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 | 97.8 | ||
Root | \(-0.662827 + 0.382683i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 588.97 |
Dual form | 588.3.d.c.97.1 |
$q$-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 | ||||||||
\(5\) | 5.82798i | 1.16560i | 0.812617 | + | 0.582798i | \(0.198042\pi\) | ||||
−0.812617 | + | 0.582798i | \(0.801958\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −6.86137 | −0.623761 | −0.311880 | − | 0.950121i | \(-0.600959\pi\) | ||||
−0.311880 | + | 0.950121i | \(0.600959\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 3.62063i | − 0.278510i | −0.990257 | − | 0.139255i | \(-0.955529\pi\) | ||||
0.990257 | − | 0.139255i | \(-0.0444708\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −10.0944 | −0.672957 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 9.71521i | 0.571483i | 0.958307 | + | 0.285742i | \(0.0922399\pi\) | ||||
−0.958307 | + | 0.285742i | \(0.907760\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 30.2903i | 1.59423i | 0.603831 | + | 0.797113i | \(0.293640\pi\) | ||||
−0.603831 | + | 0.797113i | \(0.706360\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −18.1558 | −0.789382 | −0.394691 | − | 0.918814i | \(-0.629148\pi\) | ||||
−0.394691 | + | 0.918814i | \(0.629148\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −8.96538 | −0.358615 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 5.19615i | − 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −40.4570 | −1.39507 | −0.697534 | − | 0.716552i | \(-0.745719\pi\) | ||||
−0.697534 | + | 0.716552i | \(0.745719\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 55.2124i | − 1.78104i | −0.454940 | − | 0.890522i | \(-0.650339\pi\) | ||||
0.454940 | − | 0.890522i | \(-0.349661\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 11.8842i | − 0.360129i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 54.9745 | 1.48580 | 0.742899 | − | 0.669403i | \(-0.233450\pi\) | ||||
0.742899 | + | 0.669403i | \(0.233450\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.27112 | 0.160798 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 56.3322i | − 1.37396i | −0.726678 | − | 0.686978i | \(-0.758937\pi\) | ||||
0.726678 | − | 0.686978i | \(-0.241063\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −66.0512 | −1.53608 | −0.768038 | − | 0.640405i | \(-0.778767\pi\) | ||||
−0.768038 | + | 0.640405i | \(0.778767\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 17.4839i | − 0.388532i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 49.4215i | 1.05152i | 0.850632 | + | 0.525761i | \(0.176219\pi\) | ||||
−0.850632 | + | 0.525761i | \(0.823781\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −16.8272 | −0.329946 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −81.0162 | −1.52861 | −0.764303 | − | 0.644857i | \(-0.776917\pi\) | ||||
−0.764303 | + | 0.644857i | \(0.776917\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 39.9879i | − 0.727054i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −52.4643 | −0.920426 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 34.7914i | 0.589685i | 0.955546 | + | 0.294842i | \(0.0952671\pi\) | ||||
−0.955546 | + | 0.294842i | \(0.904733\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 0.0382805i | 0 0.000627550i | −1.00000 | 0.000313775i | \(-0.999900\pi\) | |||||
1.00000 | 0.000313775i | \(-9.98776e-5\pi\) | ||||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 21.1010 | 0.324630 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −64.0898 | −0.956565 | −0.478282 | − | 0.878206i | \(-0.658740\pi\) | ||||
−0.478282 | + | 0.878206i | \(0.658740\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 31.4467i | − 0.455750i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 50.2730 | 0.708070 | 0.354035 | − | 0.935232i | \(-0.384809\pi\) | ||||
0.354035 | + | 0.935232i | \(0.384809\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 21.3464i | 0.292416i | 0.989254 | + | 0.146208i | \(0.0467069\pi\) | ||||
−0.989254 | + | 0.146208i | \(0.953293\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 15.5285i | − 0.207047i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −47.5044 | −0.601321 | −0.300660 | − | 0.953731i | \(-0.597207\pi\) | ||||
−0.300660 | + | 0.953731i | \(0.597207\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 33.6039i | − 0.404866i | −0.979296 | − | 0.202433i | \(-0.935115\pi\) | ||||
0.979296 | − | 0.202433i | \(-0.0648849\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −56.6201 | −0.666119 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 70.0735i | − 0.805443i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 156.092i | 1.75384i | 0.480636 | + | 0.876920i | \(0.340406\pi\) | ||||
−0.480636 | + | 0.876920i | \(0.659594\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 95.6306 | 1.02829 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −176.531 | −1.85822 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 43.7452i | − 0.450981i | −0.974245 | − | 0.225491i | \(-0.927601\pi\) | ||||
0.974245 | − | 0.225491i | \(-0.0723985\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 20.5841 | 0.207920 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 169.746i | 1.68066i | 0.542077 | + | 0.840329i | \(0.317638\pi\) | ||||
−0.542077 | + | 0.840329i | \(0.682362\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 59.7216i | − 0.579822i | −0.957054 | − | 0.289911i | \(-0.906374\pi\) | ||||
0.957054 | − | 0.289911i | \(-0.0936257\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −57.7678 | −0.539886 | −0.269943 | − | 0.962876i | \(-0.587005\pi\) | ||||
−0.269943 | + | 0.962876i | \(0.587005\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 179.846 | 1.64996 | 0.824980 | − | 0.565162i | \(-0.191186\pi\) | ||||
0.824980 | + | 0.565162i | \(0.191186\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 95.2187i | 0.857826i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 96.6900 | 0.855664 | 0.427832 | − | 0.903858i | \(-0.359278\pi\) | ||||
0.427832 | + | 0.903858i | \(0.359278\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 105.812i | − 0.920101i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 10.8619i | 0.0928367i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −73.9216 | −0.610922 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 97.5702 | 0.793254 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 93.4495i | 0.747596i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −136.454 | −1.07444 | −0.537221 | − | 0.843441i | \(-0.680526\pi\) | ||||
−0.537221 | + | 0.843441i | \(0.680526\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − 114.404i | − 0.886853i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 26.5364i | − 0.202568i | −0.994858 | − | 0.101284i | \(-0.967705\pi\) | ||||
0.994858 | − | 0.101284i | \(-0.0322950\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 30.2831 | 0.224319 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 210.866 | 1.53917 | 0.769583 | − | 0.638546i | \(-0.220464\pi\) | ||||
0.769583 | + | 0.638546i | \(0.220464\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 83.7490i | 0.602511i | 0.953543 | + | 0.301256i | \(0.0974057\pi\) | ||||
−0.953543 | + | 0.301256i | \(0.902594\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −85.6006 | −0.607096 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 24.8425i | 0.173724i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − 235.783i | − 1.62609i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.99481 | 0.0536564 | 0.0268282 | − | 0.999640i | \(-0.491459\pi\) | ||||
0.0268282 | + | 0.999640i | \(0.491459\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 60.8831 | 0.403199 | 0.201600 | − | 0.979468i | \(-0.435386\pi\) | ||||
0.201600 | + | 0.979468i | \(0.435386\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 29.1456i | − 0.190494i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 321.777 | 2.07598 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 29.1758i | 0.185833i | 0.995674 | + | 0.0929166i | \(0.0296190\pi\) | ||||
−0.995674 | + | 0.0929166i | \(0.970381\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − 140.324i | − 0.882542i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −62.4556 | −0.383163 | −0.191582 | − | 0.981477i | \(-0.561362\pi\) | ||||
−0.191582 | + | 0.981477i | \(0.561362\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 69.2612 | 0.419765 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 141.404i | 0.846730i | 0.905959 | + | 0.423365i | \(0.139151\pi\) | ||||
−0.905959 | + | 0.423365i | \(0.860849\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 155.891 | 0.922432 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 90.8708i | − 0.531408i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 243.848i | 1.40953i | 0.709443 | + | 0.704763i | \(0.248946\pi\) | ||||
−0.709443 | + | 0.704763i | \(0.751054\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −60.2605 | −0.340455 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −286.642 | −1.60135 | −0.800676 | − | 0.599098i | \(-0.795526\pi\) | ||||
−0.800676 | + | 0.599098i | \(0.795526\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 214.838i | 1.18695i | 0.804852 | + | 0.593475i | \(0.202245\pi\) | ||||
−0.804852 | + | 0.593475i | \(0.797755\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.0663038 | 0.000362316 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 320.391i | 1.73184i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 66.6597i | − 0.356469i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −45.3249 | −0.237303 | −0.118652 | − | 0.992936i | \(-0.537857\pi\) | ||||
−0.118652 | + | 0.992936i | \(0.537857\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 314.031 | 1.62710 | 0.813551 | − | 0.581494i | \(-0.197532\pi\) | ||||
0.813551 | + | 0.581494i | \(0.197532\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 36.5480i | 0.187425i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 259.231 | 1.31590 | 0.657948 | − | 0.753063i | \(-0.271425\pi\) | ||||
0.657948 | + | 0.753063i | \(0.271425\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 73.5255i | − 0.369475i | −0.982788 | − | 0.184737i | \(-0.940857\pi\) | ||||
0.982788 | − | 0.184737i | \(-0.0591435\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − 111.007i | − 0.552273i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 328.303 | 1.60148 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 54.4673 | 0.263127 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 207.833i | − 0.994415i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 263.537 | 1.24899 | 0.624496 | − | 0.781028i | \(-0.285304\pi\) | ||||
0.624496 | + | 0.781028i | \(0.285304\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 87.0754i | 0.408805i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 384.945i | − 1.79044i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −36.9730 | −0.168827 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 35.1752 | 0.159164 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 191.042i | 0.856689i | 0.903616 | + | 0.428344i | \(0.140903\pi\) | ||||
−0.903616 | + | 0.428344i | \(0.859097\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 26.8961 | 0.119538 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 431.405i | 1.90046i | 0.311547 | + | 0.950231i | \(0.399153\pi\) | ||||
−0.311547 | + | 0.950231i | \(0.600847\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 34.8689i | − 0.152266i | −0.997098 | − | 0.0761329i | \(-0.975743\pi\) | ||||
0.997098 | − | 0.0761329i | \(-0.0242573\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −350.771 | −1.50546 | −0.752728 | − | 0.658332i | \(-0.771262\pi\) | ||||
−0.752728 | + | 0.658332i | \(0.771262\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −288.028 | −1.22565 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 82.2800i | − 0.347173i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 167.400 | 0.700419 | 0.350209 | − | 0.936671i | \(-0.386110\pi\) | ||||
0.350209 | + | 0.936671i | \(0.386110\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − 82.0658i | − 0.340522i | −0.985399 | − | 0.170261i | \(-0.945539\pi\) | ||||
0.985399 | − | 0.170261i | \(-0.0544611\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.5885i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 109.670 | 0.444008 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 58.2037 | 0.233750 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 232.918i | 0.927959i | 0.885846 | + | 0.463979i | \(0.153579\pi\) | ||||
−0.885846 | + | 0.463979i | \(0.846421\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 124.574 | 0.492385 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − 98.0689i | − 0.384584i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 37.3589i | 0.145365i | 0.997355 | + | 0.0726827i | \(0.0231560\pi\) | ||||
−0.997355 | + | 0.0726827i | \(0.976844\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 121.371 | 0.465023 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.37261 | 0.0128236 | 0.00641181 | − | 0.999979i | \(-0.497959\pi\) | ||||
0.00641181 | + | 0.999979i | \(0.497959\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − 472.161i | − 1.78174i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −270.359 | −1.01258 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 87.2686i | − 0.324419i | −0.986756 | − | 0.162209i | \(-0.948138\pi\) | ||||
0.986756 | − | 0.162209i | \(-0.0518620\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 92.0075i | 0.339511i | 0.985486 | + | 0.169756i | \(0.0542978\pi\) | ||||
−0.985486 | + | 0.169756i | \(0.945702\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 61.5148 | 0.223690 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 152.481 | 0.550474 | 0.275237 | − | 0.961376i | \(-0.411244\pi\) | ||||
0.275237 | + | 0.961376i | \(0.411244\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 165.637i | 0.593681i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −219.880 | −0.782491 | −0.391245 | − | 0.920286i | \(-0.627956\pi\) | ||||
−0.391245 | + | 0.920286i | \(0.627956\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 387.389i | − 1.36887i | −0.729076 | − | 0.684433i | \(-0.760050\pi\) | ||||
0.729076 | − | 0.684433i | \(-0.239950\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 305.761i | − 1.07285i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 194.615 | 0.673407 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 75.7689 | 0.260374 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.8794i | 0.0507828i | 0.999678 | + | 0.0253914i | \(0.00808320\pi\) | ||||
−0.999678 | + | 0.0253914i | \(0.991917\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −202.764 | −0.687335 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 35.6527i | 0.120043i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 65.7354i | 0.219851i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −294.009 | −0.970328 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.223098 | 0.000731470 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 453.211i | 1.47626i | 0.674660 | + | 0.738128i | \(0.264290\pi\) | ||||
−0.674660 | + | 0.738128i | \(0.735710\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 103.441 | 0.334760 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 435.246i | − 1.39950i | −0.714386 | − | 0.699752i | \(-0.753294\pi\) | ||||
0.714386 | − | 0.699752i | \(-0.246706\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 54.9405i | − 0.175529i | −0.996141 | − | 0.0877644i | \(-0.972028\pi\) | ||||
0.996141 | − | 0.0877644i | \(-0.0279723\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 433.691 | 1.36811 | 0.684055 | − | 0.729430i | \(-0.260215\pi\) | ||||
0.684055 | + | 0.729430i | \(0.260215\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 277.590 | 0.870189 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − 100.057i | − 0.311703i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −294.277 | −0.911073 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 32.4603i | 0.0998780i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 311.502i | 0.952605i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −576.548 | −1.74184 | −0.870919 | − | 0.491427i | \(-0.836475\pi\) | ||||
−0.870919 | + | 0.491427i | \(0.836475\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −164.924 | −0.495266 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 373.514i | − 1.11497i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −301.108 | −0.893495 | −0.446747 | − | 0.894660i | \(-0.647418\pi\) | ||||
−0.446747 | + | 0.894660i | \(0.647418\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 167.472i | 0.494018i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 378.832i | 1.11095i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 183.271 | 0.531220 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −252.112 | −0.726547 | −0.363273 | − | 0.931683i | \(-0.618341\pi\) | ||||
−0.363273 | + | 0.931683i | \(0.618341\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 406.452i | − 1.16462i | −0.812967 | − | 0.582309i | \(-0.802149\pi\) | ||||
0.812967 | − | 0.582309i | \(-0.197851\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −18.8134 | −0.0535993 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 134.429i | 0.380819i | 0.981705 | + | 0.190410i | \(0.0609816\pi\) | ||||
−0.981705 | + | 0.190410i | \(0.939018\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 292.990i | 0.825324i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −116.676 | −0.325003 | −0.162501 | − | 0.986708i | \(-0.551956\pi\) | ||||
−0.162501 | + | 0.986708i | \(0.551956\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −556.501 | −1.54155 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 128.036i | − 0.352716i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −124.406 | −0.340839 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 419.148i | 1.14209i | 0.820918 | + | 0.571046i | \(0.193462\pi\) | ||||
−0.820918 | + | 0.571046i | \(0.806538\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 168.997i | 0.457985i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −126.992 | −0.340462 | −0.170231 | − | 0.985404i | \(-0.554451\pi\) | ||||
−0.170231 | + | 0.985404i | \(0.554451\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −161.859 | −0.431625 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 146.480i | 0.388541i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −366.675 | −0.967479 | −0.483740 | − | 0.875212i | \(-0.660722\pi\) | ||||
−0.483740 | + | 0.875212i | \(0.660722\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 236.346i | − 0.620329i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 258.364i | 0.674579i | 0.941401 | + | 0.337290i | \(0.109510\pi\) | ||||
−0.941401 | + | 0.337290i | \(0.890490\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 198.154 | 0.512025 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 542.395 | 1.39433 | 0.697166 | − | 0.716910i | \(-0.254444\pi\) | ||||
0.697166 | + | 0.716910i | \(0.254444\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 176.387i | − 0.451118i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 45.9623 | 0.116953 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 276.855i | − 0.700898i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 404.764i | 1.01956i | 0.860306 | + | 0.509778i | \(0.170273\pi\) | ||||
−0.860306 | + | 0.509778i | \(0.829727\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −473.436 | −1.18064 | −0.590319 | − | 0.807170i | \(-0.700998\pi\) | ||||
−0.590319 | + | 0.807170i | \(0.700998\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −199.904 | −0.496039 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 52.4518i | 0.129511i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −377.201 | −0.926783 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 403.658i | 0.986938i | 0.869763 | + | 0.493469i | \(0.164271\pi\) | ||||
−0.869763 | + | 0.493469i | \(0.835729\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 365.230i | 0.888638i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 195.843 | 0.471911 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −145.058 | −0.347860 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 454.684i | − 1.08517i | −0.840003 | − | 0.542583i | \(-0.817447\pi\) | ||||
0.840003 | − | 0.542583i | \(-0.182553\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −180.928 | −0.429758 | −0.214879 | − | 0.976641i | \(-0.568936\pi\) | ||||
−0.214879 | + | 0.976641i | \(0.568936\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 148.265i | − 0.350507i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 87.1006i | − 0.204943i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −43.0285 | −0.100299 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −807.892 | −1.87446 | −0.937229 | − | 0.348714i | \(-0.886618\pi\) | ||||
−0.937229 | + | 0.348714i | \(0.886618\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 166.000i | − 0.383372i | −0.981456 | − | 0.191686i | \(-0.938604\pi\) | ||||
0.981456 | − | 0.191686i | \(-0.0613955\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 408.387 | 0.938822 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 549.944i | − 1.25845i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 29.2895i | 0.0667186i | 0.999443 | + | 0.0333593i | \(0.0106206\pi\) | ||||
−0.999443 | + | 0.0333593i | \(0.989379\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 822.751 | 1.85723 | 0.928613 | − | 0.371049i | \(-0.121002\pi\) | ||||
0.928613 | + | 0.371049i | \(0.121002\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −909.701 | −2.04427 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 13.8474i | 0.0309786i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −428.131 | −0.953522 | −0.476761 | − | 0.879033i | \(-0.658189\pi\) | ||||
−0.476761 | + | 0.879033i | \(0.658189\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 386.516i | 0.857020i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 105.453i | 0.232787i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −187.311 | −0.409871 | −0.204935 | − | 0.978775i | \(-0.565698\pi\) | ||||
−0.204935 | + | 0.978775i | \(0.565698\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 50.4817 | 0.109982 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 182.821i | 0.396576i | 0.980144 | + | 0.198288i | \(0.0635381\pi\) | ||||
−0.980144 | + | 0.198288i | \(0.936462\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 232.389 | 0.501920 | 0.250960 | − | 0.967997i | \(-0.419254\pi\) | ||||
0.250960 | + | 0.967997i | \(0.419254\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 557.333i | 1.19857i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 448.927i | − 0.961299i | −0.876913 | − | 0.480650i | \(-0.840401\pi\) | ||||
0.876913 | − | 0.480650i | \(-0.159599\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −50.5340 | −0.107291 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 453.202 | 0.958144 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 271.564i | − 0.571713i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 243.049 | 0.509536 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 631.644i | − 1.31867i | −0.751848 | − | 0.659336i | \(-0.770837\pi\) | ||||
0.751848 | − | 0.659336i | \(-0.229163\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − 199.043i | − 0.413810i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 254.946 | 0.525662 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 701.535 | 1.44052 | 0.720262 | − | 0.693702i | \(-0.244022\pi\) | ||||
0.720262 | + | 0.693702i | \(0.244022\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − 108.176i | − 0.221219i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −414.789 | −0.844785 | −0.422392 | − | 0.906413i | \(-0.638810\pi\) | ||||
−0.422392 | + | 0.906413i | \(0.638810\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 393.048i | − 0.797258i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 119.964i | 0.242351i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −612.340 | −1.22713 | −0.613567 | − | 0.789643i | \(-0.710266\pi\) | ||||
−0.613567 | + | 0.789643i | \(0.710266\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −244.919 | −0.488860 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 467.449i | − 0.929323i | −0.885488 | − | 0.464661i | \(-0.846176\pi\) | ||||
0.885488 | − | 0.464661i | \(-0.153824\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −989.279 | −1.95897 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 270.011i | 0.532566i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 62.5666i | 0.122921i | 0.998110 | + | 0.0614603i | \(0.0195758\pi\) | ||||
−0.998110 | + | 0.0614603i | \(0.980424\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 157.393 | 0.306809 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 348.057 | 0.675838 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 339.099i | − 0.655898i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −422.357 | −0.813790 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 712.575i | − 1.36771i | −0.729620 | − | 0.683853i | \(-0.760303\pi\) | ||||
0.729620 | − | 0.683853i | \(-0.239697\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 280.114i | − 0.535590i | −0.963476 | − | 0.267795i | \(-0.913705\pi\) | ||||
0.963476 | − | 0.267795i | \(-0.0862950\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 536.400 | 1.01784 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −199.368 | −0.376876 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 104.374i | − 0.196562i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −203.958 | −0.382660 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 336.670i | − 0.629289i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 496.478i | − 0.924541i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 633.002 | 1.17006 | 0.585030 | − | 0.811012i | \(-0.301083\pi\) | ||||
0.585030 | + | 0.811012i | \(0.301083\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −372.110 | −0.685286 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1048.14i | 1.92319i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1047.16 | 1.91438 | 0.957189 | − | 0.289465i | \(-0.0934773\pi\) | ||||
0.957189 | + | 0.289465i | \(0.0934773\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.114842i | 0 0.000209183i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 1225.45i | − 2.22405i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −554.933 | −0.999879 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 681.732 | 1.22393 | 0.611967 | − | 0.790883i | \(-0.290378\pi\) | ||||
0.611967 | + | 0.790883i | \(0.290378\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 239.147i | 0.427812i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 115.458 | 0.205807 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 201.588i | 0.358061i | 0.983844 | + | 0.179031i | \(0.0572961\pi\) | ||||
−0.983844 | + | 0.179031i | \(0.942704\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 563.508i | 0.997359i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −684.800 | −1.20352 | −0.601758 | − | 0.798679i | \(-0.705533\pi\) | ||||
−0.601758 | + | 0.798679i | \(0.705533\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −25.0602 | −0.0438884 | −0.0219442 | − | 0.999759i | \(-0.506986\pi\) | ||||
−0.0219442 | + | 0.999759i | \(0.506986\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 78.5050i | − 0.137007i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 162.773 | 0.283084 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1019.96i | 1.76770i | 0.467773 | + | 0.883849i | \(0.345056\pi\) | ||||
−0.467773 | + | 0.883849i | \(0.654944\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 543.917i | 0.939408i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 555.882 | 0.953485 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −63.3029 | −0.108210 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 581.810i | − 0.991158i | −0.868563 | − | 0.495579i | \(-0.834956\pi\) | ||||
0.868563 | − | 0.495579i | \(-0.165044\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1672.40 | 2.83939 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 449.002i | 0.759733i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 143.863i | − 0.242602i | −0.992616 | − | 0.121301i | \(-0.961293\pi\) | ||||
0.992616 | − | 0.121301i | \(-0.0387066\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 127.350 | 0.213316 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 710.736 | 1.18654 | 0.593269 | − | 0.805005i | \(-0.297837\pi\) | ||||
0.593269 | + | 0.805005i | \(0.297837\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 914.930i | 1.52235i | 0.648549 | + | 0.761173i | \(0.275376\pi\) | ||||
−0.648549 | + | 0.761173i | \(0.724624\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 192.269 | 0.318855 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 430.814i | − 0.712089i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 622.481i | 1.02550i | 0.858537 | + | 0.512752i | \(0.171374\pi\) | ||||
−0.858537 | + | 0.512752i | \(0.828626\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 178.937 | 0.292859 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −345.019 | −0.562837 | −0.281419 | − | 0.959585i | \(-0.590805\pi\) | ||||
−0.281419 | + | 0.959585i | \(0.590805\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 568.637i | 0.924614i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −854.311 | −1.38462 | −0.692310 | − | 0.721600i | \(-0.743407\pi\) | ||||
−0.692310 | + | 0.721600i | \(0.743407\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 49.2180i | 0.0795121i | 0.999209 | + | 0.0397561i | \(0.0126581\pi\) | ||||
−0.999209 | + | 0.0397561i | \(0.987342\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 94.3402i | 0.151917i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −768.756 | −1.23001 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 359.977 | 0.574126 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 534.089i | 0.849109i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 457.699 | 0.725355 | 0.362677 | − | 0.931915i | \(-0.381863\pi\) | ||||
0.362677 | + | 0.931915i | \(0.381863\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 456.460i | 0.721106i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 795.252i | − 1.25237i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −150.819 | −0.236023 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −323.931 | −0.505353 | −0.252677 | − | 0.967551i | \(-0.581311\pi\) | ||||
−0.252677 | + | 0.967551i | \(0.581311\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 117.018i | − 0.181987i | −0.995851 | − | 0.0909935i | \(-0.970996\pi\) | ||||
0.995851 | − | 0.0909935i | \(-0.0290043\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 666.745 | 1.03371 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 539.247i | 0.833458i | 0.909031 | + | 0.416729i | \(0.136824\pi\) | ||||
−0.909031 | + | 0.416729i | \(0.863176\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − 238.717i | − 0.367822i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −797.906 | −1.22191 | −0.610954 | − | 0.791666i | \(-0.709214\pi\) | ||||
−0.610954 | + | 0.791666i | \(0.709214\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 154.654 | 0.236112 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 64.0391i | − 0.0974720i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 295.186 | 0.447929 | 0.223965 | − | 0.974597i | \(-0.428100\pi\) | ||||
0.223965 | + | 0.974597i | \(0.428100\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 1032.24i | − 1.56163i | −0.624759 | − | 0.780817i | \(-0.714803\pi\) | ||||
0.624759 | − | 0.780817i | \(-0.285197\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 60.9252i | 0.0918933i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 734.528 | 1.10124 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −330.894 | −0.494609 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.262657i | 0 0.000391441i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 418.188 | 0.621379 | 0.310689 | − | 0.950512i | \(-0.399440\pi\) | ||||
0.310689 | + | 0.950512i | \(0.399440\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 46.5855i | 0.0690155i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 465.460i | 0.687534i | 0.939055 | + | 0.343767i | \(0.111703\pi\) | ||||
−0.939055 | + | 0.343767i | \(0.888297\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −747.215 | −1.09723 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1259.41 | 1.84394 | 0.921969 | − | 0.387263i | \(-0.126580\pi\) | ||||
0.921969 | + | 0.387263i | \(0.126580\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1228.92i | 1.79405i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 60.3947 | 0.0879107 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 293.330i | 0.425732i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 458.874i | 0.664073i | 0.943267 | + | 0.332036i | \(0.107736\pi\) | ||||
−0.943267 | + | 0.332036i | \(0.892264\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −488.088 | −0.702285 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 547.279 | 0.785192 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 607.553i | − 0.869175i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 822.907 | 1.17390 | 0.586952 | − | 0.809622i | \(-0.300328\pi\) | ||||
0.586952 | + | 0.809622i | \(0.300328\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1665.19i | 2.36870i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − 498.879i | − 0.707629i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 285.908 | 0.403255 | 0.201627 | − | 0.979462i | \(-0.435377\pi\) | ||||
0.201627 | + | 0.979462i | \(0.435377\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 142.513 | 0.200440 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1002.42i | 1.40592i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −144.782 | −0.202492 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 289.945i | 0.404387i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 699.242i | − 0.972520i | −0.873814 | − | 0.486260i | \(-0.838361\pi\) | ||||
0.873814 | − | 0.486260i | \(-0.161639\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 142.142 | 0.196600 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 362.712 | 0.500293 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 216.138i | − 0.297302i | −0.988890 | − | 0.148651i | \(-0.952507\pi\) | ||||
0.988890 | − | 0.148651i | \(-0.0474930\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 641.702i | − 0.877841i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 727.188i | − 0.992071i | −0.868302 | − | 0.496035i | \(-0.834789\pi\) | ||||
0.868302 | − | 0.496035i | \(-0.165211\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 439.744 | 0.596668 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 396.413 | 0.536418 | 0.268209 | − | 0.963361i | \(-0.413568\pi\) | ||||
0.268209 | + | 0.963361i | \(0.413568\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 189.954i | 0.256348i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 739.481 | 0.995263 | 0.497632 | − | 0.867388i | \(-0.334203\pi\) | ||||
0.497632 | + | 0.867388i | \(0.334203\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 46.5936i | 0.0625417i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 100.812i | 0.134955i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −748.332 | −0.996448 | −0.498224 | − | 0.867048i | \(-0.666014\pi\) | ||||
−0.498224 | + | 0.867048i | \(0.666014\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −403.425 | −0.535757 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 354.825i | 0.469967i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 199.145 | 0.263071 | 0.131536 | − | 0.991311i | \(-0.458009\pi\) | ||||
0.131536 | + | 0.991311i | \(0.458009\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 215.768i | 0.284279i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 981.456i | − 1.28969i | −0.764312 | − | 0.644846i | \(-0.776921\pi\) | ||||
0.764312 | − | 0.644846i | \(-0.223079\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 169.860 | 0.222040 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 125.967 | 0.164233 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − 724.214i | − 0.941760i | −0.882197 | − | 0.470880i | \(-0.843936\pi\) | ||||
0.882197 | − | 0.470880i | \(-0.156064\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −64.7075 | −0.0839268 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 1404.90i | − 1.81746i | −0.417383 | − | 0.908731i | \(-0.637053\pi\) | ||||
0.417383 | − | 0.908731i | \(-0.362947\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 495.000i | 0.638709i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1706.32 | 2.19039 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −344.942 | −0.441667 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 210.221i | 0.268481i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −170.036 | −0.216607 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 255.814i | − 0.325049i | −0.986704 | − | 0.162525i | \(-0.948036\pi\) | ||||
0.986704 | − | 0.162525i | \(-0.0519637\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 5.84154i | 0.00740372i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.138600 | −0.000174779 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 817.807 | 1.02869 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 474.641i | − 0.595534i | −0.954639 | − | 0.297767i | \(-0.903758\pi\) | ||||
0.954639 | − | 0.297767i | \(-0.0962418\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −480.141 | −0.600927 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − 468.276i | − 0.584614i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 146.465i | − 0.182398i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 151.154 | 0.187303 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 467.727 | 0.578155 | 0.289077 | − | 0.957306i | \(-0.406651\pi\) | ||||
0.289077 | + | 0.957306i | \(0.406651\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1567.70i | 1.93305i | 0.256571 | + | 0.966525i | \(0.417407\pi\) | ||||
−0.256571 | + | 0.966525i | \(0.582593\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −159.362 | −0.196017 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 363.990i | − 0.446614i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 2000.71i | − 2.44885i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −438.250 | −0.533801 | −0.266900 | − | 0.963724i | \(-0.585999\pi\) | ||||
−0.266900 | + | 0.963724i | \(0.585999\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 937.213 | 1.13878 | 0.569388 | − | 0.822069i | \(-0.307180\pi\) | ||||
0.569388 | + | 0.822069i | \(0.307180\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 106.547i | 0.129148i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1160.31 | −1.40303 | −0.701516 | − | 0.712654i | \(-0.747493\pi\) | ||||
−0.701516 | + | 0.712654i | \(0.747493\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 254.599i | − 0.307116i | −0.988140 | − | 0.153558i | \(-0.950927\pi\) | ||||
0.988140 | − | 0.153558i | \(-0.0490732\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 264.105i | 0.317816i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −824.100 | −0.986946 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −286.892 | −0.342762 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 129.902i | − 0.154829i | −0.996999 | − | 0.0774146i | \(-0.975333\pi\) | ||||
0.996999 | − | 0.0774146i | \(-0.0246665\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 795.767 | 0.946215 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 380.843i | − 0.451771i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 908.530i | 1.07518i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 670.978 | 0.790315 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −998.106 | −1.17286 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 1229.45i | − 1.44133i | −0.693284 | − | 0.720665i | \(-0.743837\pi\) | ||||
0.693284 | − | 0.720665i | \(-0.256163\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 529.594 | 0.619408 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 668.190i | 0.779685i | 0.920881 | + | 0.389843i | \(0.127471\pi\) | ||||
−0.920881 | + | 0.389843i | \(0.872529\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 19.3907i | − 0.0225736i | −0.999936 | − | 0.0112868i | \(-0.996407\pi\) | ||||
0.999936 | − | 0.0112868i | \(-0.00359278\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 92.9711 | 0.107730 | 0.0538651 | − | 0.998548i | \(-0.482846\pi\) | ||||
0.0538651 | + | 0.998548i | \(0.482846\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1421.14 | −1.64294 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 337.082i | 0.388792i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 325.945 | 0.375080 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 232.046i | 0.266413i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 131.236i | 0.150327i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 312.308 | 0.356110 | 0.178055 | − | 0.984021i | \(-0.443020\pi\) | ||||
0.178055 | + | 0.984021i | \(0.443020\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −25.7718 | −0.0293195 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 772.018i | − 0.876298i | −0.898902 | − | 0.438149i | \(-0.855634\pi\) | ||||
0.898902 | − | 0.438149i | \(-0.144366\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −959.154 | −1.08624 | −0.543122 | − | 0.839654i | \(-0.682758\pi\) | ||||
−0.543122 | + | 0.839654i | \(0.682758\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 351.197i | − 0.396833i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 554.964i | 0.625664i | 0.949808 | + | 0.312832i | \(0.101278\pi\) | ||||
−0.949808 | + | 0.312832i | \(0.898722\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −61.7523 | −0.0693068 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1496.99 | −1.67636 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 1670.54i | − 1.86653i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −113.857 | −0.126931 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2233.73i | 2.48468i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 787.089i | − 0.873573i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1252.07 | −1.38351 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 573.116 | 0.631881 | 0.315940 | − | 0.948779i | \(-0.397680\pi\) | ||||
0.315940 | + | 0.948779i | \(0.397680\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 509.239i | − 0.560219i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 726.088 | 0.797023 | 0.398511 | − | 0.917163i | \(-0.369527\pi\) | ||||
0.398511 | + | 0.917163i | \(0.369527\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 230.569i | 0.252540i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.386417i | 0 0.000422314i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 784.533 | 0.853681 | 0.426840 | − | 0.904327i | \(-0.359627\pi\) | ||||
0.426840 | + | 0.904327i | \(0.359627\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −784.984 | −0.852317 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 182.020i | − 0.197205i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −492.868 | −0.532830 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 179.165i | 0.193274i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 159.109i | 0.171269i | 0.996327 | + | 0.0856347i | \(0.0272918\pi\) | ||||
−0.996327 | + | 0.0856347i | \(0.972708\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 753.868 | 0.808004 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 388.491 | 0.415499 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 728.876i | 0.777883i | 0.921262 | + | 0.388941i | \(0.127159\pi\) | ||||
−0.921262 | + | 0.388941i | \(0.872841\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 95.1597 | 0.101342 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 323.245i | − 0.343513i | −0.985139 | − | 0.171756i | \(-0.945056\pi\) | ||||
0.985139 | − | 0.171756i | \(-0.0549442\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1022.75i | 1.08458i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 673.049 | 0.710717 | 0.355359 | − | 0.934730i | \(-0.384359\pi\) | ||||
0.355359 | + | 0.934730i | \(0.384359\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 77.2873 | 0.0814408 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 751.175i | 0.789879i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −195.034 | −0.204653 | −0.102326 | − | 0.994751i | \(-0.532629\pi\) | ||||
−0.102326 | + | 0.994751i | \(0.532629\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 264.153i | − 0.276600i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 480.800i | 0.502404i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2087.40 | −2.17212 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 173.303 | 0.179962 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1830.16i | 1.89654i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −731.573 | −0.756538 | −0.378269 | − | 0.925696i | \(-0.623481\pi\) | ||||
−0.378269 | + | 0.925696i | \(0.623481\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − 509.702i | − 0.526008i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 498.822i | 0.513720i | 0.966449 | + | 0.256860i | \(0.0826879\pi\) | ||||
−0.966449 | + | 0.256860i | \(0.917312\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −56.2230 | −0.0576646 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −180.705 | −0.184959 | −0.0924794 | − | 0.995715i | \(-0.529479\pi\) | ||||
−0.0924794 | + | 0.995715i | \(0.529479\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 1071.00i | − 1.09398i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −539.537 | −0.549987 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 326.658i | − 0.332307i | −0.986100 | − | 0.166153i | \(-0.946865\pi\) | ||||
0.986100 | − | 0.166153i | \(-0.0531347\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1510.80i | 1.53380i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1199.21 | 1.21255 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1646.75 | −1.66171 | −0.830854 | − | 0.556491i | \(-0.812147\pi\) | ||||
−0.830854 | + | 0.556491i | \(0.812147\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 998.611i | − 1.00565i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 428.505 | 0.430659 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 140.158i | 0.140580i | 0.997527 | + | 0.0702900i | \(0.0223925\pi\) | ||||
−0.997527 | + | 0.0702900i | \(0.977608\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − 285.656i | − 0.285942i |
(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.97.8 | yes | 8 | |
3.2 | odd | 2 | 1764.3.d.h.685.1 | 8 | |||
4.3 | odd | 2 | 2352.3.f.j.97.4 | 8 | |||
7.2 | even | 3 | 588.3.m.e.325.4 | 8 | |||
7.3 | odd | 6 | 588.3.m.e.313.4 | 8 | |||
7.4 | even | 3 | 588.3.m.f.313.1 | 8 | |||
7.5 | odd | 6 | 588.3.m.f.325.1 | 8 | |||
7.6 | odd | 2 | inner | 588.3.d.c.97.1 | ✓ | 8 | |
21.2 | odd | 6 | 1764.3.z.m.325.1 | 8 | |||
21.5 | even | 6 | 1764.3.z.l.325.4 | 8 | |||
21.11 | odd | 6 | 1764.3.z.l.901.4 | 8 | |||
21.17 | even | 6 | 1764.3.z.m.901.1 | 8 | |||
21.20 | even | 2 | 1764.3.d.h.685.8 | 8 | |||
28.27 | even | 2 | 2352.3.f.j.97.5 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
588.3.d.c.97.1 | ✓ | 8 | 7.6 | odd | 2 | inner | |
588.3.d.c.97.8 | yes | 8 | 1.1 | even | 1 | trivial | |
588.3.m.e.313.4 | 8 | 7.3 | odd | 6 | |||
588.3.m.e.325.4 | 8 | 7.2 | even | 3 | |||
588.3.m.f.313.1 | 8 | 7.4 | even | 3 | |||
588.3.m.f.325.1 | 8 | 7.5 | odd | 6 | |||
1764.3.d.h.685.1 | 8 | 3.2 | odd | 2 | |||
1764.3.d.h.685.8 | 8 | 21.20 | even | 2 | |||
1764.3.z.l.325.4 | 8 | 21.5 | even | 6 | |||
1764.3.z.l.901.4 | 8 | 21.11 | odd | 6 | |||
1764.3.z.m.325.1 | 8 | 21.2 | odd | 6 | |||
1764.3.z.m.901.1 | 8 | 21.17 | even | 6 | |||
2352.3.f.j.97.4 | 8 | 4.3 | odd | 2 | |||
2352.3.f.j.97.5 | 8 | 28.27 | even | 2 |