Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1856,4,Mod(1,1856)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1856, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1856.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1856 = 2^{6} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1856.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: | \(109.507544971\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2 x^{11} - 217 x^{10} + 520 x^{9} + 16022 x^{8} - 37368 x^{7} - 509640 x^{6} + 989168 x^{5} + \cdots + 14751072 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{17} \) |
Twist minimal: | no (minimal twist has level 928) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(-2.71183\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1856.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.71183 | 0.329441 | 0.164721 | − | 0.986340i | \(-0.447328\pi\) | ||||
0.164721 | + | 0.986340i | \(0.447328\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −8.28780 | −0.741283 | −0.370642 | − | 0.928776i | \(-0.620862\pi\) | ||||
−0.370642 | + | 0.928776i | \(0.620862\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −9.40926 | −0.508052 | −0.254026 | − | 0.967197i | \(-0.581755\pi\) | ||||
−0.254026 | + | 0.967197i | \(0.581755\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −24.0696 | −0.891468 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 70.9884 | 1.94580 | 0.972901 | − | 0.231224i | \(-0.0742730\pi\) | ||||
0.972901 | + | 0.231224i | \(0.0742730\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 55.2478 | 1.17869 | 0.589345 | − | 0.807881i | \(-0.299386\pi\) | ||||
0.589345 | + | 0.807881i | \(0.299386\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −14.1873 | −0.244209 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −113.376 | −1.61751 | −0.808756 | − | 0.588144i | \(-0.799859\pi\) | ||||
−0.808756 | + | 0.588144i | \(0.799859\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −130.825 | −1.57965 | −0.789826 | − | 0.613331i | \(-0.789829\pi\) | ||||
−0.789826 | + | 0.613331i | \(0.789829\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −16.1070 | −0.167374 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 119.948 | 1.08743 | 0.543714 | − | 0.839270i | \(-0.317017\pi\) | ||||
0.543714 | + | 0.839270i | \(0.317017\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −56.3124 | −0.450499 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −87.4225 | −0.623128 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −29.0000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 152.679 | 0.884581 | 0.442291 | − | 0.896872i | \(-0.354166\pi\) | ||||
0.442291 | + | 0.896872i | \(0.354166\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 121.520 | 0.641028 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 77.9821 | 0.376611 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −270.093 | −1.20008 | −0.600041 | − | 0.799969i | \(-0.704849\pi\) | ||||
−0.600041 | + | 0.799969i | \(0.704849\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 94.5747 | 0.388310 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 368.077 | 1.40205 | 0.701024 | − | 0.713137i | \(-0.252726\pi\) | ||||
0.701024 | + | 0.713137i | \(0.252726\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 79.8832 | 0.283304 | 0.141652 | − | 0.989917i | \(-0.454759\pi\) | ||||
0.141652 | + | 0.989917i | \(0.454759\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 199.484 | 0.660831 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 556.119 | 1.72592 | 0.862960 | − | 0.505272i | \(-0.168608\pi\) | ||||
0.862960 | + | 0.505272i | \(0.168608\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −254.466 | −0.741883 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −194.080 | −0.532876 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −221.368 | −0.573722 | −0.286861 | − | 0.957972i | \(-0.592612\pi\) | ||||
−0.286861 | + | 0.957972i | \(0.592612\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −588.338 | −1.44239 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −223.951 | −0.520403 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −18.7179 | −0.0413027 | −0.0206514 | − | 0.999787i | \(-0.506574\pi\) | ||||
−0.0206514 | + | 0.999787i | \(0.506574\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 298.553 | 0.626652 | 0.313326 | − | 0.949646i | \(-0.398557\pi\) | ||||
0.313326 | + | 0.949646i | \(0.398557\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 226.478 | 0.452913 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −457.882 | −0.873743 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −516.187 | −0.941228 | −0.470614 | − | 0.882339i | \(-0.655968\pi\) | ||||
−0.470614 | + | 0.882339i | \(0.655968\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 205.330 | 0.358244 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −568.221 | −0.949795 | −0.474897 | − | 0.880041i | \(-0.657515\pi\) | ||||
−0.474897 | + | 0.880041i | \(0.657515\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −660.868 | −1.05957 | −0.529786 | − | 0.848131i | \(-0.677728\pi\) | ||||
−0.529786 | + | 0.848131i | \(0.677728\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −96.3971 | −0.148413 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −667.949 | −0.988569 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 35.3870 | 0.0503969 | 0.0251984 | − | 0.999682i | \(-0.491978\pi\) | ||||
0.0251984 | + | 0.999682i | \(0.491978\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 500.228 | 0.686184 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 83.5548 | 0.110498 | 0.0552490 | − | 0.998473i | \(-0.482405\pi\) | ||||
0.0552490 | + | 0.998473i | \(0.482405\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 939.637 | 1.19904 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −49.6430 | −0.0611758 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1027.44 | 1.22369 | 0.611846 | − | 0.790977i | \(-0.290427\pi\) | ||||
0.611846 | + | 0.790977i | \(0.290427\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −519.841 | −0.598836 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 261.361 | 0.291418 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1084.25 | 1.17097 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −621.640 | −0.650701 | −0.325350 | − | 0.945594i | \(-0.605482\pi\) | ||||
−0.325350 | + | 0.945594i | \(0.605482\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1708.67 | −1.73462 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −480.106 | −0.472993 | −0.236497 | − | 0.971632i | \(-0.575999\pi\) | ||||
−0.236497 | + | 0.971632i | \(0.575999\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 385.075 | 0.368375 | 0.184187 | − | 0.982891i | \(-0.441035\pi\) | ||||
0.184187 | + | 0.982891i | \(0.441035\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 133.492 | 0.124071 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1765.83 | 1.59541 | 0.797706 | − | 0.603046i | \(-0.206047\pi\) | ||||
0.797706 | + | 0.603046i | \(0.206047\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 634.006 | 0.557127 | 0.278563 | − | 0.960418i | \(-0.410142\pi\) | ||||
0.278563 | + | 0.960418i | \(0.410142\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −462.353 | −0.395357 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 717.864 | 0.597620 | 0.298810 | − | 0.954313i | \(-0.403410\pi\) | ||||
0.298810 | + | 0.954313i | \(0.403410\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −994.104 | −0.806093 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1329.79 | −1.05077 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1066.78 | 0.821781 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3708.35 | 2.78614 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 630.085 | 0.461893 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1502.68 | 1.07523 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 641.367 | 0.448127 | 0.224063 | − | 0.974575i | \(-0.428068\pi\) | ||||
0.224063 | + | 0.974575i | \(0.428068\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 136.746 | 0.0933321 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 63.1476 | 0.0421163 | 0.0210581 | − | 0.999778i | \(-0.493296\pi\) | ||||
0.0210581 | + | 0.999778i | \(0.493296\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1230.97 | 0.802546 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 724.540 | 0.461914 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1329.38 | −0.829029 | −0.414514 | − | 0.910043i | \(-0.636049\pi\) | ||||
−0.414514 | + | 0.910043i | \(0.636049\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 28.8252 | 0.0175894 | 0.00879469 | − | 0.999961i | \(-0.497201\pi\) | ||||
0.00879469 | + | 0.999961i | \(0.497201\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 951.979 | 0.568590 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3921.95 | 2.29350 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 240.346 | 0.137653 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −435.602 | −0.244407 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 623.189 | 0.342642 | 0.171321 | − | 0.985215i | \(-0.445197\pi\) | ||||
0.171321 | + | 0.985215i | \(0.445197\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2726.75 | 1.46953 | 0.734766 | − | 0.678320i | \(-0.237292\pi\) | ||||
0.734766 | + | 0.678320i | \(0.237292\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2728.92 | 1.44196 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1265.38 | −0.655725 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2576.81 | 1.30989 | 0.654943 | − | 0.755679i | \(-0.272693\pi\) | ||||
0.654943 | + | 0.755679i | \(0.272693\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −378.945 | −0.189008 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1128.62 | −0.552471 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1996.69 | −0.959467 | −0.479733 | − | 0.877414i | \(-0.659267\pi\) | ||||
−0.479733 | + | 0.877414i | \(0.659267\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1007.13 | −0.475183 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2963.72 | 1.37329 | 0.686644 | − | 0.726993i | \(-0.259083\pi\) | ||||
0.686644 | + | 0.726993i | \(0.259083\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 855.316 | 0.389311 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3148.92 | 1.40821 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2261.02 | −0.993656 | −0.496828 | − | 0.867849i | \(-0.665502\pi\) | ||||
−0.496828 | + | 0.867849i | \(0.665502\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 529.858 | 0.228877 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −32.0418 | −0.0136068 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1946.14 | 0.812633 | 0.406316 | − | 0.913733i | \(-0.366813\pi\) | ||||
0.406316 | + | 0.913733i | \(0.366813\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3260.73 | 1.33905 | 0.669526 | − | 0.742788i | \(-0.266497\pi\) | ||||
0.669526 | + | 0.742788i | \(0.266497\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 511.072 | 0.206445 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2238.48 | 0.889601 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8048.38 | −3.14736 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 822.581 | 0.316582 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3088.23 | −1.16993 | −0.584966 | − | 0.811058i | \(-0.698892\pi\) | ||||
−0.584966 | + | 0.811058i | \(0.698892\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4378.98 | 1.63319 | 0.816595 | − | 0.577210i | \(-0.195859\pi\) | ||||
0.816595 | + | 0.577210i | \(0.195859\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −783.816 | −0.287847 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3148.61 | 1.13873 | 0.569364 | − | 0.822086i | \(-0.307190\pi\) | ||||
0.569364 | + | 0.822086i | \(0.307190\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1801.03 | 0.641567 | 0.320784 | − | 0.947152i | \(-0.396054\pi\) | ||||
0.320784 | + | 0.947152i | \(0.396054\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −883.623 | −0.310080 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 272.869 | 0.0943430 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3050.55 | −1.03932 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2887.10 | −0.969408 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −9287.09 | −3.07369 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 789.717 | 0.257660 | 0.128830 | − | 0.991667i | \(-0.458878\pi\) | ||||
0.128830 | + | 0.991667i | \(0.458878\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −972.697 | −0.312902 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −662.056 | −0.210008 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1436.60 | −0.449414 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1131.29 | −0.349067 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6263.77 | −1.90655 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4287.13 | −1.28739 | −0.643693 | − | 0.765283i | \(-0.722599\pi\) | ||||
−0.643693 | + | 0.765283i | \(0.722599\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1355.42 | 0.401606 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1991.26 | −0.582221 | −0.291111 | − | 0.956689i | \(-0.594025\pi\) | ||||
−0.291111 | + | 0.956689i | \(0.594025\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3349.42 | 0.966532 | 0.483266 | − | 0.875473i | \(-0.339450\pi\) | ||||
0.483266 | + | 0.875473i | \(0.339450\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1143.41 | −0.325676 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6311.65 | 1.77463 | 0.887317 | − | 0.461159i | \(-0.152566\pi\) | ||||
0.887317 | + | 0.461159i | \(0.152566\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4609.00 | −1.27940 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 60.5766 | 0.0166028 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2352.90 | −0.636805 | −0.318403 | − | 0.947956i | \(-0.603146\pi\) | ||||
−0.318403 | + | 0.947956i | \(0.603146\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5729.54 | 1.53142 | 0.765709 | − | 0.643187i | \(-0.222388\pi\) | ||||
0.765709 | + | 0.643187i | \(0.222388\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3216.71 | 0.849186 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2108.96 | 0.549945 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7227.81 | −1.86192 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 143.031 | 0.0364026 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −710.136 | −0.178579 | −0.0892896 | − | 0.996006i | \(-0.528460\pi\) | ||||
−0.0892896 | + | 0.996006i | \(0.528460\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8514.91 | 2.11592 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1608.50 | 0.395012 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3482.49 | −0.845260 | −0.422630 | − | 0.906302i | \(-0.638893\pi\) | ||||
−0.422630 | + | 0.906302i | \(0.638893\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2541.38 | 0.609704 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 698.020 | 0.165542 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 8117.07 | 1.90312 | 0.951559 | − | 0.307466i | \(-0.0994810\pi\) | ||||
0.951559 | + | 0.307466i | \(0.0994810\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1834.66 | 0.425291 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1758.80 | 0.403135 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 109.393 | 0.0247949 | 0.0123975 | − | 0.999923i | \(-0.496054\pi\) | ||||
0.0123975 | + | 0.999923i | \(0.496054\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.75076 | −0.000840748 0 | −0.000420374 | − | 1.00000i | \(-0.500134\pi\) | ||||
−0.000420374 | 1.00000i | \(0.500134\pi\) | ||||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −889.878 | −0.197282 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3997.53 | −0.876582 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 368.156 | 0.0798568 | 0.0399284 | − | 0.999203i | \(-0.487287\pi\) | ||||
0.0399284 | + | 0.999203i | \(0.487287\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3674.94 | −0.788576 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7284.38 | 1.54644 | 0.773220 | − | 0.634138i | \(-0.218645\pi\) | ||||
0.773220 | + | 0.634138i | \(0.218645\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2747.05 | −0.577014 | −0.288507 | − | 0.957478i | \(-0.593159\pi\) | ||||
−0.288507 | + | 0.957478i | \(0.593159\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1856.06 | 0.385766 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3463.33 | −0.712314 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7941.11 | 1.61635 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1064.14 | −0.214368 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3312.98 | 0.660568 | 0.330284 | − | 0.943882i | \(-0.392856\pi\) | ||||
0.330284 | + | 0.943882i | \(0.392856\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 155.130 | 0.0306170 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −6205.98 | −1.21248 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6626.85 | 1.28174 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −751.642 | −0.143933 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −821.859 | −0.155824 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2474.35 | −0.464527 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 117.629 | 0.0218679 | 0.0109339 | − | 0.999940i | \(-0.496520\pi\) | ||||
0.0109339 | + | 0.999940i | \(0.496520\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 659.183 | 0.121358 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −755.020 | −0.137663 | −0.0688316 | − | 0.997628i | \(-0.521927\pi\) | ||||
−0.0688316 | + | 0.997628i | \(0.521927\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1478.29 | −0.266959 | −0.133479 | − | 0.991052i | \(-0.542615\pi\) | ||||
−0.133479 | + | 0.991052i | \(0.542615\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1877.00 | −0.335737 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8904.99 | 1.57777 | 0.788887 | − | 0.614538i | \(-0.210658\pi\) | ||||
0.788887 | + | 0.614538i | \(0.210658\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2058.66 | −0.361326 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3022.80 | 0.525595 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 14832.5 | 2.55511 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3111.13 | −0.530999 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1085.31 | 0.183541 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5232.66 | −0.876858 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4878.38 | 0.810090 | 0.405045 | − | 0.914297i | \(-0.367256\pi\) | ||||
0.405045 | + | 0.914297i | \(0.367256\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6501.04 | 1.06984 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4278.05 | 0.697716 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2398.08 | 0.387631 | 0.193815 | − | 0.981038i | \(-0.437914\pi\) | ||||
0.193815 | + | 0.981038i | \(0.437914\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1228.86 | 0.196881 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10838.5 | 1.72122 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5621.71 | 0.884968 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1701.74 | −0.265560 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6793.41 | −1.05098 | −0.525489 | − | 0.850801i | \(-0.676117\pi\) | ||||
−0.525489 | + | 0.850801i | \(0.676117\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4272.74 | −0.655342 | −0.327671 | − | 0.944792i | \(-0.606264\pi\) | ||||
−0.327671 | + | 0.944792i | \(0.606264\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4829.90 | −0.734475 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9012.18 | 1.35884 | 0.679419 | − | 0.733750i | \(-0.262232\pi\) | ||||
0.679419 | + | 0.733750i | \(0.262232\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4709.30 | 0.704067 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1826.15 | 0.270729 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4766.83 | 0.700790 | 0.350395 | − | 0.936602i | \(-0.386047\pi\) | ||||
0.350395 | + | 0.936602i | \(0.386047\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10256.3 | 1.49530 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6348.07 | 0.917871 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5477.14 | 0.785443 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2367.41 | 0.336724 | 0.168362 | − | 0.985725i | \(-0.446152\pi\) | ||||
0.168362 | + | 0.985725i | \(0.446152\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8859.49 | −1.24988 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2082.91 | 0.291481 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8820.15 | −1.22437 | −0.612185 | − | 0.790715i | \(-0.709709\pi\) | ||||
−0.612185 | + | 0.790715i | \(0.709709\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2572.33 | 0.354226 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1602.19 | −0.218877 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1473.35 | −0.199686 | −0.0998430 | − | 0.995003i | \(-0.531834\pi\) | ||||
−0.0998430 | + | 0.995003i | \(0.531834\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1097.91 | 0.147632 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4220.98 | 0.563138 | 0.281569 | − | 0.959541i | \(-0.409145\pi\) | ||||
0.281569 | + | 0.959541i | \(0.409145\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5535.82 | 0.732810 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1922.76 | −0.252556 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −13830.8 | −1.80270 | −0.901349 | − | 0.433094i | \(-0.857422\pi\) | ||||
−0.901349 | + | 0.433094i | \(0.857422\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −13599.2 | −1.75893 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 108.098 | 0.0138748 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −293.281 | −0.0373584 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7744.90 | −0.979107 | −0.489554 | − | 0.871973i | \(-0.662840\pi\) | ||||
−0.489554 | + | 0.871973i | \(0.662840\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2107.21 | 0.264392 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5490.40 | 0.683734 | 0.341867 | − | 0.939748i | \(-0.388941\pi\) | ||||
0.341867 | + | 0.939748i | \(0.388941\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8435.19 | 1.04265 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4145.79 | −0.508657 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −19173.5 | −2.33512 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11356.6 | −1.37297 | −0.686487 | − | 0.727142i | \(-0.740848\pi\) | ||||
−0.686487 | + | 0.727142i | \(0.740848\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2275.68 | −0.273116 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 176.122 | 0.0209840 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −692.485 | −0.0819102 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 49.3439 | 0.00579467 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −16478.5 | −1.92131 | −0.960653 | − | 0.277751i | \(-0.910411\pi\) | ||||
−0.960653 | + | 0.277751i | \(0.910411\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2653.53 | −0.307186 | −0.153593 | − | 0.988134i | \(-0.549084\pi\) | ||||
−0.153593 | + | 0.988134i | \(0.549084\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −13385.6 | −1.53860 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6384.47 | 0.728688 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2809.16 | −0.318372 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6713.71 | 0.755573 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1761.29 | −0.196841 | −0.0984203 | − | 0.995145i | \(-0.531379\pi\) | ||||
−0.0984203 | + | 0.995145i | \(0.531379\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10336.6 | −1.14722 | −0.573610 | − | 0.819129i | \(-0.694457\pi\) | ||||
−0.573610 | + | 0.819129i | \(0.694457\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 411.431 | 0.0453486 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −15692.2 | −1.71776 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13521.8 | 1.47007 | 0.735036 | − | 0.678028i | \(-0.237165\pi\) | ||||
0.735036 | + | 0.678028i | \(0.237165\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6124.90 | 0.661365 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9509.20 | 1.01986 | 0.509928 | − | 0.860217i | \(-0.329672\pi\) | ||||
0.509928 | + | 0.860217i | \(0.329672\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8515.23 | −0.907103 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1066.79 | 0.112880 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1571.72 | −0.165198 | −0.0825992 | − | 0.996583i | \(-0.526322\pi\) | ||||
−0.0825992 | + | 0.996583i | \(0.526322\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 26129.2 | 2.72811 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4667.72 | 0.484125 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4308.34 | 0.443907 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5101.82 | 0.522217 | 0.261108 | − | 0.965309i | \(-0.415912\pi\) | ||||
0.261108 | + | 0.965309i | \(0.415912\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 9911.61 | 1.00792 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10183.2 | −1.02881 | −0.514404 | − | 0.857548i | \(-0.671987\pi\) | ||||
−0.514404 | + | 0.857548i | \(0.671987\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17263.5 | −1.73283 | −0.866417 | − | 0.499322i | \(-0.833582\pi\) | ||||
−0.866417 | + | 0.499322i | \(0.833582\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2166.11 | −0.216023 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5511.73 | −0.546151 | −0.273075 | − | 0.961993i | \(-0.588041\pi\) | ||||
−0.273075 | + | 0.961993i | \(0.588041\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4856.94 | 0.478193 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4411.06 | 0.431531 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5670.78 | 0.551253 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7367.09 | 0.711632 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5328.26 | 0.511455 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −17573.4 | −1.67630 | −0.838152 | − | 0.545437i | \(-0.816364\pi\) | ||||
−0.838152 | + | 0.545437i | \(0.816364\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −14922.0 | −1.41453 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1932.01 | −0.182007 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5152.03 | 0.482353 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3865.76 | −0.359700 | −0.179850 | − | 0.983694i | \(-0.557561\pi\) | ||||
−0.179850 | + | 0.983694i | \(0.557561\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3418.00 | −0.316088 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12294.6 | −1.13004 | −0.565019 | − | 0.825078i | \(-0.691131\pi\) | ||||
−0.565019 | + | 0.825078i | \(0.691131\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3287.90 | 0.300365 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 14161.1 | 1.28584 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5346.54 | 0.482545 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8629.37 | 0.774155 | 0.387078 | − | 0.922047i | \(-0.373485\pi\) | ||||
0.387078 | + | 0.922047i | \(0.373485\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5073.37 | 0.452418 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 15188.2 | 1.34634 | 0.673168 | − | 0.739490i | \(-0.264933\pi\) | ||||
0.673168 | + | 0.739490i | \(0.264933\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3979.02 | 0.350622 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1464.15 | 0.128255 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7150.74 | 0.622694 | 0.311347 | − | 0.950296i | \(-0.399220\pi\) | ||||
0.311347 | + | 0.950296i | \(0.399220\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6218.28 | 0.538318 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 11437.1 | 0.984326 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3191.43 | −0.273070 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 39478.0 | 3.35830 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3870.49 | −0.327352 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −655.463 | −0.0551178 | −0.0275589 | − | 0.999620i | \(-0.508773\pi\) | ||||
−0.0275589 | + | 0.999620i | \(0.508773\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10838.3 | 0.906168 | 0.453084 | − | 0.891468i | \(-0.350324\pi\) | ||||
0.453084 | + | 0.891468i | \(0.350324\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 907.026 | 0.0754016 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −17310.2 | −1.43082 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2220.50 | 0.182502 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 450.533 | 0.0368201 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 20335.4 | 1.65258 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −14634.8 | −1.18265 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3331.45 | 0.267715 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −18064.1 | −1.44356 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22416.8 | 1.78147 | 0.890733 | − | 0.454526i | \(-0.150191\pi\) | ||||
0.890733 | + | 0.454526i | \(0.150191\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5581.82 | 0.441139 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5254.52 | −0.412989 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −20452.2 | −1.59867 | −0.799334 | − | 0.600886i | \(-0.794814\pi\) | ||||
−0.799334 | + | 0.600886i | \(0.794814\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −7186.07 | −0.558641 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3793.94 | 0.293334 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −332.966 | −0.0256043 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3831.89 | 0.293071 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −16769.9 | −1.27570 | −0.637848 | − | 0.770162i | \(-0.720175\pi\) | ||||
−0.637848 | + | 0.770162i | \(0.720175\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4413.37 | 0.333928 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −13777.4 | −1.03687 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1365.59 | 0.102225 | 0.0511125 | − | 0.998693i | \(-0.483723\pi\) | ||||
0.0511125 | + | 0.998693i | \(0.483723\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5949.52 | −0.443005 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4706.78 | −0.348617 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 20141.2 | 1.48394 | 0.741970 | − | 0.670433i | \(-0.233892\pi\) | ||||
0.741970 | + | 0.670433i | \(0.233892\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16801.5 | −1.23139 | −0.615693 | − | 0.787986i | \(-0.711124\pi\) | ||||
−0.615693 | + | 0.787986i | \(0.711124\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5286.53 | −0.385424 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6754.55 | −0.489886 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11696.0 | 0.843869 | 0.421935 | − | 0.906626i | \(-0.361351\pi\) | ||||
0.421935 | + | 0.906626i | \(0.361351\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7496.06 | 0.538041 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −786.189 | −0.0561387 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −15714.6 | −1.11635 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 11021.1 | 0.778915 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5954.62 | 0.418694 | 0.209347 | − | 0.977841i | \(-0.432866\pi\) | ||||
0.209347 | + | 0.977841i | \(0.432866\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −19974.3 | −1.39733 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5389.88 | 0.375144 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −15990.8 | −1.10736 | −0.553680 | − | 0.832729i | \(-0.686777\pi\) | ||||
−0.553680 | + | 0.832729i | \(0.686777\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8841.29 | −0.609173 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3083.06 | 0.211359 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12031.8 | 0.820710 | 0.410355 | − | 0.911926i | \(-0.365405\pi\) | ||||
0.410355 | + | 0.911926i | \(0.365405\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9585.65 | 0.650593 | 0.325297 | − | 0.945612i | \(-0.394536\pi\) | ||||
0.325297 | + | 0.945612i | \(0.394536\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 12424.4 | 0.839075 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −30734.1 | −2.06532 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 355.950 | 0.0238016 | 0.0119008 | − | 0.999929i | \(-0.496212\pi\) | ||||
0.0119008 | + | 0.999929i | \(0.496212\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 467.104 | 0.0310805 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 30724.3 | 2.03432 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4428.45 | −0.291783 | −0.145892 | − | 0.989301i | \(-0.546605\pi\) | ||||
−0.145892 | + | 0.989301i | \(0.546605\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5222.02 | −0.342394 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −127.787 | −0.00833794 | −0.00416897 | − | 0.999991i | \(-0.501327\pi\) | ||||
−0.00416897 | + | 0.999991i | \(0.501327\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 27816.0 | 1.80617 | 0.903086 | − | 0.429459i | \(-0.141296\pi\) | ||||
0.903086 | + | 0.429459i | \(0.141296\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −10486.1 | −0.677608 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −9667.47 | −0.621700 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5414.86 | −0.346551 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −15897.9 | −1.01260 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 30622.1 | 1.94115 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −631.928 | −0.0398679 | −0.0199340 | − | 0.999801i | \(-0.506346\pi\) | ||||
−0.0199340 | + | 0.999801i | \(0.506346\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1351.86 | 0.0848840 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5315.52 | −0.332189 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −14058.7 | −0.874450 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 13676.9 | 0.846712 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −18761.8 | −1.15608 | −0.578040 | − | 0.816008i | \(-0.696182\pi\) | ||||
−0.578040 | + | 0.816008i | \(0.696182\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4443.65 | 0.272536 | 0.136268 | − | 0.990672i | \(-0.456489\pi\) | ||||
0.136268 | + | 0.990672i | \(0.456489\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1133.33 | −0.0691855 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7906.38 | 0.480420 | 0.240210 | − | 0.970721i | \(-0.422784\pi\) | ||||
0.240210 | + | 0.970721i | \(0.422784\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1328.75 | −0.0803669 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2459.21 | −0.148055 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −25497.5 | −1.52802 | −0.764008 | − | 0.645207i | \(-0.776771\pi\) | ||||
−0.764008 | + | 0.645207i | \(0.776771\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −523.354 | −0.0312201 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 15906.9 | 0.944575 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −16034.5 | −0.947826 | −0.473913 | − | 0.880572i | \(-0.657159\pi\) | ||||
−0.473913 | + | 0.880572i | \(0.657159\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17019.8 | 1.00150 | 0.500752 | − | 0.865591i | \(-0.333057\pi\) | ||||
0.500752 | + | 0.865591i | \(0.333057\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −10722.5 | −0.628096 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −10202.0 | −0.594914 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3478.49 | −0.201930 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −7338.83 | −0.424119 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 21193.8 | 1.21934 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14092.3 | −0.807161 | −0.403580 | − | 0.914944i | \(-0.632234\pi\) | ||||
−0.403580 | + | 0.914944i | \(0.632234\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4922.97 | 0.280719 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −26148.5 | −1.48444 | −0.742221 | − | 0.670155i | \(-0.766228\pi\) | ||||
−0.742221 | + | 0.670155i | \(0.766228\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5849.17 | 0.330590 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3408.69 | −0.191808 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 11340.0 | 0.635303 | 0.317651 | − | 0.948208i | \(-0.397106\pi\) | ||||
0.317651 | + | 0.948208i | \(0.397106\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11017.7 | 0.614545 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5733.63 | 0.318416 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −12230.1 | −0.676241 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9692.86 | −0.533623 | −0.266812 | − | 0.963749i | \(-0.585970\pi\) | ||||
−0.266812 | + | 0.963749i | \(0.585970\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 16077.3 | 0.881278 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −238.898 | −0.0130387 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −41731.1 | −2.26783 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 10804.5 | 0.584638 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10537.1 | 0.567731 | 0.283866 | − | 0.958864i | \(-0.408383\pi\) | ||||
0.283866 | + | 0.958864i | \(0.408383\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 35335.0 | 1.89571 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −7889.81 | −0.421486 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4517.44 | 0.240305 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −34974.1 | −1.85258 | −0.926291 | − | 0.376809i | \(-0.877021\pi\) | ||||
−0.926291 | + | 0.376809i | \(0.877021\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −851.754 | −0.0449272 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 18313.6 | 0.961919 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −32504.3 | −1.70013 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4027.76 | −0.209790 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 31466.9 | 1.63215 | 0.816075 | − | 0.577946i | \(-0.196146\pi\) | ||||
0.816075 | + | 0.577946i | \(0.196146\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3623.27 | −0.187154 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 9807.98 | 0.504513 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1633.06 | 0.0836556 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 18510.7 | 0.944325 | 0.472162 | − | 0.881512i | \(-0.343474\pi\) | ||||
0.472162 | + | 0.881512i | \(0.343474\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −7999.70 | −0.406427 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9056.83 | −0.458248 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20105.0 | 1.01309 | 0.506546 | − | 0.862213i | \(-0.330922\pi\) | ||||
0.506546 | + | 0.862213i | \(0.330922\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3610.18 | 0.181175 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −36643.3 | −1.83144 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9123.58 | −0.454149 | −0.227075 | − | 0.973877i | \(-0.572916\pi\) | ||||
−0.227075 | + | 0.973877i | \(0.572916\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −12372.8 | −0.613394 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 19900.9 | 0.982631 | 0.491316 | − | 0.870982i | \(-0.336516\pi\) | ||||
0.491316 | + | 0.870982i | \(0.336516\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5164.86 | −0.253994 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2011.13 | −0.0985054 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −16615.1 | −0.810553 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 33574.3 | 1.63135 | 0.815674 | − | 0.578512i | \(-0.196366\pi\) | ||||
0.815674 | + | 0.578512i | \(0.196366\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1215.63 | −0.0588314 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −22598.7 | −1.08934 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11310.4 | 0.543045 | 0.271523 | − | 0.962432i | \(-0.412473\pi\) | ||||
0.271523 | + | 0.962432i | \(0.412473\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 14576.1 | 0.697072 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −21252.7 | −1.01236 | −0.506182 | − | 0.862426i | \(-0.668944\pi\) | ||||
−0.506182 | + | 0.862426i | \(0.668944\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5965.53 | −0.283050 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −22616.7 | −1.06890 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1034.12 | −0.0486831 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3825.74 | 0.179401 | 0.0897006 | − | 0.995969i | \(-0.471409\pi\) | ||||
0.0897006 | + | 0.995969i | \(0.471409\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5961.43 | −0.278464 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 22840.1 | 1.06275 | 0.531373 | − | 0.847138i | \(-0.321676\pi\) | ||||
0.531373 | + | 0.847138i | \(0.321676\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8597.74 | −0.398503 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4350.40 | 0.200862 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −48153.8 | −2.21475 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −40337.1 | −1.84811 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2535.25 | 0.115712 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −21356.1 | −0.970996 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 19668.2 | 0.890845 | 0.445422 | − | 0.895321i | \(-0.353054\pi\) | ||||
0.445422 | + | 0.895321i | \(0.353054\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 13895.0 | 0.626966 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6754.57 | −0.303622 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16494.4 | 0.738629 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3140.62 | 0.140108 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −38295.1 | −1.70199 | −0.850993 | − | 0.525176i | \(-0.823999\pi\) | ||||
−0.850993 | + | 0.525176i | \(0.823999\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −63050.5 | −2.79170 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −24730.2 | −1.09088 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −46914.0 | −2.06172 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9353.79 | 0.409537 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 187.263 | 0.00816848 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 425.248 | 0.0184808 | 0.00924038 | − | 0.999957i | \(-0.497059\pi\) | ||||
0.00924038 | + | 0.999957i | \(0.497059\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13172.8 | −0.570359 | −0.285179 | − | 0.958474i | \(-0.592053\pi\) | ||||
−0.285179 | + | 0.958474i | \(0.592053\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6.42066 | −0.000276977 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 16548.2 | 0.711236 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10450.7 | −0.447522 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 12512.4 | 0.533844 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 686.231 | 0.0291713 | 0.0145856 | − | 0.999894i | \(-0.495357\pi\) | ||||
0.0145856 | + | 0.999894i | \(0.495357\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −26137.8 | −1.10706 | −0.553528 | − | 0.832831i | \(-0.686719\pi\) | ||||
−0.553528 | + | 0.832831i | \(0.686719\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −6843.08 | −0.288782 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −11065.6 | −0.465282 | −0.232641 | − | 0.972563i | \(-0.574737\pi\) | ||||
−0.232641 | + | 0.972563i | \(0.574737\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11377.1 | −0.476649 | −0.238325 | − | 0.971186i | \(-0.576598\pi\) | ||||
−0.238325 | + | 0.971186i | \(0.576598\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 630.220 | 0.0263081 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 28850.3 | 1.20000 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −24562.7 | −1.01800 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −13347.6 | −0.551207 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 36828.9 | 1.51546 | 0.757732 | − | 0.652565i | \(-0.226307\pi\) | ||||
0.757732 | + | 0.652565i | \(0.226307\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 841.000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 12469.6 | 0.509461 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7088.69 | −0.288590 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −34892.9 | −1.41551 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4702.47 | −0.190092 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −32397.1 | −1.30500 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21309.6 | 0.855364 | 0.427682 | − | 0.903929i | \(-0.359330\pi\) | ||||
0.427682 | + | 0.903929i | \(0.359330\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −26097.6 | −1.04388 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 31171.7 | 1.24248 | 0.621241 | − | 0.783620i | \(-0.286629\pi\) | ||||
0.621241 | + | 0.783620i | \(0.286629\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 36032.4 | 1.43121 | 0.715605 | − | 0.698505i | \(-0.246151\pi\) | ||||
0.715605 | + | 0.698505i | \(0.246151\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5928.63 | −0.234666 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −10952.3 | −0.432007 | −0.216004 | − | 0.976393i | \(-0.569302\pi\) | ||||
−0.216004 | + | 0.976393i | \(0.569302\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 18738.9 | 0.736581 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 13593.8 | 0.532492 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2512.07 | 0.0980623 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −28518.2 | −1.10942 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 14962.6 | 0.580079 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −14139.1 | −0.546274 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −11601.3 | −0.446693 | −0.223346 | − | 0.974739i | \(-0.571698\pi\) | ||||
−0.223346 | + | 0.974739i | \(0.571698\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5671.25 | 0.217618 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −36417.2 | −1.39265 | −0.696326 | − | 0.717726i | \(-0.745183\pi\) | ||||
−0.696326 | + | 0.717726i | \(0.745183\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −42545.3 | −1.62147 | −0.810737 | − | 0.585410i | \(-0.800933\pi\) | ||||
−0.810737 | + | 0.585410i | \(0.800933\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 265.556 | 0.0100865 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −30330.6 | −1.14814 | −0.574071 | − | 0.818805i | \(-0.694637\pi\) | ||||
−0.574071 | + | 0.818805i | \(0.694637\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6034.79 | −0.227672 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 35510.4 | 1.33518 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −72754.4 | −2.72635 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −16129.2 | −0.602391 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 11344.0 | 0.422259 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4427.70 | −0.164263 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 25097.9 | 0.928003 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1286.68 | −0.0474176 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −27024.3 | −0.992617 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 27338.0 | 1.00082 | 0.500410 | − | 0.865789i | \(-0.333183\pi\) | ||||
0.500410 | + | 0.865789i | \(0.333183\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 11556.0 | 0.421658 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −43560.9 | −1.58423 | −0.792116 | − | 0.610370i | \(-0.791021\pi\) | ||||
−0.792116 | + | 0.610370i | \(0.791021\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5931.42 | 0.215007 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −4235.66 | −0.153034 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −594.172 | −0.0213973 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 45457.6 | 1.63167 | 0.815836 | − | 0.578283i | \(-0.196277\pi\) | ||||
0.815836 | + | 0.578283i | \(0.196277\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 201.360 | 0.00720418 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −31392.9 | −1.11951 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 15209.6 | 0.540636 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −9268.63 | −0.328394 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 6823.03 | 0.240965 | 0.120482 | − | 0.992715i | \(-0.461556\pi\) | ||||
0.120482 | + | 0.992715i | \(0.461556\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 33290.6 | 1.17192 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1292.46 | −0.0453520 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 66703.4 | 2.33308 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9758.66 | 0.340236 | 0.170118 | − | 0.985424i | \(-0.445585\pi\) | ||||
0.170118 | + | 0.985424i | \(0.445585\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2530.58 | −0.0879473 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 40689.7 | 1.40961 | 0.704806 | − | 0.709400i | \(-0.251034\pi\) | ||||
0.704806 | + | 0.709400i | \(0.251034\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 44150.1 | 1.52463 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −6817.38 | −0.234677 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 11970.4 | 0.410757 | 0.205379 | − | 0.978683i | \(-0.434157\pi\) | ||||
0.205379 | + | 0.978683i | \(0.434157\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −36511.5 | −1.24891 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 15243.8 | 0.519784 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −19048.1 | −0.647459 | −0.323729 | − | 0.946150i | \(-0.604937\pi\) | ||||
−0.323729 | + | 0.946150i | \(0.604937\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 25594.7 | 0.867250 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3524.08 | −0.119036 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 12508.5 | 0.421190 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6480.03 | −0.217516 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −42502.9 | −1.42226 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −36292.1 | −1.21066 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 27038.2 | 0.899162 | 0.449581 | − | 0.893240i | \(-0.351573\pi\) | ||||
0.449581 | + | 0.893240i | \(0.351573\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 25390.6 | 0.841759 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −9345.94 | −0.308883 | −0.154442 | − | 0.988002i | \(-0.549358\pi\) | ||||
−0.154442 | + | 0.988002i | \(0.549358\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −271.224 | −0.00893633 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −5325.73 | −0.174933 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4695.57 | 0.153761 | 0.0768806 | − | 0.997040i | \(-0.475504\pi\) | ||||
0.0768806 | + | 0.997040i | \(0.475504\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 72936.5 | 2.38106 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −15260.3 | −0.496661 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 20018.2 | 0.649522 | 0.324761 | − | 0.945796i | \(-0.394716\pi\) | ||||
0.324761 | + | 0.945796i | \(0.394716\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −26095.1 | −0.844119 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −8957.42 | −0.288873 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9581.82 | 0.308073 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12166.3 | −0.389984 | −0.194992 | − | 0.980805i | \(-0.562468\pi\) | ||||
−0.194992 | + | 0.980805i | \(0.562468\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 8350.94 | 0.266877 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −14926.6 | −0.475583 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −33451.4 | −1.06260 | −0.531302 | − | 0.847183i | \(-0.678297\pi\) | ||||
−0.531302 | + | 0.847183i | \(0.678297\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 23612.2 | 0.747805 |
(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 | 1856.4.a.bj.1.8 | 12 | ||
4.3 | odd | 2 | 1856.4.a.bl.1.5 | 12 | |||
8.3 | odd | 2 | 928.4.a.h.1.8 | ✓ | 12 | ||
8.5 | even | 2 | 928.4.a.j.1.5 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
928.4.a.h.1.8 | ✓ | 12 | 8.3 | odd | 2 | ||
928.4.a.j.1.5 | yes | 12 | 8.5 | even | 2 | ||
1856.4.a.bj.1.8 | 12 | 1.1 | even | 1 | trivial | ||
1856.4.a.bl.1.5 | 12 | 4.3 | odd | 2 |