Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4008,2,Mod(1,4008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4008, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4008 = 2^{3} \cdot 3 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4008.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: | \(32.0040411301\) |
Analytic rank: | \(1\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 3x^{8} - 16x^{7} + 45x^{6} + 67x^{5} - 166x^{4} - 83x^{3} + 152x^{2} + 51x - 10 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(0.141931\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4008.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.858069 | −0.383740 | −0.191870 | − | 0.981420i | \(-0.561455\pi\) | ||||
−0.191870 | + | 0.981420i | \(0.561455\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.33225 | 0.881509 | 0.440754 | − | 0.897628i | \(-0.354711\pi\) | ||||
0.440754 | + | 0.897628i | \(0.354711\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.664078 | 0.200227 | 0.100113 | − | 0.994976i | \(-0.468079\pi\) | ||||
0.100113 | + | 0.994976i | \(0.468079\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.80424 | −0.777757 | −0.388879 | − | 0.921289i | \(-0.627137\pi\) | ||||
−0.388879 | + | 0.921289i | \(0.627137\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.858069 | −0.221552 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.73771 | −1.14906 | −0.574532 | − | 0.818482i | \(-0.694816\pi\) | ||||
−0.574532 | + | 0.818482i | \(0.694816\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.58466 | −1.74004 | −0.870021 | − | 0.493015i | \(-0.835895\pi\) | ||||
−0.870021 | + | 0.493015i | \(0.835895\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.33225 | 0.508939 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.58999 | 1.37411 | 0.687054 | − | 0.726606i | \(-0.258903\pi\) | ||||
0.687054 | + | 0.726606i | \(0.258903\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.26372 | −0.852744 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.75833 | −0.883600 | −0.441800 | − | 0.897114i | \(-0.645660\pi\) | ||||
−0.441800 | + | 0.897114i | \(0.645660\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.96038 | −0.531700 | −0.265850 | − | 0.964014i | \(-0.585653\pi\) | ||||
−0.265850 | + | 0.964014i | \(0.585653\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.664078 | 0.115601 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.00123 | −0.338270 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.12480 | 0.678113 | 0.339056 | − | 0.940766i | \(-0.389892\pi\) | ||||
0.339056 | + | 0.940766i | \(0.389892\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.80424 | −0.449038 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.76756 | −1.21309 | −0.606544 | − | 0.795050i | \(-0.707445\pi\) | ||||
−0.606544 | + | 0.795050i | \(0.707445\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.13938 | 0.631249 | 0.315624 | − | 0.948884i | \(-0.397786\pi\) | ||||
0.315624 | + | 0.948884i | \(0.397786\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.858069 | −0.127913 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.39111 | −0.202914 | −0.101457 | − | 0.994840i | \(-0.532350\pi\) | ||||
−0.101457 | + | 0.994840i | \(0.532350\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.56060 | −0.222942 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.73771 | −0.663412 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.74469 | −0.239651 | −0.119826 | − | 0.992795i | \(-0.538234\pi\) | ||||
−0.119826 | + | 0.992795i | \(0.538234\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.569824 | −0.0768351 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.58466 | −1.00461 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −10.2363 | −1.33265 | −0.666325 | − | 0.745661i | \(-0.732134\pi\) | ||||
−0.666325 | + | 0.745661i | \(0.732134\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.762183 | −0.0975875 | −0.0487937 | − | 0.998809i | \(-0.515538\pi\) | ||||
−0.0487937 | + | 0.998809i | \(0.515538\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.33225 | 0.293836 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.40623 | 0.298457 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.00130165 | 0.000159022 0 | 7.95109e−5 | − | 1.00000i | \(-0.499975\pi\) | ||||
7.95109e−5 | 1.00000i | \(0.499975\pi\) | ||||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.58999 | 0.793342 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.99630 | −0.355596 | −0.177798 | − | 0.984067i | \(-0.556897\pi\) | ||||
−0.177798 | + | 0.984067i | \(0.556897\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −16.6717 | −1.95128 | −0.975640 | − | 0.219379i | \(-0.929597\pi\) | ||||
−0.975640 | + | 0.219379i | \(0.929597\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.26372 | −0.492332 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.54880 | 0.176502 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.5928 | −1.19178 | −0.595891 | − | 0.803065i | \(-0.703201\pi\) | ||||
−0.595891 | + | 0.803065i | \(0.703201\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 17.4041 | 1.91035 | 0.955177 | − | 0.296037i | \(-0.0956650\pi\) | ||||
0.955177 | + | 0.296037i | \(0.0956650\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.06528 | 0.440941 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.75833 | −0.510147 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.94100 | −0.523745 | −0.261872 | − | 0.965103i | \(-0.584340\pi\) | ||||
−0.261872 | + | 0.965103i | \(0.584340\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.54021 | −0.685600 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.96038 | −0.306977 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.50816 | 0.667723 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 17.4544 | 1.77222 | 0.886112 | − | 0.463471i | \(-0.153396\pi\) | ||||
0.886112 | + | 0.463471i | \(0.153396\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.664078 | 0.0667423 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.83624 | 0.282216 | 0.141108 | − | 0.989994i | \(-0.454933\pi\) | ||||
0.141108 | + | 0.989994i | \(0.454933\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.68361 | 0.165891 | 0.0829454 | − | 0.996554i | \(-0.473567\pi\) | ||||
0.0829454 | + | 0.996554i | \(0.473567\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.00123 | −0.195300 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10.4960 | 1.01468 | 0.507341 | − | 0.861745i | \(-0.330628\pi\) | ||||
0.507341 | + | 0.861745i | \(0.330628\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.61751 | −0.346494 | −0.173247 | − | 0.984878i | \(-0.555426\pi\) | ||||
−0.173247 | + | 0.984878i | \(0.555426\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.12480 | 0.391509 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.15002 | 0.202257 | 0.101129 | − | 0.994873i | \(-0.467755\pi\) | ||||
0.101129 | + | 0.994873i | \(0.467755\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.65467 | −0.527300 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.80424 | −0.259252 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −11.0495 | −1.01291 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.5590 | −0.959909 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −7.76756 | −0.700377 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 7.94891 | 0.710972 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.3626 | −1.09701 | −0.548504 | − | 0.836148i | \(-0.684802\pi\) | ||||
−0.548504 | + | 0.836148i | \(0.684802\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.13938 | 0.364452 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 20.5805 | 1.79812 | 0.899061 | − | 0.437822i | \(-0.144250\pi\) | ||||
0.899061 | + | 0.437822i | \(0.144250\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −17.6894 | −1.53386 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.858069 | −0.0738508 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.1249 | 0.865031 | 0.432515 | − | 0.901627i | \(-0.357626\pi\) | ||||
0.432515 | + | 0.901627i | \(0.357626\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.84695 | 0.156656 | 0.0783280 | − | 0.996928i | \(-0.475042\pi\) | ||||
0.0783280 | + | 0.996928i | \(0.475042\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.39111 | −0.117153 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.86224 | −0.155728 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.08297 | 0.339073 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.56060 | −0.128716 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.36994 | 0.439922 | 0.219961 | − | 0.975509i | \(-0.429407\pi\) | ||||
0.219961 | + | 0.975509i | \(0.429407\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.0563 | −1.06251 | −0.531254 | − | 0.847213i | \(-0.678279\pi\) | ||||
−0.531254 | + | 0.847213i | \(0.678279\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.73771 | −0.383021 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.54021 | 0.204034 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.47662 | 0.437082 | 0.218541 | − | 0.975828i | \(-0.429870\pi\) | ||||
0.218541 | + | 0.975828i | \(0.429870\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.74469 | −0.138363 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 15.3695 | 1.21129 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 18.0321 | 1.41239 | 0.706193 | − | 0.708019i | \(-0.250411\pi\) | ||||
0.706193 | + | 0.708019i | \(0.250411\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.569824 | −0.0443607 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.00000 | −0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.13621 | −0.395093 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.58466 | −0.580014 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.9069 | 0.905266 | 0.452633 | − | 0.891697i | \(-0.350485\pi\) | ||||
0.452633 | + | 0.891697i | \(0.350485\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −9.94407 | −0.751701 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −10.2363 | −0.769406 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.99610 | −0.747144 | −0.373572 | − | 0.927601i | \(-0.621867\pi\) | ||||
−0.373572 | + | 0.927601i | \(0.621867\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.9764 | −0.964526 | −0.482263 | − | 0.876027i | \(-0.660185\pi\) | ||||
−0.482263 | + | 0.876027i | \(0.660185\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.762183 | −0.0563422 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.53936 | −0.260219 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.14621 | −0.230073 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.33225 | 0.169646 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.780931 | −0.0565062 | −0.0282531 | − | 0.999601i | \(-0.508994\pi\) | ||||
−0.0282531 | + | 0.999601i | \(0.508994\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.18460 | −0.229232 | −0.114616 | − | 0.993410i | \(-0.536564\pi\) | ||||
−0.114616 | + | 0.993410i | \(0.536564\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.40623 | 0.172314 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.29302 | −0.519606 | −0.259803 | − | 0.965662i | \(-0.583658\pi\) | ||||
−0.259803 | + | 0.965662i | \(0.583658\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −20.4949 | −1.45284 | −0.726422 | − | 0.687249i | \(-0.758818\pi\) | ||||
−0.726422 | + | 0.687249i | \(0.758818\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.00130165 | 9.18113e−5 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −11.0976 | −0.778901 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.66510 | 0.465511 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.58999 | 0.458036 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.03681 | −0.348403 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.79418 | 0.192359 | 0.0961795 | − | 0.995364i | \(-0.469338\pi\) | ||||
0.0961795 | + | 0.995364i | \(0.469338\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.99630 | −0.205303 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.55187 | −0.242235 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.90435 | −0.468698 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −16.6717 | −1.12657 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 13.2857 | 0.893692 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.07046 | −0.0716830 | −0.0358415 | − | 0.999357i | \(-0.511411\pi\) | ||||
−0.0358415 | + | 0.999357i | \(0.511411\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.26372 | −0.284248 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.06628 | −0.203516 | −0.101758 | − | 0.994809i | \(-0.532447\pi\) | ||||
−0.101758 | + | 0.994809i | \(0.532447\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.166978 | −0.0110342 | −0.00551710 | − | 0.999985i | \(-0.501756\pi\) | ||||
−0.00551710 | + | 0.999985i | \(0.501756\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.54880 | 0.101903 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.75862 | 0.639309 | 0.319654 | − | 0.947534i | \(-0.396433\pi\) | ||||
0.319654 | + | 0.947534i | \(0.396433\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.19367 | 0.0778663 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −10.5928 | −0.688076 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −27.8243 | −1.79980 | −0.899902 | − | 0.436093i | \(-0.856362\pi\) | ||||
−0.899902 | + | 0.436093i | \(0.856362\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.03419 | −0.388696 | −0.194348 | − | 0.980933i | \(-0.562259\pi\) | ||||
−0.194348 | + | 0.980933i | \(0.562259\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.33910 | 0.0855519 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 21.2693 | 1.35333 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 17.4041 | 1.10294 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −19.2169 | −1.21296 | −0.606481 | − | 0.795098i | \(-0.707419\pi\) | ||||
−0.606481 | + | 0.795098i | \(0.707419\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.37627 | 0.275133 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.06528 | 0.254578 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −8.38942 | −0.523318 | −0.261659 | − | 0.965160i | \(-0.584270\pi\) | ||||
−0.261659 | + | 0.965160i | \(0.584270\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.62007 | 0.597762 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.75833 | −0.294533 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −16.9678 | −1.04628 | −0.523139 | − | 0.852247i | \(-0.675239\pi\) | ||||
−0.523139 | + | 0.852247i | \(0.675239\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.49706 | 0.0919638 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.94100 | −0.302384 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −13.6797 | −0.834068 | −0.417034 | − | 0.908891i | \(-0.636930\pi\) | ||||
−0.417034 | + | 0.908891i | \(0.636930\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.2857 | −0.989284 | −0.494642 | − | 0.869097i | \(-0.664701\pi\) | ||||
−0.494642 | + | 0.869097i | \(0.664701\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −6.54021 | −0.395831 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.83144 | −0.170742 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.11423 | −0.247200 | −0.123600 | − | 0.992332i | \(-0.539444\pi\) | ||||
−0.123600 | + | 0.992332i | \(0.539444\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.96038 | −0.177233 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 29.3388 | 1.75020 | 0.875102 | − | 0.483939i | \(-0.160794\pi\) | ||||
0.875102 | + | 0.483939i | \(0.160794\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −16.5471 | −0.983621 | −0.491810 | − | 0.870702i | \(-0.663665\pi\) | ||||
−0.491810 | + | 0.870702i | \(0.663665\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6.50816 | 0.385510 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −18.1159 | −1.06935 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.44589 | 0.320346 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 17.4544 | 1.02319 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −31.9181 | −1.86468 | −0.932338 | − | 0.361588i | \(-0.882235\pi\) | ||||
−0.932338 | + | 0.361588i | \(0.882235\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.78344 | 0.511391 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.664078 | 0.0385337 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −18.4799 | −1.06872 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.65407 | 0.556451 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.83624 | 0.162938 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.654005 | 0.0374482 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12.7567 | −0.728063 | −0.364031 | − | 0.931387i | \(-0.618600\pi\) | ||||
−0.364031 | + | 0.931387i | \(0.618600\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.68361 | 0.0957771 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.06532 | −0.230523 | −0.115262 | − | 0.993335i | \(-0.536771\pi\) | ||||
−0.115262 | + | 0.993335i | \(0.536771\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.87994 | −0.558447 | −0.279224 | − | 0.960226i | \(-0.590077\pi\) | ||||
−0.279224 | + | 0.960226i | \(0.590077\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.00123 | −0.112757 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 11.2409 | 0.631353 | 0.315676 | − | 0.948867i | \(-0.397769\pi\) | ||||
0.315676 | + | 0.948867i | \(0.397769\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.15990 | −0.176920 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 10.4960 | 0.585827 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 35.9339 | 1.99942 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 11.9565 | 0.663228 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.61751 | −0.200049 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.24442 | −0.178871 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.6160 | −0.803370 | −0.401685 | − | 0.915778i | \(-0.631575\pi\) | ||||
−0.401685 | + | 0.915778i | \(0.631575\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.12480 | 0.226038 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.00111690 | −6.10230e−5 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.7052 | 0.692094 | 0.346047 | − | 0.938217i | \(-0.387524\pi\) | ||||
0.346047 | + | 0.938217i | \(0.387524\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.15002 | 0.116773 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.96592 | −0.106461 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.9655 | −1.07803 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5.65467 | −0.304437 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 34.7085 | 1.86325 | 0.931625 | − | 0.363422i | \(-0.118392\pi\) | ||||
0.931625 | + | 0.363422i | \(0.118392\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.432938 | −0.0231746 | −0.0115873 | − | 0.999933i | \(-0.503688\pi\) | ||||
−0.0115873 | + | 0.999933i | \(0.503688\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.80424 | −0.149679 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 15.5524 | 0.827769 | 0.413884 | − | 0.910329i | \(-0.364172\pi\) | ||||
0.413884 | + | 0.910329i | \(0.364172\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.57103 | 0.136456 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −11.0495 | −0.584803 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 12.9062 | 0.681163 | 0.340581 | − | 0.940215i | \(-0.389376\pi\) | ||||
0.340581 | + | 0.940215i | \(0.389376\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 38.5271 | 2.02774 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −10.5590 | −0.554204 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 14.3055 | 0.748784 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −24.5614 | −1.28210 | −0.641048 | − | 0.767501i | \(-0.721500\pi\) | ||||
−0.641048 | + | 0.767501i | \(0.721500\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −7.76756 | −0.404363 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.06905 | −0.211255 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 25.7222 | 1.33184 | 0.665922 | − | 0.746021i | \(-0.268038\pi\) | ||||
0.665922 | + | 0.746021i | \(0.268038\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 7.94891 | 0.410480 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 13.3435 | 0.687226 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 34.4480 | 1.76947 | 0.884737 | − | 0.466090i | \(-0.154338\pi\) | ||||
0.884737 | + | 0.466090i | \(0.154338\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −12.3626 | −0.633358 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 19.7939 | 1.01142 | 0.505711 | − | 0.862703i | \(-0.331230\pi\) | ||||
0.505711 | + | 0.862703i | \(0.331230\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.32897 | −0.0677308 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.13938 | 0.210416 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 18.5357 | 0.939798 | 0.469899 | − | 0.882720i | \(-0.344290\pi\) | ||||
0.469899 | + | 0.882720i | \(0.344290\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −31.2215 | −1.57894 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 20.5805 | 1.03815 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 9.08935 | 0.457335 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.39197 | −0.270615 | −0.135308 | − | 0.990804i | \(-0.543202\pi\) | ||||
−0.135308 | + | 0.990804i | \(0.543202\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −17.6894 | −0.885575 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13.8183 | −0.690055 | −0.345027 | − | 0.938593i | \(-0.612130\pi\) | ||||
−0.345027 | + | 0.938593i | \(0.612130\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.30163 | 0.413534 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.858069 | −0.0426378 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.73919 | 0.135776 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.26519 | 0.309794 | 0.154897 | − | 0.987931i | \(-0.450495\pi\) | ||||
0.154897 | + | 0.987931i | \(0.450495\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 10.1249 | 0.499426 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −23.8736 | −1.17474 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −14.9340 | −0.733079 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.84695 | 0.0904454 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.914237 | 0.0446634 | 0.0223317 | − | 0.999751i | \(-0.492891\pi\) | ||||
0.0223317 | + | 0.999751i | \(0.492891\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 31.5414 | 1.53723 | 0.768617 | − | 0.639709i | \(-0.220945\pi\) | ||||
0.768617 | + | 0.639709i | \(0.220945\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.39111 | −0.0676381 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 20.2003 | 0.979856 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.77760 | −0.0860242 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.86224 | −0.0899096 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 38.5807 | 1.85837 | 0.929184 | − | 0.369619i | \(-0.120512\pi\) | ||||
0.929184 | + | 0.369619i | \(0.120512\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.12866 | 0.390639 | 0.195319 | − | 0.980740i | \(-0.437426\pi\) | ||||
0.195319 | + | 0.980740i | \(0.437426\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.08297 | 0.195764 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −49.9829 | −2.39101 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −28.3001 | −1.35069 | −0.675344 | − | 0.737503i | \(-0.736005\pi\) | ||||
−0.675344 | + | 0.737503i | \(0.736005\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.56060 | −0.0743141 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −38.5945 | −1.83368 | −0.916841 | − | 0.399253i | \(-0.869269\pi\) | ||||
−0.916841 | + | 0.399253i | \(0.869269\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.23971 | 0.200982 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.36994 | 0.253989 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.70687 | 0.458096 | 0.229048 | − | 0.973415i | \(-0.426439\pi\) | ||||
0.229048 | + | 0.973415i | \(0.426439\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.15826 | −0.242893 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −13.0563 | −0.613439 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5.61195 | 0.263092 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −25.1697 | −1.17739 | −0.588694 | − | 0.808356i | \(-0.700358\pi\) | ||||
−0.588694 | + | 0.808356i | \(0.700358\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.73771 | −0.221137 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 33.4704 | 1.55887 | 0.779435 | − | 0.626483i | \(-0.215506\pi\) | ||||
0.779435 | + | 0.626483i | \(0.215506\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 23.8185 | 1.10694 | 0.553469 | − | 0.832870i | \(-0.313304\pi\) | ||||
0.553469 | + | 0.832870i | \(0.313304\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.54021 | 0.117799 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.42414 | 0.250999 | 0.125500 | − | 0.992094i | \(-0.459947\pi\) | ||||
0.125500 | + | 0.992094i | \(0.459947\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.00303578 | 0.000140179 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.47662 | 0.252349 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.74887 | 0.126393 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 32.3389 | 1.48381 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.74469 | −0.0798838 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 12.8509 | 0.587172 | 0.293586 | − | 0.955933i | \(-0.405151\pi\) | ||||
0.293586 | + | 0.955933i | \(0.405151\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11.5669 | −0.527407 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 15.3695 | 0.699338 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −14.9771 | −0.680073 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −32.9193 | −1.49171 | −0.745857 | − | 0.666106i | \(-0.767960\pi\) | ||||
−0.745857 | + | 0.666106i | \(0.767960\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 18.0321 | 0.815442 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −23.3929 | −1.05571 | −0.527854 | − | 0.849335i | \(-0.677003\pi\) | ||||
−0.527854 | + | 0.849335i | \(0.677003\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 22.5436 | 1.01531 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.569824 | −0.0256117 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6.98813 | −0.313461 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.77468 | 0.348042 | 0.174021 | − | 0.984742i | \(-0.444324\pi\) | ||||
0.174021 | + | 0.984742i | \(0.444324\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.00000 | −0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −11.5995 | −0.517195 | −0.258597 | − | 0.965985i | \(-0.583260\pi\) | ||||
−0.258597 | + | 0.965985i | \(0.583260\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.43369 | −0.108298 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5.13621 | −0.228107 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −14.3183 | −0.634646 | −0.317323 | − | 0.948317i | \(-0.602784\pi\) | ||||
−0.317323 | + | 0.948317i | \(0.602784\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −38.8827 | −1.72007 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −7.58466 | −0.334871 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.44465 | −0.0636590 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.923805 | −0.0406289 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 11.9069 | 0.522656 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 24.7954 | 1.08631 | 0.543153 | − | 0.839633i | \(-0.317230\pi\) | ||||
0.543153 | + | 0.839633i | \(0.317230\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.8863 | 0.694660 | 0.347330 | − | 0.937743i | \(-0.387088\pi\) | ||||
0.347330 | + | 0.937743i | \(0.387088\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −9.94407 | −0.433995 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 14.0254 | 0.610957 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 20.4280 | 0.888174 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −10.2363 | −0.444217 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 21.7821 | 0.943489 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9.00625 | −0.389374 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −9.99610 | −0.431364 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.03636 | −0.0446391 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −34.8029 | −1.49629 | −0.748147 | − | 0.663532i | \(-0.769056\pi\) | ||||
−0.748147 | + | 0.663532i | \(0.769056\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −12.9764 | −0.556869 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.10407 | 0.132964 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.7384 | −0.715682 | −0.357841 | − | 0.933782i | \(-0.616487\pi\) | ||||
−0.357841 | + | 0.933782i | \(0.616487\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.762183 | −0.0325292 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 36.0903 | 1.53750 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −24.7051 | −1.05057 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.53936 | −0.150237 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4.14278 | −0.175535 | −0.0877677 | − | 0.996141i | \(-0.527973\pi\) | ||||
−0.0877677 | + | 0.996141i | \(0.527973\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −11.6078 | −0.490959 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.14621 | −0.132833 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 31.1358 | 1.31222 | 0.656109 | − | 0.754666i | \(-0.272201\pi\) | ||||
0.656109 | + | 0.754666i | \(0.272201\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.84487 | −0.0776142 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.33225 | 0.0979454 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −16.2278 | −0.680305 | −0.340153 | − | 0.940370i | \(-0.610479\pi\) | ||||
−0.340153 | + | 0.940370i | \(0.610479\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15.7948 | −0.660991 | −0.330495 | − | 0.943808i | \(-0.607216\pi\) | ||||
−0.330495 | + | 0.943808i | \(0.607216\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −0.780931 | −0.0326239 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −28.0979 | −1.17176 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 29.3450 | 1.22165 | 0.610825 | − | 0.791766i | \(-0.290838\pi\) | ||||
0.610825 | + | 0.791766i | \(0.290838\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3.18460 | −0.132347 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 40.5909 | 1.68399 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.15861 | −0.0479847 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.40623 | 0.0994855 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.97172 | 0.163931 | 0.0819653 | − | 0.996635i | \(-0.473880\pi\) | ||||
0.0819653 | + | 0.996635i | \(0.473880\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 22.4535 | 0.925180 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.29302 | −0.299995 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 13.0664 | 0.536573 | 0.268286 | − | 0.963339i | \(-0.413543\pi\) | ||||
0.268286 | + | 0.963339i | \(0.413543\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9.48126 | 0.388694 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −20.4949 | −0.838800 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 26.1897 | 1.07008 | 0.535042 | − | 0.844826i | \(-0.320296\pi\) | ||||
0.535042 | + | 0.844826i | \(0.320296\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 31.0894 | 1.26816 | 0.634082 | − | 0.773266i | \(-0.281378\pi\) | ||||
0.634082 | + | 0.773266i | \(0.281378\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.00130165 | 5.30073e−5 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9.06035 | 0.368356 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.46967 | 0.303185 | 0.151592 | − | 0.988443i | \(-0.451560\pi\) | ||||
0.151592 | + | 0.988443i | \(0.451560\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −11.0976 | −0.449699 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.90101 | 0.157818 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.66230 | −0.309477 | −0.154739 | − | 0.987955i | \(-0.549454\pi\) | ||||
−0.154739 | + | 0.987955i | \(0.549454\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 6.66510 | 0.268763 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.5871 | 0.466479 | 0.233239 | − | 0.972419i | \(-0.425067\pi\) | ||||
0.233239 | + | 0.972419i | \(0.425067\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.39728 | 0.176741 | 0.0883707 | − | 0.996088i | \(-0.471834\pi\) | ||||
0.0883707 | + | 0.996088i | \(0.471834\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.58999 | 0.264447 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −11.5237 | −0.461685 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.4979 | 0.579915 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5.03681 | −0.201151 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −19.5421 | −0.779194 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −25.3849 | −1.01056 | −0.505279 | − | 0.862956i | \(-0.668610\pi\) | ||||
−0.505279 | + | 0.862956i | \(0.668610\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.79418 | 0.111059 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 10.6080 | 0.420966 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.37629 | 0.173395 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.99630 | −0.118532 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 23.9833 | 0.947283 | 0.473642 | − | 0.880718i | \(-0.342939\pi\) | ||||
0.473642 | + | 0.880718i | \(0.342939\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −27.3549 | −1.07877 | −0.539386 | − | 0.842059i | \(-0.681344\pi\) | ||||
−0.539386 | + | 0.842059i | \(0.681344\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.55187 | −0.139855 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8.92955 | −0.351057 | −0.175528 | − | 0.984474i | \(-0.556163\pi\) | ||||
−0.175528 | + | 0.984474i | \(0.556163\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.79769 | −0.266833 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.90435 | −0.270603 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.42815 | 0.0558877 | 0.0279438 | − | 0.999609i | \(-0.491104\pi\) | ||||
0.0279438 | + | 0.999609i | \(0.491104\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −17.6594 | −0.690012 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −16.6717 | −0.650426 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −20.7009 | −0.806394 | −0.403197 | − | 0.915113i | \(-0.632101\pi\) | ||||
−0.403197 | + | 0.915113i | \(0.632101\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.2990 | 0.517272 | 0.258636 | − | 0.965975i | \(-0.416727\pi\) | ||||
0.258636 | + | 0.965975i | \(0.416727\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 13.2857 | 0.515974 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 15.1787 | 0.588604 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −31.3574 | −1.21416 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.07046 | −0.0413862 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.506148 | −0.0195396 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.6827 | 0.488882 | 0.244441 | − | 0.969664i | \(-0.421396\pi\) | ||||
0.244441 | + | 0.969664i | \(0.421396\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.26372 | −0.164111 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.60520 | 0.100126 | 0.0500629 | − | 0.998746i | \(-0.484058\pi\) | ||||
0.0500629 | + | 0.998746i | \(0.484058\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 40.7080 | 1.56223 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.06628 | −0.117500 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 24.5138 | 0.937995 | 0.468998 | − | 0.883199i | \(-0.344615\pi\) | ||||
0.468998 | + | 0.883199i | \(0.344615\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.68788 | −0.331947 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.166978 | −0.00637060 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.89253 | 0.186391 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 32.0143 | 1.21788 | 0.608941 | − | 0.793215i | \(-0.291595\pi\) | ||||
0.608941 | + | 0.793215i | \(0.291595\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.54880 | 0.0588339 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.58481 | −0.0601152 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 36.8004 | 1.39392 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 9.75862 | 0.369105 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.88152 | −0.184372 | −0.0921862 | − | 0.995742i | \(-0.529386\pi\) | ||||
−0.0921862 | + | 0.995742i | \(0.529386\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −31.2852 | −1.17994 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.19367 | 0.0449561 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.61482 | 0.248776 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 42.2523 | 1.58682 | 0.793408 | − | 0.608690i | \(-0.208305\pi\) | ||||
0.793408 | + | 0.608690i | \(0.208305\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −10.5928 | −0.397261 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −19.5089 | −0.730613 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.59793 | 0.0597590 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −27.8243 | −1.03912 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −42.4125 | −1.58172 | −0.790860 | − | 0.611997i | \(-0.790366\pi\) | ||||
−0.790860 | + | 0.611997i | \(0.790366\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.92660 | 0.146234 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6.03419 | −0.224414 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 20.2882 | 0.753484 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.1250 | 0.820570 | 0.410285 | − | 0.911957i | \(-0.365429\pi\) | ||||
0.410285 | + | 0.911957i | \(0.365429\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −19.6112 | −0.725345 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 35.9161 | 1.32659 | 0.663297 | − | 0.748357i | \(-0.269157\pi\) | ||||
0.663297 | + | 0.748357i | \(0.269157\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.33910 | 0.0493934 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.000864396 0 | 3.18404e−5 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20.3434 | −0.748344 | −0.374172 | − | 0.927359i | \(-0.622073\pi\) | ||||
−0.374172 | + | 0.927359i | \(0.622073\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 21.2693 | 0.781345 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 47.9841 | 1.76036 | 0.880182 | − | 0.474636i | \(-0.157420\pi\) | ||||
0.880182 | + | 0.474636i | \(0.157420\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.60778 | −0.168816 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 17.4041 | 0.636784 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 24.4792 | 0.894451 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 40.8830 | 1.49184 | 0.745922 | − | 0.666034i | \(-0.232009\pi\) | ||||
0.745922 | + | 0.666034i | \(0.232009\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −19.2169 | −0.700304 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 11.2032 | 0.407727 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 52.4727 | 1.90715 | 0.953576 | − | 0.301151i | \(-0.0973708\pi\) | ||||
0.953576 | + | 0.301151i | \(0.0973708\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.37627 | 0.158848 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −30.9663 | −1.12253 | −0.561264 | − | 0.827636i | \(-0.689685\pi\) | ||||
−0.561264 | + | 0.827636i | \(0.689685\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.43694 | −0.305438 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.06528 | 0.146980 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 28.7050 | 1.03648 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −24.2091 | −0.873003 | −0.436501 | − | 0.899704i | \(-0.643783\pi\) | ||||
−0.436501 | + | 0.899704i | \(0.643783\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.38942 | −0.302138 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −13.4368 | −0.483289 | −0.241644 | − | 0.970365i | \(-0.577687\pi\) | ||||
−0.241644 | + | 0.970365i | \(0.577687\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 12.6222 | 0.453404 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 9.62007 | 0.345118 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 58.9143 | 2.11082 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.98978 | −0.0711998 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.75833 | −0.170049 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.69932 | −0.167726 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −38.7500 | −1.38129 | −0.690644 | − | 0.723195i | \(-0.742673\pi\) | ||||
−0.690644 | + | 0.723195i | \(0.742673\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −16.9678 | −0.604069 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.01440 | 0.178292 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.13735 | 0.0758994 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.49706 | 0.0530953 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −4.12743 | −0.146201 | −0.0731006 | − | 0.997325i | \(-0.523289\pi\) | ||||
−0.0731006 | + | 0.997325i | \(0.523289\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.59067 | 0.233161 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.94100 | −0.174582 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −11.0713 | −0.390699 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −13.1881 | −0.464820 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −13.6797 | −0.481549 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −43.5841 | −1.53233 | −0.766167 | − | 0.642641i | \(-0.777839\pi\) | ||||
−0.766167 | + | 0.642641i | \(0.777839\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6.11071 | −0.214576 | −0.107288 | − | 0.994228i | \(-0.534217\pi\) | ||||
−0.107288 | + | 0.994228i | \(0.534217\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −16.2857 | −0.571163 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −15.4728 | −0.541989 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −31.3958 | −1.09840 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6.54021 | −0.228533 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −44.6483 | −1.55824 | −0.779118 | − | 0.626878i | \(-0.784333\pi\) | ||||
−0.779118 | + | 0.626878i | \(0.784333\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −52.0320 | −1.81372 | −0.906861 | − | 0.421429i | \(-0.861529\pi\) | ||||
−0.906861 | + | 0.421429i | \(0.861529\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.83144 | −0.0985781 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0.434728 | 0.0151170 | 0.00755849 | − | 0.999971i | \(-0.497594\pi\) | ||||
0.00755849 | + | 0.999971i | \(0.497594\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 45.0928 | 1.56614 | 0.783069 | − | 0.621935i | \(-0.213653\pi\) | ||||
0.783069 | + | 0.621935i | \(0.213653\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.11423 | −0.142721 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.39365 | 0.256175 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.858069 | 0.0296947 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.96038 | −0.102326 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −28.8473 | −0.995919 | −0.497960 | − | 0.867200i | \(-0.665917\pi\) | ||||
−0.497960 | + | 0.867200i | \(0.665917\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.35829 | −0.219251 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 29.3388 | 1.01048 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.40722 | 0.151613 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −24.6263 | −0.846168 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −16.5471 | −0.567894 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 27.1824 | 0.931800 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −34.0205 | −1.16484 | −0.582420 | − | 0.812888i | \(-0.697894\pi\) | ||||
−0.582420 | + | 0.812888i | \(0.697894\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.50816 | 0.222574 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4.41103 | −0.150678 | −0.0753389 | − | 0.997158i | \(-0.524004\pi\) | ||||
−0.0753389 | + | 0.997158i | \(0.524004\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.717858 | 0.0244930 | 0.0122465 | − | 0.999925i | \(-0.496102\pi\) | ||||
0.0122465 | + | 0.999925i | \(0.496102\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −18.1159 | −0.617388 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 37.7870 | 1.28628 | 0.643142 | − | 0.765747i | \(-0.277630\pi\) | ||||
0.643142 | + | 0.765747i | \(0.277630\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −10.2170 | −0.347387 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5.44589 | 0.184952 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7.03444 | −0.238627 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.00365014 | −0.000123680 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 17.4544 | 0.590741 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 18.5389 | 0.626728 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −33.0599 | −1.11635 | −0.558177 | − | 0.829722i | \(-0.688499\pi\) | ||||
−0.558177 | + | 0.829722i | \(0.688499\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −31.9181 | −1.07657 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −33.8792 | −1.14142 | −0.570710 | − | 0.821152i | \(-0.693332\pi\) | ||||
−0.570710 | + | 0.821152i | \(0.693332\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −36.9683 | −1.24408 | −0.622041 | − | 0.782985i | \(-0.713696\pi\) | ||||
−0.622041 | + | 0.782985i | \(0.713696\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 8.78344 | 0.295252 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 27.6020 | 0.926786 | 0.463393 | − | 0.886153i | \(-0.346632\pi\) | ||||
0.463393 | + | 0.886153i | \(0.346632\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −28.8328 | −0.967022 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.664078 | 0.0222474 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 10.5511 | 0.353079 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.57734 | 0.286709 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −18.4799 | −0.617027 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 14.0865 | 0.469810 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.26583 | 0.275375 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 9.65407 | 0.321267 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 11.1346 | 0.370127 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 35.2051 | 1.16897 | 0.584484 | − | 0.811406i | \(-0.301297\pi\) | ||||
0.584484 | + | 0.811406i | \(0.301297\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.83624 | 0.0940720 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.23223 | 0.107088 | 0.0535442 | − | 0.998565i | \(-0.482948\pi\) | ||||
0.0535442 | + | 0.998565i | \(0.482948\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 11.5577 | 0.382504 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.654005 | 0.0216207 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 47.9988 | 1.58506 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 11.7314 | 0.386984 | 0.193492 | − | 0.981102i | \(-0.438019\pi\) | ||||
0.193492 | + | 0.981102i | \(0.438019\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −12.7567 | −0.420347 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 8.40236 | 0.276567 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −17.5870 | −0.578256 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.68361 | 0.0552970 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 36.8679 | 1.20960 | 0.604798 | − | 0.796379i | \(-0.293254\pi\) | ||||
0.604798 | + | 0.796379i | \(0.293254\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11.8366 | 0.387929 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −4.06532 | −0.133093 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.69966 | 0.0882884 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −10.7009 | −0.349583 | −0.174792 | − | 0.984605i | \(-0.555925\pi\) | ||||
−0.174792 | + | 0.984605i | \(0.555925\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −9.87994 | −0.322420 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.86481 | −0.158588 | −0.0792942 | − | 0.996851i | \(-0.525267\pi\) | ||||
−0.0792942 | + | 0.996851i | \(0.525267\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −51.1881 | −1.66692 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.00123 | −0.0651001 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4.67872 | −0.152038 | −0.0760190 | − | 0.997106i | \(-0.524221\pi\) | ||||
−0.0760190 | + | 0.997106i | \(0.524221\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 46.7516 | 1.51762 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 11.2409 | 0.364512 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −38.4497 | −1.24551 | −0.622754 | − | 0.782418i | \(-0.713986\pi\) | ||||
−0.622754 | + | 0.782418i | \(0.713986\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.670092 | 0.0216837 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.15990 | −0.102145 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 23.6139 | 0.762532 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.2362 | −0.717295 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 10.4960 | 0.338227 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.73260 | 0.0879656 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 30.5693 | 0.983044 | 0.491522 | − | 0.870865i | \(-0.336441\pi\) | ||||
0.491522 | + | 0.870865i | \(0.336441\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 35.9339 | 1.15436 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.810886 | 0.0260226 | 0.0130113 | − | 0.999915i | \(-0.495858\pi\) | ||||
0.0130113 | + | 0.999915i | \(0.495858\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.30755 | 0.138094 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 11.9565 | 0.382915 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 9.23855 | 0.295567 | 0.147784 | − | 0.989020i | \(-0.452786\pi\) | ||||
0.147784 | + | 0.989020i | \(0.452786\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.28120 | −0.104868 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.61751 | −0.115498 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.30384 | −0.0415861 | −0.0207931 | − | 0.999784i | \(-0.506619\pi\) | ||||
−0.0207931 | + | 0.999784i | \(0.506619\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.25791 | 0.199394 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.24442 | −0.103271 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 27.2785 | 0.867405 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 53.9125 | 1.71259 | 0.856293 | − | 0.516490i | \(-0.172762\pi\) | ||||
0.856293 | + | 0.516490i | \(0.172762\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −14.6160 | −0.463826 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 17.5860 | 0.557515 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −47.6636 | −1.50952 | −0.754760 | − | 0.656001i | \(-0.772247\pi\) | ||||
−0.754760 | + | 0.656001i | \(0.772247\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.12480 | 0.130503 |
(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 | 4008.2.a.i.1.5 | ✓ | 9 | |
4.3 | odd | 2 | 8016.2.a.ba.1.5 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4008.2.a.i.1.5 | ✓ | 9 | 1.1 | even | 1 | trivial | |
8016.2.a.ba.1.5 | 9 | 4.3 | odd | 2 |