Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [588,3,Mod(97,588)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(588, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("588.97");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 588.d (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(16.0218395444\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.339738624.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{6} + 14x^{4} - 8x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4}\cdot 7^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 97.3 | ||
Root | \(0.662827 + 0.382683i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 588.97 |
Dual form | 588.3.d.c.97.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/588\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(295\) | \(493\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | − 1.73205i | − 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.929003i | 0.185801i | 0.995675 | + | 0.0929003i | \(0.0296138\pi\) | ||||
−0.995675 | + | 0.0929003i | \(0.970386\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 9.68980 | 0.880891 | 0.440445 | − | 0.897779i | \(-0.354821\pi\) | ||||
0.440445 | + | 0.897779i | \(0.354821\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 15.9753i | 1.22887i | 0.788968 | + | 0.614434i | \(0.210616\pi\) | ||||
−0.788968 | + | 0.614434i | \(0.789384\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.60908 | 0.107272 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 10.5557i | 0.620926i | 0.950585 | + | 0.310463i | \(0.100484\pi\) | ||||
−0.950585 | + | 0.310463i | \(0.899516\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 7.22049i | − 0.380026i | −0.981782 | − | 0.190013i | \(-0.939147\pi\) | ||||
0.981782 | − | 0.190013i | \(-0.0608530\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −11.3001 | −0.491307 | −0.245654 | − | 0.969358i | \(-0.579003\pi\) | ||||
−0.245654 | + | 0.969358i | \(0.579003\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 24.1370 | 0.965478 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.19615i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 46.3148 | 1.59706 | 0.798532 | − | 0.601953i | \(-0.205610\pi\) | ||||
0.798532 | + | 0.601953i | \(0.205610\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 0.483049i | − 0.0155822i | −0.999970 | − | 0.00779111i | \(-0.997520\pi\) | ||||
0.999970 | − | 0.00779111i | \(-0.00248001\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 16.7832i | − 0.508582i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.48131 | 0.0670623 | 0.0335312 | − | 0.999438i | \(-0.489325\pi\) | ||||
0.0335312 | + | 0.999438i | \(0.489325\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 27.6700 | 0.709487 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 55.8520i | 1.36224i | 0.732170 | + | 0.681122i | \(0.238508\pi\) | ||||
−0.732170 | + | 0.681122i | \(0.761492\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 60.6786 | 1.41113 | 0.705566 | − | 0.708645i | \(-0.250693\pi\) | ||||
0.705566 | + | 0.708645i | \(0.250693\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 2.78701i | − 0.0619335i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 36.5867i | − 0.778440i | −0.921145 | − | 0.389220i | \(-0.872745\pi\) | ||||
0.921145 | − | 0.389220i | \(-0.127255\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 18.2831 | 0.358492 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −28.5229 | −0.538169 | −0.269084 | − | 0.963117i | \(-0.586721\pi\) | ||||
−0.269084 | + | 0.963117i | \(0.586721\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 9.00185i | 0.163670i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −12.5063 | −0.219408 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 94.0715i | 1.59443i | 0.603694 | + | 0.797216i | \(0.293695\pi\) | ||||
−0.603694 | + | 0.797216i | \(0.706305\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 110.193i | − 1.80645i | −0.429171 | − | 0.903223i | \(-0.641194\pi\) | ||||
0.429171 | − | 0.903223i | \(-0.358806\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −14.8411 | −0.228324 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 82.0309 | 1.22434 | 0.612171 | − | 0.790725i | \(-0.290296\pi\) | ||||
0.612171 | + | 0.790725i | \(0.290296\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 19.5723i | 0.283656i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 127.349 | 1.79365 | 0.896827 | − | 0.442382i | \(-0.145867\pi\) | ||||
0.896827 | + | 0.442382i | \(0.145867\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 46.2546i | − 0.633625i | −0.948488 | − | 0.316812i | \(-0.897387\pi\) | ||||
0.948488 | − | 0.316812i | \(-0.102613\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 41.8064i | − 0.557419i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 18.7003 | 0.236713 | 0.118356 | − | 0.992971i | \(-0.462237\pi\) | ||||
0.118356 | + | 0.992971i | \(0.462237\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 59.6357i | − 0.718502i | −0.933241 | − | 0.359251i | \(-0.883032\pi\) | ||||
0.933241 | − | 0.359251i | \(-0.116968\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.80632 | −0.115368 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 80.2197i | − 0.922065i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 71.1281i | 0.799192i | 0.916691 | + | 0.399596i | \(0.130850\pi\) | ||||
−0.916691 | + | 0.399596i | \(0.869150\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.836665 | −0.00899640 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.70786 | 0.0706090 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 102.239i | 1.05401i | 0.849861 | + | 0.527007i | \(0.176686\pi\) | ||||
−0.849861 | + | 0.527007i | \(0.823314\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −29.0694 | −0.293630 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 108.929i | 1.07851i | 0.842143 | + | 0.539255i | \(0.181294\pi\) | ||||
−0.842143 | + | 0.539255i | \(0.818706\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.747187i | 0.00725424i | 0.999993 | + | 0.00362712i | \(0.00115455\pi\) | ||||
−0.999993 | + | 0.00362712i | \(0.998845\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.2926 | 0.142922 | 0.0714608 | − | 0.997443i | \(-0.477234\pi\) | ||||
0.0714608 | + | 0.997443i | \(0.477234\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −54.2232 | −0.497461 | −0.248730 | − | 0.968573i | \(-0.580013\pi\) | ||||
−0.248730 | + | 0.968573i | \(0.580013\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − 4.29775i | − 0.0387185i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 65.2511 | 0.577444 | 0.288722 | − | 0.957413i | \(-0.406770\pi\) | ||||
0.288722 | + | 0.957413i | \(0.406770\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 10.4978i | − 0.0912852i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 47.9259i | − 0.409623i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −27.1078 | −0.224032 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 96.7385 | 0.786492 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 45.6484i | 0.365187i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −235.761 | −1.85639 | −0.928193 | − | 0.372098i | \(-0.878639\pi\) | ||||
−0.928193 | + | 0.372098i | \(0.878639\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − 105.098i | − 0.814717i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 226.529i | 1.72923i | 0.502433 | + | 0.864616i | \(0.332439\pi\) | ||||
−0.502433 | + | 0.864616i | \(0.667561\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −4.82724 | −0.0357573 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −253.743 | −1.85214 | −0.926070 | − | 0.377353i | \(-0.876834\pi\) | ||||
−0.926070 | + | 0.377353i | \(0.876834\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 148.040i | − 1.06503i | −0.846419 | − | 0.532517i | \(-0.821246\pi\) | ||||
0.846419 | − | 0.532517i | \(-0.178754\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −63.3700 | −0.449432 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 154.797i | 1.08250i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 43.0266i | 0.296735i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −245.465 | −1.64742 | −0.823708 | − | 0.567014i | \(-0.808098\pi\) | ||||
−0.823708 | + | 0.567014i | \(0.808098\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 176.254 | 1.16725 | 0.583623 | − | 0.812025i | \(-0.301635\pi\) | ||||
0.583623 | + | 0.812025i | \(0.301635\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 31.6672i | − 0.206975i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.448754 | 0.00289519 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 207.656i | − 1.32265i | −0.750099 | − | 0.661326i | \(-0.769994\pi\) | ||||
0.750099 | − | 0.661326i | \(-0.230006\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 49.4032i | 0.310712i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 95.0241 | 0.582970 | 0.291485 | − | 0.956575i | \(-0.405851\pi\) | ||||
0.291485 | + | 0.956575i | \(0.405851\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 15.5917 | 0.0944949 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 158.478i | − 0.948972i | −0.880263 | − | 0.474486i | \(-0.842634\pi\) | ||||
0.880263 | − | 0.474486i | \(-0.157366\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −86.2098 | −0.510117 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 21.6615i | 0.126675i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 215.991i | 1.24850i | 0.781224 | + | 0.624251i | \(0.214596\pi\) | ||||
−0.781224 | + | 0.624251i | \(0.785404\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 162.937 | 0.920546 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −262.059 | −1.46402 | −0.732008 | − | 0.681296i | \(-0.761416\pi\) | ||||
−0.732008 | + | 0.681296i | \(0.761416\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 83.8554i | − 0.463290i | −0.972800 | − | 0.231645i | \(-0.925589\pi\) | ||||
0.972800 | − | 0.231645i | \(-0.0744107\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −190.860 | −1.04295 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.30514i | 0.0124602i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 102.283i | 0.546968i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 233.692 | 1.22352 | 0.611760 | − | 0.791043i | \(-0.290462\pi\) | ||||
0.611760 | + | 0.791043i | \(0.290462\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −223.639 | −1.15875 | −0.579375 | − | 0.815061i | \(-0.696703\pi\) | ||||
−0.579375 | + | 0.815061i | \(0.696703\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 25.7055i | 0.131823i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −133.006 | −0.675158 | −0.337579 | − | 0.941297i | \(-0.609608\pi\) | ||||
−0.337579 | + | 0.941297i | \(0.609608\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 60.6538i | − 0.304793i | −0.988319 | − | 0.152397i | \(-0.951301\pi\) | ||||
0.988319 | − | 0.152397i | \(-0.0486991\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − 142.082i | − 0.706874i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −51.8867 | −0.253106 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 33.9002 | 0.163769 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 69.9651i | − 0.334761i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −169.145 | −0.801637 | −0.400819 | − | 0.916157i | \(-0.631274\pi\) | ||||
−0.400819 | + | 0.916157i | \(0.631274\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 220.576i | − 1.03557i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 56.3706i | 0.262189i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −80.1153 | −0.365823 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −168.631 | −0.763036 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 162.093i | − 0.726874i | −0.931619 | − | 0.363437i | \(-0.881603\pi\) | ||||
0.931619 | − | 0.363437i | \(-0.118397\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −72.4109 | −0.321826 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 354.210i | 1.56040i | 0.625533 | + | 0.780198i | \(0.284882\pi\) | ||||
−0.625533 | + | 0.780198i | \(0.715118\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 131.456i | − 0.574043i | −0.957924 | − | 0.287021i | \(-0.907335\pi\) | ||||
0.957924 | − | 0.287021i | \(-0.0926651\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −142.949 | −0.613514 | −0.306757 | − | 0.951788i | \(-0.599244\pi\) | ||||
−0.306757 | + | 0.951788i | \(0.599244\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 33.9891 | 0.144635 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 32.3899i | − 0.136666i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 47.5259 | 0.198853 | 0.0994266 | − | 0.995045i | \(-0.468299\pi\) | ||||
0.0994266 | + | 0.995045i | \(0.468299\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − 237.152i | − 0.984033i | −0.870586 | − | 0.492017i | \(-0.836260\pi\) | ||||
0.870586 | − | 0.492017i | \(-0.163740\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 15.5885i | − 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 115.349 | 0.467002 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −103.292 | −0.414827 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 309.248i | − 1.23206i | −0.787722 | − | 0.616031i | \(-0.788739\pi\) | ||||
0.787722 | − | 0.616031i | \(-0.211261\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −109.495 | −0.432788 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 16.9850i | 0.0666080i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 179.345i | 0.697840i | 0.937153 | + | 0.348920i | \(0.113451\pi\) | ||||
−0.937153 | + | 0.348920i | \(0.886549\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −138.945 | −0.532355 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 74.7695 | 0.284295 | 0.142147 | − | 0.989846i | \(-0.454599\pi\) | ||||
0.142147 | + | 0.989846i | \(0.454599\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − 26.4979i | − 0.0999921i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 123.198 | 0.461414 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 56.8302i | − 0.211265i | −0.994405 | − | 0.105632i | \(-0.966313\pi\) | ||||
0.994405 | − | 0.105632i | \(-0.0336867\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.5044i | 0.0498316i | 0.999690 | + | 0.0249158i | \(0.00793176\pi\) | ||||
−0.999690 | + | 0.0249158i | \(0.992068\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 233.882 | 0.850481 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −249.452 | −0.900548 | −0.450274 | − | 0.892890i | \(-0.648674\pi\) | ||||
−0.450274 | + | 0.892890i | \(0.648674\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.44915i | 0.00519408i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 200.268 | 0.712696 | 0.356348 | − | 0.934353i | \(-0.384022\pi\) | ||||
0.356348 | + | 0.934353i | \(0.384022\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 68.7680i | 0.242997i | 0.992592 | + | 0.121498i | \(0.0387699\pi\) | ||||
−0.992592 | + | 0.121498i | \(0.961230\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 11.6183i | − 0.0407661i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 177.576 | 0.614451 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 177.084 | 0.608536 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 253.164i | 0.864040i | 0.901864 | + | 0.432020i | \(0.142199\pi\) | ||||
−0.901864 | + | 0.432020i | \(0.857801\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −87.3927 | −0.296247 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 50.3497i | 0.169527i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 180.522i | − 0.603752i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 188.671 | 0.622678 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 102.370 | 0.335639 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 529.913i | 1.72610i | 0.505116 | + | 0.863051i | \(0.331450\pi\) | ||||
−0.505116 | + | 0.863051i | \(0.668550\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.29417 | 0.00418824 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 30.5056i | 0.0980887i | 0.998797 | + | 0.0490444i | \(0.0156176\pi\) | ||||
−0.998797 | + | 0.0490444i | \(0.984382\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.60202i | 0.0274825i | 0.999906 | + | 0.0137412i | \(0.00437411\pi\) | ||||
−0.999906 | + | 0.0137412i | \(0.995626\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −480.152 | −1.51467 | −0.757337 | − | 0.653024i | \(-0.773500\pi\) | ||||
−0.757337 | + | 0.653024i | \(0.773500\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 448.781 | 1.40684 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − 26.4876i | − 0.0825158i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 76.2176 | 0.235968 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 385.595i | 1.18645i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 93.9174i | 0.287209i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −89.0195 | −0.268941 | −0.134471 | − | 0.990918i | \(-0.542933\pi\) | ||||
−0.134471 | + | 0.990918i | \(0.542933\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −7.44392 | −0.0223541 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 76.2070i | 0.227484i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 495.701 | 1.47092 | 0.735461 | − | 0.677567i | \(-0.236966\pi\) | ||||
0.735461 | + | 0.677567i | \(0.236966\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 113.018i | − 0.333387i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 4.68065i | − 0.0137262i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −18.1827 | −0.0527035 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −60.3534 | −0.173929 | −0.0869645 | − | 0.996211i | \(-0.527717\pi\) | ||||
−0.0869645 | + | 0.996211i | \(0.527717\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 72.2171i | − 0.206926i | −0.994633 | − | 0.103463i | \(-0.967008\pi\) | ||||
0.994633 | − | 0.103463i | \(-0.0329923\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −83.0100 | −0.236496 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 383.361i | − 1.08601i | −0.839730 | − | 0.543004i | \(-0.817287\pi\) | ||||
0.839730 | − | 0.543004i | \(-0.182713\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 118.308i | 0.333262i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −80.0448 | −0.222966 | −0.111483 | − | 0.993766i | \(-0.535560\pi\) | ||||
−0.111483 | + | 0.993766i | \(0.535560\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 308.865 | 0.855580 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 46.9521i | 0.129345i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 42.9707 | 0.117728 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 81.4316i | 0.221884i | 0.993827 | + | 0.110942i | \(0.0353868\pi\) | ||||
−0.993827 | + | 0.110942i | \(0.964613\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − 167.556i | − 0.454081i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −532.252 | −1.42695 | −0.713475 | − | 0.700681i | \(-0.752880\pi\) | ||||
−0.713475 | + | 0.700681i | \(0.752880\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 79.0653 | 0.210841 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 739.893i | 1.96258i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 440.518 | 1.16232 | 0.581159 | − | 0.813790i | \(-0.302600\pi\) | ||||
0.581159 | + | 0.813790i | \(0.302600\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 408.350i | 1.07179i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 699.290i | − 1.82582i | −0.408159 | − | 0.912911i | \(-0.633829\pi\) | ||||
0.408159 | − | 0.912911i | \(-0.366171\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −182.036 | −0.470377 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 624.462 | 1.60530 | 0.802650 | − | 0.596450i | \(-0.203423\pi\) | ||||
0.802650 | + | 0.596450i | \(0.203423\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 119.281i | − 0.305065i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 392.361 | 0.998373 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 17.3726i | 0.0439814i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 632.547i | − 1.59332i | −0.604430 | − | 0.796658i | \(-0.706599\pi\) | ||||
0.604430 | − | 0.796658i | \(-0.293401\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 467.343 | 1.16544 | 0.582721 | − | 0.812672i | \(-0.301988\pi\) | ||||
0.582721 | + | 0.812672i | \(0.301988\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.71685 | 0.0191485 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 8.36103i | 0.0206445i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 24.0434 | 0.0590746 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − 324.296i | − 0.792900i | −0.918056 | − | 0.396450i | \(-0.870242\pi\) | ||||
0.918056 | − | 0.396450i | \(-0.129758\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 439.496i | 1.06933i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 55.4017 | 0.133498 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −256.413 | −0.614898 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 28.8211i | − 0.0687854i | −0.999408 | − | 0.0343927i | \(-0.989050\pi\) | ||||
0.999408 | − | 0.0343927i | \(-0.0109497\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.326830 | −0.000776319 0 | −0.000388160 | − | 1.00000i | \(-0.500124\pi\) | ||||
−0.000388160 | 1.00000i | \(0.500124\pi\) | ||||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 109.760i | 0.259480i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 254.784i | 0.599491i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 268.117 | 0.624981 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 391.337 | 0.907975 | 0.453988 | − | 0.891008i | \(-0.350001\pi\) | ||||
0.453988 | + | 0.891008i | \(0.350001\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 470.579i | 1.08679i | 0.839478 | + | 0.543394i | \(0.182861\pi\) | ||||
−0.839478 | + | 0.543394i | \(0.817139\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 74.5243 | 0.171320 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 81.5920i | 0.186709i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 134.401i | 0.306153i | 0.988214 | + | 0.153077i | \(0.0489181\pi\) | ||||
−0.988214 | + | 0.153077i | \(0.951082\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 329.056 | 0.742790 | 0.371395 | − | 0.928475i | \(-0.378880\pi\) | ||||
0.371395 | + | 0.928475i | \(0.378880\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −66.0782 | −0.148490 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 425.158i | 0.951136i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 130.592 | 0.290851 | 0.145426 | − | 0.989369i | \(-0.453545\pi\) | ||||
0.145426 | + | 0.989369i | \(0.453545\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 541.194i | 1.19999i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 305.281i | − 0.673909i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 316.282 | 0.692082 | 0.346041 | − | 0.938219i | \(-0.387526\pi\) | ||||
0.346041 | + | 0.938219i | \(0.387526\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −54.8493 | −0.119497 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 31.4853i | − 0.0682979i | −0.999417 | − | 0.0341490i | \(-0.989128\pi\) | ||||
0.999417 | − | 0.0341490i | \(-0.0108721\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 667.424 | 1.44152 | 0.720761 | − | 0.693184i | \(-0.243793\pi\) | ||||
0.720761 | + | 0.693184i | \(0.243793\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − 0.777265i | − 0.00167154i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 864.295i | − 1.85074i | −0.379065 | − | 0.925370i | \(-0.623754\pi\) | ||||
0.379065 | − | 0.925370i | \(-0.376246\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −359.671 | −0.763633 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 587.964 | 1.24305 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 174.281i | − 0.366907i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 85.5688 | 0.179390 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 626.397i | − 1.30772i | −0.756616 | − | 0.653859i | \(-0.773149\pi\) | ||||
0.756616 | − | 0.653859i | \(-0.226851\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 39.6396i | 0.0824108i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −94.9808 | −0.195837 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −485.848 | −0.997634 | −0.498817 | − | 0.866707i | \(-0.666232\pi\) | ||||
−0.498817 | + | 0.866707i | \(0.666232\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − 164.587i | − 0.336578i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.00051 | −0.0122210 | −0.00611049 | − | 0.999981i | \(-0.501945\pi\) | ||||
−0.00611049 | + | 0.999981i | \(0.501945\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 488.888i | 0.991658i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − 27.0056i | − 0.0545567i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −687.551 | −1.37786 | −0.688929 | − | 0.724829i | \(-0.741919\pi\) | ||||
−0.688929 | + | 0.724829i | \(0.741919\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −274.492 | −0.547889 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 435.270i | − 0.865348i | −0.901550 | − | 0.432674i | \(-0.857570\pi\) | ||||
0.901550 | − | 0.432674i | \(-0.142430\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −101.196 | −0.200388 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 149.320i | 0.294516i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 483.105i | − 0.949126i | −0.880222 | − | 0.474563i | \(-0.842606\pi\) | ||||
0.880222 | − | 0.474563i | \(-0.157394\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 37.5188 | 0.0731360 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.694139 | −0.00134784 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 354.517i | − 0.685720i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 374.107 | 0.720823 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 314.569i | − 0.603779i | −0.953343 | − | 0.301890i | \(-0.902383\pi\) | ||||
0.953343 | − | 0.301890i | \(-0.0976174\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 156.567i | 0.299363i | 0.988734 | + | 0.149682i | \(0.0478249\pi\) | ||||
−0.988734 | + | 0.149682i | \(0.952175\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.09894 | 0.00967541 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −401.309 | −0.758617 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 282.215i | − 0.531478i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −892.251 | −1.67402 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 14.2069i | 0.0265549i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 453.899i | 0.845250i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 772.066 | 1.42711 | 0.713554 | − | 0.700600i | \(-0.247084\pi\) | ||||
0.713554 | + | 0.700600i | \(0.247084\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −145.242 | −0.267480 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 50.3736i | − 0.0924285i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 48.0113 | 0.0877721 | 0.0438860 | − | 0.999037i | \(-0.486026\pi\) | ||||
0.0438860 | + | 0.999037i | \(0.486026\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 330.580i | 0.602149i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 334.416i | − 0.606925i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.99262 | 0.00719391 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 151.405 | 0.271823 | 0.135911 | − | 0.990721i | \(-0.456604\pi\) | ||||
0.135911 | + | 0.990721i | \(0.456604\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 969.359i | 1.73409i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 177.159 | 0.315792 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 846.301i | − 1.50320i | −0.659620 | − | 0.751599i | \(-0.729283\pi\) | ||||
0.659620 | − | 0.751599i | \(-0.270717\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 60.6185i | 0.107289i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −21.5774 | −0.0379215 | −0.0189608 | − | 0.999820i | \(-0.506036\pi\) | ||||
−0.0189608 | + | 0.999820i | \(0.506036\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 283.245 | 0.496051 | 0.248026 | − | 0.968753i | \(-0.420218\pi\) | ||||
0.248026 | + | 0.968753i | \(0.420218\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 404.767i | − 0.706400i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −272.749 | −0.474346 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 469.306i | 0.813355i | 0.913572 | + | 0.406678i | \(0.133313\pi\) | ||||
−0.913572 | + | 0.406678i | \(0.866687\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 387.354i | 0.669004i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −276.381 | −0.474068 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 44.5233 | 0.0761082 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 554.500i | 0.944634i | 0.881429 | + | 0.472317i | \(0.156582\pi\) | ||||
−0.881429 | + | 0.472317i | \(0.843418\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.48785 | −0.00592165 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 230.373i | 0.389803i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 816.481i | 1.37687i | 0.725300 | + | 0.688433i | \(0.241701\pi\) | ||||
−0.725300 | + | 0.688433i | \(0.758299\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −105.055 | −0.175972 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −868.683 | −1.45022 | −0.725111 | − | 0.688632i | \(-0.758211\pi\) | ||||
−0.725111 | + | 0.688632i | \(0.758211\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − 705.861i | − 1.17448i | −0.809413 | − | 0.587239i | \(-0.800215\pi\) | ||||
0.809413 | − | 0.587239i | \(-0.199785\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −246.093 | −0.408114 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 25.1833i | − 0.0416252i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 535.811i | 0.882720i | 0.897330 | + | 0.441360i | \(0.145504\pi\) | ||||
−0.897330 | + | 0.441360i | \(0.854496\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 584.483 | 0.956600 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −284.494 | −0.464101 | −0.232050 | − | 0.972704i | \(-0.574543\pi\) | ||||
−0.232050 | + | 0.972704i | \(0.574543\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 89.8703i | 0.146131i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −766.565 | −1.24241 | −0.621203 | − | 0.783650i | \(-0.713356\pi\) | ||||
−0.621203 | + | 0.783650i | \(0.713356\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 543.006i | − 0.877232i | −0.898675 | − | 0.438616i | \(-0.855469\pi\) | ||||
0.898675 | − | 0.438616i | \(-0.144531\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 58.7169i | − 0.0945521i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 561.016 | 0.897626 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −121.183 | −0.193274 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 26.1920i | 0.0416408i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −967.080 | −1.53261 | −0.766307 | − | 0.642474i | \(-0.777908\pi\) | ||||
−0.766307 | + | 0.642474i | \(0.777908\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 292.969i | 0.462825i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 219.023i | − 0.344918i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −382.048 | −0.597884 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 979.024 | 1.52734 | 0.763669 | − | 0.645608i | \(-0.223396\pi\) | ||||
0.763669 | + | 0.645608i | \(0.223396\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 991.244i | − 1.54159i | −0.637081 | − | 0.770797i | \(-0.719858\pi\) | ||||
0.637081 | − | 0.770797i | \(-0.280142\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 97.6368 | 0.151375 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 1232.42i | − 1.90482i | −0.304822 | − | 0.952409i | \(-0.598597\pi\) | ||||
0.304822 | − | 0.952409i | \(-0.401403\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 911.534i | 1.40452i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −781.069 | −1.19612 | −0.598062 | − | 0.801450i | \(-0.704062\pi\) | ||||
−0.598062 | + | 0.801450i | \(0.704062\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −210.447 | −0.321293 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 138.764i | 0.211208i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −549.328 | −0.833578 | −0.416789 | − | 0.909003i | \(-0.636845\pi\) | ||||
−0.416789 | + | 0.909003i | \(0.636845\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 413.630i | 0.625764i | 0.949792 | + | 0.312882i | \(0.101294\pi\) | ||||
−0.949792 | + | 0.312882i | \(0.898706\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 292.078i | 0.440539i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −523.361 | −0.784649 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −280.753 | −0.419661 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 1067.75i | − 1.59128i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 553.924 | 0.823067 | 0.411533 | − | 0.911395i | \(-0.364993\pi\) | ||||
0.411533 | + | 0.911395i | \(0.364993\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 125.419i | 0.185806i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 110.386i | − 0.163052i | −0.996671 | − | 0.0815259i | \(-0.974021\pi\) | ||||
0.996671 | − | 0.0815259i | \(-0.0259793\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 613.509 | 0.900895 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −195.631 | −0.286429 | −0.143215 | − | 0.989692i | \(-0.545744\pi\) | ||||
−0.143215 | + | 0.989692i | \(0.545744\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 235.728i | − 0.344129i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −227.688 | −0.331424 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 455.662i | − 0.661338i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 662.950i | 0.959407i | 0.877431 | + | 0.479703i | \(0.159256\pi\) | ||||
−0.877431 | + | 0.479703i | \(0.840744\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 137.529 | 0.197884 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −589.559 | −0.845852 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 247.595i | 0.354213i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1236.29 | −1.76361 | −0.881807 | − | 0.471610i | \(-0.843673\pi\) | ||||
−0.881807 | + | 0.471610i | \(0.843673\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 17.9162i | − 0.0254854i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − 58.8709i | − 0.0835048i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −900.501 | −1.27010 | −0.635050 | − | 0.772471i | \(-0.719020\pi\) | ||||
−0.635050 | + | 0.772471i | \(0.719020\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −56.1009 | −0.0789043 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.45848i | 0.00765566i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −143.807 | −0.201129 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 82.3173i | − 0.114808i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 119.102i | 0.165649i | 0.996564 | + | 0.0828246i | \(0.0263941\pi\) | ||||
−0.996564 | + | 0.0828246i | \(0.973606\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −410.759 | −0.568132 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1117.90 | 1.54193 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 815.672i | 1.12197i | 0.827826 | + | 0.560985i | \(0.189577\pi\) | ||||
−0.827826 | + | 0.560985i | \(0.810423\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 640.508i | 0.876208i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 223.741i | 0.305241i | 0.988285 | + | 0.152620i | \(0.0487712\pi\) | ||||
−0.988285 | + | 0.152620i | \(0.951229\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 794.863 | 1.07851 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1273.79 | −1.72367 | −0.861836 | − | 0.507187i | \(-0.830685\pi\) | ||||
−0.861836 | + | 0.507187i | \(0.830685\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 199.791i | − 0.269624i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −204.339 | −0.275019 | −0.137510 | − | 0.990500i | \(-0.543910\pi\) | ||||
−0.137510 | + | 0.990500i | \(0.543910\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − 228.038i | − 0.306091i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 178.907i | 0.239501i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −386.559 | −0.514726 | −0.257363 | − | 0.966315i | \(-0.582854\pi\) | ||||
−0.257363 | + | 0.966315i | \(0.582854\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −535.633 | −0.711332 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 163.741i | 0.216875i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1254.03 | −1.65658 | −0.828290 | − | 0.560300i | \(-0.810686\pi\) | ||||
−0.828290 | + | 0.560300i | \(0.810686\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 189.651i | 0.249870i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 810.611i | 1.06519i | 0.846370 | + | 0.532596i | \(0.178783\pi\) | ||||
−0.846370 | + | 0.532596i | \(0.821217\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 29.4190 | 0.0384562 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1502.82 | −1.95935 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − 1338.07i | − 1.74002i | −0.493036 | − | 0.870009i | \(-0.664113\pi\) | ||||
0.493036 | − | 0.870009i | \(-0.335887\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 310.634 | 0.402898 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 516.124i | 0.667690i | 0.942628 | + | 0.333845i | \(0.108346\pi\) | ||||
−0.942628 | + | 0.333845i | \(0.891654\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 11.6593i | − 0.0150443i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 403.279 | 0.517688 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1233.99 | 1.58001 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 240.659i | 0.307355i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 192.913 | 0.245749 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 1504.21i | − 1.91133i | −0.294463 | − | 0.955663i | \(-0.595141\pi\) | ||||
0.294463 | − | 0.955663i | \(-0.404859\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 129.505i | − 0.164138i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1760.37 | 2.21988 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −45.8957 | −0.0577304 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 147.647i | − 0.185254i | −0.995701 | − | 0.0926268i | \(-0.970474\pi\) | ||||
0.995701 | − | 0.0926268i | \(-0.0295263\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 386.200 | 0.483354 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − 213.384i | − 0.266397i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 448.198i | − 0.558154i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −98.4328 | −0.121974 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 171.184 | 0.211600 | 0.105800 | − | 0.994387i | \(-0.466260\pi\) | ||||
0.105800 | + | 0.994387i | \(0.466260\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 668.261i | 0.823997i | 0.911185 | + | 0.411998i | \(0.135169\pi\) | ||||
−0.911185 | + | 0.411998i | \(0.864831\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 23.3902 | 0.0287703 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 88.2777i | 0.108316i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 438.130i | − 0.536266i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −16.6411 | −0.0202693 | −0.0101346 | − | 0.999949i | \(-0.503226\pi\) | ||||
−0.0101346 | + | 0.999949i | \(0.503226\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −310.695 | −0.377515 | −0.188758 | − | 0.982024i | \(-0.560446\pi\) | ||||
−0.188758 | + | 0.982024i | \(0.560446\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − 405.096i | − 0.491025i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 139.891 | 0.169155 | 0.0845777 | − | 0.996417i | \(-0.473046\pi\) | ||||
0.0845777 | + | 0.996417i | \(0.473046\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1442.37i | 1.73989i | 0.493150 | + | 0.869944i | \(0.335845\pi\) | ||||
−0.493150 | + | 0.869944i | \(0.664155\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 432.063i | 0.519932i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 147.227 | 0.176320 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.51000 | 0.00299880 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 657.634i | − 0.783831i | −0.920001 | − | 0.391915i | \(-0.871813\pi\) | ||||
0.920001 | − | 0.391915i | \(-0.128187\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1304.06 | 1.55061 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 346.874i | − 0.411475i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 80.0892i | − 0.0947801i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 119.110 | 0.140294 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −28.0389 | −0.0329482 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 121.230i | − 0.142122i | −0.997472 | − | 0.0710609i | \(-0.977362\pi\) | ||||
0.997472 | − | 0.0710609i | \(-0.0226385\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −20.1236 | −0.0235363 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 1245.58i | − 1.45342i | −0.686945 | − | 0.726710i | \(-0.741049\pi\) | ||||
0.686945 | − | 0.726710i | \(-0.258951\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 779.573i | − 0.907536i | −0.891120 | − | 0.453768i | \(-0.850080\pi\) | ||||
0.891120 | − | 0.453768i | \(-0.149920\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −840.750 | −0.974218 | −0.487109 | − | 0.873341i | \(-0.661949\pi\) | ||||
−0.487109 | + | 0.873341i | \(0.661949\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −200.656 | −0.231972 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 307.571i | − 0.354753i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 181.202 | 0.208518 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1310.47i | 1.50456i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 306.718i | − 0.351338i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1474.24 | −1.68101 | −0.840504 | − | 0.541806i | \(-0.817741\pi\) | ||||
−0.840504 | + | 0.541806i | \(0.817741\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 438.493 | 0.498854 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 583.982i | − 0.662863i | −0.943479 | − | 0.331431i | \(-0.892468\pi\) | ||||
0.943479 | − | 0.331431i | \(-0.107532\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1226.32 | −1.38882 | −0.694408 | − | 0.719581i | \(-0.744334\pi\) | ||||
−0.694408 | + | 0.719581i | \(0.744334\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 151.369i | 0.171038i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 498.376i | − 0.561867i | −0.959727 | − | 0.280934i | \(-0.909356\pi\) | ||||
0.959727 | − | 0.280934i | \(-0.0906441\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 87.2082 | 0.0978767 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −264.174 | −0.295827 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 243.453i | − 0.272015i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −312.673 | −0.348576 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 22.3723i | − 0.0248858i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 301.081i | − 0.334163i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 77.9020 | 0.0860795 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 73.8246 | 0.0813942 | 0.0406971 | − | 0.999172i | \(-0.487042\pi\) | ||||
0.0406971 | + | 0.999172i | \(0.487042\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 326.788i | − 0.359503i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1102.46 | 1.21017 | 0.605084 | − | 0.796162i | \(-0.293140\pi\) | ||||
0.605084 | + | 0.796162i | \(0.293140\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 577.857i | − 0.632922i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 177.310i | − 0.193781i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 982.172 | 1.06874 | 0.534370 | − | 0.845251i | \(-0.320549\pi\) | ||||
0.534370 | + | 0.845251i | \(0.320549\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 917.837 | 0.996566 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2034.44i | 2.20416i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 59.8912 | 0.0647472 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 2.24156i | − 0.00241808i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 648.814i | 0.698400i | 0.937048 | + | 0.349200i | \(0.113547\pi\) | ||||
−0.937048 | + | 0.349200i | \(0.886453\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 52.8372 | 0.0566316 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −95.0212 | −0.101627 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1348.17i | 1.43881i | 0.694590 | + | 0.719406i | \(0.255586\pi\) | ||||
−0.694590 | + | 0.719406i | \(0.744414\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 14.8991 | 0.0158670 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1187.26i | 1.26170i | 0.775904 | + | 0.630851i | \(0.217294\pi\) | ||||
−0.775904 | + | 0.630851i | \(0.782706\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 631.131i | − 0.669280i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −132.564 | −0.139983 | −0.0699915 | − | 0.997548i | \(-0.522297\pi\) | ||||
−0.0699915 | + | 0.997548i | \(0.522297\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 738.930 | 0.778641 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 831.648i | 0.874498i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1521.99 | 1.59705 | 0.798524 | − | 0.601963i | \(-0.205615\pi\) | ||||
0.798524 | + | 0.601963i | \(0.205615\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 217.101i | 0.227331i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 777.312i | − 0.812238i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 960.767 | 0.999757 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −45.8778 | −0.0476405 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 207.761i | − 0.215296i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 645.014 | 0.667026 | 0.333513 | − | 0.942746i | \(-0.391766\pi\) | ||||
0.333513 | + | 0.942746i | \(0.391766\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − 132.013i | − 0.136236i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 1609.85i | − 1.65793i | −0.559301 | − | 0.828964i | \(-0.688931\pi\) | ||||
0.559301 | − | 0.828964i | \(-0.311069\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 667.870 | 0.684995 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −255.143 | −0.261150 | −0.130575 | − | 0.991438i | \(-0.541682\pi\) | ||||
−0.130575 | + | 0.991438i | \(0.541682\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 689.217i | 0.704001i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 162.670 | 0.165820 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 481.938i | 0.490272i | 0.969489 | + | 0.245136i | \(0.0788327\pi\) | ||||
−0.969489 | + | 0.245136i | \(0.921167\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − 123.563i | − 0.125445i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −685.673 | −0.693299 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1126.22 | 1.13644 | 0.568222 | − | 0.822875i | \(-0.307632\pi\) | ||||
0.568222 | + | 0.822875i | \(0.307632\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 154.186i | 0.155273i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 56.3476 | 0.0566307 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 1060.71i | − 1.06391i | −0.846774 | − | 0.531953i | \(-0.821458\pi\) | ||||
0.846774 | − | 0.531953i | \(-0.178542\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 12.8932i | 0.0129062i |
(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 | 588.3.d.c.97.3 | ✓ | 8 | |
3.2 | odd | 2 | 1764.3.d.h.685.3 | 8 | |||
4.3 | odd | 2 | 2352.3.f.j.97.7 | 8 | |||
7.2 | even | 3 | 588.3.m.f.325.3 | 8 | |||
7.3 | odd | 6 | 588.3.m.f.313.3 | 8 | |||
7.4 | even | 3 | 588.3.m.e.313.2 | 8 | |||
7.5 | odd | 6 | 588.3.m.e.325.2 | 8 | |||
7.6 | odd | 2 | inner | 588.3.d.c.97.6 | yes | 8 | |
21.2 | odd | 6 | 1764.3.z.l.325.2 | 8 | |||
21.5 | even | 6 | 1764.3.z.m.325.3 | 8 | |||
21.11 | odd | 6 | 1764.3.z.m.901.3 | 8 | |||
21.17 | even | 6 | 1764.3.z.l.901.2 | 8 | |||
21.20 | even | 2 | 1764.3.d.h.685.6 | 8 | |||
28.27 | even | 2 | 2352.3.f.j.97.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
588.3.d.c.97.3 | ✓ | 8 | 1.1 | even | 1 | trivial | |
588.3.d.c.97.6 | yes | 8 | 7.6 | odd | 2 | inner | |
588.3.m.e.313.2 | 8 | 7.4 | even | 3 | |||
588.3.m.e.325.2 | 8 | 7.5 | odd | 6 | |||
588.3.m.f.313.3 | 8 | 7.3 | odd | 6 | |||
588.3.m.f.325.3 | 8 | 7.2 | even | 3 | |||
1764.3.d.h.685.3 | 8 | 3.2 | odd | 2 | |||
1764.3.d.h.685.6 | 8 | 21.20 | even | 2 | |||
1764.3.z.l.325.2 | 8 | 21.2 | odd | 6 | |||
1764.3.z.l.901.2 | 8 | 21.17 | even | 6 | |||
1764.3.z.m.325.3 | 8 | 21.5 | even | 6 | |||
1764.3.z.m.901.3 | 8 | 21.11 | odd | 6 | |||
2352.3.f.j.97.2 | 8 | 28.27 | even | 2 | |||
2352.3.f.j.97.7 | 8 | 4.3 | odd | 2 |