Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1296,3,Mod(1135,1296)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1296, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1296.1135");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1296 = 2^{4} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1296.g (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: | \(35.3134422611\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{5}\cdot 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1135.1 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1296.1135 |
Dual form | 1296.3.g.c.1135.2 |
$q$-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 \(\left(\mathbb{Z}/1296\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(1135\) | \(1217\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −7.73205 | −1.54641 | −0.773205 | − | 0.634156i | \(-0.781348\pi\) | ||||
−0.773205 | + | 0.634156i | \(0.781348\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 9.46410i | − 1.35201i | −0.736895 | − | 0.676007i | \(-0.763709\pi\) | ||||
0.736895 | − | 0.676007i | \(-0.236291\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 16.3923i | 1.49021i | 0.666947 | + | 0.745105i | \(0.267601\pi\) | ||||
−0.666947 | + | 0.745105i | \(0.732399\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 17.3923 | 1.33787 | 0.668935 | − | 0.743321i | \(-0.266751\pi\) | ||||
0.668935 | + | 0.743321i | \(0.266751\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −20.6603 | −1.21531 | −0.607655 | − | 0.794201i | \(-0.707889\pi\) | ||||
−0.607655 | + | 0.794201i | \(0.707889\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 33.4641i | 1.76127i | 0.473797 | + | 0.880634i | \(0.342883\pi\) | ||||
−0.473797 | + | 0.880634i | \(0.657117\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 7.60770i | − 0.330769i | −0.986229 | − | 0.165385i | \(-0.947113\pi\) | ||||
0.986229 | − | 0.165385i | \(-0.0528866\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 34.7846 | 1.39138 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.73205 | 0.266622 | 0.133311 | − | 0.991074i | \(-0.457439\pi\) | ||||
0.133311 | + | 0.991074i | \(0.457439\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 32.7846i | − 1.05757i | −0.848756 | − | 0.528784i | \(-0.822648\pi\) | ||||
0.848756 | − | 0.528784i | \(-0.177352\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 73.1769i | 2.09077i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −26.1769 | −0.707484 | −0.353742 | − | 0.935343i | \(-0.615091\pi\) | ||||
−0.353742 | + | 0.935343i | \(0.615091\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 41.5692 | 1.01388 | 0.506942 | − | 0.861980i | \(-0.330776\pi\) | ||||
0.506942 | + | 0.861980i | \(0.330776\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 37.1769i | − 0.864579i | −0.901735 | − | 0.432290i | \(-0.857706\pi\) | ||||
0.901735 | − | 0.432290i | \(-0.142294\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 24.0000i | 0.510638i | 0.966857 | + | 0.255319i | \(0.0821805\pi\) | ||||
−0.966857 | + | 0.255319i | \(0.917819\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −40.5692 | −0.827943 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 15.2154 | 0.287083 | 0.143541 | − | 0.989644i | \(-0.454151\pi\) | ||||
0.143541 | + | 0.989644i | \(0.454151\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 126.746i | − 2.30448i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 96.0000i | − 1.62712i | −0.581482 | − | 0.813559i | \(-0.697527\pi\) | ||||
0.581482 | − | 0.813559i | \(-0.302473\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −34.9615 | −0.573140 | −0.286570 | − | 0.958059i | \(-0.592515\pi\) | ||||
−0.286570 | + | 0.958059i | \(0.592515\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −134.478 | −2.06890 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 40.8897i | − 0.610294i | −0.952305 | − | 0.305147i | \(-0.901294\pi\) | ||||
0.952305 | − | 0.305147i | \(-0.0987057\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 51.5307i | − 0.725785i | −0.931831 | − | 0.362893i | \(-0.881789\pi\) | ||||
0.931831 | − | 0.362893i | \(-0.118211\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 132.138 | 1.81012 | 0.905058 | − | 0.425289i | \(-0.139827\pi\) | ||||
0.905058 | + | 0.425289i | \(0.139827\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 155.138 | 2.01478 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 49.6743i | − 0.628789i | −0.949292 | − | 0.314395i | \(-0.898199\pi\) | ||||
0.949292 | − | 0.314395i | \(-0.101801\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 91.9230i | − 1.10751i | −0.832681 | − | 0.553753i | \(-0.813195\pi\) | ||||
0.832681 | − | 0.553753i | \(-0.186805\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 159.746 | 1.87937 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −77.6936 | −0.872962 | −0.436481 | − | 0.899714i | \(-0.643775\pi\) | ||||
−0.436481 | + | 0.899714i | \(0.643775\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 164.603i | − 1.80882i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 258.746i | − 2.72364i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −43.5692 | −0.449167 | −0.224584 | − | 0.974455i | \(-0.572102\pi\) | ||||
−0.224584 | + | 0.974455i | \(0.572102\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 170.354 | 1.68667 | 0.843336 | − | 0.537387i | \(-0.180589\pi\) | ||||
0.843336 | + | 0.537387i | \(0.180589\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 40.2102i | − 0.390391i | −0.980764 | − | 0.195195i | \(-0.937466\pi\) | ||||
0.980764 | − | 0.195195i | \(-0.0625341\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 152.785i | 1.42789i | 0.700200 | + | 0.713947i | \(0.253094\pi\) | ||||
−0.700200 | + | 0.713947i | \(0.746906\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 80.6077 | 0.739520 | 0.369760 | − | 0.929127i | \(-0.379440\pi\) | ||||
0.369760 | + | 0.929127i | \(0.379440\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −24.7372 | −0.218913 | −0.109457 | − | 0.993992i | \(-0.534911\pi\) | ||||
−0.109457 | + | 0.993992i | \(0.534911\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 58.8231i | 0.511505i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 195.531i | 1.64312i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −147.708 | −1.22072 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −75.6551 | −0.605241 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 26.0385i | 0.205027i | 0.994732 | + | 0.102514i | \(0.0326885\pi\) | ||||
−0.994732 | + | 0.102514i | \(0.967311\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 217.177i | − 1.65784i | −0.559368 | − | 0.828920i | \(-0.688956\pi\) | ||||
0.559368 | − | 0.828920i | \(-0.311044\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 316.708 | 2.38126 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.52182 | 0.0695023 | 0.0347512 | − | 0.999396i | \(-0.488936\pi\) | ||||
0.0347512 | + | 0.999396i | \(0.488936\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 22.6410i | − 0.162885i | −0.996678 | − | 0.0814425i | \(-0.974047\pi\) | ||||
0.996678 | − | 0.0814425i | \(-0.0259527\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 285.100i | 1.99371i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −59.7846 | −0.412308 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 64.5167 | 0.432998 | 0.216499 | − | 0.976283i | \(-0.430536\pi\) | ||||
0.216499 | + | 0.976283i | \(0.430536\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 198.067i | − 1.31170i | −0.754891 | − | 0.655850i | \(-0.772310\pi\) | ||||
0.754891 | − | 0.655850i | \(-0.227690\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 253.492i | 1.63543i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 284.100 | 1.80955 | 0.904777 | − | 0.425886i | \(-0.140037\pi\) | ||||
0.904777 | + | 0.425886i | \(0.140037\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −72.0000 | −0.447205 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 23.0052i | 0.141136i | 0.997507 | + | 0.0705680i | \(0.0224812\pi\) | ||||
−0.997507 | + | 0.0705680i | \(0.977519\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 217.808i | 1.30424i | 0.758117 | + | 0.652119i | \(0.226120\pi\) | ||||
−0.758117 | + | 0.652119i | \(0.773880\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 133.492 | 0.789895 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −109.914 | −0.635342 | −0.317671 | − | 0.948201i | \(-0.602901\pi\) | ||||
−0.317671 | + | 0.948201i | \(0.602901\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 329.205i | − 1.88117i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 190.277i | − 1.06300i | −0.847059 | − | 0.531500i | \(-0.821629\pi\) | ||||
0.847059 | − | 0.531500i | \(-0.178371\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 34.8616 | 0.192605 | 0.0963027 | − | 0.995352i | \(-0.469298\pi\) | ||||
0.0963027 | + | 0.995352i | \(0.469298\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 202.401 | 1.09406 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 338.669i | − 1.81107i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 165.100i | − 0.864398i | −0.901778 | − | 0.432199i | \(-0.857738\pi\) | ||||
0.901778 | − | 0.432199i | \(-0.142262\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 42.9230 | 0.222399 | 0.111200 | − | 0.993798i | \(-0.464531\pi\) | ||||
0.111200 | + | 0.993798i | \(0.464531\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −147.406 | −0.748256 | −0.374128 | − | 0.927377i | \(-0.622058\pi\) | ||||
−0.374128 | + | 0.927377i | \(0.622058\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 278.851i | 1.40126i | 0.713524 | + | 0.700631i | \(0.247098\pi\) | ||||
−0.713524 | + | 0.700631i | \(0.752902\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 73.1769i | − 0.360477i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −321.415 | −1.56788 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −548.554 | −2.62466 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 131.818i | − 0.624730i | −0.949962 | − | 0.312365i | \(-0.898879\pi\) | ||||
0.949962 | − | 0.312365i | \(-0.101121\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 287.454i | 1.33699i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −310.277 | −1.42985 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −359.329 | −1.62593 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 34.8231i | − 0.156157i | −0.996947 | − | 0.0780787i | \(-0.975121\pi\) | ||||
0.996947 | − | 0.0780787i | \(-0.0248785\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 42.7461i | 0.188309i | 0.995558 | + | 0.0941545i | \(0.0300148\pi\) | ||||
−0.995558 | + | 0.0941545i | \(0.969985\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −192.808 | −0.841955 | −0.420977 | − | 0.907071i | \(-0.638313\pi\) | ||||
−0.420977 | + | 0.907071i | \(0.638313\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 304.583 | 1.30722 | 0.653612 | − | 0.756830i | \(-0.273253\pi\) | ||||
0.653612 | + | 0.756830i | \(0.273253\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 185.569i | − 0.789656i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 240.631i | − 1.00682i | −0.864047 | − | 0.503412i | \(-0.832078\pi\) | ||||
0.864047 | − | 0.503412i | \(-0.167922\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −294.061 | −1.22017 | −0.610086 | − | 0.792335i | \(-0.708865\pi\) | ||||
−0.610086 | + | 0.792335i | \(0.708865\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 313.683 | 1.28034 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 582.018i | 2.35635i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 51.5307i | 0.205302i | 0.994717 | + | 0.102651i | \(0.0327324\pi\) | ||||
−0.994717 | + | 0.102651i | \(0.967268\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 124.708 | 0.492916 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 459.722 | 1.78880 | 0.894400 | − | 0.447267i | \(-0.147603\pi\) | ||||
0.894400 | + | 0.447267i | \(0.147603\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 247.741i | 0.956529i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 351.846i | − 1.33782i | −0.743344 | − | 0.668909i | \(-0.766762\pi\) | ||||
0.743344 | − | 0.668909i | \(-0.233238\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −117.646 | −0.443948 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −219.655 | −0.816562 | −0.408281 | − | 0.912856i | \(-0.633872\pi\) | ||||
−0.408281 | + | 0.912856i | \(0.633872\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 355.244i | − 1.31086i | −0.755255 | − | 0.655431i | \(-0.772487\pi\) | ||||
0.755255 | − | 0.655431i | \(-0.227513\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 570.200i | 2.07345i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 415.415 | 1.49969 | 0.749847 | − | 0.661611i | \(-0.230127\pi\) | ||||
0.749847 | + | 0.661611i | \(0.230127\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 240.986 | 0.857601 | 0.428801 | − | 0.903399i | \(-0.358936\pi\) | ||||
0.428801 | + | 0.903399i | \(0.358936\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 107.138i | − 0.378581i | −0.981921 | − | 0.189291i | \(-0.939381\pi\) | ||||
0.981921 | − | 0.189291i | \(-0.0606188\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 393.415i | − 1.37079i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 137.846 | 0.476976 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −366.640 | −1.25133 | −0.625665 | − | 0.780092i | \(-0.715172\pi\) | ||||
−0.625665 | + | 0.780092i | \(0.715172\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 742.277i | 2.51619i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 132.315i | − 0.442526i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −351.846 | −1.16892 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 270.324 | 0.886309 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 173.338i | 0.564620i | 0.959323 | + | 0.282310i | \(0.0911007\pi\) | ||||
−0.959323 | + | 0.282310i | \(0.908899\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 107.769i | − 0.346525i | −0.984876 | − | 0.173262i | \(-0.944569\pi\) | ||||
0.984876 | − | 0.173262i | \(-0.0554308\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −65.9385 | −0.210666 | −0.105333 | − | 0.994437i | \(-0.533591\pi\) | ||||
−0.105333 | + | 0.994437i | \(0.533591\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 547.883 | 1.72834 | 0.864169 | − | 0.503202i | \(-0.167845\pi\) | ||||
0.864169 | + | 0.503202i | \(0.167845\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 126.746i | 0.397323i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 691.377i | − 2.14049i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 604.985 | 1.86149 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 227.138 | 0.690390 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 159.167i | 0.480866i | 0.970666 | + | 0.240433i | \(0.0772894\pi\) | ||||
−0.970666 | + | 0.240433i | \(0.922711\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 316.161i | 0.943766i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 634.400 | 1.88249 | 0.941246 | − | 0.337722i | \(-0.109656\pi\) | ||||
0.941246 | + | 0.337722i | \(0.109656\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 537.415 | 1.57600 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 79.7898i | − 0.232623i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 30.9770i | 0.0892709i | 0.999003 | + | 0.0446354i | \(0.0142126\pi\) | ||||
−0.999003 | + | 0.0446354i | \(0.985787\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 176.431 | 0.505532 | 0.252766 | − | 0.967527i | \(-0.418660\pi\) | ||||
0.252766 | + | 0.967527i | \(0.418660\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 38.5847 | 0.109305 | 0.0546525 | − | 0.998505i | \(-0.482595\pi\) | ||||
0.0546525 | + | 0.998505i | \(0.482595\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 398.438i | 1.12236i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 573.100i | − 1.59638i | −0.602407 | − | 0.798189i | \(-0.705791\pi\) | ||||
0.602407 | − | 0.798189i | \(-0.294209\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −758.846 | −2.10207 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1021.70 | −2.79918 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 273.051i | 0.744009i | 0.928231 | + | 0.372004i | \(0.121329\pi\) | ||||
−0.928231 | + | 0.372004i | \(0.878671\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 144.000i | − 0.388140i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −210.554 | −0.564487 | −0.282244 | − | 0.959343i | \(-0.591079\pi\) | ||||
−0.282244 | + | 0.959343i | \(0.591079\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 134.478 | 0.356706 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 310.641i | 0.819633i | 0.912168 | + | 0.409817i | \(0.134407\pi\) | ||||
−0.912168 | + | 0.409817i | \(0.865593\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 465.962i | 1.21661i | 0.793703 | + | 0.608305i | \(0.208150\pi\) | ||||
−0.793703 | + | 0.608305i | \(0.791850\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1199.54 | −3.11568 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 90.1999 | 0.231876 | 0.115938 | − | 0.993256i | \(-0.463013\pi\) | ||||
0.115938 | + | 0.993256i | \(0.463013\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 157.177i | 0.401987i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 384.084i | 0.972366i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 89.7461 | 0.226061 | 0.113030 | − | 0.993592i | \(-0.463944\pi\) | ||||
0.113030 | + | 0.993592i | \(0.463944\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −588.755 | −1.46822 | −0.734109 | − | 0.679032i | \(-0.762400\pi\) | ||||
−0.734109 | + | 0.679032i | \(0.762400\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 570.200i | − 1.41489i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 429.100i | − 1.05430i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −721.354 | −1.76370 | −0.881851 | − | 0.471529i | \(-0.843702\pi\) | ||||
−0.881851 | + | 0.471529i | \(0.843702\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −908.554 | −2.19989 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 710.754i | 1.71266i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 792.631i | 1.89172i | 0.324575 | + | 0.945860i | \(0.394779\pi\) | ||||
−0.324575 | + | 0.945860i | \(0.605221\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 397.946 | 0.945240 | 0.472620 | − | 0.881266i | \(-0.343308\pi\) | ||||
0.472620 | + | 0.881266i | \(0.343308\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −718.659 | −1.69096 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 330.879i | 0.774893i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 48.6307i | 0.112832i | 0.998407 | + | 0.0564161i | \(0.0179674\pi\) | ||||
−0.998407 | + | 0.0564161i | \(0.982033\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −379.200 | −0.875750 | −0.437875 | − | 0.899036i | \(-0.644269\pi\) | ||||
−0.437875 | + | 0.899036i | \(0.644269\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 254.585 | 0.582574 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 224.154i | − 0.510601i | −0.966862 | − | 0.255301i | \(-0.917826\pi\) | ||||
0.966862 | − | 0.255301i | \(-0.0821744\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 299.138i | − 0.675256i | −0.941280 | − | 0.337628i | \(-0.890375\pi\) | ||||
0.941280 | − | 0.337628i | \(-0.109625\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 600.731 | 1.34996 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 396.400 | 0.882850 | 0.441425 | − | 0.897298i | \(-0.354473\pi\) | ||||
0.441425 | + | 0.897298i | \(0.354473\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 681.415i | 1.51090i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1272.72i | 2.79718i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 43.1999 | 0.0945294 | 0.0472647 | − | 0.998882i | \(-0.484950\pi\) | ||||
0.0472647 | + | 0.998882i | \(0.484950\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −31.5232 | −0.0683800 | −0.0341900 | − | 0.999415i | \(-0.510885\pi\) | ||||
−0.0341900 | + | 0.999415i | \(0.510885\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 6.16421i | − 0.0133136i | −0.999978 | − | 0.00665682i | \(-0.997881\pi\) | ||||
0.999978 | − | 0.00665682i | \(-0.00211895\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 330.200i | 0.707066i | 0.935422 | + | 0.353533i | \(0.115020\pi\) | ||||
−0.935422 | + | 0.353533i | \(0.884980\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −386.985 | −0.825127 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 609.415 | 1.28840 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1164.04i | 2.45060i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 66.7461i | 0.139345i | 0.997570 | + | 0.0696724i | \(0.0221954\pi\) | ||||
−0.997570 | + | 0.0696724i | \(0.977805\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −455.277 | −0.946522 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 336.879 | 0.694597 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 313.359i | 0.643448i | 0.946834 | + | 0.321724i | \(0.104262\pi\) | ||||
−0.946834 | + | 0.321724i | \(0.895738\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 172.161i | − 0.350634i | −0.984512 | − | 0.175317i | \(-0.943905\pi\) | ||||
0.984512 | − | 0.175317i | \(-0.0560951\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −159.746 | −0.324029 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −487.692 | −0.981272 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 20.2384i | − 0.0405579i | −0.999794 | − | 0.0202790i | \(-0.993545\pi\) | ||||
0.999794 | − | 0.0202790i | \(-0.00645544\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 368.785i | − 0.733170i | −0.930385 | − | 0.366585i | \(-0.880527\pi\) | ||||
0.930385 | − | 0.366585i | \(-0.119473\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1317.18 | −2.60829 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −234.200 | −0.460118 | −0.230059 | − | 0.973177i | \(-0.573892\pi\) | ||||
−0.230059 | + | 0.973177i | \(0.573892\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 1250.57i | − 2.44730i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 310.908i | 0.603704i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −393.415 | −0.760958 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1010.98 | 1.94047 | 0.970235 | − | 0.242167i | \(-0.0778581\pi\) | ||||
0.970235 | + | 0.242167i | \(0.0778581\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 525.864i | 1.00548i | 0.864439 | + | 0.502738i | \(0.167674\pi\) | ||||
−0.864439 | + | 0.502738i | \(0.832326\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 677.338i | 1.28527i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 471.123 | 0.890592 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 722.985 | 1.35644 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 1181.34i | − 2.20811i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 665.023i | − 1.23381i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 412.531 | 0.762534 | 0.381267 | − | 0.924465i | \(-0.375488\pi\) | ||||
0.381267 | + | 0.924465i | \(0.375488\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −623.263 | −1.14360 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 939.251i | 1.71710i | 0.512734 | + | 0.858548i | \(0.328633\pi\) | ||||
−0.512734 | + | 0.858548i | \(0.671367\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 258.746i | 0.469594i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −470.123 | −0.850132 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −631.022 | −1.13289 | −0.566447 | − | 0.824098i | \(-0.691682\pi\) | ||||
−0.566447 | + | 0.824098i | \(0.691682\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 646.592i | − 1.15669i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 94.2769i | − 0.167454i | −0.996489 | − | 0.0837272i | \(-0.973318\pi\) | ||||
0.996489 | − | 0.0837272i | \(-0.0266824\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 191.269 | 0.338530 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −42.9371 | −0.0754607 | −0.0377303 | − | 0.999288i | \(-0.512013\pi\) | ||||
−0.0377303 | + | 0.999288i | \(0.512013\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 423.118i | 0.741012i | 0.928830 | + | 0.370506i | \(0.120816\pi\) | ||||
−0.928830 | + | 0.370506i | \(0.879184\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 264.631i | − 0.460227i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 937.523 | 1.62482 | 0.812411 | − | 0.583085i | \(-0.198154\pi\) | ||||
0.812411 | + | 0.583085i | \(0.198154\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −869.969 | −1.49737 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 249.415i | 0.427814i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 604.161i | − 1.02924i | −0.857420 | − | 0.514618i | \(-0.827934\pi\) | ||||
0.857420 | − | 0.514618i | \(-0.172066\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1097.11 | 1.86266 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 91.5678 | 0.154415 | 0.0772073 | − | 0.997015i | \(-0.475400\pi\) | ||||
0.0772073 | + | 0.997015i | \(0.475400\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 1511.85i | − 2.54093i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 949.031i | − 1.58436i | −0.610289 | − | 0.792179i | \(-0.708947\pi\) | ||||
0.610289 | − | 0.792179i | \(-0.291053\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −362.723 | −0.603533 | −0.301766 | − | 0.953382i | \(-0.597576\pi\) | ||||
−0.301766 | + | 0.953382i | \(0.597576\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1142.08 | 1.88774 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1051.24i | 1.73187i | 0.500159 | + | 0.865934i | \(0.333275\pi\) | ||||
−0.500159 | + | 0.865934i | \(0.666725\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 417.415i | 0.683167i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 208.585 | 0.340269 | 0.170134 | − | 0.985421i | \(-0.445580\pi\) | ||||
0.170134 | + | 0.985421i | \(0.445580\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 689.845 | 1.11806 | 0.559031 | − | 0.829147i | \(-0.311173\pi\) | ||||
0.559031 | + | 0.829147i | \(0.311173\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 885.451i | − 1.43045i | −0.698892 | − | 0.715227i | \(-0.746323\pi\) | ||||
0.698892 | − | 0.715227i | \(-0.253677\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 735.300i | 1.18026i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −284.646 | −0.455434 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 540.822 | 0.859812 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 790.179i | 1.25227i | 0.779717 | + | 0.626133i | \(0.215363\pi\) | ||||
−0.779717 | + | 0.626133i | \(0.784637\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 201.331i | − 0.317056i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −705.592 | −1.10768 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −364.601 | −0.568801 | −0.284400 | − | 0.958706i | \(-0.591794\pi\) | ||||
−0.284400 | + | 0.958706i | \(0.591794\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1189.49i | 1.84991i | 0.380076 | + | 0.924955i | \(0.375898\pi\) | ||||
−0.380076 | + | 0.924955i | \(0.624102\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 68.0075i | − 0.105112i | −0.998618 | − | 0.0525561i | \(-0.983263\pi\) | ||||
0.998618 | − | 0.0525561i | \(-0.0167368\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1573.66 | 2.42475 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 416.785 | 0.638261 | 0.319131 | − | 0.947711i | \(-0.396609\pi\) | ||||
0.319131 | + | 0.947711i | \(0.396609\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1679.22i | 2.56370i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 1204.33i | − 1.82751i | −0.406263 | − | 0.913756i | \(-0.633168\pi\) | ||||
0.406263 | − | 0.913756i | \(-0.366832\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1205.52 | 1.82378 | 0.911888 | − | 0.410440i | \(-0.134625\pi\) | ||||
0.911888 | + | 0.410440i | \(0.134625\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2448.80 | −3.68241 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 58.8231i | − 0.0881905i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 573.100i | − 0.854098i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 41.6616 | 0.0619044 | 0.0309522 | − | 0.999521i | \(-0.490146\pi\) | ||||
0.0309522 | + | 0.999521i | \(0.490146\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −15.2154 | −0.0224747 | −0.0112374 | − | 0.999937i | \(-0.503577\pi\) | ||||
−0.0112374 | + | 0.999937i | \(0.503577\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 412.344i | 0.607281i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 951.384i | − 1.39295i | −0.717581 | − | 0.696475i | \(-0.754751\pi\) | ||||
0.717581 | − | 0.696475i | \(-0.245249\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −73.6232 | −0.107479 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 264.631 | 0.384079 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 131.454i | 0.190237i | 0.995466 | + | 0.0951185i | \(0.0303230\pi\) | ||||
−0.995466 | + | 0.0951185i | \(0.969677\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 175.061i | 0.251887i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −858.831 | −1.23218 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 466.930 | 0.666091 | 0.333045 | − | 0.942911i | \(-0.391924\pi\) | ||||
0.333045 | + | 0.942911i | \(0.391924\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 875.987i | − 1.24607i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 1612.25i | − 2.28040i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 327.038 | 0.461267 | 0.230634 | − | 0.973041i | \(-0.425920\pi\) | ||||
0.230634 | + | 0.973041i | \(0.425920\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −249.415 | −0.349811 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 2204.41i | − 3.08309i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 670.361i | 0.932352i | 0.884692 | + | 0.466176i | \(0.154369\pi\) | ||||
−0.884692 | + | 0.466176i | \(0.845631\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −380.554 | −0.527814 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 268.956 | 0.370974 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 693.500i | − 0.953920i | −0.878925 | − | 0.476960i | \(-0.841739\pi\) | ||||
0.878925 | − | 0.476960i | \(-0.158261\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 768.084i | 1.05073i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −314.000 | −0.428377 | −0.214188 | − | 0.976792i | \(-0.568711\pi\) | ||||
−0.214188 | + | 0.976792i | \(0.568711\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 670.277 | 0.909467 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 233.569i | − 0.316061i | −0.987434 | − | 0.158031i | \(-0.949486\pi\) | ||||
0.987434 | − | 0.158031i | \(-0.0505145\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 927.846i | − 1.24878i | −0.781111 | − | 0.624392i | \(-0.785347\pi\) | ||||
0.781111 | − | 0.624392i | \(-0.214653\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −498.846 | −0.669592 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1445.97 | 1.93053 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 428.505i | − 0.570579i | −0.958441 | − | 0.285290i | \(-0.907910\pi\) | ||||
0.958441 | − | 0.285290i | \(-0.0920898\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1531.46i | 2.02843i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −342.246 | −0.452108 | −0.226054 | − | 0.974115i | \(-0.572583\pi\) | ||||
−0.226054 | + | 0.974115i | \(0.572583\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 469.768 | 0.617303 | 0.308652 | − | 0.951175i | \(-0.400122\pi\) | ||||
0.308652 | + | 0.951175i | \(0.400122\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 762.879i | − 0.999842i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 1669.66i | − 2.17687i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 272.246 | 0.354026 | 0.177013 | − | 0.984208i | \(-0.443356\pi\) | ||||
0.177013 | + | 0.984208i | \(0.443356\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1135.27 | 1.46866 | 0.734328 | − | 0.678795i | \(-0.237498\pi\) | ||||
0.734328 | + | 0.678795i | \(0.237498\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 1140.40i | − 1.47148i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1391.08i | 1.78572i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 844.708 | 1.08157 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2196.68 | −2.79831 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 613.905i | − 0.780057i | −0.920803 | − | 0.390029i | \(-0.872465\pi\) | ||||
0.920803 | − | 0.390029i | \(-0.127535\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 234.115i | 0.295974i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −608.061 | −0.766786 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 596.763 | 0.748761 | 0.374381 | − | 0.927275i | \(-0.377855\pi\) | ||||
0.374381 | + | 0.927275i | \(0.377855\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 495.846i | − 0.620583i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2166.05i | 2.69745i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 556.708 | 0.691562 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −23.8935 | −0.0295346 | −0.0147673 | − | 0.999891i | \(-0.504701\pi\) | ||||
−0.0147673 | + | 0.999891i | \(0.504701\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 548.092i | − 0.675822i | −0.941178 | − | 0.337911i | \(-0.890280\pi\) | ||||
0.941178 | − | 0.337911i | \(-0.109720\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 177.877i | − 0.218254i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1244.09 | 1.52276 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −976.055 | −1.18886 | −0.594431 | − | 0.804147i | \(-0.702622\pi\) | ||||
−0.594431 | + | 0.804147i | \(0.702622\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 1359.65i | − 1.65207i | −0.563621 | − | 0.826033i | \(-0.690592\pi\) | ||||
0.563621 | − | 0.826033i | \(-0.309408\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 663.762i | 0.802614i | 0.915944 | + | 0.401307i | \(0.131444\pi\) | ||||
−0.915944 | + | 0.401307i | \(0.868556\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −403.108 | −0.486258 | −0.243129 | − | 0.969994i | \(-0.578174\pi\) | ||||
−0.243129 | + | 0.969994i | \(0.578174\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 838.170 | 1.00621 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 1684.10i | − 2.01689i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1029.73i | 1.22733i | 0.789566 | + | 0.613665i | \(0.210306\pi\) | ||||
−0.789566 | + | 0.613665i | \(0.789694\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −781.215 | −0.928912 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1032.17 | −1.22150 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1397.92i | 1.65044i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 199.146i | 0.234014i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 467.415 | 0.547966 | 0.273983 | − | 0.961734i | \(-0.411659\pi\) | ||||
0.273983 | + | 0.961734i | \(0.411659\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −480.355 | −0.560508 | −0.280254 | − | 0.959926i | \(-0.590419\pi\) | ||||
−0.280254 | + | 0.959926i | \(0.590419\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 342.964i | − 0.399260i | −0.979871 | − | 0.199630i | \(-0.936026\pi\) | ||||
0.979871 | − | 0.199630i | \(-0.0639739\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 888.084i | 1.02907i | 0.857470 | + | 0.514533i | \(0.172035\pi\) | ||||
−0.857470 | + | 0.514533i | \(0.827965\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 849.862 | 0.982499 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 814.277 | 0.937027 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 711.167i | − 0.816494i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 716.008i | 0.818294i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −709.946 | −0.809517 | −0.404758 | − | 0.914424i | \(-0.632644\pi\) | ||||
−0.404758 | + | 0.914424i | \(0.632644\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −996.862 | −1.13151 | −0.565756 | − | 0.824573i | \(-0.691415\pi\) | ||||
−0.565756 | + | 0.824573i | \(0.691415\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 897.513i | 1.01644i | 0.861228 | + | 0.508218i | \(0.169696\pi\) | ||||
−0.861228 | + | 0.508218i | \(0.830304\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 1268.47i | − 1.43007i | −0.699090 | − | 0.715033i | \(-0.746411\pi\) | ||||
0.699090 | − | 0.715033i | \(-0.253589\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 246.431 | 0.277200 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −803.138 | −0.899371 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1471.23i | 1.64383i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 253.492i | − 0.281971i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −314.354 | −0.348894 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −269.551 | −0.297847 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 52.8052i | − 0.0582197i | −0.999576 | − | 0.0291098i | \(-0.990733\pi\) | ||||
0.999576 | − | 0.0291098i | \(-0.00926726\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 629.423i | − 0.690914i | −0.938435 | − | 0.345457i | \(-0.887724\pi\) | ||||
0.938435 | − | 0.345457i | \(-0.112276\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1506.83 | 1.65042 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2055.38 | −2.24142 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 1112.18i | − 1.21020i | −0.796148 | − | 0.605101i | \(-0.793133\pi\) | ||||
0.796148 | − | 0.605101i | \(-0.206867\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 896.238i | − 0.971006i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −910.554 | −0.984382 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 374.940 | 0.403595 | 0.201798 | − | 0.979427i | \(-0.435322\pi\) | ||||
0.201798 | + | 0.979427i | \(0.435322\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 1357.61i | − 1.45823i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2618.61i | 2.80065i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 555.246 | 0.592578 | 0.296289 | − | 0.955098i | \(-0.404251\pi\) | ||||
0.296289 | + | 0.955098i | \(0.404251\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 646.486 | 0.687020 | 0.343510 | − | 0.939149i | \(-0.388384\pi\) | ||||
0.343510 | + | 0.939149i | \(0.388384\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 316.246i | − 0.335362i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 255.931i | 0.270254i | 0.990828 | + | 0.135127i | \(0.0431443\pi\) | ||||
−0.990828 | + | 0.135127i | \(0.956856\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2298.19 | 2.42170 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 45.1220 | 0.0473473 | 0.0236736 | − | 0.999720i | \(-0.492464\pi\) | ||||
0.0236736 | + | 0.999720i | \(0.492464\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1276.56i | 1.33671i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 90.1154i | − 0.0939681i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −113.831 | −0.118450 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −331.883 | −0.343920 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 1029.60i | − 1.06473i | −0.846514 | − | 0.532367i | \(-0.821303\pi\) | ||||
0.846514 | − | 0.532367i | \(-0.178697\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 405.731i | − 0.417848i | −0.977932 | − | 0.208924i | \(-0.933004\pi\) | ||||
0.977932 | − | 0.208924i | \(-0.0669962\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −214.277 | −0.220223 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1094.12 | −1.11988 | −0.559940 | − | 0.828533i | \(-0.689176\pi\) | ||||
−0.559940 | + | 0.828533i | \(0.689176\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 1273.58i | − 1.30090i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 405.184i | − 0.412192i | −0.978532 | − | 0.206096i | \(-0.933924\pi\) | ||||
0.978532 | − | 0.206096i | \(-0.0660759\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1139.75 | 1.15711 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −282.831 | −0.285976 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 181.905i | 0.183557i | 0.995779 | + | 0.0917786i | \(0.0292552\pi\) | ||||
−0.995779 | + | 0.0917786i | \(0.970745\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 2156.09i | − 2.16693i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 877.038 | 0.879678 | 0.439839 | − | 0.898077i | \(-0.355036\pi\) | ||||
0.439839 | + | 0.898077i | \(0.355036\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1296.3.g.c.1135.1 | ✓ | 4 | |
3.2 | odd | 2 | 1296.3.g.i.1135.3 | yes | 4 | ||
4.3 | odd | 2 | inner | 1296.3.g.c.1135.2 | yes | 4 | |
9.2 | odd | 6 | 1296.3.o.q.271.1 | 4 | |||
9.4 | even | 3 | 1296.3.o.bf.703.2 | 4 | |||
9.5 | odd | 6 | 1296.3.o.r.703.1 | 4 | |||
9.7 | even | 3 | 1296.3.o.be.271.2 | 4 | |||
12.11 | even | 2 | 1296.3.g.i.1135.4 | yes | 4 | ||
36.7 | odd | 6 | 1296.3.o.bf.271.2 | 4 | |||
36.11 | even | 6 | 1296.3.o.r.271.1 | 4 | |||
36.23 | even | 6 | 1296.3.o.q.703.1 | 4 | |||
36.31 | odd | 6 | 1296.3.o.be.703.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1296.3.g.c.1135.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
1296.3.g.c.1135.2 | yes | 4 | 4.3 | odd | 2 | inner | |
1296.3.g.i.1135.3 | yes | 4 | 3.2 | odd | 2 | ||
1296.3.g.i.1135.4 | yes | 4 | 12.11 | even | 2 | ||
1296.3.o.q.271.1 | 4 | 9.2 | odd | 6 | |||
1296.3.o.q.703.1 | 4 | 36.23 | even | 6 | |||
1296.3.o.r.271.1 | 4 | 36.11 | even | 6 | |||
1296.3.o.r.703.1 | 4 | 9.5 | odd | 6 | |||
1296.3.o.be.271.2 | 4 | 9.7 | even | 3 | |||
1296.3.o.be.703.2 | 4 | 36.31 | odd | 6 | |||
1296.3.o.bf.271.2 | 4 | 36.7 | odd | 6 | |||
1296.3.o.bf.703.2 | 4 | 9.4 | even | 3 |