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: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2667) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.56155\) of defining polynomial | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.00000 | −1.00000 | ||||||||
\(5\) | 3.56155 | 1.59277 | 0.796387 | − | 0.604787i | \(-0.206742\pi\) | ||||
0.796387 | + | 0.604787i | \(0.206742\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.12311 | −0.941652 | −0.470826 | − | 0.882226i | \(-0.656044\pi\) | ||||
−0.470826 | + | 0.882226i | \(0.656044\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.56155 | −0.987797 | −0.493899 | − | 0.869520i | \(-0.664429\pi\) | ||||
−0.493899 | + | 0.869520i | \(0.664429\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 1.00000 | ||||||||
\(17\) | −6.56155 | −1.59141 | −0.795705 | − | 0.605684i | \(-0.792900\pi\) | ||||
−0.795705 | + | 0.605684i | \(0.792900\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.00000 | 0.917663 | 0.458831 | − | 0.888523i | \(-0.348268\pi\) | ||||
0.458831 | + | 0.888523i | \(0.348268\pi\) | |||||||
\(20\) | −7.12311 | −1.59277 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.68466 | 0.976819 | 0.488409 | − | 0.872615i | \(-0.337577\pi\) | ||||
0.488409 | + | 0.872615i | \(0.337577\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.68466 | 1.53693 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.00000 | 0.377964 | ||||||||
\(29\) | −4.12311 | −0.765641 | −0.382821 | − | 0.923823i | \(-0.625047\pi\) | ||||
−0.382821 | + | 0.923823i | \(0.625047\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.68466 | 0.841389 | 0.420695 | − | 0.907202i | \(-0.361786\pi\) | ||||
0.420695 | + | 0.907202i | \(0.361786\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.56155 | −0.602012 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.87689 | −0.308560 | −0.154280 | − | 0.988027i | \(-0.549306\pi\) | ||||
−0.154280 | + | 0.988027i | \(0.549306\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.8078 | 1.68789 | 0.843945 | − | 0.536430i | \(-0.180228\pi\) | ||||
0.843945 | + | 0.536430i | \(0.180228\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.24621 | −0.647541 | −0.323771 | − | 0.946136i | \(-0.604951\pi\) | ||||
−0.323771 | + | 0.946136i | \(0.604951\pi\) | |||||||
\(44\) | 6.24621 | 0.941652 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.87689 | 0.711368 | 0.355684 | − | 0.934606i | \(-0.384248\pi\) | ||||
0.355684 | + | 0.934606i | \(0.384248\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 7.12311 | 0.987797 | ||||||||
\(53\) | 11.0000 | 1.51097 | 0.755483 | − | 0.655168i | \(-0.227402\pi\) | ||||
0.755483 | + | 0.655168i | \(0.227402\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −11.1231 | −1.49984 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.43845 | 0.577837 | 0.288918 | − | 0.957354i | \(-0.406704\pi\) | ||||
0.288918 | + | 0.957354i | \(0.406704\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.56155 | −1.22423 | −0.612116 | − | 0.790768i | \(-0.709681\pi\) | ||||
−0.612116 | + | 0.790768i | \(0.709681\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.00000 | −1.00000 | ||||||||
\(65\) | −12.6847 | −1.57334 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.00000 | −0.244339 | −0.122169 | − | 0.992509i | \(-0.538985\pi\) | ||||
−0.122169 | + | 0.992509i | \(0.538985\pi\) | |||||||
\(68\) | 13.1231 | 1.59141 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.1231 | 1.55743 | 0.778713 | − | 0.627380i | \(-0.215873\pi\) | ||||
0.778713 | + | 0.627380i | \(0.215873\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.43845 | −0.519481 | −0.259740 | − | 0.965678i | \(-0.583637\pi\) | ||||
−0.259740 | + | 0.965678i | \(0.583637\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −8.00000 | −0.917663 | ||||||||
\(77\) | 3.12311 | 0.355911 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.315342 | −0.0354787 | −0.0177393 | − | 0.999843i | \(-0.505647\pi\) | ||||
−0.0177393 | + | 0.999843i | \(0.505647\pi\) | |||||||
\(80\) | 14.2462 | 1.59277 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −17.8078 | −1.95466 | −0.977328 | − | 0.211731i | \(-0.932090\pi\) | ||||
−0.977328 | + | 0.211731i | \(0.932090\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −23.3693 | −2.53476 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.80776 | −0.827621 | −0.413811 | − | 0.910363i | \(-0.635802\pi\) | ||||
−0.413811 | + | 0.910363i | \(0.635802\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.56155 | 0.373352 | ||||||||
\(92\) | −9.36932 | −0.976819 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 14.2462 | 1.46163 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.80776 | −0.894293 | −0.447146 | − | 0.894461i | \(-0.647560\pi\) | ||||
−0.447146 | + | 0.894461i | \(0.647560\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −15.3693 | −1.53693 | ||||||||
\(101\) | −19.8078 | −1.97095 | −0.985473 | − | 0.169832i | \(-0.945678\pi\) | ||||
−0.985473 | + | 0.169832i | \(0.945678\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.0000 | −1.18240 | −0.591198 | − | 0.806527i | \(-0.701345\pi\) | ||||
−0.591198 | + | 0.806527i | \(0.701345\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.00000 | −0.386695 | −0.193347 | − | 0.981130i | \(-0.561934\pi\) | ||||
−0.193347 | + | 0.981130i | \(0.561934\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.00000 | 0.191565 | 0.0957826 | − | 0.995402i | \(-0.469465\pi\) | ||||
0.0957826 | + | 0.995402i | \(0.469465\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −4.00000 | −0.377964 | ||||||||
\(113\) | −2.87689 | −0.270635 | −0.135318 | − | 0.990802i | \(-0.543206\pi\) | ||||
−0.135318 | + | 0.990802i | \(0.543206\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 16.6847 | 1.55585 | ||||||||
\(116\) | 8.24621 | 0.765641 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.56155 | 0.601497 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.24621 | −0.113292 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −9.36932 | −0.841389 | ||||||||
\(125\) | 9.56155 | 0.855211 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.00000 | 0.0887357 | ||||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.6847 | −1.19563 | −0.597817 | − | 0.801633i | \(-0.703965\pi\) | ||||
−0.597817 | + | 0.801633i | \(0.703965\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.00000 | −0.346844 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 19.5616 | 1.67126 | 0.835628 | − | 0.549296i | \(-0.185104\pi\) | ||||
0.835628 | + | 0.549296i | \(0.185104\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.5616 | 1.06546 | 0.532729 | − | 0.846286i | \(-0.321167\pi\) | ||||
0.532729 | + | 0.846286i | \(0.321167\pi\) | |||||||
\(140\) | 7.12311 | 0.602012 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 11.1231 | 0.930161 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −14.6847 | −1.21949 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.75379 | 0.308560 | ||||||||
\(149\) | −14.0000 | −1.14692 | −0.573462 | − | 0.819232i | \(-0.694400\pi\) | ||||
−0.573462 | + | 0.819232i | \(0.694400\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −22.4924 | −1.83041 | −0.915204 | − | 0.402992i | \(-0.867970\pi\) | ||||
−0.915204 | + | 0.402992i | \(0.867970\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 16.6847 | 1.34014 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.246211 | 0.0196498 | 0.00982490 | − | 0.999952i | \(-0.496873\pi\) | ||||
0.00982490 | + | 0.999952i | \(0.496873\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.68466 | −0.369203 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −22.6155 | −1.77138 | −0.885692 | − | 0.464272i | \(-0.846316\pi\) | ||||
−0.885692 | + | 0.464272i | \(0.846316\pi\) | |||||||
\(164\) | −21.6155 | −1.68789 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −10.2462 | −0.792876 | −0.396438 | − | 0.918062i | \(-0.629754\pi\) | ||||
−0.396438 | + | 0.918062i | \(0.629754\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.315342 | −0.0242570 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 8.49242 | 0.647541 | ||||||||
\(173\) | 1.36932 | 0.104107 | 0.0520536 | − | 0.998644i | \(-0.483423\pi\) | ||||
0.0520536 | + | 0.998644i | \(0.483423\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.68466 | −0.580906 | ||||||||
\(176\) | −12.4924 | −0.941652 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.87689 | 0.215029 | 0.107515 | − | 0.994204i | \(-0.465711\pi\) | ||||
0.107515 | + | 0.994204i | \(0.465711\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.19224 | −0.237277 | −0.118639 | − | 0.992938i | \(-0.537853\pi\) | ||||
−0.118639 | + | 0.992938i | \(0.537853\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.68466 | −0.491466 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 20.4924 | 1.49855 | ||||||||
\(188\) | −9.75379 | −0.711368 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −19.3693 | −1.40151 | −0.700757 | − | 0.713400i | \(-0.747154\pi\) | ||||
−0.700757 | + | 0.713400i | \(0.747154\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.12311 | 0.512732 | 0.256366 | − | 0.966580i | \(-0.417475\pi\) | ||||
0.256366 | + | 0.966580i | \(0.417475\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.00000 | −0.142857 | ||||||||
\(197\) | 27.3693 | 1.94998 | 0.974992 | − | 0.222242i | \(-0.0713375\pi\) | ||||
0.974992 | + | 0.222242i | \(0.0713375\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.56155 | −0.677801 | −0.338900 | − | 0.940822i | \(-0.610055\pi\) | ||||
−0.338900 | + | 0.940822i | \(0.610055\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.12311 | 0.289385 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 38.4924 | 2.68843 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −14.2462 | −0.987797 | ||||||||
\(209\) | −12.4924 | −0.864119 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −28.6847 | −1.97473 | −0.987367 | − | 0.158452i | \(-0.949350\pi\) | ||||
−0.987367 | + | 0.158452i | \(0.949350\pi\) | |||||||
\(212\) | −22.0000 | −1.51097 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −15.1231 | −1.03139 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.68466 | −0.318015 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 22.2462 | 1.49984 | ||||||||
\(221\) | 23.3693 | 1.57199 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.8078 | −0.723741 | −0.361871 | − | 0.932228i | \(-0.617862\pi\) | ||||
−0.361871 | + | 0.932228i | \(0.617862\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 13.3693 | 0.887353 | 0.443676 | − | 0.896187i | \(-0.353674\pi\) | ||||
0.443676 | + | 0.896187i | \(0.353674\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.43845 | −0.623710 | −0.311855 | − | 0.950130i | \(-0.600950\pi\) | ||||
−0.311855 | + | 0.950130i | \(0.600950\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −24.3693 | −1.59649 | −0.798244 | − | 0.602335i | \(-0.794237\pi\) | ||||
−0.798244 | + | 0.602335i | \(0.794237\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 17.3693 | 1.13305 | ||||||||
\(236\) | −8.87689 | −0.577837 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.63068 | −0.234849 | −0.117425 | − | 0.993082i | \(-0.537464\pi\) | ||||
−0.117425 | + | 0.993082i | \(0.537464\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.43845 | −0.350321 | −0.175161 | − | 0.984540i | \(-0.556044\pi\) | ||||
−0.175161 | + | 0.984540i | \(0.556044\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 19.1231 | 1.22423 | ||||||||
\(245\) | 3.56155 | 0.227539 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −14.2462 | −0.906465 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 22.8078 | 1.43961 | 0.719807 | − | 0.694175i | \(-0.244230\pi\) | ||||
0.719807 | + | 0.694175i | \(0.244230\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −14.6307 | −0.919823 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 1.00000 | ||||||||
\(257\) | 10.0540 | 0.627150 | 0.313575 | − | 0.949563i | \(-0.398473\pi\) | ||||
0.313575 | + | 0.949563i | \(0.398473\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.87689 | 0.116625 | ||||||||
\(260\) | 25.3693 | 1.57334 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 13.6155 | 0.839569 | 0.419785 | − | 0.907624i | \(-0.362106\pi\) | ||||
0.419785 | + | 0.907624i | \(0.362106\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 39.1771 | 2.40663 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4.00000 | 0.244339 | ||||||||
\(269\) | 4.80776 | 0.293135 | 0.146567 | − | 0.989201i | \(-0.453178\pi\) | ||||
0.146567 | + | 0.989201i | \(0.453178\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.9309 | 0.785494 | 0.392747 | − | 0.919646i | \(-0.371525\pi\) | ||||
0.392747 | + | 0.919646i | \(0.371525\pi\) | |||||||
\(272\) | −26.2462 | −1.59141 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −24.0000 | −1.44725 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.75379 | −0.105375 | −0.0526875 | − | 0.998611i | \(-0.516779\pi\) | ||||
−0.0526875 | + | 0.998611i | \(0.516779\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.56155 | −0.510739 | −0.255370 | − | 0.966843i | \(-0.582197\pi\) | ||||
−0.255370 | + | 0.966843i | \(0.582197\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.6847 | −0.932356 | −0.466178 | − | 0.884691i | \(-0.654369\pi\) | ||||
−0.466178 | + | 0.884691i | \(0.654369\pi\) | |||||||
\(284\) | −26.2462 | −1.55743 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.8078 | −0.637962 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 26.0540 | 1.53259 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 8.87689 | 0.519481 | ||||||||
\(293\) | 10.0000 | 0.584206 | 0.292103 | − | 0.956387i | \(-0.405645\pi\) | ||||
0.292103 | + | 0.956387i | \(0.405645\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 15.8078 | 0.920364 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −16.6847 | −0.964899 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.24621 | 0.244748 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 16.0000 | 0.917663 | ||||||||
\(305\) | −34.0540 | −1.94992 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −34.8078 | −1.98658 | −0.993292 | − | 0.115633i | \(-0.963110\pi\) | ||||
−0.993292 | + | 0.115633i | \(0.963110\pi\) | |||||||
\(308\) | −6.24621 | −0.355911 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −20.0540 | −1.13716 | −0.568578 | − | 0.822629i | \(-0.692506\pi\) | ||||
−0.568578 | + | 0.822629i | \(0.692506\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.9309 | 0.674373 | 0.337186 | − | 0.941438i | \(-0.390525\pi\) | ||||
0.337186 | + | 0.941438i | \(0.390525\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.630683 | 0.0354787 | ||||||||
\(317\) | 7.75379 | 0.435496 | 0.217748 | − | 0.976005i | \(-0.430129\pi\) | ||||
0.217748 | + | 0.976005i | \(0.430129\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.8769 | 0.720968 | ||||||||
\(320\) | −28.4924 | −1.59277 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −26.2462 | −1.46038 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −27.3693 | −1.51818 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.87689 | −0.268872 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.24621 | −0.343323 | −0.171661 | − | 0.985156i | \(-0.554914\pi\) | ||||
−0.171661 | + | 0.985156i | \(0.554914\pi\) | |||||||
\(332\) | 35.6155 | 1.95466 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7.12311 | −0.389177 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.75379 | 0.531323 | 0.265661 | − | 0.964066i | \(-0.414410\pi\) | ||||
0.265661 | + | 0.964066i | \(0.414410\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 46.7386 | 2.53476 | ||||||||
\(341\) | −14.6307 | −0.792296 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 25.4924 | 1.36850 | 0.684252 | − | 0.729245i | \(-0.260129\pi\) | ||||
0.684252 | + | 0.729245i | \(0.260129\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 21.0540 | 1.12699 | 0.563497 | − | 0.826118i | \(-0.309456\pi\) | ||||
0.563497 | + | 0.826118i | \(0.309456\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.87689 | 0.153122 | 0.0765608 | − | 0.997065i | \(-0.475606\pi\) | ||||
0.0765608 | + | 0.997065i | \(0.475606\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 46.7386 | 2.48063 | ||||||||
\(356\) | 15.6155 | 0.827621 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −21.9309 | −1.15747 | −0.578734 | − | 0.815517i | \(-0.696453\pi\) | ||||
−0.578734 | + | 0.815517i | \(0.696453\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.00000 | −0.157895 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −7.12311 | −0.373352 | ||||||||
\(365\) | −15.8078 | −0.827416 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.17708 | −0.374641 | −0.187320 | − | 0.982299i | \(-0.559980\pi\) | ||||
−0.187320 | + | 0.982299i | \(0.559980\pi\) | |||||||
\(368\) | 18.7386 | 0.976819 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −11.0000 | −0.571092 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.12311 | 0.161708 | 0.0808541 | − | 0.996726i | \(-0.474235\pi\) | ||||
0.0808541 | + | 0.996726i | \(0.474235\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 14.6847 | 0.756298 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −27.1231 | −1.39322 | −0.696610 | − | 0.717450i | \(-0.745309\pi\) | ||||
−0.696610 | + | 0.717450i | \(0.745309\pi\) | |||||||
\(380\) | −28.4924 | −1.46163 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 33.9309 | 1.73379 | 0.866893 | − | 0.498494i | \(-0.166113\pi\) | ||||
0.866893 | + | 0.498494i | \(0.166113\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 11.1231 | 0.566886 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 17.6155 | 0.894293 | ||||||||
\(389\) | 16.4924 | 0.836199 | 0.418100 | − | 0.908401i | \(-0.362696\pi\) | ||||
0.418100 | + | 0.908401i | \(0.362696\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −30.7386 | −1.55452 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.12311 | −0.0565096 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 38.0540 | 1.90987 | 0.954937 | − | 0.296808i | \(-0.0959222\pi\) | ||||
0.954937 | + | 0.296808i | \(0.0959222\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 30.7386 | 1.53693 | ||||||||
\(401\) | 14.3693 | 0.717569 | 0.358785 | − | 0.933420i | \(-0.383191\pi\) | ||||
0.358785 | + | 0.933420i | \(0.383191\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −16.6847 | −0.831122 | ||||||||
\(404\) | 39.6155 | 1.97095 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.86174 | 0.290556 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −18.0000 | −0.890043 | −0.445021 | − | 0.895520i | \(-0.646804\pi\) | ||||
−0.445021 | + | 0.895520i | \(0.646804\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 24.0000 | 1.18240 | ||||||||
\(413\) | −4.43845 | −0.218402 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −63.4233 | −3.11333 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −0.876894 | −0.0428391 | −0.0214195 | − | 0.999771i | \(-0.506819\pi\) | ||||
−0.0214195 | + | 0.999771i | \(0.506819\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −38.2462 | −1.86401 | −0.932003 | − | 0.362450i | \(-0.881940\pi\) | ||||
−0.932003 | + | 0.362450i | \(0.881940\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −50.4233 | −2.44589 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.56155 | 0.462716 | ||||||||
\(428\) | 8.00000 | 0.386695 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 18.4924 | 0.890749 | 0.445374 | − | 0.895344i | \(-0.353071\pi\) | ||||
0.445374 | + | 0.895344i | \(0.353071\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −30.4924 | −1.46537 | −0.732686 | − | 0.680567i | \(-0.761734\pi\) | ||||
−0.732686 | + | 0.680567i | \(0.761734\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.00000 | −0.191565 | ||||||||
\(437\) | 18.7386 | 0.896390 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.19224 | −0.0569023 | −0.0284512 | − | 0.999595i | \(-0.509058\pi\) | ||||
−0.0284512 | + | 0.999595i | \(0.509058\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.00000 | −0.190046 | −0.0950229 | − | 0.995475i | \(-0.530292\pi\) | ||||
−0.0950229 | + | 0.995475i | \(0.530292\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −27.8078 | −1.31821 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 8.00000 | 0.377964 | ||||||||
\(449\) | −23.6155 | −1.11449 | −0.557243 | − | 0.830350i | \(-0.688141\pi\) | ||||
−0.557243 | + | 0.830350i | \(0.688141\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −33.7538 | −1.58940 | ||||||||
\(452\) | 5.75379 | 0.270635 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 12.6847 | 0.594666 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.00000 | 0.140334 | 0.0701670 | − | 0.997535i | \(-0.477647\pi\) | ||||
0.0701670 | + | 0.997535i | \(0.477647\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −33.3693 | −1.55585 | ||||||||
\(461\) | −18.0000 | −0.838344 | −0.419172 | − | 0.907907i | \(-0.637680\pi\) | ||||
−0.419172 | + | 0.907907i | \(0.637680\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.68466 | 0.403610 | 0.201805 | − | 0.979426i | \(-0.435319\pi\) | ||||
0.201805 | + | 0.979426i | \(0.435319\pi\) | |||||||
\(464\) | −16.4924 | −0.765641 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.43845 | 0.297936 | 0.148968 | − | 0.988842i | \(-0.452405\pi\) | ||||
0.148968 | + | 0.988842i | \(0.452405\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.00000 | 0.0923514 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 13.2614 | 0.609758 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 30.7386 | 1.41039 | ||||||||
\(476\) | −13.1231 | −0.601497 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −35.4384 | −1.61922 | −0.809612 | − | 0.586965i | \(-0.800322\pi\) | ||||
−0.809612 | + | 0.586965i | \(0.800322\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.68466 | 0.304794 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.49242 | 0.113292 | ||||||||
\(485\) | −31.3693 | −1.42441 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 26.2462 | 1.18933 | 0.594665 | − | 0.803974i | \(-0.297285\pi\) | ||||
0.594665 | + | 0.803974i | \(0.297285\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 40.4924 | 1.82740 | 0.913699 | − | 0.406392i | \(-0.133213\pi\) | ||||
0.913699 | + | 0.406392i | \(0.133213\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 27.0540 | 1.21845 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 18.7386 | 0.841389 | ||||||||
\(497\) | −13.1231 | −0.588652 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −32.4924 | −1.45456 | −0.727280 | − | 0.686341i | \(-0.759216\pi\) | ||||
−0.727280 | + | 0.686341i | \(0.759216\pi\) | |||||||
\(500\) | −19.1231 | −0.855211 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.68466 | 0.164291 | 0.0821454 | − | 0.996620i | \(-0.473823\pi\) | ||||
0.0821454 | + | 0.996620i | \(0.473823\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −70.5464 | −3.13927 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2.00000 | −0.0887357 | ||||||||
\(509\) | 15.6847 | 0.695210 | 0.347605 | − | 0.937641i | \(-0.386995\pi\) | ||||
0.347605 | + | 0.937641i | \(0.386995\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.43845 | 0.196345 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −42.7386 | −1.88329 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −15.2311 | −0.669861 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.12311 | 0.224447 | 0.112224 | − | 0.993683i | \(-0.464203\pi\) | ||||
0.112224 | + | 0.993683i | \(0.464203\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −15.1771 | −0.663647 | −0.331824 | − | 0.943341i | \(-0.607664\pi\) | ||||
−0.331824 | + | 0.943341i | \(0.607664\pi\) | |||||||
\(524\) | 27.3693 | 1.19563 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −30.7386 | −1.33900 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.05398 | −0.0458250 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 8.00000 | 0.346844 | ||||||||
\(533\) | −38.4924 | −1.66729 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −14.2462 | −0.615917 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.12311 | −0.134522 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.24621 | −0.0965722 | −0.0482861 | − | 0.998834i | \(-0.515376\pi\) | ||||
−0.0482861 | + | 0.998834i | \(0.515376\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.12311 | 0.305120 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.49242 | −0.192082 | −0.0960411 | − | 0.995377i | \(-0.530618\pi\) | ||||
−0.0960411 | + | 0.995377i | \(0.530618\pi\) | |||||||
\(548\) | −39.1231 | −1.67126 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −16.4924 | −0.702601 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.315342 | 0.0134097 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −25.1231 | −1.06546 | ||||||||
\(557\) | 8.87689 | 0.376126 | 0.188063 | − | 0.982157i | \(-0.439779\pi\) | ||||
0.188063 | + | 0.982157i | \(0.439779\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 15.1231 | 0.639639 | ||||||||
\(560\) | −14.2462 | −0.602012 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10.7386 | 0.452579 | 0.226290 | − | 0.974060i | \(-0.427340\pi\) | ||||
0.226290 | + | 0.974060i | \(0.427340\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.2462 | −0.431061 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −12.6307 | −0.529506 | −0.264753 | − | 0.964316i | \(-0.585290\pi\) | ||||
−0.264753 | + | 0.964316i | \(0.585290\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12.8769 | −0.538881 | −0.269441 | − | 0.963017i | \(-0.586839\pi\) | ||||
−0.269441 | + | 0.963017i | \(0.586839\pi\) | |||||||
\(572\) | −22.2462 | −0.930161 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 36.0000 | 1.50130 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.80776 | −0.408303 | −0.204151 | − | 0.978939i | \(-0.565443\pi\) | ||||
−0.204151 | + | 0.978939i | \(0.565443\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 29.3693 | 1.21949 | ||||||||
\(581\) | 17.8078 | 0.738791 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −34.3542 | −1.42280 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 31.3002 | 1.29190 | 0.645948 | − | 0.763381i | \(-0.276462\pi\) | ||||
0.645948 | + | 0.763381i | \(0.276462\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 18.7386 | 0.772112 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −7.50758 | −0.308560 | ||||||||
\(593\) | −24.6847 | −1.01368 | −0.506839 | − | 0.862041i | \(-0.669186\pi\) | ||||
−0.506839 | + | 0.862041i | \(0.669186\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 23.3693 | 0.958049 | ||||||||
\(596\) | 28.0000 | 1.14692 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −46.6155 | −1.90466 | −0.952329 | − | 0.305072i | \(-0.901320\pi\) | ||||
−0.952329 | + | 0.305072i | \(0.901320\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23.9309 | 0.976161 | 0.488080 | − | 0.872799i | \(-0.337697\pi\) | ||||
0.488080 | + | 0.872799i | \(0.337697\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 44.9848 | 1.83041 | ||||||||
\(605\) | −4.43845 | −0.180449 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.80776 | −0.154552 | −0.0772762 | − | 0.997010i | \(-0.524622\pi\) | ||||
−0.0772762 | + | 0.997010i | \(0.524622\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −17.3693 | −0.702687 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 31.3693 | 1.26699 | 0.633497 | − | 0.773745i | \(-0.281619\pi\) | ||||
0.633497 | + | 0.773745i | \(0.281619\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −33.1080 | −1.33288 | −0.666438 | − | 0.745560i | \(-0.732182\pi\) | ||||
−0.666438 | + | 0.745560i | \(0.732182\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22.3153 | 0.896929 | 0.448465 | − | 0.893801i | \(-0.351971\pi\) | ||||
0.448465 | + | 0.893801i | \(0.351971\pi\) | |||||||
\(620\) | −33.3693 | −1.34014 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.80776 | 0.312811 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.36932 | −0.174773 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −0.492423 | −0.0196498 | ||||||||
\(629\) | 12.3153 | 0.491045 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10.4924 | −0.417697 | −0.208848 | − | 0.977948i | \(-0.566972\pi\) | ||||
−0.208848 | + | 0.977948i | \(0.566972\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.56155 | 0.141336 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.56155 | −0.141114 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14.8078 | 0.584872 | 0.292436 | − | 0.956285i | \(-0.405534\pi\) | ||||
0.292436 | + | 0.956285i | \(0.405534\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 30.7386 | 1.21221 | 0.606107 | − | 0.795383i | \(-0.292730\pi\) | ||||
0.606107 | + | 0.795383i | \(0.292730\pi\) | |||||||
\(644\) | 9.36932 | 0.369203 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −16.0540 | −0.631147 | −0.315573 | − | 0.948901i | \(-0.602197\pi\) | ||||
−0.315573 | + | 0.948901i | \(0.602197\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13.8617 | −0.544121 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 45.2311 | 1.77138 | ||||||||
\(653\) | 21.8617 | 0.855516 | 0.427758 | − | 0.903893i | \(-0.359304\pi\) | ||||
0.427758 | + | 0.903893i | \(0.359304\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −48.7386 | −1.90438 | ||||||||
\(656\) | 43.2311 | 1.68789 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −30.4384 | −1.18571 | −0.592857 | − | 0.805308i | \(-0.702000\pi\) | ||||
−0.592857 | + | 0.805308i | \(0.702000\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.5616 | 0.760856 | 0.380428 | − | 0.924810i | \(-0.375777\pi\) | ||||
0.380428 | + | 0.924810i | \(0.375777\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −14.2462 | −0.552444 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −19.3153 | −0.747893 | ||||||||
\(668\) | 20.4924 | 0.792876 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 29.8617 | 1.15280 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 25.1080 | 0.967840 | 0.483920 | − | 0.875112i | \(-0.339212\pi\) | ||||
0.483920 | + | 0.875112i | \(0.339212\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.630683 | 0.0242570 | ||||||||
\(677\) | −21.9309 | −0.842872 | −0.421436 | − | 0.906858i | \(-0.638474\pi\) | ||||
−0.421436 | + | 0.906858i | \(0.638474\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.80776 | 0.338011 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −30.7386 | −1.17618 | −0.588091 | − | 0.808795i | \(-0.700120\pi\) | ||||
−0.588091 | + | 0.808795i | \(0.700120\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 69.6695 | 2.66193 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −16.9848 | −0.647541 | ||||||||
\(689\) | −39.1771 | −1.49253 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.3002 | 0.658130 | 0.329065 | − | 0.944307i | \(-0.393266\pi\) | ||||
0.329065 | + | 0.944307i | \(0.393266\pi\) | |||||||
\(692\) | −2.73863 | −0.104107 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 44.7386 | 1.69703 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −70.9157 | −2.68612 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 15.3693 | 0.580906 | ||||||||
\(701\) | −20.9309 | −0.790548 | −0.395274 | − | 0.918563i | \(-0.629350\pi\) | ||||
−0.395274 | + | 0.918563i | \(0.629350\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.50758 | −0.283154 | ||||||||
\(704\) | 24.9848 | 0.941652 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 19.8078 | 0.744948 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.06913 | −0.303043 | −0.151521 | − | 0.988454i | \(-0.548417\pi\) | ||||
−0.151521 | + | 0.988454i | \(0.548417\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 21.9460 | 0.821885 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 39.6155 | 1.48154 | ||||||||
\(716\) | −5.75379 | −0.215029 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 12.1771 | 0.454128 | 0.227064 | − | 0.973880i | \(-0.427087\pi\) | ||||
0.227064 | + | 0.973880i | \(0.427087\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.0000 | 0.446903 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 6.38447 | 0.237277 | ||||||||
\(725\) | −31.6847 | −1.17674 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −14.1771 | −0.525799 | −0.262899 | − | 0.964823i | \(-0.584679\pi\) | ||||
−0.262899 | + | 0.964823i | \(0.584679\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 27.8617 | 1.03050 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.68466 | −0.320775 | −0.160388 | − | 0.987054i | \(-0.551274\pi\) | ||||
−0.160388 | + | 0.987054i | \(0.551274\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.24621 | 0.230082 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.87689 | 0.142614 | 0.0713069 | − | 0.997454i | \(-0.477283\pi\) | ||||
0.0713069 | + | 0.997454i | \(0.477283\pi\) | |||||||
\(740\) | 13.3693 | 0.491466 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −27.1080 | −0.994494 | −0.497247 | − | 0.867609i | \(-0.665656\pi\) | ||||
−0.497247 | + | 0.867609i | \(0.665656\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −49.8617 | −1.82679 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −40.9848 | −1.49855 | ||||||||
\(749\) | 4.00000 | 0.146157 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −37.1231 | −1.35464 | −0.677321 | − | 0.735688i | \(-0.736859\pi\) | ||||
−0.677321 | + | 0.735688i | \(0.736859\pi\) | |||||||
\(752\) | 19.5076 | 0.711368 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −80.1080 | −2.91543 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −33.1080 | −1.20333 | −0.601664 | − | 0.798749i | \(-0.705496\pi\) | ||||
−0.601664 | + | 0.798749i | \(0.705496\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −44.5464 | −1.61481 | −0.807403 | − | 0.590001i | \(-0.799128\pi\) | ||||
−0.807403 | + | 0.590001i | \(0.799128\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.00000 | −0.0724049 | ||||||||
\(764\) | 38.7386 | 1.40151 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −15.8078 | −0.570785 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.05398 | −0.182251 | −0.0911255 | − | 0.995839i | \(-0.529046\pi\) | ||||
−0.0911255 | + | 0.995839i | \(0.529046\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −14.2462 | −0.512732 | ||||||||
\(773\) | 23.3002 | 0.838049 | 0.419025 | − | 0.907975i | \(-0.362372\pi\) | ||||
0.419025 | + | 0.907975i | \(0.362372\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 36.0000 | 1.29316 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 43.2311 | 1.54891 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −40.9848 | −1.46655 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 4.00000 | 0.142857 | ||||||||
\(785\) | 0.876894 | 0.0312977 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 40.7926 | 1.45410 | 0.727050 | − | 0.686585i | \(-0.240891\pi\) | ||||
0.727050 | + | 0.686585i | \(0.240891\pi\) | |||||||
\(788\) | −54.7386 | −1.94998 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.87689 | 0.102291 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 34.0540 | 1.20929 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 19.1231 | 0.677801 | ||||||||
\(797\) | 11.7538 | 0.416341 | 0.208170 | − | 0.978093i | \(-0.433249\pi\) | ||||
0.208170 | + | 0.978093i | \(0.433249\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −32.0000 | −1.13208 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 13.8617 | 0.489170 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −16.6847 | −0.588057 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −6.87689 | −0.241779 | −0.120889 | − | 0.992666i | \(-0.538575\pi\) | ||||
−0.120889 | + | 0.992666i | \(0.538575\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.56155 | 0.0548335 | 0.0274168 | − | 0.999624i | \(-0.491272\pi\) | ||||
0.0274168 | + | 0.999624i | \(0.491272\pi\) | |||||||
\(812\) | −8.24621 | −0.289385 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −80.5464 | −2.82142 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −16.9848 | −0.594225 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −76.9848 | −2.68843 | ||||||||
\(821\) | 47.0000 | 1.64031 | 0.820156 | − | 0.572140i | \(-0.193887\pi\) | ||||
0.820156 | + | 0.572140i | \(0.193887\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 26.4233 | 0.921058 | 0.460529 | − | 0.887645i | \(-0.347660\pi\) | ||||
0.460529 | + | 0.887645i | \(0.347660\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 31.0000 | 1.07798 | 0.538988 | − | 0.842314i | \(-0.318807\pi\) | ||||
0.538988 | + | 0.842314i | \(0.318807\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 29.2311 | 1.01524 | 0.507618 | − | 0.861582i | \(-0.330526\pi\) | ||||
0.507618 | + | 0.861582i | \(0.330526\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 28.4924 | 0.987797 | ||||||||
\(833\) | −6.56155 | −0.227344 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −36.4924 | −1.26287 | ||||||||
\(836\) | 24.9848 | 0.864119 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −51.4233 | −1.77533 | −0.887665 | − | 0.460491i | \(-0.847674\pi\) | ||||
−0.887665 | + | 0.460491i | \(0.847674\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12.0000 | −0.413793 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 57.3693 | 1.97473 | ||||||||
\(845\) | −1.12311 | −0.0386360 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.24621 | 0.0428203 | ||||||||
\(848\) | 44.0000 | 1.51097 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.79261 | −0.301407 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.43845 | −0.254688 | −0.127344 | − | 0.991859i | \(-0.540645\pi\) | ||||
−0.127344 | + | 0.991859i | \(0.540645\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −56.0540 | −1.91477 | −0.957384 | − | 0.288819i | \(-0.906737\pi\) | ||||
−0.957384 | + | 0.288819i | \(0.906737\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 38.9157 | 1.32779 | 0.663894 | − | 0.747827i | \(-0.268903\pi\) | ||||
0.663894 | + | 0.747827i | \(0.268903\pi\) | |||||||
\(860\) | 30.2462 | 1.03139 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −38.1231 | −1.29773 | −0.648863 | − | 0.760905i | \(-0.724755\pi\) | ||||
−0.648863 | + | 0.760905i | \(0.724755\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.87689 | 0.165819 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 9.36932 | 0.318015 | ||||||||
\(869\) | 0.984845 | 0.0334086 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.12311 | 0.241357 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −9.56155 | −0.323239 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 49.5464 | 1.67306 | 0.836531 | − | 0.547919i | \(-0.184580\pi\) | ||||
0.836531 | + | 0.547919i | \(0.184580\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −44.4924 | −1.49984 | ||||||||
\(881\) | −46.9309 | −1.58114 | −0.790571 | − | 0.612371i | \(-0.790216\pi\) | ||||
−0.790571 | + | 0.612371i | \(0.790216\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 22.9309 | 0.771685 | 0.385843 | − | 0.922565i | \(-0.373911\pi\) | ||||
0.385843 | + | 0.922565i | \(0.373911\pi\) | |||||||
\(884\) | −46.7386 | −1.57199 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −26.4384 | −0.887716 | −0.443858 | − | 0.896097i | \(-0.646391\pi\) | ||||
−0.443858 | + | 0.896097i | \(0.646391\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.00000 | −0.0335389 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 21.6155 | 0.723741 | ||||||||
\(893\) | 19.5076 | 0.652796 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 10.2462 | 0.342493 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −19.3153 | −0.644203 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −72.1771 | −2.40457 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −11.3693 | −0.377929 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −37.4924 | −1.24492 | −0.622458 | − | 0.782653i | \(-0.713866\pi\) | ||||
−0.622458 | + | 0.782653i | \(0.713866\pi\) | |||||||
\(908\) | −26.7386 | −0.887353 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0.630683 | 0.0208955 | 0.0104477 | − | 0.999945i | \(-0.496674\pi\) | ||||
0.0104477 | + | 0.999945i | \(0.496674\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 55.6155 | 1.84061 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 18.8769 | 0.623710 | ||||||||
\(917\) | 13.6847 | 0.451907 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.86174 | 0.160374 | 0.0801870 | − | 0.996780i | \(-0.474448\pi\) | ||||
0.0801870 | + | 0.996780i | \(0.474448\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −46.7386 | −1.53842 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −14.4233 | −0.474235 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.61553 | 0.118622 | 0.0593108 | − | 0.998240i | \(-0.481110\pi\) | ||||
0.0593108 | + | 0.998240i | \(0.481110\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.00000 | 0.131095 | ||||||||
\(932\) | 48.7386 | 1.59649 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 72.9848 | 2.38686 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.12311 | −0.0366903 | −0.0183451 | − | 0.999832i | \(-0.505840\pi\) | ||||
−0.0183451 | + | 0.999832i | \(0.505840\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −34.7386 | −1.13305 | ||||||||
\(941\) | 37.0540 | 1.20793 | 0.603963 | − | 0.797013i | \(-0.293588\pi\) | ||||
0.603963 | + | 0.797013i | \(0.293588\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 50.6307 | 1.64876 | ||||||||
\(944\) | 17.7538 | 0.577837 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 38.4233 | 1.24859 | 0.624295 | − | 0.781189i | \(-0.285386\pi\) | ||||
0.624295 | + | 0.781189i | \(0.285386\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 15.8078 | 0.513142 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −24.7386 | −0.801363 | −0.400681 | − | 0.916217i | \(-0.631227\pi\) | ||||
−0.400681 | + | 0.916217i | \(0.631227\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −68.9848 | −2.23230 | ||||||||
\(956\) | 7.26137 | 0.234849 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −19.5616 | −0.631675 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.05398 | −0.292064 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 10.8769 | 0.350321 | ||||||||
\(965\) | 25.3693 | 0.816667 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −50.3542 | −1.61928 | −0.809640 | − | 0.586926i | \(-0.800338\pi\) | ||||
−0.809640 | + | 0.586926i | \(0.800338\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −29.3693 | −0.942506 | −0.471253 | − | 0.881998i | \(-0.656198\pi\) | ||||
−0.471253 | + | 0.881998i | \(0.656198\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12.5616 | −0.402705 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −38.2462 | −1.22423 | ||||||||
\(977\) | 52.9848 | 1.69514 | 0.847568 | − | 0.530687i | \(-0.178066\pi\) | ||||
0.847568 | + | 0.530687i | \(0.178066\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 24.3845 | 0.779331 | ||||||||
\(980\) | −7.12311 | −0.227539 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 10.8078 | 0.344714 | 0.172357 | − | 0.985035i | \(-0.444862\pi\) | ||||
0.172357 | + | 0.985035i | \(0.444862\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 97.4773 | 3.10588 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 28.4924 | 0.906465 | ||||||||
\(989\) | −19.8920 | −0.632530 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.0000 | 0.508257 | 0.254128 | − | 0.967170i | \(-0.418211\pi\) | ||||
0.254128 | + | 0.967170i | \(0.418211\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −34.0540 | −1.07958 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 26.0000 | 0.823428 | 0.411714 | − | 0.911313i | \(-0.364930\pi\) | ||||
0.411714 | + | 0.911313i | \(0.364930\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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.i.1.2 | 2 | ||
3.2 | odd | 2 | 2667.2.a.f.1.1 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2667.2.a.f.1.1 | ✓ | 2 | 3.2 | odd | 2 | ||
8001.2.a.i.1.2 | 2 | 1.1 | even | 1 | trivial |