Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1078,4,Mod(1,1078)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1078, 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("1078.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1078 = 2 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1078.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: | \(63.6040589862\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 154) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 1078.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00000 | 0.707107 | ||||||||
\(3\) | 10.0000 | 1.92450 | 0.962250 | − | 0.272166i | \(-0.0877398\pi\) | ||||
0.962250 | + | 0.272166i | \(0.0877398\pi\) | |||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | 14.0000 | 1.25220 | 0.626099 | − | 0.779744i | \(-0.284651\pi\) | ||||
0.626099 | + | 0.779744i | \(0.284651\pi\) | |||||||
\(6\) | 20.0000 | 1.36083 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | 73.0000 | 2.70370 | ||||||||
\(10\) | 28.0000 | 0.885438 | ||||||||
\(11\) | −11.0000 | −0.301511 | ||||||||
\(12\) | 40.0000 | 0.962250 | ||||||||
\(13\) | 16.0000 | 0.341354 | 0.170677 | − | 0.985327i | \(-0.445405\pi\) | ||||
0.170677 | + | 0.985327i | \(0.445405\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 140.000 | 2.40986 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | −108.000 | −1.54081 | −0.770407 | − | 0.637552i | \(-0.779947\pi\) | ||||
−0.770407 | + | 0.637552i | \(0.779947\pi\) | |||||||
\(18\) | 146.000 | 1.91181 | ||||||||
\(19\) | −116.000 | −1.40064 | −0.700322 | − | 0.713827i | \(-0.746960\pi\) | ||||
−0.700322 | + | 0.713827i | \(0.746960\pi\) | |||||||
\(20\) | 56.0000 | 0.626099 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −22.0000 | −0.213201 | ||||||||
\(23\) | 68.0000 | 0.616477 | 0.308239 | − | 0.951309i | \(-0.400260\pi\) | ||||
0.308239 | + | 0.951309i | \(0.400260\pi\) | |||||||
\(24\) | 80.0000 | 0.680414 | ||||||||
\(25\) | 71.0000 | 0.568000 | ||||||||
\(26\) | 32.0000 | 0.241374 | ||||||||
\(27\) | 460.000 | 3.27878 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 122.000 | 0.781201 | 0.390601 | − | 0.920560i | \(-0.372267\pi\) | ||||
0.390601 | + | 0.920560i | \(0.372267\pi\) | |||||||
\(30\) | 280.000 | 1.70403 | ||||||||
\(31\) | 262.000 | 1.51795 | 0.758977 | − | 0.651117i | \(-0.225699\pi\) | ||||
0.758977 | + | 0.651117i | \(0.225699\pi\) | |||||||
\(32\) | 32.0000 | 0.176777 | ||||||||
\(33\) | −110.000 | −0.580259 | ||||||||
\(34\) | −216.000 | −1.08952 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 292.000 | 1.35185 | ||||||||
\(37\) | 130.000 | 0.577618 | 0.288809 | − | 0.957387i | \(-0.406741\pi\) | ||||
0.288809 | + | 0.957387i | \(0.406741\pi\) | |||||||
\(38\) | −232.000 | −0.990404 | ||||||||
\(39\) | 160.000 | 0.656936 | ||||||||
\(40\) | 112.000 | 0.442719 | ||||||||
\(41\) | −204.000 | −0.777060 | −0.388530 | − | 0.921436i | \(-0.627017\pi\) | ||||
−0.388530 | + | 0.921436i | \(0.627017\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −396.000 | −1.40441 | −0.702203 | − | 0.711977i | \(-0.747800\pi\) | ||||
−0.702203 | + | 0.711977i | \(0.747800\pi\) | |||||||
\(44\) | −44.0000 | −0.150756 | ||||||||
\(45\) | 1022.00 | 3.38557 | ||||||||
\(46\) | 136.000 | 0.435915 | ||||||||
\(47\) | −166.000 | −0.515183 | −0.257591 | − | 0.966254i | \(-0.582929\pi\) | ||||
−0.257591 | + | 0.966254i | \(0.582929\pi\) | |||||||
\(48\) | 160.000 | 0.481125 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 142.000 | 0.401637 | ||||||||
\(51\) | −1080.00 | −2.96530 | ||||||||
\(52\) | 64.0000 | 0.170677 | ||||||||
\(53\) | 442.000 | 1.14554 | 0.572768 | − | 0.819718i | \(-0.305870\pi\) | ||||
0.572768 | + | 0.819718i | \(0.305870\pi\) | |||||||
\(54\) | 920.000 | 2.31845 | ||||||||
\(55\) | −154.000 | −0.377552 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1160.00 | −2.69554 | ||||||||
\(58\) | 244.000 | 0.552393 | ||||||||
\(59\) | −702.000 | −1.54903 | −0.774514 | − | 0.632557i | \(-0.782005\pi\) | ||||
−0.774514 | + | 0.632557i | \(0.782005\pi\) | |||||||
\(60\) | 560.000 | 1.20493 | ||||||||
\(61\) | −196.000 | −0.411397 | −0.205699 | − | 0.978615i | \(-0.565947\pi\) | ||||
−0.205699 | + | 0.978615i | \(0.565947\pi\) | |||||||
\(62\) | 524.000 | 1.07336 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 224.000 | 0.427443 | ||||||||
\(66\) | −220.000 | −0.410305 | ||||||||
\(67\) | −416.000 | −0.758545 | −0.379272 | − | 0.925285i | \(-0.623826\pi\) | ||||
−0.379272 | + | 0.925285i | \(0.623826\pi\) | |||||||
\(68\) | −432.000 | −0.770407 | ||||||||
\(69\) | 680.000 | 1.18641 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 492.000 | 0.822390 | 0.411195 | − | 0.911548i | \(-0.365112\pi\) | ||||
0.411195 | + | 0.911548i | \(0.365112\pi\) | |||||||
\(72\) | 584.000 | 0.955904 | ||||||||
\(73\) | −408.000 | −0.654148 | −0.327074 | − | 0.944999i | \(-0.606063\pi\) | ||||
−0.327074 | + | 0.944999i | \(0.606063\pi\) | |||||||
\(74\) | 260.000 | 0.408438 | ||||||||
\(75\) | 710.000 | 1.09312 | ||||||||
\(76\) | −464.000 | −0.700322 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 320.000 | 0.464524 | ||||||||
\(79\) | 600.000 | 0.854497 | 0.427249 | − | 0.904134i | \(-0.359483\pi\) | ||||
0.427249 | + | 0.904134i | \(0.359483\pi\) | |||||||
\(80\) | 224.000 | 0.313050 | ||||||||
\(81\) | 2629.00 | 3.60631 | ||||||||
\(82\) | −408.000 | −0.549464 | ||||||||
\(83\) | 1212.00 | 1.60282 | 0.801411 | − | 0.598114i | \(-0.204083\pi\) | ||||
0.801411 | + | 0.598114i | \(0.204083\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1512.00 | −1.92941 | ||||||||
\(86\) | −792.000 | −0.993065 | ||||||||
\(87\) | 1220.00 | 1.50342 | ||||||||
\(88\) | −88.0000 | −0.106600 | ||||||||
\(89\) | −1146.00 | −1.36490 | −0.682448 | − | 0.730934i | \(-0.739085\pi\) | ||||
−0.682448 | + | 0.730934i | \(0.739085\pi\) | |||||||
\(90\) | 2044.00 | 2.39396 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 272.000 | 0.308239 | ||||||||
\(93\) | 2620.00 | 2.92130 | ||||||||
\(94\) | −332.000 | −0.364289 | ||||||||
\(95\) | −1624.00 | −1.75388 | ||||||||
\(96\) | 320.000 | 0.340207 | ||||||||
\(97\) | 482.000 | 0.504533 | 0.252266 | − | 0.967658i | \(-0.418824\pi\) | ||||
0.252266 | + | 0.967658i | \(0.418824\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −803.000 | −0.815197 | ||||||||
\(100\) | 284.000 | 0.284000 | ||||||||
\(101\) | −1216.00 | −1.19799 | −0.598993 | − | 0.800754i | \(-0.704432\pi\) | ||||
−0.598993 | + | 0.800754i | \(0.704432\pi\) | |||||||
\(102\) | −2160.00 | −2.09678 | ||||||||
\(103\) | −1406.00 | −1.34502 | −0.672511 | − | 0.740087i | \(-0.734784\pi\) | ||||
−0.672511 | + | 0.740087i | \(0.734784\pi\) | |||||||
\(104\) | 128.000 | 0.120687 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 884.000 | 0.810016 | ||||||||
\(107\) | −588.000 | −0.531253 | −0.265627 | − | 0.964076i | \(-0.585579\pi\) | ||||
−0.265627 | + | 0.964076i | \(0.585579\pi\) | |||||||
\(108\) | 1840.00 | 1.63939 | ||||||||
\(109\) | 154.000 | 0.135326 | 0.0676630 | − | 0.997708i | \(-0.478446\pi\) | ||||
0.0676630 | + | 0.997708i | \(0.478446\pi\) | |||||||
\(110\) | −308.000 | −0.266970 | ||||||||
\(111\) | 1300.00 | 1.11163 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1902.00 | −1.58341 | −0.791704 | − | 0.610905i | \(-0.790806\pi\) | ||||
−0.791704 | + | 0.610905i | \(0.790806\pi\) | |||||||
\(114\) | −2320.00 | −1.90603 | ||||||||
\(115\) | 952.000 | 0.771952 | ||||||||
\(116\) | 488.000 | 0.390601 | ||||||||
\(117\) | 1168.00 | 0.922920 | ||||||||
\(118\) | −1404.00 | −1.09533 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1120.00 | 0.852013 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | −392.000 | −0.290902 | ||||||||
\(123\) | −2040.00 | −1.49545 | ||||||||
\(124\) | 1048.00 | 0.758977 | ||||||||
\(125\) | −756.000 | −0.540950 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 64.0000 | 0.0447172 | 0.0223586 | − | 0.999750i | \(-0.492882\pi\) | ||||
0.0223586 | + | 0.999750i | \(0.492882\pi\) | |||||||
\(128\) | 128.000 | 0.0883883 | ||||||||
\(129\) | −3960.00 | −2.70278 | ||||||||
\(130\) | 448.000 | 0.302248 | ||||||||
\(131\) | 1584.00 | 1.05645 | 0.528224 | − | 0.849105i | \(-0.322858\pi\) | ||||
0.528224 | + | 0.849105i | \(0.322858\pi\) | |||||||
\(132\) | −440.000 | −0.290129 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −832.000 | −0.536372 | ||||||||
\(135\) | 6440.00 | 4.10568 | ||||||||
\(136\) | −864.000 | −0.544760 | ||||||||
\(137\) | 998.000 | 0.622371 | 0.311186 | − | 0.950349i | \(-0.399274\pi\) | ||||
0.311186 | + | 0.950349i | \(0.399274\pi\) | |||||||
\(138\) | 1360.00 | 0.838919 | ||||||||
\(139\) | −276.000 | −0.168417 | −0.0842087 | − | 0.996448i | \(-0.526836\pi\) | ||||
−0.0842087 | + | 0.996448i | \(0.526836\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1660.00 | −0.991470 | ||||||||
\(142\) | 984.000 | 0.581517 | ||||||||
\(143\) | −176.000 | −0.102922 | ||||||||
\(144\) | 1168.00 | 0.675926 | ||||||||
\(145\) | 1708.00 | 0.978218 | ||||||||
\(146\) | −816.000 | −0.462552 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 520.000 | 0.288809 | ||||||||
\(149\) | 1318.00 | 0.724663 | 0.362331 | − | 0.932049i | \(-0.381981\pi\) | ||||
0.362331 | + | 0.932049i | \(0.381981\pi\) | |||||||
\(150\) | 1420.00 | 0.772950 | ||||||||
\(151\) | −984.000 | −0.530310 | −0.265155 | − | 0.964206i | \(-0.585423\pi\) | ||||
−0.265155 | + | 0.964206i | \(0.585423\pi\) | |||||||
\(152\) | −928.000 | −0.495202 | ||||||||
\(153\) | −7884.00 | −4.16591 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3668.00 | 1.90078 | ||||||||
\(156\) | 640.000 | 0.328468 | ||||||||
\(157\) | −1706.00 | −0.867221 | −0.433610 | − | 0.901101i | \(-0.642761\pi\) | ||||
−0.433610 | + | 0.901101i | \(0.642761\pi\) | |||||||
\(158\) | 1200.00 | 0.604221 | ||||||||
\(159\) | 4420.00 | 2.20458 | ||||||||
\(160\) | 448.000 | 0.221359 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 5258.00 | 2.55005 | ||||||||
\(163\) | 1168.00 | 0.561257 | 0.280628 | − | 0.959817i | \(-0.409457\pi\) | ||||
0.280628 | + | 0.959817i | \(0.409457\pi\) | |||||||
\(164\) | −816.000 | −0.388530 | ||||||||
\(165\) | −1540.00 | −0.726599 | ||||||||
\(166\) | 2424.00 | 1.13337 | ||||||||
\(167\) | −72.0000 | −0.0333624 | −0.0166812 | − | 0.999861i | \(-0.505310\pi\) | ||||
−0.0166812 | + | 0.999861i | \(0.505310\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1941.00 | −0.883477 | ||||||||
\(170\) | −3024.00 | −1.36430 | ||||||||
\(171\) | −8468.00 | −3.78692 | ||||||||
\(172\) | −1584.00 | −0.702203 | ||||||||
\(173\) | 4328.00 | 1.90203 | 0.951017 | − | 0.309140i | \(-0.100041\pi\) | ||||
0.951017 | + | 0.309140i | \(0.100041\pi\) | |||||||
\(174\) | 2440.00 | 1.06308 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −176.000 | −0.0753778 | ||||||||
\(177\) | −7020.00 | −2.98110 | ||||||||
\(178\) | −2292.00 | −0.965127 | ||||||||
\(179\) | −1924.00 | −0.803388 | −0.401694 | − | 0.915774i | \(-0.631579\pi\) | ||||
−0.401694 | + | 0.915774i | \(0.631579\pi\) | |||||||
\(180\) | 4088.00 | 1.69279 | ||||||||
\(181\) | −2230.00 | −0.915771 | −0.457886 | − | 0.889011i | \(-0.651393\pi\) | ||||
−0.457886 | + | 0.889011i | \(0.651393\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1960.00 | −0.791734 | ||||||||
\(184\) | 544.000 | 0.217958 | ||||||||
\(185\) | 1820.00 | 0.723292 | ||||||||
\(186\) | 5240.00 | 2.06567 | ||||||||
\(187\) | 1188.00 | 0.464573 | ||||||||
\(188\) | −664.000 | −0.257591 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3248.00 | −1.24018 | ||||||||
\(191\) | 2176.00 | 0.824345 | 0.412172 | − | 0.911106i | \(-0.364770\pi\) | ||||
0.412172 | + | 0.911106i | \(0.364770\pi\) | |||||||
\(192\) | 640.000 | 0.240563 | ||||||||
\(193\) | −3126.00 | −1.16588 | −0.582939 | − | 0.812516i | \(-0.698097\pi\) | ||||
−0.582939 | + | 0.812516i | \(0.698097\pi\) | |||||||
\(194\) | 964.000 | 0.356759 | ||||||||
\(195\) | 2240.00 | 0.822614 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1122.00 | −0.405783 | −0.202891 | − | 0.979201i | \(-0.565034\pi\) | ||||
−0.202891 | + | 0.979201i | \(0.565034\pi\) | |||||||
\(198\) | −1606.00 | −0.576432 | ||||||||
\(199\) | 5586.00 | 1.98985 | 0.994927 | − | 0.100597i | \(-0.0320753\pi\) | ||||
0.994927 | + | 0.100597i | \(0.0320753\pi\) | |||||||
\(200\) | 568.000 | 0.200818 | ||||||||
\(201\) | −4160.00 | −1.45982 | ||||||||
\(202\) | −2432.00 | −0.847104 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −4320.00 | −1.48265 | ||||||||
\(205\) | −2856.00 | −0.973033 | ||||||||
\(206\) | −2812.00 | −0.951074 | ||||||||
\(207\) | 4964.00 | 1.66677 | ||||||||
\(208\) | 256.000 | 0.0853385 | ||||||||
\(209\) | 1276.00 | 0.422310 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3372.00 | 1.10018 | 0.550090 | − | 0.835105i | \(-0.314593\pi\) | ||||
0.550090 | + | 0.835105i | \(0.314593\pi\) | |||||||
\(212\) | 1768.00 | 0.572768 | ||||||||
\(213\) | 4920.00 | 1.58269 | ||||||||
\(214\) | −1176.00 | −0.375653 | ||||||||
\(215\) | −5544.00 | −1.75859 | ||||||||
\(216\) | 3680.00 | 1.15922 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 308.000 | 0.0956899 | ||||||||
\(219\) | −4080.00 | −1.25891 | ||||||||
\(220\) | −616.000 | −0.188776 | ||||||||
\(221\) | −1728.00 | −0.525963 | ||||||||
\(222\) | 2600.00 | 0.786039 | ||||||||
\(223\) | −606.000 | −0.181977 | −0.0909883 | − | 0.995852i | \(-0.529003\pi\) | ||||
−0.0909883 | + | 0.995852i | \(0.529003\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5183.00 | 1.53570 | ||||||||
\(226\) | −3804.00 | −1.11964 | ||||||||
\(227\) | −144.000 | −0.0421040 | −0.0210520 | − | 0.999778i | \(-0.506702\pi\) | ||||
−0.0210520 | + | 0.999778i | \(0.506702\pi\) | |||||||
\(228\) | −4640.00 | −1.34777 | ||||||||
\(229\) | 1010.00 | 0.291453 | 0.145726 | − | 0.989325i | \(-0.453448\pi\) | ||||
0.145726 | + | 0.989325i | \(0.453448\pi\) | |||||||
\(230\) | 1904.00 | 0.545852 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 976.000 | 0.276196 | ||||||||
\(233\) | 3790.00 | 1.06563 | 0.532814 | − | 0.846233i | \(-0.321135\pi\) | ||||
0.532814 | + | 0.846233i | \(0.321135\pi\) | |||||||
\(234\) | 2336.00 | 0.652603 | ||||||||
\(235\) | −2324.00 | −0.645111 | ||||||||
\(236\) | −2808.00 | −0.774514 | ||||||||
\(237\) | 6000.00 | 1.64448 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2184.00 | 0.591093 | 0.295546 | − | 0.955328i | \(-0.404498\pi\) | ||||
0.295546 | + | 0.955328i | \(0.404498\pi\) | |||||||
\(240\) | 2240.00 | 0.602464 | ||||||||
\(241\) | 4268.00 | 1.14077 | 0.570386 | − | 0.821377i | \(-0.306794\pi\) | ||||
0.570386 | + | 0.821377i | \(0.306794\pi\) | |||||||
\(242\) | 242.000 | 0.0642824 | ||||||||
\(243\) | 13870.0 | 3.66157 | ||||||||
\(244\) | −784.000 | −0.205699 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −4080.00 | −1.05744 | ||||||||
\(247\) | −1856.00 | −0.478115 | ||||||||
\(248\) | 2096.00 | 0.536678 | ||||||||
\(249\) | 12120.0 | 3.08463 | ||||||||
\(250\) | −1512.00 | −0.382509 | ||||||||
\(251\) | −7922.00 | −1.99216 | −0.996080 | − | 0.0884559i | \(-0.971807\pi\) | ||||
−0.996080 | + | 0.0884559i | \(0.971807\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −748.000 | −0.185875 | ||||||||
\(254\) | 128.000 | 0.0316198 | ||||||||
\(255\) | −15120.0 | −3.71314 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −4002.00 | −0.971354 | −0.485677 | − | 0.874138i | \(-0.661427\pi\) | ||||
−0.485677 | + | 0.874138i | \(0.661427\pi\) | |||||||
\(258\) | −7920.00 | −1.91115 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 896.000 | 0.213721 | ||||||||
\(261\) | 8906.00 | 2.11214 | ||||||||
\(262\) | 3168.00 | 0.747022 | ||||||||
\(263\) | −3960.00 | −0.928457 | −0.464228 | − | 0.885716i | \(-0.653668\pi\) | ||||
−0.464228 | + | 0.885716i | \(0.653668\pi\) | |||||||
\(264\) | −880.000 | −0.205152 | ||||||||
\(265\) | 6188.00 | 1.43444 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −11460.0 | −2.62674 | ||||||||
\(268\) | −1664.00 | −0.379272 | ||||||||
\(269\) | −1878.00 | −0.425664 | −0.212832 | − | 0.977089i | \(-0.568269\pi\) | ||||
−0.212832 | + | 0.977089i | \(0.568269\pi\) | |||||||
\(270\) | 12880.0 | 2.90315 | ||||||||
\(271\) | 4740.00 | 1.06249 | 0.531244 | − | 0.847219i | \(-0.321725\pi\) | ||||
0.531244 | + | 0.847219i | \(0.321725\pi\) | |||||||
\(272\) | −1728.00 | −0.385204 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1996.00 | 0.440083 | ||||||||
\(275\) | −781.000 | −0.171258 | ||||||||
\(276\) | 2720.00 | 0.593206 | ||||||||
\(277\) | 710.000 | 0.154006 | 0.0770032 | − | 0.997031i | \(-0.475465\pi\) | ||||
0.0770032 | + | 0.997031i | \(0.475465\pi\) | |||||||
\(278\) | −552.000 | −0.119089 | ||||||||
\(279\) | 19126.0 | 4.10410 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −90.0000 | −0.0191066 | −0.00955329 | − | 0.999954i | \(-0.503041\pi\) | ||||
−0.00955329 | + | 0.999954i | \(0.503041\pi\) | |||||||
\(282\) | −3320.00 | −0.701075 | ||||||||
\(283\) | 3448.00 | 0.724248 | 0.362124 | − | 0.932130i | \(-0.382052\pi\) | ||||
0.362124 | + | 0.932130i | \(0.382052\pi\) | |||||||
\(284\) | 1968.00 | 0.411195 | ||||||||
\(285\) | −16240.0 | −3.37535 | ||||||||
\(286\) | −352.000 | −0.0727769 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 2336.00 | 0.477952 | ||||||||
\(289\) | 6751.00 | 1.37411 | ||||||||
\(290\) | 3416.00 | 0.691705 | ||||||||
\(291\) | 4820.00 | 0.970974 | ||||||||
\(292\) | −1632.00 | −0.327074 | ||||||||
\(293\) | 2804.00 | 0.559083 | 0.279542 | − | 0.960134i | \(-0.409817\pi\) | ||||
0.279542 | + | 0.960134i | \(0.409817\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9828.00 | −1.93969 | ||||||||
\(296\) | 1040.00 | 0.204219 | ||||||||
\(297\) | −5060.00 | −0.988589 | ||||||||
\(298\) | 2636.00 | 0.512414 | ||||||||
\(299\) | 1088.00 | 0.210437 | ||||||||
\(300\) | 2840.00 | 0.546558 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −1968.00 | −0.374986 | ||||||||
\(303\) | −12160.0 | −2.30552 | ||||||||
\(304\) | −1856.00 | −0.350161 | ||||||||
\(305\) | −2744.00 | −0.515151 | ||||||||
\(306\) | −15768.0 | −2.94574 | ||||||||
\(307\) | −1320.00 | −0.245395 | −0.122698 | − | 0.992444i | \(-0.539155\pi\) | ||||
−0.122698 | + | 0.992444i | \(0.539155\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −14060.0 | −2.58850 | ||||||||
\(310\) | 7336.00 | 1.34405 | ||||||||
\(311\) | 1066.00 | 0.194364 | 0.0971822 | − | 0.995267i | \(-0.469017\pi\) | ||||
0.0971822 | + | 0.995267i | \(0.469017\pi\) | |||||||
\(312\) | 1280.00 | 0.232262 | ||||||||
\(313\) | 9254.00 | 1.67114 | 0.835570 | − | 0.549384i | \(-0.185137\pi\) | ||||
0.835570 | + | 0.549384i | \(0.185137\pi\) | |||||||
\(314\) | −3412.00 | −0.613218 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2400.00 | 0.427249 | ||||||||
\(317\) | −9722.00 | −1.72253 | −0.861265 | − | 0.508156i | \(-0.830327\pi\) | ||||
−0.861265 | + | 0.508156i | \(0.830327\pi\) | |||||||
\(318\) | 8840.00 | 1.55888 | ||||||||
\(319\) | −1342.00 | −0.235541 | ||||||||
\(320\) | 896.000 | 0.156525 | ||||||||
\(321\) | −5880.00 | −1.02240 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12528.0 | 2.15813 | ||||||||
\(324\) | 10516.0 | 1.80316 | ||||||||
\(325\) | 1136.00 | 0.193889 | ||||||||
\(326\) | 2336.00 | 0.396868 | ||||||||
\(327\) | 1540.00 | 0.260435 | ||||||||
\(328\) | −1632.00 | −0.274732 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −3080.00 | −0.513783 | ||||||||
\(331\) | 2620.00 | 0.435070 | 0.217535 | − | 0.976053i | \(-0.430198\pi\) | ||||
0.217535 | + | 0.976053i | \(0.430198\pi\) | |||||||
\(332\) | 4848.00 | 0.801411 | ||||||||
\(333\) | 9490.00 | 1.56171 | ||||||||
\(334\) | −144.000 | −0.0235908 | ||||||||
\(335\) | −5824.00 | −0.949848 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2806.00 | 0.453568 | 0.226784 | − | 0.973945i | \(-0.427179\pi\) | ||||
0.226784 | + | 0.973945i | \(0.427179\pi\) | |||||||
\(338\) | −3882.00 | −0.624713 | ||||||||
\(339\) | −19020.0 | −3.04727 | ||||||||
\(340\) | −6048.00 | −0.964703 | ||||||||
\(341\) | −2882.00 | −0.457680 | ||||||||
\(342\) | −16936.0 | −2.67776 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −3168.00 | −0.496532 | ||||||||
\(345\) | 9520.00 | 1.48562 | ||||||||
\(346\) | 8656.00 | 1.34494 | ||||||||
\(347\) | 5564.00 | 0.860781 | 0.430391 | − | 0.902643i | \(-0.358376\pi\) | ||||
0.430391 | + | 0.902643i | \(0.358376\pi\) | |||||||
\(348\) | 4880.00 | 0.751711 | ||||||||
\(349\) | −10060.0 | −1.54298 | −0.771489 | − | 0.636242i | \(-0.780488\pi\) | ||||
−0.771489 | + | 0.636242i | \(0.780488\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7360.00 | 1.11922 | ||||||||
\(352\) | −352.000 | −0.0533002 | ||||||||
\(353\) | 5102.00 | 0.769269 | 0.384635 | − | 0.923069i | \(-0.374327\pi\) | ||||
0.384635 | + | 0.923069i | \(0.374327\pi\) | |||||||
\(354\) | −14040.0 | −2.10796 | ||||||||
\(355\) | 6888.00 | 1.02979 | ||||||||
\(356\) | −4584.00 | −0.682448 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3848.00 | −0.568081 | ||||||||
\(359\) | 7976.00 | 1.17258 | 0.586291 | − | 0.810100i | \(-0.300587\pi\) | ||||
0.586291 | + | 0.810100i | \(0.300587\pi\) | |||||||
\(360\) | 8176.00 | 1.19698 | ||||||||
\(361\) | 6597.00 | 0.961802 | ||||||||
\(362\) | −4460.00 | −0.647548 | ||||||||
\(363\) | 1210.00 | 0.174955 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5712.00 | −0.819123 | ||||||||
\(366\) | −3920.00 | −0.559841 | ||||||||
\(367\) | 1234.00 | 0.175516 | 0.0877579 | − | 0.996142i | \(-0.472030\pi\) | ||||
0.0877579 | + | 0.996142i | \(0.472030\pi\) | |||||||
\(368\) | 1088.00 | 0.154119 | ||||||||
\(369\) | −14892.0 | −2.10094 | ||||||||
\(370\) | 3640.00 | 0.511445 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 10480.0 | 1.46065 | ||||||||
\(373\) | 8030.00 | 1.11469 | 0.557343 | − | 0.830283i | \(-0.311821\pi\) | ||||
0.557343 | + | 0.830283i | \(0.311821\pi\) | |||||||
\(374\) | 2376.00 | 0.328503 | ||||||||
\(375\) | −7560.00 | −1.04106 | ||||||||
\(376\) | −1328.00 | −0.182145 | ||||||||
\(377\) | 1952.00 | 0.266666 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5184.00 | −0.702597 | −0.351298 | − | 0.936264i | \(-0.614260\pi\) | ||||
−0.351298 | + | 0.936264i | \(0.614260\pi\) | |||||||
\(380\) | −6496.00 | −0.876941 | ||||||||
\(381\) | 640.000 | 0.0860583 | ||||||||
\(382\) | 4352.00 | 0.582900 | ||||||||
\(383\) | −7570.00 | −1.00994 | −0.504972 | − | 0.863135i | \(-0.668497\pi\) | ||||
−0.504972 | + | 0.863135i | \(0.668497\pi\) | |||||||
\(384\) | 1280.00 | 0.170103 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −6252.00 | −0.824400 | ||||||||
\(387\) | −28908.0 | −3.79710 | ||||||||
\(388\) | 1928.00 | 0.252266 | ||||||||
\(389\) | −5370.00 | −0.699922 | −0.349961 | − | 0.936764i | \(-0.613805\pi\) | ||||
−0.349961 | + | 0.936764i | \(0.613805\pi\) | |||||||
\(390\) | 4480.00 | 0.581676 | ||||||||
\(391\) | −7344.00 | −0.949877 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 15840.0 | 2.03314 | ||||||||
\(394\) | −2244.00 | −0.286932 | ||||||||
\(395\) | 8400.00 | 1.07000 | ||||||||
\(396\) | −3212.00 | −0.407599 | ||||||||
\(397\) | −11442.0 | −1.44649 | −0.723246 | − | 0.690590i | \(-0.757351\pi\) | ||||
−0.723246 | + | 0.690590i | \(0.757351\pi\) | |||||||
\(398\) | 11172.0 | 1.40704 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1136.00 | 0.142000 | ||||||||
\(401\) | 2362.00 | 0.294146 | 0.147073 | − | 0.989126i | \(-0.453015\pi\) | ||||
0.147073 | + | 0.989126i | \(0.453015\pi\) | |||||||
\(402\) | −8320.00 | −1.03225 | ||||||||
\(403\) | 4192.00 | 0.518160 | ||||||||
\(404\) | −4864.00 | −0.598993 | ||||||||
\(405\) | 36806.0 | 4.51581 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1430.00 | −0.174158 | ||||||||
\(408\) | −8640.00 | −1.04839 | ||||||||
\(409\) | 16.0000 | 0.00193435 | 0.000967175 | − | 1.00000i | \(-0.499692\pi\) | ||||
0.000967175 | 1.00000i | \(0.499692\pi\) | ||||||||
\(410\) | −5712.00 | −0.688038 | ||||||||
\(411\) | 9980.00 | 1.19775 | ||||||||
\(412\) | −5624.00 | −0.672511 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 9928.00 | 1.17859 | ||||||||
\(415\) | 16968.0 | 2.00705 | ||||||||
\(416\) | 512.000 | 0.0603434 | ||||||||
\(417\) | −2760.00 | −0.324119 | ||||||||
\(418\) | 2552.00 | 0.298618 | ||||||||
\(419\) | −9462.00 | −1.10322 | −0.551610 | − | 0.834102i | \(-0.685986\pi\) | ||||
−0.551610 | + | 0.834102i | \(0.685986\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6302.00 | −0.729550 | −0.364775 | − | 0.931096i | \(-0.618854\pi\) | ||||
−0.364775 | + | 0.931096i | \(0.618854\pi\) | |||||||
\(422\) | 6744.00 | 0.777945 | ||||||||
\(423\) | −12118.0 | −1.39290 | ||||||||
\(424\) | 3536.00 | 0.405008 | ||||||||
\(425\) | −7668.00 | −0.875183 | ||||||||
\(426\) | 9840.00 | 1.11913 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −2352.00 | −0.265627 | ||||||||
\(429\) | −1760.00 | −0.198074 | ||||||||
\(430\) | −11088.0 | −1.24351 | ||||||||
\(431\) | 7816.00 | 0.873512 | 0.436756 | − | 0.899580i | \(-0.356127\pi\) | ||||
0.436756 | + | 0.899580i | \(0.356127\pi\) | |||||||
\(432\) | 7360.00 | 0.819695 | ||||||||
\(433\) | 9506.00 | 1.05503 | 0.527516 | − | 0.849545i | \(-0.323123\pi\) | ||||
0.527516 | + | 0.849545i | \(0.323123\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 17080.0 | 1.88258 | ||||||||
\(436\) | 616.000 | 0.0676630 | ||||||||
\(437\) | −7888.00 | −0.863465 | ||||||||
\(438\) | −8160.00 | −0.890182 | ||||||||
\(439\) | 8228.00 | 0.894535 | 0.447268 | − | 0.894400i | \(-0.352397\pi\) | ||||
0.447268 | + | 0.894400i | \(0.352397\pi\) | |||||||
\(440\) | −1232.00 | −0.133485 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3456.00 | −0.371912 | ||||||||
\(443\) | 7668.00 | 0.822388 | 0.411194 | − | 0.911548i | \(-0.365112\pi\) | ||||
0.411194 | + | 0.911548i | \(0.365112\pi\) | |||||||
\(444\) | 5200.00 | 0.555813 | ||||||||
\(445\) | −16044.0 | −1.70912 | ||||||||
\(446\) | −1212.00 | −0.128677 | ||||||||
\(447\) | 13180.0 | 1.39461 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −922.000 | −0.0969084 | −0.0484542 | − | 0.998825i | \(-0.515429\pi\) | ||||
−0.0484542 | + | 0.998825i | \(0.515429\pi\) | |||||||
\(450\) | 10366.0 | 1.08591 | ||||||||
\(451\) | 2244.00 | 0.234292 | ||||||||
\(452\) | −7608.00 | −0.791704 | ||||||||
\(453\) | −9840.00 | −1.02058 | ||||||||
\(454\) | −288.000 | −0.0297720 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −9280.00 | −0.953017 | ||||||||
\(457\) | 3386.00 | 0.346587 | 0.173294 | − | 0.984870i | \(-0.444559\pi\) | ||||
0.173294 | + | 0.984870i | \(0.444559\pi\) | |||||||
\(458\) | 2020.00 | 0.206088 | ||||||||
\(459\) | −49680.0 | −5.05199 | ||||||||
\(460\) | 3808.00 | 0.385976 | ||||||||
\(461\) | 3300.00 | 0.333398 | 0.166699 | − | 0.986008i | \(-0.446689\pi\) | ||||
0.166699 | + | 0.986008i | \(0.446689\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14236.0 | 1.42895 | 0.714474 | − | 0.699662i | \(-0.246666\pi\) | ||||
0.714474 | + | 0.699662i | \(0.246666\pi\) | |||||||
\(464\) | 1952.00 | 0.195300 | ||||||||
\(465\) | 36680.0 | 3.65805 | ||||||||
\(466\) | 7580.00 | 0.753512 | ||||||||
\(467\) | −3770.00 | −0.373565 | −0.186782 | − | 0.982401i | \(-0.559806\pi\) | ||||
−0.186782 | + | 0.982401i | \(0.559806\pi\) | |||||||
\(468\) | 4672.00 | 0.461460 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −4648.00 | −0.456162 | ||||||||
\(471\) | −17060.0 | −1.66897 | ||||||||
\(472\) | −5616.00 | −0.547664 | ||||||||
\(473\) | 4356.00 | 0.423444 | ||||||||
\(474\) | 12000.0 | 1.16282 | ||||||||
\(475\) | −8236.00 | −0.795565 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 32266.0 | 3.09719 | ||||||||
\(478\) | 4368.00 | 0.417966 | ||||||||
\(479\) | −17796.0 | −1.69754 | −0.848768 | − | 0.528765i | \(-0.822655\pi\) | ||||
−0.848768 | + | 0.528765i | \(0.822655\pi\) | |||||||
\(480\) | 4480.00 | 0.426006 | ||||||||
\(481\) | 2080.00 | 0.197172 | ||||||||
\(482\) | 8536.00 | 0.806648 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 484.000 | 0.0454545 | ||||||||
\(485\) | 6748.00 | 0.631775 | ||||||||
\(486\) | 27740.0 | 2.58912 | ||||||||
\(487\) | −3684.00 | −0.342788 | −0.171394 | − | 0.985203i | \(-0.554827\pi\) | ||||
−0.171394 | + | 0.985203i | \(0.554827\pi\) | |||||||
\(488\) | −1568.00 | −0.145451 | ||||||||
\(489\) | 11680.0 | 1.08014 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −17236.0 | −1.58422 | −0.792108 | − | 0.610381i | \(-0.791016\pi\) | ||||
−0.792108 | + | 0.610381i | \(0.791016\pi\) | |||||||
\(492\) | −8160.00 | −0.747726 | ||||||||
\(493\) | −13176.0 | −1.20369 | ||||||||
\(494\) | −3712.00 | −0.338078 | ||||||||
\(495\) | −11242.0 | −1.02079 | ||||||||
\(496\) | 4192.00 | 0.379489 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 24240.0 | 2.18117 | ||||||||
\(499\) | 13176.0 | 1.18204 | 0.591021 | − | 0.806656i | \(-0.298725\pi\) | ||||
0.591021 | + | 0.806656i | \(0.298725\pi\) | |||||||
\(500\) | −3024.00 | −0.270475 | ||||||||
\(501\) | −720.000 | −0.0642060 | ||||||||
\(502\) | −15844.0 | −1.40867 | ||||||||
\(503\) | −15428.0 | −1.36760 | −0.683798 | − | 0.729672i | \(-0.739673\pi\) | ||||
−0.683798 | + | 0.729672i | \(0.739673\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −17024.0 | −1.50011 | ||||||||
\(506\) | −1496.00 | −0.131433 | ||||||||
\(507\) | −19410.0 | −1.70025 | ||||||||
\(508\) | 256.000 | 0.0223586 | ||||||||
\(509\) | 7842.00 | 0.682889 | 0.341445 | − | 0.939902i | \(-0.389084\pi\) | ||||
0.341445 | + | 0.939902i | \(0.389084\pi\) | |||||||
\(510\) | −30240.0 | −2.62559 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | −53360.0 | −4.59240 | ||||||||
\(514\) | −8004.00 | −0.686851 | ||||||||
\(515\) | −19684.0 | −1.68423 | ||||||||
\(516\) | −15840.0 | −1.35139 | ||||||||
\(517\) | 1826.00 | 0.155333 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 43280.0 | 3.66046 | ||||||||
\(520\) | 1792.00 | 0.151124 | ||||||||
\(521\) | 17250.0 | 1.45055 | 0.725275 | − | 0.688460i | \(-0.241713\pi\) | ||||
0.725275 | + | 0.688460i | \(0.241713\pi\) | |||||||
\(522\) | 17812.0 | 1.49351 | ||||||||
\(523\) | −1032.00 | −0.0862834 | −0.0431417 | − | 0.999069i | \(-0.513737\pi\) | ||||
−0.0431417 | + | 0.999069i | \(0.513737\pi\) | |||||||
\(524\) | 6336.00 | 0.528224 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7920.00 | −0.656518 | ||||||||
\(527\) | −28296.0 | −2.33889 | ||||||||
\(528\) | −1760.00 | −0.145065 | ||||||||
\(529\) | −7543.00 | −0.619956 | ||||||||
\(530\) | 12376.0 | 1.01430 | ||||||||
\(531\) | −51246.0 | −4.18811 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3264.00 | −0.265252 | ||||||||
\(534\) | −22920.0 | −1.85739 | ||||||||
\(535\) | −8232.00 | −0.665234 | ||||||||
\(536\) | −3328.00 | −0.268186 | ||||||||
\(537\) | −19240.0 | −1.54612 | ||||||||
\(538\) | −3756.00 | −0.300990 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 25760.0 | 2.05284 | ||||||||
\(541\) | 94.0000 | 0.00747020 | 0.00373510 | − | 0.999993i | \(-0.498811\pi\) | ||||
0.00373510 | + | 0.999993i | \(0.498811\pi\) | |||||||
\(542\) | 9480.00 | 0.751293 | ||||||||
\(543\) | −22300.0 | −1.76240 | ||||||||
\(544\) | −3456.00 | −0.272380 | ||||||||
\(545\) | 2156.00 | 0.169455 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11676.0 | −0.912669 | −0.456334 | − | 0.889808i | \(-0.650838\pi\) | ||||
−0.456334 | + | 0.889808i | \(0.650838\pi\) | |||||||
\(548\) | 3992.00 | 0.311186 | ||||||||
\(549\) | −14308.0 | −1.11230 | ||||||||
\(550\) | −1562.00 | −0.121098 | ||||||||
\(551\) | −14152.0 | −1.09418 | ||||||||
\(552\) | 5440.00 | 0.419460 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 1420.00 | 0.108899 | ||||||||
\(555\) | 18200.0 | 1.39198 | ||||||||
\(556\) | −1104.00 | −0.0842087 | ||||||||
\(557\) | −1858.00 | −0.141339 | −0.0706696 | − | 0.997500i | \(-0.522514\pi\) | ||||
−0.0706696 | + | 0.997500i | \(0.522514\pi\) | |||||||
\(558\) | 38252.0 | 2.90204 | ||||||||
\(559\) | −6336.00 | −0.479399 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 11880.0 | 0.894071 | ||||||||
\(562\) | −180.000 | −0.0135104 | ||||||||
\(563\) | 23028.0 | 1.72383 | 0.861913 | − | 0.507056i | \(-0.169266\pi\) | ||||
0.861913 | + | 0.507056i | \(0.169266\pi\) | |||||||
\(564\) | −6640.00 | −0.495735 | ||||||||
\(565\) | −26628.0 | −1.98274 | ||||||||
\(566\) | 6896.00 | 0.512121 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3936.00 | 0.290759 | ||||||||
\(569\) | −17066.0 | −1.25737 | −0.628685 | − | 0.777660i | \(-0.716407\pi\) | ||||
−0.628685 | + | 0.777660i | \(0.716407\pi\) | |||||||
\(570\) | −32480.0 | −2.38673 | ||||||||
\(571\) | −10252.0 | −0.751371 | −0.375686 | − | 0.926747i | \(-0.622593\pi\) | ||||
−0.375686 | + | 0.926747i | \(0.622593\pi\) | |||||||
\(572\) | −704.000 | −0.0514610 | ||||||||
\(573\) | 21760.0 | 1.58645 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4828.00 | 0.350159 | ||||||||
\(576\) | 4672.00 | 0.337963 | ||||||||
\(577\) | −2142.00 | −0.154545 | −0.0772726 | − | 0.997010i | \(-0.524621\pi\) | ||||
−0.0772726 | + | 0.997010i | \(0.524621\pi\) | |||||||
\(578\) | 13502.0 | 0.971642 | ||||||||
\(579\) | −31260.0 | −2.24373 | ||||||||
\(580\) | 6832.00 | 0.489109 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 9640.00 | 0.686582 | ||||||||
\(583\) | −4862.00 | −0.345392 | ||||||||
\(584\) | −3264.00 | −0.231276 | ||||||||
\(585\) | 16352.0 | 1.15568 | ||||||||
\(586\) | 5608.00 | 0.395332 | ||||||||
\(587\) | −3474.00 | −0.244271 | −0.122136 | − | 0.992513i | \(-0.538974\pi\) | ||||
−0.122136 | + | 0.992513i | \(0.538974\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −30392.0 | −2.12611 | ||||||||
\(590\) | −19656.0 | −1.37157 | ||||||||
\(591\) | −11220.0 | −0.780929 | ||||||||
\(592\) | 2080.00 | 0.144405 | ||||||||
\(593\) | 17424.0 | 1.20661 | 0.603303 | − | 0.797512i | \(-0.293851\pi\) | ||||
0.603303 | + | 0.797512i | \(0.293851\pi\) | |||||||
\(594\) | −10120.0 | −0.699038 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 5272.00 | 0.362331 | ||||||||
\(597\) | 55860.0 | 3.82948 | ||||||||
\(598\) | 2176.00 | 0.148801 | ||||||||
\(599\) | 6916.00 | 0.471753 | 0.235877 | − | 0.971783i | \(-0.424204\pi\) | ||||
0.235877 | + | 0.971783i | \(0.424204\pi\) | |||||||
\(600\) | 5680.00 | 0.386475 | ||||||||
\(601\) | −16468.0 | −1.11771 | −0.558855 | − | 0.829265i | \(-0.688759\pi\) | ||||
−0.558855 | + | 0.829265i | \(0.688759\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −30368.0 | −2.05088 | ||||||||
\(604\) | −3936.00 | −0.265155 | ||||||||
\(605\) | 1694.00 | 0.113836 | ||||||||
\(606\) | −24320.0 | −1.63025 | ||||||||
\(607\) | 17176.0 | 1.14852 | 0.574261 | − | 0.818673i | \(-0.305290\pi\) | ||||
0.574261 | + | 0.818673i | \(0.305290\pi\) | |||||||
\(608\) | −3712.00 | −0.247601 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −5488.00 | −0.364267 | ||||||||
\(611\) | −2656.00 | −0.175860 | ||||||||
\(612\) | −31536.0 | −2.08295 | ||||||||
\(613\) | 11402.0 | 0.751260 | 0.375630 | − | 0.926770i | \(-0.377426\pi\) | ||||
0.375630 | + | 0.926770i | \(0.377426\pi\) | |||||||
\(614\) | −2640.00 | −0.173521 | ||||||||
\(615\) | −28560.0 | −1.87260 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3654.00 | 0.238419 | 0.119209 | − | 0.992869i | \(-0.461964\pi\) | ||||
0.119209 | + | 0.992869i | \(0.461964\pi\) | |||||||
\(618\) | −28120.0 | −1.83034 | ||||||||
\(619\) | 11318.0 | 0.734909 | 0.367455 | − | 0.930041i | \(-0.380229\pi\) | ||||
0.367455 | + | 0.930041i | \(0.380229\pi\) | |||||||
\(620\) | 14672.0 | 0.950390 | ||||||||
\(621\) | 31280.0 | 2.02129 | ||||||||
\(622\) | 2132.00 | 0.137436 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 2560.00 | 0.164234 | ||||||||
\(625\) | −19459.0 | −1.24538 | ||||||||
\(626\) | 18508.0 | 1.18167 | ||||||||
\(627\) | 12760.0 | 0.812736 | ||||||||
\(628\) | −6824.00 | −0.433610 | ||||||||
\(629\) | −14040.0 | −0.890002 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23872.0 | −1.50607 | −0.753034 | − | 0.657981i | \(-0.771411\pi\) | ||||
−0.753034 | + | 0.657981i | \(0.771411\pi\) | |||||||
\(632\) | 4800.00 | 0.302110 | ||||||||
\(633\) | 33720.0 | 2.11730 | ||||||||
\(634\) | −19444.0 | −1.21801 | ||||||||
\(635\) | 896.000 | 0.0559948 | ||||||||
\(636\) | 17680.0 | 1.10229 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −2684.00 | −0.166553 | ||||||||
\(639\) | 35916.0 | 2.22350 | ||||||||
\(640\) | 1792.00 | 0.110680 | ||||||||
\(641\) | −27026.0 | −1.66531 | −0.832654 | − | 0.553793i | \(-0.813180\pi\) | ||||
−0.832654 | + | 0.553793i | \(0.813180\pi\) | |||||||
\(642\) | −11760.0 | −0.722944 | ||||||||
\(643\) | −6498.00 | −0.398532 | −0.199266 | − | 0.979945i | \(-0.563856\pi\) | ||||
−0.199266 | + | 0.979945i | \(0.563856\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −55440.0 | −3.38442 | ||||||||
\(646\) | 25056.0 | 1.52603 | ||||||||
\(647\) | 6422.00 | 0.390224 | 0.195112 | − | 0.980781i | \(-0.437493\pi\) | ||||
0.195112 | + | 0.980781i | \(0.437493\pi\) | |||||||
\(648\) | 21032.0 | 1.27502 | ||||||||
\(649\) | 7722.00 | 0.467049 | ||||||||
\(650\) | 2272.00 | 0.137100 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 4672.00 | 0.280628 | ||||||||
\(653\) | 23670.0 | 1.41850 | 0.709249 | − | 0.704958i | \(-0.249034\pi\) | ||||
0.709249 | + | 0.704958i | \(0.249034\pi\) | |||||||
\(654\) | 3080.00 | 0.184155 | ||||||||
\(655\) | 22176.0 | 1.32288 | ||||||||
\(656\) | −3264.00 | −0.194265 | ||||||||
\(657\) | −29784.0 | −1.76862 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9812.00 | −0.580002 | −0.290001 | − | 0.957026i | \(-0.593656\pi\) | ||||
−0.290001 | + | 0.957026i | \(0.593656\pi\) | |||||||
\(660\) | −6160.00 | −0.363300 | ||||||||
\(661\) | 5190.00 | 0.305397 | 0.152699 | − | 0.988273i | \(-0.451204\pi\) | ||||
0.152699 | + | 0.988273i | \(0.451204\pi\) | |||||||
\(662\) | 5240.00 | 0.307641 | ||||||||
\(663\) | −17280.0 | −1.01222 | ||||||||
\(664\) | 9696.00 | 0.566683 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 18980.0 | 1.10429 | ||||||||
\(667\) | 8296.00 | 0.481593 | ||||||||
\(668\) | −288.000 | −0.0166812 | ||||||||
\(669\) | −6060.00 | −0.350214 | ||||||||
\(670\) | −11648.0 | −0.671644 | ||||||||
\(671\) | 2156.00 | 0.124041 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 94.0000 | 0.00538400 | 0.00269200 | − | 0.999996i | \(-0.499143\pi\) | ||||
0.00269200 | + | 0.999996i | \(0.499143\pi\) | |||||||
\(674\) | 5612.00 | 0.320721 | ||||||||
\(675\) | 32660.0 | 1.86235 | ||||||||
\(676\) | −7764.00 | −0.441739 | ||||||||
\(677\) | 12432.0 | 0.705762 | 0.352881 | − | 0.935668i | \(-0.385202\pi\) | ||||
0.352881 | + | 0.935668i | \(0.385202\pi\) | |||||||
\(678\) | −38040.0 | −2.15475 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −12096.0 | −0.682148 | ||||||||
\(681\) | −1440.00 | −0.0810293 | ||||||||
\(682\) | −5764.00 | −0.323629 | ||||||||
\(683\) | −2308.00 | −0.129302 | −0.0646509 | − | 0.997908i | \(-0.520593\pi\) | ||||
−0.0646509 | + | 0.997908i | \(0.520593\pi\) | |||||||
\(684\) | −33872.0 | −1.89346 | ||||||||
\(685\) | 13972.0 | 0.779332 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10100.0 | 0.560901 | ||||||||
\(688\) | −6336.00 | −0.351101 | ||||||||
\(689\) | 7072.00 | 0.391033 | ||||||||
\(690\) | 19040.0 | 1.05049 | ||||||||
\(691\) | −26446.0 | −1.45594 | −0.727969 | − | 0.685610i | \(-0.759536\pi\) | ||||
−0.727969 | + | 0.685610i | \(0.759536\pi\) | |||||||
\(692\) | 17312.0 | 0.951017 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 11128.0 | 0.608664 | ||||||||
\(695\) | −3864.00 | −0.210892 | ||||||||
\(696\) | 9760.00 | 0.531540 | ||||||||
\(697\) | 22032.0 | 1.19730 | ||||||||
\(698\) | −20120.0 | −1.09105 | ||||||||
\(699\) | 37900.0 | 2.05080 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 26450.0 | 1.42511 | 0.712555 | − | 0.701616i | \(-0.247538\pi\) | ||||
0.712555 | + | 0.701616i | \(0.247538\pi\) | |||||||
\(702\) | 14720.0 | 0.791411 | ||||||||
\(703\) | −15080.0 | −0.809037 | ||||||||
\(704\) | −704.000 | −0.0376889 | ||||||||
\(705\) | −23240.0 | −1.24152 | ||||||||
\(706\) | 10204.0 | 0.543956 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −28080.0 | −1.49055 | ||||||||
\(709\) | 17102.0 | 0.905894 | 0.452947 | − | 0.891537i | \(-0.350373\pi\) | ||||
0.452947 | + | 0.891537i | \(0.350373\pi\) | |||||||
\(710\) | 13776.0 | 0.728175 | ||||||||
\(711\) | 43800.0 | 2.31031 | ||||||||
\(712\) | −9168.00 | −0.482564 | ||||||||
\(713\) | 17816.0 | 0.935785 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2464.00 | −0.128879 | ||||||||
\(716\) | −7696.00 | −0.401694 | ||||||||
\(717\) | 21840.0 | 1.13756 | ||||||||
\(718\) | 15952.0 | 0.829141 | ||||||||
\(719\) | 16854.0 | 0.874198 | 0.437099 | − | 0.899413i | \(-0.356006\pi\) | ||||
0.437099 | + | 0.899413i | \(0.356006\pi\) | |||||||
\(720\) | 16352.0 | 0.846393 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 13194.0 | 0.680097 | ||||||||
\(723\) | 42680.0 | 2.19542 | ||||||||
\(724\) | −8920.00 | −0.457886 | ||||||||
\(725\) | 8662.00 | 0.443722 | ||||||||
\(726\) | 2420.00 | 0.123712 | ||||||||
\(727\) | 34670.0 | 1.76869 | 0.884346 | − | 0.466832i | \(-0.154605\pi\) | ||||
0.884346 | + | 0.466832i | \(0.154605\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 67717.0 | 3.44038 | ||||||||
\(730\) | −11424.0 | −0.579207 | ||||||||
\(731\) | 42768.0 | 2.16393 | ||||||||
\(732\) | −7840.00 | −0.395867 | ||||||||
\(733\) | −11716.0 | −0.590369 | −0.295184 | − | 0.955440i | \(-0.595381\pi\) | ||||
−0.295184 | + | 0.955440i | \(0.595381\pi\) | |||||||
\(734\) | 2468.00 | 0.124108 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2176.00 | 0.108979 | ||||||||
\(737\) | 4576.00 | 0.228710 | ||||||||
\(738\) | −29784.0 | −1.48559 | ||||||||
\(739\) | 29772.0 | 1.48198 | 0.740988 | − | 0.671518i | \(-0.234357\pi\) | ||||
0.740988 | + | 0.671518i | \(0.234357\pi\) | |||||||
\(740\) | 7280.00 | 0.361646 | ||||||||
\(741\) | −18560.0 | −0.920133 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −24928.0 | −1.23085 | −0.615424 | − | 0.788196i | \(-0.711015\pi\) | ||||
−0.615424 | + | 0.788196i | \(0.711015\pi\) | |||||||
\(744\) | 20960.0 | 1.03284 | ||||||||
\(745\) | 18452.0 | 0.907421 | ||||||||
\(746\) | 16060.0 | 0.788202 | ||||||||
\(747\) | 88476.0 | 4.33356 | ||||||||
\(748\) | 4752.00 | 0.232287 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −15120.0 | −0.736139 | ||||||||
\(751\) | −4652.00 | −0.226037 | −0.113019 | − | 0.993593i | \(-0.536052\pi\) | ||||
−0.113019 | + | 0.993593i | \(0.536052\pi\) | |||||||
\(752\) | −2656.00 | −0.128796 | ||||||||
\(753\) | −79220.0 | −3.83391 | ||||||||
\(754\) | 3904.00 | 0.188561 | ||||||||
\(755\) | −13776.0 | −0.664053 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1802.00 | −0.0865189 | −0.0432594 | − | 0.999064i | \(-0.513774\pi\) | ||||
−0.0432594 | + | 0.999064i | \(0.513774\pi\) | |||||||
\(758\) | −10368.0 | −0.496811 | ||||||||
\(759\) | −7480.00 | −0.357716 | ||||||||
\(760\) | −12992.0 | −0.620091 | ||||||||
\(761\) | 808.000 | 0.0384888 | 0.0192444 | − | 0.999815i | \(-0.493874\pi\) | ||||
0.0192444 | + | 0.999815i | \(0.493874\pi\) | |||||||
\(762\) | 1280.00 | 0.0608524 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 8704.00 | 0.412172 | ||||||||
\(765\) | −110376. | −5.21654 | ||||||||
\(766\) | −15140.0 | −0.714139 | ||||||||
\(767\) | −11232.0 | −0.528767 | ||||||||
\(768\) | 2560.00 | 0.120281 | ||||||||
\(769\) | −23144.0 | −1.08530 | −0.542649 | − | 0.839960i | \(-0.682579\pi\) | ||||
−0.542649 | + | 0.839960i | \(0.682579\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −40020.0 | −1.86937 | ||||||||
\(772\) | −12504.0 | −0.582939 | ||||||||
\(773\) | 27466.0 | 1.27799 | 0.638993 | − | 0.769212i | \(-0.279351\pi\) | ||||
0.638993 | + | 0.769212i | \(0.279351\pi\) | |||||||
\(774\) | −57816.0 | −2.68495 | ||||||||
\(775\) | 18602.0 | 0.862198 | ||||||||
\(776\) | 3856.00 | 0.178379 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −10740.0 | −0.494920 | ||||||||
\(779\) | 23664.0 | 1.08838 | ||||||||
\(780\) | 8960.00 | 0.411307 | ||||||||
\(781\) | −5412.00 | −0.247960 | ||||||||
\(782\) | −14688.0 | −0.671665 | ||||||||
\(783\) | 56120.0 | 2.56139 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −23884.0 | −1.08593 | ||||||||
\(786\) | 31680.0 | 1.43764 | ||||||||
\(787\) | −23604.0 | −1.06911 | −0.534556 | − | 0.845133i | \(-0.679521\pi\) | ||||
−0.534556 | + | 0.845133i | \(0.679521\pi\) | |||||||
\(788\) | −4488.00 | −0.202891 | ||||||||
\(789\) | −39600.0 | −1.78682 | ||||||||
\(790\) | 16800.0 | 0.756604 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −6424.00 | −0.288216 | ||||||||
\(793\) | −3136.00 | −0.140432 | ||||||||
\(794\) | −22884.0 | −1.02282 | ||||||||
\(795\) | 61880.0 | 2.76058 | ||||||||
\(796\) | 22344.0 | 0.994927 | ||||||||
\(797\) | −4122.00 | −0.183198 | −0.0915990 | − | 0.995796i | \(-0.529198\pi\) | ||||
−0.0915990 | + | 0.995796i | \(0.529198\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 17928.0 | 0.793801 | ||||||||
\(800\) | 2272.00 | 0.100409 | ||||||||
\(801\) | −83658.0 | −3.69027 | ||||||||
\(802\) | 4724.00 | 0.207993 | ||||||||
\(803\) | 4488.00 | 0.197233 | ||||||||
\(804\) | −16640.0 | −0.729910 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 8384.00 | 0.366394 | ||||||||
\(807\) | −18780.0 | −0.819191 | ||||||||
\(808\) | −9728.00 | −0.423552 | ||||||||
\(809\) | −9110.00 | −0.395909 | −0.197955 | − | 0.980211i | \(-0.563430\pi\) | ||||
−0.197955 | + | 0.980211i | \(0.563430\pi\) | |||||||
\(810\) | 73612.0 | 3.19316 | ||||||||
\(811\) | 28352.0 | 1.22759 | 0.613794 | − | 0.789466i | \(-0.289643\pi\) | ||||
0.613794 | + | 0.789466i | \(0.289643\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 47400.0 | 2.04476 | ||||||||
\(814\) | −2860.00 | −0.123149 | ||||||||
\(815\) | 16352.0 | 0.702804 | ||||||||
\(816\) | −17280.0 | −0.741325 | ||||||||
\(817\) | 45936.0 | 1.96707 | ||||||||
\(818\) | 32.0000 | 0.00136779 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −11424.0 | −0.486516 | ||||||||
\(821\) | −14002.0 | −0.595217 | −0.297609 | − | 0.954688i | \(-0.596189\pi\) | ||||
−0.297609 | + | 0.954688i | \(0.596189\pi\) | |||||||
\(822\) | 19960.0 | 0.846940 | ||||||||
\(823\) | −14848.0 | −0.628881 | −0.314440 | − | 0.949277i | \(-0.601817\pi\) | ||||
−0.314440 | + | 0.949277i | \(0.601817\pi\) | |||||||
\(824\) | −11248.0 | −0.475537 | ||||||||
\(825\) | −7810.00 | −0.329587 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 10500.0 | 0.441500 | 0.220750 | − | 0.975330i | \(-0.429149\pi\) | ||||
0.220750 | + | 0.975330i | \(0.429149\pi\) | |||||||
\(828\) | 19856.0 | 0.833386 | ||||||||
\(829\) | −23890.0 | −1.00089 | −0.500443 | − | 0.865770i | \(-0.666829\pi\) | ||||
−0.500443 | + | 0.865770i | \(0.666829\pi\) | |||||||
\(830\) | 33936.0 | 1.41920 | ||||||||
\(831\) | 7100.00 | 0.296385 | ||||||||
\(832\) | 1024.00 | 0.0426692 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −5520.00 | −0.229187 | ||||||||
\(835\) | −1008.00 | −0.0417764 | ||||||||
\(836\) | 5104.00 | 0.211155 | ||||||||
\(837\) | 120520. | 4.97704 | ||||||||
\(838\) | −18924.0 | −0.780094 | ||||||||
\(839\) | 670.000 | 0.0275697 | 0.0137848 | − | 0.999905i | \(-0.495612\pi\) | ||||
0.0137848 | + | 0.999905i | \(0.495612\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9505.00 | −0.389725 | ||||||||
\(842\) | −12604.0 | −0.515870 | ||||||||
\(843\) | −900.000 | −0.0367706 | ||||||||
\(844\) | 13488.0 | 0.550090 | ||||||||
\(845\) | −27174.0 | −1.10629 | ||||||||
\(846\) | −24236.0 | −0.984930 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 7072.00 | 0.286384 | ||||||||
\(849\) | 34480.0 | 1.39382 | ||||||||
\(850\) | −15336.0 | −0.618848 | ||||||||
\(851\) | 8840.00 | 0.356088 | ||||||||
\(852\) | 19680.0 | 0.791345 | ||||||||
\(853\) | 4776.00 | 0.191708 | 0.0958541 | − | 0.995395i | \(-0.469442\pi\) | ||||
0.0958541 | + | 0.995395i | \(0.469442\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −118552. | −4.74198 | ||||||||
\(856\) | −4704.00 | −0.187826 | ||||||||
\(857\) | 13024.0 | 0.519126 | 0.259563 | − | 0.965726i | \(-0.416421\pi\) | ||||
0.259563 | + | 0.965726i | \(0.416421\pi\) | |||||||
\(858\) | −3520.00 | −0.140059 | ||||||||
\(859\) | 32998.0 | 1.31068 | 0.655342 | − | 0.755332i | \(-0.272525\pi\) | ||||
0.655342 | + | 0.755332i | \(0.272525\pi\) | |||||||
\(860\) | −22176.0 | −0.879297 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 15632.0 | 0.617666 | ||||||||
\(863\) | 22272.0 | 0.878503 | 0.439251 | − | 0.898364i | \(-0.355244\pi\) | ||||
0.439251 | + | 0.898364i | \(0.355244\pi\) | |||||||
\(864\) | 14720.0 | 0.579612 | ||||||||
\(865\) | 60592.0 | 2.38172 | ||||||||
\(866\) | 19012.0 | 0.746021 | ||||||||
\(867\) | 67510.0 | 2.64447 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6600.00 | −0.257641 | ||||||||
\(870\) | 34160.0 | 1.33119 | ||||||||
\(871\) | −6656.00 | −0.258932 | ||||||||
\(872\) | 1232.00 | 0.0478449 | ||||||||
\(873\) | 35186.0 | 1.36411 | ||||||||
\(874\) | −15776.0 | −0.610562 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −16320.0 | −0.629454 | ||||||||
\(877\) | −30398.0 | −1.17043 | −0.585215 | − | 0.810878i | \(-0.698990\pi\) | ||||
−0.585215 | + | 0.810878i | \(0.698990\pi\) | |||||||
\(878\) | 16456.0 | 0.632532 | ||||||||
\(879\) | 28040.0 | 1.07596 | ||||||||
\(880\) | −2464.00 | −0.0943880 | ||||||||
\(881\) | −1630.00 | −0.0623338 | −0.0311669 | − | 0.999514i | \(-0.509922\pi\) | ||||
−0.0311669 | + | 0.999514i | \(0.509922\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −20228.0 | −0.770925 | −0.385462 | − | 0.922724i | \(-0.625958\pi\) | ||||
−0.385462 | + | 0.922724i | \(0.625958\pi\) | |||||||
\(884\) | −6912.00 | −0.262982 | ||||||||
\(885\) | −98280.0 | −3.73293 | ||||||||
\(886\) | 15336.0 | 0.581516 | ||||||||
\(887\) | −38908.0 | −1.47283 | −0.736416 | − | 0.676528i | \(-0.763484\pi\) | ||||
−0.736416 | + | 0.676528i | \(0.763484\pi\) | |||||||
\(888\) | 10400.0 | 0.393019 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −32088.0 | −1.20853 | ||||||||
\(891\) | −28919.0 | −1.08734 | ||||||||
\(892\) | −2424.00 | −0.0909883 | ||||||||
\(893\) | 19256.0 | 0.721587 | ||||||||
\(894\) | 26360.0 | 0.986141 | ||||||||
\(895\) | −26936.0 | −1.00600 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 10880.0 | 0.404986 | ||||||||
\(898\) | −1844.00 | −0.0685246 | ||||||||
\(899\) | 31964.0 | 1.18583 | ||||||||
\(900\) | 20732.0 | 0.767852 | ||||||||
\(901\) | −47736.0 | −1.76506 | ||||||||
\(902\) | 4488.00 | 0.165670 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −15216.0 | −0.559819 | ||||||||
\(905\) | −31220.0 | −1.14673 | ||||||||
\(906\) | −19680.0 | −0.721660 | ||||||||
\(907\) | −20936.0 | −0.766448 | −0.383224 | − | 0.923655i | \(-0.625186\pi\) | ||||
−0.383224 | + | 0.923655i | \(0.625186\pi\) | |||||||
\(908\) | −576.000 | −0.0210520 | ||||||||
\(909\) | −88768.0 | −3.23900 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 48204.0 | 1.75310 | 0.876548 | − | 0.481315i | \(-0.159841\pi\) | ||||
0.876548 | + | 0.481315i | \(0.159841\pi\) | |||||||
\(912\) | −18560.0 | −0.673885 | ||||||||
\(913\) | −13332.0 | −0.483269 | ||||||||
\(914\) | 6772.00 | 0.245074 | ||||||||
\(915\) | −27440.0 | −0.991408 | ||||||||
\(916\) | 4040.00 | 0.145726 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −99360.0 | −3.57230 | ||||||||
\(919\) | −27304.0 | −0.980061 | −0.490030 | − | 0.871705i | \(-0.663014\pi\) | ||||
−0.490030 | + | 0.871705i | \(0.663014\pi\) | |||||||
\(920\) | 7616.00 | 0.272926 | ||||||||
\(921\) | −13200.0 | −0.472264 | ||||||||
\(922\) | 6600.00 | 0.235748 | ||||||||
\(923\) | 7872.00 | 0.280726 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9230.00 | 0.328087 | ||||||||
\(926\) | 28472.0 | 1.01042 | ||||||||
\(927\) | −102638. | −3.63654 | ||||||||
\(928\) | 3904.00 | 0.138098 | ||||||||
\(929\) | −30.0000 | −0.00105949 | −0.000529746 | − | 1.00000i | \(-0.500169\pi\) | ||||
−0.000529746 | 1.00000i | \(0.500169\pi\) | ||||||||
\(930\) | 73360.0 | 2.58663 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 15160.0 | 0.532814 | ||||||||
\(933\) | 10660.0 | 0.374054 | ||||||||
\(934\) | −7540.00 | −0.264150 | ||||||||
\(935\) | 16632.0 | 0.581737 | ||||||||
\(936\) | 9344.00 | 0.326301 | ||||||||
\(937\) | −4736.00 | −0.165121 | −0.0825605 | − | 0.996586i | \(-0.526310\pi\) | ||||
−0.0825605 | + | 0.996586i | \(0.526310\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 92540.0 | 3.21611 | ||||||||
\(940\) | −9296.00 | −0.322555 | ||||||||
\(941\) | −19996.0 | −0.692722 | −0.346361 | − | 0.938101i | \(-0.612583\pi\) | ||||
−0.346361 | + | 0.938101i | \(0.612583\pi\) | |||||||
\(942\) | −34120.0 | −1.18014 | ||||||||
\(943\) | −13872.0 | −0.479040 | ||||||||
\(944\) | −11232.0 | −0.387257 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8712.00 | 0.299420 | ||||||||
\(947\) | −1252.00 | −0.0429615 | −0.0214807 | − | 0.999769i | \(-0.506838\pi\) | ||||
−0.0214807 | + | 0.999769i | \(0.506838\pi\) | |||||||
\(948\) | 24000.0 | 0.822240 | ||||||||
\(949\) | −6528.00 | −0.223296 | ||||||||
\(950\) | −16472.0 | −0.562550 | ||||||||
\(951\) | −97220.0 | −3.31501 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 17986.0 | 0.611357 | 0.305679 | − | 0.952135i | \(-0.401117\pi\) | ||||
0.305679 | + | 0.952135i | \(0.401117\pi\) | |||||||
\(954\) | 64532.0 | 2.19004 | ||||||||
\(955\) | 30464.0 | 1.03224 | ||||||||
\(956\) | 8736.00 | 0.295546 | ||||||||
\(957\) | −13420.0 | −0.453299 | ||||||||
\(958\) | −35592.0 | −1.20034 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 8960.00 | 0.301232 | ||||||||
\(961\) | 38853.0 | 1.30419 | ||||||||
\(962\) | 4160.00 | 0.139422 | ||||||||
\(963\) | −42924.0 | −1.43635 | ||||||||
\(964\) | 17072.0 | 0.570386 | ||||||||
\(965\) | −43764.0 | −1.45991 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 14256.0 | 0.474087 | 0.237043 | − | 0.971499i | \(-0.423822\pi\) | ||||
0.237043 | + | 0.971499i | \(0.423822\pi\) | |||||||
\(968\) | 968.000 | 0.0321412 | ||||||||
\(969\) | 125280. | 4.15333 | ||||||||
\(970\) | 13496.0 | 0.446732 | ||||||||
\(971\) | 50214.0 | 1.65957 | 0.829786 | − | 0.558082i | \(-0.188463\pi\) | ||||
0.829786 | + | 0.558082i | \(0.188463\pi\) | |||||||
\(972\) | 55480.0 | 1.83078 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −7368.00 | −0.242388 | ||||||||
\(975\) | 11360.0 | 0.373140 | ||||||||
\(976\) | −3136.00 | −0.102849 | ||||||||
\(977\) | −35814.0 | −1.17276 | −0.586382 | − | 0.810034i | \(-0.699448\pi\) | ||||
−0.586382 | + | 0.810034i | \(0.699448\pi\) | |||||||
\(978\) | 23360.0 | 0.763773 | ||||||||
\(979\) | 12606.0 | 0.411532 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11242.0 | 0.365881 | ||||||||
\(982\) | −34472.0 | −1.12021 | ||||||||
\(983\) | 19274.0 | 0.625377 | 0.312688 | − | 0.949856i | \(-0.398770\pi\) | ||||
0.312688 | + | 0.949856i | \(0.398770\pi\) | |||||||
\(984\) | −16320.0 | −0.528722 | ||||||||
\(985\) | −15708.0 | −0.508120 | ||||||||
\(986\) | −26352.0 | −0.851135 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −7424.00 | −0.239058 | ||||||||
\(989\) | −26928.0 | −0.865784 | ||||||||
\(990\) | −22484.0 | −0.721806 | ||||||||
\(991\) | 59996.0 | 1.92314 | 0.961572 | − | 0.274553i | \(-0.0885298\pi\) | ||||
0.961572 | + | 0.274553i | \(0.0885298\pi\) | |||||||
\(992\) | 8384.00 | 0.268339 | ||||||||
\(993\) | 26200.0 | 0.837293 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 78204.0 | 2.49169 | ||||||||
\(996\) | 48480.0 | 1.54232 | ||||||||
\(997\) | −24344.0 | −0.773302 | −0.386651 | − | 0.922226i | \(-0.626368\pi\) | ||||
−0.386651 | + | 0.922226i | \(0.626368\pi\) | |||||||
\(998\) | 26352.0 | 0.835830 | ||||||||
\(999\) | 59800.0 | 1.89388 |
(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 | 1078.4.a.h.1.1 | 1 | ||
7.6 | odd | 2 | 154.4.a.c.1.1 | ✓ | 1 | ||
21.20 | even | 2 | 1386.4.a.g.1.1 | 1 | |||
28.27 | even | 2 | 1232.4.a.i.1.1 | 1 | |||
77.76 | even | 2 | 1694.4.a.a.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
154.4.a.c.1.1 | ✓ | 1 | 7.6 | odd | 2 | ||
1078.4.a.h.1.1 | 1 | 1.1 | even | 1 | trivial | ||
1232.4.a.i.1.1 | 1 | 28.27 | even | 2 | |||
1386.4.a.g.1.1 | 1 | 21.20 | even | 2 | |||
1694.4.a.a.1.1 | 1 | 77.76 | even | 2 |