Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [350,4,Mod(1,350)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(350, 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("350.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 350 = 2 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 350.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: | \(20.6506685020\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 350.1 |
$q$-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 | ||||||||
\(3\) | 2.00000 | 0.384900 | 0.192450 | − | 0.981307i | \(-0.438357\pi\) | ||||
0.192450 | + | 0.981307i | \(0.438357\pi\) | |||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −4.00000 | −0.272166 | ||||||||
\(7\) | −7.00000 | −0.377964 | ||||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | −23.0000 | −0.851852 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −27.0000 | −0.740073 | −0.370037 | − | 0.929017i | \(-0.620655\pi\) | ||||
−0.370037 | + | 0.929017i | \(0.620655\pi\) | |||||||
\(12\) | 8.00000 | 0.192450 | ||||||||
\(13\) | 64.0000 | 1.36542 | 0.682708 | − | 0.730691i | \(-0.260802\pi\) | ||||
0.682708 | + | 0.730691i | \(0.260802\pi\) | |||||||
\(14\) | 14.0000 | 0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 24.0000 | 0.342403 | 0.171202 | − | 0.985236i | \(-0.445235\pi\) | ||||
0.171202 | + | 0.985236i | \(0.445235\pi\) | |||||||
\(18\) | 46.0000 | 0.602350 | ||||||||
\(19\) | 62.0000 | 0.748620 | 0.374310 | − | 0.927304i | \(-0.377880\pi\) | ||||
0.374310 | + | 0.927304i | \(0.377880\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −14.0000 | −0.145479 | ||||||||
\(22\) | 54.0000 | 0.523311 | ||||||||
\(23\) | 105.000 | 0.951914 | 0.475957 | − | 0.879469i | \(-0.342102\pi\) | ||||
0.475957 | + | 0.879469i | \(0.342102\pi\) | |||||||
\(24\) | −16.0000 | −0.136083 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −128.000 | −0.965495 | ||||||||
\(27\) | −100.000 | −0.712778 | ||||||||
\(28\) | −28.0000 | −0.188982 | ||||||||
\(29\) | 141.000 | 0.902864 | 0.451432 | − | 0.892306i | \(-0.350913\pi\) | ||||
0.451432 | + | 0.892306i | \(0.350913\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −124.000 | −0.718421 | −0.359211 | − | 0.933257i | \(-0.616954\pi\) | ||||
−0.359211 | + | 0.933257i | \(0.616954\pi\) | |||||||
\(32\) | −32.0000 | −0.176777 | ||||||||
\(33\) | −54.0000 | −0.284854 | ||||||||
\(34\) | −48.0000 | −0.242116 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −92.0000 | −0.425926 | ||||||||
\(37\) | 439.000 | 1.95057 | 0.975286 | − | 0.220947i | \(-0.0709147\pi\) | ||||
0.975286 | + | 0.220947i | \(0.0709147\pi\) | |||||||
\(38\) | −124.000 | −0.529354 | ||||||||
\(39\) | 128.000 | 0.525549 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −354.000 | −1.34843 | −0.674214 | − | 0.738536i | \(-0.735517\pi\) | ||||
−0.674214 | + | 0.738536i | \(0.735517\pi\) | |||||||
\(42\) | 28.0000 | 0.102869 | ||||||||
\(43\) | 211.000 | 0.748307 | 0.374153 | − | 0.927367i | \(-0.377933\pi\) | ||||
0.374153 | + | 0.927367i | \(0.377933\pi\) | |||||||
\(44\) | −108.000 | −0.370037 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −210.000 | −0.673105 | ||||||||
\(47\) | 102.000 | 0.316558 | 0.158279 | − | 0.987394i | \(-0.449405\pi\) | ||||
0.158279 | + | 0.987394i | \(0.449405\pi\) | |||||||
\(48\) | 32.0000 | 0.0962250 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 48.0000 | 0.131791 | ||||||||
\(52\) | 256.000 | 0.682708 | ||||||||
\(53\) | 306.000 | 0.793063 | 0.396531 | − | 0.918021i | \(-0.370214\pi\) | ||||
0.396531 | + | 0.918021i | \(0.370214\pi\) | |||||||
\(54\) | 200.000 | 0.504010 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 56.0000 | 0.133631 | ||||||||
\(57\) | 124.000 | 0.288144 | ||||||||
\(58\) | −282.000 | −0.638421 | ||||||||
\(59\) | 348.000 | 0.767894 | 0.383947 | − | 0.923355i | \(-0.374565\pi\) | ||||
0.383947 | + | 0.923355i | \(0.374565\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 410.000 | 0.860576 | 0.430288 | − | 0.902692i | \(-0.358412\pi\) | ||||
0.430288 | + | 0.902692i | \(0.358412\pi\) | |||||||
\(62\) | 248.000 | 0.508001 | ||||||||
\(63\) | 161.000 | 0.321970 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 108.000 | 0.201422 | ||||||||
\(67\) | 349.000 | 0.636375 | 0.318188 | − | 0.948028i | \(-0.396926\pi\) | ||||
0.318188 | + | 0.948028i | \(0.396926\pi\) | |||||||
\(68\) | 96.0000 | 0.171202 | ||||||||
\(69\) | 210.000 | 0.366392 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −339.000 | −0.566646 | −0.283323 | − | 0.959024i | \(-0.591437\pi\) | ||||
−0.283323 | + | 0.959024i | \(0.591437\pi\) | |||||||
\(72\) | 184.000 | 0.301175 | ||||||||
\(73\) | 70.0000 | 0.112231 | 0.0561156 | − | 0.998424i | \(-0.482128\pi\) | ||||
0.0561156 | + | 0.998424i | \(0.482128\pi\) | |||||||
\(74\) | −878.000 | −1.37926 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 248.000 | 0.374310 | ||||||||
\(77\) | 189.000 | 0.279721 | ||||||||
\(78\) | −256.000 | −0.371619 | ||||||||
\(79\) | 731.000 | 1.04106 | 0.520531 | − | 0.853843i | \(-0.325734\pi\) | ||||
0.520531 | + | 0.853843i | \(0.325734\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 421.000 | 0.577503 | ||||||||
\(82\) | 708.000 | 0.953482 | ||||||||
\(83\) | −528.000 | −0.698259 | −0.349130 | − | 0.937074i | \(-0.613523\pi\) | ||||
−0.349130 | + | 0.937074i | \(0.613523\pi\) | |||||||
\(84\) | −56.0000 | −0.0727393 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −422.000 | −0.529133 | ||||||||
\(87\) | 282.000 | 0.347512 | ||||||||
\(88\) | 216.000 | 0.261655 | ||||||||
\(89\) | 960.000 | 1.14337 | 0.571684 | − | 0.820474i | \(-0.306290\pi\) | ||||
0.571684 | + | 0.820474i | \(0.306290\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −448.000 | −0.516079 | ||||||||
\(92\) | 420.000 | 0.475957 | ||||||||
\(93\) | −248.000 | −0.276520 | ||||||||
\(94\) | −204.000 | −0.223840 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −64.0000 | −0.0680414 | ||||||||
\(97\) | −1340.00 | −1.40264 | −0.701322 | − | 0.712845i | \(-0.747406\pi\) | ||||
−0.701322 | + | 0.712845i | \(0.747406\pi\) | |||||||
\(98\) | −98.0000 | −0.101015 | ||||||||
\(99\) | 621.000 | 0.630433 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1470.00 | 1.44822 | 0.724111 | − | 0.689683i | \(-0.242250\pi\) | ||||
0.724111 | + | 0.689683i | \(0.242250\pi\) | |||||||
\(102\) | −96.0000 | −0.0931904 | ||||||||
\(103\) | 1870.00 | 1.78890 | 0.894449 | − | 0.447169i | \(-0.147568\pi\) | ||||
0.894449 | + | 0.447169i | \(0.147568\pi\) | |||||||
\(104\) | −512.000 | −0.482747 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −612.000 | −0.560780 | ||||||||
\(107\) | 204.000 | 0.184312 | 0.0921562 | − | 0.995745i | \(-0.470624\pi\) | ||||
0.0921562 | + | 0.995745i | \(0.470624\pi\) | |||||||
\(108\) | −400.000 | −0.356389 | ||||||||
\(109\) | −499.000 | −0.438491 | −0.219246 | − | 0.975670i | \(-0.570360\pi\) | ||||
−0.219246 | + | 0.975670i | \(0.570360\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 878.000 | 0.750775 | ||||||||
\(112\) | −112.000 | −0.0944911 | ||||||||
\(113\) | 57.0000 | 0.0474523 | 0.0237261 | − | 0.999718i | \(-0.492447\pi\) | ||||
0.0237261 | + | 0.999718i | \(0.492447\pi\) | |||||||
\(114\) | −248.000 | −0.203748 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 564.000 | 0.451432 | ||||||||
\(117\) | −1472.00 | −1.16313 | ||||||||
\(118\) | −696.000 | −0.542983 | ||||||||
\(119\) | −168.000 | −0.129416 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −602.000 | −0.452292 | ||||||||
\(122\) | −820.000 | −0.608519 | ||||||||
\(123\) | −708.000 | −0.519010 | ||||||||
\(124\) | −496.000 | −0.359211 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −322.000 | −0.227667 | ||||||||
\(127\) | −1379.00 | −0.963515 | −0.481758 | − | 0.876304i | \(-0.660001\pi\) | ||||
−0.481758 | + | 0.876304i | \(0.660001\pi\) | |||||||
\(128\) | −128.000 | −0.0883883 | ||||||||
\(129\) | 422.000 | 0.288023 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 180.000 | 0.120051 | 0.0600255 | − | 0.998197i | \(-0.480882\pi\) | ||||
0.0600255 | + | 0.998197i | \(0.480882\pi\) | |||||||
\(132\) | −216.000 | −0.142427 | ||||||||
\(133\) | −434.000 | −0.282952 | ||||||||
\(134\) | −698.000 | −0.449985 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −192.000 | −0.121058 | ||||||||
\(137\) | −1122.00 | −0.699700 | −0.349850 | − | 0.936806i | \(-0.613767\pi\) | ||||
−0.349850 | + | 0.936806i | \(0.613767\pi\) | |||||||
\(138\) | −420.000 | −0.259078 | ||||||||
\(139\) | −178.000 | −0.108617 | −0.0543085 | − | 0.998524i | \(-0.517295\pi\) | ||||
−0.0543085 | + | 0.998524i | \(0.517295\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 204.000 | 0.121843 | ||||||||
\(142\) | 678.000 | 0.400680 | ||||||||
\(143\) | −1728.00 | −1.01051 | ||||||||
\(144\) | −368.000 | −0.212963 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −140.000 | −0.0793595 | ||||||||
\(147\) | 98.0000 | 0.0549857 | ||||||||
\(148\) | 1756.00 | 0.975286 | ||||||||
\(149\) | −2097.00 | −1.15297 | −0.576486 | − | 0.817107i | \(-0.695577\pi\) | ||||
−0.576486 | + | 0.817107i | \(0.695577\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −787.000 | −0.424140 | −0.212070 | − | 0.977254i | \(-0.568020\pi\) | ||||
−0.212070 | + | 0.977254i | \(0.568020\pi\) | |||||||
\(152\) | −496.000 | −0.264677 | ||||||||
\(153\) | −552.000 | −0.291677 | ||||||||
\(154\) | −378.000 | −0.197793 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 512.000 | 0.262774 | ||||||||
\(157\) | −950.000 | −0.482919 | −0.241459 | − | 0.970411i | \(-0.577626\pi\) | ||||
−0.241459 | + | 0.970411i | \(0.577626\pi\) | |||||||
\(158\) | −1462.00 | −0.736142 | ||||||||
\(159\) | 612.000 | 0.305250 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −735.000 | −0.359790 | ||||||||
\(162\) | −842.000 | −0.408357 | ||||||||
\(163\) | 2740.00 | 1.31665 | 0.658323 | − | 0.752735i | \(-0.271266\pi\) | ||||
0.658323 | + | 0.752735i | \(0.271266\pi\) | |||||||
\(164\) | −1416.00 | −0.674214 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1056.00 | 0.493744 | ||||||||
\(167\) | −4104.00 | −1.90166 | −0.950830 | − | 0.309715i | \(-0.899766\pi\) | ||||
−0.950830 | + | 0.309715i | \(0.899766\pi\) | |||||||
\(168\) | 112.000 | 0.0514344 | ||||||||
\(169\) | 1899.00 | 0.864360 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1426.00 | −0.637713 | ||||||||
\(172\) | 844.000 | 0.374153 | ||||||||
\(173\) | 858.000 | 0.377067 | 0.188533 | − | 0.982067i | \(-0.439627\pi\) | ||||
0.188533 | + | 0.982067i | \(0.439627\pi\) | |||||||
\(174\) | −564.000 | −0.245728 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −432.000 | −0.185018 | ||||||||
\(177\) | 696.000 | 0.295563 | ||||||||
\(178\) | −1920.00 | −0.808484 | ||||||||
\(179\) | −4608.00 | −1.92412 | −0.962062 | − | 0.272832i | \(-0.912040\pi\) | ||||
−0.962062 | + | 0.272832i | \(0.912040\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4442.00 | 1.82415 | 0.912075 | − | 0.410023i | \(-0.134479\pi\) | ||||
0.912075 | + | 0.410023i | \(0.134479\pi\) | |||||||
\(182\) | 896.000 | 0.364923 | ||||||||
\(183\) | 820.000 | 0.331236 | ||||||||
\(184\) | −840.000 | −0.336552 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 496.000 | 0.195529 | ||||||||
\(187\) | −648.000 | −0.253403 | ||||||||
\(188\) | 408.000 | 0.158279 | ||||||||
\(189\) | 700.000 | 0.269405 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −516.000 | −0.195479 | −0.0977394 | − | 0.995212i | \(-0.531161\pi\) | ||||
−0.0977394 | + | 0.995212i | \(0.531161\pi\) | |||||||
\(192\) | 128.000 | 0.0481125 | ||||||||
\(193\) | 265.000 | 0.0988348 | 0.0494174 | − | 0.998778i | \(-0.484264\pi\) | ||||
0.0494174 | + | 0.998778i | \(0.484264\pi\) | |||||||
\(194\) | 2680.00 | 0.991818 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 196.000 | 0.0714286 | ||||||||
\(197\) | 2157.00 | 0.780101 | 0.390050 | − | 0.920793i | \(-0.372458\pi\) | ||||
0.390050 | + | 0.920793i | \(0.372458\pi\) | |||||||
\(198\) | −1242.00 | −0.445783 | ||||||||
\(199\) | −5014.00 | −1.78610 | −0.893048 | − | 0.449962i | \(-0.851438\pi\) | ||||
−0.893048 | + | 0.449962i | \(0.851438\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 698.000 | 0.244941 | ||||||||
\(202\) | −2940.00 | −1.02405 | ||||||||
\(203\) | −987.000 | −0.341250 | ||||||||
\(204\) | 192.000 | 0.0658955 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −3740.00 | −1.26494 | ||||||||
\(207\) | −2415.00 | −0.810889 | ||||||||
\(208\) | 1024.00 | 0.341354 | ||||||||
\(209\) | −1674.00 | −0.554033 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1772.00 | 0.578149 | 0.289075 | − | 0.957307i | \(-0.406652\pi\) | ||||
0.289075 | + | 0.957307i | \(0.406652\pi\) | |||||||
\(212\) | 1224.00 | 0.396531 | ||||||||
\(213\) | −678.000 | −0.218102 | ||||||||
\(214\) | −408.000 | −0.130329 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 800.000 | 0.252005 | ||||||||
\(217\) | 868.000 | 0.271538 | ||||||||
\(218\) | 998.000 | 0.310060 | ||||||||
\(219\) | 140.000 | 0.0431978 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1536.00 | 0.467523 | ||||||||
\(222\) | −1756.00 | −0.530878 | ||||||||
\(223\) | 1618.00 | 0.485871 | 0.242936 | − | 0.970042i | \(-0.421890\pi\) | ||||
0.242936 | + | 0.970042i | \(0.421890\pi\) | |||||||
\(224\) | 224.000 | 0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −114.000 | −0.0335538 | ||||||||
\(227\) | 1806.00 | 0.528055 | 0.264027 | − | 0.964515i | \(-0.414949\pi\) | ||||
0.264027 | + | 0.964515i | \(0.414949\pi\) | |||||||
\(228\) | 496.000 | 0.144072 | ||||||||
\(229\) | 6734.00 | 1.94321 | 0.971605 | − | 0.236607i | \(-0.0760355\pi\) | ||||
0.971605 | + | 0.236607i | \(0.0760355\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 378.000 | 0.107665 | ||||||||
\(232\) | −1128.00 | −0.319210 | ||||||||
\(233\) | −6333.00 | −1.78064 | −0.890319 | − | 0.455337i | \(-0.849519\pi\) | ||||
−0.890319 | + | 0.455337i | \(0.849519\pi\) | |||||||
\(234\) | 2944.00 | 0.822459 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1392.00 | 0.383947 | ||||||||
\(237\) | 1462.00 | 0.400705 | ||||||||
\(238\) | 336.000 | 0.0915111 | ||||||||
\(239\) | 7032.00 | 1.90319 | 0.951595 | − | 0.307356i | \(-0.0994441\pi\) | ||||
0.951595 | + | 0.307356i | \(0.0994441\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4010.00 | 1.07181 | 0.535906 | − | 0.844278i | \(-0.319970\pi\) | ||||
0.535906 | + | 0.844278i | \(0.319970\pi\) | |||||||
\(242\) | 1204.00 | 0.319818 | ||||||||
\(243\) | 3542.00 | 0.935059 | ||||||||
\(244\) | 1640.00 | 0.430288 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1416.00 | 0.366995 | ||||||||
\(247\) | 3968.00 | 1.02218 | ||||||||
\(248\) | 992.000 | 0.254000 | ||||||||
\(249\) | −1056.00 | −0.268760 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6180.00 | −1.55410 | −0.777048 | − | 0.629441i | \(-0.783284\pi\) | ||||
−0.777048 | + | 0.629441i | \(0.783284\pi\) | |||||||
\(252\) | 644.000 | 0.160985 | ||||||||
\(253\) | −2835.00 | −0.704486 | ||||||||
\(254\) | 2758.00 | 0.681308 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −780.000 | −0.189319 | −0.0946597 | − | 0.995510i | \(-0.530176\pi\) | ||||
−0.0946597 | + | 0.995510i | \(0.530176\pi\) | |||||||
\(258\) | −844.000 | −0.203663 | ||||||||
\(259\) | −3073.00 | −0.737247 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3243.00 | −0.769106 | ||||||||
\(262\) | −360.000 | −0.0848888 | ||||||||
\(263\) | −6813.00 | −1.59737 | −0.798684 | − | 0.601751i | \(-0.794470\pi\) | ||||
−0.798684 | + | 0.601751i | \(0.794470\pi\) | |||||||
\(264\) | 432.000 | 0.100711 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 868.000 | 0.200077 | ||||||||
\(267\) | 1920.00 | 0.440083 | ||||||||
\(268\) | 1396.00 | 0.318188 | ||||||||
\(269\) | −5784.00 | −1.31099 | −0.655496 | − | 0.755199i | \(-0.727540\pi\) | ||||
−0.655496 | + | 0.755199i | \(0.727540\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1528.00 | −0.342507 | −0.171253 | − | 0.985227i | \(-0.554782\pi\) | ||||
−0.171253 | + | 0.985227i | \(0.554782\pi\) | |||||||
\(272\) | 384.000 | 0.0856008 | ||||||||
\(273\) | −896.000 | −0.198639 | ||||||||
\(274\) | 2244.00 | 0.494763 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 840.000 | 0.183196 | ||||||||
\(277\) | 8926.00 | 1.93614 | 0.968071 | − | 0.250676i | \(-0.0806529\pi\) | ||||
0.968071 | + | 0.250676i | \(0.0806529\pi\) | |||||||
\(278\) | 356.000 | 0.0768038 | ||||||||
\(279\) | 2852.00 | 0.611988 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 777.000 | 0.164954 | 0.0824768 | − | 0.996593i | \(-0.473717\pi\) | ||||
0.0824768 | + | 0.996593i | \(0.473717\pi\) | |||||||
\(282\) | −408.000 | −0.0861562 | ||||||||
\(283\) | 7018.00 | 1.47412 | 0.737061 | − | 0.675826i | \(-0.236213\pi\) | ||||
0.737061 | + | 0.675826i | \(0.236213\pi\) | |||||||
\(284\) | −1356.00 | −0.283323 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3456.00 | 0.714537 | ||||||||
\(287\) | 2478.00 | 0.509658 | ||||||||
\(288\) | 736.000 | 0.150588 | ||||||||
\(289\) | −4337.00 | −0.882760 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2680.00 | −0.539878 | ||||||||
\(292\) | 280.000 | 0.0561156 | ||||||||
\(293\) | −1932.00 | −0.385217 | −0.192609 | − | 0.981276i | \(-0.561695\pi\) | ||||
−0.192609 | + | 0.981276i | \(0.561695\pi\) | |||||||
\(294\) | −196.000 | −0.0388808 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −3512.00 | −0.689631 | ||||||||
\(297\) | 2700.00 | 0.527508 | ||||||||
\(298\) | 4194.00 | 0.815275 | ||||||||
\(299\) | 6720.00 | 1.29976 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1477.00 | −0.282833 | ||||||||
\(302\) | 1574.00 | 0.299912 | ||||||||
\(303\) | 2940.00 | 0.557421 | ||||||||
\(304\) | 992.000 | 0.187155 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1104.00 | 0.206247 | ||||||||
\(307\) | −4796.00 | −0.891603 | −0.445802 | − | 0.895132i | \(-0.647081\pi\) | ||||
−0.445802 | + | 0.895132i | \(0.647081\pi\) | |||||||
\(308\) | 756.000 | 0.139861 | ||||||||
\(309\) | 3740.00 | 0.688547 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5988.00 | −1.09180 | −0.545898 | − | 0.837852i | \(-0.683811\pi\) | ||||
−0.545898 | + | 0.837852i | \(0.683811\pi\) | |||||||
\(312\) | −1024.00 | −0.185810 | ||||||||
\(313\) | 8590.00 | 1.55123 | 0.775616 | − | 0.631205i | \(-0.217439\pi\) | ||||
0.775616 | + | 0.631205i | \(0.217439\pi\) | |||||||
\(314\) | 1900.00 | 0.341475 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2924.00 | 0.520531 | ||||||||
\(317\) | 8049.00 | 1.42611 | 0.713055 | − | 0.701108i | \(-0.247311\pi\) | ||||
0.713055 | + | 0.701108i | \(0.247311\pi\) | |||||||
\(318\) | −1224.00 | −0.215844 | ||||||||
\(319\) | −3807.00 | −0.668185 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 408.000 | 0.0709419 | ||||||||
\(322\) | 1470.00 | 0.254410 | ||||||||
\(323\) | 1488.00 | 0.256330 | ||||||||
\(324\) | 1684.00 | 0.288752 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −5480.00 | −0.931010 | ||||||||
\(327\) | −998.000 | −0.168775 | ||||||||
\(328\) | 2832.00 | 0.476741 | ||||||||
\(329\) | −714.000 | −0.119648 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4885.00 | −0.811190 | −0.405595 | − | 0.914053i | \(-0.632936\pi\) | ||||
−0.405595 | + | 0.914053i | \(0.632936\pi\) | |||||||
\(332\) | −2112.00 | −0.349130 | ||||||||
\(333\) | −10097.0 | −1.66160 | ||||||||
\(334\) | 8208.00 | 1.34468 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −224.000 | −0.0363696 | ||||||||
\(337\) | 526.000 | 0.0850239 | 0.0425119 | − | 0.999096i | \(-0.486464\pi\) | ||||
0.0425119 | + | 0.999096i | \(0.486464\pi\) | |||||||
\(338\) | −3798.00 | −0.611195 | ||||||||
\(339\) | 114.000 | 0.0182644 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3348.00 | 0.531684 | ||||||||
\(342\) | 2852.00 | 0.450931 | ||||||||
\(343\) | −343.000 | −0.0539949 | ||||||||
\(344\) | −1688.00 | −0.264566 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1716.00 | −0.266626 | ||||||||
\(347\) | 4467.00 | 0.691070 | 0.345535 | − | 0.938406i | \(-0.387698\pi\) | ||||
0.345535 | + | 0.938406i | \(0.387698\pi\) | |||||||
\(348\) | 1128.00 | 0.173756 | ||||||||
\(349\) | −1798.00 | −0.275773 | −0.137886 | − | 0.990448i | \(-0.544031\pi\) | ||||
−0.137886 | + | 0.990448i | \(0.544031\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6400.00 | −0.973239 | ||||||||
\(352\) | 864.000 | 0.130828 | ||||||||
\(353\) | 1020.00 | 0.153794 | 0.0768968 | − | 0.997039i | \(-0.475499\pi\) | ||||
0.0768968 | + | 0.997039i | \(0.475499\pi\) | |||||||
\(354\) | −1392.00 | −0.208994 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 3840.00 | 0.571684 | ||||||||
\(357\) | −336.000 | −0.0498123 | ||||||||
\(358\) | 9216.00 | 1.36056 | ||||||||
\(359\) | −12639.0 | −1.85811 | −0.929054 | − | 0.369944i | \(-0.879377\pi\) | ||||
−0.929054 | + | 0.369944i | \(0.879377\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3015.00 | −0.439568 | ||||||||
\(362\) | −8884.00 | −1.28987 | ||||||||
\(363\) | −1204.00 | −0.174087 | ||||||||
\(364\) | −1792.00 | −0.258039 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1640.00 | −0.234219 | ||||||||
\(367\) | 4714.00 | 0.670487 | 0.335244 | − | 0.942131i | \(-0.391181\pi\) | ||||
0.335244 | + | 0.942131i | \(0.391181\pi\) | |||||||
\(368\) | 1680.00 | 0.237978 | ||||||||
\(369\) | 8142.00 | 1.14866 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2142.00 | −0.299750 | ||||||||
\(372\) | −992.000 | −0.138260 | ||||||||
\(373\) | −503.000 | −0.0698240 | −0.0349120 | − | 0.999390i | \(-0.511115\pi\) | ||||
−0.0349120 | + | 0.999390i | \(0.511115\pi\) | |||||||
\(374\) | 1296.00 | 0.179183 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −816.000 | −0.111920 | ||||||||
\(377\) | 9024.00 | 1.23278 | ||||||||
\(378\) | −1400.00 | −0.190498 | ||||||||
\(379\) | −10057.0 | −1.36304 | −0.681522 | − | 0.731798i | \(-0.738681\pi\) | ||||
−0.681522 | + | 0.731798i | \(0.738681\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2758.00 | −0.370857 | ||||||||
\(382\) | 1032.00 | 0.138224 | ||||||||
\(383\) | 1500.00 | 0.200121 | 0.100061 | − | 0.994981i | \(-0.468096\pi\) | ||||
0.100061 | + | 0.994981i | \(0.468096\pi\) | |||||||
\(384\) | −256.000 | −0.0340207 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −530.000 | −0.0698868 | ||||||||
\(387\) | −4853.00 | −0.637447 | ||||||||
\(388\) | −5360.00 | −0.701322 | ||||||||
\(389\) | 2349.00 | 0.306167 | 0.153084 | − | 0.988213i | \(-0.451080\pi\) | ||||
0.153084 | + | 0.988213i | \(0.451080\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2520.00 | 0.325938 | ||||||||
\(392\) | −392.000 | −0.0505076 | ||||||||
\(393\) | 360.000 | 0.0462076 | ||||||||
\(394\) | −4314.00 | −0.551615 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2484.00 | 0.315216 | ||||||||
\(397\) | −9794.00 | −1.23815 | −0.619077 | − | 0.785331i | \(-0.712493\pi\) | ||||
−0.619077 | + | 0.785331i | \(0.712493\pi\) | |||||||
\(398\) | 10028.0 | 1.26296 | ||||||||
\(399\) | −868.000 | −0.108908 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5793.00 | 0.721418 | 0.360709 | − | 0.932678i | \(-0.382535\pi\) | ||||
0.360709 | + | 0.932678i | \(0.382535\pi\) | |||||||
\(402\) | −1396.00 | −0.173199 | ||||||||
\(403\) | −7936.00 | −0.980944 | ||||||||
\(404\) | 5880.00 | 0.724111 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1974.00 | 0.241300 | ||||||||
\(407\) | −11853.0 | −1.44357 | ||||||||
\(408\) | −384.000 | −0.0465952 | ||||||||
\(409\) | −5530.00 | −0.668560 | −0.334280 | − | 0.942474i | \(-0.608493\pi\) | ||||
−0.334280 | + | 0.942474i | \(0.608493\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2244.00 | −0.269315 | ||||||||
\(412\) | 7480.00 | 0.894449 | ||||||||
\(413\) | −2436.00 | −0.290237 | ||||||||
\(414\) | 4830.00 | 0.573385 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2048.00 | −0.241374 | ||||||||
\(417\) | −356.000 | −0.0418067 | ||||||||
\(418\) | 3348.00 | 0.391761 | ||||||||
\(419\) | 8208.00 | 0.957010 | 0.478505 | − | 0.878085i | \(-0.341179\pi\) | ||||
0.478505 | + | 0.878085i | \(0.341179\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5375.00 | 0.622236 | 0.311118 | − | 0.950371i | \(-0.399297\pi\) | ||||
0.311118 | + | 0.950371i | \(0.399297\pi\) | |||||||
\(422\) | −3544.00 | −0.408813 | ||||||||
\(423\) | −2346.00 | −0.269661 | ||||||||
\(424\) | −2448.00 | −0.280390 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1356.00 | 0.154222 | ||||||||
\(427\) | −2870.00 | −0.325267 | ||||||||
\(428\) | 816.000 | 0.0921562 | ||||||||
\(429\) | −3456.00 | −0.388945 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10476.0 | −1.17079 | −0.585396 | − | 0.810748i | \(-0.699061\pi\) | ||||
−0.585396 | + | 0.810748i | \(0.699061\pi\) | |||||||
\(432\) | −1600.00 | −0.178195 | ||||||||
\(433\) | 8392.00 | 0.931394 | 0.465697 | − | 0.884944i | \(-0.345804\pi\) | ||||
0.465697 | + | 0.884944i | \(0.345804\pi\) | |||||||
\(434\) | −1736.00 | −0.192006 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1996.00 | −0.219246 | ||||||||
\(437\) | 6510.00 | 0.712621 | ||||||||
\(438\) | −280.000 | −0.0305455 | ||||||||
\(439\) | 224.000 | 0.0243529 | 0.0121765 | − | 0.999926i | \(-0.496124\pi\) | ||||
0.0121765 | + | 0.999926i | \(0.496124\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1127.00 | −0.121693 | ||||||||
\(442\) | −3072.00 | −0.330589 | ||||||||
\(443\) | −1068.00 | −0.114542 | −0.0572711 | − | 0.998359i | \(-0.518240\pi\) | ||||
−0.0572711 | + | 0.998359i | \(0.518240\pi\) | |||||||
\(444\) | 3512.00 | 0.375388 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −3236.00 | −0.343563 | ||||||||
\(447\) | −4194.00 | −0.443779 | ||||||||
\(448\) | −448.000 | −0.0472456 | ||||||||
\(449\) | 17295.0 | 1.81782 | 0.908910 | − | 0.416992i | \(-0.136916\pi\) | ||||
0.908910 | + | 0.416992i | \(0.136916\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9558.00 | 0.997935 | ||||||||
\(452\) | 228.000 | 0.0237261 | ||||||||
\(453\) | −1574.00 | −0.163252 | ||||||||
\(454\) | −3612.00 | −0.373391 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −992.000 | −0.101874 | ||||||||
\(457\) | 4381.00 | 0.448434 | 0.224217 | − | 0.974539i | \(-0.428017\pi\) | ||||
0.224217 | + | 0.974539i | \(0.428017\pi\) | |||||||
\(458\) | −13468.0 | −1.37406 | ||||||||
\(459\) | −2400.00 | −0.244058 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −312.000 | −0.0315212 | −0.0157606 | − | 0.999876i | \(-0.505017\pi\) | ||||
−0.0157606 | + | 0.999876i | \(0.505017\pi\) | |||||||
\(462\) | −756.000 | −0.0761305 | ||||||||
\(463\) | 9736.00 | 0.977258 | 0.488629 | − | 0.872492i | \(-0.337497\pi\) | ||||
0.488629 | + | 0.872492i | \(0.337497\pi\) | |||||||
\(464\) | 2256.00 | 0.225716 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 12666.0 | 1.25910 | ||||||||
\(467\) | −14862.0 | −1.47266 | −0.736329 | − | 0.676624i | \(-0.763442\pi\) | ||||
−0.736329 | + | 0.676624i | \(0.763442\pi\) | |||||||
\(468\) | −5888.00 | −0.581566 | ||||||||
\(469\) | −2443.00 | −0.240527 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1900.00 | −0.185876 | ||||||||
\(472\) | −2784.00 | −0.271491 | ||||||||
\(473\) | −5697.00 | −0.553802 | ||||||||
\(474\) | −2924.00 | −0.283341 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −672.000 | −0.0647081 | ||||||||
\(477\) | −7038.00 | −0.675572 | ||||||||
\(478\) | −14064.0 | −1.34576 | ||||||||
\(479\) | −13248.0 | −1.26371 | −0.631854 | − | 0.775087i | \(-0.717706\pi\) | ||||
−0.631854 | + | 0.775087i | \(0.717706\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 28096.0 | 2.66334 | ||||||||
\(482\) | −8020.00 | −0.757886 | ||||||||
\(483\) | −1470.00 | −0.138483 | ||||||||
\(484\) | −2408.00 | −0.226146 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −7084.00 | −0.661187 | ||||||||
\(487\) | −5597.00 | −0.520789 | −0.260395 | − | 0.965502i | \(-0.583853\pi\) | ||||
−0.260395 | + | 0.965502i | \(0.583853\pi\) | |||||||
\(488\) | −3280.00 | −0.304259 | ||||||||
\(489\) | 5480.00 | 0.506777 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13533.0 | 1.24386 | 0.621930 | − | 0.783072i | \(-0.286349\pi\) | ||||
0.621930 | + | 0.783072i | \(0.286349\pi\) | |||||||
\(492\) | −2832.00 | −0.259505 | ||||||||
\(493\) | 3384.00 | 0.309143 | ||||||||
\(494\) | −7936.00 | −0.722789 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1984.00 | −0.179605 | ||||||||
\(497\) | 2373.00 | 0.214172 | ||||||||
\(498\) | 2112.00 | 0.190042 | ||||||||
\(499\) | −17092.0 | −1.53335 | −0.766676 | − | 0.642034i | \(-0.778091\pi\) | ||||
−0.766676 | + | 0.642034i | \(0.778091\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8208.00 | −0.731949 | ||||||||
\(502\) | 12360.0 | 1.09891 | ||||||||
\(503\) | −8682.00 | −0.769605 | −0.384802 | − | 0.922999i | \(-0.625730\pi\) | ||||
−0.384802 | + | 0.922999i | \(0.625730\pi\) | |||||||
\(504\) | −1288.00 | −0.113833 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 5670.00 | 0.498147 | ||||||||
\(507\) | 3798.00 | 0.332693 | ||||||||
\(508\) | −5516.00 | −0.481758 | ||||||||
\(509\) | 5208.00 | 0.453518 | 0.226759 | − | 0.973951i | \(-0.427187\pi\) | ||||
0.226759 | + | 0.973951i | \(0.427187\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −490.000 | −0.0424194 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | −6200.00 | −0.533600 | ||||||||
\(514\) | 1560.00 | 0.133869 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1688.00 | 0.144012 | ||||||||
\(517\) | −2754.00 | −0.234276 | ||||||||
\(518\) | 6146.00 | 0.521312 | ||||||||
\(519\) | 1716.00 | 0.145133 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 19374.0 | 1.62916 | 0.814578 | − | 0.580054i | \(-0.196969\pi\) | ||||
0.814578 | + | 0.580054i | \(0.196969\pi\) | |||||||
\(522\) | 6486.00 | 0.543840 | ||||||||
\(523\) | 20956.0 | 1.75209 | 0.876044 | − | 0.482231i | \(-0.160174\pi\) | ||||
0.876044 | + | 0.482231i | \(0.160174\pi\) | |||||||
\(524\) | 720.000 | 0.0600255 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 13626.0 | 1.12951 | ||||||||
\(527\) | −2976.00 | −0.245990 | ||||||||
\(528\) | −864.000 | −0.0712136 | ||||||||
\(529\) | −1142.00 | −0.0938604 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8004.00 | −0.654132 | ||||||||
\(532\) | −1736.00 | −0.141476 | ||||||||
\(533\) | −22656.0 | −1.84116 | ||||||||
\(534\) | −3840.00 | −0.311185 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −2792.00 | −0.224993 | ||||||||
\(537\) | −9216.00 | −0.740595 | ||||||||
\(538\) | 11568.0 | 0.927011 | ||||||||
\(539\) | −1323.00 | −0.105725 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14483.0 | 1.15097 | 0.575483 | − | 0.817814i | \(-0.304814\pi\) | ||||
0.575483 | + | 0.817814i | \(0.304814\pi\) | |||||||
\(542\) | 3056.00 | 0.242189 | ||||||||
\(543\) | 8884.00 | 0.702116 | ||||||||
\(544\) | −768.000 | −0.0605289 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1792.00 | 0.140459 | ||||||||
\(547\) | −12935.0 | −1.01108 | −0.505540 | − | 0.862803i | \(-0.668707\pi\) | ||||
−0.505540 | + | 0.862803i | \(0.668707\pi\) | |||||||
\(548\) | −4488.00 | −0.349850 | ||||||||
\(549\) | −9430.00 | −0.733083 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8742.00 | 0.675901 | ||||||||
\(552\) | −1680.00 | −0.129539 | ||||||||
\(553\) | −5117.00 | −0.393485 | ||||||||
\(554\) | −17852.0 | −1.36906 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −712.000 | −0.0543085 | ||||||||
\(557\) | 7593.00 | 0.577605 | 0.288802 | − | 0.957389i | \(-0.406743\pi\) | ||||
0.288802 | + | 0.957389i | \(0.406743\pi\) | |||||||
\(558\) | −5704.00 | −0.432741 | ||||||||
\(559\) | 13504.0 | 1.02175 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1296.00 | −0.0975350 | ||||||||
\(562\) | −1554.00 | −0.116640 | ||||||||
\(563\) | 13674.0 | 1.02361 | 0.511803 | − | 0.859103i | \(-0.328978\pi\) | ||||
0.511803 | + | 0.859103i | \(0.328978\pi\) | |||||||
\(564\) | 816.000 | 0.0609216 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −14036.0 | −1.04236 | ||||||||
\(567\) | −2947.00 | −0.218276 | ||||||||
\(568\) | 2712.00 | 0.200340 | ||||||||
\(569\) | 15477.0 | 1.14030 | 0.570149 | − | 0.821541i | \(-0.306885\pi\) | ||||
0.570149 | + | 0.821541i | \(0.306885\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11509.0 | −0.843497 | −0.421748 | − | 0.906713i | \(-0.638583\pi\) | ||||
−0.421748 | + | 0.906713i | \(0.638583\pi\) | |||||||
\(572\) | −6912.00 | −0.505254 | ||||||||
\(573\) | −1032.00 | −0.0752398 | ||||||||
\(574\) | −4956.00 | −0.360382 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1472.00 | −0.106481 | ||||||||
\(577\) | 20254.0 | 1.46133 | 0.730663 | − | 0.682738i | \(-0.239211\pi\) | ||||
0.730663 | + | 0.682738i | \(0.239211\pi\) | |||||||
\(578\) | 8674.00 | 0.624206 | ||||||||
\(579\) | 530.000 | 0.0380415 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3696.00 | 0.263917 | ||||||||
\(582\) | 5360.00 | 0.381751 | ||||||||
\(583\) | −8262.00 | −0.586925 | ||||||||
\(584\) | −560.000 | −0.0396797 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3864.00 | 0.272390 | ||||||||
\(587\) | 6882.00 | 0.483902 | 0.241951 | − | 0.970288i | \(-0.422213\pi\) | ||||
0.241951 | + | 0.970288i | \(0.422213\pi\) | |||||||
\(588\) | 392.000 | 0.0274929 | ||||||||
\(589\) | −7688.00 | −0.537824 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4314.00 | 0.300261 | ||||||||
\(592\) | 7024.00 | 0.487643 | ||||||||
\(593\) | −9444.00 | −0.653994 | −0.326997 | − | 0.945025i | \(-0.606037\pi\) | ||||
−0.326997 | + | 0.945025i | \(0.606037\pi\) | |||||||
\(594\) | −5400.00 | −0.373005 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −8388.00 | −0.576486 | ||||||||
\(597\) | −10028.0 | −0.687469 | ||||||||
\(598\) | −13440.0 | −0.919068 | ||||||||
\(599\) | −3309.00 | −0.225713 | −0.112856 | − | 0.993611i | \(-0.536000\pi\) | ||||
−0.112856 | + | 0.993611i | \(0.536000\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7672.00 | −0.520711 | −0.260356 | − | 0.965513i | \(-0.583840\pi\) | ||||
−0.260356 | + | 0.965513i | \(0.583840\pi\) | |||||||
\(602\) | 2954.00 | 0.199993 | ||||||||
\(603\) | −8027.00 | −0.542097 | ||||||||
\(604\) | −3148.00 | −0.212070 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −5880.00 | −0.394156 | ||||||||
\(607\) | −1568.00 | −0.104849 | −0.0524243 | − | 0.998625i | \(-0.516695\pi\) | ||||
−0.0524243 | + | 0.998625i | \(0.516695\pi\) | |||||||
\(608\) | −1984.00 | −0.132339 | ||||||||
\(609\) | −1974.00 | −0.131347 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6528.00 | 0.432233 | ||||||||
\(612\) | −2208.00 | −0.145838 | ||||||||
\(613\) | 11779.0 | 0.776100 | 0.388050 | − | 0.921638i | \(-0.373149\pi\) | ||||
0.388050 | + | 0.921638i | \(0.373149\pi\) | |||||||
\(614\) | 9592.00 | 0.630459 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1512.00 | −0.0988965 | ||||||||
\(617\) | −24129.0 | −1.57439 | −0.787194 | − | 0.616706i | \(-0.788467\pi\) | ||||
−0.787194 | + | 0.616706i | \(0.788467\pi\) | |||||||
\(618\) | −7480.00 | −0.486877 | ||||||||
\(619\) | 9788.00 | 0.635562 | 0.317781 | − | 0.948164i | \(-0.397062\pi\) | ||||
0.317781 | + | 0.948164i | \(0.397062\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −10500.0 | −0.678503 | ||||||||
\(622\) | 11976.0 | 0.772016 | ||||||||
\(623\) | −6720.00 | −0.432153 | ||||||||
\(624\) | 2048.00 | 0.131387 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −17180.0 | −1.09689 | ||||||||
\(627\) | −3348.00 | −0.213248 | ||||||||
\(628\) | −3800.00 | −0.241459 | ||||||||
\(629\) | 10536.0 | 0.667882 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −26833.0 | −1.69288 | −0.846438 | − | 0.532487i | \(-0.821257\pi\) | ||||
−0.846438 | + | 0.532487i | \(0.821257\pi\) | |||||||
\(632\) | −5848.00 | −0.368071 | ||||||||
\(633\) | 3544.00 | 0.222530 | ||||||||
\(634\) | −16098.0 | −1.00841 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2448.00 | 0.152625 | ||||||||
\(637\) | 3136.00 | 0.195059 | ||||||||
\(638\) | 7614.00 | 0.472478 | ||||||||
\(639\) | 7797.00 | 0.482699 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11985.0 | 0.738501 | 0.369250 | − | 0.929330i | \(-0.379614\pi\) | ||||
0.369250 | + | 0.929330i | \(0.379614\pi\) | |||||||
\(642\) | −816.000 | −0.0501635 | ||||||||
\(643\) | 23200.0 | 1.42289 | 0.711445 | − | 0.702741i | \(-0.248041\pi\) | ||||
0.711445 | + | 0.702741i | \(0.248041\pi\) | |||||||
\(644\) | −2940.00 | −0.179895 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2976.00 | −0.181253 | ||||||||
\(647\) | −25722.0 | −1.56296 | −0.781481 | − | 0.623929i | \(-0.785535\pi\) | ||||
−0.781481 | + | 0.623929i | \(0.785535\pi\) | |||||||
\(648\) | −3368.00 | −0.204178 | ||||||||
\(649\) | −9396.00 | −0.568298 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1736.00 | 0.104515 | ||||||||
\(652\) | 10960.0 | 0.658323 | ||||||||
\(653\) | 25242.0 | 1.51270 | 0.756352 | − | 0.654165i | \(-0.226980\pi\) | ||||
0.756352 | + | 0.654165i | \(0.226980\pi\) | |||||||
\(654\) | 1996.00 | 0.119342 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −5664.00 | −0.337107 | ||||||||
\(657\) | −1610.00 | −0.0956044 | ||||||||
\(658\) | 1428.00 | 0.0846037 | ||||||||
\(659\) | 26076.0 | 1.54139 | 0.770696 | − | 0.637204i | \(-0.219909\pi\) | ||||
0.770696 | + | 0.637204i | \(0.219909\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9250.00 | −0.544302 | −0.272151 | − | 0.962255i | \(-0.587735\pi\) | ||||
−0.272151 | + | 0.962255i | \(0.587735\pi\) | |||||||
\(662\) | 9770.00 | 0.573598 | ||||||||
\(663\) | 3072.00 | 0.179950 | ||||||||
\(664\) | 4224.00 | 0.246872 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 20194.0 | 1.17493 | ||||||||
\(667\) | 14805.0 | 0.859448 | ||||||||
\(668\) | −16416.0 | −0.950830 | ||||||||
\(669\) | 3236.00 | 0.187012 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −11070.0 | −0.636889 | ||||||||
\(672\) | 448.000 | 0.0257172 | ||||||||
\(673\) | 8674.00 | 0.496817 | 0.248409 | − | 0.968655i | \(-0.420092\pi\) | ||||
0.248409 | + | 0.968655i | \(0.420092\pi\) | |||||||
\(674\) | −1052.00 | −0.0601210 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 7596.00 | 0.432180 | ||||||||
\(677\) | 15990.0 | 0.907748 | 0.453874 | − | 0.891066i | \(-0.350042\pi\) | ||||
0.453874 | + | 0.891066i | \(0.350042\pi\) | |||||||
\(678\) | −228.000 | −0.0129149 | ||||||||
\(679\) | 9380.00 | 0.530149 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3612.00 | 0.203248 | ||||||||
\(682\) | −6696.00 | −0.375958 | ||||||||
\(683\) | −5709.00 | −0.319837 | −0.159919 | − | 0.987130i | \(-0.551123\pi\) | ||||
−0.159919 | + | 0.987130i | \(0.551123\pi\) | |||||||
\(684\) | −5704.00 | −0.318857 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 686.000 | 0.0381802 | ||||||||
\(687\) | 13468.0 | 0.747942 | ||||||||
\(688\) | 3376.00 | 0.187077 | ||||||||
\(689\) | 19584.0 | 1.08286 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9394.00 | −0.517170 | −0.258585 | − | 0.965988i | \(-0.583256\pi\) | ||||
−0.258585 | + | 0.965988i | \(0.583256\pi\) | |||||||
\(692\) | 3432.00 | 0.188533 | ||||||||
\(693\) | −4347.00 | −0.238281 | ||||||||
\(694\) | −8934.00 | −0.488660 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −2256.00 | −0.122864 | ||||||||
\(697\) | −8496.00 | −0.461706 | ||||||||
\(698\) | 3596.00 | 0.195001 | ||||||||
\(699\) | −12666.0 | −0.685368 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9930.00 | −0.535023 | −0.267511 | − | 0.963555i | \(-0.586201\pi\) | ||||
−0.267511 | + | 0.963555i | \(0.586201\pi\) | |||||||
\(702\) | 12800.0 | 0.688184 | ||||||||
\(703\) | 27218.0 | 1.46024 | ||||||||
\(704\) | −1728.00 | −0.0925092 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2040.00 | −0.108748 | ||||||||
\(707\) | −10290.0 | −0.547377 | ||||||||
\(708\) | 2784.00 | 0.147781 | ||||||||
\(709\) | −11962.0 | −0.633628 | −0.316814 | − | 0.948488i | \(-0.602613\pi\) | ||||
−0.316814 | + | 0.948488i | \(0.602613\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −16813.0 | −0.886831 | ||||||||
\(712\) | −7680.00 | −0.404242 | ||||||||
\(713\) | −13020.0 | −0.683875 | ||||||||
\(714\) | 672.000 | 0.0352226 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −18432.0 | −0.962062 | ||||||||
\(717\) | 14064.0 | 0.732538 | ||||||||
\(718\) | 25278.0 | 1.31388 | ||||||||
\(719\) | 28950.0 | 1.50160 | 0.750802 | − | 0.660528i | \(-0.229667\pi\) | ||||
0.750802 | + | 0.660528i | \(0.229667\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13090.0 | −0.676140 | ||||||||
\(722\) | 6030.00 | 0.310822 | ||||||||
\(723\) | 8020.00 | 0.412541 | ||||||||
\(724\) | 17768.0 | 0.912075 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 2408.00 | 0.123098 | ||||||||
\(727\) | 22168.0 | 1.13090 | 0.565451 | − | 0.824782i | \(-0.308702\pi\) | ||||
0.565451 | + | 0.824782i | \(0.308702\pi\) | |||||||
\(728\) | 3584.00 | 0.182461 | ||||||||
\(729\) | −4283.00 | −0.217599 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5064.00 | 0.256223 | ||||||||
\(732\) | 3280.00 | 0.165618 | ||||||||
\(733\) | −3980.00 | −0.200552 | −0.100276 | − | 0.994960i | \(-0.531973\pi\) | ||||
−0.100276 | + | 0.994960i | \(0.531973\pi\) | |||||||
\(734\) | −9428.00 | −0.474106 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3360.00 | −0.168276 | ||||||||
\(737\) | −9423.00 | −0.470964 | ||||||||
\(738\) | −16284.0 | −0.812225 | ||||||||
\(739\) | 10145.0 | 0.504993 | 0.252497 | − | 0.967598i | \(-0.418748\pi\) | ||||
0.252497 | + | 0.967598i | \(0.418748\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7936.00 | 0.393436 | ||||||||
\(742\) | 4284.00 | 0.211955 | ||||||||
\(743\) | −2328.00 | −0.114948 | −0.0574738 | − | 0.998347i | \(-0.518305\pi\) | ||||
−0.0574738 | + | 0.998347i | \(0.518305\pi\) | |||||||
\(744\) | 1984.00 | 0.0977647 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 1006.00 | 0.0493730 | ||||||||
\(747\) | 12144.0 | 0.594814 | ||||||||
\(748\) | −2592.00 | −0.126702 | ||||||||
\(749\) | −1428.00 | −0.0696635 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13484.0 | 0.655177 | 0.327589 | − | 0.944820i | \(-0.393764\pi\) | ||||
0.327589 | + | 0.944820i | \(0.393764\pi\) | |||||||
\(752\) | 1632.00 | 0.0791395 | ||||||||
\(753\) | −12360.0 | −0.598172 | ||||||||
\(754\) | −18048.0 | −0.871710 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2800.00 | 0.134702 | ||||||||
\(757\) | 4783.00 | 0.229645 | 0.114822 | − | 0.993386i | \(-0.463370\pi\) | ||||
0.114822 | + | 0.993386i | \(0.463370\pi\) | |||||||
\(758\) | 20114.0 | 0.963817 | ||||||||
\(759\) | −5670.00 | −0.271157 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6144.00 | −0.292667 | −0.146334 | − | 0.989235i | \(-0.546747\pi\) | ||||
−0.146334 | + | 0.989235i | \(0.546747\pi\) | |||||||
\(762\) | 5516.00 | 0.262236 | ||||||||
\(763\) | 3493.00 | 0.165734 | ||||||||
\(764\) | −2064.00 | −0.0977394 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3000.00 | −0.141507 | ||||||||
\(767\) | 22272.0 | 1.04849 | ||||||||
\(768\) | 512.000 | 0.0240563 | ||||||||
\(769\) | 31922.0 | 1.49693 | 0.748463 | − | 0.663176i | \(-0.230792\pi\) | ||||
0.748463 | + | 0.663176i | \(0.230792\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1560.00 | −0.0728690 | ||||||||
\(772\) | 1060.00 | 0.0494174 | ||||||||
\(773\) | 15516.0 | 0.721956 | 0.360978 | − | 0.932574i | \(-0.382443\pi\) | ||||
0.360978 | + | 0.932574i | \(0.382443\pi\) | |||||||
\(774\) | 9706.00 | 0.450743 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 10720.0 | 0.495909 | ||||||||
\(777\) | −6146.00 | −0.283766 | ||||||||
\(778\) | −4698.00 | −0.216493 | ||||||||
\(779\) | −21948.0 | −1.00946 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9153.00 | 0.419360 | ||||||||
\(782\) | −5040.00 | −0.230473 | ||||||||
\(783\) | −14100.0 | −0.643541 | ||||||||
\(784\) | 784.000 | 0.0357143 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −720.000 | −0.0326737 | ||||||||
\(787\) | 11758.0 | 0.532563 | 0.266282 | − | 0.963895i | \(-0.414205\pi\) | ||||
0.266282 | + | 0.963895i | \(0.414205\pi\) | |||||||
\(788\) | 8628.00 | 0.390050 | ||||||||
\(789\) | −13626.0 | −0.614827 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −399.000 | −0.0179353 | ||||||||
\(792\) | −4968.00 | −0.222892 | ||||||||
\(793\) | 26240.0 | 1.17504 | ||||||||
\(794\) | 19588.0 | 0.875506 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −20056.0 | −0.893048 | ||||||||
\(797\) | 3780.00 | 0.167998 | 0.0839990 | − | 0.996466i | \(-0.473231\pi\) | ||||
0.0839990 | + | 0.996466i | \(0.473231\pi\) | |||||||
\(798\) | 1736.00 | 0.0770097 | ||||||||
\(799\) | 2448.00 | 0.108391 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −22080.0 | −0.973981 | ||||||||
\(802\) | −11586.0 | −0.510120 | ||||||||
\(803\) | −1890.00 | −0.0830593 | ||||||||
\(804\) | 2792.00 | 0.122470 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 15872.0 | 0.693632 | ||||||||
\(807\) | −11568.0 | −0.504601 | ||||||||
\(808\) | −11760.0 | −0.512024 | ||||||||
\(809\) | 43179.0 | 1.87651 | 0.938253 | − | 0.345951i | \(-0.112444\pi\) | ||||
0.938253 | + | 0.345951i | \(0.112444\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13426.0 | −0.581320 | −0.290660 | − | 0.956826i | \(-0.593875\pi\) | ||||
−0.290660 | + | 0.956826i | \(0.593875\pi\) | |||||||
\(812\) | −3948.00 | −0.170625 | ||||||||
\(813\) | −3056.00 | −0.131831 | ||||||||
\(814\) | 23706.0 | 1.02076 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 768.000 | 0.0329478 | ||||||||
\(817\) | 13082.0 | 0.560197 | ||||||||
\(818\) | 11060.0 | 0.472743 | ||||||||
\(819\) | 10304.0 | 0.439623 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5886.00 | −0.250210 | −0.125105 | − | 0.992143i | \(-0.539927\pi\) | ||||
−0.125105 | + | 0.992143i | \(0.539927\pi\) | |||||||
\(822\) | 4488.00 | 0.190434 | ||||||||
\(823\) | −7523.00 | −0.318633 | −0.159317 | − | 0.987228i | \(-0.550929\pi\) | ||||
−0.159317 | + | 0.987228i | \(0.550929\pi\) | |||||||
\(824\) | −14960.0 | −0.632471 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 4872.00 | 0.205228 | ||||||||
\(827\) | 14547.0 | 0.611667 | 0.305834 | − | 0.952085i | \(-0.401065\pi\) | ||||
0.305834 | + | 0.952085i | \(0.401065\pi\) | |||||||
\(828\) | −9660.00 | −0.405445 | ||||||||
\(829\) | −39436.0 | −1.65219 | −0.826097 | − | 0.563528i | \(-0.809444\pi\) | ||||
−0.826097 | + | 0.563528i | \(0.809444\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 17852.0 | 0.745221 | ||||||||
\(832\) | 4096.00 | 0.170677 | ||||||||
\(833\) | 1176.00 | 0.0489147 | ||||||||
\(834\) | 712.000 | 0.0295618 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −6696.00 | −0.277017 | ||||||||
\(837\) | 12400.0 | 0.512075 | ||||||||
\(838\) | −16416.0 | −0.676708 | ||||||||
\(839\) | 1566.00 | 0.0644390 | 0.0322195 | − | 0.999481i | \(-0.489742\pi\) | ||||
0.0322195 | + | 0.999481i | \(0.489742\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4508.00 | −0.184837 | ||||||||
\(842\) | −10750.0 | −0.439987 | ||||||||
\(843\) | 1554.00 | 0.0634906 | ||||||||
\(844\) | 7088.00 | 0.289075 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 4692.00 | 0.190679 | ||||||||
\(847\) | 4214.00 | 0.170950 | ||||||||
\(848\) | 4896.00 | 0.198266 | ||||||||
\(849\) | 14036.0 | 0.567390 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 46095.0 | 1.85678 | ||||||||
\(852\) | −2712.00 | −0.109051 | ||||||||
\(853\) | −35300.0 | −1.41694 | −0.708470 | − | 0.705741i | \(-0.750614\pi\) | ||||
−0.708470 | + | 0.705741i | \(0.750614\pi\) | |||||||
\(854\) | 5740.00 | 0.229999 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1632.00 | −0.0651643 | ||||||||
\(857\) | 810.000 | 0.0322860 | 0.0161430 | − | 0.999870i | \(-0.494861\pi\) | ||||
0.0161430 | + | 0.999870i | \(0.494861\pi\) | |||||||
\(858\) | 6912.00 | 0.275025 | ||||||||
\(859\) | −38734.0 | −1.53852 | −0.769259 | − | 0.638937i | \(-0.779374\pi\) | ||||
−0.769259 | + | 0.638937i | \(0.779374\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4956.00 | 0.196167 | ||||||||
\(862\) | 20952.0 | 0.827875 | ||||||||
\(863\) | −9549.00 | −0.376653 | −0.188327 | − | 0.982106i | \(-0.560306\pi\) | ||||
−0.188327 | + | 0.982106i | \(0.560306\pi\) | |||||||
\(864\) | 3200.00 | 0.126003 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −16784.0 | −0.658595 | ||||||||
\(867\) | −8674.00 | −0.339774 | ||||||||
\(868\) | 3472.00 | 0.135769 | ||||||||
\(869\) | −19737.0 | −0.770462 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 22336.0 | 0.868917 | ||||||||
\(872\) | 3992.00 | 0.155030 | ||||||||
\(873\) | 30820.0 | 1.19484 | ||||||||
\(874\) | −13020.0 | −0.503899 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 560.000 | 0.0215989 | ||||||||
\(877\) | 22966.0 | 0.884272 | 0.442136 | − | 0.896948i | \(-0.354221\pi\) | ||||
0.442136 | + | 0.896948i | \(0.354221\pi\) | |||||||
\(878\) | −448.000 | −0.0172201 | ||||||||
\(879\) | −3864.00 | −0.148270 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 20484.0 | 0.783341 | 0.391671 | − | 0.920106i | \(-0.371897\pi\) | ||||
0.391671 | + | 0.920106i | \(0.371897\pi\) | |||||||
\(882\) | 2254.00 | 0.0860500 | ||||||||
\(883\) | −41651.0 | −1.58739 | −0.793696 | − | 0.608314i | \(-0.791846\pi\) | ||||
−0.793696 | + | 0.608314i | \(0.791846\pi\) | |||||||
\(884\) | 6144.00 | 0.233761 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2136.00 | 0.0809936 | ||||||||
\(887\) | 50598.0 | 1.91535 | 0.957675 | − | 0.287853i | \(-0.0929416\pi\) | ||||
0.957675 | + | 0.287853i | \(0.0929416\pi\) | |||||||
\(888\) | −7024.00 | −0.265439 | ||||||||
\(889\) | 9653.00 | 0.364175 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −11367.0 | −0.427395 | ||||||||
\(892\) | 6472.00 | 0.242936 | ||||||||
\(893\) | 6324.00 | 0.236982 | ||||||||
\(894\) | 8388.00 | 0.313799 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 896.000 | 0.0334077 | ||||||||
\(897\) | 13440.0 | 0.500277 | ||||||||
\(898\) | −34590.0 | −1.28539 | ||||||||
\(899\) | −17484.0 | −0.648636 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7344.00 | 0.271547 | ||||||||
\(902\) | −19116.0 | −0.705647 | ||||||||
\(903\) | −2954.00 | −0.108863 | ||||||||
\(904\) | −456.000 | −0.0167769 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 3148.00 | 0.115436 | ||||||||
\(907\) | −45092.0 | −1.65078 | −0.825389 | − | 0.564565i | \(-0.809044\pi\) | ||||
−0.825389 | + | 0.564565i | \(0.809044\pi\) | |||||||
\(908\) | 7224.00 | 0.264027 | ||||||||
\(909\) | −33810.0 | −1.23367 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −36069.0 | −1.31177 | −0.655883 | − | 0.754862i | \(-0.727704\pi\) | ||||
−0.655883 | + | 0.754862i | \(0.727704\pi\) | |||||||
\(912\) | 1984.00 | 0.0720360 | ||||||||
\(913\) | 14256.0 | 0.516763 | ||||||||
\(914\) | −8762.00 | −0.317091 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 26936.0 | 0.971605 | ||||||||
\(917\) | −1260.00 | −0.0453750 | ||||||||
\(918\) | 4800.00 | 0.172575 | ||||||||
\(919\) | 15479.0 | 0.555609 | 0.277805 | − | 0.960638i | \(-0.410393\pi\) | ||||
0.277805 | + | 0.960638i | \(0.410393\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9592.00 | −0.343178 | ||||||||
\(922\) | 624.000 | 0.0222889 | ||||||||
\(923\) | −21696.0 | −0.773708 | ||||||||
\(924\) | 1512.00 | 0.0538324 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −19472.0 | −0.691026 | ||||||||
\(927\) | −43010.0 | −1.52388 | ||||||||
\(928\) | −4512.00 | −0.159605 | ||||||||
\(929\) | −39222.0 | −1.38518 | −0.692590 | − | 0.721332i | \(-0.743530\pi\) | ||||
−0.692590 | + | 0.721332i | \(0.743530\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3038.00 | 0.106946 | ||||||||
\(932\) | −25332.0 | −0.890319 | ||||||||
\(933\) | −11976.0 | −0.420232 | ||||||||
\(934\) | 29724.0 | 1.04133 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 11776.0 | 0.411229 | ||||||||
\(937\) | −42518.0 | −1.48239 | −0.741197 | − | 0.671288i | \(-0.765741\pi\) | ||||
−0.741197 | + | 0.671288i | \(0.765741\pi\) | |||||||
\(938\) | 4886.00 | 0.170078 | ||||||||
\(939\) | 17180.0 | 0.597069 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 21924.0 | 0.759513 | 0.379757 | − | 0.925086i | \(-0.376008\pi\) | ||||
0.379757 | + | 0.925086i | \(0.376008\pi\) | |||||||
\(942\) | 3800.00 | 0.131434 | ||||||||
\(943\) | −37170.0 | −1.28359 | ||||||||
\(944\) | 5568.00 | 0.191973 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 11394.0 | 0.391597 | ||||||||
\(947\) | 36.0000 | 0.00123531 | 0.000617657 | − | 1.00000i | \(-0.499803\pi\) | ||||
0.000617657 | 1.00000i | \(0.499803\pi\) | ||||||||
\(948\) | 5848.00 | 0.200353 | ||||||||
\(949\) | 4480.00 | 0.153242 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 16098.0 | 0.548910 | ||||||||
\(952\) | 1344.00 | 0.0457556 | ||||||||
\(953\) | −9291.00 | −0.315808 | −0.157904 | − | 0.987454i | \(-0.550474\pi\) | ||||
−0.157904 | + | 0.987454i | \(0.550474\pi\) | |||||||
\(954\) | 14076.0 | 0.477702 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 28128.0 | 0.951595 | ||||||||
\(957\) | −7614.00 | −0.257185 | ||||||||
\(958\) | 26496.0 | 0.893577 | ||||||||
\(959\) | 7854.00 | 0.264462 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14415.0 | −0.483871 | ||||||||
\(962\) | −56192.0 | −1.88327 | ||||||||
\(963\) | −4692.00 | −0.157007 | ||||||||
\(964\) | 16040.0 | 0.535906 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 2940.00 | 0.0979223 | ||||||||
\(967\) | −3512.00 | −0.116792 | −0.0583962 | − | 0.998293i | \(-0.518599\pi\) | ||||
−0.0583962 | + | 0.998293i | \(0.518599\pi\) | |||||||
\(968\) | 4816.00 | 0.159909 | ||||||||
\(969\) | 2976.00 | 0.0986614 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −41226.0 | −1.36252 | −0.681259 | − | 0.732042i | \(-0.738567\pi\) | ||||
−0.681259 | + | 0.732042i | \(0.738567\pi\) | |||||||
\(972\) | 14168.0 | 0.467530 | ||||||||
\(973\) | 1246.00 | 0.0410534 | ||||||||
\(974\) | 11194.0 | 0.368253 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6560.00 | 0.215144 | ||||||||
\(977\) | −58989.0 | −1.93165 | −0.965827 | − | 0.259189i | \(-0.916545\pi\) | ||||
−0.965827 | + | 0.259189i | \(0.916545\pi\) | |||||||
\(978\) | −10960.0 | −0.358346 | ||||||||
\(979\) | −25920.0 | −0.846176 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11477.0 | 0.373529 | ||||||||
\(982\) | −27066.0 | −0.879543 | ||||||||
\(983\) | 30084.0 | 0.976125 | 0.488062 | − | 0.872809i | \(-0.337704\pi\) | ||||
0.488062 | + | 0.872809i | \(0.337704\pi\) | |||||||
\(984\) | 5664.00 | 0.183498 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −6768.00 | −0.218597 | ||||||||
\(987\) | −1428.00 | −0.0460524 | ||||||||
\(988\) | 15872.0 | 0.511089 | ||||||||
\(989\) | 22155.0 | 0.712324 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2795.00 | 0.0895924 | 0.0447962 | − | 0.998996i | \(-0.485736\pi\) | ||||
0.0447962 | + | 0.998996i | \(0.485736\pi\) | |||||||
\(992\) | 3968.00 | 0.127000 | ||||||||
\(993\) | −9770.00 | −0.312227 | ||||||||
\(994\) | −4746.00 | −0.151443 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −4224.00 | −0.134380 | ||||||||
\(997\) | −21134.0 | −0.671334 | −0.335667 | − | 0.941981i | \(-0.608962\pi\) | ||||
−0.335667 | + | 0.941981i | \(0.608962\pi\) | |||||||
\(998\) | 34184.0 | 1.08424 | ||||||||
\(999\) | −43900.0 | −1.39032 |
(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 | 350.4.a.e.1.1 | ✓ | 1 | |
5.2 | odd | 4 | 350.4.c.f.99.1 | 2 | |||
5.3 | odd | 4 | 350.4.c.f.99.2 | 2 | |||
5.4 | even | 2 | 350.4.a.q.1.1 | yes | 1 | ||
7.6 | odd | 2 | 2450.4.a.h.1.1 | 1 | |||
35.34 | odd | 2 | 2450.4.a.bi.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
350.4.a.e.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
350.4.a.q.1.1 | yes | 1 | 5.4 | even | 2 | ||
350.4.c.f.99.1 | 2 | 5.2 | odd | 4 | |||
350.4.c.f.99.2 | 2 | 5.3 | odd | 4 | |||
2450.4.a.h.1.1 | 1 | 7.6 | odd | 2 | |||
2450.4.a.bi.1.1 | 1 | 35.34 | odd | 2 |