Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8024,2,Mod(1,8024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8024, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8024.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8024 = 2^{3} \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8024.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: | \(64.0719625819\) |
Analytic rank: | \(1\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 2 x^{19} - 29 x^{18} + 51 x^{17} + 341 x^{16} - 514 x^{15} - 2114 x^{14} + 2629 x^{13} + \cdots + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Root | \(-1.42163\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8024.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.42163 | 0.820778 | 0.410389 | − | 0.911911i | \(-0.365393\pi\) | ||||
0.410389 | + | 0.911911i | \(0.365393\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.52594 | −1.57685 | −0.788424 | − | 0.615132i | \(-0.789103\pi\) | ||||
−0.788424 | + | 0.615132i | \(0.789103\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.45144 | −0.548594 | −0.274297 | − | 0.961645i | \(-0.588445\pi\) | ||||
−0.274297 | + | 0.961645i | \(0.588445\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.978971 | −0.326324 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.46002 | 0.741724 | 0.370862 | − | 0.928688i | \(-0.379062\pi\) | ||||
0.370862 | + | 0.928688i | \(0.379062\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.945268 | −0.262170 | −0.131085 | − | 0.991371i | \(-0.541846\pi\) | ||||
−0.131085 | + | 0.991371i | \(0.541846\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −5.01258 | −1.29424 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.98603 | −0.914459 | −0.457229 | − | 0.889349i | \(-0.651158\pi\) | ||||
−0.457229 | + | 0.889349i | \(0.651158\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.06341 | −0.450274 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.79298 | 1.83346 | 0.916731 | − | 0.399505i | \(-0.130818\pi\) | ||||
0.916731 | + | 0.399505i | \(0.130818\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.43225 | 1.48645 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.65662 | −1.08862 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.21441 | 0.596902 | 0.298451 | − | 0.954425i | \(-0.403530\pi\) | ||||
0.298451 | + | 0.954425i | \(0.403530\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.26049 | 1.48363 | 0.741814 | − | 0.670606i | \(-0.233966\pi\) | ||||
0.741814 | + | 0.670606i | \(0.233966\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.49724 | 0.608791 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.11770 | 0.865049 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.00359 | 0.164989 | 0.0824946 | − | 0.996592i | \(-0.473711\pi\) | ||||
0.0824946 | + | 0.996592i | \(0.473711\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.34382 | −0.215183 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.565045 | −0.0882453 | −0.0441226 | − | 0.999026i | \(-0.514049\pi\) | ||||
−0.0441226 | + | 0.999026i | \(0.514049\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.42262 | 0.521945 | 0.260973 | − | 0.965346i | \(-0.415957\pi\) | ||||
0.260973 | + | 0.965346i | \(0.415957\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.45179 | 0.514563 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −11.2479 | −1.64068 | −0.820341 | − | 0.571875i | \(-0.806216\pi\) | ||||
−0.820341 | + | 0.571875i | \(0.806216\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.89331 | −0.699045 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.42163 | 0.199068 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.73587 | −0.650522 | −0.325261 | − | 0.945624i | \(-0.605452\pi\) | ||||
−0.325261 | + | 0.945624i | \(0.605452\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.67388 | −1.16959 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.66666 | −0.750568 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.00000 | −0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.48342 | 1.21423 | 0.607113 | − | 0.794615i | \(-0.292327\pi\) | ||||
0.607113 | + | 0.794615i | \(0.292327\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.42092 | 0.179019 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.33296 | 0.413403 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.29503 | 0.280383 | 0.140191 | − | 0.990124i | \(-0.455228\pi\) | ||||
0.140191 | + | 0.990124i | \(0.455228\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 12.5004 | 1.50487 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.2817 | 1.22021 | 0.610104 | − | 0.792321i | \(-0.291128\pi\) | ||||
0.610104 | + | 0.792321i | \(0.291128\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.35982 | 0.627319 | 0.313660 | − | 0.949535i | \(-0.398445\pi\) | ||||
0.313660 | + | 0.949535i | \(0.398445\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 10.5659 | 1.22005 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.57058 | −0.406905 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.48062 | −0.841635 | −0.420817 | − | 0.907145i | \(-0.638257\pi\) | ||||
−0.420817 | + | 0.907145i | \(0.638257\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.10470 | −0.567189 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.32111 | −0.913361 | −0.456680 | − | 0.889631i | \(-0.650962\pi\) | ||||
−0.456680 | + | 0.889631i | \(0.650962\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.52594 | −0.382442 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.56971 | 0.489924 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −10.7297 | −1.13735 | −0.568675 | − | 0.822562i | \(-0.692544\pi\) | ||||
−0.568675 | + | 0.822562i | \(0.692544\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.37200 | 0.143825 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 11.7434 | 1.21773 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 14.0545 | 1.44196 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.97182 | 0.504812 | 0.252406 | − | 0.967621i | \(-0.418778\pi\) | ||||
0.252406 | + | 0.967621i | \(0.418778\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.40829 | −0.242042 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.297319 | −0.0295843 | −0.0147922 | − | 0.999891i | \(-0.504709\pi\) | ||||
−0.0147922 | + | 0.999891i | \(0.504709\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.1375 | −1.29448 | −0.647239 | − | 0.762288i | \(-0.724076\pi\) | ||||
−0.647239 | + | 0.762288i | \(0.724076\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 7.27547 | 0.710014 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.03846 | −0.197065 | −0.0985327 | − | 0.995134i | \(-0.531415\pi\) | ||||
−0.0985327 | + | 0.995134i | \(0.531415\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.2488 | 0.981656 | 0.490828 | − | 0.871257i | \(-0.336694\pi\) | ||||
0.490828 | + | 0.871257i | \(0.336694\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.42673 | 0.135419 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −13.9800 | −1.31513 | −0.657565 | − | 0.753398i | \(-0.728414\pi\) | ||||
−0.657565 | + | 0.753398i | \(0.728414\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −31.0035 | −2.89109 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.925389 | 0.0855523 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.45144 | −0.133054 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.94830 | −0.449846 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.803285 | −0.0724298 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.57598 | −0.767059 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −18.6372 | −1.65378 | −0.826891 | − | 0.562363i | \(-0.809892\pi\) | ||||
−0.826891 | + | 0.562363i | \(0.809892\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.86570 | 0.428401 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.1975 | −0.890961 | −0.445481 | − | 0.895292i | \(-0.646967\pi\) | ||||
−0.445481 | + | 0.895292i | \(0.646967\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.78550 | 0.501667 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 19.9449 | 1.71658 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −11.9651 | −1.02225 | −0.511124 | − | 0.859507i | \(-0.670771\pi\) | ||||
−0.511124 | + | 0.859507i | \(0.670771\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.13361 | −0.774703 | −0.387351 | − | 0.921932i | \(-0.626610\pi\) | ||||
−0.387351 | + | 0.921932i | \(0.626610\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −15.9904 | −1.34664 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.32538 | −0.194458 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −11.3338 | −0.941224 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.95648 | −0.573761 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.707517 | 0.0579620 | 0.0289810 | − | 0.999580i | \(-0.490774\pi\) | ||||
0.0289810 | + | 0.999580i | \(0.490774\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −19.3599 | −1.57548 | −0.787742 | − | 0.616005i | \(-0.788750\pi\) | ||||
−0.787742 | + | 0.616005i | \(0.788750\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.978971 | −0.0791451 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −29.1260 | −2.33946 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 22.3213 | 1.78143 | 0.890715 | − | 0.454562i | \(-0.150204\pi\) | ||||
0.890715 | + | 0.454562i | \(0.150204\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.73266 | −0.533934 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −12.7625 | −1.00583 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.266638 | 0.0208847 | 0.0104424 | − | 0.999945i | \(-0.496676\pi\) | ||||
0.0104424 | + | 0.999945i | \(0.496676\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −12.3310 | −0.959970 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 20.5696 | 1.59173 | 0.795863 | − | 0.605476i | \(-0.207017\pi\) | ||||
0.795863 | + | 0.605476i | \(0.207017\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.1065 | −0.931267 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.90221 | 0.298409 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.22846 | 0.701627 | 0.350813 | − | 0.936445i | \(-0.385905\pi\) | ||||
0.350813 | + | 0.936445i | \(0.385905\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −10.7875 | −0.815458 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.42163 | −0.106856 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.06033 | −0.228740 | −0.114370 | − | 0.993438i | \(-0.536485\pi\) | ||||
−0.114370 | + | 0.993438i | \(0.536485\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −17.0151 | −1.26472 | −0.632361 | − | 0.774674i | \(-0.717914\pi\) | ||||
−0.632361 | + | 0.774674i | \(0.717914\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 13.4819 | 0.996611 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.53860 | −0.260163 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.46002 | 0.179894 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 8.21026 | 0.597209 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.33478 | 0.386011 | 0.193005 | − | 0.981198i | \(-0.438176\pi\) | ||||
0.193005 | + | 0.981198i | \(0.438176\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.242876 | 0.0174826 | 0.00874131 | − | 0.999962i | \(-0.497218\pi\) | ||||
0.00874131 | + | 0.999962i | \(0.497218\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.73823 | 0.339312 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.691853 | −0.0492925 | −0.0246462 | − | 0.999696i | \(-0.507846\pi\) | ||||
−0.0246462 | + | 0.999696i | \(0.507846\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −24.8116 | −1.75885 | −0.879424 | − | 0.476040i | \(-0.842072\pi\) | ||||
−0.879424 | + | 0.476040i | \(0.842072\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.26269 | 0.230132 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.66554 | −0.327457 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.99232 | 0.139149 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −8.60807 | −0.598302 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −9.80572 | −0.678276 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 22.1152 | 1.52247 | 0.761237 | − | 0.648473i | \(-0.224592\pi\) | ||||
0.761237 | + | 0.648473i | \(0.224592\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 14.6167 | 1.00152 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −12.0680 | −0.823029 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −11.9896 | −0.813909 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 7.61967 | 0.514890 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.945268 | −0.0635856 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.44184 | 0.632272 | 0.316136 | − | 0.948714i | \(-0.397614\pi\) | ||||
0.316136 | + | 0.948714i | \(0.397614\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −7.27596 | −0.485064 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −19.5975 | −1.30073 | −0.650365 | − | 0.759622i | \(-0.725384\pi\) | ||||
−0.650365 | + | 0.759622i | \(0.725384\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.21349 | 0.476681 | 0.238340 | − | 0.971182i | \(-0.423397\pi\) | ||||
0.238340 | + | 0.971182i | \(0.423397\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.07604 | −0.333979 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 15.1352 | 0.991542 | 0.495771 | − | 0.868453i | \(-0.334885\pi\) | ||||
0.495771 | + | 0.868453i | \(0.334885\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 39.6596 | 2.58711 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −10.6347 | −0.690795 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −19.0479 | −1.23210 | −0.616052 | − | 0.787705i | \(-0.711269\pi\) | ||||
−0.616052 | + | 0.787705i | \(0.711269\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.42054 | −0.413583 | −0.206792 | − | 0.978385i | \(-0.566302\pi\) | ||||
−0.206792 | + | 0.978385i | \(0.566302\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 9.71286 | 0.623081 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 17.2535 | 1.10229 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.76787 | 0.239744 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −11.8295 | −0.749666 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −11.1890 | −0.706244 | −0.353122 | − | 0.935577i | \(-0.614880\pi\) | ||||
−0.353122 | + | 0.935577i | \(0.614880\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 21.6309 | 1.35992 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.01258 | −0.313900 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.2434 | 0.888481 | 0.444241 | − | 0.895908i | \(-0.353474\pi\) | ||||
0.444241 | + | 0.895908i | \(0.353474\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.45665 | −0.0905120 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.14682 | −0.194783 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.2989 | −0.635057 | −0.317528 | − | 0.948249i | \(-0.602853\pi\) | ||||
−0.317528 | + | 0.948249i | \(0.602853\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 16.6984 | 1.02578 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −15.2537 | −0.933513 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.72971 | −0.288375 | −0.144188 | − | 0.989550i | \(-0.546057\pi\) | ||||
−0.144188 | + | 0.989550i | \(0.546057\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.8668 | −0.660113 | −0.330057 | − | 0.943961i | \(-0.607068\pi\) | ||||
−0.330057 | + | 0.943961i | \(0.607068\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.95048 | 0.118048 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 18.2835 | 1.10254 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18.8813 | −1.13447 | −0.567234 | − | 0.823557i | \(-0.691986\pi\) | ||||
−0.567234 | + | 0.823557i | \(0.691986\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −8.08678 | −0.484143 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.4452 | 0.623106 | 0.311553 | − | 0.950229i | \(-0.399151\pi\) | ||||
0.311553 | + | 0.950229i | \(0.399151\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.8237 | 1.00007 | 0.500034 | − | 0.866006i | \(-0.333321\pi\) | ||||
0.500034 | + | 0.866006i | \(0.333321\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 19.9803 | 1.18353 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.820131 | 0.0484108 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.06808 | 0.414338 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 15.8707 | 0.927175 | 0.463587 | − | 0.886051i | \(-0.346562\pi\) | ||||
0.463587 | + | 0.886051i | \(0.346562\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.52594 | 0.205288 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −13.9154 | −0.807453 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.31172 | −0.480679 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.96774 | −0.286336 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.422677 | −0.0242822 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −33.4380 | −1.91465 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −23.6707 | −1.35096 | −0.675479 | − | 0.737380i | \(-0.736063\pi\) | ||||
−0.675479 | + | 0.737380i | \(0.736063\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −18.6767 | −1.06248 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.76667 | −0.497112 | −0.248556 | − | 0.968618i | \(-0.579956\pi\) | ||||
−0.248556 | + | 0.968618i | \(0.579956\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −21.3662 | −1.20769 | −0.603845 | − | 0.797102i | \(-0.706365\pi\) | ||||
−0.603845 | + | 0.797102i | \(0.706365\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −5.01008 | −0.282286 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7.96564 | −0.447395 | −0.223697 | − | 0.974659i | \(-0.571813\pi\) | ||||
−0.223697 | + | 0.974659i | \(0.571813\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.90752 | 0.442736 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.89794 | −0.161747 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.98603 | −0.221789 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.02547 | −0.389703 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 14.5700 | 0.805722 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 16.3258 | 0.900068 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.4286 | 0.793070 | 0.396535 | − | 0.918020i | \(-0.370213\pi\) | ||||
0.396535 | + | 0.918020i | \(0.370213\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.982485 | −0.0538398 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.09215 | −0.442121 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.24268 | −0.285587 | −0.142793 | − | 0.989753i | \(-0.545608\pi\) | ||||
−0.142793 | + | 0.989753i | \(0.545608\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −19.8744 | −1.07943 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 20.3210 | 1.10044 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.2625 | 0.932086 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −44.0755 | −2.37294 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −29.4741 | −1.58225 | −0.791127 | − | 0.611652i | \(-0.790505\pi\) | ||||
−0.791127 | + | 0.611652i | \(0.790505\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −14.1069 | −0.755127 | −0.377563 | − | 0.925984i | \(-0.623238\pi\) | ||||
−0.377563 | + | 0.925984i | \(0.623238\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.34702 | 0.285403 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −15.3656 | −0.817828 | −0.408914 | − | 0.912573i | \(-0.634092\pi\) | ||||
−0.408914 | + | 0.912573i | \(0.634092\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −36.2525 | −1.92408 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.06341 | −0.109207 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.27288 | −0.119958 | −0.0599789 | − | 0.998200i | \(-0.519103\pi\) | ||||
−0.0599789 | + | 0.998200i | \(0.519103\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.11154 | −0.163765 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −7.03465 | −0.369223 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −18.8984 | −0.989187 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −18.5230 | −0.966891 | −0.483446 | − | 0.875374i | \(-0.660615\pi\) | ||||
−0.483446 | + | 0.875374i | \(0.660615\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.553163 | 0.0287965 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.87385 | 0.356873 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 28.9273 | 1.49780 | 0.748898 | − | 0.662685i | \(-0.230583\pi\) | ||||
0.748898 | + | 0.662685i | \(0.230583\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −12.1919 | −0.629585 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.03848 | −0.156490 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.3334 | −0.530790 | −0.265395 | − | 0.964140i | \(-0.585502\pi\) | ||||
−0.265395 | + | 0.964140i | \(0.585502\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −26.4951 | −1.35739 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 22.6183 | 1.15574 | 0.577872 | − | 0.816128i | \(-0.303883\pi\) | ||||
0.577872 | + | 0.816128i | \(0.303883\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 12.5896 | 0.641628 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.35065 | −0.170323 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −25.5775 | −1.29683 | −0.648416 | − | 0.761286i | \(-0.724568\pi\) | ||||
−0.648416 | + | 0.761286i | \(0.724568\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.79298 | 0.444680 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −14.4971 | −0.731281 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 26.3762 | 1.32713 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −35.0669 | −1.75996 | −0.879978 | − | 0.475014i | \(-0.842443\pi\) | ||||
−0.879978 | + | 0.475014i | \(0.842443\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 8.22484 | 0.411757 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −19.6821 | −0.982876 | −0.491438 | − | 0.870913i | \(-0.663529\pi\) | ||||
−0.491438 | + | 0.870913i | \(0.663529\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.80838 | −0.388963 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 17.9989 | 0.894372 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.46885 | 0.122376 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.02732 | −0.298032 | −0.149016 | − | 0.988835i | \(-0.547611\pi\) | ||||
−0.149016 | + | 0.988835i | \(0.547611\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −17.0099 | −0.839039 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.45144 | 0.0714208 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 29.3397 | 1.44023 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −12.9846 | −0.635859 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −34.5792 | −1.68931 | −0.844653 | − | 0.535314i | \(-0.820193\pi\) | ||||
−0.844653 | + | 0.535314i | \(0.820193\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.42313 | −0.118096 | −0.0590481 | − | 0.998255i | \(-0.518807\pi\) | ||||
−0.0590481 | + | 0.998255i | \(0.518807\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 11.0114 | 0.535393 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.43225 | 0.360517 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −13.7646 | −0.666117 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.30582 | −0.159607 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 38.8102 | 1.86942 | 0.934710 | − | 0.355411i | \(-0.115659\pi\) | ||||
0.934710 | + | 0.355411i | \(0.115659\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −23.0853 | −1.10941 | −0.554703 | − | 0.832048i | \(-0.687168\pi\) | ||||
−0.554703 | + | 0.832048i | \(0.687168\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −16.1125 | −0.772536 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −35.0491 | −1.67663 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.0408 | 0.813311 | 0.406655 | − | 0.913582i | \(-0.366695\pi\) | ||||
0.406655 | + | 0.913582i | \(0.366695\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.79041 | 0.228115 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.2125 | 0.770277 | 0.385139 | − | 0.922859i | \(-0.374154\pi\) | ||||
0.385139 | + | 0.922859i | \(0.374154\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 37.8324 | 1.79343 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.00583 | 0.0475740 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14.8813 | 0.702291 | 0.351146 | − | 0.936321i | \(-0.385792\pi\) | ||||
0.351146 | + | 0.936321i | \(0.385792\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.39002 | −0.0654536 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −27.5226 | −1.29312 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.83760 | −0.226790 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.63909 | 0.310563 | 0.155282 | − | 0.987870i | \(-0.450371\pi\) | ||||
0.155282 | + | 0.987870i | \(0.450371\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.65662 | −0.264028 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 28.0074 | 1.30444 | 0.652218 | − | 0.758032i | \(-0.273839\pi\) | ||||
0.652218 | + | 0.758032i | \(0.273839\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −25.5994 | −1.18970 | −0.594852 | − | 0.803835i | \(-0.702790\pi\) | ||||
−0.594852 | + | 0.803835i | \(0.702790\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −41.4064 | −1.92017 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 41.7472 | 1.93183 | 0.965914 | − | 0.258864i | \(-0.0833480\pi\) | ||||
0.965914 | + | 0.258864i | \(0.0833480\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.33111 | −0.153816 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 31.7326 | 1.46216 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.41972 | 0.387139 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −29.6252 | −1.35930 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.63628 | 0.212281 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10.1642 | 0.464416 | 0.232208 | − | 0.972666i | \(-0.425405\pi\) | ||||
0.232208 | + | 0.972666i | \(0.425405\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.948661 | −0.0432552 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −18.1435 | −0.825560 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −17.5303 | −0.796012 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.6181 | 0.934297 | 0.467148 | − | 0.884179i | \(-0.345281\pi\) | ||||
0.467148 | + | 0.884179i | \(0.345281\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.379061 | 0.0171417 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 32.4839 | 1.46598 | 0.732988 | − | 0.680242i | \(-0.238125\pi\) | ||||
0.732988 | + | 0.680242i | \(0.238125\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.21441 | 0.144770 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 8.49148 | 0.381663 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −14.9232 | −0.669399 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.60093 | 0.161200 | 0.0805998 | − | 0.996747i | \(-0.474316\pi\) | ||||
0.0805998 | + | 0.996747i | \(0.474316\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 29.2424 | 1.30645 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 36.0997 | 1.60961 | 0.804803 | − | 0.593542i | \(-0.202271\pi\) | ||||
0.804803 | + | 0.593542i | \(0.202271\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.04833 | 0.0466500 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −17.2109 | −0.764363 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −14.8563 | −0.658494 | −0.329247 | − | 0.944244i | \(-0.606795\pi\) | ||||
−0.329247 | + | 0.944244i | \(0.606795\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.77947 | −0.344144 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 22.5475 | 0.995496 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 46.3221 | 2.04119 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −27.6702 | −1.21693 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 13.1194 | 0.575880 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −31.2865 | −1.37069 | −0.685343 | − | 0.728220i | \(-0.740348\pi\) | ||||
−0.685343 | + | 0.728220i | \(0.740348\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −27.2974 | −1.19363 | −0.596816 | − | 0.802378i | \(-0.703568\pi\) | ||||
−0.596816 | + | 0.802378i | \(0.703568\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −15.3358 | −0.669310 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.26049 | 0.359833 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 54.3164 | 2.36158 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.978971 | 0.0424837 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.534119 | 0.0231353 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.18749 | 0.310742 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4.35066 | −0.187745 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −12.0376 | −0.518498 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.1384 | 0.521871 | 0.260935 | − | 0.965356i | \(-0.415969\pi\) | ||||
0.260935 | + | 0.965356i | \(0.415969\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −24.1892 | −1.03806 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −36.1366 | −1.54792 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.41034 | −0.316843 | −0.158422 | − | 0.987372i | \(-0.550641\pi\) | ||||
−0.158422 | + | 0.987372i | \(0.550641\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −9.28398 | −0.396231 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −12.8128 | −0.545842 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10.8577 | 0.461716 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −5.03057 | −0.213536 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.92334 | 0.166237 | 0.0831185 | − | 0.996540i | \(-0.473512\pi\) | ||||
0.0831185 | + | 0.996540i | \(0.473512\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.23530 | −0.136838 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.49724 | 0.147653 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −31.6240 | −1.33279 | −0.666396 | − | 0.745598i | \(-0.732164\pi\) | ||||
−0.666396 | + | 0.745598i | \(0.732164\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 49.2927 | 2.07376 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 7.40919 | 0.311157 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 28.5007 | 1.19481 | 0.597407 | − | 0.801939i | \(-0.296198\pi\) | ||||
0.597407 | + | 0.801939i | \(0.296198\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −35.6311 | −1.49112 | −0.745558 | − | 0.666441i | \(-0.767817\pi\) | ||||
−0.745558 | + | 0.666441i | \(0.767817\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 7.58408 | 0.316829 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 65.3516 | 2.72535 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.56321 | −0.189969 | −0.0949844 | − | 0.995479i | \(-0.530280\pi\) | ||||
−0.0949844 | + | 0.995479i | \(0.530280\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.345280 | 0.0143494 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.0776 | 0.501064 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11.6503 | −0.482508 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.26287 | −0.134903 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.21966 | −0.0503409 | −0.0251704 | − | 0.999683i | \(-0.508013\pi\) | ||||
−0.0251704 | + | 0.999683i | \(0.508013\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −32.9266 | −1.35672 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.983559 | −0.0404582 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −22.9943 | −0.944265 | −0.472132 | − | 0.881528i | \(-0.656516\pi\) | ||||
−0.472132 | + | 0.881528i | \(0.656516\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.11770 | 0.209805 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −35.2729 | −1.44362 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −26.6086 | −1.08720 | −0.543599 | − | 0.839345i | \(-0.682939\pi\) | ||||
−0.543599 | + | 0.839345i | \(0.682939\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19.3997 | −0.791330 | −0.395665 | − | 0.918395i | \(-0.629486\pi\) | ||||
−0.395665 | + | 0.918395i | \(0.629486\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.24677 | −0.0914955 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 17.4474 | 0.709339 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −21.8562 | −0.887118 | −0.443559 | − | 0.896245i | \(-0.646284\pi\) | ||||
−0.443559 | + | 0.896245i | \(0.646284\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6.63267 | −0.268769 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10.6323 | 0.430138 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −22.9347 | −0.926325 | −0.463163 | − | 0.886273i | \(-0.653285\pi\) | ||||
−0.463163 | + | 0.886273i | \(0.653285\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.83234 | 0.114211 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12.4215 | 0.500070 | 0.250035 | − | 0.968237i | \(-0.419558\pi\) | ||||
0.250035 | + | 0.968237i | \(0.419558\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14.0505 | 0.564737 | 0.282369 | − | 0.959306i | \(-0.408880\pi\) | ||||
0.282369 | + | 0.959306i | \(0.408880\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −49.7385 | −1.99594 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 15.5736 | 0.623944 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.92286 | −0.276915 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −13.9401 | −0.556714 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.00359 | 0.0400157 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 38.5811 | 1.53589 | 0.767944 | − | 0.640517i | \(-0.221280\pi\) | ||||
0.767944 | + | 0.640517i | \(0.221280\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 31.4396 | 1.24961 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 65.7135 | 2.60776 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.62549 | 0.183269 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −10.0654 | −0.398183 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −27.4319 | −1.08349 | −0.541746 | − | 0.840542i | \(-0.682237\pi\) | ||||
−0.541746 | + | 0.840542i | \(0.682237\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −41.2304 | −1.62597 | −0.812984 | − | 0.582285i | \(-0.802159\pi\) | ||||
−0.812984 | + | 0.582285i | \(0.802159\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −17.1562 | −0.675524 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.7635 | 0.501786 | 0.250893 | − | 0.968015i | \(-0.419276\pi\) | ||||
0.250893 | + | 0.968015i | \(0.419276\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.46002 | −0.0965642 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −17.0448 | −0.668039 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −0.994666 | −0.0389243 | −0.0194621 | − | 0.999811i | \(-0.506195\pi\) | ||||
−0.0194621 | + | 0.999811i | \(0.506195\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 35.9558 | 1.40491 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.24710 | −0.204709 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.20620 | −0.280714 | −0.140357 | − | 0.990101i | \(-0.544825\pi\) | ||||
−0.140357 | + | 0.990101i | \(0.544825\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 46.7487 | 1.81831 | 0.909156 | − | 0.416455i | \(-0.136728\pi\) | ||||
0.909156 | + | 0.416455i | \(0.136728\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.34382 | −0.0521897 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −20.3993 | −0.791052 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 28.2643 | 1.09440 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 13.4228 | 0.518955 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 23.3294 | 0.900621 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −20.2077 | −0.778948 | −0.389474 | − | 0.921038i | \(-0.627343\pi\) | ||||
−0.389474 | + | 0.921038i | \(0.627343\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −42.0414 | −1.61818 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 22.4834 | 0.864107 | 0.432054 | − | 0.901848i | \(-0.357789\pi\) | ||||
0.432054 | + | 0.901848i | \(0.357789\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.21631 | −0.276937 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −27.8603 | −1.06761 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 33.1886 | 1.26992 | 0.634962 | − | 0.772543i | \(-0.281016\pi\) | ||||
0.634962 | + | 0.772543i | \(0.281016\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 42.1882 | 1.61193 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10.2549 | 0.391249 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.47667 | 0.170548 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18.3913 | 0.699637 | 0.349819 | − | 0.936817i | \(-0.386243\pi\) | ||||
0.349819 | + | 0.936817i | \(0.386243\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.49549 | 0.132783 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 32.2046 | 1.22159 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.565045 | −0.0214026 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 21.5167 | 0.813836 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.38257 | −0.241066 | −0.120533 | − | 0.992709i | \(-0.538460\pi\) | ||||
−0.120533 | + | 0.992709i | \(0.538460\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.00034 | −0.150876 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 56.3812 | 2.12344 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.431542 | 0.0162298 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 44.5980 | 1.67491 | 0.837457 | − | 0.546504i | \(-0.184042\pi\) | ||||
0.837457 | + | 0.546504i | \(0.184042\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.32330 | 0.274645 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 72.6343 | 2.72018 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.19914 | 0.306631 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −27.0790 | −1.01128 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 28.6723 | 1.06930 | 0.534649 | − | 0.845074i | \(-0.320444\pi\) | ||||
0.534649 | + | 0.845074i | \(0.320444\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 19.0683 | 0.710142 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −9.12763 | −0.339460 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 23.8903 | 0.887265 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 33.1073 | 1.22788 | 0.613942 | − | 0.789351i | \(-0.289583\pi\) | ||||
0.613942 | + | 0.789351i | \(0.289583\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.1222 | 1.07860 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.42262 | 0.126590 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −13.9123 | −0.513861 | −0.256930 | − | 0.966430i | \(-0.582711\pi\) | ||||
−0.256930 | + | 0.966430i | \(0.582711\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 24.5281 | 0.904733 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.64583 | 0.207967 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −24.0590 | −0.885025 | −0.442513 | − | 0.896762i | \(-0.645913\pi\) | ||||
−0.442513 | + | 0.896762i | \(0.645913\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.35651 | 0.196776 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.41295 | 0.161895 | 0.0809477 | − | 0.996718i | \(-0.474205\pi\) | ||||
0.0809477 | + | 0.996718i | \(0.474205\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.49466 | −0.0913974 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 8.14612 | 0.298051 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.95871 | 0.108109 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.92300 | −0.252624 | −0.126312 | − | 0.991991i | \(-0.540314\pi\) | ||||
−0.126312 | + | 0.991991i | \(0.540314\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −15.9066 | −0.579670 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 68.2618 | 2.48430 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −24.9883 | −0.908214 | −0.454107 | − | 0.890947i | \(-0.650042\pi\) | ||||
−0.454107 | + | 0.890947i | \(0.650042\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 30.7511 | 1.11619 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −36.1186 | −1.30930 | −0.654649 | − | 0.755933i | \(-0.727183\pi\) | ||||
−0.654649 | + | 0.755933i | \(0.727183\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −14.8755 | −0.538530 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.45179 | 0.124800 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.945268 | 0.0341316 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −18.5030 | −0.667235 | −0.333617 | − | 0.942709i | \(-0.608269\pi\) | ||||
−0.333617 | + | 0.942709i | \(0.608269\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 20.2489 | 0.729246 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.22268 | −0.151879 | −0.0759397 | − | 0.997112i | \(-0.524196\pi\) | ||||
−0.0759397 | + | 0.997112i | \(0.524196\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 61.3941 | 2.20534 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.07082 | −0.0742903 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.25229 | 0.0806967 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 25.2931 | 0.905057 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −18.1827 | −0.649798 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −78.7034 | −2.80905 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11.3648 | 0.405112 | 0.202556 | − | 0.979271i | \(-0.435075\pi\) | ||||
0.202556 | + | 0.979271i | \(0.435075\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −14.6412 | −0.521240 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 20.2912 | 0.721472 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.96437 | −0.318334 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 23.7389 | 0.841934 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.44727 | 0.157531 | 0.0787653 | − | 0.996893i | \(-0.474902\pi\) | ||||
0.0787653 | + | 0.996893i | \(0.474902\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −11.2479 | −0.397924 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 10.5041 | 0.371144 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 13.1853 | 0.465298 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 44.9998 | 1.58604 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6.72389 | −0.236692 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −17.5322 | −0.616401 | −0.308200 | − | 0.951321i | \(-0.599727\pi\) | ||||
−0.308200 | + | 0.951321i | \(0.599727\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −37.2243 | −1.30712 | −0.653561 | − | 0.756874i | \(-0.726726\pi\) | ||||
−0.653561 | + | 0.756874i | \(0.726726\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −15.4486 | −0.541806 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.940151 | −0.0329320 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −13.6427 | −0.477297 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.34315 | −0.0469335 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 40.6841 | 1.41989 | 0.709943 | − | 0.704259i | \(-0.248721\pi\) | ||||
0.709943 | + | 0.704259i | \(0.248721\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.448070 | 0.0156187 | 0.00780937 | − | 0.999970i | \(-0.497514\pi\) | ||||
0.00780937 | + | 0.999970i | \(0.497514\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 25.9923 | 0.904937 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 27.9648 | 0.972433 | 0.486216 | − | 0.873838i | \(-0.338377\pi\) | ||||
0.486216 | + | 0.873838i | \(0.338377\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −42.5068 | −1.47632 | −0.738162 | − | 0.674624i | \(-0.764306\pi\) | ||||
−0.738162 | + | 0.674624i | \(0.764306\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −26.8422 | −0.931146 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.89331 | −0.169543 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −72.5273 | −2.50991 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −46.7265 | −1.61510 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 32.8383 | 1.13370 | 0.566852 | − | 0.823820i | \(-0.308161\pi\) | ||||
0.566852 | + | 0.823820i | \(0.308161\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.6675 | −0.643708 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 14.8492 | 0.511432 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 42.6867 | 1.46847 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.18218 | 0.246783 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 23.9171 | 0.820834 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.82454 | 0.302501 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −45.4387 | −1.55579 | −0.777897 | − | 0.628392i | \(-0.783713\pi\) | ||||
−0.777897 | + | 0.628392i | \(0.783713\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −13.7590 | −0.470546 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −12.3292 | −0.421158 | −0.210579 | − | 0.977577i | \(-0.567535\pi\) | ||||
−0.210579 | + | 0.977577i | \(0.567535\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −28.5658 | −0.974652 | −0.487326 | − | 0.873220i | \(-0.662028\pi\) | ||||
−0.487326 | + | 0.873220i | \(0.662028\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.16592 | 0.0397345 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −29.6500 | −1.00930 | −0.504649 | − | 0.863324i | \(-0.668378\pi\) | ||||
−0.504649 | + | 0.863324i | \(0.668378\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −32.5390 | −1.10636 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.42163 | 0.0482811 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −18.4025 | −0.624261 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.16942 | −0.0735080 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.86726 | −0.164732 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 12.4476 | 0.420804 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 33.9966 | 1.14798 | 0.573992 | − | 0.818861i | \(-0.305394\pi\) | ||||
0.573992 | + | 0.818861i | \(0.305394\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 22.5622 | 0.761005 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −16.4546 | −0.554370 | −0.277185 | − | 0.960816i | \(-0.589402\pi\) | ||||
−0.277185 | + | 0.960816i | \(0.589402\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10.1939 | 0.343052 | 0.171526 | − | 0.985180i | \(-0.445130\pi\) | ||||
0.171526 | + | 0.985180i | \(0.445130\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.01258 | 0.168496 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 10.7407 | 0.360639 | 0.180319 | − | 0.983608i | \(-0.442287\pi\) | ||||
0.180319 | + | 0.983608i | \(0.442287\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 27.0508 | 0.907254 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −12.5577 | −0.420698 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 44.8347 | 1.50034 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 10.7906 | 0.360688 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −11.8162 | −0.394531 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 26.5526 | 0.885580 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.73587 | −0.157775 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −7.06229 | −0.235018 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 59.9942 | 1.99428 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 27.2652 | 0.905327 | 0.452664 | − | 0.891681i | \(-0.350474\pi\) | ||||
0.452664 | + | 0.891681i | \(0.350474\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.291067 | 0.00965407 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −49.9965 | −1.65646 | −0.828230 | − | 0.560389i | \(-0.810652\pi\) | ||||
−0.828230 | + | 0.560389i | \(0.810652\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −20.4701 | −0.677461 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −47.5364 | −1.57150 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 14.8011 | 0.488776 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −18.2302 | −0.601359 | −0.300679 | − | 0.953725i | \(-0.597213\pi\) | ||||
−0.300679 | + | 0.953725i | \(0.597213\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −33.6509 | −1.10884 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −9.71892 | −0.319902 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.45893 | 0.245248 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 12.8612 | 0.422418 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −6.86345 | −0.225182 | −0.112591 | − | 0.993641i | \(-0.535915\pi\) | ||||
−0.112591 | + | 0.993641i | \(0.535915\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 19.5049 | 0.639248 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −12.4629 | −0.408019 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −8.67388 | −0.283666 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −33.8587 | −1.10611 | −0.553057 | − | 0.833143i | \(-0.686539\pi\) | ||||
−0.553057 | + | 0.833143i | \(0.686539\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −30.3748 | −0.991245 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −32.1888 | −1.04933 | −0.524663 | − | 0.851310i | \(-0.675809\pi\) | ||||
−0.524663 | + | 0.851310i | \(0.675809\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.96843 | −0.161794 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −28.9489 | −0.941708 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −28.2531 | −0.918102 | −0.459051 | − | 0.888410i | \(-0.651811\pi\) | ||||
−0.459051 | + | 0.888410i | \(0.651811\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.06646 | −0.164464 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −11.3242 | −0.367212 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 49.2358 | 1.59490 | 0.797452 | − | 0.603382i | \(-0.206181\pi\) | ||||
0.797452 | + | 0.603382i | \(0.206181\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −18.8101 | −0.608681 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 11.2416 | 0.363388 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 17.3667 | 0.560799 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 37.2357 | 1.20115 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.99559 | 0.0643071 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.856368 | −0.0275674 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −38.5398 | −1.23936 | −0.619678 | − | 0.784856i | \(-0.712737\pi\) | ||||
−0.619678 | + | 0.784856i | \(0.712737\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5.66666 | −0.182039 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 46.6236 | 1.49622 | 0.748111 | − | 0.663574i | \(-0.230961\pi\) | ||||
0.748111 | + | 0.663574i | \(0.230961\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 13.2569 | 0.424997 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −9.98761 | −0.319860 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 20.9300 | 0.669609 | 0.334805 | − | 0.942288i | \(-0.391330\pi\) | ||||
0.334805 | + | 0.942288i | \(0.391330\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −26.3954 | −0.843600 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10.0333 | −0.320337 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.35555 | −0.0751304 | −0.0375652 | − | 0.999294i | \(-0.511960\pi\) | ||||
−0.0375652 | + | 0.999294i | \(0.511960\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.43943 | 0.0777268 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 23.2092 | 0.738756 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 30.0951 | 0.956967 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 50.3398 | 1.59910 | 0.799549 | − | 0.600601i | \(-0.205072\pi\) | ||||
0.799549 | + | 0.600601i | \(0.205072\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 20.5122 | 0.650934 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 87.4842 | 2.77344 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6.90365 | 0.218641 | 0.109320 | − | 0.994007i | \(-0.465133\pi\) | ||||
0.109320 | + | 0.994007i | \(0.465133\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.67693 | −0.179610 |
(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 | 8024.2.a.w.1.16 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8024.2.a.w.1.16 | ✓ | 20 | 1.1 | even | 1 | trivial |