Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8001,2,Mod(1,8001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8001, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("8001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8001 = 3^{2} \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8001.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(63.8883066572\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Character | \(\chi\) | \(=\) | 8001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.09235 | −1.47952 | −0.739759 | − | 0.672872i | \(-0.765061\pi\) | ||||
−0.739759 | + | 0.672872i | \(0.765061\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.37795 | 1.18897 | ||||||||
\(5\) | −3.96692 | −1.77406 | −0.887030 | − | 0.461712i | \(-0.847235\pi\) | ||||
−0.887030 | + | 0.461712i | \(0.847235\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −0.790800 | −0.279590 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 8.30020 | 2.62475 | ||||||||
\(11\) | −3.36492 | −1.01456 | −0.507280 | − | 0.861781i | \(-0.669349\pi\) | ||||
−0.507280 | + | 0.861781i | \(0.669349\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.92494 | −0.533881 | −0.266941 | − | 0.963713i | \(-0.586013\pi\) | ||||
−0.266941 | + | 0.963713i | \(0.586013\pi\) | |||||||
\(14\) | −2.09235 | −0.559205 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.10126 | −0.775315 | ||||||||
\(17\) | 1.09693 | 0.266045 | 0.133023 | − | 0.991113i | \(-0.457532\pi\) | ||||
0.133023 | + | 0.991113i | \(0.457532\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.50219 | 0.344626 | 0.172313 | − | 0.985042i | \(-0.444876\pi\) | ||||
0.172313 | + | 0.985042i | \(0.444876\pi\) | |||||||
\(20\) | −9.43312 | −2.10931 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 7.04060 | 1.50106 | ||||||||
\(23\) | 6.96998 | 1.45334 | 0.726670 | − | 0.686987i | \(-0.241067\pi\) | ||||
0.726670 | + | 0.686987i | \(0.241067\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 10.7364 | 2.14729 | ||||||||
\(26\) | 4.02765 | 0.789887 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.37795 | 0.449390 | ||||||||
\(29\) | −8.74282 | −1.62350 | −0.811751 | − | 0.584004i | \(-0.801485\pi\) | ||||
−0.811751 | + | 0.584004i | \(0.801485\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.96336 | 1.43026 | 0.715131 | − | 0.698991i | \(-0.246367\pi\) | ||||
0.715131 | + | 0.698991i | \(0.246367\pi\) | |||||||
\(32\) | 8.07054 | 1.42668 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.29517 | −0.393619 | ||||||||
\(35\) | −3.96692 | −0.670532 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.395595 | 0.0650354 | 0.0325177 | − | 0.999471i | \(-0.489647\pi\) | ||||
0.0325177 | + | 0.999471i | \(0.489647\pi\) | |||||||
\(38\) | −3.14311 | −0.509880 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.13704 | 0.496009 | ||||||||
\(41\) | −5.12703 | −0.800707 | −0.400354 | − | 0.916361i | \(-0.631113\pi\) | ||||
−0.400354 | + | 0.916361i | \(0.631113\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.08571 | 0.623065 | 0.311533 | − | 0.950235i | \(-0.399158\pi\) | ||||
0.311533 | + | 0.950235i | \(0.399158\pi\) | |||||||
\(44\) | −8.00159 | −1.20629 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −14.5837 | −2.15024 | ||||||||
\(47\) | 8.64796 | 1.26143 | 0.630717 | − | 0.776013i | \(-0.282761\pi\) | ||||
0.630717 | + | 0.776013i | \(0.282761\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −22.4644 | −3.17695 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.57740 | −0.634771 | ||||||||
\(53\) | 1.42610 | 0.195889 | 0.0979446 | − | 0.995192i | \(-0.468773\pi\) | ||||
0.0979446 | + | 0.995192i | \(0.468773\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 13.3483 | 1.79989 | ||||||||
\(56\) | −0.790800 | −0.105675 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 18.2931 | 2.40200 | ||||||||
\(59\) | −7.32907 | −0.954164 | −0.477082 | − | 0.878859i | \(-0.658305\pi\) | ||||
−0.477082 | + | 0.878859i | \(0.658305\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.24548 | −1.05573 | −0.527863 | − | 0.849330i | \(-0.677006\pi\) | ||||
−0.527863 | + | 0.849330i | \(0.677006\pi\) | |||||||
\(62\) | −16.6622 | −2.11610 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −10.6839 | −1.33549 | ||||||||
\(65\) | 7.63607 | 0.947137 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.895891 | −0.109451 | −0.0547253 | − | 0.998501i | \(-0.517428\pi\) | ||||
−0.0547253 | + | 0.998501i | \(0.517428\pi\) | |||||||
\(68\) | 2.60845 | 0.316321 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 8.30020 | 0.992064 | ||||||||
\(71\) | −12.9035 | −1.53136 | −0.765682 | − | 0.643220i | \(-0.777598\pi\) | ||||
−0.765682 | + | 0.643220i | \(0.777598\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −14.8018 | −1.73242 | −0.866209 | − | 0.499682i | \(-0.833450\pi\) | ||||
−0.866209 | + | 0.499682i | \(0.833450\pi\) | |||||||
\(74\) | −0.827725 | −0.0962210 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.57213 | 0.409751 | ||||||||
\(77\) | −3.36492 | −0.383468 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.4969 | −1.18099 | −0.590495 | − | 0.807041i | \(-0.701067\pi\) | ||||
−0.590495 | + | 0.807041i | \(0.701067\pi\) | |||||||
\(80\) | 12.3024 | 1.37546 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 10.7276 | 1.18466 | ||||||||
\(83\) | −13.0258 | −1.42977 | −0.714883 | − | 0.699244i | \(-0.753520\pi\) | ||||
−0.714883 | + | 0.699244i | \(0.753520\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.35144 | −0.471980 | ||||||||
\(86\) | −8.54876 | −0.921836 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.66097 | 0.283661 | ||||||||
\(89\) | 1.78663 | 0.189383 | 0.0946913 | − | 0.995507i | \(-0.469814\pi\) | ||||
0.0946913 | + | 0.995507i | \(0.469814\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.92494 | −0.201788 | ||||||||
\(92\) | 16.5742 | 1.72798 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −18.0946 | −1.86631 | ||||||||
\(95\) | −5.95906 | −0.611387 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15.4051 | 1.56415 | 0.782075 | − | 0.623185i | \(-0.214162\pi\) | ||||
0.782075 | + | 0.623185i | \(0.214162\pi\) | |||||||
\(98\) | −2.09235 | −0.211360 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 25.5307 | 2.55307 | ||||||||
\(101\) | −13.4223 | −1.33557 | −0.667786 | − | 0.744353i | \(-0.732758\pi\) | ||||
−0.667786 | + | 0.744353i | \(0.732758\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 19.8444 | 1.95533 | 0.977664 | − | 0.210174i | \(-0.0674032\pi\) | ||||
0.977664 | + | 0.210174i | \(0.0674032\pi\) | |||||||
\(104\) | 1.52224 | 0.149268 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.98390 | −0.289822 | ||||||||
\(107\) | −6.88756 | −0.665845 | −0.332923 | − | 0.942954i | \(-0.608035\pi\) | ||||
−0.332923 | + | 0.942954i | \(0.608035\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 18.2912 | 1.75198 | 0.875990 | − | 0.482329i | \(-0.160209\pi\) | ||||
0.875990 | + | 0.482329i | \(0.160209\pi\) | |||||||
\(110\) | −27.9295 | −2.66297 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.10126 | −0.293042 | ||||||||
\(113\) | 17.1246 | 1.61095 | 0.805476 | − | 0.592629i | \(-0.201910\pi\) | ||||
0.805476 | + | 0.592629i | \(0.201910\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −27.6493 | −2.57831 | ||||||||
\(116\) | −20.7900 | −1.93030 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 15.3350 | 1.41170 | ||||||||
\(119\) | 1.09693 | 0.100556 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.322654 | 0.0293321 | ||||||||
\(122\) | 17.2525 | 1.56196 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 18.9364 | 1.70054 | ||||||||
\(125\) | −22.7560 | −2.03536 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.00000 | −0.0887357 | ||||||||
\(128\) | 6.21344 | 0.549195 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −15.9774 | −1.40131 | ||||||||
\(131\) | 14.5754 | 1.27346 | 0.636729 | − | 0.771088i | \(-0.280287\pi\) | ||||
0.636729 | + | 0.771088i | \(0.280287\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.50219 | 0.130256 | ||||||||
\(134\) | 1.87452 | 0.161934 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.867454 | −0.0743836 | ||||||||
\(137\) | −5.22293 | −0.446225 | −0.223113 | − | 0.974793i | \(-0.571622\pi\) | ||||
−0.223113 | + | 0.974793i | \(0.571622\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.32979 | −0.621705 | −0.310852 | − | 0.950458i | \(-0.600614\pi\) | ||||
−0.310852 | + | 0.950458i | \(0.600614\pi\) | |||||||
\(140\) | −9.43312 | −0.797244 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 26.9987 | 2.26568 | ||||||||
\(143\) | 6.47725 | 0.541655 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 34.6821 | 2.88019 | ||||||||
\(146\) | 30.9706 | 2.56314 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.940704 | 0.0773254 | ||||||||
\(149\) | 21.4541 | 1.75759 | 0.878796 | − | 0.477198i | \(-0.158347\pi\) | ||||
0.878796 | + | 0.477198i | \(0.158347\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.93525 | −0.727140 | −0.363570 | − | 0.931567i | \(-0.618442\pi\) | ||||
−0.363570 | + | 0.931567i | \(0.618442\pi\) | |||||||
\(152\) | −1.18793 | −0.0963539 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 7.04060 | 0.567347 | ||||||||
\(155\) | −31.5900 | −2.53737 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −20.9666 | −1.67332 | −0.836660 | − | 0.547723i | \(-0.815495\pi\) | ||||
−0.836660 | + | 0.547723i | \(0.815495\pi\) | |||||||
\(158\) | 21.9632 | 1.74730 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −32.0152 | −2.53102 | ||||||||
\(161\) | 6.96998 | 0.549311 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −18.1296 | −1.42002 | −0.710008 | − | 0.704194i | \(-0.751309\pi\) | ||||
−0.710008 | + | 0.704194i | \(0.751309\pi\) | |||||||
\(164\) | −12.1918 | −0.952020 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 27.2546 | 2.11536 | ||||||||
\(167\) | 0.641839 | 0.0496670 | 0.0248335 | − | 0.999692i | \(-0.492094\pi\) | ||||
0.0248335 | + | 0.999692i | \(0.492094\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.29462 | −0.714971 | ||||||||
\(170\) | 9.10476 | 0.698303 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 9.71561 | 0.740808 | ||||||||
\(173\) | 6.95360 | 0.528673 | 0.264336 | − | 0.964431i | \(-0.414847\pi\) | ||||
0.264336 | + | 0.964431i | \(0.414847\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10.7364 | 0.811599 | ||||||||
\(176\) | 10.4355 | 0.786604 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.73827 | −0.280195 | ||||||||
\(179\) | −7.79665 | −0.582749 | −0.291375 | − | 0.956609i | \(-0.594113\pi\) | ||||
−0.291375 | + | 0.956609i | \(0.594113\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.99767 | −0.148486 | −0.0742429 | − | 0.997240i | \(-0.523654\pi\) | ||||
−0.0742429 | + | 0.997240i | \(0.523654\pi\) | |||||||
\(182\) | 4.02765 | 0.298549 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −5.51186 | −0.406339 | ||||||||
\(185\) | −1.56929 | −0.115377 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.69108 | −0.269919 | ||||||||
\(188\) | 20.5644 | 1.49981 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 12.4685 | 0.904558 | ||||||||
\(191\) | −3.62932 | −0.262609 | −0.131304 | − | 0.991342i | \(-0.541916\pi\) | ||||
−0.131304 | + | 0.991342i | \(0.541916\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 26.3305 | 1.89531 | 0.947656 | − | 0.319293i | \(-0.103445\pi\) | ||||
0.947656 | + | 0.319293i | \(0.103445\pi\) | |||||||
\(194\) | −32.2329 | −2.31419 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.37795 | 0.169853 | ||||||||
\(197\) | −6.30796 | −0.449423 | −0.224712 | − | 0.974425i | \(-0.572144\pi\) | ||||
−0.224712 | + | 0.974425i | \(0.572144\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −23.8239 | −1.68883 | −0.844416 | − | 0.535687i | \(-0.820053\pi\) | ||||
−0.844416 | + | 0.535687i | \(0.820053\pi\) | |||||||
\(200\) | −8.49037 | −0.600360 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 28.0843 | 1.97600 | ||||||||
\(203\) | −8.74282 | −0.613626 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 20.3385 | 1.42050 | ||||||||
\(206\) | −41.5215 | −2.89294 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 5.96973 | 0.413926 | ||||||||
\(209\) | −5.05474 | −0.349644 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.03762 | −0.622176 | −0.311088 | − | 0.950381i | \(-0.600693\pi\) | ||||
−0.311088 | + | 0.950381i | \(0.600693\pi\) | |||||||
\(212\) | 3.39118 | 0.232907 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 14.4112 | 0.985130 | ||||||||
\(215\) | −16.2077 | −1.10536 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.96336 | 0.540588 | ||||||||
\(218\) | −38.2717 | −2.59209 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 31.7417 | 2.14002 | ||||||||
\(221\) | −2.11153 | −0.142037 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −24.6428 | −1.65021 | −0.825103 | − | 0.564982i | \(-0.808883\pi\) | ||||
−0.825103 | + | 0.564982i | \(0.808883\pi\) | |||||||
\(224\) | 8.07054 | 0.539235 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −35.8308 | −2.38343 | ||||||||
\(227\) | 3.90263 | 0.259027 | 0.129513 | − | 0.991578i | \(-0.458659\pi\) | ||||
0.129513 | + | 0.991578i | \(0.458659\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −26.0183 | −1.71934 | −0.859670 | − | 0.510850i | \(-0.829331\pi\) | ||||
−0.859670 | + | 0.510850i | \(0.829331\pi\) | |||||||
\(230\) | 57.8522 | 3.81466 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.91382 | 0.453915 | ||||||||
\(233\) | −2.53200 | −0.165877 | −0.0829386 | − | 0.996555i | \(-0.526431\pi\) | ||||
−0.0829386 | + | 0.996555i | \(0.526431\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −34.3057 | −2.23786 | ||||||||
\(236\) | −17.4281 | −1.13448 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.29517 | −0.148774 | ||||||||
\(239\) | 28.8611 | 1.86687 | 0.933436 | − | 0.358744i | \(-0.116795\pi\) | ||||
0.933436 | + | 0.358744i | \(0.116795\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.5365 | 1.12963 | 0.564813 | − | 0.825219i | \(-0.308948\pi\) | ||||
0.564813 | + | 0.825219i | \(0.308948\pi\) | |||||||
\(242\) | −0.675106 | −0.0433974 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −19.6073 | −1.25523 | ||||||||
\(245\) | −3.96692 | −0.253437 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.89162 | −0.183989 | ||||||||
\(248\) | −6.29742 | −0.399887 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 47.6136 | 3.01135 | ||||||||
\(251\) | 0.675957 | 0.0426660 | 0.0213330 | − | 0.999772i | \(-0.493209\pi\) | ||||
0.0213330 | + | 0.999772i | \(0.493209\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −23.4534 | −1.47450 | ||||||||
\(254\) | 2.09235 | 0.131286 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 8.36709 | 0.522943 | ||||||||
\(257\) | 17.2714 | 1.07736 | 0.538679 | − | 0.842511i | \(-0.318924\pi\) | ||||
0.538679 | + | 0.842511i | \(0.318924\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.395595 | 0.0245811 | ||||||||
\(260\) | 18.1582 | 1.12612 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −30.4969 | −1.88410 | ||||||||
\(263\) | 19.5148 | 1.20333 | 0.601667 | − | 0.798747i | \(-0.294503\pi\) | ||||
0.601667 | + | 0.798747i | \(0.294503\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.65720 | −0.347519 | ||||||||
\(266\) | −3.14311 | −0.192717 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2.13038 | −0.130134 | ||||||||
\(269\) | −7.20512 | −0.439304 | −0.219652 | − | 0.975578i | \(-0.570492\pi\) | ||||
−0.219652 | + | 0.975578i | \(0.570492\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.50972 | 0.0917087 | 0.0458543 | − | 0.998948i | \(-0.485399\pi\) | ||||
0.0458543 | + | 0.998948i | \(0.485399\pi\) | |||||||
\(272\) | −3.40187 | −0.206269 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 10.9282 | 0.660198 | ||||||||
\(275\) | −36.1272 | −2.17855 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.49701 | −0.450452 | −0.225226 | − | 0.974307i | \(-0.572312\pi\) | ||||
−0.225226 | + | 0.974307i | \(0.572312\pi\) | |||||||
\(278\) | 15.3365 | 0.919823 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 3.13704 | 0.187474 | ||||||||
\(281\) | 10.2223 | 0.609813 | 0.304907 | − | 0.952382i | \(-0.401375\pi\) | ||||
0.304907 | + | 0.952382i | \(0.401375\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.7912 | 0.641470 | 0.320735 | − | 0.947169i | \(-0.396070\pi\) | ||||
0.320735 | + | 0.947169i | \(0.396070\pi\) | |||||||
\(284\) | −30.6838 | −1.82075 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −13.5527 | −0.801388 | ||||||||
\(287\) | −5.12703 | −0.302639 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.7967 | −0.929220 | ||||||||
\(290\) | −72.5672 | −4.26129 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −35.1979 | −2.05980 | ||||||||
\(293\) | 0.963362 | 0.0562802 | 0.0281401 | − | 0.999604i | \(-0.491042\pi\) | ||||
0.0281401 | + | 0.999604i | \(0.491042\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 29.0738 | 1.69274 | ||||||||
\(296\) | −0.312836 | −0.0181832 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −44.8897 | −2.60039 | ||||||||
\(299\) | −13.4168 | −0.775911 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.08571 | 0.235497 | ||||||||
\(302\) | 18.6957 | 1.07582 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −4.65868 | −0.267194 | ||||||||
\(305\) | 32.7091 | 1.87292 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.41653 | −0.0808455 | −0.0404227 | − | 0.999183i | \(-0.512870\pi\) | ||||
−0.0404227 | + | 0.999183i | \(0.512870\pi\) | |||||||
\(308\) | −8.00159 | −0.455933 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 66.0975 | 3.75408 | ||||||||
\(311\) | −20.8547 | −1.18256 | −0.591281 | − | 0.806466i | \(-0.701377\pi\) | ||||
−0.591281 | + | 0.806466i | \(0.701377\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −34.2479 | −1.93581 | −0.967903 | − | 0.251325i | \(-0.919134\pi\) | ||||
−0.967903 | + | 0.251325i | \(0.919134\pi\) | |||||||
\(314\) | 43.8696 | 2.47571 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −24.9610 | −1.40417 | ||||||||
\(317\) | −4.40061 | −0.247163 | −0.123581 | − | 0.992334i | \(-0.539438\pi\) | ||||
−0.123581 | + | 0.992334i | \(0.539438\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 29.4189 | 1.64714 | ||||||||
\(320\) | 42.3822 | 2.36924 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −14.5837 | −0.812716 | ||||||||
\(323\) | 1.64780 | 0.0916860 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −20.6670 | −1.14640 | ||||||||
\(326\) | 37.9334 | 2.10094 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 4.05445 | 0.223870 | ||||||||
\(329\) | 8.64796 | 0.476777 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.58462 | 0.526818 | 0.263409 | − | 0.964684i | \(-0.415153\pi\) | ||||
0.263409 | + | 0.964684i | \(0.415153\pi\) | |||||||
\(332\) | −30.9746 | −1.69995 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.34295 | −0.0734832 | ||||||||
\(335\) | 3.55393 | 0.194172 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.04491 | −0.0569201 | −0.0284600 | − | 0.999595i | \(-0.509060\pi\) | ||||
−0.0284600 | + | 0.999595i | \(0.509060\pi\) | |||||||
\(338\) | 19.4476 | 1.05781 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −10.3475 | −0.561172 | ||||||||
\(341\) | −26.7960 | −1.45109 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −3.23098 | −0.174203 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −14.5494 | −0.782181 | ||||||||
\(347\) | −24.4688 | −1.31355 | −0.656777 | − | 0.754085i | \(-0.728081\pi\) | ||||
−0.656777 | + | 0.754085i | \(0.728081\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.10143 | 0.112487 | 0.0562436 | − | 0.998417i | \(-0.482088\pi\) | ||||
0.0562436 | + | 0.998417i | \(0.482088\pi\) | |||||||
\(350\) | −22.4644 | −1.20077 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −27.1567 | −1.44746 | ||||||||
\(353\) | 6.53053 | 0.347585 | 0.173793 | − | 0.984782i | \(-0.444398\pi\) | ||||
0.173793 | + | 0.984782i | \(0.444398\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 51.1871 | 2.71673 | ||||||||
\(356\) | 4.24852 | 0.225171 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 16.3134 | 0.862188 | ||||||||
\(359\) | 4.49262 | 0.237111 | 0.118556 | − | 0.992947i | \(-0.462174\pi\) | ||||
0.118556 | + | 0.992947i | \(0.462174\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.7434 | −0.881233 | ||||||||
\(362\) | 4.17984 | 0.219688 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −4.57740 | −0.239921 | ||||||||
\(365\) | 58.7175 | 3.07341 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.923799 | 0.0482219 | 0.0241110 | − | 0.999709i | \(-0.492325\pi\) | ||||
0.0241110 | + | 0.999709i | \(0.492325\pi\) | |||||||
\(368\) | −21.6157 | −1.12680 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 3.28352 | 0.170702 | ||||||||
\(371\) | 1.42610 | 0.0740392 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.2352 | −0.529961 | −0.264980 | − | 0.964254i | \(-0.585366\pi\) | ||||
−0.264980 | + | 0.964254i | \(0.585366\pi\) | |||||||
\(374\) | 7.72306 | 0.399350 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.83880 | −0.352684 | ||||||||
\(377\) | 16.8294 | 0.866757 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 24.0858 | 1.23720 | 0.618602 | − | 0.785704i | \(-0.287699\pi\) | ||||
0.618602 | + | 0.785704i | \(0.287699\pi\) | |||||||
\(380\) | −14.1703 | −0.726923 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 7.59383 | 0.388534 | ||||||||
\(383\) | −5.47064 | −0.279537 | −0.139768 | − | 0.990184i | \(-0.544636\pi\) | ||||
−0.139768 | + | 0.990184i | \(0.544636\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 13.3483 | 0.680295 | ||||||||
\(386\) | −55.0928 | −2.80415 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 36.6325 | 1.85973 | ||||||||
\(389\) | −14.5911 | −0.739798 | −0.369899 | − | 0.929072i | \(-0.620608\pi\) | ||||
−0.369899 | + | 0.929072i | \(0.620608\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.64559 | 0.386654 | ||||||||
\(392\) | −0.790800 | −0.0399414 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 13.1985 | 0.664930 | ||||||||
\(395\) | 41.6402 | 2.09515 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 32.9307 | 1.65274 | 0.826371 | − | 0.563126i | \(-0.190401\pi\) | ||||
0.826371 | + | 0.563126i | \(0.190401\pi\) | |||||||
\(398\) | 49.8481 | 2.49866 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −33.2965 | −1.66483 | ||||||||
\(401\) | 26.3376 | 1.31524 | 0.657619 | − | 0.753351i | \(-0.271564\pi\) | ||||
0.657619 | + | 0.753351i | \(0.271564\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −15.3290 | −0.763590 | ||||||||
\(404\) | −31.9176 | −1.58796 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 18.2931 | 0.907871 | ||||||||
\(407\) | −1.33114 | −0.0659823 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.402040 | −0.0198796 | −0.00993979 | − | 0.999951i | \(-0.503164\pi\) | ||||
−0.00993979 | + | 0.999951i | \(0.503164\pi\) | |||||||
\(410\) | −42.5554 | −2.10166 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 47.1890 | 2.32483 | ||||||||
\(413\) | −7.32907 | −0.360640 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 51.6722 | 2.53649 | ||||||||
\(416\) | −15.5353 | −0.761679 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 10.5763 | 0.517304 | ||||||||
\(419\) | 13.6019 | 0.664495 | 0.332248 | − | 0.943192i | \(-0.392193\pi\) | ||||
0.332248 | + | 0.943192i | \(0.392193\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 24.9947 | 1.21817 | 0.609084 | − | 0.793106i | \(-0.291537\pi\) | ||||
0.609084 | + | 0.793106i | \(0.291537\pi\) | |||||||
\(422\) | 18.9099 | 0.920520 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.12776 | −0.0547687 | ||||||||
\(425\) | 11.7771 | 0.571276 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.24548 | −0.399027 | ||||||||
\(428\) | −16.3783 | −0.791673 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 33.9122 | 1.63539 | ||||||||
\(431\) | −33.8505 | −1.63052 | −0.815260 | − | 0.579095i | \(-0.803406\pi\) | ||||
−0.815260 | + | 0.579095i | \(0.803406\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 25.8901 | 1.24420 | 0.622100 | − | 0.782937i | \(-0.286280\pi\) | ||||
0.622100 | + | 0.782937i | \(0.286280\pi\) | |||||||
\(434\) | −16.6622 | −0.799810 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 43.4955 | 2.08306 | ||||||||
\(437\) | 10.4702 | 0.500858 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 24.4846 | 1.16859 | 0.584294 | − | 0.811542i | \(-0.301371\pi\) | ||||
0.584294 | + | 0.811542i | \(0.301371\pi\) | |||||||
\(440\) | −10.5559 | −0.503231 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4.41806 | 0.210146 | ||||||||
\(443\) | 20.9781 | 0.996701 | 0.498350 | − | 0.866976i | \(-0.333939\pi\) | ||||
0.498350 | + | 0.866976i | \(0.333939\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.08743 | −0.335976 | ||||||||
\(446\) | 51.5615 | 2.44151 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −10.6839 | −0.504767 | ||||||||
\(449\) | 6.21606 | 0.293354 | 0.146677 | − | 0.989184i | \(-0.453142\pi\) | ||||
0.146677 | + | 0.989184i | \(0.453142\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 17.2520 | 0.812366 | ||||||||
\(452\) | 40.7215 | 1.91538 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −8.16568 | −0.383234 | ||||||||
\(455\) | 7.63607 | 0.357984 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.14940 | 0.194101 | 0.0970504 | − | 0.995279i | \(-0.469059\pi\) | ||||
0.0970504 | + | 0.995279i | \(0.469059\pi\) | |||||||
\(458\) | 54.4396 | 2.54379 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −65.7486 | −3.06555 | ||||||||
\(461\) | 18.7754 | 0.874455 | 0.437228 | − | 0.899351i | \(-0.355960\pi\) | ||||
0.437228 | + | 0.899351i | \(0.355960\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.26619 | −0.337688 | −0.168844 | − | 0.985643i | \(-0.554003\pi\) | ||||
−0.168844 | + | 0.985643i | \(0.554003\pi\) | |||||||
\(464\) | 27.1138 | 1.25873 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5.29785 | 0.245418 | ||||||||
\(467\) | 7.37026 | 0.341055 | 0.170527 | − | 0.985353i | \(-0.445453\pi\) | ||||
0.170527 | + | 0.985353i | \(0.445453\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.895891 | −0.0413684 | ||||||||
\(470\) | 71.7798 | 3.31095 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 5.79583 | 0.266775 | ||||||||
\(473\) | −13.7481 | −0.632137 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 16.1282 | 0.740011 | ||||||||
\(476\) | 2.60845 | 0.119558 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −60.3877 | −2.76207 | ||||||||
\(479\) | 13.8941 | 0.634839 | 0.317419 | − | 0.948285i | \(-0.397184\pi\) | ||||
0.317419 | + | 0.948285i | \(0.397184\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.761495 | −0.0347212 | ||||||||
\(482\) | −36.6926 | −1.67130 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.767253 | 0.0348751 | ||||||||
\(485\) | −61.1107 | −2.77489 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.72227 | 0.440558 | 0.220279 | − | 0.975437i | \(-0.429303\pi\) | ||||
0.220279 | + | 0.975437i | \(0.429303\pi\) | |||||||
\(488\) | 6.52052 | 0.295170 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 8.30020 | 0.374965 | ||||||||
\(491\) | −15.8783 | −0.716580 | −0.358290 | − | 0.933610i | \(-0.616640\pi\) | ||||
−0.358290 | + | 0.933610i | \(0.616640\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.59029 | −0.431925 | ||||||||
\(494\) | 6.05029 | 0.272215 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −24.6965 | −1.10890 | ||||||||
\(497\) | −12.9035 | −0.578801 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 36.7007 | 1.64295 | 0.821474 | − | 0.570246i | \(-0.193152\pi\) | ||||
0.821474 | + | 0.570246i | \(0.193152\pi\) | |||||||
\(500\) | −54.1125 | −2.41999 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1.41434 | −0.0631252 | ||||||||
\(503\) | −10.2539 | −0.457198 | −0.228599 | − | 0.973521i | \(-0.573414\pi\) | ||||
−0.228599 | + | 0.973521i | \(0.573414\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 53.2453 | 2.36938 | ||||||||
\(506\) | 49.0728 | 2.18155 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2.37795 | −0.105504 | ||||||||
\(509\) | −5.05177 | −0.223916 | −0.111958 | − | 0.993713i | \(-0.535712\pi\) | ||||
−0.111958 | + | 0.993713i | \(0.535712\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14.8018 | −0.654792 | ||||||||
\(512\) | −29.9338 | −1.32290 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −36.1378 | −1.59397 | ||||||||
\(515\) | −78.7212 | −3.46887 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −29.0996 | −1.27980 | ||||||||
\(518\) | −0.827725 | −0.0363681 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −6.03860 | −0.264810 | ||||||||
\(521\) | 19.0791 | 0.835869 | 0.417935 | − | 0.908477i | \(-0.362754\pi\) | ||||
0.417935 | + | 0.908477i | \(0.362754\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.59855 | 0.0698997 | 0.0349498 | − | 0.999389i | \(-0.488873\pi\) | ||||
0.0349498 | + | 0.999389i | \(0.488873\pi\) | |||||||
\(524\) | 34.6595 | 1.51411 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −40.8319 | −1.78036 | ||||||||
\(527\) | 8.73527 | 0.380514 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 25.5806 | 1.11220 | ||||||||
\(530\) | 11.8369 | 0.514161 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 3.57213 | 0.154871 | ||||||||
\(533\) | 9.86920 | 0.427483 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 27.3224 | 1.18125 | ||||||||
\(536\) | 0.708471 | 0.0306013 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 15.0757 | 0.649958 | ||||||||
\(539\) | −3.36492 | −0.144937 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 30.5583 | 1.31380 | 0.656902 | − | 0.753976i | \(-0.271867\pi\) | ||||
0.656902 | + | 0.753976i | \(0.271867\pi\) | |||||||
\(542\) | −3.15886 | −0.135685 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 8.85283 | 0.379562 | ||||||||
\(545\) | −72.5597 | −3.10812 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.6932 | 0.628235 | 0.314118 | − | 0.949384i | \(-0.398291\pi\) | ||||
0.314118 | + | 0.949384i | \(0.398291\pi\) | |||||||
\(548\) | −12.4199 | −0.530550 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 75.5909 | 3.22321 | ||||||||
\(551\) | −13.1334 | −0.559500 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10.4969 | −0.446372 | ||||||||
\(554\) | 15.6864 | 0.666452 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −17.4299 | −0.739190 | ||||||||
\(557\) | 27.1940 | 1.15225 | 0.576124 | − | 0.817362i | \(-0.304565\pi\) | ||||
0.576124 | + | 0.817362i | \(0.304565\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.86474 | −0.332643 | ||||||||
\(560\) | 12.3024 | 0.519873 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −21.3887 | −0.902230 | ||||||||
\(563\) | 24.2738 | 1.02302 | 0.511510 | − | 0.859277i | \(-0.329086\pi\) | ||||
0.511510 | + | 0.859277i | \(0.329086\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −67.9321 | −2.85792 | ||||||||
\(566\) | −22.5790 | −0.949066 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 10.2041 | 0.428154 | ||||||||
\(569\) | 10.7187 | 0.449350 | 0.224675 | − | 0.974434i | \(-0.427868\pi\) | ||||
0.224675 | + | 0.974434i | \(0.427868\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.74727 | 0.282365 | 0.141182 | − | 0.989984i | \(-0.454910\pi\) | ||||
0.141182 | + | 0.989984i | \(0.454910\pi\) | |||||||
\(572\) | 15.4026 | 0.644013 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 10.7276 | 0.447760 | ||||||||
\(575\) | 74.8327 | 3.12074 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −14.0711 | −0.585788 | −0.292894 | − | 0.956145i | \(-0.594618\pi\) | ||||
−0.292894 | + | 0.956145i | \(0.594618\pi\) | |||||||
\(578\) | 33.0524 | 1.37480 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 82.4721 | 3.42447 | ||||||||
\(581\) | −13.0258 | −0.540400 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.79869 | −0.198741 | ||||||||
\(584\) | 11.7053 | 0.484367 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.01569 | −0.0832676 | ||||||||
\(587\) | 2.55038 | 0.105265 | 0.0526327 | − | 0.998614i | \(-0.483239\pi\) | ||||
0.0526327 | + | 0.998614i | \(0.483239\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.9625 | 0.492905 | ||||||||
\(590\) | −60.8327 | −2.50444 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.22684 | −0.0504229 | ||||||||
\(593\) | 44.5795 | 1.83066 | 0.915331 | − | 0.402702i | \(-0.131929\pi\) | ||||
0.915331 | + | 0.402702i | \(0.131929\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.35144 | −0.178392 | ||||||||
\(596\) | 51.0168 | 2.08973 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 28.0726 | 1.14797 | ||||||||
\(599\) | −27.4284 | −1.12069 | −0.560347 | − | 0.828258i | \(-0.689332\pi\) | ||||
−0.560347 | + | 0.828258i | \(0.689332\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −39.6149 | −1.61593 | −0.807963 | − | 0.589233i | \(-0.799430\pi\) | ||||
−0.807963 | + | 0.589233i | \(0.799430\pi\) | |||||||
\(602\) | −8.54876 | −0.348421 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −21.2476 | −0.864551 | ||||||||
\(605\) | −1.27994 | −0.0520370 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 30.6434 | 1.24378 | 0.621889 | − | 0.783106i | \(-0.286366\pi\) | ||||
0.621889 | + | 0.783106i | \(0.286366\pi\) | |||||||
\(608\) | 12.1235 | 0.491672 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −68.4391 | −2.77102 | ||||||||
\(611\) | −16.6468 | −0.673456 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 32.6688 | 1.31948 | 0.659741 | − | 0.751493i | \(-0.270666\pi\) | ||||
0.659741 | + | 0.751493i | \(0.270666\pi\) | |||||||
\(614\) | 2.96388 | 0.119612 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.66097 | 0.107214 | ||||||||
\(617\) | −30.1631 | −1.21432 | −0.607160 | − | 0.794580i | \(-0.707691\pi\) | ||||
−0.607160 | + | 0.794580i | \(0.707691\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.57715 | −0.183971 | −0.0919856 | − | 0.995760i | \(-0.529321\pi\) | ||||
−0.0919856 | + | 0.995760i | \(0.529321\pi\) | |||||||
\(620\) | −75.1193 | −3.01687 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 43.6354 | 1.74962 | ||||||||
\(623\) | 1.78663 | 0.0715799 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 36.5889 | 1.46356 | ||||||||
\(626\) | 71.6587 | 2.86406 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −49.8575 | −1.98953 | ||||||||
\(629\) | 0.433941 | 0.0173024 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15.8483 | −0.630911 | −0.315455 | − | 0.948940i | \(-0.602157\pi\) | ||||
−0.315455 | + | 0.948940i | \(0.602157\pi\) | |||||||
\(632\) | 8.30092 | 0.330193 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 9.20763 | 0.365682 | ||||||||
\(635\) | 3.96692 | 0.157422 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.92494 | −0.0762688 | ||||||||
\(638\) | −61.5547 | −2.43697 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −24.6482 | −0.974306 | ||||||||
\(641\) | −22.9792 | −0.907624 | −0.453812 | − | 0.891097i | \(-0.649936\pi\) | ||||
−0.453812 | + | 0.891097i | \(0.649936\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8.56313 | −0.337697 | −0.168848 | − | 0.985642i | \(-0.554005\pi\) | ||||
−0.168848 | + | 0.985642i | \(0.554005\pi\) | |||||||
\(644\) | 16.5742 | 0.653116 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.44778 | −0.135651 | ||||||||
\(647\) | −37.9948 | −1.49373 | −0.746865 | − | 0.664976i | \(-0.768442\pi\) | ||||
−0.746865 | + | 0.664976i | \(0.768442\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 24.6617 | 0.968056 | ||||||||
\(650\) | 43.2426 | 1.69611 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −43.1111 | −1.68836 | ||||||||
\(653\) | 26.3329 | 1.03048 | 0.515242 | − | 0.857045i | \(-0.327702\pi\) | ||||
0.515242 | + | 0.857045i | \(0.327702\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −57.8194 | −2.25919 | ||||||||
\(656\) | 15.9003 | 0.620801 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −18.0946 | −0.705401 | ||||||||
\(659\) | −9.50560 | −0.370286 | −0.185143 | − | 0.982712i | \(-0.559275\pi\) | ||||
−0.185143 | + | 0.982712i | \(0.559275\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.6702 | 0.687292 | 0.343646 | − | 0.939099i | \(-0.388338\pi\) | ||||
0.343646 | + | 0.939099i | \(0.388338\pi\) | |||||||
\(662\) | −20.0544 | −0.779437 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 10.3008 | 0.399748 | ||||||||
\(665\) | −5.95906 | −0.231082 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −60.9373 | −2.35950 | ||||||||
\(668\) | 1.52626 | 0.0590528 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −7.43608 | −0.287281 | ||||||||
\(671\) | 27.7453 | 1.07110 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −40.0668 | −1.54446 | −0.772231 | − | 0.635342i | \(-0.780859\pi\) | ||||
−0.772231 | + | 0.635342i | \(0.780859\pi\) | |||||||
\(674\) | 2.18633 | 0.0842142 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −22.1021 | −0.850081 | ||||||||
\(677\) | 45.5736 | 1.75153 | 0.875767 | − | 0.482734i | \(-0.160356\pi\) | ||||
0.875767 | + | 0.482734i | \(0.160356\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 15.4051 | 0.591193 | ||||||||
\(680\) | 3.44112 | 0.131961 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 56.0668 | 2.14691 | ||||||||
\(683\) | −8.24883 | −0.315633 | −0.157816 | − | 0.987468i | \(-0.550445\pi\) | ||||
−0.157816 | + | 0.987468i | \(0.550445\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 20.7189 | 0.791630 | ||||||||
\(686\) | −2.09235 | −0.0798865 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −12.6709 | −0.483072 | ||||||||
\(689\) | −2.74514 | −0.104582 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21.3610 | −0.812610 | −0.406305 | − | 0.913738i | \(-0.633183\pi\) | ||||
−0.406305 | + | 0.913738i | \(0.633183\pi\) | |||||||
\(692\) | 16.5353 | 0.628578 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 51.1974 | 1.94343 | ||||||||
\(695\) | 29.0767 | 1.10294 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.62400 | −0.213024 | ||||||||
\(698\) | −4.39695 | −0.166427 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 25.5307 | 0.964969 | ||||||||
\(701\) | −19.5387 | −0.737968 | −0.368984 | − | 0.929436i | \(-0.620294\pi\) | ||||
−0.368984 | + | 0.929436i | \(0.620294\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.594258 | 0.0224129 | ||||||||
\(704\) | 35.9504 | 1.35493 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −13.6642 | −0.514258 | ||||||||
\(707\) | −13.4223 | −0.504799 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 37.3661 | 1.40331 | 0.701657 | − | 0.712515i | \(-0.252444\pi\) | ||||
0.701657 | + | 0.712515i | \(0.252444\pi\) | |||||||
\(710\) | −107.102 | −4.01945 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.41287 | −0.0529495 | ||||||||
\(713\) | 55.5044 | 2.07866 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −25.6947 | −0.960928 | ||||||||
\(716\) | −18.5400 | −0.692874 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −9.40015 | −0.350811 | ||||||||
\(719\) | −6.79800 | −0.253523 | −0.126761 | − | 0.991933i | \(-0.540458\pi\) | ||||
−0.126761 | + | 0.991933i | \(0.540458\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 19.8444 | 0.739044 | ||||||||
\(722\) | 35.0332 | 1.30380 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −4.75036 | −0.176546 | ||||||||
\(725\) | −93.8668 | −3.48613 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −11.9071 | −0.441608 | −0.220804 | − | 0.975318i | \(-0.570868\pi\) | ||||
−0.220804 | + | 0.975318i | \(0.570868\pi\) | |||||||
\(728\) | 1.52224 | 0.0564179 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −122.858 | −4.54717 | ||||||||
\(731\) | 4.48175 | 0.165764 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −15.9489 | −0.589086 | −0.294543 | − | 0.955638i | \(-0.595167\pi\) | ||||
−0.294543 | + | 0.955638i | \(0.595167\pi\) | |||||||
\(734\) | −1.93291 | −0.0713452 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 56.2514 | 2.07346 | ||||||||
\(737\) | 3.01460 | 0.111044 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 32.3318 | 1.18934 | 0.594671 | − | 0.803969i | \(-0.297282\pi\) | ||||
0.594671 | + | 0.803969i | \(0.297282\pi\) | |||||||
\(740\) | −3.73169 | −0.137180 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.98390 | −0.109542 | ||||||||
\(743\) | 47.8459 | 1.75530 | 0.877648 | − | 0.479306i | \(-0.159112\pi\) | ||||
0.877648 | + | 0.479306i | \(0.159112\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −85.1068 | −3.11807 | ||||||||
\(746\) | 21.4158 | 0.784087 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −8.77720 | −0.320926 | ||||||||
\(749\) | −6.88756 | −0.251666 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.64951 | 0.169663 | 0.0848315 | − | 0.996395i | \(-0.472965\pi\) | ||||
0.0848315 | + | 0.996395i | \(0.472965\pi\) | |||||||
\(752\) | −26.8196 | −0.978009 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −35.2130 | −1.28238 | ||||||||
\(755\) | 35.4454 | 1.28999 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.97451 | 0.144456 | 0.0722279 | − | 0.997388i | \(-0.476989\pi\) | ||||
0.0722279 | + | 0.997388i | \(0.476989\pi\) | |||||||
\(758\) | −50.3960 | −1.83047 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.71242 | 0.170938 | ||||||||
\(761\) | −24.8801 | −0.901903 | −0.450952 | − | 0.892548i | \(-0.648915\pi\) | ||||
−0.450952 | + | 0.892548i | \(0.648915\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 18.2912 | 0.662186 | ||||||||
\(764\) | −8.63034 | −0.312235 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 11.4465 | 0.413580 | ||||||||
\(767\) | 14.1080 | 0.509410 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −50.9477 | −1.83722 | −0.918611 | − | 0.395164i | \(-0.870688\pi\) | ||||
−0.918611 | + | 0.395164i | \(0.870688\pi\) | |||||||
\(770\) | −27.9295 | −1.00651 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 62.6126 | 2.25348 | ||||||||
\(773\) | 3.65460 | 0.131447 | 0.0657233 | − | 0.997838i | \(-0.479065\pi\) | ||||
0.0657233 | + | 0.997838i | \(0.479065\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 85.4981 | 3.07118 | ||||||||
\(776\) | −12.1823 | −0.437320 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 30.5298 | 1.09455 | ||||||||
\(779\) | −7.70176 | −0.275944 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 43.4192 | 1.55366 | ||||||||
\(782\) | −15.9973 | −0.572062 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.10126 | −0.110759 | ||||||||
\(785\) | 83.1729 | 2.96857 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −40.4237 | −1.44095 | −0.720474 | − | 0.693482i | \(-0.756076\pi\) | ||||
−0.720474 | + | 0.693482i | \(0.756076\pi\) | |||||||
\(788\) | −15.0000 | −0.534353 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −87.1261 | −3.09981 | ||||||||
\(791\) | 17.1246 | 0.608882 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15.8720 | 0.563632 | ||||||||
\(794\) | −68.9026 | −2.44526 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −56.6520 | −2.00798 | ||||||||
\(797\) | 8.44675 | 0.299199 | 0.149600 | − | 0.988747i | \(-0.452202\pi\) | ||||
0.149600 | + | 0.988747i | \(0.452202\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.48623 | 0.335599 | ||||||||
\(800\) | 86.6488 | 3.06350 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −55.1076 | −1.94592 | ||||||||
\(803\) | 49.8068 | 1.75764 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −27.6493 | −0.974511 | ||||||||
\(806\) | 32.0736 | 1.12975 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 10.6144 | 0.373413 | ||||||||
\(809\) | 23.3390 | 0.820556 | 0.410278 | − | 0.911960i | \(-0.365432\pi\) | ||||
0.410278 | + | 0.911960i | \(0.365432\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15.5167 | 0.544864 | 0.272432 | − | 0.962175i | \(-0.412172\pi\) | ||||
0.272432 | + | 0.962175i | \(0.412172\pi\) | |||||||
\(812\) | −20.7900 | −0.729585 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2.78522 | 0.0976220 | ||||||||
\(815\) | 71.9184 | 2.51919 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.13751 | 0.214724 | ||||||||
\(818\) | 0.841209 | 0.0294122 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 48.3639 | 1.68894 | ||||||||
\(821\) | 41.1428 | 1.43590 | 0.717948 | − | 0.696097i | \(-0.245082\pi\) | ||||
0.717948 | + | 0.696097i | \(0.245082\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −36.6572 | −1.27779 | −0.638895 | − | 0.769294i | \(-0.720608\pi\) | ||||
−0.638895 | + | 0.769294i | \(0.720608\pi\) | |||||||
\(824\) | −15.6930 | −0.546690 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 15.3350 | 0.533573 | ||||||||
\(827\) | 37.3911 | 1.30022 | 0.650109 | − | 0.759841i | \(-0.274723\pi\) | ||||
0.650109 | + | 0.759841i | \(0.274723\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20.0071 | −0.694877 | −0.347438 | − | 0.937703i | \(-0.612948\pi\) | ||||
−0.347438 | + | 0.937703i | \(0.612948\pi\) | |||||||
\(830\) | −108.117 | −3.75278 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 20.5658 | 0.712992 | ||||||||
\(833\) | 1.09693 | 0.0380065 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.54612 | −0.0881122 | ||||||||
\(836\) | −12.0199 | −0.415717 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −28.4600 | −0.983133 | ||||||||
\(839\) | −18.1768 | −0.627534 | −0.313767 | − | 0.949500i | \(-0.601591\pi\) | ||||
−0.313767 | + | 0.949500i | \(0.601591\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 47.4370 | 1.63576 | ||||||||
\(842\) | −52.2978 | −1.80230 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −21.4910 | −0.739751 | ||||||||
\(845\) | 36.8710 | 1.26840 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.322654 | 0.0110865 | ||||||||
\(848\) | −4.42269 | −0.151876 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −24.6420 | −0.845213 | ||||||||
\(851\) | 2.75729 | 0.0945186 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −14.0356 | −0.480569 | −0.240285 | − | 0.970702i | \(-0.577241\pi\) | ||||
−0.240285 | + | 0.970702i | \(0.577241\pi\) | |||||||
\(854\) | 17.2525 | 0.590367 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5.44668 | 0.186164 | ||||||||
\(857\) | 47.3584 | 1.61773 | 0.808866 | − | 0.587993i | \(-0.200082\pi\) | ||||
0.808866 | + | 0.587993i | \(0.200082\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 42.4759 | 1.44926 | 0.724629 | − | 0.689139i | \(-0.242011\pi\) | ||||
0.724629 | + | 0.689139i | \(0.242011\pi\) | |||||||
\(860\) | −38.5410 | −1.31424 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 70.8272 | 2.41238 | ||||||||
\(863\) | −17.4580 | −0.594276 | −0.297138 | − | 0.954834i | \(-0.596032\pi\) | ||||
−0.297138 | + | 0.954834i | \(0.596032\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −27.5844 | −0.937897 | ||||||||
\(866\) | −54.1714 | −1.84082 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 18.9364 | 0.642745 | ||||||||
\(869\) | 35.3211 | 1.19819 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.72453 | 0.0584336 | ||||||||
\(872\) | −14.4647 | −0.489836 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −21.9074 | −0.741029 | ||||||||
\(875\) | −22.7560 | −0.769293 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 24.2333 | 0.818299 | 0.409150 | − | 0.912467i | \(-0.365825\pi\) | ||||
0.409150 | + | 0.912467i | \(0.365825\pi\) | |||||||
\(878\) | −51.2306 | −1.72895 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −41.3967 | −1.39548 | ||||||||
\(881\) | 31.1584 | 1.04975 | 0.524877 | − | 0.851178i | \(-0.324111\pi\) | ||||
0.524877 | + | 0.851178i | \(0.324111\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −47.0978 | −1.58497 | −0.792483 | − | 0.609894i | \(-0.791212\pi\) | ||||
−0.792483 | + | 0.609894i | \(0.791212\pi\) | |||||||
\(884\) | −5.02110 | −0.168878 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −43.8937 | −1.47464 | ||||||||
\(887\) | 51.6181 | 1.73317 | 0.866583 | − | 0.499034i | \(-0.166312\pi\) | ||||
0.866583 | + | 0.499034i | \(0.166312\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.00000 | −0.0335389 | ||||||||
\(890\) | 14.8294 | 0.497083 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −58.5994 | −1.96205 | ||||||||
\(893\) | 12.9909 | 0.434723 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 30.9287 | 1.03383 | ||||||||
\(896\) | 6.21344 | 0.207576 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −13.0062 | −0.434023 | ||||||||
\(899\) | −69.6223 | −2.32203 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.56433 | 0.0521154 | ||||||||
\(902\) | −36.0973 | −1.20191 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −13.5422 | −0.450406 | ||||||||
\(905\) | 7.92461 | 0.263423 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 56.8898 | 1.88899 | 0.944497 | − | 0.328519i | \(-0.106550\pi\) | ||||
0.944497 | + | 0.328519i | \(0.106550\pi\) | |||||||
\(908\) | 9.28024 | 0.307976 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −15.9774 | −0.529644 | ||||||||
\(911\) | 38.1640 | 1.26443 | 0.632214 | − | 0.774794i | \(-0.282146\pi\) | ||||
0.632214 | + | 0.774794i | \(0.282146\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 43.8307 | 1.45058 | ||||||||
\(914\) | −8.68202 | −0.287176 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −61.8702 | −2.04425 | ||||||||
\(917\) | 14.5754 | 0.481322 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 19.8403 | 0.654473 | 0.327236 | − | 0.944943i | \(-0.393883\pi\) | ||||
0.327236 | + | 0.944943i | \(0.393883\pi\) | |||||||
\(920\) | 21.8651 | 0.720870 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −39.2847 | −1.29377 | ||||||||
\(923\) | 24.8384 | 0.817566 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.24728 | 0.139650 | ||||||||
\(926\) | 15.2034 | 0.499616 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −70.5593 | −2.31622 | ||||||||
\(929\) | 25.0484 | 0.821813 | 0.410906 | − | 0.911678i | \(-0.365212\pi\) | ||||
0.410906 | + | 0.911678i | \(0.365212\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.50219 | 0.0492322 | ||||||||
\(932\) | −6.02097 | −0.197224 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −15.4212 | −0.504597 | ||||||||
\(935\) | 14.6422 | 0.478852 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −10.5239 | −0.343800 | −0.171900 | − | 0.985114i | \(-0.554991\pi\) | ||||
−0.171900 | + | 0.985114i | \(0.554991\pi\) | |||||||
\(938\) | 1.87452 | 0.0612053 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −81.5772 | −2.66076 | ||||||||
\(941\) | 44.8694 | 1.46270 | 0.731351 | − | 0.682001i | \(-0.238890\pi\) | ||||
0.731351 | + | 0.682001i | \(0.238890\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −35.7353 | −1.16370 | ||||||||
\(944\) | 22.7294 | 0.739778 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 28.7659 | 0.935259 | ||||||||
\(947\) | −22.9147 | −0.744629 | −0.372315 | − | 0.928107i | \(-0.621436\pi\) | ||||
−0.372315 | + | 0.928107i | \(0.621436\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 28.4925 | 0.924906 | ||||||||
\(950\) | −33.7458 | −1.09486 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −0.867454 | −0.0281143 | ||||||||
\(953\) | −22.6679 | −0.734285 | −0.367143 | − | 0.930165i | \(-0.619664\pi\) | ||||
−0.367143 | + | 0.930165i | \(0.619664\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 14.3972 | 0.465883 | ||||||||
\(956\) | 68.6303 | 2.21966 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −29.0714 | −0.939255 | ||||||||
\(959\) | −5.22293 | −0.168657 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 32.4151 | 1.04565 | ||||||||
\(962\) | 1.59332 | 0.0513706 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 41.7009 | 1.34309 | ||||||||
\(965\) | −104.451 | −3.36240 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 37.7740 | 1.21473 | 0.607365 | − | 0.794423i | \(-0.292226\pi\) | ||||
0.607365 | + | 0.794423i | \(0.292226\pi\) | |||||||
\(968\) | −0.255154 | −0.00820097 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 127.865 | 4.10551 | ||||||||
\(971\) | 56.9817 | 1.82863 | 0.914315 | − | 0.405005i | \(-0.132730\pi\) | ||||
0.914315 | + | 0.405005i | \(0.132730\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.32979 | −0.234982 | ||||||||
\(974\) | −20.3424 | −0.651814 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 25.5714 | 0.818520 | ||||||||
\(977\) | 36.8275 | 1.17822 | 0.589109 | − | 0.808054i | \(-0.299479\pi\) | ||||
0.589109 | + | 0.808054i | \(0.299479\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.01187 | −0.192140 | ||||||||
\(980\) | −9.43312 | −0.301330 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 33.2231 | 1.06019 | ||||||||
\(983\) | −8.77102 | −0.279752 | −0.139876 | − | 0.990169i | \(-0.544670\pi\) | ||||
−0.139876 | + | 0.990169i | \(0.544670\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 25.0232 | 0.797304 | ||||||||
\(986\) | 20.0663 | 0.639041 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −6.87612 | −0.218758 | ||||||||
\(989\) | 28.4773 | 0.905526 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 53.2754 | 1.69235 | 0.846175 | − | 0.532905i | \(-0.178900\pi\) | ||||
0.846175 | + | 0.532905i | \(0.178900\pi\) | |||||||
\(992\) | 64.2686 | 2.04053 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 26.9987 | 0.856347 | ||||||||
\(995\) | 94.5075 | 2.99609 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −43.2333 | −1.36921 | −0.684606 | − | 0.728914i | \(-0.740026\pi\) | ||||
−0.684606 | + | 0.728914i | \(0.740026\pi\) | |||||||
\(998\) | −76.7909 | −2.43077 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8001.2.a.ba.1.9 | ✓ | 40 | |
3.2 | odd | 2 | inner | 8001.2.a.ba.1.32 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8001.2.a.ba.1.9 | ✓ | 40 | 1.1 | even | 1 | trivial | |
8001.2.a.ba.1.32 | yes | 40 | 3.2 | odd | 2 | inner |