Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3696,2,Mod(1,3696)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3696, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3696.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3696 = 2^{4} \cdot 3 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3696.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(29.5127085871\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.229.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 4x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 231) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.86081\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3696.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.39821 | 1.07251 | 0.536255 | − | 0.844056i | \(-0.319838\pi\) | ||||
0.536255 | + | 0.844056i | \(0.319838\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.04502 | 1.39924 | 0.699618 | − | 0.714517i | \(-0.253354\pi\) | ||||
0.699618 | + | 0.714517i | \(0.253354\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.39821 | −0.619214 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.36842 | −1.54457 | −0.772284 | − | 0.635277i | \(-0.780886\pi\) | ||||
−0.772284 | + | 0.635277i | \(0.780886\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.32340 | 1.22127 | 0.610636 | − | 0.791911i | \(-0.290914\pi\) | ||||
0.610636 | + | 0.791911i | \(0.290914\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.92520 | −1.02697 | −0.513487 | − | 0.858097i | \(-0.671647\pi\) | ||||
−0.513487 | + | 0.858097i | \(0.671647\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.751399 | 0.150280 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.04502 | 0.936836 | 0.468418 | − | 0.883507i | \(-0.344824\pi\) | ||||
0.468418 | + | 0.883507i | \(0.344824\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.57201 | 1.35997 | 0.679986 | − | 0.733225i | \(-0.261986\pi\) | ||||
0.679986 | + | 0.733225i | \(0.261986\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.39821 | 0.405371 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.24860 | 0.698466 | 0.349233 | − | 0.937036i | \(-0.386442\pi\) | ||||
0.349233 | + | 0.937036i | \(0.386442\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.04502 | −0.807849 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.646809 | −0.101015 | −0.0505073 | − | 0.998724i | \(-0.516084\pi\) | ||||
−0.0505073 | + | 0.998724i | \(0.516084\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.5180 | 1.60398 | 0.801992 | − | 0.597335i | \(-0.203774\pi\) | ||||
0.801992 | + | 0.597335i | \(0.203774\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.39821 | 0.357504 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.526989 | −0.0768693 | −0.0384347 | − | 0.999261i | \(-0.512237\pi\) | ||||
−0.0384347 | + | 0.999261i | \(0.512237\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.36842 | 0.891757 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.72161 | 0.511203 | 0.255601 | − | 0.966782i | \(-0.417727\pi\) | ||||
0.255601 | + | 0.966782i | \(0.417727\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.39821 | 0.323374 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.32340 | −0.705102 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.97021 | −1.03763 | −0.518817 | − | 0.854886i | \(-0.673627\pi\) | ||||
−0.518817 | + | 0.854886i | \(0.673627\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.00000 | −0.256074 | −0.128037 | − | 0.991769i | \(-0.540868\pi\) | ||||
−0.128037 | + | 0.991769i | \(0.540868\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 12.0990 | 1.50070 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.76663 | −1.07101 | −0.535507 | − | 0.844531i | \(-0.679879\pi\) | ||||
−0.535507 | + | 0.844531i | \(0.679879\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.92520 | 0.592924 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.4432 | 1.35806 | 0.679030 | − | 0.734110i | \(-0.262400\pi\) | ||||
0.679030 | + | 0.734110i | \(0.262400\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −13.0450 | −1.52680 | −0.763402 | − | 0.645924i | \(-0.776472\pi\) | ||||
−0.763402 | + | 0.645924i | \(0.776472\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.751399 | −0.0867641 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.00000 | 0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.4432 | −1.28746 | −0.643732 | − | 0.765251i | \(-0.722615\pi\) | ||||
−0.643732 | + | 0.765251i | \(0.722615\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −13.1648 | −1.44503 | −0.722514 | − | 0.691356i | \(-0.757014\pi\) | ||||
−0.722514 | + | 0.691356i | \(0.757014\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −15.2728 | −1.65657 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.04502 | −0.540882 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.8504 | 1.25614 | 0.628070 | − | 0.778157i | \(-0.283845\pi\) | ||||
0.628070 | + | 0.778157i | \(0.283845\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.04502 | 0.528861 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.57201 | −0.785180 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 12.7666 | 1.30983 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.87122 | −0.189993 | −0.0949967 | − | 0.995478i | \(-0.530284\pi\) | ||||
−0.0949967 | + | 0.995478i | \(0.530284\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.51803 | 0.449560 | 0.224780 | − | 0.974409i | \(-0.427834\pi\) | ||||
0.224780 | + | 0.974409i | \(0.427834\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.6468 | 1.04906 | 0.524531 | − | 0.851392i | \(-0.324241\pi\) | ||||
0.524531 | + | 0.851392i | \(0.324241\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.39821 | −0.234041 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −15.9702 | −1.54390 | −0.771949 | − | 0.635684i | \(-0.780718\pi\) | ||||
−0.771949 | + | 0.635684i | \(0.780718\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.7756 | 1.22368 | 0.611840 | − | 0.790982i | \(-0.290430\pi\) | ||||
0.611840 | + | 0.790982i | \(0.290430\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.24860 | −0.403259 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 18.7368 | 1.76261 | 0.881307 | − | 0.472544i | \(-0.156664\pi\) | ||||
0.881307 | + | 0.472544i | \(0.156664\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −11.8116 | −1.10144 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.04502 | 0.466412 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.36842 | −0.583792 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.646809 | 0.0583208 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.1890 | −0.911334 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.27839 | 0.202174 | 0.101087 | − | 0.994878i | \(-0.467768\pi\) | ||||
0.101087 | + | 0.994878i | \(0.467768\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −10.5180 | −0.926061 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.00000 | −0.349482 | −0.174741 | − | 0.984614i | \(-0.555909\pi\) | ||||
−0.174741 | + | 0.984614i | \(0.555909\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.32340 | 0.461598 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.39821 | −0.206405 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.77559 | −0.408006 | −0.204003 | − | 0.978970i | \(-0.565395\pi\) | ||||
−0.204003 | + | 0.978970i | \(0.565395\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.4432 | 1.30988 | 0.654939 | − | 0.755682i | \(-0.272694\pi\) | ||||
0.654939 | + | 0.755682i | \(0.272694\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.526989 | 0.0443805 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.04502 | 0.421885 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 12.0990 | 1.00477 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −9.84143 | −0.806241 | −0.403121 | − | 0.915147i | \(-0.632075\pi\) | ||||
−0.403121 | + | 0.915147i | \(0.632075\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.12878 | 0.335996 | 0.167998 | − | 0.985787i | \(-0.446270\pi\) | ||||
0.167998 | + | 0.985787i | \(0.446270\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −6.36842 | −0.514856 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 18.1592 | 1.45859 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.946021 | −0.0755007 | −0.0377504 | − | 0.999287i | \(-0.512019\pi\) | ||||
−0.0377504 | + | 0.999287i | \(0.512019\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.72161 | −0.295143 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.92520 | −0.388160 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.76663 | −0.686655 | −0.343328 | − | 0.939216i | \(-0.611554\pi\) | ||||
−0.343328 | + | 0.939216i | \(0.611554\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.39821 | −0.186700 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 24.3684 | 1.88568 | 0.942842 | − | 0.333239i | \(-0.108142\pi\) | ||||
0.942842 | + | 0.333239i | \(0.108142\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.4522 | 0.957860 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.32340 | 0.407091 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.3476 | 0.938770 | 0.469385 | − | 0.882994i | \(-0.344476\pi\) | ||||
0.469385 | + | 0.882994i | \(0.344476\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.751399 | 0.0568004 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.97021 | 0.599078 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.59283 | 0.418028 | 0.209014 | − | 0.977913i | \(-0.432975\pi\) | ||||
0.209014 | + | 0.977913i | \(0.432975\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.5720 | 1.00880 | 0.504400 | − | 0.863470i | \(-0.331714\pi\) | ||||
0.504400 | + | 0.863470i | \(0.331714\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.00000 | 0.147844 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 10.1890 | 0.749112 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.36842 | −0.465705 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.42240 | 0.681781 | 0.340890 | − | 0.940103i | \(-0.389271\pi\) | ||||
0.340890 | + | 0.940103i | \(0.389271\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.1288 | −0.729086 | −0.364543 | − | 0.931187i | \(-0.618775\pi\) | ||||
−0.364543 | + | 0.931187i | \(0.618775\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −12.0990 | −0.866427 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.25756 | −0.160845 | −0.0804224 | − | 0.996761i | \(-0.525627\pi\) | ||||
−0.0804224 | + | 0.996761i | \(0.525627\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.07480 | −0.217967 | −0.108984 | − | 0.994044i | \(-0.534760\pi\) | ||||
−0.108984 | + | 0.994044i | \(0.534760\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.76663 | 0.618350 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.04502 | 0.354091 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.55118 | −0.108339 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.92520 | −0.342325 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.32340 | 0.368228 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.6468 | 1.00833 | 0.504164 | − | 0.863608i | \(-0.331801\pi\) | ||||
0.504164 | + | 0.863608i | \(0.331801\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −11.4432 | −0.784077 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 25.2244 | 1.72029 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.57201 | 0.514021 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 13.0450 | 0.881500 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −32.1288 | −2.16122 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.90997 | 0.127901 | 0.0639505 | − | 0.997953i | \(-0.479630\pi\) | ||||
0.0639505 | + | 0.997953i | \(0.479630\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.751399 | 0.0500933 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.20359 | 0.212629 | 0.106315 | − | 0.994333i | \(-0.466095\pi\) | ||||
0.106315 | + | 0.994333i | \(0.466095\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −18.3088 | −1.20988 | −0.604941 | − | 0.796270i | \(-0.706803\pi\) | ||||
−0.604941 | + | 0.796270i | \(0.706803\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.00000 | −0.0657952 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −16.5872 | −1.08667 | −0.543333 | − | 0.839517i | \(-0.682838\pi\) | ||||
−0.543333 | + | 0.839517i | \(0.682838\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.26383 | −0.0824432 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 11.4432 | 0.743317 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.91623 | −0.188635 | −0.0943177 | − | 0.995542i | \(-0.530067\pi\) | ||||
−0.0943177 | + | 0.995542i | \(0.530067\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.09899 | −0.392871 | −0.196435 | − | 0.980517i | \(-0.562937\pi\) | ||||
−0.196435 | + | 0.980517i | \(0.562937\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.39821 | 0.153216 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 26.8567 | 1.70885 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 13.1648 | 0.834288 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.62262 | −0.102419 | −0.0512093 | − | 0.998688i | \(-0.516308\pi\) | ||||
−0.0512093 | + | 0.998688i | \(0.516308\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.92520 | −0.309644 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 15.2728 | 0.956419 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.89541 | −0.430124 | −0.215062 | − | 0.976600i | \(-0.568995\pi\) | ||||
−0.215062 | + | 0.976600i | \(0.568995\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.24860 | 0.263995 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.04502 | 0.312279 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.08377 | −0.313478 | −0.156739 | − | 0.987640i | \(-0.550098\pi\) | ||||
−0.156739 | + | 0.987640i | \(0.550098\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.92520 | 0.548270 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −11.8504 | −0.725232 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −0.886447 | −0.0540476 | −0.0270238 | − | 0.999635i | \(-0.508603\pi\) | ||||
−0.0270238 | + | 0.999635i | \(0.508603\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 25.3234 | 1.53829 | 0.769144 | − | 0.639076i | \(-0.220683\pi\) | ||||
0.769144 | + | 0.639076i | \(0.220683\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5.04502 | −0.305338 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.751399 | 0.0453111 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −24.8269 | −1.49170 | −0.745851 | − | 0.666113i | \(-0.767957\pi\) | ||||
−0.745851 | + | 0.666113i | \(0.767957\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7.57201 | 0.453324 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.90101 | 0.113404 | 0.0567022 | − | 0.998391i | \(-0.481941\pi\) | ||||
0.0567022 | + | 0.998391i | \(0.481941\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 22.3178 | 1.32666 | 0.663328 | − | 0.748329i | \(-0.269143\pi\) | ||||
0.663328 | + | 0.748329i | \(0.269143\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −12.7666 | −0.756230 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.646809 | −0.0381799 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 23.5568 | 1.38569 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.87122 | 0.109693 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12.0900 | 0.706307 | 0.353154 | − | 0.935565i | \(-0.385109\pi\) | ||||
0.353154 | + | 0.935565i | \(0.385109\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −19.1142 | −1.11287 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −24.8477 | −1.43698 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.5180 | 0.606249 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4.51803 | −0.259554 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.79641 | −0.274642 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 13.5928 | 0.775784 | 0.387892 | − | 0.921705i | \(-0.373203\pi\) | ||||
0.387892 | + | 0.921705i | \(0.373203\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −10.6468 | −0.605676 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.00000 | −0.453638 | −0.226819 | − | 0.973937i | \(-0.572833\pi\) | ||||
−0.226819 | + | 0.973937i | \(0.572833\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.9252 | 0.843622 | 0.421811 | − | 0.906684i | \(-0.361395\pi\) | ||||
0.421811 | + | 0.906684i | \(0.361395\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.39821 | 0.135124 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.97918 | 0.223493 | 0.111746 | − | 0.993737i | \(-0.464356\pi\) | ||||
0.111746 | + | 0.993737i | \(0.464356\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.04502 | 0.282467 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 15.9702 | 0.891370 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −33.9017 | −1.88634 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.79082 | 0.210277 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −12.7756 | −0.706492 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.526989 | −0.0290539 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −23.4432 | −1.28856 | −0.644278 | − | 0.764791i | \(-0.722842\pi\) | ||||
−0.644278 | + | 0.764791i | \(0.722842\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.24860 | 0.232822 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −21.0242 | −1.14867 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.1648 | 0.608187 | 0.304094 | − | 0.952642i | \(-0.401646\pi\) | ||||
0.304094 | + | 0.952642i | \(0.401646\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −18.7368 | −1.01765 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.57201 | 0.410047 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 11.8116 | 0.635918 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 22.5872 | 1.21255 | 0.606273 | − | 0.795256i | \(-0.292664\pi\) | ||||
0.606273 | + | 0.795256i | \(0.292664\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 27.9315 | 1.49514 | 0.747568 | − | 0.664185i | \(-0.231221\pi\) | ||||
0.747568 | + | 0.664185i | \(0.231221\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.04502 | −0.269283 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −16.5478 | −0.880751 | −0.440376 | − | 0.897814i | \(-0.645155\pi\) | ||||
−0.440376 | + | 0.897814i | \(0.645155\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 27.4432 | 1.45654 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6.36842 | 0.337053 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −22.0305 | −1.16272 | −0.581362 | − | 0.813645i | \(-0.697480\pi\) | ||||
−0.581362 | + | 0.813645i | \(0.697480\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.33863 | 0.491507 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −31.2847 | −1.63751 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 19.3836 | 1.01182 | 0.505909 | − | 0.862587i | \(-0.331157\pi\) | ||||
0.505909 | + | 0.862587i | \(0.331157\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.646809 | −0.0336715 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.72161 | 0.193216 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 29.2549 | 1.51476 | 0.757380 | − | 0.652975i | \(-0.226479\pi\) | ||||
0.757380 | + | 0.652975i | \(0.226479\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 10.1890 | 0.526159 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 25.4522 | 1.31085 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.5270 | −0.643468 | −0.321734 | − | 0.946830i | \(-0.604266\pi\) | ||||
−0.321734 | + | 0.946830i | \(0.604266\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.27839 | −0.116725 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 17.5928 | 0.898952 | 0.449476 | − | 0.893293i | \(-0.351611\pi\) | ||||
0.449476 | + | 0.893293i | \(0.351611\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.39821 | 0.122224 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 10.5180 | 0.534661 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 20.0900 | 1.01861 | 0.509303 | − | 0.860588i | \(-0.329903\pi\) | ||||
0.509303 | + | 0.860588i | \(0.329903\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 31.3657 | 1.58623 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.00000 | 0.201773 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −27.4432 | −1.38082 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −35.1053 | −1.76188 | −0.880941 | − | 0.473226i | \(-0.843090\pi\) | ||||
−0.880941 | + | 0.473226i | \(0.843090\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −5.32340 | −0.266504 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.57201 | 0.478003 | 0.239002 | − | 0.971019i | \(-0.423180\pi\) | ||||
0.239002 | + | 0.971019i | \(0.423180\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 38.2009 | 1.90292 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.39821 | 0.119168 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.24860 | 0.210595 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 38.1801 | 1.88788 | 0.943941 | − | 0.330113i | \(-0.107087\pi\) | ||||
0.943941 | + | 0.330113i | \(0.107087\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.77559 | 0.235563 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7.97021 | −0.392189 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −31.5720 | −1.54981 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −15.4432 | −0.756258 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7.17380 | −0.350463 | −0.175231 | − | 0.984527i | \(-0.556067\pi\) | ||||
−0.175231 | + | 0.984527i | \(0.556067\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.1530 | 0.738511 | 0.369255 | − | 0.929328i | \(-0.379613\pi\) | ||||
0.369255 | + | 0.929328i | \(0.379613\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.526989 | −0.0256231 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.78522 | −0.232117 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.00000 | −0.0967868 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.04502 | −0.243576 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.56304 | −0.267962 | −0.133981 | − | 0.990984i | \(-0.542776\pi\) | ||||
−0.133981 | + | 0.990984i | \(0.542776\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −25.6412 | −1.23224 | −0.616119 | − | 0.787653i | \(-0.711296\pi\) | ||||
−0.616119 | + | 0.787653i | \(0.711296\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −12.0990 | −0.580102 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −26.2188 | −1.25422 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −23.6710 | −1.12976 | −0.564878 | − | 0.825175i | \(-0.691077\pi\) | ||||
−0.564878 | + | 0.825175i | \(0.691077\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 18.0305 | 0.856653 | 0.428326 | − | 0.903624i | \(-0.359103\pi\) | ||||
0.428326 | + | 0.903624i | \(0.359103\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 28.4197 | 1.34722 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 9.84143 | 0.465484 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −34.9765 | −1.65064 | −0.825321 | − | 0.564664i | \(-0.809006\pi\) | ||||
−0.825321 | + | 0.564664i | \(0.809006\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.646809 | −0.0304570 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.12878 | −0.193987 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 12.0990 | 0.567210 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.53595 | 0.212183 | 0.106091 | − | 0.994356i | \(-0.466166\pi\) | ||||
0.106091 | + | 0.994356i | \(0.466166\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.36842 | 0.297252 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.79641 | −0.130242 | −0.0651210 | − | 0.997877i | \(-0.520743\pi\) | ||||
−0.0651210 | + | 0.997877i | \(0.520743\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −38.3595 | −1.78272 | −0.891358 | − | 0.453301i | \(-0.850246\pi\) | ||||
−0.891358 | + | 0.453301i | \(0.850246\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −18.1592 | −0.842115 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 20.4674 | 0.947119 | 0.473560 | − | 0.880762i | \(-0.342969\pi\) | ||||
0.473560 | + | 0.880762i | \(0.342969\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.76663 | −0.404805 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.946021 | 0.0435904 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 10.5180 | 0.483619 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.00000 | 0.183533 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.72161 | 0.170401 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11.6137 | 0.530641 | 0.265321 | − | 0.964160i | \(-0.414522\pi\) | ||||
0.265321 | + | 0.964160i | \(0.414522\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 21.4343 | 0.977318 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.92520 | 0.224104 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.48757 | −0.203770 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −32.4793 | −1.47178 | −0.735888 | − | 0.677103i | \(-0.763235\pi\) | ||||
−0.735888 | + | 0.677103i | \(0.763235\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8.76663 | 0.396441 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −26.6766 | −1.20390 | −0.601949 | − | 0.798535i | \(-0.705609\pi\) | ||||
−0.601949 | + | 0.798535i | \(0.705609\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −32.1288 | −1.44701 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.39821 | 0.107791 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 11.4432 | 0.513299 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 41.2459 | 1.84642 | 0.923210 | − | 0.384296i | \(-0.125556\pi\) | ||||
0.923210 | + | 0.384296i | \(0.125556\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −24.3684 | −1.08870 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −30.5180 | −1.36073 | −0.680366 | − | 0.732873i | \(-0.738179\pi\) | ||||
−0.680366 | + | 0.732873i | \(0.738179\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.8352 | 0.482159 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.4522 | −0.553021 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −18.9944 | −0.841912 | −0.420956 | − | 0.907081i | \(-0.638305\pi\) | ||||
−0.420956 | + | 0.907081i | \(0.638305\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −13.0450 | −0.577078 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.32340 | −0.235034 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 25.5333 | 1.12513 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.526989 | −0.0231770 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −12.3476 | −0.541999 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 25.2430 | 1.10592 | 0.552958 | − | 0.833209i | \(-0.313499\pi\) | ||||
0.552958 | + | 0.833209i | \(0.313499\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.93416 | 0.128302 | 0.0641509 | − | 0.997940i | \(-0.479566\pi\) | ||||
0.0641509 | + | 0.997940i | \(0.479566\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.751399 | −0.0327937 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −48.2217 | −2.10057 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.25756 | 0.0546767 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.97021 | −0.345878 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.26316 | −0.141343 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −38.2999 | −1.65585 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5.59283 | −0.241348 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.90437 | 0.382829 | 0.191414 | − | 0.981509i | \(-0.438693\pi\) | ||||
0.191414 | + | 0.981509i | \(0.438693\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −13.5720 | −0.582430 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 30.6385 | 1.31241 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 29.4737 | 1.26020 | 0.630102 | − | 0.776513i | \(-0.283013\pi\) | ||||
0.630102 | + | 0.776513i | \(0.283013\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.00000 | −0.0853579 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 26.8567 | 1.14413 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −11.4432 | −0.486615 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −10.1890 | −0.432500 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14.8954 | 0.631139 | 0.315569 | − | 0.948903i | \(-0.397804\pi\) | ||||
0.315569 | + | 0.948903i | \(0.397804\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 53.0636 | 2.24435 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.36842 | 0.268875 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.81164 | 0.329222 | 0.164611 | − | 0.986359i | \(-0.447363\pi\) | ||||
0.164611 | + | 0.986359i | \(0.447363\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 44.9348 | 1.89042 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 10.0000 | 0.419222 | 0.209611 | − | 0.977785i | \(-0.432780\pi\) | ||||
0.209611 | + | 0.977785i | \(0.432780\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −25.5512 | −1.06928 | −0.534642 | − | 0.845079i | \(-0.679553\pi\) | ||||
−0.534642 | + | 0.845079i | \(0.679553\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9.42240 | −0.393626 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.70079 | −0.154334 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −29.5124 | −1.22862 | −0.614309 | − | 0.789065i | \(-0.710565\pi\) | ||||
−0.614309 | + | 0.789065i | \(0.710565\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 10.1288 | 0.420938 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −13.1648 | −0.546169 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.72161 | 0.154133 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 12.0990 | 0.500232 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −31.3955 | −1.29583 | −0.647916 | − | 0.761712i | \(-0.724359\pi\) | ||||
−0.647916 | + | 0.761712i | \(0.724359\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 40.3088 | 1.66090 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.25756 | 0.0928638 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −7.90997 | −0.324823 | −0.162412 | − | 0.986723i | \(-0.551927\pi\) | ||||
−0.162412 | + | 0.986723i | \(0.551927\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −15.2728 | −0.626123 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.07480 | 0.125843 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −27.4432 | −1.12130 | −0.560650 | − | 0.828053i | \(-0.689449\pi\) | ||||
−0.560650 | + | 0.828053i | \(0.689449\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 31.9910 | 1.30494 | 0.652471 | − | 0.757814i | \(-0.273732\pi\) | ||||
0.652471 | + | 0.757814i | \(0.273732\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.76663 | −0.357005 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.39821 | 0.0975010 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.41344 | −0.300902 | −0.150451 | − | 0.988617i | \(-0.548073\pi\) | ||||
−0.150451 | + | 0.988617i | \(0.548073\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.04502 | −0.204434 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.65867 | −0.107558 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −33.9917 | −1.37291 | −0.686456 | − | 0.727171i | \(-0.740835\pi\) | ||||
−0.686456 | + | 0.727171i | \(0.740835\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.55118 | 0.0625497 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −44.0305 | −1.77260 | −0.886300 | − | 0.463112i | \(-0.846733\pi\) | ||||
−0.886300 | + | 0.463112i | \(0.846733\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −40.0096 | −1.60812 | −0.804061 | − | 0.594546i | \(-0.797332\pi\) | ||||
−0.804061 | + | 0.594546i | \(0.797332\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.92520 | 0.197641 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 11.8504 | 0.474776 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −28.1924 | −1.12770 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5.32340 | −0.212596 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −27.0569 | −1.07883 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −28.5568 | −1.13683 | −0.568414 | − | 0.822743i | \(-0.692443\pi\) | ||||
−0.568414 | + | 0.822743i | \(0.692443\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −14.6468 | −0.582158 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5.46405 | 0.216834 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.04502 | 0.199891 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 11.4432 | 0.452687 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −31.1053 | −1.22858 | −0.614292 | − | 0.789079i | \(-0.710558\pi\) | ||||
−0.614292 | + | 0.789079i | \(0.710558\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.48197 | 0.216188 | 0.108094 | − | 0.994141i | \(-0.465525\pi\) | ||||
0.108094 | + | 0.994141i | \(0.465525\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −25.2244 | −0.993210 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9.26383 | 0.364199 | 0.182099 | − | 0.983280i | \(-0.441711\pi\) | ||||
0.182099 | + | 0.983280i | \(0.441711\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.97021 | −0.312858 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7.57201 | −0.296770 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −29.9821 | −1.17329 | −0.586645 | − | 0.809844i | \(-0.699551\pi\) | ||||
−0.586645 | + | 0.809844i | \(0.699551\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.59283 | −0.374823 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −13.0450 | −0.508935 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −23.9702 | −0.933747 | −0.466873 | − | 0.884324i | \(-0.654620\pi\) | ||||
−0.466873 | + | 0.884324i | \(0.654620\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −40.4585 | −1.57365 | −0.786826 | − | 0.617175i | \(-0.788277\pi\) | ||||
−0.786826 | + | 0.617175i | \(0.788277\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 32.1288 | 1.24778 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 12.7666 | 0.495069 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −24.8477 | −0.962107 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.90997 | −0.0738436 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.00000 | −0.0772091 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 21.8712 | 0.843073 | 0.421537 | − | 0.906811i | \(-0.361491\pi\) | ||||
0.421537 | + | 0.906811i | \(0.361491\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.751399 | −0.0289214 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.26316 | −0.0485472 | −0.0242736 | − | 0.999705i | \(-0.507727\pi\) | ||||
−0.0242736 | + | 0.999705i | \(0.507727\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.87122 | −0.0718108 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.20359 | −0.122762 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −37.6441 | −1.44041 | −0.720206 | − | 0.693760i | \(-0.755953\pi\) | ||||
−0.720206 | + | 0.693760i | \(0.755953\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11.4529 | −0.437591 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 18.3088 | 0.698526 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 18.7756 | 0.715293 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.3892 | −0.547393 | −0.273696 | − | 0.961816i | \(-0.588246\pi\) | ||||
−0.273696 | + | 0.961816i | \(0.588246\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.00000 | 0.0379869 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 37.0361 | 1.40486 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.11915 | 0.156024 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 16.5872 | 0.627387 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −39.2936 | −1.48410 | −0.742050 | − | 0.670345i | \(-0.766146\pi\) | ||||
−0.742050 | + | 0.670345i | \(0.766146\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 22.6170 | 0.853017 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.26383 | 0.0475986 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.51803 | 0.169918 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −49.2430 | −1.84936 | −0.924680 | − | 0.380745i | \(-0.875667\pi\) | ||||
−0.924680 | + | 0.380745i | \(0.875667\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −11.4432 | −0.429154 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −37.2936 | −1.39666 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12.0990 | 0.452477 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.91623 | 0.108909 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 7.41344 | 0.276475 | 0.138237 | − | 0.990399i | \(-0.455856\pi\) | ||||
0.138237 | + | 0.990399i | \(0.455856\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.6468 | 0.396508 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6.09899 | 0.226824 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.79082 | 0.140787 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −18.9557 | −0.703026 | −0.351513 | − | 0.936183i | \(-0.614333\pi\) | ||||
−0.351513 | + | 0.936183i | \(0.614333\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −66.9832 | −2.47746 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.59283 | −0.132704 | −0.0663521 | − | 0.997796i | \(-0.521136\pi\) | ||||
−0.0663521 | + | 0.997796i | \(0.521136\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.39821 | −0.0884592 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −8.76663 | −0.322923 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 26.7756 | 0.984956 | 0.492478 | − | 0.870325i | \(-0.336091\pi\) | ||||
0.492478 | + | 0.870325i | \(0.336091\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −26.8567 | −0.986604 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 33.8027 | 1.24010 | 0.620050 | − | 0.784562i | \(-0.287112\pi\) | ||||
0.620050 | + | 0.784562i | \(0.287112\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −23.6018 | −0.864703 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −13.1648 | −0.481676 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −15.9702 | −0.583539 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −35.3955 | −1.29160 | −0.645800 | − | 0.763506i | \(-0.723476\pi\) | ||||
−0.645800 | + | 0.763506i | \(0.723476\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.62262 | 0.0591314 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 9.90168 | 0.360359 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −29.3442 | −1.06653 | −0.533267 | − | 0.845947i | \(-0.679036\pi\) | ||||
−0.533267 | + | 0.845947i | \(0.679036\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.92520 | 0.178773 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12.9044 | 0.467783 | 0.233892 | − | 0.972263i | \(-0.424854\pi\) | ||||
0.233892 | + | 0.972263i | \(0.424854\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12.7756 | 0.462507 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −15.2728 | −0.552189 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −40.2099 | −1.45189 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9.78186 | 0.352743 | 0.176371 | − | 0.984324i | \(-0.443564\pi\) | ||||
0.176371 | + | 0.984324i | \(0.443564\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.89541 | 0.248332 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 29.7223 | 1.06904 | 0.534518 | − | 0.845157i | \(-0.320493\pi\) | ||||
0.534518 | + | 0.845157i | \(0.320493\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.68960 | 0.204376 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.24860 | −0.152418 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.44322 | −0.123366 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.4432 | 0.409471 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.04502 | −0.180294 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.26875 | −0.0809753 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −17.0242 | −0.606847 | −0.303423 | − | 0.952856i | \(-0.598130\pi\) | ||||
−0.303423 | + | 0.952856i | \(0.598130\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 5.08377 | 0.180987 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 18.7368 | 0.666205 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.0900 | −0.358308 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −8.92520 | −0.316544 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −36.4287 | −1.29037 | −0.645185 | − | 0.764027i | \(-0.723220\pi\) | ||||
−0.645185 | + | 0.764027i | \(0.723220\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.35609 | 0.118730 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 11.8504 | 0.418713 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −13.0450 | −0.460349 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −11.8116 | −0.416306 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.886447 | 0.0312044 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 44.4882 | 1.56412 | 0.782062 | − | 0.623201i | \(-0.214168\pi\) | ||||
0.782062 | + | 0.623201i | \(0.214168\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.65307 | −0.268736 | −0.134368 | − | 0.990932i | \(-0.542900\pi\) | ||||
−0.134368 | + | 0.990932i | \(0.542900\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −25.3234 | −0.888131 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −21.0242 | −0.736445 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 55.9917 | 1.95890 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.04502 | 0.176287 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −44.3691 | −1.54849 | −0.774246 | − | 0.632885i | \(-0.781871\pi\) | ||||
−0.774246 | + | 0.632885i | \(0.781871\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.61702 | −0.230655 | −0.115327 | − | 0.993328i | \(-0.536792\pi\) | ||||
−0.115327 | + | 0.993328i | \(0.536792\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.751399 | −0.0261604 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −39.7126 | −1.38094 | −0.690472 | − | 0.723359i | \(-0.742597\pi\) | ||||
−0.690472 | + | 0.723359i | \(0.742597\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.90997 | −0.135799 | −0.0678994 | − | 0.997692i | \(-0.521630\pi\) | ||||
−0.0678994 | + | 0.997692i | \(0.521630\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 24.8269 | 0.861235 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.36842 | −0.220653 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 58.4405 | 2.02242 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.57201 | −0.261727 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9.58097 | 0.330772 | 0.165386 | − | 0.986229i | \(-0.447113\pi\) | ||||
0.165386 | + | 0.986229i | \(0.447113\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.54781 | −0.122338 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.90101 | −0.0654741 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 29.8629 | 1.02732 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.00000 | 0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −22.3178 | −0.765945 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −20.9252 | −0.717307 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −14.5568 | −0.498415 | −0.249207 | − | 0.968450i | \(-0.580170\pi\) | ||||
−0.249207 | + | 0.968450i | \(0.580170\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 12.7666 | 0.436609 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 10.4793 | 0.357965 | 0.178983 | − | 0.983852i | \(-0.442719\pi\) | ||||
0.178983 | + | 0.983852i | \(0.442719\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.88645 | −0.0984843 | −0.0492421 | − | 0.998787i | \(-0.515681\pi\) | ||||
−0.0492421 | + | 0.998787i | \(0.515681\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.646809 | 0.0220432 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 20.5485 | 0.699479 | 0.349739 | − | 0.936847i | \(-0.386270\pi\) | ||||
0.349739 | + | 0.936847i | \(0.386270\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 29.6121 | 1.00684 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −23.5568 | −0.800030 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −11.4432 | −0.388185 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −44.2278 | −1.49860 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.87122 | −0.0633311 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −10.1890 | −0.344452 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 59.1149 | 1.99617 | 0.998084 | − | 0.0618724i | \(-0.0197072\pi\) | ||||
0.998084 | + | 0.0618724i | \(0.0197072\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −12.0900 | −0.407787 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 30.3982 | 1.02414 | 0.512071 | − | 0.858943i | \(-0.328879\pi\) | ||||
0.512071 | + | 0.858943i | \(0.328879\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 35.6114 | 1.19842 | 0.599210 | − | 0.800592i | \(-0.295481\pi\) | ||||
0.599210 | + | 0.800592i | \(0.295481\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 19.1142 | 0.642518 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −22.9736 | −0.771377 | −0.385689 | − | 0.922629i | \(-0.626036\pi\) | ||||
−0.385689 | + | 0.922629i | \(0.626036\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.27839 | 0.0764147 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.80538 | −0.0938784 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 13.4128 | 0.448339 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 24.8477 | 0.829640 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 38.2009 | 1.27407 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −23.7008 | −0.789588 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −10.5180 | −0.350018 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 32.5485 | 1.08195 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 57.1745 | 1.89845 | 0.949224 | − | 0.314602i | \(-0.101871\pi\) | ||||
0.949224 | + | 0.314602i | \(0.101871\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.51803 | 0.149853 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.82687 | −0.226184 | −0.113092 | − | 0.993584i | \(-0.536076\pi\) | ||||
−0.113092 | + | 0.993584i | \(0.536076\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −13.1648 | −0.435692 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 4.79641 | 0.158565 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.00000 | −0.132092 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −12.0692 | −0.398126 | −0.199063 | − | 0.979987i | \(-0.563790\pi\) | ||||
−0.199063 | + | 0.979987i | \(0.563790\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −13.5928 | −0.447899 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 57.7312 | 1.90025 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.19239 | 0.104965 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 10.6468 | 0.349687 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 26.8954 | 0.882410 | 0.441205 | − | 0.897406i | \(-0.354551\pi\) | ||||
0.441205 | + | 0.897406i | \(0.354551\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.32340 | 0.174468 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 8.00000 | 0.261908 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −15.2728 | −0.499474 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −14.9944 | −0.489846 | −0.244923 | − | 0.969543i | \(-0.578763\pi\) | ||||
−0.244923 | + | 0.969543i | \(0.578763\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −14.9252 | −0.487065 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −30.1205 | −0.981900 | −0.490950 | − | 0.871188i | \(-0.663350\pi\) | ||||
−0.490950 | + | 0.871188i | \(0.663350\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.18566 | 0.103739 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.39821 | −0.0780137 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 17.3532 | 0.563903 | 0.281951 | − | 0.959429i | \(-0.409018\pi\) | ||||
0.281951 | + | 0.959429i | \(0.409018\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −65.8123 | −2.13636 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.97918 | −0.129034 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.14064 | −0.0693422 | −0.0346711 | − | 0.999399i | \(-0.511038\pi\) | ||||
−0.0346711 | + | 0.999399i | \(0.511038\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 22.5969 | 0.731217 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −5.04502 | −0.163082 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.77559 | −0.154212 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 26.3353 | 0.849525 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −15.9702 | −0.514633 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −24.2909 | −0.781952 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.53326 | 0.0493062 | 0.0246531 | − | 0.999696i | \(-0.492152\pi\) | ||||
0.0246531 | + | 0.999696i | \(0.492152\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 33.9017 | 1.08908 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 26.5574 | 0.852269 | 0.426135 | − | 0.904660i | \(-0.359875\pi\) | ||||
0.426135 | + | 0.904660i | \(0.359875\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 15.4432 | 0.495087 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.79082 | −0.121403 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −55.9017 | −1.78845 | −0.894227 | − | 0.447615i | \(-0.852274\pi\) | ||||
−0.894227 | + | 0.447615i | \(0.852274\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 11.8504 | 0.378740 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12.7756 | 0.407893 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 53.0361 | 1.69159 | 0.845794 | − | 0.533510i | \(-0.179127\pi\) | ||||
0.845794 | + | 0.533510i | \(0.179127\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.41411 | −0.172508 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.526989 | 0.0167743 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −51.8034 | −1.64725 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −14.7362 | −0.468110 | −0.234055 | − | 0.972223i | \(-0.575200\pi\) | ||||
−0.234055 | + | 0.972223i | \(0.575200\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 23.4432 | 0.743948 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −7.37402 | −0.233772 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −45.0665 | −1.42727 | −0.713635 | − | 0.700517i | \(-0.752953\pi\) | ||||
−0.713635 | + | 0.700517i | \(0.752953\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.24860 | −0.134420 |
(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 | 3696.2.a.bo.1.2 | 3 | ||
4.3 | odd | 2 | 231.2.a.e.1.2 | ✓ | 3 | ||
12.11 | even | 2 | 693.2.a.l.1.2 | 3 | |||
20.19 | odd | 2 | 5775.2.a.bp.1.2 | 3 | |||
28.27 | even | 2 | 1617.2.a.t.1.2 | 3 | |||
44.43 | even | 2 | 2541.2.a.bg.1.2 | 3 | |||
84.83 | odd | 2 | 4851.2.a.bi.1.2 | 3 | |||
132.131 | odd | 2 | 7623.2.a.cd.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
231.2.a.e.1.2 | ✓ | 3 | 4.3 | odd | 2 | ||
693.2.a.l.1.2 | 3 | 12.11 | even | 2 | |||
1617.2.a.t.1.2 | 3 | 28.27 | even | 2 | |||
2541.2.a.bg.1.2 | 3 | 44.43 | even | 2 | |||
3696.2.a.bo.1.2 | 3 | 1.1 | even | 1 | trivial | ||
4851.2.a.bi.1.2 | 3 | 84.83 | odd | 2 | |||
5775.2.a.bp.1.2 | 3 | 20.19 | odd | 2 | |||
7623.2.a.cd.1.2 | 3 | 132.131 | odd | 2 |