Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2352,3,Mod(97,2352)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2352, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2352.97");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 2352.f (of order \(2\), degree \(1\), not 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: | \(64.0873581775\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{65})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 17x^{2} + 16x + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3 \) |
Twist minimal: | no (minimal twist has level 84) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 97.1 | ||
Root | \(2.26556 - 3.92407i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2352.97 |
Dual form | 2352.3.f.f.97.4 |
$q$-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 \(\left(\mathbb{Z}/2352\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1471\) | \(1765\) | \(2257\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − 1.73205i | − 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 9.58020i | − 1.91604i | −0.286703 | − | 0.958020i | \(-0.592559\pi\) | ||||
0.286703 | − | 0.958020i | \(-0.407441\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.59339 | −0.417581 | −0.208790 | − | 0.977960i | \(-0.566953\pi\) | ||||
−0.208790 | + | 0.977960i | \(0.566953\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 7.84815i | − 0.603703i | −0.953355 | − | 0.301852i | \(-0.902395\pi\) | ||||
0.953355 | − | 0.301852i | \(-0.0976048\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −16.5934 | −1.10623 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 19.1604i | 1.12708i | 0.826088 | + | 0.563541i | \(0.190561\pi\) | ||||
−0.826088 | + | 0.563541i | \(0.809439\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 16.4006i | 0.863188i | 0.902068 | + | 0.431594i | \(0.142049\pi\) | ||||
−0.902068 | + | 0.431594i | \(0.857951\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 24.0000 | 1.04348 | 0.521739 | − | 0.853105i | \(-0.325283\pi\) | ||||
0.521739 | + | 0.853105i | \(0.325283\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −66.7802 | −2.67121 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.19615i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −10.5934 | −0.365289 | −0.182645 | − | 0.983179i | \(-0.558466\pi\) | ||||
−0.182645 | + | 0.983179i | \(0.558466\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 55.7491i | 1.79836i | 0.437580 | + | 0.899179i | \(0.355836\pi\) | ||||
−0.437580 | + | 0.899179i | \(0.644164\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 7.95598i | 0.241090i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −24.4066 | −0.659638 | −0.329819 | − | 0.944044i | \(-0.606988\pi\) | ||||
−0.329819 | + | 0.944044i | \(0.606988\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −13.5934 | −0.348548 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 48.7131i | 1.18812i | 0.804419 | + | 0.594062i | \(0.202477\pi\) | ||||
−0.804419 | + | 0.594062i | \(0.797523\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 18.7802 | 0.436748 | 0.218374 | − | 0.975865i | \(-0.429925\pi\) | ||||
0.218374 | + | 0.975865i | \(0.429925\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 28.7406i | 0.638680i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 12.0165i | 0.255671i | 0.991795 | + | 0.127835i | \(0.0408029\pi\) | ||||
−0.991795 | + | 0.127835i | \(0.959197\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 33.1868 | 0.650721 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −37.4066 | −0.705785 | −0.352893 | − | 0.935664i | \(-0.614802\pi\) | ||||
−0.352893 | + | 0.935664i | \(0.614802\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 44.0055i | 0.800101i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 28.4066 | 0.498362 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 63.1659i | 1.07061i | 0.844659 | + | 0.535305i | \(0.179803\pi\) | ||||
−0.844659 | + | 0.535305i | \(0.820197\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 111.283i | − 1.82430i | −0.409851 | − | 0.912152i | \(-0.634419\pi\) | ||||
0.409851 | − | 0.912152i | \(-0.365581\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −75.1868 | −1.15672 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −63.9669 | −0.954730 | −0.477365 | − | 0.878705i | \(-0.658408\pi\) | ||||
−0.477365 | + | 0.878705i | \(0.658408\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 41.5692i | − 0.602452i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −21.5603 | −0.303666 | −0.151833 | − | 0.988406i | \(-0.548518\pi\) | ||||
−0.151833 | + | 0.988406i | \(0.548518\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 61.8652i | 0.847469i | 0.905786 | + | 0.423734i | \(0.139281\pi\) | ||||
−0.905786 | + | 0.423734i | \(0.860719\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 115.667i | 1.54222i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.81323 | 0.0482687 | 0.0241343 | − | 0.999709i | \(-0.492317\pi\) | ||||
0.0241343 | + | 0.999709i | \(0.492317\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 100.510i | 1.21096i | 0.795861 | + | 0.605479i | \(0.207018\pi\) | ||||
−0.795861 | + | 0.605479i | \(0.792982\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 183.560 | 2.15953 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 18.3483i | 0.210900i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 99.0504i | 1.11293i | 0.830872 | + | 0.556463i | \(0.187842\pi\) | ||||
−0.830872 | + | 0.556463i | \(0.812158\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 96.5603 | 1.03828 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 157.121 | 1.65390 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 63.5973i | − 0.655642i | −0.944740 | − | 0.327821i | \(-0.893686\pi\) | ||||
0.944740 | − | 0.327821i | \(-0.106314\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 13.7802 | 0.139194 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 120.482i | − 1.19289i | −0.802654 | − | 0.596446i | \(-0.796579\pi\) | ||||
0.802654 | − | 0.596446i | \(-0.203421\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 18.8875i | − 0.183373i | −0.995788 | − | 0.0916867i | \(-0.970774\pi\) | ||||
0.995788 | − | 0.0916867i | \(-0.0292258\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −16.9669 | −0.158569 | −0.0792847 | − | 0.996852i | \(-0.525264\pi\) | ||||
−0.0792847 | + | 0.996852i | \(0.525264\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 56.7802 | 0.520919 | 0.260459 | − | 0.965485i | \(-0.416126\pi\) | ||||
0.260459 | + | 0.965485i | \(0.416126\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 42.2735i | 0.380842i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −156.374 | −1.38384 | −0.691918 | − | 0.721976i | \(-0.743234\pi\) | ||||
−0.691918 | + | 0.721976i | \(0.743234\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 229.925i | − 1.99935i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 23.5444i | 0.201234i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −99.9008 | −0.825626 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 84.3735 | 0.685964 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 400.262i | 3.20210i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 25.0000 | 0.196850 | 0.0984252 | − | 0.995144i | \(-0.468619\pi\) | ||||
0.0984252 | + | 0.995144i | \(0.468619\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − 32.5282i | − 0.252157i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 100.840i | − 0.769769i | −0.922965 | − | 0.384884i | \(-0.874241\pi\) | ||||
0.922965 | − | 0.384884i | \(-0.125759\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 49.7802 | 0.368742 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 43.1206 | 0.314749 | 0.157375 | − | 0.987539i | \(-0.449697\pi\) | ||||
0.157375 | + | 0.987539i | \(0.449697\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 117.938i | − 0.848474i | −0.905551 | − | 0.424237i | \(-0.860542\pi\) | ||||
0.905551 | − | 0.424237i | \(-0.139458\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 20.8132 | 0.147612 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 36.0496i | 0.252095i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 101.487i | 0.699908i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 177.187 | 1.18917 | 0.594586 | − | 0.804032i | \(-0.297316\pi\) | ||||
0.594586 | + | 0.804032i | \(0.297316\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −182.967 | −1.21170 | −0.605851 | − | 0.795578i | \(-0.707167\pi\) | ||||
−0.605851 | + | 0.795578i | \(0.707167\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 57.4812i | − 0.375694i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 534.088 | 3.44573 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 84.4324i | − 0.537786i | −0.963170 | − | 0.268893i | \(-0.913342\pi\) | ||||
0.963170 | − | 0.268893i | \(-0.0866578\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 64.7902i | 0.407485i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −143.934 | −0.883030 | −0.441515 | − | 0.897254i | \(-0.645559\pi\) | ||||
−0.441515 | + | 0.897254i | \(0.645559\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 76.2198 | 0.461938 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 123.730i | − 0.740901i | −0.928852 | − | 0.370450i | \(-0.879203\pi\) | ||||
0.928852 | − | 0.370450i | \(-0.120797\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 107.407 | 0.635542 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 49.2017i | − 0.287729i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 134.453i | 0.777185i | 0.921410 | + | 0.388592i | \(0.127039\pi\) | ||||
−0.921410 | + | 0.388592i | \(0.872961\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 109.407 | 0.618116 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −138.000 | −0.770950 | −0.385475 | − | 0.922718i | \(-0.625962\pi\) | ||||
−0.385475 | + | 0.922718i | \(0.625962\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 98.5618i | − 0.544540i | −0.962221 | − | 0.272270i | \(-0.912226\pi\) | ||||
0.962221 | − | 0.272270i | \(-0.0877744\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −192.747 | −1.05326 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 233.820i | 1.26389i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 88.0111i | − 0.470648i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 166.307 | 0.870719 | 0.435360 | − | 0.900257i | \(-0.356621\pi\) | ||||
0.435360 | + | 0.900257i | \(0.356621\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −63.3074 | −0.328018 | −0.164009 | − | 0.986459i | \(-0.552443\pi\) | ||||
−0.164009 | + | 0.986459i | \(0.552443\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 130.227i | 0.667832i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 184.307 | 0.935571 | 0.467785 | − | 0.883842i | \(-0.345052\pi\) | ||||
0.467785 | + | 0.883842i | \(0.345052\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 35.5037i | 0.178410i | 0.996013 | + | 0.0892052i | \(0.0284327\pi\) | ||||
−0.996013 | + | 0.0892052i | \(0.971567\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 110.794i | 0.551214i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 466.681 | 2.27649 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −72.0000 | −0.347826 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 75.3341i | − 0.360450i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.69259 | 0.0459364 | 0.0229682 | − | 0.999736i | \(-0.492688\pi\) | ||||
0.0229682 | + | 0.999736i | \(0.492688\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 37.3436i | 0.175322i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 179.918i | − 0.836826i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 107.154 | 0.489286 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 150.374 | 0.680423 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 430.462i | 1.93032i | 0.261657 | + | 0.965161i | \(0.415731\pi\) | ||||
−0.261657 | + | 0.965161i | \(0.584269\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 200.340 | 0.890402 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 190.145i | 0.837642i | 0.908069 | + | 0.418821i | \(0.137557\pi\) | ||||
−0.908069 | + | 0.418821i | \(0.862443\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 115.667i | − 0.505094i | −0.967585 | − | 0.252547i | \(-0.918732\pi\) | ||||
0.967585 | − | 0.252547i | \(-0.0812683\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 415.494 | 1.78324 | 0.891618 | − | 0.452788i | \(-0.149570\pi\) | ||||
0.891618 | + | 0.452788i | \(0.149570\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 115.121 | 0.489875 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 6.60470i | − 0.0278679i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −82.3074 | −0.344382 | −0.172191 | − | 0.985064i | \(-0.555085\pi\) | ||||
−0.172191 | + | 0.985064i | \(0.555085\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − 201.730i | − 0.837054i | −0.908204 | − | 0.418527i | \(-0.862547\pi\) | ||||
0.908204 | − | 0.418527i | \(-0.137453\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 15.5885i | − 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 128.714 | 0.521109 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 174.088 | 0.699147 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 117.068i | − 0.466408i | −0.972428 | − | 0.233204i | \(-0.925079\pi\) | ||||
0.972428 | − | 0.233204i | \(-0.0749210\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −110.241 | −0.435736 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − 317.936i | − 1.24681i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 261.102i | 1.01596i | 0.861369 | + | 0.507980i | \(0.169608\pi\) | ||||
−0.861369 | + | 0.507980i | \(0.830392\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 31.7802 | 0.121763 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −454.681 | −1.72882 | −0.864412 | − | 0.502783i | \(-0.832309\pi\) | ||||
−0.864412 | + | 0.502783i | \(0.832309\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 358.363i | 1.35231i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 171.560 | 0.642548 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 139.161i | 0.517325i | 0.965968 | + | 0.258663i | \(0.0832818\pi\) | ||||
−0.965968 | + | 0.258663i | \(0.916718\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 58.7246i | 0.216696i | 0.994113 | + | 0.108348i | \(0.0345561\pi\) | ||||
−0.994113 | + | 0.108348i | \(0.965444\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 306.747 | 1.11544 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −44.7802 | −0.161661 | −0.0808306 | − | 0.996728i | \(-0.525757\pi\) | ||||
−0.0808306 | + | 0.996728i | \(0.525757\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − 167.247i | − 0.599453i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −325.494 | −1.15834 | −0.579171 | − | 0.815206i | \(-0.696624\pi\) | ||||
−0.579171 | + | 0.815206i | \(0.696624\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 333.143i | 1.17719i | 0.808430 | + | 0.588593i | \(0.200318\pi\) | ||||
−0.808430 | + | 0.588593i | \(0.799682\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 272.141i | − 0.954880i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −78.1206 | −0.270314 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −110.154 | −0.378535 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 405.135i | 1.38271i | 0.722514 | + | 0.691356i | \(0.242986\pi\) | ||||
−0.722514 | + | 0.691356i | \(0.757014\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 605.142 | 2.05133 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 23.8679i | − 0.0803634i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 188.355i | − 0.629951i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −208.681 | −0.688716 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1066.11 | −3.49544 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 24.9530i | − 0.0812801i | −0.999174 | − | 0.0406400i | \(-0.987060\pi\) | ||||
0.999174 | − | 0.0406400i | \(-0.0129397\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −32.7140 | −0.105871 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 361.776i | 1.16327i | 0.813451 | + | 0.581634i | \(0.197586\pi\) | ||||
−0.813451 | + | 0.581634i | \(0.802414\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 136.401i | − 0.435785i | −0.975973 | − | 0.217892i | \(-0.930082\pi\) | ||||
0.975973 | − | 0.217892i | \(-0.0699182\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −543.648 | −1.71498 | −0.857489 | − | 0.514503i | \(-0.827977\pi\) | ||||
−0.857489 | + | 0.514503i | \(0.827977\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 48.6595 | 0.152538 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 29.3876i | 0.0915501i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −314.241 | −0.972883 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 524.100i | 1.61262i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 98.3461i | − 0.300753i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 140.099 | 0.423260 | 0.211630 | − | 0.977350i | \(-0.432123\pi\) | ||||
0.211630 | + | 0.977350i | \(0.432123\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 73.2198 | 0.219879 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 612.816i | 1.82930i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 311.681 | 0.924869 | 0.462435 | − | 0.886653i | \(-0.346976\pi\) | ||||
0.462435 | + | 0.886653i | \(0.346976\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 270.847i | 0.798958i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 256.077i | − 0.750960i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −398.241 | −1.15432 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −112.307 | −0.323652 | −0.161826 | − | 0.986819i | \(-0.551738\pi\) | ||||
−0.161826 | + | 0.986819i | \(0.551738\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 211.526i | 0.606091i | 0.952976 | + | 0.303046i | \(0.0980035\pi\) | ||||
−0.952976 | + | 0.303046i | \(0.901997\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 40.7802 | 0.116183 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 91.9065i | 0.260358i | 0.991490 | + | 0.130179i | \(0.0415553\pi\) | ||||
−0.991490 | + | 0.130179i | \(0.958445\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 206.552i | 0.581837i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −470.988 | −1.31195 | −0.655973 | − | 0.754785i | \(-0.727741\pi\) | ||||
−0.655973 | + | 0.754785i | \(0.727741\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 92.0214 | 0.254907 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 173.033i | 0.476676i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 592.681 | 1.62378 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 446.862i | − 1.21761i | −0.793320 | − | 0.608804i | \(-0.791649\pi\) | ||||
0.793320 | − | 0.608804i | \(-0.208351\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − 146.139i | − 0.396041i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −53.2198 | −0.142681 | −0.0713403 | − | 0.997452i | \(-0.522728\pi\) | ||||
−0.0713403 | + | 0.997452i | \(0.522728\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 693.274 | 1.84873 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 83.1384i | 0.220526i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −700.076 | −1.84717 | −0.923583 | − | 0.383398i | \(-0.874754\pi\) | ||||
−0.923583 | + | 0.383398i | \(0.874754\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 43.3013i | − 0.113652i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 623.208i | 1.62718i | 0.581442 | + | 0.813588i | \(0.302489\pi\) | ||||
−0.581442 | + | 0.813588i | \(0.697511\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −56.3405 | −0.145583 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −397.868 | −1.02280 | −0.511398 | − | 0.859344i | \(-0.670872\pi\) | ||||
−0.511398 | + | 0.859344i | \(0.670872\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 459.849i | 1.17609i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −174.660 | −0.444426 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 36.5315i | − 0.0924847i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 338.131i | 0.851715i | 0.904790 | + | 0.425857i | \(0.140027\pi\) | ||||
−0.904790 | + | 0.425857i | \(0.859973\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 19.8677 | 0.0495455 | 0.0247727 | − | 0.999693i | \(-0.492114\pi\) | ||||
0.0247727 | + | 0.999693i | \(0.492114\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 437.527 | 1.08568 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 86.2218i | − 0.212893i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 112.109 | 0.275452 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − 410.280i | − 1.00313i | −0.865120 | − | 0.501565i | \(-0.832758\pi\) | ||||
0.865120 | − | 0.501565i | \(-0.167242\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 74.6871i | − 0.181721i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 962.901 | 2.32024 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −204.274 | −0.489867 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 564.750i | 1.34785i | 0.738799 | + | 0.673926i | \(0.235393\pi\) | ||||
−0.738799 | + | 0.673926i | \(0.764607\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 384.582 | 0.913496 | 0.456748 | − | 0.889596i | \(-0.349014\pi\) | ||||
0.456748 | + | 0.889596i | \(0.349014\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 36.0496i | − 0.0852236i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 1279.53i | − 3.01067i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 62.4397 | 0.145547 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −553.868 | −1.28508 | −0.642538 | − | 0.766254i | \(-0.722119\pi\) | ||||
−0.642538 | + | 0.766254i | \(0.722119\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 221.760i | − 0.512147i | −0.966657 | − | 0.256074i | \(-0.917571\pi\) | ||||
0.966657 | − | 0.256074i | \(-0.0824290\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 175.780 | 0.404092 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 393.614i | 0.900718i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 555.169i | 1.26462i | 0.774714 | + | 0.632311i | \(0.217894\pi\) | ||||
−0.774714 | + | 0.632311i | \(0.782106\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 385.582 | 0.870388 | 0.435194 | − | 0.900337i | \(-0.356680\pi\) | ||||
0.435194 | + | 0.900337i | \(0.356680\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 948.922 | 2.13241 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 306.896i | − 0.686569i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −107.802 | −0.240093 | −0.120046 | − | 0.992768i | \(-0.538304\pi\) | ||||
−0.120046 | + | 0.992768i | \(0.538304\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 223.758i | − 0.496138i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 316.908i | 0.699576i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.0000 | −0.0240700 | −0.0120350 | − | 0.999928i | \(-0.503831\pi\) | ||||
−0.0120350 | + | 0.999928i | \(0.503831\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −99.5603 | −0.216907 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 636.532i | − 1.38076i | −0.723445 | − | 0.690382i | \(-0.757443\pi\) | ||||
0.723445 | − | 0.690382i | \(-0.242557\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −179.660 | −0.388034 | −0.194017 | − | 0.980998i | \(-0.562152\pi\) | ||||
−0.194017 | + | 0.980998i | \(0.562152\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − 925.067i | − 1.98939i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 45.7949i | − 0.0980618i | −0.998797 | − | 0.0490309i | \(-0.984387\pi\) | ||||
0.998797 | − | 0.0490309i | \(-0.0156133\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −146.241 | −0.310491 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −86.2645 | −0.182377 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 1095.23i | − 2.30575i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 112.220 | 0.235262 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 162.065i | 0.338340i | 0.985587 | + | 0.169170i | \(0.0541086\pi\) | ||||
−0.985587 | + | 0.169170i | \(0.945891\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 191.547i | 0.398226i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −609.274 | −1.25624 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 664.802 | 1.36510 | 0.682548 | − | 0.730841i | \(-0.260872\pi\) | ||||
0.682548 | + | 0.730841i | \(0.260872\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 249.301i | 0.509818i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 379.955 | 0.773840 | 0.386920 | − | 0.922113i | \(-0.373539\pi\) | ||||
0.386920 | + | 0.922113i | \(0.373539\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 202.973i | − 0.411711i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − 132.017i | − 0.266700i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −526.099 | −1.05431 | −0.527154 | − | 0.849770i | \(-0.676741\pi\) | ||||
−0.527154 | + | 0.849770i | \(0.676741\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −214.307 | −0.427759 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 573.504i | − 1.14017i | −0.821587 | − | 0.570084i | \(-0.806911\pi\) | ||||
0.821587 | − | 0.570084i | \(-0.193089\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1154.24 | −2.28563 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 186.034i | − 0.366930i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 116.091i | 0.228077i | 0.993476 | + | 0.114039i | \(0.0363787\pi\) | ||||
−0.993476 | + | 0.114039i | \(0.963621\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −85.2198 | −0.166121 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −180.945 | −0.351350 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 55.1965i | − 0.106763i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 232.879 | 0.448708 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 164.653i | − 0.316032i | −0.987437 | − | 0.158016i | \(-0.949490\pi\) | ||||
0.987437 | − | 0.158016i | \(-0.0505098\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 503.316i | − 0.962363i | −0.876621 | − | 0.481181i | \(-0.840208\pi\) | ||||
0.876621 | − | 0.481181i | \(-0.159792\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1068.18 | −2.02690 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 47.0000 | 0.0888469 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 189.498i | − 0.356870i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 382.307 | 0.717275 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 162.547i | 0.303825i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 239.023i | 0.445108i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −562.099 | −1.03900 | −0.519500 | − | 0.854470i | \(-0.673882\pi\) | ||||
−0.519500 | + | 0.854470i | \(0.673882\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −170.714 | −0.314390 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 543.965i | − 0.998101i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −200.374 | −0.366314 | −0.183157 | − | 0.983084i | \(-0.558632\pi\) | ||||
−0.183157 | + | 0.983084i | \(0.558632\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 333.848i | 0.608102i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 173.738i | − 0.315313i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 404.988 | 0.729709 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 436.593 | 0.783830 | 0.391915 | − | 0.920001i | \(-0.371813\pi\) | ||||
0.391915 | + | 0.920001i | \(0.371813\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 147.389i | − 0.263666i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −152.440 | −0.271728 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 109.594i | 0.194661i | 0.995252 | + | 0.0973307i | \(0.0310305\pi\) | ||||
−0.995252 | + | 0.0973307i | \(0.968970\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1498.09i | 2.65149i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 530.615 | 0.932539 | 0.466270 | − | 0.884643i | \(-0.345598\pi\) | ||||
0.466270 | + | 0.884643i | \(0.345598\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 877.263 | 1.53636 | 0.768181 | − | 0.640233i | \(-0.221162\pi\) | ||||
0.768181 | + | 0.640233i | \(0.221162\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 288.053i | − 0.502710i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1602.72 | −2.78735 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 610.969i | − 1.05887i | −0.848350 | − | 0.529436i | \(-0.822404\pi\) | ||||
0.848350 | − | 0.529436i | \(-0.177596\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 109.652i | 0.189381i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 171.823 | 0.294722 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 225.560 | 0.385573 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 352.196i | 0.599993i | 0.953940 | + | 0.299997i | \(0.0969856\pi\) | ||||
−0.953940 | + | 0.299997i | \(0.903014\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −914.317 | −1.55232 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − 319.230i | − 0.540152i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 331.577i | − 0.559151i | −0.960124 | − | 0.279575i | \(-0.909806\pi\) | ||||
0.960124 | − | 0.279575i | \(-0.0901937\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 61.4942 | 0.103005 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 365.230 | 0.609732 | 0.304866 | − | 0.952395i | \(-0.401388\pi\) | ||||
0.304866 | + | 0.952395i | \(0.401388\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − 749.102i | − 1.24643i | −0.782052 | − | 0.623213i | \(-0.785827\pi\) | ||||
0.782052 | − | 0.623213i | \(-0.214173\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 191.901 | 0.318243 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 957.069i | 1.58193i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1058.69i | 1.74413i | 0.489389 | + | 0.872066i | \(0.337220\pi\) | ||||
−0.489389 | + | 0.872066i | \(0.662780\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 94.3074 | 0.154349 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 218.572 | 0.356561 | 0.178281 | − | 0.983980i | \(-0.442947\pi\) | ||||
0.178281 | + | 0.983980i | \(0.442947\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − 808.315i | − 1.31433i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 559.669 | 0.907082 | 0.453541 | − | 0.891236i | \(-0.350161\pi\) | ||||
0.453541 | + | 0.891236i | \(0.350161\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 531.345i | 0.858393i | 0.903211 | + | 0.429197i | \(0.141203\pi\) | ||||
−0.903211 | + | 0.429197i | \(0.858797\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 124.708i | 0.200817i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2165.09 | 3.46414 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −130.483 | −0.208106 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 467.640i | − 0.743466i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1086.53 | 1.72191 | 0.860957 | − | 0.508678i | \(-0.169866\pi\) | ||||
0.860957 | + | 0.508678i | \(0.169866\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 16.7881i | − 0.0265214i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 239.505i | − 0.377173i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 64.6810 | 0.101222 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 463.868 | 0.723663 | 0.361831 | − | 0.932244i | \(-0.382152\pi\) | ||||
0.361831 | + | 0.932244i | \(0.382152\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 1055.85i | − 1.64206i | −0.570883 | − | 0.821032i | \(-0.693399\pi\) | ||||
0.570883 | − | 0.821032i | \(-0.306601\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −311.626 | −0.483142 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 788.178i | − 1.21820i | −0.793092 | − | 0.609102i | \(-0.791530\pi\) | ||||
0.793092 | − | 0.609102i | \(-0.208470\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − 290.146i | − 0.447066i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1015.76 | −1.55552 | −0.777762 | − | 0.628559i | \(-0.783645\pi\) | ||||
−0.777762 | + | 0.628559i | \(0.783645\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −966.064 | −1.47491 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 185.596i | − 0.282490i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1254.55 | −1.90372 | −0.951858 | − | 0.306540i | \(-0.900829\pi\) | ||||
−0.951858 | + | 0.306540i | \(0.900829\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 624.330i | 0.944524i | 0.881458 | + | 0.472262i | \(0.156562\pi\) | ||||
−0.881458 | + | 0.472262i | \(0.843438\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 260.455i | − 0.392843i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −254.241 | −0.381171 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 745.582 | 1.11447 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 511.164i | 0.761794i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 41.4826 | 0.0616383 | 0.0308191 | − | 0.999525i | \(-0.490188\pi\) | ||||
0.0308191 | + | 0.999525i | \(0.490188\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 347.000i | − 0.514074i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 721.446i | 1.06565i | 0.846225 | + | 0.532826i | \(0.178870\pi\) | ||||
−0.846225 | + | 0.532826i | \(0.821130\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 329.340 | 0.483613 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −839.516 | −1.22916 | −0.614580 | − | 0.788855i | \(-0.710674\pi\) | ||||
−0.614580 | + | 0.788855i | \(0.710674\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 413.104i | − 0.603072i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −200.340 | −0.291616 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 293.573i | 0.426085i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 555.911i | 0.804502i | 0.915529 | + | 0.402251i | \(0.131772\pi\) | ||||
−0.915529 | + | 0.402251i | \(0.868228\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1129.87 | −1.62571 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −933.362 | −1.33911 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 719.657i | − 1.02955i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −994.769 | −1.41907 | −0.709535 | − | 0.704670i | \(-0.751095\pi\) | ||||
−0.709535 | + | 0.704670i | \(0.751095\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 400.282i | − 0.569392i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − 199.395i | − 0.282829i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −835.977 | −1.17909 | −0.589546 | − | 0.807735i | \(-0.700693\pi\) | ||||
−0.589546 | + | 0.807735i | \(0.700693\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −11.4397 | −0.0160896 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1337.98i | 1.87655i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 345.362 | 0.483024 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 142.561i | 0.198829i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 479.327i | − 0.666657i | −0.942811 | − | 0.333329i | \(-0.891828\pi\) | ||||
0.942811 | − | 0.333329i | \(-0.108172\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −349.407 | −0.483273 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 707.428 | 0.975763 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 949.487i | − 1.30603i | −0.757343 | − | 0.653017i | \(-0.773503\pi\) | ||||
0.757343 | − | 0.653017i | \(-0.226497\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 359.835i | 0.492251i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 448.106i | − 0.611331i | −0.952139 | − | 0.305666i | \(-0.901121\pi\) | ||||
0.952139 | − | 0.305666i | \(-0.0988790\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 293.825 | 0.398677 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 58.0992 | 0.0786187 | 0.0393093 | − | 0.999227i | \(-0.487484\pi\) | ||||
0.0393093 | + | 0.999227i | \(0.487484\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 222.939i | − 0.300863i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 386.043 | 0.519573 | 0.259787 | − | 0.965666i | \(-0.416348\pi\) | ||||
0.259787 | + | 0.965666i | \(0.416348\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − 1697.48i | − 2.27850i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 301.529i | − 0.403653i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −550.362 | −0.732839 | −0.366419 | − | 0.930450i | \(-0.619416\pi\) | ||||
−0.366419 | + | 0.930450i | \(0.619416\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −202.769 | −0.269281 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1752.86i | 2.32167i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 379.187 | 0.500907 | 0.250454 | − | 0.968129i | \(-0.419420\pi\) | ||||
0.250454 | + | 0.968129i | \(0.419420\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 190.943i | 0.251572i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 515.706i | − 0.677669i | −0.940846 | − | 0.338835i | \(-0.889967\pi\) | ||||
0.940846 | − | 0.338835i | \(-0.110033\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −550.681 | −0.719844 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 495.735 | 0.646330 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 548.514i | 0.713282i | 0.934241 | + | 0.356641i | \(0.116078\pi\) | ||||
−0.934241 | + | 0.356641i | \(0.883922\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 452.241 | 0.586565 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 119.848i | 0.155043i | 0.996991 | + | 0.0775216i | \(0.0247007\pi\) | ||||
−0.996991 | + | 0.0775216i | \(0.975299\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 3722.94i | − 4.80379i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −798.922 | −1.02557 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 99.0349 | 0.126805 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 55.0449i | − 0.0702999i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −808.879 | −1.03042 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 1012.78i | − 1.28689i | −0.765491 | − | 0.643447i | \(-0.777504\pi\) | ||||
0.765491 | − | 0.643447i | \(-0.222496\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 787.531i | 0.998138i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −873.362 | −1.10134 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 620.702 | 0.780758 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1067.63i | 1.33956i | 0.742561 | + | 0.669779i | \(0.233611\pi\) | ||||
−0.742561 | + | 0.669779i | \(0.766389\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −230.241 | −0.288162 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − 297.151i | − 0.370975i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 284.171i | − 0.353887i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 241.033 | 0.298678 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −851.055 | −1.05198 | −0.525992 | − | 0.850490i | \(-0.676306\pi\) | ||||
−0.525992 | + | 0.850490i | \(0.676306\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 364.378i | 0.449294i | 0.974440 | + | 0.224647i | \(0.0721229\pi\) | ||||
−0.974440 | + | 0.224647i | \(0.927877\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 101.714 | 0.125110 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1378.91i | 1.69192i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 308.005i | 0.376995i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 43.0098 | 0.0523871 | 0.0261936 | − | 0.999657i | \(-0.491661\pi\) | ||||
0.0261936 | + | 0.999657i | \(0.491661\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −663.494 | −0.806190 | −0.403095 | − | 0.915158i | \(-0.632066\pi\) | ||||
−0.403095 | + | 0.915158i | \(0.632066\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − 531.302i | − 0.644002i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 684.811 | 0.828067 | 0.414034 | − | 0.910262i | \(-0.364120\pi\) | ||||
0.414034 | + | 0.910262i | \(0.364120\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1247.87i | 1.50527i | 0.658438 | + | 0.752635i | \(0.271217\pi\) | ||||
−0.658438 | + | 0.752635i | \(0.728783\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 77.5615i | 0.0933352i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1185.36 | −1.41960 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −289.681 | −0.346094 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 1289.61i | − 1.53708i | −0.639802 | − | 0.768540i | \(-0.720984\pi\) | ||||
0.639802 | − | 0.768540i | \(-0.279016\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −728.780 | −0.866564 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 563.772i | 0.668769i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 1028.98i | − 1.21772i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 577.021 | 0.679648 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −585.759 | −0.688318 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 141.122i | − 0.165442i | −0.996573 | − | 0.0827208i | \(-0.973639\pi\) | ||||
0.996573 | − | 0.0827208i | \(-0.0263610\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −471.362 | −0.551300 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 163.028i | − 0.190232i | −0.995466 | − | 0.0951158i | \(-0.969678\pi\) | ||||
0.995466 | − | 0.0951158i | \(-0.0303221\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 305.400i | 0.355530i | 0.984073 | + | 0.177765i | \(0.0568867\pi\) | ||||
−0.984073 | + | 0.177765i | \(0.943113\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 495.362 | 0.574000 | 0.287000 | − | 0.957931i | \(-0.407342\pi\) | ||||
0.287000 | + | 0.957931i | \(0.407342\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1288.09 | 1.48912 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 135.309i | 0.156066i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −17.5156 | −0.0201561 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 502.022i | 0.576374i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 190.792i | 0.218547i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −90.7900 | −0.103523 | −0.0517617 | − | 0.998659i | \(-0.516484\pi\) | ||||
−0.0517617 | + | 0.998659i | \(0.516484\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 701.714 | 0.798309 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 1403.61i | − 1.59320i | −0.604508 | − | 0.796599i | \(-0.706630\pi\) | ||||
0.604508 | − | 0.796599i | \(-0.293370\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1595.94 | −1.80741 | −0.903705 | − | 0.428155i | \(-0.859164\pi\) | ||||
−0.903705 | + | 0.428155i | \(0.859164\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 1048.14i | − 1.18434i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 205.548i | 0.231734i | 0.993265 | + | 0.115867i | \(0.0369646\pi\) | ||||
−0.993265 | + | 0.115867i | \(0.963035\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −41.3405 | −0.0463978 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −197.078 | −0.220692 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1322.07i | 1.47717i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −326.241 | −0.363703 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 590.572i | − 0.656921i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 716.725i | − 0.795478i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −944.241 | −1.04336 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −410.757 | −0.452874 | −0.226437 | − | 0.974026i | \(-0.572708\pi\) | ||||
−0.226437 | + | 0.974026i | \(0.572708\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 361.446i | 0.397630i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −800.218 | −0.878395 | −0.439198 | − | 0.898390i | \(-0.644737\pi\) | ||||
−0.439198 | + | 0.898390i | \(0.644737\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 461.679i | − 0.505673i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1846.55i | 2.01809i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1432.14 | 1.55837 | 0.779185 | − | 0.626794i | \(-0.215633\pi\) | ||||
0.779185 | + | 0.626794i | \(0.215633\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −43.2198 | −0.0469271 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 169.209i | 0.183325i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1629.88 | 1.76203 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 56.6624i | 0.0611244i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 337.110i | − 0.362874i | −0.983403 | − | 0.181437i | \(-0.941925\pi\) | ||||
0.983403 | − | 0.181437i | \(-0.0580748\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 626.615 | 0.671613 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −843.164 | −0.901779 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 53.3634i | − 0.0569513i | −0.999594 | − | 0.0284756i | \(-0.990935\pi\) | ||||
0.999594 | − | 0.0284756i | \(-0.00906531\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −236.253 | −0.251601 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1271.23i | 1.35094i | 0.737388 | + | 0.675470i | \(0.236059\pi\) | ||||
−0.737388 | + | 0.675470i | \(0.763941\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1169.11i | 1.23978i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −532.856 | −0.562678 | −0.281339 | − | 0.959608i | \(-0.590779\pi\) | ||||
−0.281339 | + | 0.959608i | \(0.590779\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 485.527 | 0.511620 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 941.626i | 0.990143i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1665.54 | −1.74768 | −0.873839 | − | 0.486215i | \(-0.838377\pi\) | ||||
−0.873839 | + | 0.486215i | \(0.838377\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 1593.26i | − 1.66833i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 84.2808i | − 0.0880677i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2146.97 | −2.23409 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 50.9008 | 0.0528565 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 606.497i | 0.628495i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1328.19 | −1.37351 | −0.686756 | − | 0.726888i | \(-0.740966\pi\) | ||||
−0.686756 | + | 0.726888i | \(0.740966\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 544.282i | 0.561694i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 213.834i | 0.220221i | 0.993919 | + | 0.110110i | \(0.0351204\pi\) | ||||
−0.993919 | + | 0.110110i | \(0.964880\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 907.769 | 0.931045 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1016.24 | −1.04017 | −0.520083 | − | 0.854116i | \(-0.674099\pi\) | ||||
−0.520083 | + | 0.854116i | \(0.674099\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 454.977i | − 0.464736i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −170.340 | −0.173640 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 416.656i | 0.423862i | 0.977285 | + | 0.211931i | \(0.0679751\pi\) | ||||
−0.977285 | + | 0.211931i | \(0.932025\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − 1765.70i | − 1.79259i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 450.724 | 0.455737 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1246.43 | 1.25775 | 0.628874 | − | 0.777507i | \(-0.283516\pi\) | ||||
0.628874 | + | 0.777507i | \(0.283516\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 242.659i | − 0.244370i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 340.132 | 0.341841 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 709.666i | 0.711801i | 0.934524 | + | 0.355901i | \(0.115826\pi\) | ||||
−0.934524 | + | 0.355901i | \(0.884174\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − 126.820i | − 0.126947i |
(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 | 2352.3.f.f.97.1 | 4 | ||
4.3 | odd | 2 | 588.3.d.b.97.3 | 4 | |||
7.2 | even | 3 | 336.3.bh.f.241.1 | 4 | |||
7.3 | odd | 6 | 336.3.bh.f.145.1 | 4 | |||
7.6 | odd | 2 | inner | 2352.3.f.f.97.4 | 4 | ||
12.11 | even | 2 | 1764.3.d.f.685.4 | 4 | |||
21.2 | odd | 6 | 1008.3.cg.m.577.2 | 4 | |||
21.17 | even | 6 | 1008.3.cg.m.145.2 | 4 | |||
28.3 | even | 6 | 84.3.m.b.61.1 | ✓ | 4 | ||
28.11 | odd | 6 | 588.3.m.d.313.2 | 4 | |||
28.19 | even | 6 | 588.3.m.d.325.2 | 4 | |||
28.23 | odd | 6 | 84.3.m.b.73.1 | yes | 4 | ||
28.27 | even | 2 | 588.3.d.b.97.2 | 4 | |||
84.11 | even | 6 | 1764.3.z.h.901.1 | 4 | |||
84.23 | even | 6 | 252.3.z.e.73.2 | 4 | |||
84.47 | odd | 6 | 1764.3.z.h.325.1 | 4 | |||
84.59 | odd | 6 | 252.3.z.e.145.2 | 4 | |||
84.83 | odd | 2 | 1764.3.d.f.685.1 | 4 | |||
140.3 | odd | 12 | 2100.3.be.d.649.1 | 8 | |||
140.23 | even | 12 | 2100.3.be.d.1249.4 | 8 | |||
140.59 | even | 6 | 2100.3.bd.f.901.2 | 4 | |||
140.79 | odd | 6 | 2100.3.bd.f.1501.1 | 4 | |||
140.87 | odd | 12 | 2100.3.be.d.649.4 | 8 | |||
140.107 | even | 12 | 2100.3.be.d.1249.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.3.m.b.61.1 | ✓ | 4 | 28.3 | even | 6 | ||
84.3.m.b.73.1 | yes | 4 | 28.23 | odd | 6 | ||
252.3.z.e.73.2 | 4 | 84.23 | even | 6 | |||
252.3.z.e.145.2 | 4 | 84.59 | odd | 6 | |||
336.3.bh.f.145.1 | 4 | 7.3 | odd | 6 | |||
336.3.bh.f.241.1 | 4 | 7.2 | even | 3 | |||
588.3.d.b.97.2 | 4 | 28.27 | even | 2 | |||
588.3.d.b.97.3 | 4 | 4.3 | odd | 2 | |||
588.3.m.d.313.2 | 4 | 28.11 | odd | 6 | |||
588.3.m.d.325.2 | 4 | 28.19 | even | 6 | |||
1008.3.cg.m.145.2 | 4 | 21.17 | even | 6 | |||
1008.3.cg.m.577.2 | 4 | 21.2 | odd | 6 | |||
1764.3.d.f.685.1 | 4 | 84.83 | odd | 2 | |||
1764.3.d.f.685.4 | 4 | 12.11 | even | 2 | |||
1764.3.z.h.325.1 | 4 | 84.47 | odd | 6 | |||
1764.3.z.h.901.1 | 4 | 84.11 | even | 6 | |||
2100.3.bd.f.901.2 | 4 | 140.59 | even | 6 | |||
2100.3.bd.f.1501.1 | 4 | 140.79 | odd | 6 | |||
2100.3.be.d.649.1 | 8 | 140.3 | odd | 12 | |||
2100.3.be.d.649.4 | 8 | 140.87 | odd | 12 | |||
2100.3.be.d.1249.1 | 8 | 140.107 | even | 12 | |||
2100.3.be.d.1249.4 | 8 | 140.23 | even | 12 | |||
2352.3.f.f.97.1 | 4 | 1.1 | even | 1 | trivial | ||
2352.3.f.f.97.4 | 4 | 7.6 | odd | 2 | inner |