||||
\(80\) | 114.391 | 0.159866 | ||||||||
\(81\) | 2987.53 | 4.09812 | ||||||||
\(82\) | 122.861 | 0.165460 | ||||||||
\(83\) | −559.333 | −0.739696 | −0.369848 | − | 0.929092i | \(-0.620590\pi\) | ||||
−0.369848 | + | 0.929092i | \(0.620590\pi\) | |||||||
\(84\) | 401.368 | 0.521343 | ||||||||
\(85\) | 345.630 | 0.441046 | ||||||||
\(86\) | −53.8156 | −0.0674777 | ||||||||
\(87\) | −388.609 | −0.478888 | ||||||||
\(88\) | 230.132 | 0.278775 | ||||||||
\(89\) | −1523.75 | −1.81480 | −0.907401 | − | 0.420265i | \(-0.861937\pi\) | ||||
−0.907401 | + | 0.420265i | \(0.861937\pi\) | |||||||
\(90\) | 1012.51 | 1.18586 | ||||||||
\(91\) | 534.501 | 0.615724 | ||||||||
\(92\) | −492.829 | −0.558488 | ||||||||
\(93\) | −1887.87 | −2.10497 | ||||||||
\(94\) | −433.125 | −0.475249 | ||||||||
\(95\) | −243.491 | −0.262965 | ||||||||
\(96\) | 1902.56 | 2.02270 | ||||||||
\(97\) | 664.651 | 0.695723 | 0.347861 | − | 0.937546i | \(-0.386908\pi\) | ||||
0.347861 | + | 0.937546i | \(0.386908\pi\) | |||||||
\(98\) | 75.0941 | 0.0774046 | ||||||||
\(99\) | −835.342 | −0.848031 | ||||||||
\(100\) | 278.672 | 0.278672 | ||||||||
\(101\) | 1495.68 | 1.47352 | 0.736761 | − | 0.676153i | \(-0.236354\pi\) | ||||
0.736761 | + | 0.676153i | \(0.236354\pi\) | |||||||
\(102\) | 617.728 | 0.599649 | ||||||||
\(103\) | 874.379 | 0.836457 | 0.418229 | − | 0.908342i | \(-0.362651\pi\) | ||||
0.418229 | + | 0.908342i | \(0.362651\pi\) | |||||||
\(104\) | 1597.48 | 1.50621 | ||||||||
\(105\) | −617.885 | −0.574280 | ||||||||
\(106\) | 222.671 | 0.204035 | ||||||||
\(107\) | 783.854 | 0.708205 | 0.354103 | − | 0.935207i | \(-0.384786\pi\) | ||||
0.354103 | + | 0.935207i | \(0.384786\pi\) | |||||||
\(108\) | −2806.15 | −2.50020 | ||||||||
\(109\) | −1351.08 | −1.18725 | −0.593623 | − | 0.804743i | \(-0.702303\pi\) | ||||
−0.593623 | + | 0.804743i | \(0.702303\pi\) | |||||||
\(110\) | −146.663 | −0.127125 | ||||||||
\(111\) | −2219.74 | −1.89809 | ||||||||
\(112\) | −92.0393 | −0.0776508 | ||||||||
\(113\) | −188.362 | −0.156811 | −0.0784055 | − | 0.996922i | \(-0.524983\pi\) | ||||
−0.0784055 | + | 0.996922i | \(0.524983\pi\) | |||||||
\(114\) | −435.179 | −0.357529 | ||||||||
\(115\) | 758.684 | 0.615197 | ||||||||
\(116\) | 216.457 | 0.173255 | ||||||||
\(117\) | −5798.58 | −4.58187 | ||||||||
\(118\) | 139.531 | 0.108855 | ||||||||
\(119\) | −278.095 | −0.214226 | ||||||||
\(120\) | −1846.69 | −1.40483 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | 1238.50 | 0.919089 | ||||||||
\(123\) | 813.388 | 0.596266 | ||||||||
\(124\) | 1051.55 | 0.761549 | ||||||||
\(125\) | −1516.50 | −1.08512 | ||||||||
\(126\) | −814.666 | −0.576002 | ||||||||
\(127\) | 586.957 | 0.410110 | 0.205055 | − | 0.978750i | \(-0.434263\pi\) | ||||
0.205055 | + | 0.978750i | \(0.434263\pi\) | |||||||
\(128\) | −1220.94 | −0.843101 | ||||||||
\(129\) | −356.280 | −0.243168 | ||||||||
\(130\) | −1018.07 | −0.686850 | ||||||||
\(131\) | 623.054 | 0.415546 | 0.207773 | − | 0.978177i | \(-0.433379\pi\) | ||||
0.207773 | + | 0.978177i | \(0.433379\pi\) | |||||||
\(132\) | 630.721 | 0.415888 | ||||||||
\(133\) | 195.913 | 0.127728 | ||||||||
\(134\) | 1217.17 | 0.784683 | ||||||||
\(135\) | 4319.92 | 2.75407 | ||||||||
\(136\) | −831.151 | −0.524049 | ||||||||
\(137\) | −954.859 | −0.595468 | −0.297734 | − | 0.954649i | \(-0.596231\pi\) | ||||
−0.297734 | + | 0.954649i | \(0.596231\pi\) | |||||||
\(138\) | 1355.96 | 0.836426 | ||||||||
\(139\) | 1590.62 | 0.970610 | 0.485305 | − | 0.874345i | \(-0.338709\pi\) | ||||
0.485305 | + | 0.874345i | \(0.338709\pi\) | |||||||
\(140\) | 344.165 | 0.207766 | ||||||||
\(141\) | −2867.45 | −1.71265 | ||||||||
\(142\) | 1451.16 | 0.857594 | ||||||||
\(143\) | 839.929 | 0.491178 | ||||||||
\(144\) | 998.498 | 0.577834 | ||||||||
\(145\) | −333.225 | −0.190847 | ||||||||
\(146\) | 1228.05 | 0.696127 | ||||||||
\(147\) | 497.151 | 0.278941 | ||||||||
\(148\) | 1236.41 | 0.686702 | ||||||||
\(149\) | −1415.84 | −0.778459 | −0.389229 | − | 0.921141i | \(-0.627259\pi\) | ||||
−0.389229 | + | 0.921141i | \(0.627259\pi\) | |||||||
\(150\) | −766.733 | −0.417357 | ||||||||
\(151\) | 411.564 | 0.221806 | 0.110903 | − | 0.993831i | \(-0.464626\pi\) | ||||
0.110903 | + | 0.993831i | \(0.464626\pi\) | |||||||
\(152\) | 585.532 | 0.312454 | ||||||||
\(153\) | 3016.94 | 1.59415 | ||||||||
\(154\) | 118.005 | 0.0617475 | ||||||||
\(155\) | −1618.81 | −0.838876 | ||||||||
\(156\) | 4378.19 | 2.24702 | ||||||||
\(157\) | −1417.29 | −0.720460 | −0.360230 | − | 0.932864i | \(-0.617302\pi\) | ||||
−0.360230 | + | 0.932864i | \(0.617302\pi\) | |||||||
\(158\) | −1365.08 | −0.687343 | ||||||||
\(159\) | 1474.17 | 0.735278 | ||||||||
\(160\) | 1631.41 | 0.806090 | ||||||||
\(161\) | −610.439 | −0.298816 | ||||||||
\(162\) | 4578.49 | 2.22049 | ||||||||
\(163\) | −441.401 | −0.212105 | −0.106053 | − | 0.994361i | \(-0.533821\pi\) | ||||
−0.106053 | + | 0.994361i | \(0.533821\pi\) | |||||||
\(164\) | −453.061 | −0.215720 | ||||||||
\(165\) | −970.962 | −0.458117 | ||||||||
\(166\) | −857.196 | −0.400791 | ||||||||
\(167\) | −1486.39 | −0.688742 | −0.344371 | − | 0.938834i | \(-0.611908\pi\) | ||||
−0.344371 | + | 0.938834i | \(0.611908\pi\) | |||||||
\(168\) | 1485.85 | 0.682357 | ||||||||
\(169\) | 3633.43 | 1.65381 | ||||||||
\(170\) | 529.690 | 0.238973 | ||||||||
\(171\) | −2125.39 | −0.950481 | ||||||||
\(172\) | 198.450 | 0.0879747 | ||||||||
\(173\) | −2957.39 | −1.29969 | −0.649844 | − | 0.760068i | \(-0.725166\pi\) | ||||
−0.649844 | + | 0.760068i | \(0.725166\pi\) | |||||||
\(174\) | −595.555 | −0.259477 | ||||||||
\(175\) | 345.176 | 0.149102 | ||||||||
\(176\) | −144.633 | −0.0619439 | ||||||||
\(177\) | 923.748 | 0.392278 | ||||||||
\(178\) | −2335.20 | −0.983318 | ||||||||
\(179\) | −24.4424 | −0.0102062 | −0.00510310 | − | 0.999987i | \(-0.501624\pi\) | ||||
−0.00510310 | + | 0.999987i | \(0.501624\pi\) | |||||||
\(180\) | −3733.71 | −1.54608 | ||||||||
\(181\) | −120.126 | −0.0493308 | −0.0246654 | − | 0.999696i | \(-0.507852\pi\) | ||||
−0.0246654 | + | 0.999696i | \(0.507852\pi\) | |||||||
\(182\) | 819.139 | 0.333619 | ||||||||
\(183\) | 8199.37 | 3.31210 | ||||||||
\(184\) | −1824.44 | −0.730975 | ||||||||
\(185\) | −1903.38 | −0.756429 | ||||||||
\(186\) | −2893.22 | −1.14054 | ||||||||
\(187\) | −437.006 | −0.170893 | ||||||||
\(188\) | 1597.19 | 0.619610 | ||||||||
\(189\) | −3475.81 | −1.33772 | ||||||||
\(190\) | −373.158 | −0.142483 | ||||||||
\(191\) | −2059.27 | −0.780123 | −0.390061 | − | 0.920789i | \(-0.627546\pi\) | ||||
−0.390061 | + | 0.920789i | \(0.627546\pi\) | |||||||
\(192\) | 1848.51 | 0.694816 | ||||||||
\(193\) | −4371.31 | −1.63033 | −0.815165 | − | 0.579229i | \(-0.803354\pi\) | ||||
−0.815165 | + | 0.579229i | \(0.803354\pi\) | |||||||
\(194\) | 1018.60 | 0.376965 | ||||||||
\(195\) | −6740.00 | −2.47519 | ||||||||
\(196\) | −276.916 | −0.100917 | ||||||||
\(197\) | −2185.70 | −0.790479 | −0.395240 | − | 0.918578i | \(-0.629338\pi\) | ||||
−0.395240 | + | 0.918578i | \(0.629338\pi\) | |||||||
\(198\) | −1280.19 | −0.459490 | ||||||||
\(199\) | −2420.84 | −0.862356 | −0.431178 | − | 0.902267i | \(-0.641902\pi\) | ||||
−0.431178 | + | 0.902267i | \(0.641902\pi\) | |||||||
\(200\) | 1031.64 | 0.364739 | ||||||||
\(201\) | 8058.13 | 2.82774 | ||||||||
\(202\) | 2292.18 | 0.798401 | ||||||||
\(203\) | 268.113 | 0.0926988 | ||||||||
\(204\) | −2277.93 | −0.781797 | ||||||||
\(205\) | 697.464 | 0.237624 | ||||||||
\(206\) | 1340.01 | 0.453219 | ||||||||
\(207\) | 6622.41 | 2.22362 | ||||||||
\(208\) | −1003.98 | −0.334680 | ||||||||
\(209\) | 307.864 | 0.101892 | ||||||||
\(210\) | −946.928 | −0.311163 | ||||||||
\(211\) | −3888.39 | −1.26866 | −0.634331 | − | 0.773062i | \(-0.718724\pi\) | ||||
−0.634331 | + | 0.773062i | \(0.718724\pi\) | |||||||
\(212\) | −821.120 | −0.266013 | ||||||||
\(213\) | 9607.21 | 3.09049 | ||||||||
\(214\) | 1201.28 | 0.383728 | ||||||||
\(215\) | −305.503 | −0.0969076 | ||||||||
\(216\) | −10388.3 | −3.27237 | ||||||||
\(217\) | 1302.50 | 0.407462 | ||||||||
\(218\) | −2070.57 | −0.643288 | ||||||||
\(219\) | 8130.19 | 2.50862 | ||||||||
\(220\) | 540.831 | 0.165740 | ||||||||
\(221\) | −3033.51 | −0.923330 | ||||||||
\(222\) | −3401.82 | −1.02845 | ||||||||
\(223\) | 641.467 | 0.192627 | 0.0963135 | − | 0.995351i | \(-0.469295\pi\) | ||||
0.0963135 | + | 0.995351i | \(0.469295\pi\) | |||||||
\(224\) | −1312.64 | −0.391537 | ||||||||
\(225\) | −3744.67 | −1.10953 | ||||||||
\(226\) | −288.672 | −0.0849652 | ||||||||
\(227\) | 3619.11 | 1.05819 | 0.529094 | − | 0.848563i | \(-0.322532\pi\) | ||||
0.529094 | + | 0.848563i | \(0.322532\pi\) | |||||||
\(228\) | 1604.76 | 0.466131 | ||||||||
\(229\) | 2518.14 | 0.726652 | 0.363326 | − | 0.931662i | \(-0.381641\pi\) | ||||
0.363326 | + | 0.931662i | \(0.381641\pi\) | |||||||
\(230\) | 1162.71 | 0.333333 | ||||||||
\(231\) | 781.238 | 0.222518 | ||||||||
\(232\) | 801.318 | 0.226763 | ||||||||
\(233\) | −4187.89 | −1.17750 | −0.588751 | − | 0.808315i | \(-0.700380\pi\) | ||||
−0.588751 | + | 0.808315i | \(0.700380\pi\) | |||||||
\(234\) | −8886.52 | −2.48261 | ||||||||
\(235\) | −2458.79 | −0.682525 | ||||||||
\(236\) | −514.533 | −0.141920 | ||||||||
\(237\) | −9037.37 | −2.47696 | ||||||||
\(238\) | −426.189 | −0.116075 | ||||||||
\(239\) | 2582.63 | 0.698981 | 0.349490 | − | 0.936940i | \(-0.386355\pi\) | ||||
0.349490 | + | 0.936940i | \(0.386355\pi\) | |||||||
\(240\) | 1160.61 | 0.312153 | ||||||||
\(241\) | 1522.09 | 0.406832 | 0.203416 | − | 0.979092i | \(-0.434796\pi\) | ||||
0.203416 | + | 0.979092i | \(0.434796\pi\) | |||||||
\(242\) | 185.436 | 0.0492574 | ||||||||
\(243\) | 16904.6 | 4.46268 | ||||||||
\(244\) | −4567.09 | −1.19827 | ||||||||
\(245\) | 426.298 | 0.111164 | ||||||||
\(246\) | 1246.54 | 0.323076 | ||||||||
\(247\) | 2137.06 | 0.550517 | ||||||||
\(248\) | 3892.81 | 0.996750 | ||||||||
\(249\) | −5674.96 | −1.44432 | ||||||||
\(250\) | −2324.08 | −0.587951 | ||||||||
\(251\) | 1463.19 | 0.367952 | 0.183976 | − | 0.982931i | \(-0.441103\pi\) | ||||
0.183976 | + | 0.982931i | \(0.441103\pi\) | |||||||
\(252\) | 3004.15 | 0.750967 | ||||||||
\(253\) | −959.261 | −0.238372 | ||||||||
\(254\) | 899.531 | 0.222211 | ||||||||
\(255\) | 3506.75 | 0.861181 | ||||||||
\(256\) | −3328.67 | −0.812662 | ||||||||
\(257\) | −1183.89 | −0.287350 | −0.143675 | − | 0.989625i | \(-0.545892\pi\) | ||||
−0.143675 | + | 0.989625i | \(0.545892\pi\) | |||||||
\(258\) | −546.010 | −0.131756 | ||||||||
\(259\) | 1531.46 | 0.367415 | ||||||||
\(260\) | 3754.21 | 0.895486 | ||||||||
\(261\) | −2908.65 | −0.689813 | ||||||||
\(262\) | 954.850 | 0.225156 | ||||||||
\(263\) | 151.973 | 0.0356315 | 0.0178158 | − | 0.999841i | \(-0.494329\pi\) | ||||
0.0178158 | + | 0.999841i | \(0.494329\pi\) | |||||||
\(264\) | 2334.91 | 0.544333 | ||||||||
\(265\) | 1264.07 | 0.293024 | ||||||||
\(266\) | 300.243 | 0.0692072 | ||||||||
\(267\) | −15459.9 | −3.54356 | ||||||||
\(268\) | −4488.42 | −1.02304 | ||||||||
\(269\) | −255.543 | −0.0579209 | −0.0289604 | − | 0.999581i | \(-0.509220\pi\) | ||||
−0.0289604 | + | 0.999581i | \(0.509220\pi\) | |||||||
\(270\) | 6620.41 | 1.49224 | ||||||||
\(271\) | 2589.73 | 0.580497 | 0.290248 | − | 0.956951i | \(-0.406262\pi\) | ||||
0.290248 | + | 0.956951i | \(0.406262\pi\) | |||||||
\(272\) | 522.360 | 0.116444 | ||||||||
\(273\) | 5423.01 | 1.20226 | ||||||||
\(274\) | −1463.35 | −0.322644 | ||||||||
\(275\) | 542.419 | 0.118942 | ||||||||
\(276\) | −5000.21 | −1.09050 | ||||||||
\(277\) | −4441.49 | −0.963404 | −0.481702 | − | 0.876335i | \(-0.659981\pi\) | ||||
−0.481702 | + | 0.876335i | \(0.659981\pi\) | |||||||
\(278\) | 2437.68 | 0.525907 | ||||||||
\(279\) | −14130.3 | −3.03210 | ||||||||
\(280\) | 1274.09 | 0.271934 | ||||||||
\(281\) | 1577.34 | 0.334861 | 0.167431 | − | 0.985884i | \(-0.446453\pi\) | ||||
0.167431 | + | 0.985884i | \(0.446453\pi\) | |||||||
\(282\) | −4394.46 | −0.927966 | ||||||||
\(283\) | 3429.29 | 0.720317 | 0.360159 | − | 0.932891i | \(-0.382723\pi\) | ||||
0.360159 | + | 0.932891i | \(0.382723\pi\) | |||||||
\(284\) | −5351.27 | −1.11810 | ||||||||
\(285\) | −2470.45 | −0.513462 | ||||||||
\(286\) | 1287.22 | 0.266136 | ||||||||
\(287\) | −561.181 | −0.115420 | ||||||||
\(288\) | 14240.3 | 2.91360 | ||||||||
\(289\) | −3334.70 | −0.678750 | ||||||||
\(290\) | −510.677 | −0.103407 | ||||||||
\(291\) | 6743.51 | 1.35846 | ||||||||
\(292\) | −4528.56 | −0.907581 | ||||||||
\(293\) | 4601.37 | 0.917458 | 0.458729 | − | 0.888576i | \(-0.348305\pi\) | ||||
0.458729 | + | 0.888576i | \(0.348305\pi\) | |||||||
\(294\) | 761.900 | 0.151139 | ||||||||
\(295\) | 792.096 | 0.156331 | ||||||||
\(296\) | 4577.14 | 0.898786 | ||||||||
\(297\) | −5461.99 | −1.06713 | ||||||||
\(298\) | −2169.82 | −0.421794 | ||||||||
\(299\) | −6658.77 | −1.28792 | ||||||||
\(300\) | 2827.40 | 0.544132 | ||||||||
\(301\) | 245.808 | 0.0470703 | ||||||||
\(302\) | 630.736 | 0.120181 | ||||||||
\(303\) | 15175.1 | 2.87718 | ||||||||
\(304\) | −367.994 | −0.0694274 | ||||||||
\(305\) | 7030.80 | 1.31994 | ||||||||
\(306\) | 4623.56 | 0.863762 | ||||||||
\(307\) | 4990.18 | 0.927702 | 0.463851 | − | 0.885913i | \(-0.346467\pi\) | ||||
0.463851 | + | 0.885913i | \(0.346467\pi\) | |||||||
\(308\) | −435.154 | −0.0805038 | ||||||||
\(309\) | 8871.40 | 1.63326 | ||||||||
\(310\) | −2480.88 | −0.454530 | ||||||||
\(311\) | 3139.78 | 0.572478 | 0.286239 | − | 0.958158i | \(-0.407595\pi\) | ||||
0.286239 | + | 0.958158i | \(0.407595\pi\) | |||||||
\(312\) | 16207.9 | 2.94101 | ||||||||
\(313\) | −4723.12 | −0.852929 | −0.426464 | − | 0.904504i | \(-0.640241\pi\) | ||||
−0.426464 | + | 0.904504i | \(0.640241\pi\) | |||||||
\(314\) | −2172.04 | −0.390368 | ||||||||
\(315\) | −4624.74 | −0.827220 | ||||||||
\(316\) | 5033.86 | 0.896130 | ||||||||
\(317\) | 5935.83 | 1.05170 | 0.525851 | − | 0.850577i | \(-0.323747\pi\) | ||||
0.525851 | + | 0.850577i | \(0.323747\pi\) | |||||||
\(318\) | 2259.21 | 0.398397 | ||||||||
\(319\) | 421.321 | 0.0739481 | ||||||||
\(320\) | 1585.06 | 0.276899 | ||||||||
\(321\) | 7952.94 | 1.38283 | ||||||||
\(322\) | −935.517 | −0.161908 | ||||||||
\(323\) | −1111.89 | −0.191539 | ||||||||
\(324\) | −16883.6 | −2.89499 | ||||||||
\(325\) | 3765.24 | 0.642639 | ||||||||
\(326\) | −676.461 | −0.114925 | ||||||||
\(327\) | −13708.0 | −2.31820 | ||||||||
\(328\) | −1677.22 | −0.282344 | ||||||||
\(329\) | 1978.34 | 0.331519 | ||||||||
\(330\) | −1488.03 | −0.248222 | ||||||||
\(331\) | −6390.75 | −1.06123 | −0.530615 | − | 0.847613i | \(-0.678039\pi\) | ||||
−0.530615 | + | 0.847613i | \(0.678039\pi\) | |||||||
\(332\) | 3160.98 | 0.522535 | ||||||||
\(333\) | −16614.3 | −2.73410 | ||||||||
\(334\) | −2277.93 | −0.373183 | ||||||||
\(335\) | 6909.69 | 1.12692 | ||||||||
\(336\) | −933.826 | −0.151620 | ||||||||
\(337\) | 8916.41 | 1.44127 | 0.720635 | − | 0.693315i | \(-0.243851\pi\) | ||||
0.720635 | + | 0.693315i | \(0.243851\pi\) | |||||||
\(338\) | 5568.34 | 0.896088 | ||||||||
\(339\) | −1911.12 | −0.306187 | ||||||||
\(340\) | −1953.28 | −0.311563 | ||||||||
\(341\) | 2046.78 | 0.325042 | ||||||||
\(342\) | −3257.22 | −0.515001 | ||||||||
\(343\) | −343.000 | −0.0539949 | ||||||||
\(344\) | 734.655 | 0.115145 | ||||||||
\(345\) | 7697.57 | 1.20123 | ||||||||
\(346\) | −4532.29 | −0.704212 | ||||||||
\(347\) | 1400.52 | 0.216668 | 0.108334 | − | 0.994115i | \(-0.465448\pi\) | ||||
0.108334 | + | 0.994115i | \(0.465448\pi\) | |||||||
\(348\) | 2196.16 | 0.338295 | ||||||||
\(349\) | −8985.39 | −1.37816 | −0.689079 | − | 0.724686i | \(-0.741985\pi\) | ||||
−0.689079 | + | 0.724686i | \(0.741985\pi\) | |||||||
\(350\) | 528.993 | 0.0807881 | ||||||||
\(351\) | −37914.8 | −5.76565 | ||||||||
\(352\) | −2062.71 | −0.312338 | ||||||||
\(353\) | 1767.91 | 0.266562 | 0.133281 | − | 0.991078i | \(-0.457449\pi\) | ||||
0.133281 | + | 0.991078i | \(0.457449\pi\) | |||||||
\(354\) | 1415.67 | 0.212549 | ||||||||
\(355\) | 8238.00 | 1.23163 | ||||||||
\(356\) | 8611.25 | 1.28201 | ||||||||
\(357\) | −2821.54 | −0.418296 | ||||||||
\(358\) | −37.4587 | −0.00553004 | ||||||||
\(359\) | −1110.48 | −0.163256 | −0.0816278 | − | 0.996663i | \(-0.526012\pi\) | ||||
−0.0816278 | + | 0.996663i | \(0.526012\pi\) | |||||||
\(360\) | −13822.1 | −2.02358 | ||||||||
\(361\) | −6075.69 | −0.885799 | ||||||||
\(362\) | −184.096 | −0.0267290 | ||||||||
\(363\) | 1227.66 | 0.177508 | ||||||||
\(364\) | −3020.65 | −0.434959 | ||||||||
\(365\) | 6971.48 | 0.999737 | ||||||||
\(366\) | 12565.8 | 1.79460 | ||||||||
\(367\) | −5342.61 | −0.759896 | −0.379948 | − | 0.925008i | \(-0.624058\pi\) | ||||
−0.379948 | + | 0.925008i | \(0.624058\pi\) | |||||||
\(368\) | 1146.62 | 0.162423 | ||||||||
\(369\) | 6088.03 | 0.858890 | ||||||||
\(370\) | −2916.99 | −0.409858 | ||||||||
\(371\) | −1017.07 | −0.142329 | ||||||||
\(372\) | 10669.0 | 1.48699 | ||||||||
\(373\) | 6829.95 | 0.948101 | 0.474050 | − | 0.880498i | \(-0.342791\pi\) | ||||
0.474050 | + | 0.880498i | \(0.342791\pi\) | |||||||
\(374\) | −669.726 | −0.0925955 | ||||||||
\(375\) | −15386.3 | −2.11879 | ||||||||
\(376\) | 5912.74 | 0.810974 | ||||||||
\(377\) | 2924.63 | 0.399538 | ||||||||
\(378\) | −5326.80 | −0.724817 | ||||||||
\(379\) | 7826.62 | 1.06076 | 0.530378 | − | 0.847761i | \(-0.322050\pi\) | ||||
0.530378 | + | 0.847761i | \(0.322050\pi\) | |||||||
\(380\) | 1376.05 | 0.185763 | ||||||||
\(381\) | 5955.24 | 0.800777 | ||||||||
\(382\) | −3155.90 | −0.422695 | ||||||||
\(383\) | −7534.69 | −1.00523 | −0.502617 | − | 0.864509i | \(-0.667629\pi\) | ||||
−0.502617 | + | 0.864509i | \(0.667629\pi\) | |||||||
\(384\) | −12387.6 | −1.64623 | ||||||||
\(385\) | 669.896 | 0.0886781 | ||||||||
\(386\) | −6699.17 | −0.883364 | ||||||||
\(387\) | −2666.68 | −0.350271 | ||||||||
\(388\) | −3756.17 | −0.491471 | ||||||||
\(389\) | −13071.8 | −1.70376 | −0.851882 | − | 0.523734i | \(-0.824539\pi\) | ||||
−0.851882 | + | 0.523734i | \(0.824539\pi\) | |||||||
\(390\) | −10329.3 | −1.34113 | ||||||||
\(391\) | 3464.49 | 0.448099 | ||||||||
\(392\) | −1025.14 | −0.132085 | ||||||||
\(393\) | 6321.47 | 0.811390 | ||||||||
\(394\) | −3349.65 | −0.428307 | ||||||||
\(395\) | −7749.37 | −0.987122 | ||||||||
\(396\) | 4720.81 | 0.599065 | ||||||||
\(397\) | −3692.51 | −0.466806 | −0.233403 | − | 0.972380i | \(-0.574986\pi\) | ||||
−0.233403 | + | 0.972380i | \(0.574986\pi\) | |||||||
\(398\) | −3710.02 | −0.467252 | ||||||||
\(399\) | 1987.73 | 0.249400 | ||||||||
\(400\) | −648.362 | −0.0810452 | ||||||||
\(401\) | 8223.85 | 1.02414 | 0.512069 | − | 0.858944i | \(-0.328879\pi\) | ||||
0.512069 | + | 0.858944i | \(0.328879\pi\) | |||||||
\(402\) | 12349.3 | 1.53216 | ||||||||
\(403\) | 14207.9 | 1.75619 | ||||||||
\(404\) | −8452.61 | −1.04092 | ||||||||
\(405\) | 25991.4 | 3.18894 | ||||||||
\(406\) | 410.892 | 0.0502272 | ||||||||
\(407\) | 2406.59 | 0.293096 | ||||||||
\(408\) | −8432.82 | −1.02325 | ||||||||
\(409\) | 3689.61 | 0.446062 | 0.223031 | − | 0.974811i | \(-0.428405\pi\) | ||||
0.223031 | + | 0.974811i | \(0.428405\pi\) | |||||||
\(410\) | 1068.89 | 0.128753 | ||||||||
\(411\) | −9687.95 | −1.16270 | ||||||||
\(412\) | −4941.42 | −0.590889 | ||||||||
\(413\) | −637.322 | −0.0759336 | ||||||||
\(414\) | 10149.1 | 1.20483 | ||||||||
\(415\) | −4866.17 | −0.575593 | ||||||||
\(416\) | −14318.5 | −1.68755 | ||||||||
\(417\) | 16138.4 | 1.89520 | ||||||||
\(418\) | 471.811 | 0.0552082 | ||||||||
\(419\) | 15657.0 | 1.82552 | 0.912762 | − | 0.408492i | \(-0.133945\pi\) | ||||
0.912762 | + | 0.408492i | \(0.133945\pi\) | |||||||
\(420\) | 3491.88 | 0.405682 | ||||||||
\(421\) | −6007.30 | −0.695435 | −0.347717 | − | 0.937599i | \(-0.613043\pi\) | ||||
−0.347717 | + | 0.937599i | \(0.613043\pi\) | |||||||
\(422\) | −5959.08 | −0.687402 | ||||||||
\(423\) | −21462.3 | −2.46698 | ||||||||
\(424\) | −3039.76 | −0.348170 | ||||||||
\(425\) | −1959.01 | −0.223591 | ||||||||
\(426\) | 14723.4 | 1.67453 | ||||||||
\(427\) | −5656.99 | −0.641127 | ||||||||
\(428\) | −4429.83 | −0.500289 | ||||||||
\(429\) | 8521.88 | 0.959068 | ||||||||
\(430\) | −468.193 | −0.0525076 | ||||||||
\(431\) | 13139.0 | 1.46841 | 0.734203 | − | 0.678931i | \(-0.237556\pi\) | ||||
0.734203 | + | 0.678931i | \(0.237556\pi\) | |||||||
\(432\) | 6528.81 | 0.727123 | ||||||||
\(433\) | −4392.47 | −0.487502 | −0.243751 | − | 0.969838i | \(-0.578378\pi\) | ||||
−0.243751 | + | 0.969838i | \(0.578378\pi\) | |||||||
\(434\) | 1996.12 | 0.220776 | ||||||||
\(435\) | −3380.88 | −0.372645 | ||||||||
\(436\) | 7635.41 | 0.838692 | ||||||||
\(437\) | −2440.67 | −0.267170 | ||||||||
\(438\) | 12459.8 | 1.35925 | ||||||||
\(439\) | 12676.2 | 1.37813 | 0.689066 | − | 0.724699i | \(-0.258021\pi\) | ||||
0.689066 | + | 0.724699i | \(0.258021\pi\) | |||||||
\(440\) | 2002.14 | 0.216928 | ||||||||
\(441\) | 3721.07 | 0.401800 | ||||||||
\(442\) | −4648.95 | −0.500289 | ||||||||
\(443\) | −17489.2 | −1.87571 | −0.937855 | − | 0.347028i | \(-0.887191\pi\) | ||||
−0.937855 | + | 0.347028i | \(0.887191\pi\) | |||||||
\(444\) | 12544.5 | 1.34085 | ||||||||
\(445\) | −13256.6 | −1.41218 | ||||||||
\(446\) | 983.069 | 0.104371 | ||||||||
\(447\) | −14365.1 | −1.52001 | ||||||||
\(448\) | −1275.34 | −0.134496 | ||||||||
\(449\) | −15491.8 | −1.62830 | −0.814148 | − | 0.580658i | \(-0.802796\pi\) | ||||
−0.814148 | + | 0.580658i | \(0.802796\pi\) | |||||||
\(450\) | −5738.83 | −0.601180 | ||||||||
\(451\) | −881.856 | −0.0920731 | ||||||||
\(452\) | 1064.50 | 0.110774 | ||||||||
\(453\) | 4175.71 | 0.433095 | ||||||||
\(454\) | 5546.40 | 0.573360 | ||||||||
\(455\) | 4650.13 | 0.479124 | ||||||||
\(456\) | 5940.78 | 0.610093 | ||||||||
\(457\) | −7789.99 | −0.797375 | −0.398688 | − | 0.917087i | \(-0.630534\pi\) | ||||
−0.398688 | + | 0.917087i | \(0.630534\pi\) | |||||||
\(458\) | 3859.13 | 0.393723 | ||||||||
\(459\) | 19726.7 | 2.00602 | ||||||||
\(460\) | −4287.59 | −0.434586 | ||||||||
\(461\) | −8497.44 | −0.858493 | −0.429247 | − | 0.903187i | \(-0.641221\pi\) | ||||
−0.429247 | + | 0.903187i | \(0.641221\pi\) | |||||||
\(462\) | 1197.27 | 0.120567 | ||||||||
\(463\) | 875.113 | 0.0878401 | 0.0439200 | − | 0.999035i | \(-0.486015\pi\) | ||||
0.0439200 | + | 0.999035i | \(0.486015\pi\) | |||||||
\(464\) | −503.611 | −0.0503870 | ||||||||
\(465\) | −16424.3 | −1.63798 | ||||||||
\(466\) | −6418.08 | −0.638008 | ||||||||
\(467\) | 17652.5 | 1.74917 | 0.874584 | − | 0.484874i | \(-0.161134\pi\) | ||||
0.874584 | + | 0.484874i | \(0.161134\pi\) | |||||||
\(468\) | 32769.8 | 3.23672 | ||||||||
\(469\) | −5559.55 | −0.547369 | ||||||||
\(470\) | −3768.17 | −0.369814 | ||||||||
\(471\) | −14379.8 | −1.40676 | ||||||||
\(472\) | −1904.79 | −0.185752 | ||||||||
\(473\) | 386.270 | 0.0375491 | ||||||||
\(474\) | −13850.1 | −1.34210 | ||||||||
\(475\) | 1380.09 | 0.133311 | ||||||||
\(476\) | 1571.61 | 0.151333 | ||||||||
\(477\) | 11033.8 | 1.05913 | ||||||||
\(478\) | 3957.96 | 0.378730 | ||||||||
\(479\) | 3129.76 | 0.298544 | 0.149272 | − | 0.988796i | \(-0.452307\pi\) | ||||
0.149272 | + | 0.988796i | \(0.452307\pi\) | |||||||
\(480\) | 16552.2 | 1.57396 | ||||||||
\(481\) | 16705.5 | 1.58359 | ||||||||
\(482\) | 2332.66 | 0.220435 | ||||||||
\(483\) | −6193.48 | −0.583464 | ||||||||
\(484\) | −683.813 | −0.0642198 | ||||||||
\(485\) | 5782.43 | 0.541375 | ||||||||
\(486\) | 25906.9 | 2.41802 | ||||||||
\(487\) | −366.055 | −0.0340606 | −0.0170303 | − | 0.999855i | \(-0.505421\pi\) | ||||
−0.0170303 | + | 0.999855i | \(0.505421\pi\) | |||||||
\(488\) | −16907.2 | −1.56835 | ||||||||
\(489\) | −4478.43 | −0.414154 | ||||||||
\(490\) | 653.315 | 0.0602322 | ||||||||
\(491\) | −14577.2 | −1.33984 | −0.669919 | − | 0.742434i | \(-0.733671\pi\) | ||||
−0.669919 | + | 0.742434i | \(0.733671\pi\) | |||||||
\(492\) | −4596.73 | −0.421213 | ||||||||
\(493\) | −1521.65 | −0.139010 | ||||||||
\(494\) | 3275.11 | 0.298288 | ||||||||
\(495\) | −7267.44 | −0.659893 | ||||||||
\(496\) | −2446.55 | −0.221478 | ||||||||
\(497\) | −6628.31 | −0.598230 | ||||||||
\(498\) | −8697.06 | −0.782580 | ||||||||
\(499\) | 9504.05 | 0.852624 | 0.426312 | − | 0.904576i | \(-0.359813\pi\) | ||||
0.426312 | + | 0.904576i | \(0.359813\pi\) | |||||||
\(500\) | 8570.24 | 0.766546 | ||||||||
\(501\) | −15080.8 | −1.34483 | ||||||||
\(502\) | 2242.39 | 0.199368 | ||||||||
\(503\) | −6149.90 | −0.545150 | −0.272575 | − | 0.962134i | \(-0.587875\pi\) | ||||
−0.272575 | + | 0.962134i | \(0.587875\pi\) | |||||||
\(504\) | 11121.3 | 0.982900 | ||||||||
\(505\) | 13012.3 | 1.14662 | ||||||||
\(506\) | −1470.10 | −0.129158 | ||||||||
\(507\) | 36864.5 | 3.22921 | ||||||||
\(508\) | −3317.10 | −0.289709 | ||||||||
\(509\) | −16132.0 | −1.40479 | −0.702396 | − | 0.711787i | \(-0.747886\pi\) | ||||
−0.702396 | + | 0.711787i | \(0.747886\pi\) | |||||||
\(510\) | 5374.20 | 0.466615 | ||||||||
\(511\) | −5609.27 | −0.485596 | ||||||||
\(512\) | 4666.24 | 0.402775 | ||||||||
\(513\) | −13897.1 | −1.19605 | ||||||||
\(514\) | −1814.35 | −0.155695 | ||||||||
\(515\) | 7607.06 | 0.650887 | ||||||||
\(516\) | 2013.46 | 0.171778 | ||||||||
\(517\) | 3108.83 | 0.264460 | ||||||||
\(518\) | 2347.02 | 0.199077 | ||||||||
\(519\) | −30005.5 | −2.53775 | ||||||||
\(520\) | 13898.0 | 1.17205 | ||||||||
\(521\) | 7654.31 | 0.643650 | 0.321825 | − | 0.946799i | \(-0.395704\pi\) | ||||
0.321825 | + | 0.946799i | \(0.395704\pi\) | |||||||
\(522\) | −4457.60 | −0.373763 | ||||||||
\(523\) | 21493.7 | 1.79705 | 0.898523 | − | 0.438926i | \(-0.144641\pi\) | ||||
0.898523 | + | 0.438926i | \(0.144641\pi\) | |||||||
\(524\) | −3521.09 | −0.293549 | ||||||||
\(525\) | 3502.13 | 0.291135 | ||||||||
\(526\) | 232.904 | 0.0193063 | ||||||||
\(527\) | −7392.20 | −0.611023 | ||||||||
\(528\) | −1467.44 | −0.120951 | ||||||||
\(529\) | −4562.20 | −0.374965 | ||||||||
\(530\) | 1937.23 | 0.158770 | ||||||||
\(531\) | 6914.06 | 0.565056 | ||||||||
\(532\) | −1107.17 | −0.0902294 | ||||||||
\(533\) | −6121.46 | −0.497467 | ||||||||
\(534\) | −23692.8 | −1.92001 | ||||||||
\(535\) | 6819.49 | 0.551088 | ||||||||
\(536\) | −16616.0 | −1.33900 | ||||||||
\(537\) | −247.991 | −0.0199285 | ||||||||
\(538\) | −391.628 | −0.0313834 | ||||||||
\(539\) | −539.000 | −0.0430730 | ||||||||
\(540\) | −24413.3 | −1.94552 | ||||||||
\(541\) | −8661.03 | −0.688293 | −0.344147 | − | 0.938916i | \(-0.611832\pi\) | ||||
−0.344147 | + | 0.938916i | \(0.611832\pi\) | |||||||
\(542\) | 3968.84 | 0.314532 | ||||||||
\(543\) | −1218.79 | −0.0963227 | ||||||||
\(544\) | 7449.74 | 0.587142 | ||||||||
\(545\) | −11754.3 | −0.923853 | ||||||||
\(546\) | 8310.94 | 0.651420 | ||||||||
\(547\) | 21372.9 | 1.67064 | 0.835321 | − | 0.549763i | \(-0.185282\pi\) | ||||
0.835321 | + | 0.549763i | \(0.185282\pi\) | |||||||
\(548\) | 5396.24 | 0.420650 | ||||||||
\(549\) | 61370.5 | 4.77091 | ||||||||
\(550\) | 831.274 | 0.0644466 | ||||||||
\(551\) | 1071.98 | 0.0828817 | ||||||||
\(552\) | −18510.6 | −1.42729 | ||||||||
\(553\) | 6235.16 | 0.479468 | ||||||||
\(554\) | −6806.72 | −0.522003 | ||||||||
\(555\) | −19311.6 | −1.47700 | ||||||||
\(556\) | −8989.15 | −0.685656 | ||||||||
\(557\) | 18062.1 | 1.37399 | 0.686997 | − | 0.726660i | \(-0.258929\pi\) | ||||
0.686997 | + | 0.726660i | \(0.258929\pi\) | |||||||
\(558\) | −21655.1 | −1.64289 | ||||||||
\(559\) | 2681.32 | 0.202876 | ||||||||
\(560\) | −800.738 | −0.0604238 | ||||||||
\(561\) | −4433.84 | −0.333684 | ||||||||
\(562\) | 2417.32 | 0.181438 | ||||||||
\(563\) | 962.299 | 0.0720356 | 0.0360178 | − | 0.999351i | \(-0.488533\pi\) | ||||
0.0360178 | + | 0.999351i | \(0.488533\pi\) | |||||||
\(564\) | 16205.0 | 1.20984 | ||||||||
\(565\) | −1638.74 | −0.122022 | ||||||||
\(566\) | 5255.49 | 0.390291 | ||||||||
\(567\) | −20912.7 | −1.54894 | ||||||||
\(568\) | −19810.2 | −1.46341 | ||||||||
\(569\) | −25409.7 | −1.87211 | −0.936055 | − | 0.351853i | \(-0.885552\pi\) | ||||
−0.936055 | + | 0.351853i | \(0.885552\pi\) | |||||||
\(570\) | −3786.04 | −0.278210 | ||||||||
\(571\) | −5211.13 | −0.381925 | −0.190962 | − | 0.981597i | \(-0.561161\pi\) | ||||
−0.190962 | + | 0.981597i | \(0.561161\pi\) | |||||||
\(572\) | −4746.73 | −0.346977 | ||||||||
\(573\) | −20893.2 | −1.52326 | ||||||||
\(574\) | −860.028 | −0.0625381 | ||||||||
\(575\) | −4300.17 | −0.311878 | ||||||||
\(576\) | 13835.7 | 1.00085 | ||||||||
\(577\) | 409.463 | 0.0295428 | 0.0147714 | − | 0.999891i | \(-0.495298\pi\) | ||||
0.0147714 | + | 0.999891i | \(0.495298\pi\) | |||||||
\(578\) | −5110.53 | −0.367768 | ||||||||
\(579\) | −44351.0 | −3.18336 | ||||||||
\(580\) | 1883.17 | 0.134818 | ||||||||
\(581\) | 3915.33 | 0.279579 | ||||||||
\(582\) | 10334.7 | 0.736057 | ||||||||
\(583\) | −1598.26 | −0.113539 | ||||||||
\(584\) | −16764.6 | −1.18788 | ||||||||
\(585\) | −50447.4 | −3.56537 | ||||||||
\(586\) | 7051.75 | 0.497108 | ||||||||
\(587\) | −11756.7 | −0.826661 | −0.413331 | − | 0.910581i | \(-0.635635\pi\) | ||||
−0.413331 | + | 0.910581i | \(0.635635\pi\) | |||||||
\(588\) | −2809.57 | −0.197049 | ||||||||
\(589\) | 5207.68 | 0.364310 | ||||||||
\(590\) | 1213.91 | 0.0847051 | ||||||||
\(591\) | −22176.0 | −1.54348 | ||||||||
\(592\) | −2876.63 | −0.199711 | ||||||||
\(593\) | −312.172 | −0.0216178 | −0.0108089 | − | 0.999942i | \(-0.503441\pi\) | ||||
−0.0108089 | + | 0.999942i | \(0.503441\pi\) | |||||||
\(594\) | −8370.68 | −0.578204 | ||||||||
\(595\) | −2419.41 | −0.166700 | ||||||||
\(596\) | 8001.42 | 0.549918 | ||||||||
\(597\) | −24561.7 | −1.68383 | ||||||||
\(598\) | −10204.8 | −0.697834 | ||||||||
\(599\) | 22486.4 | 1.53384 | 0.766918 | − | 0.641745i | \(-0.221789\pi\) | ||||
0.766918 | + | 0.641745i | \(0.221789\pi\) | |||||||
\(600\) | 10466.9 | 0.712185 | ||||||||
\(601\) | 25019.6 | 1.69812 | 0.849061 | − | 0.528295i | \(-0.177168\pi\) | ||||
0.849061 | + | 0.528295i | \(0.177168\pi\) | |||||||
\(602\) | 376.709 | 0.0255042 | ||||||||
\(603\) | 60313.4 | 4.07322 | ||||||||
\(604\) | −2325.89 | −0.156687 | ||||||||
\(605\) | 1052.69 | 0.0707407 | ||||||||
\(606\) | 23256.3 | 1.55895 | ||||||||
\(607\) | 7074.22 | 0.473037 | 0.236519 | − | 0.971627i | \(-0.423994\pi\) | ||||
0.236519 | + | 0.971627i | \(0.423994\pi\) | |||||||
\(608\) | −5248.22 | −0.350072 | ||||||||
\(609\) | 2720.26 | 0.181003 | ||||||||
\(610\) | 10774.9 | 0.715187 | ||||||||
\(611\) | 21580.1 | 1.42887 | ||||||||
\(612\) | −17049.8 | −1.12614 | ||||||||
\(613\) | 4934.94 | 0.325155 | 0.162578 | − | 0.986696i | \(-0.448019\pi\) | ||||
0.162578 | + | 0.986696i | \(0.448019\pi\) | |||||||
\(614\) | 7647.61 | 0.502658 | ||||||||
\(615\) | 7076.43 | 0.463983 | ||||||||
\(616\) | −1610.93 | −0.105367 | ||||||||
\(617\) | 2125.51 | 0.138687 | 0.0693434 | − | 0.997593i | \(-0.477910\pi\) | ||||
0.0693434 | + | 0.997593i | \(0.477910\pi\) | |||||||
\(618\) | 13595.7 | 0.884951 | ||||||||
\(619\) | 8168.09 | 0.530377 | 0.265188 | − | 0.964197i | \(-0.414566\pi\) | ||||
0.265188 | + | 0.964197i | \(0.414566\pi\) | |||||||
\(620\) | 9148.45 | 0.592598 | ||||||||
\(621\) | 43301.5 | 2.79811 | ||||||||
\(622\) | 4811.81 | 0.310187 | ||||||||
\(623\) | 10666.3 | 0.685931 | ||||||||
\(624\) | −10186.3 | −0.653493 | ||||||||
\(625\) | −7029.59 | −0.449894 | ||||||||
\(626\) | −7238.34 | −0.462144 | ||||||||
\(627\) | 3123.57 | 0.198953 | ||||||||
\(628\) | 8009.60 | 0.508946 | ||||||||
\(629\) | −8691.69 | −0.550970 | ||||||||
\(630\) | −7087.55 | −0.448214 | ||||||||
\(631\) | −8419.88 | −0.531205 | −0.265602 | − | 0.964083i | \(-0.585571\pi\) | ||||
−0.265602 | + | 0.964083i | \(0.585571\pi\) | |||||||
\(632\) | 18635.2 | 1.17289 | ||||||||
\(633\) | −39451.4 | −2.47717 | ||||||||
\(634\) | 9096.85 | 0.569846 | ||||||||
\(635\) | 5106.50 | 0.319126 | ||||||||
\(636\) | −8331.04 | −0.519414 | ||||||||
\(637\) | −3741.50 | −0.232722 | ||||||||
\(638\) | 645.687 | 0.0400674 | ||||||||
\(639\) | 71907.9 | 4.45169 | ||||||||
\(640\) | −10622.1 | −0.656057 | ||||||||
\(641\) | 27238.9 | 1.67843 | 0.839213 | − | 0.543803i | \(-0.183016\pi\) | ||||
0.839213 | + | 0.543803i | \(0.183016\pi\) | |||||||
\(642\) | 12188.1 | 0.749263 | ||||||||
\(643\) | −12438.7 | −0.762882 | −0.381441 | − | 0.924393i | \(-0.624572\pi\) | ||||
−0.381441 | + | 0.924393i | \(0.624572\pi\) | |||||||
\(644\) | 3449.80 | 0.211089 | ||||||||
\(645\) | −3099.62 | −0.189221 | ||||||||
\(646\) | −1704.00 | −0.103782 | ||||||||
\(647\) | −9788.76 | −0.594801 | −0.297400 | − | 0.954753i | \(-0.596120\pi\) | ||||
−0.297400 | + | 0.954753i | \(0.596120\pi\) | |||||||
\(648\) | −62502.5 | −3.78909 | ||||||||
\(649\) | −1001.51 | −0.0605741 | ||||||||
\(650\) | 5770.35 | 0.348202 | ||||||||
\(651\) | 13215.1 | 0.795605 | ||||||||
\(652\) | 2494.51 | 0.149835 | ||||||||
\(653\) | 5539.90 | 0.331996 | 0.165998 | − | 0.986126i | \(-0.446916\pi\) | ||||
0.165998 | + | 0.986126i | \(0.446916\pi\) | |||||||
\(654\) | −21007.9 | −1.25608 | ||||||||
\(655\) | 5420.54 | 0.323356 | ||||||||
\(656\) | 1054.10 | 0.0627371 | ||||||||
\(657\) | 60852.7 | 3.61353 | ||||||||
\(658\) | 3031.87 | 0.179627 | ||||||||
\(659\) | −18751.7 | −1.10844 | −0.554221 | − | 0.832370i | \(-0.686984\pi\) | ||||
−0.554221 | + | 0.832370i | \(0.686984\pi\) | |||||||
\(660\) | 5487.24 | 0.323622 | ||||||||
\(661\) | 24849.3 | 1.46222 | 0.731108 | − | 0.682262i | \(-0.239004\pi\) | ||||
0.731108 | + | 0.682262i | \(0.239004\pi\) | |||||||
\(662\) | −9794.03 | −0.575009 | ||||||||
\(663\) | −30777.8 | −1.80288 | ||||||||
\(664\) | 11701.9 | 0.683917 | ||||||||
\(665\) | 1704.44 | 0.0993913 | ||||||||
\(666\) | −25461.9 | −1.48142 | ||||||||
\(667\) | −3340.14 | −0.193899 | ||||||||
\(668\) | 8400.08 | 0.486540 | ||||||||
\(669\) | 6508.29 | 0.376121 | ||||||||
\(670\) | 10589.3 | 0.610599 | ||||||||
\(671\) | −8889.56 | −0.511442 | ||||||||
\(672\) | −13317.9 | −0.764510 | ||||||||
\(673\) | −9532.72 | −0.546002 | −0.273001 | − | 0.962014i | \(-0.588016\pi\) | ||||
−0.273001 | + | 0.962014i | \(0.588016\pi\) | |||||||
\(674\) | 13664.7 | 0.780926 | ||||||||
\(675\) | −24485.0 | −1.39619 | ||||||||
\(676\) | −20533.7 | −1.16828 | ||||||||
\(677\) | −6544.90 | −0.371552 | −0.185776 | − | 0.982592i | \(-0.559480\pi\) | ||||
−0.185776 | + | 0.982592i | \(0.559480\pi\) | |||||||
\(678\) | −2928.85 | −0.165902 | ||||||||
\(679\) | −4652.56 | −0.262958 | ||||||||
\(680\) | −7230.98 | −0.407787 | ||||||||
\(681\) | 36719.3 | 2.06621 | ||||||||
\(682\) | 3136.76 | 0.176118 | ||||||||
\(683\) | 8438.16 | 0.472734 | 0.236367 | − | 0.971664i | \(-0.424043\pi\) | ||||
0.236367 | + | 0.971664i | \(0.424043\pi\) | |||||||
\(684\) | 12011.3 | 0.671437 | ||||||||
\(685\) | −8307.23 | −0.463362 | ||||||||
\(686\) | −525.658 | −0.0292562 | ||||||||
\(687\) | 25548.9 | 1.41885 | ||||||||
\(688\) | −461.715 | −0.0255853 | ||||||||
\(689\) | −11094.4 | −0.613446 | ||||||||
\(690\) | 11796.8 | 0.650863 | ||||||||
\(691\) | −8196.16 | −0.451225 | −0.225613 | − | 0.974217i | \(-0.572438\pi\) | ||||
−0.225613 | + | 0.974217i | \(0.572438\pi\) | |||||||
\(692\) | 16713.2 | 0.918123 | ||||||||
\(693\) | 5847.40 | 0.320526 | ||||||||
\(694\) | 2146.34 | 0.117398 | ||||||||
\(695\) | 13838.3 | 0.755278 | ||||||||
\(696\) | 8130.13 | 0.442776 | ||||||||
\(697\) | 3184.93 | 0.173082 | ||||||||
\(698\) | −13770.4 | −0.746730 | ||||||||
\(699\) | −42490.1 | −2.29918 | ||||||||
\(700\) | −1950.71 | −0.105328 | ||||||||
\(701\) | −7172.05 | −0.386426 | −0.193213 | − | 0.981157i | \(-0.561891\pi\) | ||||
−0.193213 | + | 0.981157i | \(0.561891\pi\) | |||||||
\(702\) | −58105.6 | −3.12401 | ||||||||
\(703\) | 6123.15 | 0.328505 | ||||||||
\(704\) | −2004.11 | −0.107291 | ||||||||
\(705\) | −24946.7 | −1.33269 | ||||||||
\(706\) | 2709.38 | 0.144432 | ||||||||
\(707\) | −10469.8 | −0.556939 | ||||||||
\(708\) | −5220.42 | −0.277112 | ||||||||
\(709\) | −16766.6 | −0.888127 | −0.444063 | − | 0.895995i | \(-0.646464\pi\) | ||||
−0.444063 | + | 0.895995i | \(0.646464\pi\) | |||||||
\(710\) | 12625.0 | 0.667335 | ||||||||
\(711\) | −67642.8 | −3.56794 | ||||||||
\(712\) | 31878.6 | 1.67795 | ||||||||
\(713\) | −16226.4 | −0.852292 | ||||||||
\(714\) | −4324.09 | −0.226646 | ||||||||
\(715\) | 7307.35 | 0.382209 | ||||||||
\(716\) | 138.132 | 0.00720984 | ||||||||
\(717\) | 26203.2 | 1.36482 | ||||||||
\(718\) | −1701.84 | −0.0884571 | ||||||||
\(719\) | −5923.31 | −0.307235 | −0.153618 | − | 0.988130i | \(-0.549092\pi\) | ||||
−0.153618 | + | 0.988130i | \(0.549092\pi\) | |||||||
\(720\) | 8686.88 | 0.449640 | ||||||||
\(721\) | −6120.65 | −0.316151 | ||||||||
\(722\) | −9311.20 | −0.479954 | ||||||||
\(723\) | 15443.1 | 0.794376 | ||||||||
\(724\) | 678.872 | 0.0348482 | ||||||||
\(725\) | 1888.70 | 0.0967509 | ||||||||
\(726\) | 1881.43 | 0.0961795 | ||||||||
\(727\) | −4256.80 | −0.217161 | −0.108581 | − | 0.994088i | \(-0.534631\pi\) | ||||
−0.108581 | + | 0.994088i | \(0.534631\pi\) | |||||||
\(728\) | −11182.4 | −0.569293 | ||||||||
\(729\) | 90850.1 | 4.61566 | ||||||||
\(730\) | 10684.0 | 0.541689 | ||||||||
\(731\) | −1395.06 | −0.0705858 | ||||||||
\(732\) | −46337.4 | −2.33973 | ||||||||
\(733\) | 24556.4 | 1.23740 | 0.618698 | − | 0.785629i | \(-0.287660\pi\) | ||||
0.618698 | + | 0.785629i | \(0.287660\pi\) | |||||||
\(734\) | −8187.72 | −0.411736 | ||||||||
\(735\) | 4325.19 | 0.217057 | ||||||||
\(736\) | 16352.7 | 0.818981 | ||||||||
\(737\) | −8736.44 | −0.436650 | ||||||||
\(738\) | 9330.10 | 0.465374 | ||||||||
\(739\) | 27603.8 | 1.37405 | 0.687025 | − | 0.726634i | \(-0.258916\pi\) | ||||
0.687025 | + | 0.726634i | \(0.258916\pi\) | |||||||
\(740\) | 10756.7 | 0.534355 | ||||||||
\(741\) | 21682.5 | 1.07493 | ||||||||
\(742\) | −1558.70 | −0.0771181 | ||||||||
\(743\) | 19808.8 | 0.978082 | 0.489041 | − | 0.872261i | \(-0.337347\pi\) | ||||
0.489041 | + | 0.872261i | \(0.337347\pi\) | |||||||
\(744\) | 39496.3 | 1.94624 | ||||||||
\(745\) | −12317.8 | −0.605756 | ||||||||
\(746\) | 10467.1 | 0.513711 | ||||||||
\(747\) | −42475.9 | −2.08047 | ||||||||
\(748\) | 2469.67 | 0.120722 | ||||||||
\(749\) | −5486.98 | −0.267677 | ||||||||
\(750\) | −23580.0 | −1.14803 | ||||||||
\(751\) | 596.125 | 0.0289653 | 0.0144826 | − | 0.999895i | \(-0.495390\pi\) | ||||
0.0144826 | + | 0.999895i | \(0.495390\pi\) | |||||||
\(752\) | −3716.03 | −0.180199 | ||||||||
\(753\) | 14845.5 | 0.718459 | ||||||||
\(754\) | 4482.08 | 0.216482 | ||||||||
\(755\) | 3580.59 | 0.172597 | ||||||||
\(756\) | 19643.0 | 0.944987 | ||||||||
\(757\) | −1845.87 | −0.0886253 | −0.0443127 | − | 0.999018i | \(-0.514110\pi\) | ||||
−0.0443127 | + | 0.999018i | \(0.514110\pi\) | |||||||
\(758\) | 11994.6 | 0.574752 | ||||||||
\(759\) | −9732.61 | −0.465443 | ||||||||
\(760\) | 5094.10 | 0.243135 | ||||||||
\(761\) | −13034.2 | −0.620877 | −0.310439 | − | 0.950593i | \(-0.600476\pi\) | ||||
−0.310439 | + | 0.950593i | \(0.600476\pi\) | |||||||
\(762\) | 9126.59 | 0.433886 | ||||||||
\(763\) | 9457.55 | 0.448737 | ||||||||
\(764\) | 11637.6 | 0.551093 | ||||||||
\(765\) | 26247.3 | 1.24049 | ||||||||
\(766\) | −11547.2 | −0.544668 | ||||||||
\(767\) | −6952.02 | −0.327279 | ||||||||
\(768\) | −33772.5 | −1.58680 | ||||||||
\(769\) | −38530.6 | −1.80683 | −0.903413 | − | 0.428770i | \(-0.858947\pi\) | ||||
−0.903413 | + | 0.428770i | \(0.858947\pi\) | |||||||
\(770\) | 1026.64 | 0.0480486 | ||||||||
\(771\) | −12011.7 | −0.561076 | ||||||||
\(772\) | 24703.8 | 1.15169 | ||||||||
\(773\) | 13835.1 | 0.643745 | 0.321873 | − | 0.946783i | \(-0.395688\pi\) | ||||
0.321873 | + | 0.946783i | \(0.395688\pi\) | |||||||
\(774\) | −4086.77 | −0.189788 | ||||||||
\(775\) | 9175.31 | 0.425273 | ||||||||
\(776\) | −13905.2 | −0.643259 | ||||||||
\(777\) | 15538.2 | 0.717411 | ||||||||
\(778\) | −20032.9 | −0.923154 | ||||||||
\(779\) | −2243.73 | −0.103196 | ||||||||
\(780\) | 38090.0 | 1.74852 | ||||||||
\(781\) | −10415.9 | −0.477222 | ||||||||
\(782\) | 5309.44 | 0.242794 | ||||||||
\(783\) | −19018.6 | −0.868032 | ||||||||
\(784\) | 644.275 | 0.0293493 | ||||||||
\(785\) | −12330.4 | −0.560624 | ||||||||
\(786\) | 9687.86 | 0.439637 | ||||||||
\(787\) | 11704.2 | 0.530125 | 0.265062 | − | 0.964231i | \(-0.414607\pi\) | ||||
0.265062 | + | 0.964231i | \(0.414607\pi\) | |||||||
\(788\) | 12352.1 | 0.558409 | ||||||||
\(789\) | 1541.91 | 0.0695737 | ||||||||
\(790\) | −11876.2 | −0.534854 | ||||||||
\(791\) | 1318.54 | 0.0592690 | ||||||||
\(792\) | 17476.3 | 0.784083 | ||||||||
\(793\) | −61707.5 | −2.76330 | ||||||||
\(794\) | −5658.89 | −0.252930 | ||||||||
\(795\) | 12825.2 | 0.572155 | ||||||||
\(796\) | 13681.0 | 0.609184 | ||||||||
\(797\) | −3367.27 | −0.149655 | −0.0748274 | − | 0.997196i | \(-0.523841\pi\) | ||||
−0.0748274 | + | 0.997196i | \(0.523841\pi\) | |||||||
\(798\) | 3046.25 | 0.135133 | ||||||||
\(799\) | −11227.9 | −0.497140 | ||||||||
\(800\) | −9246.73 | −0.408652 | ||||||||
\(801\) | −115714. | −5.10432 | ||||||||
\(802\) | 12603.3 | 0.554911 | ||||||||
\(803\) | −8814.56 | −0.387371 | ||||||||
\(804\) | −45539.3 | −1.99757 | ||||||||
\(805\) | −5310.79 | −0.232523 | ||||||||
\(806\) | 21774.0 | 0.951559 | ||||||||
\(807\) | −2592.72 | −0.113096 | ||||||||
\(808\) | −31291.3 | −1.36241 | ||||||||
\(809\) | 20869.5 | 0.906961 | 0.453481 | − | 0.891266i | \(-0.350182\pi\) | ||||
0.453481 | + | 0.891266i | \(0.350182\pi\) | |||||||
\(810\) | 39832.6 | 1.72787 | ||||||||
\(811\) | −22445.9 | −0.971863 | −0.485931 | − | 0.873997i | \(-0.661520\pi\) | ||||
−0.485931 | + | 0.873997i | \(0.661520\pi\) | |||||||
\(812\) | −1515.20 | −0.0654841 | ||||||||
\(813\) | 26275.2 | 1.13347 | ||||||||
\(814\) | 3688.17 | 0.158809 | ||||||||
\(815\) | −3840.17 | −0.165049 | ||||||||
\(816\) | 5299.84 | 0.227367 | ||||||||
\(817\) | 982.798 | 0.0420854 | ||||||||
\(818\) | 5654.45 | 0.241691 | ||||||||
\(819\) | 40590.1 | 1.73179 | ||||||||
\(820\) | −3941.61 | −0.167862 | ||||||||
\(821\) | −25516.4 | −1.08469 | −0.542343 | − | 0.840157i | \(-0.682463\pi\) | ||||
−0.542343 | + | 0.840157i | \(0.682463\pi\) | |||||||
\(822\) | −14847.1 | −0.629990 | ||||||||
\(823\) | 36376.7 | 1.54072 | 0.770360 | − | 0.637609i | \(-0.220076\pi\) | ||||
0.770360 | + | 0.637609i | \(0.220076\pi\) | |||||||
\(824\) | −18293.0 | −0.773382 | ||||||||
\(825\) | 5503.35 | 0.232245 | ||||||||
\(826\) | −976.717 | −0.0411433 | ||||||||
\(827\) | 25520.1 | 1.07306 | 0.536530 | − | 0.843881i | \(-0.319735\pi\) | ||||
0.536530 | + | 0.843881i | \(0.319735\pi\) | |||||||
\(828\) | −37425.5 | −1.57080 | ||||||||
\(829\) | 23202.5 | 0.972084 | 0.486042 | − | 0.873936i | \(-0.338440\pi\) | ||||
0.486042 | + | 0.873936i | \(0.338440\pi\) | |||||||
\(830\) | −7457.56 | −0.311875 | ||||||||
\(831\) | −45063.1 | −1.88113 | ||||||||
\(832\) | −13911.7 | −0.579688 | ||||||||
\(833\) | 1946.66 | 0.0809699 | ||||||||
\(834\) | 24732.6 | 1.02688 | ||||||||
\(835\) | −12931.5 | −0.535943 | ||||||||
\(836\) | −1739.84 | −0.0719782 | ||||||||
\(837\) | −92392.6 | −3.81548 | ||||||||
\(838\) | 23994.9 | 0.989127 | ||||||||
\(839\) | −10538.6 | −0.433649 | −0.216824 | − | 0.976211i | \(-0.569570\pi\) | ||||
−0.216824 | + | 0.976211i | \(0.569570\pi\) | |||||||
\(840\) | 12926.8 | 0.530974 | ||||||||
\(841\) | −22922.0 | −0.939849 | ||||||||
\(842\) | −9206.38 | −0.376809 | ||||||||
\(843\) | 16003.6 | 0.653846 | ||||||||
\(844\) | 21974.6 | 0.896206 | ||||||||
\(845\) | 31610.6 | 1.28691 | ||||||||
\(846\) | −32891.6 | −1.33669 | ||||||||
\(847\) | −847.000 | −0.0343604 | ||||||||
\(848\) | 1910.42 | 0.0773635 | ||||||||
\(849\) | 34793.3 | 1.40648 | ||||||||
\(850\) | −3002.25 | −0.121149 | ||||||||
\(851\) | −19078.9 | −0.768526 | ||||||||
\(852\) | −54293.7 | −2.18318 | ||||||||
\(853\) | 40061.0 | 1.60805 | 0.804023 | − | 0.594598i | \(-0.202689\pi\) | ||||
0.804023 | + | 0.594598i | \(0.202689\pi\) | |||||||
\(854\) | −8669.52 | −0.347383 | ||||||||
\(855\) | −18490.8 | −0.739615 | ||||||||
\(856\) | −16399.1 | −0.654801 | ||||||||
\(857\) | 775.719 | 0.0309195 | 0.0154598 | − | 0.999880i | \(-0.495079\pi\) | ||||
0.0154598 | + | 0.999880i | \(0.495079\pi\) | |||||||
\(858\) | 13060.1 | 0.519654 | ||||||||
\(859\) | −10241.5 | −0.406792 | −0.203396 | − | 0.979097i | \(-0.565198\pi\) | ||||
−0.203396 | + | 0.979097i | \(0.565198\pi\) | |||||||
\(860\) | 1726.50 | 0.0684573 | ||||||||
\(861\) | −5693.71 | −0.225367 | ||||||||
\(862\) | 20135.9 | 0.795629 | ||||||||
\(863\) | −1268.51 | −0.0500356 | −0.0250178 | − | 0.999687i | \(-0.507964\pi\) | ||||
−0.0250178 | + | 0.999687i | \(0.507964\pi\) | |||||||
\(864\) | 93111.8 | 3.66635 | ||||||||
\(865\) | −25729.1 | −1.01135 | ||||||||
\(866\) | −6731.60 | −0.264144 | ||||||||
\(867\) | −33833.7 | −1.32532 | ||||||||
\(868\) | −7360.86 | −0.287839 | ||||||||
\(869\) | 9798.11 | 0.382483 | ||||||||
\(870\) | −5181.30 | −0.201911 | ||||||||
\(871\) | −60644.6 | −2.35920 | ||||||||
\(872\) | 28266.1 | 1.09772 | ||||||||
\(873\) | 50473.8 | 1.95679 | ||||||||
\(874\) | −3740.41 | −0.144761 | ||||||||
\(875\) | 10615.5 | 0.410135 | ||||||||
\(876\) | −45946.5 | −1.77213 | ||||||||
\(877\) | 6691.33 | 0.257640 | 0.128820 | − | 0.991668i | \(-0.458881\pi\) | ||||
0.128820 | + | 0.991668i | \(0.458881\pi\) | |||||||
\(878\) | 19426.6 | 0.746716 | ||||||||
\(879\) | 46685.3 | 1.79142 | ||||||||
\(880\) | −1258.30 | −0.0482015 | ||||||||
\(881\) | 14514.6 | 0.555063 | 0.277531 | − | 0.960717i | \(-0.410484\pi\) | ||||
0.277531 | + | 0.960717i | \(0.410484\pi\) | |||||||
\(882\) | 5702.66 | 0.217708 | ||||||||
\(883\) | 10335.2 | 0.393891 | 0.196946 | − | 0.980414i | \(-0.436898\pi\) | ||||
0.196946 | + | 0.980414i | \(0.436898\pi\) | |||||||
\(884\) | 17143.4 | 0.652257 | ||||||||
\(885\) | 8036.57 | 0.305250 | ||||||||
\(886\) | −26802.8 | −1.01632 | ||||||||
\(887\) | 42946.3 | 1.62570 | 0.812851 | − | 0.582472i | \(-0.197914\pi\) | ||||
0.812851 | + | 0.582472i | \(0.197914\pi\) | |||||||
\(888\) | 46439.4 | 1.75496 | ||||||||
\(889\) | −4108.70 | −0.155007 | ||||||||
\(890\) | −20316.1 | −0.765166 | ||||||||
\(891\) | −32862.8 | −1.23563 | ||||||||
\(892\) | −3625.15 | −0.136075 | ||||||||
\(893\) | 7909.87 | 0.296410 | ||||||||
\(894\) | −22014.9 | −0.823590 | ||||||||
\(895\) | −212.648 | −0.00794193 | ||||||||
\(896\) | 8546.59 | 0.318662 | ||||||||
\(897\) | −67559.5 | −2.51477 | ||||||||
\(898\) | −23741.7 | −0.882263 | ||||||||
\(899\) | 7126.87 | 0.264399 | ||||||||
\(900\) | 21162.4 | 0.783794 | ||||||||
\(901\) | 5772.31 | 0.213434 | ||||||||
\(902\) | −1351.47 | −0.0498882 | ||||||||
\(903\) | 2493.96 | 0.0919089 | ||||||||
\(904\) | 3940.75 | 0.144986 | ||||||||
\(905\) | −1045.09 | −0.0383866 | ||||||||
\(906\) | 6399.41 | 0.234665 | ||||||||
\(907\) | 8376.30 | 0.306649 | 0.153324 | − | 0.988176i | \(-0.451002\pi\) | ||||
0.153324 | + | 0.988176i | \(0.451002\pi\) | |||||||
\(908\) | −20452.8 | −0.747524 | ||||||||
\(909\) | 113582. | 4.14443 | ||||||||
\(910\) | 7126.47 | 0.259605 | ||||||||
\(911\) | 17335.4 | 0.630460 | 0.315230 | − | 0.949015i | \(-0.397918\pi\) | ||||
0.315230 | + | 0.949015i | \(0.397918\pi\) | |||||||
\(912\) | −3733.65 | −0.135563 | ||||||||
\(913\) | 6152.66 | 0.223027 | ||||||||
\(914\) | −11938.4 | −0.432043 | ||||||||
\(915\) | 71334.1 | 2.57730 | ||||||||
\(916\) | −14230.9 | −0.513321 | ||||||||
\(917\) | −4361.38 | −0.157061 | ||||||||
\(918\) | 30231.7 | 1.08692 | ||||||||
\(919\) | −34995.3 | −1.25613 | −0.628067 | − | 0.778159i | \(-0.716154\pi\) | ||||
−0.628067 | + | 0.778159i | \(0.716154\pi\) | |||||||
\(920\) | −15872.5 | −0.568806 | ||||||||
\(921\) | 50630.1 | 1.81142 | ||||||||
\(922\) | −13022.6 | −0.465159 | ||||||||
\(923\) | −72302.8 | −2.57841 | ||||||||
\(924\) | −4415.05 | −0.157191 | ||||||||
\(925\) | 10788.3 | 0.383476 | ||||||||
\(926\) | 1341.14 | 0.0475945 | ||||||||
\(927\) | 66400.5 | 2.35262 | ||||||||
\(928\) | −7182.35 | −0.254065 | ||||||||
\(929\) | −10671.6 | −0.376882 | −0.188441 | − | 0.982084i | \(-0.560343\pi\) | ||||
−0.188441 | + | 0.982084i | \(0.560343\pi\) | |||||||
\(930\) | −25170.8 | −0.887510 | ||||||||
\(931\) | −1371.39 | −0.0482767 | ||||||||
\(932\) | 23667.2 | 0.831808 | ||||||||
\(933\) | 31856.0 | 1.11781 | ||||||||
\(934\) | 27053.1 | 0.947755 | ||||||||
\(935\) | −3801.93 | −0.132980 | ||||||||
\(936\) | 121313. | 4.23636 | ||||||||
\(937\) | −1855.85 | −0.0647045 | −0.0323522 | − | 0.999477i | \(-0.510300\pi\) | ||||
−0.0323522 | + | 0.999477i | \(0.510300\pi\) | |||||||
\(938\) | −8520.19 | −0.296582 | ||||||||
\(939\) | −47920.6 | −1.66542 | ||||||||
\(940\) | 13895.4 | 0.482148 | ||||||||
\(941\) | 15378.8 | 0.532766 | 0.266383 | − | 0.963867i | \(-0.414171\pi\) | ||||
0.266383 | + | 0.963867i | \(0.414171\pi\) | |||||||
\(942\) | −22037.4 | −0.762228 | ||||||||
\(943\) | 6991.16 | 0.241425 | ||||||||
\(944\) | 1197.12 | 0.0412742 | ||||||||
\(945\) | −30239.4 | −1.04094 | ||||||||
\(946\) | 591.972 | 0.0203453 | ||||||||
\(947\) | −14600.9 | −0.501020 | −0.250510 | − | 0.968114i | \(-0.580598\pi\) | ||||
−0.250510 | + | 0.968114i | \(0.580598\pi\) | |||||||
\(948\) | 51073.3 | 1.74977 | ||||||||
\(949\) | −61186.9 | −2.09295 | ||||||||
\(950\) | 2115.03 | 0.0722324 | ||||||||
\(951\) | 60224.6 | 2.05354 | ||||||||
\(952\) | 5818.06 | 0.198072 | ||||||||
\(953\) | −2114.27 | −0.0718658 | −0.0359329 | − | 0.999354i | \(-0.511440\pi\) | ||||
−0.0359329 | + | 0.999354i | \(0.511440\pi\) | |||||||
\(954\) | 16909.7 | 0.573870 | ||||||||
\(955\) | −17915.5 | −0.607051 | ||||||||
\(956\) | −14595.3 | −0.493773 | ||||||||
\(957\) | 4274.70 | 0.144390 | ||||||||
\(958\) | 4796.46 | 0.161761 | ||||||||
\(959\) | 6684.02 | 0.225066 | ||||||||
\(960\) | 16081.9 | 0.540669 | ||||||||
\(961\) | 4831.40 | 0.162177 | ||||||||
\(962\) | 25601.7 | 0.858037 | ||||||||
\(963\) | 59526.0 | 1.99190 | ||||||||
\(964\) | −8601.87 | −0.287394 | ||||||||
\(965\) | −38030.2 | −1.26864 | ||||||||
\(966\) | −9491.70 | −0.316139 | ||||||||
\(967\) | 7251.75 | 0.241159 | 0.120579 | − | 0.992704i | \(-0.461525\pi\) | ||||
0.120579 | + | 0.992704i | \(0.461525\pi\) | |||||||
\(968\) | −2531.46 | −0.0840538 | ||||||||
\(969\) | −11281.2 | −0.373997 | ||||||||
\(970\) | 8861.77 | 0.293334 | ||||||||
\(971\) | 2742.57 | 0.0906420 | 0.0453210 | − | 0.998972i | \(-0.485569\pi\) | ||||
0.0453210 | + | 0.998972i | \(0.485569\pi\) | |||||||
\(972\) | −95533.9 | −3.15252 | ||||||||
\(973\) | −11134.4 | −0.366856 | ||||||||
\(974\) | −560.991 | −0.0184551 | ||||||||
\(975\) | 38201.9 | 1.25481 | ||||||||
\(976\) | 10625.8 | 0.348488 | ||||||||
\(977\) | 23770.4 | 0.778384 | 0.389192 | − | 0.921157i | \(-0.372754\pi\) | ||||
0.389192 | + | 0.921157i | \(0.372754\pi\) | |||||||
\(978\) | −6863.34 | −0.224402 | ||||||||
\(979\) | 16761.3 | 0.547184 | ||||||||
\(980\) | −2409.16 | −0.0785282 | ||||||||
\(981\) | −102601. | −3.33925 | ||||||||
\(982\) | −22340.1 | −0.725967 | ||||||||
\(983\) | −49265.4 | −1.59850 | −0.799249 | − | 0.601000i | \(-0.794769\pi\) | ||||
−0.799249 | + | 0.601000i | \(0.794769\pi\) | |||||||
\(984\) | −17017.0 | −0.551302 | ||||||||
\(985\) | −19015.5 | −0.615109 | ||||||||
\(986\) | −2331.98 | −0.0753198 | ||||||||
\(987\) | 20072.2 | 0.647319 | ||||||||
\(988\) | −12077.2 | −0.388895 | ||||||||
\(989\) | −3062.26 | −0.0984574 | ||||||||
\(990\) | −11137.6 | −0.357551 | ||||||||
\(991\) | −17123.5 | −0.548884 | −0.274442 | − | 0.961604i | \(-0.588493\pi\) | ||||
−0.274442 | + | 0.961604i | \(0.588493\pi\) | |||||||
\(992\) | −34891.9 | −1.11675 | ||||||||
\(993\) | −64840.2 | −2.07215 | ||||||||
\(994\) | −10158.1 | −0.324140 | ||||||||
\(995\) | −21061.2 | −0.671040 | ||||||||
\(996\) | 32071.2 | 1.02030 | ||||||||
\(997\) | −41275.5 | −1.31114 | −0.655571 | − | 0.755134i | \(-0.727572\pi\) | ||||
−0.655571 | + | 0.755134i | \(0.727572\pi\) | |||||||
\(998\) | 14565.3 | 0.461979 | ||||||||
\(999\) | −108634. | −3.44048 |
(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 | 77.4.a.d.1.3 | ✓ | 4 | |
3.2 | odd | 2 | 693.4.a.l.1.2 | 4 | |||
4.3 | odd | 2 | 1232.4.a.s.1.1 | 4 | |||
5.4 | even | 2 | 1925.4.a.p.1.2 | 4 | |||
7.6 | odd | 2 | 539.4.a.g.1.3 | 4 | |||
11.10 | odd | 2 | 847.4.a.d.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
77.4.a.d.1.3 | ✓ | 4 | 1.1 | even | 1 | trivial | |
539.4.a.g.1.3 | 4 | 7.6 | odd | 2 | |||
693.4.a.l.1.2 | 4 | 3.2 | odd | 2 | |||
847.4.a.d.1.2 | 4 | 11.10 | odd | 2 | |||
1232.4.a.s.1.1 | 4 | 4.3 | odd | 2 | |||
1925.4.a.p.1.2 | 4 | 5.4 | even | 2 |