Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1521,4,Mod(1,1521)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1521, 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("1521.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1521 = 3^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1521.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: | \(89.7419051187\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{3}, \sqrt{17})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 13x^{2} + 14x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 39) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(0.829502\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1521.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.12311 | 1.45774 | 0.728869 | − | 0.684653i | \(-0.240046\pi\) | ||||
0.728869 | + | 0.684653i | \(0.240046\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 9.00000 | 1.12500 | ||||||||
\(5\) | −13.4424 | −1.20232 | −0.601161 | − | 0.799128i | \(-0.705295\pi\) | ||||
−0.601161 | + | 0.799128i | \(0.705295\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −31.4219 | −1.69662 | −0.848311 | − | 0.529498i | \(-0.822380\pi\) | ||||
−0.848311 | + | 0.529498i | \(0.822380\pi\) | |||||||
\(8\) | 4.12311 | 0.182217 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −55.4243 | −1.75267 | ||||||||
\(11\) | −40.4962 | −1.11001 | −0.555003 | − | 0.831849i | \(-0.687283\pi\) | ||||
−0.555003 | + | 0.831849i | \(0.687283\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −129.556 | −2.47323 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −55.0000 | −0.859375 | ||||||||
\(17\) | 43.1414 | 0.615490 | 0.307745 | − | 0.951469i | \(-0.400426\pi\) | ||||
0.307745 | + | 0.951469i | \(0.400426\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −26.9779 | −0.325745 | −0.162873 | − | 0.986647i | \(-0.552076\pi\) | ||||
−0.162873 | + | 0.986647i | \(0.552076\pi\) | |||||||
\(20\) | −120.981 | −1.35261 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −166.970 | −1.61810 | ||||||||
\(23\) | 19.0100 | 0.172342 | 0.0861709 | − | 0.996280i | \(-0.472537\pi\) | ||||
0.0861709 | + | 0.996280i | \(0.472537\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 55.6971 | 0.445577 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −282.797 | −1.90870 | ||||||||
\(29\) | 154.111 | 0.986820 | 0.493410 | − | 0.869797i | \(-0.335750\pi\) | ||||
0.493410 | + | 0.869797i | \(0.335750\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 308.270 | 1.78603 | 0.893016 | − | 0.450025i | \(-0.148585\pi\) | ||||
0.893016 | + | 0.450025i | \(0.148585\pi\) | |||||||
\(32\) | −259.756 | −1.43496 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 177.877 | 0.897223 | ||||||||
\(35\) | 422.384 | 2.03988 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 43.5116 | 0.193331 | 0.0966657 | − | 0.995317i | \(-0.469182\pi\) | ||||
0.0966657 | + | 0.995317i | \(0.469182\pi\) | |||||||
\(38\) | −111.233 | −0.474851 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −55.4243 | −0.219084 | ||||||||
\(41\) | −47.8384 | −0.182222 | −0.0911110 | − | 0.995841i | \(-0.529042\pi\) | ||||
−0.0911110 | + | 0.995841i | \(0.529042\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 342.121 | 1.21333 | 0.606663 | − | 0.794959i | \(-0.292508\pi\) | ||||
0.606663 | + | 0.794959i | \(0.292508\pi\) | |||||||
\(44\) | −364.466 | −1.24876 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 78.3802 | 0.251229 | ||||||||
\(47\) | −133.468 | −0.414218 | −0.207109 | − | 0.978318i | \(-0.566406\pi\) | ||||
−0.207109 | + | 0.978318i | \(0.566406\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 644.334 | 1.87853 | ||||||||
\(50\) | 229.645 | 0.649535 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 438.454 | 1.13635 | 0.568173 | − | 0.822909i | \(-0.307650\pi\) | ||||
0.568173 | + | 0.822909i | \(0.307650\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 544.364 | 1.33458 | ||||||||
\(56\) | −129.556 | −0.309154 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 635.418 | 1.43852 | ||||||||
\(59\) | −590.553 | −1.30311 | −0.651555 | − | 0.758601i | \(-0.725883\pi\) | ||||
−0.651555 | + | 0.758601i | \(0.725883\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −541.304 | −1.13618 | −0.568089 | − | 0.822967i | \(-0.692317\pi\) | ||||
−0.568089 | + | 0.822967i | \(0.692317\pi\) | |||||||
\(62\) | 1271.03 | 2.60357 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −631.000 | −1.23242 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −230.345 | −0.420018 | −0.210009 | − | 0.977700i | \(-0.567349\pi\) | ||||
−0.210009 | + | 0.977700i | \(0.567349\pi\) | |||||||
\(68\) | 388.273 | 0.692426 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1741.54 | 2.97362 | ||||||||
\(71\) | −449.412 | −0.751203 | −0.375601 | − | 0.926781i | \(-0.622564\pi\) | ||||
−0.375601 | + | 0.926781i | \(0.622564\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −389.711 | −0.624826 | −0.312413 | − | 0.949946i | \(-0.601137\pi\) | ||||
−0.312413 | + | 0.949946i | \(0.601137\pi\) | |||||||
\(74\) | 179.403 | 0.281826 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −242.801 | −0.366464 | ||||||||
\(77\) | 1272.47 | 1.88326 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −897.820 | −1.27864 | −0.639321 | − | 0.768940i | \(-0.720784\pi\) | ||||
−0.639321 | + | 0.768940i | \(0.720784\pi\) | |||||||
\(80\) | 739.330 | 1.03325 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −197.243 | −0.265632 | ||||||||
\(83\) | 1300.24 | 1.71952 | 0.859759 | − | 0.510700i | \(-0.170614\pi\) | ||||
0.859759 | + | 0.510700i | \(0.170614\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −579.923 | −0.740017 | ||||||||
\(86\) | 1410.60 | 1.76871 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −166.970 | −0.202262 | ||||||||
\(89\) | 925.045 | 1.10174 | 0.550869 | − | 0.834592i | \(-0.314297\pi\) | ||||
0.550869 | + | 0.834592i | \(0.314297\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 171.090 | 0.193884 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −550.301 | −0.603822 | ||||||||
\(95\) | 362.647 | 0.391651 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1560.49 | −1.63344 | −0.816722 | − | 0.577031i | \(-0.804211\pi\) | ||||
−0.816722 | + | 0.577031i | \(0.804211\pi\) | |||||||
\(98\) | 2656.66 | 2.73840 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 501.274 | 0.501274 | ||||||||
\(101\) | −958.840 | −0.944635 | −0.472318 | − | 0.881428i | \(-0.656582\pi\) | ||||
−0.472318 | + | 0.881428i | \(0.656582\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 635.153 | 0.607606 | 0.303803 | − | 0.952735i | \(-0.401743\pi\) | ||||
0.303803 | + | 0.952735i | \(0.401743\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1807.79 | 1.65649 | ||||||||
\(107\) | 1448.32 | 1.30855 | 0.654275 | − | 0.756257i | \(-0.272974\pi\) | ||||
0.654275 | + | 0.756257i | \(0.272974\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −331.084 | −0.290937 | −0.145468 | − | 0.989363i | \(-0.546469\pi\) | ||||
−0.145468 | + | 0.989363i | \(0.546469\pi\) | |||||||
\(110\) | 2244.47 | 1.94547 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1728.20 | 1.45803 | ||||||||
\(113\) | −695.204 | −0.578755 | −0.289378 | − | 0.957215i | \(-0.593448\pi\) | ||||
−0.289378 | + | 0.957215i | \(0.593448\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −255.539 | −0.207210 | ||||||||
\(116\) | 1387.00 | 1.11017 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2434.91 | −1.89959 | ||||||||
\(119\) | −1355.58 | −1.04425 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 308.940 | 0.232111 | ||||||||
\(122\) | −2231.85 | −1.65625 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2774.43 | 2.00929 | ||||||||
\(125\) | 931.594 | 0.666595 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 247.154 | 0.172688 | 0.0863441 | − | 0.996265i | \(-0.472482\pi\) | ||||
0.0863441 | + | 0.996265i | \(0.472482\pi\) | |||||||
\(128\) | −523.634 | −0.361587 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −472.243 | −0.314962 | −0.157481 | − | 0.987522i | \(-0.550337\pi\) | ||||
−0.157481 | + | 0.987522i | \(0.550337\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 847.697 | 0.552667 | ||||||||
\(134\) | −949.739 | −0.612275 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 177.877 | 0.112153 | ||||||||
\(137\) | 1830.70 | 1.14166 | 0.570829 | − | 0.821069i | \(-0.306622\pi\) | ||||
0.570829 | + | 0.821069i | \(0.306622\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −100.000 | −0.0610208 | −0.0305104 | − | 0.999534i | \(-0.509713\pi\) | ||||
−0.0305104 | + | 0.999534i | \(0.509713\pi\) | |||||||
\(140\) | 3801.46 | 2.29487 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1852.97 | −1.09506 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2071.62 | −1.18647 | ||||||||
\(146\) | −1606.82 | −0.910832 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 391.604 | 0.217498 | ||||||||
\(149\) | −149.557 | −0.0822293 | −0.0411147 | − | 0.999154i | \(-0.513091\pi\) | ||||
−0.0411147 | + | 0.999154i | \(0.513091\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −800.032 | −0.431163 | −0.215582 | − | 0.976486i | \(-0.569165\pi\) | ||||
−0.215582 | + | 0.976486i | \(0.569165\pi\) | |||||||
\(152\) | −111.233 | −0.0593564 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 5246.51 | 2.74530 | ||||||||
\(155\) | −4143.88 | −2.14739 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2706.16 | −1.37564 | −0.687818 | − | 0.725884i | \(-0.741431\pi\) | ||||
−0.687818 | + | 0.725884i | \(0.741431\pi\) | |||||||
\(158\) | −3701.81 | −1.86392 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3491.73 | 1.72528 | ||||||||
\(161\) | −597.330 | −0.292399 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3678.25 | 1.76750 | 0.883750 | − | 0.467959i | \(-0.155010\pi\) | ||||
0.883750 | + | 0.467959i | \(0.155010\pi\) | |||||||
\(164\) | −430.546 | −0.205000 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5361.03 | 2.50661 | ||||||||
\(167\) | 3223.11 | 1.49348 | 0.746742 | − | 0.665114i | \(-0.231617\pi\) | ||||
0.746742 | + | 0.665114i | \(0.231617\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −2391.08 | −1.07875 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3079.09 | 1.36499 | ||||||||
\(173\) | 2689.54 | 1.18198 | 0.590988 | − | 0.806680i | \(-0.298738\pi\) | ||||
0.590988 | + | 0.806680i | \(0.298738\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1750.11 | −0.755976 | ||||||||
\(176\) | 2227.29 | 0.953911 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3814.06 | 1.60604 | ||||||||
\(179\) | 1524.04 | 0.636381 | 0.318191 | − | 0.948027i | \(-0.396925\pi\) | ||||
0.318191 | + | 0.948027i | \(0.396925\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 476.881 | 0.195836 | 0.0979180 | − | 0.995194i | \(-0.468782\pi\) | ||||
0.0979180 | + | 0.995194i | \(0.468782\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 78.3802 | 0.0314036 | ||||||||
\(185\) | −584.899 | −0.232446 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1747.06 | −0.683197 | ||||||||
\(188\) | −1201.21 | −0.465996 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1495.23 | 0.570924 | ||||||||
\(191\) | 1369.74 | 0.518906 | 0.259453 | − | 0.965756i | \(-0.416458\pi\) | ||||
0.259453 | + | 0.965756i | \(0.416458\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2144.72 | −0.799898 | −0.399949 | − | 0.916537i | \(-0.630972\pi\) | ||||
−0.399949 | + | 0.916537i | \(0.630972\pi\) | |||||||
\(194\) | −6434.08 | −2.38113 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5799.01 | 2.11334 | ||||||||
\(197\) | 239.739 | 0.0867040 | 0.0433520 | − | 0.999060i | \(-0.486196\pi\) | ||||
0.0433520 | + | 0.999060i | \(0.486196\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1589.94 | −0.566371 | −0.283185 | − | 0.959065i | \(-0.591391\pi\) | ||||
−0.283185 | + | 0.959065i | \(0.591391\pi\) | |||||||
\(200\) | 229.645 | 0.0811918 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −3953.40 | −1.37703 | ||||||||
\(203\) | −4842.47 | −1.67426 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 643.061 | 0.219090 | ||||||||
\(206\) | 2618.80 | 0.885731 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1092.50 | 0.361579 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1872.85 | −0.611055 | −0.305527 | − | 0.952183i | \(-0.598833\pi\) | ||||
−0.305527 | + | 0.952183i | \(0.598833\pi\) | |||||||
\(212\) | 3946.09 | 1.27839 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 5971.59 | 1.90752 | ||||||||
\(215\) | −4598.92 | −1.45881 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9686.43 | −3.03022 | ||||||||
\(218\) | −1365.09 | −0.424109 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 4899.28 | 1.50141 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −56.1283 | −0.0168548 | −0.00842742 | − | 0.999964i | \(-0.502683\pi\) | ||||
−0.00842742 | + | 0.999964i | \(0.502683\pi\) | |||||||
\(224\) | 8162.01 | 2.43459 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2866.40 | −0.843673 | ||||||||
\(227\) | 667.390 | 0.195137 | 0.0975687 | − | 0.995229i | \(-0.468893\pi\) | ||||
0.0975687 | + | 0.995229i | \(0.468893\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 723.299 | 0.208720 | 0.104360 | − | 0.994540i | \(-0.466721\pi\) | ||||
0.104360 | + | 0.994540i | \(0.466721\pi\) | |||||||
\(230\) | −1053.62 | −0.302058 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 635.418 | 0.179816 | ||||||||
\(233\) | 275.451 | 0.0774482 | 0.0387241 | − | 0.999250i | \(-0.487671\pi\) | ||||
0.0387241 | + | 0.999250i | \(0.487671\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1794.12 | 0.498024 | ||||||||
\(236\) | −5314.98 | −1.46600 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −5589.22 | −1.52225 | ||||||||
\(239\) | 1529.39 | 0.413925 | 0.206963 | − | 0.978349i | \(-0.433642\pi\) | ||||
0.206963 | + | 0.978349i | \(0.433642\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 975.526 | 0.260743 | 0.130372 | − | 0.991465i | \(-0.458383\pi\) | ||||
0.130372 | + | 0.991465i | \(0.458383\pi\) | |||||||
\(242\) | 1273.79 | 0.338357 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −4871.74 | −1.27820 | ||||||||
\(245\) | −8661.38 | −2.25859 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 1271.03 | 0.325446 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 3841.06 | 0.971720 | ||||||||
\(251\) | 1874.14 | 0.471294 | 0.235647 | − | 0.971839i | \(-0.424279\pi\) | ||||
0.235647 | + | 0.971839i | \(0.424279\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −769.832 | −0.191300 | ||||||||
\(254\) | 1019.04 | 0.251734 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2889.00 | 0.705322 | ||||||||
\(257\) | 1818.19 | 0.441305 | 0.220653 | − | 0.975352i | \(-0.429181\pi\) | ||||
0.220653 | + | 0.975352i | \(0.429181\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1367.22 | −0.328010 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1947.11 | −0.459132 | ||||||||
\(263\) | −673.799 | −0.157978 | −0.0789890 | − | 0.996875i | \(-0.525169\pi\) | ||||
−0.0789890 | + | 0.996875i | \(0.525169\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5893.86 | −1.36625 | ||||||||
\(266\) | 3495.14 | 0.805643 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2073.11 | −0.472520 | ||||||||
\(269\) | 3356.40 | 0.760756 | 0.380378 | − | 0.924831i | \(-0.375794\pi\) | ||||
0.380378 | + | 0.924831i | \(0.375794\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8915.55 | 1.99845 | 0.999227 | − | 0.0393133i | \(-0.0125170\pi\) | ||||
0.999227 | + | 0.0393133i | \(0.0125170\pi\) | |||||||
\(272\) | −2372.78 | −0.528937 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 7548.16 | 1.66424 | ||||||||
\(275\) | −2255.52 | −0.494593 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4017.31 | 0.871396 | 0.435698 | − | 0.900093i | \(-0.356502\pi\) | ||||
0.435698 | + | 0.900093i | \(0.356502\pi\) | |||||||
\(278\) | −412.311 | −0.0889523 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1741.54 | 0.371702 | ||||||||
\(281\) | −1841.12 | −0.390860 | −0.195430 | − | 0.980718i | \(-0.562610\pi\) | ||||
−0.195430 | + | 0.980718i | \(0.562610\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4849.40 | 1.01861 | 0.509305 | − | 0.860586i | \(-0.329902\pi\) | ||||
0.509305 | + | 0.860586i | \(0.329902\pi\) | |||||||
\(284\) | −4044.71 | −0.845103 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1503.17 | 0.309162 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3051.82 | −0.621172 | ||||||||
\(290\) | −8541.52 | −1.72957 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −3507.40 | −0.702929 | ||||||||
\(293\) | 1413.85 | 0.281905 | 0.140953 | − | 0.990016i | \(-0.454983\pi\) | ||||
0.140953 | + | 0.990016i | \(0.454983\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7938.43 | 1.56676 | ||||||||
\(296\) | 179.403 | 0.0352283 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −616.639 | −0.119869 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10750.1 | −2.05856 | ||||||||
\(302\) | −3298.62 | −0.628523 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1483.79 | 0.279937 | ||||||||
\(305\) | 7276.41 | 1.36605 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4625.64 | −0.859932 | −0.429966 | − | 0.902845i | \(-0.641474\pi\) | ||||
−0.429966 | + | 0.902845i | \(0.641474\pi\) | |||||||
\(308\) | 11452.2 | 2.11867 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −17085.7 | −3.13032 | ||||||||
\(311\) | 6060.79 | 1.10507 | 0.552534 | − | 0.833490i | \(-0.313661\pi\) | ||||
0.552534 | + | 0.833490i | \(0.313661\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 969.946 | 0.175158 | 0.0875792 | − | 0.996158i | \(-0.472087\pi\) | ||||
0.0875792 | + | 0.996158i | \(0.472087\pi\) | |||||||
\(314\) | −11157.8 | −2.00532 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8080.38 | −1.43847 | ||||||||
\(317\) | −8741.63 | −1.54883 | −0.774414 | − | 0.632679i | \(-0.781955\pi\) | ||||
−0.774414 | + | 0.632679i | \(0.781955\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6240.92 | −1.09537 | ||||||||
\(320\) | 8482.13 | 1.48177 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2462.85 | −0.426241 | ||||||||
\(323\) | −1163.87 | −0.200493 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 15165.8 | 2.57655 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −197.243 | −0.0332040 | ||||||||
\(329\) | 4193.81 | 0.702772 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6987.76 | 1.16037 | 0.580184 | − | 0.814485i | \(-0.302981\pi\) | ||||
0.580184 | + | 0.814485i | \(0.302981\pi\) | |||||||
\(332\) | 11702.2 | 1.93446 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 13289.2 | 2.17711 | ||||||||
\(335\) | 3096.39 | 0.504996 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4156.59 | −0.671881 | −0.335940 | − | 0.941883i | \(-0.609054\pi\) | ||||
−0.335940 | + | 0.941883i | \(0.609054\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −5219.30 | −0.832519 | ||||||||
\(341\) | −12483.8 | −1.98250 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −9468.49 | −1.49053 | ||||||||
\(344\) | 1410.60 | 0.221089 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 11089.3 | 1.72301 | ||||||||
\(347\) | 312.513 | 0.0483475 | 0.0241737 | − | 0.999708i | \(-0.492305\pi\) | ||||
0.0241737 | + | 0.999708i | \(0.492305\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4458.75 | −0.683872 | −0.341936 | − | 0.939723i | \(-0.611083\pi\) | ||||
−0.341936 | + | 0.939723i | \(0.611083\pi\) | |||||||
\(350\) | −7215.88 | −1.10201 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 10519.1 | 1.59281 | ||||||||
\(353\) | 2249.17 | 0.339126 | 0.169563 | − | 0.985519i | \(-0.445764\pi\) | ||||
0.169563 | + | 0.985519i | \(0.445764\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6041.16 | 0.903187 | ||||||||
\(356\) | 8325.41 | 1.23945 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6283.78 | 0.927677 | ||||||||
\(359\) | 7842.79 | 1.15300 | 0.576499 | − | 0.817098i | \(-0.304418\pi\) | ||||
0.576499 | + | 0.817098i | \(0.304418\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6131.19 | −0.893890 | ||||||||
\(362\) | 1966.23 | 0.285478 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5238.64 | 0.751241 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6660.24 | 0.947307 | 0.473653 | − | 0.880711i | \(-0.342935\pi\) | ||||
0.473653 | + | 0.880711i | \(0.342935\pi\) | |||||||
\(368\) | −1045.55 | −0.148106 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −2411.60 | −0.338846 | ||||||||
\(371\) | −13777.1 | −1.92795 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −36.9873 | −0.00513439 | −0.00256720 | − | 0.999997i | \(-0.500817\pi\) | ||||
−0.00256720 | + | 0.999997i | \(0.500817\pi\) | |||||||
\(374\) | −7203.32 | −0.995923 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −550.301 | −0.0754777 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12079.9 | 1.63721 | 0.818603 | − | 0.574360i | \(-0.194749\pi\) | ||||
0.818603 | + | 0.574360i | \(0.194749\pi\) | |||||||
\(380\) | 3263.82 | 0.440607 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 5647.59 | 0.756429 | ||||||||
\(383\) | 10567.4 | 1.40984 | 0.704919 | − | 0.709287i | \(-0.250983\pi\) | ||||
0.704919 | + | 0.709287i | \(0.250983\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −17104.9 | −2.26428 | ||||||||
\(386\) | −8842.90 | −1.16604 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −14044.4 | −1.83763 | ||||||||
\(389\) | 9757.49 | 1.27179 | 0.635893 | − | 0.771778i | \(-0.280632\pi\) | ||||
0.635893 | + | 0.771778i | \(0.280632\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 820.119 | 0.106075 | ||||||||
\(392\) | 2656.66 | 0.342300 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 988.469 | 0.126392 | ||||||||
\(395\) | 12068.8 | 1.53734 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14200.5 | −1.79522 | −0.897612 | − | 0.440786i | \(-0.854700\pi\) | ||||
−0.897612 | + | 0.440786i | \(0.854700\pi\) | |||||||
\(398\) | −6555.48 | −0.825620 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3063.34 | −0.382918 | ||||||||
\(401\) | 12676.4 | 1.57863 | 0.789313 | − | 0.613992i | \(-0.210437\pi\) | ||||
0.789313 | + | 0.613992i | \(0.210437\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −8629.56 | −1.06271 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −19966.0 | −2.44063 | ||||||||
\(407\) | −1762.05 | −0.214599 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1533.68 | 0.185417 | 0.0927083 | − | 0.995693i | \(-0.470448\pi\) | ||||
0.0927083 | + | 0.995693i | \(0.470448\pi\) | |||||||
\(410\) | 2651.41 | 0.319375 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 5716.38 | 0.683557 | ||||||||
\(413\) | 18556.3 | 2.21089 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −17478.3 | −2.06741 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 4504.50 | 0.527087 | ||||||||
\(419\) | 2165.89 | 0.252532 | 0.126266 | − | 0.991996i | \(-0.459701\pi\) | ||||
0.126266 | + | 0.991996i | \(0.459701\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 734.575 | 0.0850380 | 0.0425190 | − | 0.999096i | \(-0.486462\pi\) | ||||
0.0425190 | + | 0.999096i | \(0.486462\pi\) | |||||||
\(422\) | −7721.98 | −0.890758 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1807.79 | 0.207062 | ||||||||
\(425\) | 2402.85 | 0.274248 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 17008.8 | 1.92767 | ||||||||
\(428\) | 13034.9 | 1.47212 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −18961.8 | −2.12656 | ||||||||
\(431\) | 13709.3 | 1.53215 | 0.766073 | − | 0.642754i | \(-0.222208\pi\) | ||||
0.766073 | + | 0.642754i | \(0.222208\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10049.9 | 1.11540 | 0.557701 | − | 0.830042i | \(-0.311684\pi\) | ||||
0.557701 | + | 0.830042i | \(0.311684\pi\) | |||||||
\(434\) | −39938.2 | −4.41727 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2979.76 | −0.327304 | ||||||||
\(437\) | −512.850 | −0.0561395 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8133.47 | −0.884258 | −0.442129 | − | 0.896951i | \(-0.645777\pi\) | ||||
−0.442129 | + | 0.896951i | \(0.645777\pi\) | |||||||
\(440\) | 2244.47 | 0.243184 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2370.78 | 0.254264 | 0.127132 | − | 0.991886i | \(-0.459423\pi\) | ||||
0.127132 | + | 0.991886i | \(0.459423\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −12434.8 | −1.32464 | ||||||||
\(446\) | −231.423 | −0.0245699 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 19827.2 | 2.09095 | ||||||||
\(449\) | −12923.2 | −1.35832 | −0.679158 | − | 0.733992i | \(-0.737655\pi\) | ||||
−0.679158 | + | 0.733992i | \(0.737655\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1937.27 | 0.202267 | ||||||||
\(452\) | −6256.84 | −0.651099 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 2751.72 | 0.284459 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8401.26 | 0.859944 | 0.429972 | − | 0.902842i | \(-0.358523\pi\) | ||||
0.429972 | + | 0.902842i | \(0.358523\pi\) | |||||||
\(458\) | 2982.24 | 0.304260 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2299.85 | −0.233111 | ||||||||
\(461\) | −17627.3 | −1.78088 | −0.890441 | − | 0.455098i | \(-0.849604\pi\) | ||||
−0.890441 | + | 0.455098i | \(0.849604\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5461.81 | −0.548233 | −0.274116 | − | 0.961697i | \(-0.588385\pi\) | ||||
−0.274116 | + | 0.961697i | \(0.588385\pi\) | |||||||
\(464\) | −8476.13 | −0.848048 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1135.72 | 0.112899 | ||||||||
\(467\) | −8262.19 | −0.818691 | −0.409345 | − | 0.912379i | \(-0.634243\pi\) | ||||
−0.409345 | + | 0.912379i | \(0.634243\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7237.89 | 0.712611 | ||||||||
\(470\) | 7397.35 | 0.725988 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2434.91 | −0.237449 | ||||||||
\(473\) | −13854.6 | −1.34680 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1502.59 | −0.145145 | ||||||||
\(476\) | −12200.3 | −1.17479 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 6305.84 | 0.603395 | ||||||||
\(479\) | 1575.87 | 0.150320 | 0.0751601 | − | 0.997171i | \(-0.476053\pi\) | ||||
0.0751601 | + | 0.997171i | \(0.476053\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 4022.20 | 0.380095 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2780.46 | 0.261125 | ||||||||
\(485\) | 20976.7 | 1.96393 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12595.7 | −1.17200 | −0.586001 | − | 0.810310i | \(-0.699299\pi\) | ||||
−0.586001 | + | 0.810310i | \(0.699299\pi\) | |||||||
\(488\) | −2231.85 | −0.207031 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −35711.8 | −3.29244 | ||||||||
\(491\) | 1071.21 | 0.0984586 | 0.0492293 | − | 0.998788i | \(-0.484323\pi\) | ||||
0.0492293 | + | 0.998788i | \(0.484323\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6648.59 | 0.607378 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −16954.9 | −1.53487 | ||||||||
\(497\) | 14121.4 | 1.27451 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1422.30 | −0.127597 | −0.0637985 | − | 0.997963i | \(-0.520322\pi\) | ||||
−0.0637985 | + | 0.997963i | \(0.520322\pi\) | |||||||
\(500\) | 8384.35 | 0.749919 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 7727.28 | 0.687022 | ||||||||
\(503\) | 9349.34 | 0.828760 | 0.414380 | − | 0.910104i | \(-0.363998\pi\) | ||||
0.414380 | + | 0.910104i | \(0.363998\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12889.1 | 1.13576 | ||||||||
\(506\) | −3174.10 | −0.278866 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2224.39 | 0.194274 | ||||||||
\(509\) | −13736.3 | −1.19617 | −0.598086 | − | 0.801432i | \(-0.704072\pi\) | ||||
−0.598086 | + | 0.801432i | \(0.704072\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12245.5 | 1.06009 | ||||||||
\(512\) | 16100.7 | 1.38976 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 7496.58 | 0.643307 | ||||||||
\(515\) | −8537.96 | −0.730538 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5404.93 | 0.459785 | ||||||||
\(518\) | −5637.17 | −0.478153 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11052.3 | −0.929386 | −0.464693 | − | 0.885472i | \(-0.653835\pi\) | ||||
−0.464693 | + | 0.885472i | \(0.653835\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6477.04 | 0.541532 | 0.270766 | − | 0.962645i | \(-0.412723\pi\) | ||||
0.270766 | + | 0.962645i | \(0.412723\pi\) | |||||||
\(524\) | −4250.19 | −0.354332 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2778.14 | −0.230290 | ||||||||
\(527\) | 13299.2 | 1.09929 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11805.6 | −0.970298 | ||||||||
\(530\) | −24301.0 | −1.99164 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 7629.27 | 0.621750 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −19468.9 | −1.57330 | ||||||||
\(536\) | −949.739 | −0.0765344 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 13838.8 | 1.10898 | ||||||||
\(539\) | −26093.1 | −2.08517 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18341.5 | 1.45761 | 0.728803 | − | 0.684723i | \(-0.240077\pi\) | ||||
0.728803 | + | 0.684723i | \(0.240077\pi\) | |||||||
\(542\) | 36759.7 | 2.91322 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −11206.2 | −0.883204 | ||||||||
\(545\) | 4450.55 | 0.349799 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −18943.1 | −1.48071 | −0.740356 | − | 0.672215i | \(-0.765343\pi\) | ||||
−0.740356 | + | 0.672215i | \(0.765343\pi\) | |||||||
\(548\) | 16476.3 | 1.28436 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −9299.75 | −0.720987 | ||||||||
\(551\) | −4157.61 | −0.321452 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 28211.2 | 2.16937 | ||||||||
\(554\) | 16563.8 | 1.27027 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −900.000 | −0.0686484 | ||||||||
\(557\) | −415.532 | −0.0316098 | −0.0158049 | − | 0.999875i | \(-0.505031\pi\) | ||||
−0.0158049 | + | 0.999875i | \(0.505031\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −23231.1 | −1.75303 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −7591.12 | −0.569772 | ||||||||
\(563\) | −18291.8 | −1.36929 | −0.684643 | − | 0.728879i | \(-0.740042\pi\) | ||||
−0.684643 | + | 0.728879i | \(0.740042\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9345.19 | 0.695850 | ||||||||
\(566\) | 19994.6 | 1.48487 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1852.97 | −0.136882 | ||||||||
\(569\) | −4347.47 | −0.320308 | −0.160154 | − | 0.987092i | \(-0.551199\pi\) | ||||
−0.160154 | + | 0.987092i | \(0.551199\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16756.0 | −1.22805 | −0.614024 | − | 0.789288i | \(-0.710450\pi\) | ||||
−0.614024 | + | 0.789288i | \(0.710450\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 6197.74 | 0.450677 | ||||||||
\(575\) | 1058.80 | 0.0767915 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 19974.7 | 1.44117 | 0.720587 | − | 0.693364i | \(-0.243872\pi\) | ||||
0.720587 | + | 0.693364i | \(0.243872\pi\) | |||||||
\(578\) | −12583.0 | −0.905506 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −18644.6 | −1.33478 | ||||||||
\(581\) | −40856.0 | −2.91737 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −17755.7 | −1.26135 | ||||||||
\(584\) | −1606.82 | −0.113854 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5829.47 | 0.410944 | ||||||||
\(587\) | 15748.7 | 1.10735 | 0.553677 | − | 0.832732i | \(-0.313224\pi\) | ||||
0.553677 | + | 0.832732i | \(0.313224\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8316.50 | −0.581792 | ||||||||
\(590\) | 32731.0 | 2.28392 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2393.14 | −0.166144 | ||||||||
\(593\) | −13318.4 | −0.922297 | −0.461148 | − | 0.887323i | \(-0.652562\pi\) | ||||
−0.461148 | + | 0.887323i | \(0.652562\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 18222.3 | 1.25553 | ||||||||
\(596\) | −1346.01 | −0.0925080 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2970.80 | −0.202644 | −0.101322 | − | 0.994854i | \(-0.532307\pi\) | ||||
−0.101322 | + | 0.994854i | \(0.532307\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10632.6 | 0.721654 | 0.360827 | − | 0.932633i | \(-0.382495\pi\) | ||||
0.360827 | + | 0.932633i | \(0.382495\pi\) | |||||||
\(602\) | −44323.8 | −3.00083 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −7200.29 | −0.485059 | ||||||||
\(605\) | −4152.88 | −0.279072 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11587.9 | 0.774856 | 0.387428 | − | 0.921900i | \(-0.373364\pi\) | ||||
0.387428 | + | 0.921900i | \(0.373364\pi\) | |||||||
\(608\) | 7007.67 | 0.467432 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 30001.4 | 1.99135 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 20792.3 | 1.36998 | 0.684988 | − | 0.728555i | \(-0.259808\pi\) | ||||
0.684988 | + | 0.728555i | \(0.259808\pi\) | |||||||
\(614\) | −19072.0 | −1.25356 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 5246.51 | 0.343162 | ||||||||
\(617\) | 1562.78 | 0.101969 | 0.0509846 | − | 0.998699i | \(-0.483764\pi\) | ||||
0.0509846 | + | 0.998699i | \(0.483764\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 758.406 | 0.0492454 | 0.0246227 | − | 0.999697i | \(-0.492162\pi\) | ||||
0.0246227 | + | 0.999697i | \(0.492162\pi\) | |||||||
\(620\) | −37294.9 | −2.41581 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 24989.3 | 1.61090 | ||||||||
\(623\) | −29066.7 | −1.86923 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19485.0 | −1.24704 | ||||||||
\(626\) | 3999.19 | 0.255335 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −24355.4 | −1.54759 | ||||||||
\(629\) | 1877.15 | 0.118994 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14265.2 | −0.899981 | −0.449990 | − | 0.893033i | \(-0.648573\pi\) | ||||
−0.449990 | + | 0.893033i | \(0.648573\pi\) | |||||||
\(632\) | −3701.81 | −0.232990 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −36042.7 | −2.25779 | ||||||||
\(635\) | −3322.34 | −0.207627 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −25732.0 | −1.59677 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 7038.88 | 0.434744 | ||||||||
\(641\) | −3985.64 | −0.245590 | −0.122795 | − | 0.992432i | \(-0.539186\pi\) | ||||
−0.122795 | + | 0.992432i | \(0.539186\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8156.55 | −0.500254 | −0.250127 | − | 0.968213i | \(-0.580472\pi\) | ||||
−0.250127 | + | 0.968213i | \(0.580472\pi\) | |||||||
\(644\) | −5375.97 | −0.328949 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4798.74 | −0.292266 | ||||||||
\(647\) | −11279.2 | −0.685368 | −0.342684 | − | 0.939451i | \(-0.611336\pi\) | ||||
−0.342684 | + | 0.939451i | \(0.611336\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 23915.2 | 1.44646 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 33104.2 | 1.98844 | ||||||||
\(653\) | −6565.75 | −0.393473 | −0.196736 | − | 0.980456i | \(-0.563034\pi\) | ||||
−0.196736 | + | 0.980456i | \(0.563034\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6348.06 | 0.378686 | ||||||||
\(656\) | 2631.11 | 0.156597 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 17291.5 | 1.02446 | ||||||||
\(659\) | −4799.35 | −0.283696 | −0.141848 | − | 0.989888i | \(-0.545304\pi\) | ||||
−0.141848 | + | 0.989888i | \(0.545304\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15593.6 | 0.917581 | 0.458790 | − | 0.888545i | \(-0.348283\pi\) | ||||
0.458790 | + | 0.888545i | \(0.348283\pi\) | |||||||
\(662\) | 28811.3 | 1.69151 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5361.03 | 0.313326 | ||||||||
\(665\) | −11395.1 | −0.664483 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2929.66 | 0.170070 | ||||||||
\(668\) | 29008.0 | 1.68017 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 12766.7 | 0.736152 | ||||||||
\(671\) | 21920.8 | 1.26116 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2205.54 | −0.126326 | −0.0631630 | − | 0.998003i | \(-0.520119\pi\) | ||||
−0.0631630 | + | 0.998003i | \(0.520119\pi\) | |||||||
\(674\) | −17138.1 | −0.979426 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 15046.4 | 0.854182 | 0.427091 | − | 0.904209i | \(-0.359538\pi\) | ||||
0.427091 | + | 0.904209i | \(0.359538\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 49033.6 | 2.77134 | ||||||||
\(680\) | −2391.08 | −0.134844 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −51471.9 | −2.88997 | ||||||||
\(683\) | −30632.5 | −1.71614 | −0.858068 | − | 0.513537i | \(-0.828335\pi\) | ||||
−0.858068 | + | 0.513537i | \(0.828335\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −24608.9 | −1.37264 | ||||||||
\(686\) | −39039.6 | −2.17280 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −18816.7 | −1.04270 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2175.72 | 0.119780 | 0.0598901 | − | 0.998205i | \(-0.480925\pi\) | ||||
0.0598901 | + | 0.998205i | \(0.480925\pi\) | |||||||
\(692\) | 24205.9 | 1.32972 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1288.52 | 0.0704780 | ||||||||
\(695\) | 1344.24 | 0.0733666 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2063.82 | −0.112156 | ||||||||
\(698\) | −18383.9 | −0.996906 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −15751.0 | −0.850473 | ||||||||
\(701\) | 32718.2 | 1.76284 | 0.881419 | − | 0.472335i | \(-0.156589\pi\) | ||||
0.881419 | + | 0.472335i | \(0.156589\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1173.85 | −0.0629768 | ||||||||
\(704\) | 25553.1 | 1.36799 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 9273.58 | 0.494356 | ||||||||
\(707\) | 30128.6 | 1.60269 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −25219.7 | −1.33589 | −0.667945 | − | 0.744211i | \(-0.732826\pi\) | ||||
−0.667945 | + | 0.744211i | \(0.732826\pi\) | |||||||
\(710\) | 24908.3 | 1.31661 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3814.06 | 0.200756 | ||||||||
\(713\) | 5860.22 | 0.307808 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 13716.4 | 0.715929 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 32336.6 | 1.68077 | ||||||||
\(719\) | 35466.2 | 1.83959 | 0.919796 | − | 0.392398i | \(-0.128354\pi\) | ||||
0.919796 | + | 0.392398i | \(0.128354\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −19957.7 | −1.03088 | ||||||||
\(722\) | −25279.5 | −1.30306 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 4291.93 | 0.220315 | ||||||||
\(725\) | 8583.57 | 0.439704 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −14262.2 | −0.727588 | −0.363794 | − | 0.931479i | \(-0.618519\pi\) | ||||
−0.363794 | + | 0.931479i | \(0.618519\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 21599.5 | 1.09511 | ||||||||
\(731\) | 14759.6 | 0.746790 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16022.5 | 0.807371 | 0.403685 | − | 0.914898i | \(-0.367729\pi\) | ||||
0.403685 | + | 0.914898i | \(0.367729\pi\) | |||||||
\(734\) | 27460.9 | 1.38093 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4937.96 | −0.247304 | ||||||||
\(737\) | 9328.11 | 0.466222 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3796.21 | 0.188966 | 0.0944830 | − | 0.995526i | \(-0.469880\pi\) | ||||
0.0944830 | + | 0.995526i | \(0.469880\pi\) | |||||||
\(740\) | −5264.09 | −0.261502 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −56804.3 | −2.81044 | ||||||||
\(743\) | 30329.3 | 1.49754 | 0.748772 | − | 0.662827i | \(-0.230644\pi\) | ||||
0.748772 | + | 0.662827i | \(0.230644\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2010.40 | 0.0988661 | ||||||||
\(746\) | −152.502 | −0.00748460 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −15723.6 | −0.768597 | ||||||||
\(749\) | −45509.1 | −2.22011 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21551.9 | 1.04719 | 0.523595 | − | 0.851967i | \(-0.324591\pi\) | ||||
0.523595 | + | 0.851967i | \(0.324591\pi\) | |||||||
\(752\) | 7340.72 | 0.355969 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 10754.3 | 0.518397 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20417.6 | −0.980306 | −0.490153 | − | 0.871637i | \(-0.663059\pi\) | ||||
−0.490153 | + | 0.871637i | \(0.663059\pi\) | |||||||
\(758\) | 49806.5 | 2.38662 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1495.23 | 0.0713655 | ||||||||
\(761\) | 31375.4 | 1.49456 | 0.747278 | − | 0.664512i | \(-0.231360\pi\) | ||||
0.747278 | + | 0.664512i | \(0.231360\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10403.3 | 0.493609 | ||||||||
\(764\) | 12327.7 | 0.583770 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 43570.5 | 2.05518 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 12452.7 | 0.583946 | 0.291973 | − | 0.956427i | \(-0.405688\pi\) | ||||
0.291973 | + | 0.956427i | \(0.405688\pi\) | |||||||
\(770\) | −70525.5 | −3.30073 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −19302.5 | −0.899885 | ||||||||
\(773\) | 37449.8 | 1.74253 | 0.871264 | − | 0.490815i | \(-0.163301\pi\) | ||||
0.871264 | + | 0.490815i | \(0.163301\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 17169.8 | 0.795815 | ||||||||
\(776\) | −6434.08 | −0.297642 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 40231.2 | 1.85393 | ||||||||
\(779\) | 1290.58 | 0.0593580 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 18199.5 | 0.833839 | ||||||||
\(782\) | 3381.44 | 0.154629 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −35438.4 | −1.61436 | ||||||||
\(785\) | 36377.1 | 1.65396 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −26460.2 | −1.19848 | −0.599240 | − | 0.800570i | \(-0.704530\pi\) | ||||
−0.599240 | + | 0.800570i | \(0.704530\pi\) | |||||||
\(788\) | 2157.65 | 0.0975420 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 49761.0 | 2.24104 | ||||||||
\(791\) | 21844.6 | 0.981928 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −58550.3 | −2.61697 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −14309.4 | −0.637167 | ||||||||
\(797\) | −4749.47 | −0.211085 | −0.105543 | − | 0.994415i | \(-0.533658\pi\) | ||||
−0.105543 | + | 0.994415i | \(0.533658\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5757.99 | −0.254947 | ||||||||
\(800\) | −14467.6 | −0.639386 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 52266.1 | 2.30122 | ||||||||
\(803\) | 15781.8 | 0.693560 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8029.53 | 0.351557 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −3953.40 | −0.172129 | ||||||||
\(809\) | 4464.04 | 0.194002 | 0.0970009 | − | 0.995284i | \(-0.469075\pi\) | ||||
0.0970009 | + | 0.995284i | \(0.469075\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −20774.6 | −0.899499 | −0.449749 | − | 0.893155i | \(-0.648487\pi\) | ||||
−0.449749 | + | 0.893155i | \(0.648487\pi\) | |||||||
\(812\) | −43582.2 | −1.88354 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −7265.13 | −0.312829 | ||||||||
\(815\) | −49444.3 | −2.12510 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9229.73 | −0.395235 | ||||||||
\(818\) | 6323.51 | 0.270289 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 5787.55 | 0.246476 | ||||||||
\(821\) | −35769.2 | −1.52053 | −0.760264 | − | 0.649614i | \(-0.774930\pi\) | ||||
−0.760264 | + | 0.649614i | \(0.774930\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2945.44 | 0.124753 | 0.0623764 | − | 0.998053i | \(-0.480132\pi\) | ||||
0.0623764 | + | 0.998053i | \(0.480132\pi\) | |||||||
\(824\) | 2618.80 | 0.110716 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 76509.6 | 3.22289 | ||||||||
\(827\) | −17878.6 | −0.751753 | −0.375877 | − | 0.926670i | \(-0.622658\pi\) | ||||
−0.375877 | + | 0.926670i | \(0.622658\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13423.8 | 0.562398 | 0.281199 | − | 0.959649i | \(-0.409268\pi\) | ||||
0.281199 | + | 0.959649i | \(0.409268\pi\) | |||||||
\(830\) | −72065.0 | −3.01375 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 27797.5 | 1.15621 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −43326.2 | −1.79565 | ||||||||
\(836\) | 9832.53 | 0.406776 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 8930.21 | 0.368125 | ||||||||
\(839\) | −31542.7 | −1.29794 | −0.648971 | − | 0.760813i | \(-0.724800\pi\) | ||||
−0.648971 | + | 0.760813i | \(0.724800\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −638.669 | −0.0261867 | ||||||||
\(842\) | 3028.73 | 0.123963 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −16855.7 | −0.687437 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9707.47 | −0.393805 | ||||||||
\(848\) | −24115.0 | −0.976547 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 9907.22 | 0.399782 | ||||||||
\(851\) | 827.155 | 0.0333191 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −21810.6 | −0.875476 | −0.437738 | − | 0.899103i | \(-0.644220\pi\) | ||||
−0.437738 | + | 0.899103i | \(0.644220\pi\) | |||||||
\(854\) | 70129.1 | 2.81003 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5971.59 | 0.238440 | ||||||||
\(857\) | −33234.6 | −1.32470 | −0.662352 | − | 0.749193i | \(-0.730442\pi\) | ||||
−0.662352 | + | 0.749193i | \(0.730442\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 42697.7 | 1.69596 | 0.847978 | − | 0.530032i | \(-0.177820\pi\) | ||||
0.847978 | + | 0.530032i | \(0.177820\pi\) | |||||||
\(860\) | −41390.3 | −1.64116 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 56525.0 | 2.23347 | ||||||||
\(863\) | −27419.2 | −1.08153 | −0.540765 | − | 0.841174i | \(-0.681865\pi\) | ||||
−0.540765 | + | 0.841174i | \(0.681865\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −36153.8 | −1.42112 | ||||||||
\(866\) | 41437.0 | 1.62596 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −87177.9 | −3.40900 | ||||||||
\(869\) | 36358.3 | 1.41930 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −1365.09 | −0.0530137 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2114.54 | −0.0818367 | ||||||||
\(875\) | −29272.4 | −1.13096 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 42604.2 | 1.64041 | 0.820206 | − | 0.572068i | \(-0.193859\pi\) | ||||
0.820206 | + | 0.572068i | \(0.193859\pi\) | |||||||
\(878\) | −33535.2 | −1.28902 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −29940.0 | −1.14691 | ||||||||
\(881\) | 4699.40 | 0.179712 | 0.0898562 | − | 0.995955i | \(-0.471359\pi\) | ||||
0.0898562 | + | 0.995955i | \(0.471359\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 22233.5 | 0.847358 | 0.423679 | − | 0.905812i | \(-0.360738\pi\) | ||||
0.423679 | + | 0.905812i | \(0.360738\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 9774.98 | 0.370651 | ||||||||
\(887\) | 8852.46 | 0.335103 | 0.167552 | − | 0.985863i | \(-0.446414\pi\) | ||||
0.167552 | + | 0.985863i | \(0.446414\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7766.05 | −0.292986 | ||||||||
\(890\) | −51270.0 | −1.93098 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −505.155 | −0.0189617 | ||||||||
\(893\) | 3600.68 | 0.134930 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −20486.7 | −0.765135 | ||||||||
\(896\) | 16453.6 | 0.613477 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −53283.7 | −1.98007 | ||||||||
\(899\) | 47508.0 | 1.76249 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 18915.5 | 0.699410 | ||||||||
\(902\) | 7987.58 | 0.294853 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2866.40 | −0.105459 | ||||||||
\(905\) | −6410.41 | −0.235458 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 37172.4 | 1.36085 | 0.680424 | − | 0.732818i | \(-0.261795\pi\) | ||||
0.680424 | + | 0.732818i | \(0.261795\pi\) | |||||||
\(908\) | 6006.51 | 0.219530 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −38035.1 | −1.38327 | −0.691635 | − | 0.722247i | \(-0.743109\pi\) | ||||
−0.691635 | + | 0.722247i | \(0.743109\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −52654.8 | −1.90867 | ||||||||
\(914\) | 34639.3 | 1.25357 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 6509.70 | 0.234810 | ||||||||
\(917\) | 14838.8 | 0.534372 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8352.27 | −0.299800 | −0.149900 | − | 0.988701i | \(-0.547895\pi\) | ||||
−0.149900 | + | 0.988701i | \(0.547895\pi\) | |||||||
\(920\) | −1053.62 | −0.0377573 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −72679.4 | −2.59606 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2423.47 | 0.0861440 | ||||||||
\(926\) | −22519.6 | −0.799179 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −40031.3 | −1.41605 | ||||||||
\(929\) | −20232.1 | −0.714524 | −0.357262 | − | 0.934004i | \(-0.616290\pi\) | ||||
−0.357262 | + | 0.934004i | \(0.616290\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −17382.8 | −0.611921 | ||||||||
\(932\) | 2479.06 | 0.0871292 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −34065.9 | −1.19344 | ||||||||
\(935\) | 23484.7 | 0.821423 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −27766.9 | −0.968095 | −0.484048 | − | 0.875042i | \(-0.660834\pi\) | ||||
−0.484048 | + | 0.875042i | \(0.660834\pi\) | |||||||
\(938\) | 29842.6 | 1.03880 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 16147.1 | 0.560277 | ||||||||
\(941\) | 400.765 | 0.0138837 | 0.00694185 | − | 0.999976i | \(-0.497790\pi\) | ||||
0.00694185 | + | 0.999976i | \(0.497790\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −909.408 | −0.0314045 | ||||||||
\(944\) | 32480.4 | 1.11986 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −57124.0 | −1.96328 | ||||||||
\(947\) | −21804.4 | −0.748201 | −0.374101 | − | 0.927388i | \(-0.622049\pi\) | ||||
−0.374101 | + | 0.927388i | \(0.622049\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −6195.35 | −0.211583 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −5589.22 | −0.190281 | ||||||||
\(953\) | −30480.4 | −1.03605 | −0.518026 | − | 0.855365i | \(-0.673333\pi\) | ||||
−0.518026 | + | 0.855365i | \(0.673333\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −18412.6 | −0.623892 | ||||||||
\(956\) | 13764.5 | 0.465666 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 6497.48 | 0.219127 | ||||||||
\(959\) | −57524.0 | −1.93696 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 65239.6 | 2.18991 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 8779.73 | 0.293336 | ||||||||
\(965\) | 28830.1 | 0.961734 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23864.1 | 0.793608 | 0.396804 | − | 0.917903i | \(-0.370119\pi\) | ||||
0.396804 | + | 0.917903i | \(0.370119\pi\) | |||||||
\(968\) | 1273.79 | 0.0422947 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 86489.2 | 2.86289 | ||||||||
\(971\) | 14010.3 | 0.463040 | 0.231520 | − | 0.972830i | \(-0.425630\pi\) | ||||
0.231520 | + | 0.972830i | \(0.425630\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3142.19 | 0.103529 | ||||||||
\(974\) | −51933.3 | −1.70847 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 29771.7 | 0.976404 | ||||||||
\(977\) | 25448.2 | 0.833326 | 0.416663 | − | 0.909061i | \(-0.363200\pi\) | ||||
0.416663 | + | 0.909061i | \(0.363200\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −37460.8 | −1.22293 | ||||||||
\(980\) | −77952.4 | −2.54092 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 4416.72 | 0.143527 | ||||||||
\(983\) | −52479.9 | −1.70280 | −0.851399 | − | 0.524519i | \(-0.824245\pi\) | ||||
−0.851399 | + | 0.524519i | \(0.824245\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3222.66 | −0.104246 | ||||||||
\(986\) | 27412.8 | 0.885398 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6503.73 | 0.209107 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 38048.5 | 1.21963 | 0.609814 | − | 0.792545i | \(-0.291244\pi\) | ||||
0.609814 | + | 0.792545i | \(0.291244\pi\) | |||||||
\(992\) | −80075.0 | −2.56289 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 58223.9 | 1.85790 | ||||||||
\(995\) | 21372.5 | 0.680960 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −31236.6 | −0.992251 | −0.496125 | − | 0.868251i | \(-0.665244\pi\) | ||||
−0.496125 | + | 0.868251i | \(0.665244\pi\) | |||||||
\(998\) | −5864.30 | −0.186003 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1521.4.a.z.1.3 | 4 | ||
3.2 | odd | 2 | 507.4.a.k.1.2 | 4 | |||
13.2 | odd | 12 | 117.4.q.d.82.2 | 4 | |||
13.7 | odd | 12 | 117.4.q.d.10.2 | 4 | |||
13.12 | even | 2 | inner | 1521.4.a.z.1.2 | 4 | ||
39.2 | even | 12 | 39.4.j.b.4.1 | ✓ | 4 | ||
39.5 | even | 4 | 507.4.b.e.337.3 | 4 | |||
39.8 | even | 4 | 507.4.b.e.337.2 | 4 | |||
39.20 | even | 12 | 39.4.j.b.10.1 | yes | 4 | ||
39.38 | odd | 2 | 507.4.a.k.1.3 | 4 | |||
156.59 | odd | 12 | 624.4.bv.c.49.2 | 4 | |||
156.119 | odd | 12 | 624.4.bv.c.433.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.4.j.b.4.1 | ✓ | 4 | 39.2 | even | 12 | ||
39.4.j.b.10.1 | yes | 4 | 39.20 | even | 12 | ||
117.4.q.d.10.2 | 4 | 13.7 | odd | 12 | |||
117.4.q.d.82.2 | 4 | 13.2 | odd | 12 | |||
507.4.a.k.1.2 | 4 | 3.2 | odd | 2 | |||
507.4.a.k.1.3 | 4 | 39.38 | odd | 2 | |||
507.4.b.e.337.2 | 4 | 39.8 | even | 4 | |||
507.4.b.e.337.3 | 4 | 39.5 | even | 4 | |||
624.4.bv.c.49.2 | 4 | 156.59 | odd | 12 | |||
624.4.bv.c.433.1 | 4 | 156.119 | odd | 12 | |||
1521.4.a.z.1.2 | 4 | 13.12 | even | 2 | inner | ||
1521.4.a.z.1.3 | 4 | 1.1 | even | 1 | trivial |