Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1840,4,Mod(1,1840)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1840, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1840.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1840 = 2^{4} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1840.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: | \(108.563514411\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 5 x^{9} - 192 x^{8} + 762 x^{7} + 12246 x^{6} - 33828 x^{5} - 298243 x^{4} + 383603 x^{3} + 2423016 x^{2} + 864576 x + 57408 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | no (minimal twist has level 920) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(-2.78233\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1840.1 |
$q$-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 | ||||||||
\(3\) | 2.78233 | 0.535459 | 0.267730 | − | 0.963494i | \(-0.413727\pi\) | ||||
0.267730 | + | 0.963494i | \(0.413727\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 11.8146 | 0.637930 | 0.318965 | − | 0.947767i | \(-0.396665\pi\) | ||||
0.318965 | + | 0.947767i | \(0.396665\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −19.2586 | −0.713283 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.796382 | −0.0218289 | −0.0109145 | − | 0.999940i | \(-0.503474\pi\) | ||||
−0.0109145 | + | 0.999940i | \(0.503474\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 13.0701 | 0.278845 | 0.139423 | − | 0.990233i | \(-0.455475\pi\) | ||||
0.139423 | + | 0.990233i | \(0.455475\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 13.9116 | 0.239465 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −99.3670 | −1.41765 | −0.708825 | − | 0.705385i | \(-0.750774\pi\) | ||||
−0.708825 | + | 0.705385i | \(0.750774\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −54.5930 | −0.659184 | −0.329592 | − | 0.944123i | \(-0.606911\pi\) | ||||
−0.329592 | + | 0.944123i | \(0.606911\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 32.8722 | 0.341586 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 23.0000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −128.707 | −0.917394 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −38.4110 | −0.245956 | −0.122978 | − | 0.992409i | \(-0.539245\pi\) | ||||
−0.122978 | + | 0.992409i | \(0.539245\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 219.099 | 1.26940 | 0.634700 | − | 0.772758i | \(-0.281123\pi\) | ||||
0.634700 | + | 0.772758i | \(0.281123\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.21580 | −0.0116885 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 59.0731 | 0.285291 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 381.602 | 1.69554 | 0.847769 | − | 0.530365i | \(-0.177945\pi\) | ||||
0.847769 | + | 0.530365i | \(0.177945\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 36.3653 | 0.149310 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 266.522 | 1.01521 | 0.507607 | − | 0.861589i | \(-0.330530\pi\) | ||||
0.507607 | + | 0.861589i | \(0.330530\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −41.4155 | −0.146879 | −0.0734395 | − | 0.997300i | \(-0.523398\pi\) | ||||
−0.0734395 | + | 0.997300i | \(0.523398\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −96.2932 | −0.318990 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 314.164 | 0.975012 | 0.487506 | − | 0.873120i | \(-0.337907\pi\) | ||||
0.487506 | + | 0.873120i | \(0.337907\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −203.415 | −0.593045 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −276.472 | −0.759094 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 532.322 | 1.37962 | 0.689812 | − | 0.723989i | \(-0.257693\pi\) | ||||
0.689812 | + | 0.723989i | \(0.257693\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.98191 | −0.00976220 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −151.896 | −0.352966 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 433.619 | 0.956820 | 0.478410 | − | 0.878137i | \(-0.341213\pi\) | ||||
0.478410 | + | 0.878137i | \(0.341213\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 438.950 | 0.921340 | 0.460670 | − | 0.887571i | \(-0.347609\pi\) | ||||
0.460670 | + | 0.887571i | \(0.347609\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −227.534 | −0.455025 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 65.3504 | 0.124703 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 61.2709 | 0.111723 | 0.0558614 | − | 0.998439i | \(-0.482210\pi\) | ||||
0.0558614 | + | 0.998439i | \(0.482210\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 63.9936 | 0.111651 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 652.909 | 1.09135 | 0.545677 | − | 0.837996i | \(-0.316273\pi\) | ||||
0.545677 | + | 0.837996i | \(0.316273\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 373.885 | 0.599452 | 0.299726 | − | 0.954025i | \(-0.403105\pi\) | ||||
0.299726 | + | 0.954025i | \(0.403105\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 69.5582 | 0.107092 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −9.40896 | −0.0139253 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −716.640 | −1.02061 | −0.510306 | − | 0.859993i | \(-0.670468\pi\) | ||||
−0.510306 | + | 0.859993i | \(0.670468\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 161.879 | 0.222056 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1241.01 | −1.64119 | −0.820597 | − | 0.571508i | \(-0.806359\pi\) | ||||
−0.820597 | + | 0.571508i | \(0.806359\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −496.835 | −0.633992 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −106.872 | −0.131700 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −476.408 | −0.567406 | −0.283703 | − | 0.958912i | \(-0.591563\pi\) | ||||
−0.283703 | + | 0.958912i | \(0.591563\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 154.418 | 0.177884 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 609.607 | 0.679713 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −272.965 | −0.294796 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 701.769 | 0.734576 | 0.367288 | − | 0.930107i | \(-0.380286\pi\) | ||||
0.367288 | + | 0.930107i | \(0.380286\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 15.3372 | 0.0155702 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1226.44 | 1.20827 | 0.604134 | − | 0.796883i | \(-0.293519\pi\) | ||||
0.604134 | + | 0.796883i | \(0.293519\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 904.021 | 0.864814 | 0.432407 | − | 0.901679i | \(-0.357664\pi\) | ||||
0.432407 | + | 0.901679i | \(0.357664\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 164.361 | 0.152762 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1888.98 | 1.70668 | 0.853339 | − | 0.521357i | \(-0.174574\pi\) | ||||
0.853339 | + | 0.521357i | \(0.174574\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1887.37 | 1.65851 | 0.829255 | − | 0.558870i | \(-0.188765\pi\) | ||||
0.829255 | + | 0.558870i | \(0.188765\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1061.74 | 0.907892 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −534.175 | −0.444699 | −0.222349 | − | 0.974967i | \(-0.571373\pi\) | ||||
−0.222349 | + | 0.974967i | \(0.571373\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 115.000 | 0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −251.712 | −0.198896 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1173.98 | −0.904361 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1330.37 | −0.999523 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 741.552 | 0.543606 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1754.75 | −1.22605 | −0.613027 | − | 0.790062i | \(-0.710048\pi\) | ||||
−0.613027 | + | 0.790062i | \(0.710048\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −115.231 | −0.0786478 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −983.194 | −0.655741 | −0.327870 | − | 0.944723i | \(-0.606331\pi\) | ||||
−0.327870 | + | 0.944723i | \(0.606331\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −644.996 | −0.420513 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −643.534 | −0.410271 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3174.46 | 1.97965 | 0.989826 | − | 0.142286i | \(-0.0454451\pi\) | ||||
0.989826 | + | 0.142286i | \(0.0454451\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2106.78 | −1.28557 | −0.642787 | − | 0.766045i | \(-0.722222\pi\) | ||||
−0.642787 | + | 0.766045i | \(0.722222\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 874.108 | 0.522079 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −10.4088 | −0.00608690 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −192.055 | −0.109995 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −565.966 | −0.317552 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3228.82 | 1.77527 | 0.887635 | − | 0.460548i | \(-0.152347\pi\) | ||||
0.887635 | + | 0.460548i | \(0.152347\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1843.21 | −0.993368 | −0.496684 | − | 0.867931i | \(-0.665449\pi\) | ||||
−0.496684 | + | 0.867931i | \(0.665449\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1913.67 | 1.01119 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1095.50 | 0.567693 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1104.59 | 0.561503 | 0.280752 | − | 0.959780i | \(-0.409416\pi\) | ||||
0.280752 | + | 0.959780i | \(0.409416\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1481.09 | 0.738732 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 271.736 | 0.133018 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1912.97 | −0.919234 | −0.459617 | − | 0.888117i | \(-0.652013\pi\) | ||||
−0.459617 | + | 0.888117i | \(0.652013\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −11.0790 | −0.00522726 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −257.835 | −0.119472 | −0.0597362 | − | 0.998214i | \(-0.519026\pi\) | ||||
−0.0597362 | + | 0.998214i | \(0.519026\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2026.17 | −0.922245 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1051.39 | 0.470185 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3749.16 | 1.64765 | 0.823824 | − | 0.566846i | \(-0.191836\pi\) | ||||
0.823824 | + | 0.566846i | \(0.191836\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 295.366 | 0.127586 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1206.47 | 0.512338 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2040.75 | −0.852137 | −0.426068 | − | 0.904691i | \(-0.640102\pi\) | ||||
−0.426068 | + | 0.904691i | \(0.640102\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3926.66 | −1.61252 | −0.806261 | − | 0.591561i | \(-0.798512\pi\) | ||||
−0.806261 | + | 0.591561i | \(0.798512\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1221.30 | 0.493340 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1908.01 | 0.758268 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 79.1341 | 0.0309458 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1520.62 | −0.585233 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2334.49 | −0.884386 | −0.442193 | − | 0.896920i | \(-0.645799\pi\) | ||||
−0.442193 | + | 0.896920i | \(0.645799\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4396.43 | 1.63970 | 0.819849 | − | 0.572580i | \(-0.194057\pi\) | ||||
0.819849 | + | 0.572580i | \(0.194057\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 181.826 | 0.0667737 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2513.52 | −0.909039 | −0.454519 | − | 0.890737i | \(-0.650189\pi\) | ||||
−0.454519 | + | 0.890737i | \(0.650189\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1817.29 | 0.647360 | 0.323680 | − | 0.946167i | \(-0.395080\pi\) | ||||
0.323680 | + | 0.946167i | \(0.395080\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 170.476 | 0.0598230 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −453.811 | −0.156903 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1332.61 | 0.454017 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −442.949 | −0.148730 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 43.4769 | 0.0143893 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3223.78 | 1.05182 | 0.525911 | − | 0.850540i | \(-0.323725\pi\) | ||||
0.525911 | + | 0.850540i | \(0.323725\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1816.61 | 0.584375 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −207.077 | −0.0656863 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2588.58 | 0.809789 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1040.27 | 0.320982 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1298.74 | −0.395305 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1399.93 | 0.420387 | 0.210194 | − | 0.977660i | \(-0.432591\pi\) | ||||
0.210194 | + | 0.977660i | \(0.432591\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −481.466 | −0.142657 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4637.45 | −1.35594 | −0.677970 | − | 0.735089i | \(-0.737140\pi\) | ||||
−0.677970 | + | 0.735089i | \(0.737140\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2676.10 | −0.772235 | −0.386117 | − | 0.922450i | \(-0.626184\pi\) | ||||
−0.386117 | + | 0.922450i | \(0.626184\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −26.1788 | −0.00745645 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 119.364 | 0.0335615 | 0.0167807 | − | 0.999859i | \(-0.494658\pi\) | ||||
0.0167807 | + | 0.999859i | \(0.494658\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1570.82 | 0.436039 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1993.93 | −0.546496 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1128.32 | 0.305376 | 0.152688 | − | 0.988274i | \(-0.451207\pi\) | ||||
0.152688 | + | 0.988274i | \(0.451207\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1945.38 | −0.519972 | −0.259986 | − | 0.965612i | \(-0.583718\pi\) | ||||
−0.259986 | + | 0.965612i | \(0.583718\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3925.48 | 1.03630 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1017.07 | −0.265218 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −713.536 | −0.183810 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3452.91 | −0.878792 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3354.62 | 0.843593 | 0.421796 | − | 0.906691i | \(-0.361400\pi\) | ||||
0.421796 | + | 0.906691i | \(0.361400\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −18.3168 | −0.00455165 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1382.36 | −0.339477 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3182.83 | −0.772527 | −0.386263 | − | 0.922388i | \(-0.626234\pi\) | ||||
−0.386263 | + | 0.922388i | \(0.626234\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4508.48 | 1.08163 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 739.743 | 0.175437 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 216.610 | 0.0507861 | 0.0253930 | − | 0.999678i | \(-0.491916\pi\) | ||||
0.0253930 | + | 0.999678i | \(0.491916\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2661.61 | 0.616986 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1325.52 | −0.303823 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2941.31 | 0.666672 | 0.333336 | − | 0.942808i | \(-0.391826\pi\) | ||||
0.333336 | + | 0.942808i | \(0.391826\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5696.98 | 1.27700 | 0.638500 | − | 0.769622i | \(-0.279555\pi\) | ||||
0.638500 | + | 0.769622i | \(0.279555\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 429.642 | 0.0952496 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −19.9096 | −0.00436579 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7180.55 | 1.55754 | 0.778768 | − | 0.627312i | \(-0.215845\pi\) | ||||
0.778768 | + | 0.627312i | \(0.215845\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4219.56 | −0.905442 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 676.626 | 0.143644 | 0.0718222 | − | 0.997417i | \(-0.477119\pi\) | ||||
0.0718222 | + | 0.997417i | \(0.477119\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3513.90 | −0.738092 | −0.369046 | − | 0.929411i | \(-0.620315\pi\) | ||||
−0.369046 | + | 0.929411i | \(0.620315\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −759.478 | −0.157851 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3148.86 | 0.647635 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4960.80 | 1.00973 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1952.55 | 0.393336 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5774.30 | 1.15132 | 0.575662 | − | 0.817688i | \(-0.304744\pi\) | ||||
0.575662 | + | 0.817688i | \(0.304744\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2168.10 | 0.427903 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 102.500 | 0.0200257 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 300.612 | 0.0581433 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −489.308 | −0.0936985 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3412.35 | 0.646978 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2194.75 | 0.412036 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9182.94 | 1.70716 | 0.853580 | − | 0.520962i | \(-0.174427\pi\) | ||||
0.853580 | + | 0.520962i | \(0.174427\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2515.28 | 0.463073 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5497.37 | 1.00234 | 0.501169 | − | 0.865349i | \(-0.332903\pi\) | ||||
0.501169 | + | 0.865349i | \(0.332903\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8163.92 | −1.47429 | −0.737144 | − | 0.675736i | \(-0.763826\pi\) | ||||
−0.737144 | + | 0.675736i | \(0.763826\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1137.67 | −0.203493 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7450.10 | −1.32000 | −0.659999 | − | 0.751267i | \(-0.729443\pi\) | ||||
−0.659999 | + | 0.751267i | \(0.729443\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 30.5898 | 0.00536897 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5255.76 | 0.913857 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5424.74 | 0.934492 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 326.752 | 0.0557691 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5251.30 | 0.888065 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3711.73 | 0.621989 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 413.619 | 0.0686845 | 0.0343422 | − | 0.999410i | \(-0.489066\pi\) | ||||
0.0343422 | + | 0.999410i | \(0.489066\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −7349.13 | −1.20940 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 306.354 | 0.0499640 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5197.04 | 0.840061 | 0.420031 | − | 0.907510i | \(-0.362019\pi\) | ||||
0.420031 | + | 0.907510i | \(0.362019\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1486.25 | −0.238118 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −174.487 | −0.0277097 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6455.68 | −1.01625 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 319.968 | 0.0499318 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2307.38 | 0.356964 | 0.178482 | − | 0.983943i | \(-0.442881\pi\) | ||||
0.178482 | + | 0.983943i | \(0.442881\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6718.97 | −1.03054 | −0.515270 | − | 0.857028i | \(-0.672308\pi\) | ||||
−0.515270 | + | 0.857028i | \(0.672308\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1682.21 | −0.255811 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3970.93 | 0.598728 | 0.299364 | − | 0.954139i | \(-0.403225\pi\) | ||||
0.299364 | + | 0.954139i | \(0.403225\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3264.55 | 0.488068 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3266.41 | −0.484248 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6042.26 | 0.888296 | 0.444148 | − | 0.895953i | \(-0.353506\pi\) | ||||
0.444148 | + | 0.895953i | \(0.353506\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3878.60 | −0.565477 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3701.52 | −0.535204 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1869.43 | 0.268083 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1233.72 | −0.175476 | −0.0877381 | − | 0.996144i | \(-0.527964\pi\) | ||||
−0.0877381 | + | 0.996144i | \(0.527964\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5132.86 | −0.724135 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6289.18 | 0.880103 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 372.550 | 0.0517156 | 0.0258578 | − | 0.999666i | \(-0.491768\pi\) | ||||
0.0258578 | + | 0.999666i | \(0.491768\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 347.791 | 0.0478929 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −502.035 | −0.0685838 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1488.11 | −0.201686 | −0.100843 | − | 0.994902i | \(-0.532154\pi\) | ||||
−0.100843 | + | 0.994902i | \(0.532154\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4882.29 | −0.656503 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6945.88 | −0.926678 | −0.463339 | − | 0.886181i | \(-0.653349\pi\) | ||||
−0.463339 | + | 0.886181i | \(0.653349\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −47.0448 | −0.00622760 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 797.606 | 0.104766 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 988.407 | 0.128828 | 0.0644141 | − | 0.997923i | \(-0.479482\pi\) | ||||
0.0644141 | + | 0.997923i | \(0.479482\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2285.44 | −0.295600 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2735.57 | −0.351123 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3583.20 | −0.456431 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7028.59 | 0.888552 | 0.444276 | − | 0.895890i | \(-0.353461\pi\) | ||||
0.444276 | + | 0.895890i | \(0.353461\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1794.59 | −0.225168 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8768.39 | −1.09195 | −0.545976 | − | 0.837801i | \(-0.683841\pi\) | ||||
−0.545976 | + | 0.837801i | \(0.683841\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2863.65 | 0.353967 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 809.395 | 0.0993065 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −303.901 | −0.0370118 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10656.9 | 1.28838 | 0.644191 | − | 0.764865i | \(-0.277194\pi\) | ||||
0.644191 | + | 0.764865i | \(0.277194\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8832.39 | 1.06002 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5123.05 | 0.610384 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6205.07 | −0.733964 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5861.76 | −0.688373 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13788.2 | −1.60764 | −0.803818 | − | 0.594875i | \(-0.797202\pi\) | ||||
−0.803818 | + | 0.594875i | \(0.797202\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1826.43 | −0.211436 | −0.105718 | − | 0.994396i | \(-0.533714\pi\) | ||||
−0.105718 | + | 0.994396i | \(0.533714\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6050.38 | −0.695460 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2484.17 | −0.283530 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5186.03 | 0.587750 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −28.9607 | −0.00325929 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9130.86 | 1.02046 | 0.510230 | − | 0.860038i | \(-0.329560\pi\) | ||||
0.510230 | + | 0.860038i | \(0.329560\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10619.7 | 1.17864 | 0.589318 | − | 0.807901i | \(-0.299396\pi\) | ||||
0.589318 | + | 0.807901i | \(0.299396\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −534.360 | −0.0588979 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1255.64 | −0.137449 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −17399.5 | −1.89165 | −0.945826 | − | 0.324675i | \(-0.894745\pi\) | ||||
−0.945826 | + | 0.324675i | \(0.894745\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3917.49 | 0.423009 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1827.41 | 0.195988 | 0.0979942 | − | 0.995187i | \(-0.468757\pi\) | ||||
0.0979942 | + | 0.995187i | \(0.468757\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2382.04 | −0.253752 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8983.64 | 0.950585 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11699.1 | −1.22966 | −0.614828 | − | 0.788661i | \(-0.710775\pi\) | ||||
−0.614828 | + | 0.788661i | \(0.710775\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −212.254 | −0.0221610 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5128.43 | −0.531908 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 772.091 | 0.0795521 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7472.63 | −0.764890 | −0.382445 | − | 0.923978i | \(-0.624918\pi\) | ||||
−0.382445 | + | 0.923978i | \(0.624918\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 12789.2 | 1.30054 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10572.2 | −1.06811 | −0.534053 | − | 0.845451i | \(-0.679332\pi\) | ||||
−0.534053 | + | 0.845451i | \(0.679332\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14833.5 | −1.48892 | −0.744461 | − | 0.667666i | \(-0.767293\pi\) | ||||
−0.744461 | + | 0.667666i | \(0.767293\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3048.03 | 0.303977 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10795.7 | 1.06974 | 0.534868 | − | 0.844936i | \(-0.320361\pi\) | ||||
0.534868 | + | 0.844936i | \(0.320361\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 723.892 | 0.0712713 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3073.34 | 0.300662 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 32.9825 | 0.00320621 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1364.83 | −0.131837 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −10251.8 | −0.984062 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 18591.9 | 1.77346 | 0.886730 | − | 0.462287i | \(-0.152971\pi\) | ||||
0.886730 | + | 0.462287i | \(0.152971\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4987.57 | 0.472793 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 756.060 | 0.0712255 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3508.85 | 0.328512 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2239.82 | −0.208410 | −0.104205 | − | 0.994556i | \(-0.533230\pi\) | ||||
−0.104205 | + | 0.994556i | \(0.533230\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −5322.50 | −0.492212 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20077.9 | 1.84543 | 0.922714 | − | 0.385486i | \(-0.125966\pi\) | ||||
0.922714 | + | 0.385486i | \(0.125966\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3816.78 | 0.348680 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 76.6862 | 0.00696321 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7713.88 | 0.696207 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6629.39 | 0.594734 | 0.297367 | − | 0.954763i | \(-0.403892\pi\) | ||||
0.297367 | + | 0.954763i | \(0.403892\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −717.383 | −0.0639727 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 17560.4 | 1.55662 | 0.778308 | − | 0.627882i | \(-0.216078\pi\) | ||||
0.778308 | + | 0.627882i | \(0.216078\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6132.19 | 0.540354 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5637.48 | −0.493825 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 754.641 | 0.0657149 | 0.0328574 | − | 0.999460i | \(-0.489539\pi\) | ||||
0.0328574 | + | 0.999460i | \(0.489539\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4417.32 | 0.382408 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7026.49 | 0.604731 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4520.10 | 0.386756 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −250.195 | −0.0212835 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 10431.4 | 0.882249 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9578.48 | 0.805452 | 0.402726 | − | 0.915320i | \(-0.368063\pi\) | ||||
0.402726 | + | 0.915320i | \(0.368063\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −17200.1 | −1.43806 | −0.719031 | − | 0.694978i | \(-0.755414\pi\) | ||||
−0.719031 | + | 0.694978i | \(0.755414\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 821.804 | 0.0683171 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −21771.3 | −1.79957 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 529.000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8350.92 | −0.682484 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3483.47 | 0.283088 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9444.89 | 0.763249 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5678.02 | −0.456285 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 161.996 | 0.0129455 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13456.9 | 1.06942 | 0.534712 | − | 0.845034i | \(-0.320420\pi\) | ||||
0.534712 | + | 0.845034i | \(0.320420\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −10925.3 | −0.863440 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9436.87 | 0.741709 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20923.9 | 1.63554 | 0.817771 | − | 0.575543i | \(-0.195209\pi\) | ||||
0.817771 | + | 0.575543i | \(0.195209\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8453.58 | −0.657176 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2096.97 | 0.162131 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8466.84 | −0.651079 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5308.71 | 0.406022 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −7522.86 | −0.572269 | −0.286135 | − | 0.958189i | \(-0.592370\pi\) | ||||
−0.286135 | + | 0.958189i | \(0.592370\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −541.304 | −0.0409566 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 220.177 | 0.0165702 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −18991.9 | −1.42169 | −0.710845 | − | 0.703349i | \(-0.751687\pi\) | ||||
−0.710845 | + | 0.703349i | \(0.751687\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2670.88 | −0.198875 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1912.54 | 0.141656 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5469.43 | 0.402971 | 0.201485 | − | 0.979492i | \(-0.435423\pi\) | ||||
0.201485 | + | 0.979492i | \(0.435423\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6785.97 | 0.497345 | 0.248673 | − | 0.968588i | \(-0.420006\pi\) | ||||
0.248673 | + | 0.968588i | \(0.420006\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6495.32 | −0.473553 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 575.000 | 0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10572.1 | −0.762778 | −0.381389 | − | 0.924415i | \(-0.624554\pi\) | ||||
−0.381389 | + | 0.924415i | \(0.624554\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 12232.3 | 0.877992 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −14662.1 | −1.04697 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −423.932 | −0.0301157 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1258.56 | −0.0889489 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7392.04 | −0.519765 | −0.259883 | − | 0.965640i | \(-0.583684\pi\) | ||||
−0.259883 | + | 0.965640i | \(0.583684\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −11961.3 | −0.836769 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6993.43 | −0.486753 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9214.68 | 0.638114 | 0.319057 | − | 0.947735i | \(-0.396634\pi\) | ||||
0.319057 | + | 0.947735i | \(0.396634\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5869.92 | −0.404442 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5056.31 | 0.346635 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7519.28 | 0.512904 | 0.256452 | − | 0.966557i | \(-0.417446\pi\) | ||||
0.256452 | + | 0.966557i | \(0.417446\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19066.1 | 1.29405 | 0.647025 | − | 0.762469i | \(-0.276013\pi\) | ||||
0.647025 | + | 0.762469i | \(0.276013\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1179.99 | −0.0796900 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6651.83 | −0.447000 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16134.2 | 1.07886 | 0.539428 | − | 0.842032i | \(-0.318640\pi\) | ||||
0.539428 | + | 0.842032i | \(0.318640\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1262.65 | −0.0840152 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4106.16 | 0.271878 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4349.49 | 0.286581 | 0.143291 | − | 0.989681i | \(-0.454232\pi\) | ||||
0.143291 | + | 0.989681i | \(0.454232\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3707.76 | 0.243108 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18710.3 | 1.22082 | 0.610412 | − | 0.792084i | \(-0.291004\pi\) | ||||
0.610412 | + | 0.792084i | \(0.291004\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −18079.4 | −1.17395 | −0.586973 | − | 0.809606i | \(-0.699681\pi\) | ||||
−0.586973 | + | 0.809606i | \(0.699681\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2960.26 | −0.191290 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5628.58 | −0.361965 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 120.967 | 0.00770488 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −37918.6 | −2.40368 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1360.87 | −0.0858565 | −0.0429282 | − | 0.999078i | \(-0.513669\pi\) | ||||
−0.0429282 | + | 0.999078i | \(0.513669\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 8969.62 | 0.563208 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8773.75 | −0.548308 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2658.65 | −0.165368 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −12574.1 | −0.778444 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10888.4 | 0.670927 | 0.335464 | − | 0.942053i | \(-0.391107\pi\) | ||||
0.335464 | + | 0.942053i | \(0.391107\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −16758.6 | −1.02783 | −0.513915 | − | 0.857841i | \(-0.671806\pi\) | ||||
−0.513915 | + | 0.857841i | \(0.671806\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −576.157 | −0.0351724 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −415.017 | −0.0252180 | −0.0126090 | − | 0.999921i | \(-0.504014\pi\) | ||||
−0.0126090 | + | 0.999921i | \(0.504014\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −345.327 | −0.0208864 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7202.28 | 0.433609 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −25781.0 | −1.54501 | −0.772503 | − | 0.635011i | \(-0.780995\pi\) | ||||
−0.772503 | + | 0.635011i | \(0.780995\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4915.97 | −0.293256 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −7200.53 | −0.427579 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8667.93 | 0.512374 | 0.256187 | − | 0.966627i | \(-0.417534\pi\) | ||||
0.256187 | + | 0.966627i | \(0.417534\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10039.2 | −0.590740 | −0.295370 | − | 0.955383i | \(-0.595443\pi\) | ||||
−0.295370 | + | 0.955383i | \(0.595443\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3613.51 | −0.211670 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3224.98 | −0.188059 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −883.452 | −0.0512855 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3895.07 | 0.225100 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −349.572 | −0.0201119 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24776.4 | 1.41911 | 0.709554 | − | 0.704651i | \(-0.248896\pi\) | ||||
0.709554 | + | 0.704651i | \(0.248896\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3217.67 | −0.183479 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5458.64 | −0.309885 | −0.154943 | − | 0.987923i | \(-0.549519\pi\) | ||||
−0.154943 | + | 0.987923i | \(0.549519\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8291.14 | 0.468608 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −12902.9 | −0.726051 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −22846.9 | −1.27996 | −0.639981 | − | 0.768391i | \(-0.721058\pi\) | ||||
−0.639981 | + | 0.768391i | \(0.721058\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 15872.3 | 0.885327 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7445.80 | −0.413500 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6957.50 | 0.384702 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9932.95 | 0.546841 | 0.273421 | − | 0.961895i | \(-0.411845\pi\) | ||||
0.273421 | + | 0.961895i | \(0.411845\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 181.204 | 0.00993270 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −10533.9 | −0.574926 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −26483.5 | −1.43922 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 332.111 | 0.0179708 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3272.30 | −0.176310 | −0.0881549 | − | 0.996107i | \(-0.528097\pi\) | ||||
−0.0881549 | + | 0.996107i | \(0.528097\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −20832.8 | −1.11767 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4370.54 | 0.233481 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 14489.9 | 0.770790 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11979.8 | 0.634573 | 0.317287 | − | 0.948330i | \(-0.397228\pi\) | ||||
0.317287 | + | 0.948330i | \(0.397228\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 13801.5 | 0.727985 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5039.29 | 0.264688 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −52.0439 | −0.00272214 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3139.35 | 0.163516 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −33489.7 | −1.73707 | −0.868537 | − | 0.495625i | \(-0.834939\pi\) | ||||
−0.868537 | + | 0.495625i | \(0.834939\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10680.7 | 0.551690 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −5412.70 | −0.278424 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −960.274 | −0.0491913 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −26092.7 | −1.33112 | −0.665559 | − | 0.746345i | \(-0.731807\pi\) | ||||
−0.665559 | + | 0.746345i | \(0.731807\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 6551.25 | 0.332838 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4115.33 | 0.208223 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1802.12 | 0.0908088 | 0.0454044 | − | 0.998969i | \(-0.485542\pi\) | ||||
0.0454044 | + | 0.998969i | \(0.485542\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2829.83 | −0.142013 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −48.7950 | −0.00243879 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −17571.0 | −0.874639 | −0.437319 | − | 0.899306i | \(-0.644072\pi\) | ||||
−0.437319 | + | 0.899306i | \(0.644072\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1985.29 | −0.0984230 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −9110.13 | −0.449823 | −0.224911 | − | 0.974379i | \(-0.572209\pi\) | ||||
−0.224911 | + | 0.974379i | \(0.572209\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 16144.1 | 0.793925 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 23900.3 | 1.17064 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 22317.6 | 1.08874 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5447.61 | −0.264695 | −0.132348 | − | 0.991203i | \(-0.542252\pi\) | ||||
−0.132348 | + | 0.991203i | \(0.542252\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 9333.66 | 0.451710 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −9216.07 | −0.444248 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13631.5 | 0.654486 | 0.327243 | − | 0.944940i | \(-0.393880\pi\) | ||||
0.327243 | + | 0.944940i | \(0.393880\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −50.9633 | −0.00243722 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5851.77 | −0.278747 | −0.139374 | − | 0.990240i | \(-0.544509\pi\) | ||||
−0.139374 | + | 0.990240i | \(0.544509\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 22298.6 | 1.05801 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 9568.37 | 0.452216 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5667.44 | 0.266805 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −36459.9 | −1.70972 | −0.854862 | − | 0.518856i | \(-0.826358\pi\) | ||||
−0.854862 | + | 0.518856i | \(0.826358\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8855.68 | −0.413657 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −28659.7 | −1.33353 | −0.666765 | − | 0.745268i | \(-0.732321\pi\) | ||||
−0.666765 | + | 0.745268i | \(0.732321\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5477.49 | 0.253880 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 12544.1 | 0.579171 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −14550.2 | −0.669213 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −519.965 | −0.0238231 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4943.75 | 0.225639 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5522.96 | 0.251112 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −43165.1 | −1.95511 | −0.977553 | − | 0.210691i | \(-0.932429\pi\) | ||||
−0.977553 | + | 0.210691i | \(0.932429\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 602.680 | 0.0271939 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6311.08 | −0.283687 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5737.11 | 0.256911 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 7405.47 | 0.330371 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −32530.8 | −1.44580 | −0.722898 | − | 0.690955i | \(-0.757190\pi\) | ||||
−0.722898 | + | 0.690955i | \(0.757190\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −31217.6 | −1.38222 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9174.97 | 0.404721 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −297.756 | −0.0130854 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1358.68 | 0.0594873 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8183.69 | 0.356976 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −27629.4 | −1.20074 | −0.600369 | − | 0.799723i | \(-0.704980\pi\) | ||||
−0.600369 | + | 0.799723i | \(0.704980\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −26826.1 | −1.16152 | −0.580758 | − | 0.814076i | \(-0.697244\pi\) | ||||
−0.580758 | + | 0.814076i | \(0.697244\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 15850.9 | 0.683782 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9564.83 | −0.411094 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2260.99 | 0.0968203 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2973.89 | −0.126882 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 647.832 | 0.0275390 | 0.0137695 | − | 0.999905i | \(-0.495617\pi\) | ||||
0.0137695 | + | 0.999905i | \(0.495617\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8631.34 | 0.365577 | 0.182788 | − | 0.983152i | \(-0.441488\pi\) | ||||
0.182788 | + | 0.983152i | \(0.441488\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −55.3949 | −0.00233770 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −32459.8 | −1.36486 | −0.682430 | − | 0.730951i | \(-0.739077\pi\) | ||||
−0.682430 | + | 0.730951i | \(0.739077\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7056.18 | 0.295623 | 0.147811 | − | 0.989016i | \(-0.452777\pi\) | ||||
0.147811 | + | 0.989016i | \(0.452777\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 19978.7 | 0.833998 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 20212.7 | 0.840730 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1289.18 | −0.0534297 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −28199.6 | −1.16454 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 23143.8 | 0.952341 | 0.476171 | − | 0.879353i | \(-0.342024\pi\) | ||||
0.476171 | + | 0.879353i | \(0.342024\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22913.6 | −0.939505 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1882.59 | 0.0769158 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −10130.9 | −0.412441 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −15717.8 | −0.637626 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −9776.84 | −0.395218 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8776.84 | 0.353544 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 27135.9 | 1.08923 | 0.544616 | − | 0.838686i | \(-0.316676\pi\) | ||||
0.544616 | + | 0.838686i | \(0.316676\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5256.94 | 0.210273 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −45885.3 | −1.82895 | −0.914475 | − | 0.404642i | \(-0.867396\pi\) | ||||
−0.914475 | + | 0.404642i | \(0.867396\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −39582.8 | −1.57223 | −0.786116 | − | 0.618079i | \(-0.787911\pi\) | ||||
−0.786116 | + | 0.618079i | \(0.787911\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8761.16 | 0.346782 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −27037.8 | −1.06648 | −0.533242 | − | 0.845963i | \(-0.679027\pi\) | ||||
−0.533242 | + | 0.845963i | \(0.679027\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 18745.8 | 0.736851 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 13802.6 | 0.540669 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 570.719 | 0.0222789 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 800.816 | 0.0311534 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −13515.1 | −0.523961 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1476.83 | 0.0570582 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 17048.2 | 0.656416 | 0.328208 | − | 0.944605i | \(-0.393555\pi\) | ||||
0.328208 | + | 0.944605i | \(0.393555\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 16066.0 | 0.616488 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 41694.6 | 1.59447 | 0.797235 | − | 0.603669i | \(-0.206295\pi\) | ||||
0.797235 | + | 0.603669i | \(0.206295\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −43429.5 | −1.65517 | −0.827587 | − | 0.561338i | \(-0.810287\pi\) | ||||
−0.827587 | + | 0.561338i | \(0.810287\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6032.35 | 0.229125 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −25491.5 | −0.964960 | −0.482480 | − | 0.875907i | \(-0.660264\pi\) | ||||
−0.482480 | + | 0.875907i | \(0.660264\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −20731.7 | −0.782137 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −128.917 | −0.00484725 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −17151.2 | −0.642712 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −10203.7 | −0.381087 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 836.402 | 0.0311334 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −8415.82 | −0.312217 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −52895.2 | −1.95582 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1361.42 | −0.0501718 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −19633.3 | −0.721141 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −27372.8 | −1.00209 | −0.501046 | − | 0.865420i | \(-0.667051\pi\) | ||||
−0.501046 | + | 0.865420i | \(0.667051\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −23619.5 | −0.861837 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 36324.8 | 1.32107 | 0.660535 | − | 0.750796i | \(-0.270330\pi\) | ||||
0.660535 | + | 0.750796i | \(0.270330\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 988.322 | 0.0358255 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 6106.51 | 0.220628 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −11616.1 | −0.418317 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 19730.6 | 0.708217 | 0.354108 | − | 0.935204i | \(-0.384784\pi\) | ||||
0.354108 | + | 0.935204i | \(0.384784\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 25550.0 | 0.914115 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 8533.58 | 0.304319 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9540.04 | 0.339108 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −17410.2 | −0.616857 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 41756.0 | 1.47467 | 0.737336 | − | 0.675526i | \(-0.236083\pi\) | ||||
0.737336 | + | 0.675526i | \(0.236083\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11105.0 | 0.390926 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 15295.5 | 0.536712 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 395.670 | 0.0138394 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9708.13 | 0.338475 | 0.169237 | − | 0.985575i | \(-0.445870\pi\) | ||||
0.169237 | + | 0.985575i | \(0.445870\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −22714.7 | −0.789421 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4191.60 | −0.145210 | −0.0726049 | − | 0.997361i | \(-0.523131\pi\) | ||||
−0.0726049 | + | 0.997361i | \(0.523131\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6130.01 | 0.211687 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −7603.11 | −0.261724 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 5517.16 | 0.189318 | 0.0946588 | − | 0.995510i | \(-0.469824\pi\) | ||||
0.0946588 | + | 0.995510i | \(0.469824\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4886.72 | 0.167154 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −20728.6 | −0.706805 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 42788.0 | 1.45440 | 0.727198 | − | 0.686427i | \(-0.240822\pi\) | ||||
0.727198 | + | 0.686427i | \(0.240822\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −11672.5 | −0.395510 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 85.1109 | 0.00287486 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 37505.0 | 1.26288 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 18213.6 | 0.611379 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −36379.2 | −1.21734 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 21982.1 | 0.733295 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8776.98 | 0.291881 | 0.145940 | − | 0.989293i | \(-0.453379\pi\) | ||||
0.145940 | + | 0.989293i | \(0.453379\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 15093.4 | 0.500382 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −23660.2 | −0.781968 | −0.390984 | − | 0.920397i | \(-0.627865\pi\) | ||||
−0.390984 | + | 0.920397i | \(0.627865\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −24890.8 | −0.820106 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 909.132 | 0.0298621 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −9077.16 | −0.297241 | −0.148620 | − | 0.988894i | \(-0.547483\pi\) | ||||
−0.148620 | + | 0.988894i | \(0.547483\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 379.403 | 0.0123859 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −36348.3 | −1.18299 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 56743.7 | 1.84114 | 0.920571 | − | 0.390576i | \(-0.127724\pi\) | ||||
0.920571 | + | 0.390576i | \(0.127724\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12567.6 | −0.406534 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 10327.3 | 0.333050 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −952.556 | −0.0306264 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −20911.3 | −0.670302 | −0.335151 | − | 0.942165i | \(-0.608787\pi\) | ||||
−0.335151 | + | 0.942165i | \(0.608787\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1150.82 | 0.0367778 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 9086.47 | 0.289508 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −34257.9 | −1.08822 | −0.544112 | − | 0.839013i | \(-0.683133\pi\) | ||||
−0.544112 | + | 0.839013i | \(0.683133\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −49114.7 | −1.55548 |
(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 | 1840.4.a.ba.1.7 | 10 | ||
4.3 | odd | 2 | 920.4.a.h.1.4 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
920.4.a.h.1.4 | ✓ | 10 | 4.3 | odd | 2 | ||
1840.4.a.ba.1.7 | 10 | 1.1 | even | 1 | trivial |