Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [912,4,Mod(1,912)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(912, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("912.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 912 = 2^{4} \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 912.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: | \(53.8097419252\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 228) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 912.1 |
$q$-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 | ||||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.00000 | 0.357771 | 0.178885 | − | 0.983870i | \(-0.442751\pi\) | ||||
0.178885 | + | 0.983870i | \(0.442751\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 12.0000 | 0.647939 | 0.323970 | − | 0.946068i | \(-0.394982\pi\) | ||||
0.323970 | + | 0.946068i | \(0.394982\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −40.0000 | −1.09640 | −0.548202 | − | 0.836346i | \(-0.684688\pi\) | ||||
−0.548202 | + | 0.836346i | \(0.684688\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −40.0000 | −0.853385 | −0.426692 | − | 0.904397i | \(-0.640321\pi\) | ||||
−0.426692 | + | 0.904397i | \(0.640321\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 12.0000 | 0.206559 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −66.0000 | −0.941609 | −0.470804 | − | 0.882238i | \(-0.656036\pi\) | ||||
−0.470804 | + | 0.882238i | \(0.656036\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 19.0000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 36.0000 | 0.374088 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 98.0000 | 0.888453 | 0.444226 | − | 0.895915i | \(-0.353479\pi\) | ||||
0.444226 | + | 0.895915i | \(0.353479\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −109.000 | −0.872000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −130.000 | −0.832427 | −0.416214 | − | 0.909267i | \(-0.636643\pi\) | ||||
−0.416214 | + | 0.909267i | \(0.636643\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −262.000 | −1.51795 | −0.758977 | − | 0.651117i | \(-0.774301\pi\) | ||||
−0.758977 | + | 0.651117i | \(0.774301\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −120.000 | −0.633010 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 48.0000 | 0.231814 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −296.000 | −1.31519 | −0.657596 | − | 0.753371i | \(-0.728427\pi\) | ||||
−0.657596 | + | 0.753371i | \(0.728427\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −120.000 | −0.492702 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −442.000 | −1.68363 | −0.841815 | − | 0.539767i | \(-0.818512\pi\) | ||||
−0.841815 | + | 0.539767i | \(0.818512\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 164.000 | 0.581622 | 0.290811 | − | 0.956780i | \(-0.406075\pi\) | ||||
0.290811 | + | 0.956780i | \(0.406075\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 36.0000 | 0.119257 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 542.000 | 1.68210 | 0.841051 | − | 0.540955i | \(-0.181937\pi\) | ||||
0.841051 | + | 0.540955i | \(0.181937\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −199.000 | −0.580175 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −198.000 | −0.543638 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 334.000 | 0.865631 | 0.432815 | − | 0.901483i | \(-0.357520\pi\) | ||||
0.432815 | + | 0.901483i | \(0.357520\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −160.000 | −0.392262 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 57.0000 | 0.132453 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −60.0000 | −0.132396 | −0.0661978 | − | 0.997807i | \(-0.521087\pi\) | ||||
−0.0661978 | + | 0.997807i | \(0.521087\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 614.000 | 1.28876 | 0.644382 | − | 0.764703i | \(-0.277115\pi\) | ||||
0.644382 | + | 0.764703i | \(0.277115\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 108.000 | 0.215980 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −160.000 | −0.305316 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 294.000 | 0.512948 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −400.000 | −0.668609 | −0.334305 | − | 0.942465i | \(-0.608501\pi\) | ||||
−0.334305 | + | 0.942465i | \(0.608501\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 318.000 | 0.509850 | 0.254925 | − | 0.966961i | \(-0.417949\pi\) | ||||
0.254925 | + | 0.966961i | \(0.417949\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −327.000 | −0.503449 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −480.000 | −0.710404 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1154.00 | −1.64348 | −0.821741 | − | 0.569861i | \(-0.806997\pi\) | ||||
−0.821741 | + | 0.569861i | \(0.806997\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 636.000 | 0.841085 | 0.420543 | − | 0.907273i | \(-0.361840\pi\) | ||||
0.420543 | + | 0.907273i | \(0.361840\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −264.000 | −0.336880 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −390.000 | −0.480602 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −630.000 | −0.750336 | −0.375168 | − | 0.926957i | \(-0.622415\pi\) | ||||
−0.375168 | + | 0.926957i | \(0.622415\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −480.000 | −0.552941 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −786.000 | −0.876391 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 76.0000 | 0.0820783 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1006.00 | 1.05303 | 0.526515 | − | 0.850166i | \(-0.323499\pi\) | ||||
0.526515 | + | 0.850166i | \(0.323499\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −360.000 | −0.365468 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −140.000 | −0.137926 | −0.0689630 | − | 0.997619i | \(-0.521969\pi\) | ||||
−0.0689630 | + | 0.997619i | \(0.521969\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −66.0000 | −0.0631376 | −0.0315688 | − | 0.999502i | \(-0.510050\pi\) | ||||
−0.0315688 | + | 0.999502i | \(0.510050\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 144.000 | 0.133838 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1012.00 | −0.914334 | −0.457167 | − | 0.889381i | \(-0.651136\pi\) | ||||
−0.457167 | + | 0.889381i | \(0.651136\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −588.000 | −0.516699 | −0.258349 | − | 0.966052i | \(-0.583179\pi\) | ||||
−0.258349 | + | 0.966052i | \(0.583179\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −888.000 | −0.759326 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 622.000 | 0.517813 | 0.258906 | − | 0.965902i | \(-0.416638\pi\) | ||||
0.258906 | + | 0.965902i | \(0.416638\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 392.000 | 0.317863 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −360.000 | −0.284462 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −792.000 | −0.610105 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 269.000 | 0.202104 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1326.00 | −0.972044 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −936.000 | −0.669747 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −198.000 | −0.138344 | −0.0691719 | − | 0.997605i | \(-0.522036\pi\) | ||||
−0.0691719 | + | 0.997605i | \(0.522036\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 492.000 | 0.335800 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1524.00 | 1.01643 | 0.508216 | − | 0.861230i | \(-0.330305\pi\) | ||||
0.508216 | + | 0.861230i | \(0.330305\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 228.000 | 0.148647 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 108.000 | 0.0688530 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1546.00 | −0.964115 | −0.482057 | − | 0.876140i | \(-0.660110\pi\) | ||||
−0.482057 | + | 0.876140i | \(0.660110\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2508.00 | −1.53040 | −0.765201 | − | 0.643792i | \(-0.777360\pi\) | ||||
−0.765201 | + | 0.643792i | \(0.777360\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1626.00 | 0.971162 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1600.00 | 0.935655 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −520.000 | −0.297818 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −597.000 | −0.334964 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 936.000 | 0.514632 | 0.257316 | − | 0.966327i | \(-0.417162\pi\) | ||||
0.257316 | + | 0.966327i | \(0.417162\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −98.0000 | −0.0528154 | −0.0264077 | − | 0.999651i | \(-0.508407\pi\) | ||||
−0.0264077 | + | 0.999651i | \(0.508407\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −594.000 | −0.313870 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1048.00 | −0.543080 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −926.000 | −0.470719 | −0.235359 | − | 0.971908i | \(-0.575627\pi\) | ||||
−0.235359 | + | 0.971908i | \(0.575627\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1002.00 | 0.499772 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1176.00 | 0.575663 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1268.00 | −0.609309 | −0.304655 | − | 0.952463i | \(-0.598541\pi\) | ||||
−0.304655 | + | 0.952463i | \(0.598541\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −480.000 | −0.226472 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 612.000 | 0.283581 | 0.141790 | − | 0.989897i | \(-0.454714\pi\) | ||||
0.141790 | + | 0.989897i | \(0.454714\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −597.000 | −0.271734 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 171.000 | 0.0764719 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3294.00 | −1.44762 | −0.723810 | − | 0.690000i | \(-0.757611\pi\) | ||||
−0.723810 | + | 0.690000i | \(0.757611\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1308.00 | −0.565003 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −180.000 | −0.0764386 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3684.00 | 1.53830 | 0.769148 | − | 0.639070i | \(-0.220681\pi\) | ||||
0.769148 | + | 0.639070i | \(0.220681\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3404.00 | −1.39789 | −0.698943 | − | 0.715177i | \(-0.746346\pi\) | ||||
−0.698943 | + | 0.715177i | \(0.746346\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1842.00 | 0.744069 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1184.00 | −0.470537 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2640.00 | 1.03238 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 324.000 | 0.124696 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2534.00 | −0.959968 | −0.479984 | − | 0.877277i | \(-0.659357\pi\) | ||||
−0.479984 | + | 0.877277i | \(0.659357\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5118.00 | 1.90882 | 0.954409 | − | 0.298503i | \(-0.0964874\pi\) | ||||
0.954409 | + | 0.298503i | \(0.0964874\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −480.000 | −0.176274 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 328.000 | 0.118625 | 0.0593123 | − | 0.998239i | \(-0.481109\pi\) | ||||
0.0593123 | + | 0.998239i | \(0.481109\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1348.00 | 0.480187 | 0.240093 | − | 0.970750i | \(-0.422822\pi\) | ||||
0.240093 | + | 0.970750i | \(0.422822\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1560.00 | −0.539362 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1768.00 | −0.602354 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 882.000 | 0.296151 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −760.000 | −0.251533 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2196.00 | 0.716488 | 0.358244 | − | 0.933628i | \(-0.383376\pi\) | ||||
0.358244 | + | 0.933628i | \(0.383376\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1200.00 | −0.386022 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 656.000 | 0.208088 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3144.00 | −0.983542 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 954.000 | 0.294362 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2640.00 | 0.803555 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2942.00 | −0.883457 | −0.441728 | − | 0.897149i | \(-0.645635\pi\) | ||||
−0.441728 | + | 0.897149i | \(0.645635\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −981.000 | −0.290667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1340.00 | −0.391801 | −0.195901 | − | 0.980624i | \(-0.562763\pi\) | ||||
−0.195901 | + | 0.980624i | \(0.562763\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6466.00 | −1.86587 | −0.932937 | − | 0.360039i | \(-0.882763\pi\) | ||||
−0.932937 | + | 0.360039i | \(0.882763\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1440.00 | −0.410152 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −294.000 | −0.0826634 | −0.0413317 | − | 0.999145i | \(-0.513160\pi\) | ||||
−0.0413317 | + | 0.999145i | \(0.513160\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2168.00 | 0.601807 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3462.00 | −0.948865 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3546.00 | −0.959714 | −0.479857 | − | 0.877347i | \(-0.659311\pi\) | ||||
−0.479857 | + | 0.877347i | \(0.659311\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1514.00 | −0.404669 | −0.202335 | − | 0.979316i | \(-0.564853\pi\) | ||||
−0.202335 | + | 0.979316i | \(0.564853\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −796.000 | −0.207570 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −760.000 | −0.195780 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1908.00 | 0.485601 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7364.00 | 1.85184 | 0.925919 | − | 0.377721i | \(-0.123292\pi\) | ||||
0.925919 | + | 0.377721i | \(0.123292\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3920.00 | −0.974104 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −792.000 | −0.194498 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2002.00 | 0.485920 | 0.242960 | − | 0.970036i | \(-0.421882\pi\) | ||||
0.242960 | + | 0.970036i | \(0.421882\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3552.00 | −0.852164 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1170.00 | −0.277476 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 582.000 | 0.136455 | 0.0682275 | − | 0.997670i | \(-0.478266\pi\) | ||||
0.0682275 | + | 0.997670i | \(0.478266\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1336.00 | 0.309697 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1890.00 | −0.433206 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6090.00 | 1.38035 | 0.690174 | − | 0.723643i | \(-0.257534\pi\) | ||||
0.690174 | + | 0.723643i | \(0.257534\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5452.00 | −1.22209 | −0.611043 | − | 0.791597i | \(-0.709250\pi\) | ||||
−0.611043 | + | 0.791597i | \(0.709250\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1440.00 | −0.319241 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4360.00 | 0.956065 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4894.00 | 1.06156 | 0.530780 | − | 0.847510i | \(-0.321899\pi\) | ||||
0.530780 | + | 0.847510i | \(0.321899\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2358.00 | −0.505985 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4958.00 | 1.05256 | 0.526280 | − | 0.850311i | \(-0.323586\pi\) | ||||
0.526280 | + | 0.850311i | \(0.323586\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1308.00 | 0.274744 | 0.137372 | − | 0.990520i | \(-0.456134\pi\) | ||||
0.137372 | + | 0.990520i | \(0.456134\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 228.000 | 0.0473879 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5304.00 | −1.09089 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −557.000 | −0.113373 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3018.00 | 0.607967 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7722.00 | 1.53967 | 0.769836 | − | 0.638241i | \(-0.220338\pi\) | ||||
0.769836 | + | 0.638241i | \(0.220338\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −240.000 | −0.0473673 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1080.00 | −0.211003 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3920.00 | −0.758192 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1968.00 | 0.376856 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −420.000 | −0.0796316 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2456.00 | 0.461082 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3912.00 | 0.727263 | 0.363631 | − | 0.931543i | \(-0.381537\pi\) | ||||
0.363631 | + | 0.931543i | \(0.381537\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −198.000 | −0.0364525 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1994.00 | −0.363567 | −0.181784 | − | 0.983339i | \(-0.558187\pi\) | ||||
−0.181784 | + | 0.983339i | \(0.558187\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3226.00 | −0.582570 | −0.291285 | − | 0.956636i | \(-0.594083\pi\) | ||||
−0.291285 | + | 0.956636i | \(0.594083\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 432.000 | 0.0772712 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 498.000 | 0.0882349 | 0.0441175 | − | 0.999026i | \(-0.485952\pi\) | ||||
0.0441175 | + | 0.999026i | \(0.485952\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5200.00 | 0.912677 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3036.00 | −0.527891 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1254.00 | −0.216020 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4360.00 | 0.744152 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1764.00 | −0.298316 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6504.00 | 1.08990 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3440.00 | −0.571237 | −0.285619 | − | 0.958343i | \(-0.592199\pi\) | ||||
−0.285619 | + | 0.958343i | \(0.592199\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2664.00 | −0.438397 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6014.00 | −0.972117 | −0.486059 | − | 0.873926i | \(-0.661566\pi\) | ||||
−0.486059 | + | 0.873926i | \(0.661566\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1866.00 | 0.298959 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10480.0 | 1.66429 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6504.00 | −1.02386 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1176.00 | 0.183518 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10144.0 | 1.56933 | 0.784666 | − | 0.619918i | \(-0.212834\pi\) | ||||
0.784666 | + | 0.619918i | \(0.212834\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8818.00 | 1.35248 | 0.676242 | − | 0.736680i | \(-0.263607\pi\) | ||||
0.676242 | + | 0.736680i | \(0.263607\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1080.00 | −0.164234 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8010.00 | 1.20773 | 0.603866 | − | 0.797086i | \(-0.293626\pi\) | ||||
0.603866 | + | 0.797086i | \(0.293626\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1600.00 | −0.239209 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2376.00 | −0.352244 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3426.00 | 0.503670 | 0.251835 | − | 0.967770i | \(-0.418966\pi\) | ||||
0.251835 | + | 0.967770i | \(0.418966\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 361.000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 807.000 | 0.116685 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1272.00 | 0.182410 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8396.00 | 1.19419 | 0.597095 | − | 0.802171i | \(-0.296322\pi\) | ||||
0.597095 | + | 0.802171i | \(0.296322\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3978.00 | −0.561210 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4008.00 | 0.560876 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2200.00 | −0.305393 | −0.152697 | − | 0.988273i | \(-0.548796\pi\) | ||||
−0.152697 | + | 0.988273i | \(0.548796\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2808.00 | −0.386679 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5200.00 | 0.710381 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2304.00 | −0.312265 | −0.156133 | − | 0.987736i | \(-0.549903\pi\) | ||||
−0.156133 | + | 0.987736i | \(0.549903\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −594.000 | −0.0798728 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10376.0 | −1.38431 | −0.692153 | − | 0.721751i | \(-0.743337\pi\) | ||||
−0.692153 | + | 0.721751i | \(0.743337\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1920.00 | −0.254162 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1476.00 | 0.193874 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8436.00 | −1.09954 | −0.549771 | − | 0.835315i | \(-0.685285\pi\) | ||||
−0.549771 | + | 0.835315i | \(0.685285\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6468.00 | −0.836575 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4572.00 | 0.586837 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4616.00 | −0.587990 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9142.00 | −1.15573 | −0.577864 | − | 0.816133i | \(-0.696114\pi\) | ||||
−0.577864 | + | 0.816133i | \(0.696114\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 684.000 | 0.0858216 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6350.00 | 0.790783 | 0.395391 | − | 0.918513i | \(-0.370609\pi\) | ||||
0.395391 | + | 0.918513i | \(0.370609\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10480.0 | 1.29540 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 324.000 | 0.0397523 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11840.0 | 1.44198 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10586.0 | −1.27981 | −0.639907 | − | 0.768452i | \(-0.721027\pi\) | ||||
−0.639907 | + | 0.768452i | \(0.721027\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4638.00 | −0.556632 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −720.000 | −0.0857842 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2544.00 | 0.300916 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7524.00 | −0.883578 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 14856.0 | 1.73213 | 0.866066 | − | 0.499930i | \(-0.166641\pi\) | ||||
0.866066 | + | 0.499930i | \(0.166641\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11696.0 | 1.35399 | 0.676993 | − | 0.735989i | \(-0.263283\pi\) | ||||
0.676993 | + | 0.735989i | \(0.263283\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4878.00 | 0.560701 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7194.00 | 0.821083 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7368.00 | 0.835041 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4800.00 | 0.540201 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1356.00 | −0.151546 | −0.0757729 | − | 0.997125i | \(-0.524142\pi\) | ||||
−0.0757729 | + | 0.997125i | \(0.524142\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10862.0 | 1.20553 | 0.602765 | − | 0.797919i | \(-0.294066\pi\) | ||||
0.602765 | + | 0.797919i | \(0.294066\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1560.00 | −0.171945 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1862.00 | 0.203825 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13838.0 | −1.50445 | −0.752223 | − | 0.658909i | \(-0.771018\pi\) | ||||
−0.752223 | + | 0.658909i | \(0.771018\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1791.00 | −0.193392 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1088.00 | −0.116687 | −0.0583436 | − | 0.998297i | \(-0.518582\pi\) | ||||
−0.0583436 | + | 0.998297i | \(0.518582\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2520.00 | −0.268448 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2808.00 | 0.297123 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10078.0 | −1.05927 | −0.529633 | − | 0.848227i | \(-0.677670\pi\) | ||||
−0.529633 | + | 0.848227i | \(0.677670\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 17680.0 | 1.84594 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −294.000 | −0.0304930 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1920.00 | −0.197826 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 13634.0 | 1.39556 | 0.697781 | − | 0.716311i | \(-0.254171\pi\) | ||||
0.697781 | + | 0.716311i | \(0.254171\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1782.00 | −0.181213 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5848.00 | 0.590821 | 0.295411 | − | 0.955370i | \(-0.404544\pi\) | ||||
0.295411 | + | 0.955370i | \(0.404544\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10508.0 | 1.05475 | 0.527374 | − | 0.849633i | \(-0.323177\pi\) | ||||
0.527374 | + | 0.849633i | \(0.323177\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3144.00 | −0.313547 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 17236.0 | 1.70789 | 0.853947 | − | 0.520359i | \(-0.174202\pi\) | ||||
0.853947 | + | 0.520359i | \(0.174202\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2778.00 | −0.271770 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6560.00 | −0.637694 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2071.00 | −0.200051 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3006.00 | 0.288544 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5890.00 | 0.561839 | 0.280920 | − | 0.959731i | \(-0.409361\pi\) | ||||
0.280920 | + | 0.959731i | \(0.409361\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11840.0 | 1.12236 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3528.00 | 0.332359 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4024.00 | 0.376743 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7982.00 | 0.742708 | 0.371354 | − | 0.928491i | \(-0.378894\pi\) | ||||
0.371354 | + | 0.928491i | \(0.378894\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3804.00 | −0.351785 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2732.00 | 0.251107 | 0.125553 | − | 0.992087i | \(-0.459929\pi\) | ||||
0.125553 | + | 0.992087i | \(0.459929\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8580.00 | 0.783821 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1440.00 | −0.130754 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4800.00 | −0.433218 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17548.0 | −1.57426 | −0.787131 | − | 0.616786i | \(-0.788434\pi\) | ||||
−0.787131 | + | 0.616786i | \(0.788434\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1836.00 | 0.163725 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2082.00 | −0.184556 | −0.0922781 | − | 0.995733i | \(-0.529415\pi\) | ||||
−0.0922781 | + | 0.995733i | \(0.529415\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −560.000 | −0.0493459 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1791.00 | −0.156886 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −15654.0 | −1.36317 | −0.681583 | − | 0.731741i | \(-0.738708\pi\) | ||||
−0.681583 | + | 0.731741i | \(0.738708\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3816.00 | 0.330352 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 513.000 | 0.0441511 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −264.000 | −0.0225888 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −21680.0 | −1.84427 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −9882.00 | −0.835784 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −16382.0 | −1.37756 | −0.688780 | − | 0.724971i | \(-0.741853\pi\) | ||||
−0.688780 | + | 0.724971i | \(0.741853\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 19216.0 | 1.60661 | 0.803305 | − | 0.595568i | \(-0.203073\pi\) | ||||
0.803305 | + | 0.595568i | \(0.203073\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3924.00 | −0.326205 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 17292.0 | 1.42932 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2563.00 | −0.210652 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −540.000 | −0.0441318 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 17680.0 | 1.43678 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4048.00 | −0.327122 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 11052.0 | 0.888136 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7960.00 | 0.636107 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11302.0 | −0.898172 | −0.449086 | − | 0.893489i | \(-0.648250\pi\) | ||||
−0.449086 | + | 0.893489i | \(0.648250\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −10212.0 | −0.807070 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2352.00 | −0.184860 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10120.0 | −0.791042 | −0.395521 | − | 0.918457i | \(-0.629436\pi\) | ||||
−0.395521 | + | 0.918457i | \(0.629436\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5526.00 | 0.429588 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2470.00 | −0.190972 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −13848.0 | −1.06488 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3552.00 | −0.271665 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14984.0 | 1.13984 | 0.569921 | − | 0.821699i | \(-0.306974\pi\) | ||||
0.569921 | + | 0.821699i | \(0.306974\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6560.00 | −0.496348 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7920.00 | 0.596048 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 13020.0 | 0.974649 | 0.487325 | − | 0.873221i | \(-0.337973\pi\) | ||||
0.487325 | + | 0.873221i | \(0.337973\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2488.00 | 0.185258 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 972.000 | 0.0719932 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 11546.0 | 0.850674 | 0.425337 | − | 0.905035i | \(-0.360156\pi\) | ||||
0.425337 | + | 0.905035i | \(0.360156\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2084.00 | −0.152737 | −0.0763684 | − | 0.997080i | \(-0.524333\pi\) | ||||
−0.0763684 | + | 0.997080i | \(0.524333\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7602.00 | −0.554238 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −10682.0 | −0.774731 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9022.00 | −0.650937 | −0.325469 | − | 0.945553i | \(-0.605522\pi\) | ||||
−0.325469 | + | 0.945553i | \(0.605522\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 15354.0 | 1.10206 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7632.00 | 0.544972 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −13360.0 | −0.949082 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1440.00 | −0.101772 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 25800.0 | 1.81411 | 0.907053 | − | 0.421017i | \(-0.138327\pi\) | ||||
0.907053 | + | 0.421017i | \(0.138327\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4978.00 | −0.348243 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 984.000 | 0.0684879 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −19606.0 | −1.35771 | −0.678855 | − | 0.734272i | \(-0.737523\pi\) | ||||
−0.678855 | + | 0.734272i | \(0.737523\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3168.00 | −0.218278 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4044.00 | 0.277236 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 21300.0 | 1.45291 | 0.726456 | − | 0.687213i | \(-0.241166\pi\) | ||||
0.726456 | + | 0.687213i | \(0.241166\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11818.0 | 0.802107 | 0.401053 | − | 0.916055i | \(-0.368644\pi\) | ||||
0.401053 | + | 0.916055i | \(0.368644\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1076.00 | 0.0723068 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −28154.0 | −1.88260 | −0.941298 | − | 0.337577i | \(-0.890393\pi\) | ||||
−0.941298 | + | 0.337577i | \(0.890393\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4680.00 | −0.311401 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −21680.0 | −1.43548 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5966.00 | −0.393090 | −0.196545 | − | 0.980495i | \(-0.562972\pi\) | ||||
−0.196545 | + | 0.980495i | \(0.562972\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5304.00 | −0.347769 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −19278.0 | −1.25787 | −0.628933 | − | 0.777460i | \(-0.716508\pi\) | ||||
−0.628933 | + | 0.777460i | \(0.716508\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10492.0 | −0.681275 | −0.340637 | − | 0.940195i | \(-0.610643\pi\) | ||||
−0.340637 | + | 0.940195i | \(0.610643\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2646.00 | 0.170983 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −7560.00 | −0.486172 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9881.00 | 0.632384 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2280.00 | −0.145222 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 19536.0 | 1.23840 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20768.0 | −1.31024 | −0.655120 | − | 0.755525i | \(-0.727382\pi\) | ||||
−0.655120 | + | 0.755525i | \(0.727382\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6588.00 | 0.413664 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −792.000 | −0.0494954 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7960.00 | 0.495113 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3600.00 | −0.222870 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13110.0 | −0.807822 | −0.403911 | − | 0.914798i | \(-0.632349\pi\) | ||||
−0.403911 | + | 0.914798i | \(0.632349\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11612.0 | 0.712181 | 0.356091 | − | 0.934451i | \(-0.384109\pi\) | ||||
0.356091 | + | 0.934451i | \(0.384109\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1968.00 | 0.120139 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −12094.0 | −0.734875 | −0.367438 | − | 0.930048i | \(-0.619765\pi\) | ||||
−0.367438 | + | 0.930048i | \(0.619765\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2400.00 | 0.145159 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −9432.00 | −0.567848 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 15072.0 | 0.903236 | 0.451618 | − | 0.892211i | \(-0.350847\pi\) | ||||
0.451618 | + | 0.892211i | \(0.350847\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6096.00 | 0.363650 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2862.00 | 0.169950 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −11572.0 | −0.684038 | −0.342019 | − | 0.939693i | \(-0.611111\pi\) | ||||
−0.342019 | + | 0.939693i | \(0.611111\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26680.0 | 1.56994 | 0.784971 | − | 0.619532i | \(-0.212678\pi\) | ||||
0.784971 | + | 0.619532i | \(0.212678\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 7920.00 | 0.463933 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 912.000 | 0.0531817 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −12740.0 | −0.739572 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8826.00 | −0.510064 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −24560.0 | −1.41301 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5726.00 | 0.327966 | 0.163983 | − | 0.986463i | \(-0.447566\pi\) | ||||
0.163983 | + | 0.986463i | \(0.447566\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2943.00 | −0.167816 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −7786.00 | −0.442009 | −0.221005 | − | 0.975273i | \(-0.570934\pi\) | ||||
−0.221005 | + | 0.975273i | \(0.570934\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12072.0 | 0.682299 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4020.00 | −0.226207 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 19372.0 | 1.08528 | 0.542642 | − | 0.839964i | \(-0.317424\pi\) | ||||
0.542642 | + | 0.839964i | \(0.317424\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6184.00 | −0.344932 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −19398.0 | −1.07726 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −13360.0 | −0.738716 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −24996.0 | −1.37611 | −0.688055 | − | 0.725658i | \(-0.741535\pi\) | ||||
−0.688055 | + | 0.725658i | \(0.741535\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4320.00 | −0.236801 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −10032.0 | −0.547533 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 29172.0 | 1.58532 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −882.000 | −0.0477258 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −14972.0 | −0.806683 | −0.403341 | − | 0.915050i | \(-0.632151\pi\) | ||||
−0.403341 | + | 0.915050i | \(0.632151\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5624.00 | −0.301726 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6504.00 | 0.347454 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1680.00 | −0.0893676 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12258.0 | −0.649307 | −0.324654 | − | 0.945833i | \(-0.605248\pi\) | ||||
−0.324654 | + | 0.945833i | \(0.605248\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −10386.0 | −0.547828 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −25676.0 | −1.34863 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6400.00 | 0.334750 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −10638.0 | −0.554091 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 19846.0 | 1.02939 | 0.514695 | − | 0.857374i | \(-0.327905\pi\) | ||||
0.514695 | + | 0.857374i | \(0.327905\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −792.000 | −0.0409093 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −4542.00 | −0.233636 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 14170.0 | 0.725877 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2744.00 | 0.139985 | 0.0699927 | − | 0.997548i | \(-0.477702\pi\) | ||||
0.0699927 | + | 0.997548i | \(0.477702\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −10824.0 | −0.547661 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 834.000 | 0.0420252 | 0.0210126 | − | 0.999779i | \(-0.493311\pi\) | ||||
0.0210126 | + | 0.999779i | \(0.493311\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2388.00 | −0.119840 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 30892.0 | 1.53773 | 0.768864 | − | 0.639413i | \(-0.220822\pi\) | ||||
0.768864 | + | 0.639413i | \(0.220822\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2280.00 | −0.113034 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4636.00 | −0.228908 | −0.114454 | − | 0.993429i | \(-0.536512\pi\) | ||||
−0.114454 | + | 0.993429i | \(0.536512\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3744.00 | 0.184120 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5724.00 | 0.280362 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −12144.0 | −0.592433 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17666.0 | −0.858377 | −0.429189 | − | 0.903215i | \(-0.641200\pi\) | ||||
−0.429189 | + | 0.903215i | \(0.641200\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 22092.0 | 1.06916 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −392.000 | −0.0188958 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −27374.0 | −1.31430 | −0.657150 | − | 0.753760i | \(-0.728238\pi\) | ||||
−0.657150 | + | 0.753760i | \(0.728238\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −11760.0 | −0.562399 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 22350.0 | 1.06463 | 0.532317 | − | 0.846545i | \(-0.321321\pi\) | ||||
0.532317 | + | 0.846545i | \(0.321321\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7056.00 | −0.334789 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2376.00 | −0.112293 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2400.00 | 0.112984 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −37586.0 | −1.76253 | −0.881265 | − | 0.472622i | \(-0.843308\pi\) | ||||
−0.881265 | + | 0.472622i | \(0.843308\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6006.00 | 0.280546 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −27462.0 | −1.27780 | −0.638900 | − | 0.769290i | \(-0.720610\pi\) | ||||
−0.638900 | + | 0.769290i | \(0.720610\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 28558.0 | 1.32366 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −10656.0 | −0.491997 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8398.00 | −0.386251 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16000.0 | 0.733067 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3510.00 | −0.160201 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3704.00 | −0.168409 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6244.00 | −0.282814 | −0.141407 | − | 0.989952i | \(-0.545163\pi\) | ||||
−0.141407 | + | 0.989952i | \(0.545163\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1746.00 | 0.0787823 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7464.00 | 0.335511 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −24560.0 | −1.09981 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4008.00 | 0.178804 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1362.00 | 0.0605326 | 0.0302663 | − | 0.999542i | \(-0.490364\pi\) | ||||
0.0302663 | + | 0.999542i | \(0.490364\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −35772.0 | −1.58388 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5670.00 | −0.250112 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −12720.0 | −0.559003 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4704.00 | 0.205956 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 18270.0 | 0.796945 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 18222.0 | 0.791905 | 0.395953 | − | 0.918271i | \(-0.370414\pi\) | ||||
0.395953 | + | 0.918271i | \(0.370414\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12216.0 | 0.528929 | 0.264465 | − | 0.964395i | \(-0.414805\pi\) | ||||
0.264465 | + | 0.964395i | \(0.414805\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −16356.0 | −0.705572 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5072.00 | −0.217993 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3116.00 | 0.133433 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4320.00 | −0.184314 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −29268.0 | −1.24417 | −0.622083 | − | 0.782951i | \(-0.713713\pi\) | ||||
−0.622083 | + | 0.782951i | \(0.713713\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −19568.0 | −0.828794 | −0.414397 | − | 0.910096i | \(-0.636008\pi\) | ||||
−0.414397 | + | 0.910096i | \(0.636008\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 13080.0 | 0.551984 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −14308.0 | −0.601618 | −0.300809 | − | 0.953684i | \(-0.597257\pi\) | ||||
−0.300809 | + | 0.953684i | \(0.597257\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −15036.0 | −0.629942 | −0.314971 | − | 0.949101i | \(-0.601995\pi\) | ||||
−0.314971 | + | 0.949101i | \(0.601995\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14682.0 | 0.612892 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 13134.0 | 0.546298 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2448.00 | 0.101457 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7074.00 | −0.292130 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9092.00 | 0.374125 | 0.187062 | − | 0.982348i | \(-0.440103\pi\) | ||||
0.187062 | + | 0.982348i | \(0.440103\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7489.00 | −0.307065 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 14874.0 | 0.607696 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2388.00 | −0.0972186 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3228.00 | 0.130951 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3924.00 | 0.158623 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −29008.0 | −1.16849 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −16242.0 | −0.651953 | −0.325976 | − | 0.945378i | \(-0.605693\pi\) | ||||
−0.325976 | + | 0.945378i | \(0.605693\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 684.000 | 0.0273594 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −9966.00 | −0.397237 | −0.198618 | − | 0.980077i | \(-0.563645\pi\) | ||||
−0.198618 | + | 0.980077i | \(0.563645\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 33788.0 | 1.34206 | 0.671031 | − | 0.741429i | \(-0.265852\pi\) | ||||
0.671031 | + | 0.741429i | \(0.265852\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −15912.0 | −0.629825 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1524.00 | −0.0601131 | −0.0300565 | − | 0.999548i | \(-0.509569\pi\) | ||||
−0.0300565 | + | 0.999548i | \(0.509569\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −13176.0 | −0.517916 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1671.00 | −0.0654558 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 46160.0 | 1.80192 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 9054.00 | 0.351010 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −11232.0 | −0.433955 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9688.00 | 0.373022 | 0.186511 | − | 0.982453i | \(-0.440282\pi\) | ||||
0.186511 | + | 0.982453i | \(0.440282\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 23166.0 | 0.888930 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −23262.0 | −0.889576 | −0.444788 | − | 0.895636i | \(-0.646721\pi\) | ||||
−0.444788 | + | 0.895636i | \(0.646721\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 39452.0 | 1.50358 | 0.751792 | − | 0.659400i | \(-0.229190\pi\) | ||||
0.751792 | + | 0.659400i | \(0.229190\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −720.000 | −0.0273475 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 22492.0 | 0.851418 | 0.425709 | − | 0.904860i | \(-0.360025\pi\) | ||||
0.425709 | + | 0.904860i | \(0.360025\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2376.00 | −0.0896383 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3240.00 | −0.121823 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 10298.0 | 0.385901 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 14736.0 | 0.550358 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −11760.0 | −0.437742 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 34060.0 | 1.26359 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −22044.0 | −0.815086 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5904.00 | 0.217578 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −13616.0 | −0.500123 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5504.00 | −0.201496 | −0.100748 | − | 0.994912i | \(-0.532124\pi\) | ||||
−0.100748 | + | 0.994912i | \(0.532124\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1260.00 | −0.0459753 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −23412.0 | −0.851454 | −0.425727 | − | 0.904852i | \(-0.639982\pi\) | ||||
−0.425727 | + | 0.904852i | \(0.639982\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −25440.0 | −0.922170 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 7368.00 | 0.266206 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 18288.0 | 0.658586 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −11360.0 | −0.407760 | −0.203880 | − | 0.978996i | \(-0.565355\pi\) | ||||
−0.203880 | + | 0.978996i | \(0.565355\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 11736.0 | 0.419885 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 16000.0 | 0.570581 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 32264.0 | 1.14685 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −594.000 | −0.0210459 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 12766.0 | 0.450849 | 0.225425 | − | 0.974261i | \(-0.427623\pi\) | ||||
0.225425 | + | 0.974261i | \(0.427623\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3781.00 | −0.133101 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5982.00 | −0.209906 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 10560.0 | 0.369357 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −17002.0 | −0.592776 | −0.296388 | − | 0.955068i | \(-0.595782\pi\) | ||||
−0.296388 | + | 0.955068i | \(0.595782\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −9678.00 | −0.336347 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −48046.0 | −1.66446 | −0.832229 | − | 0.554432i | \(-0.812935\pi\) | ||||
−0.832229 | + | 0.554432i | \(0.812935\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −43316.0 | −1.49583 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1296.00 | 0.0446126 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −20964.0 | −0.719365 | −0.359682 | − | 0.933075i | \(-0.617115\pi\) | ||||
−0.359682 | + | 0.933075i | \(0.617115\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12720.0 | −0.435099 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1494.00 | 0.0509424 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 31270.0 | 1.06289 | 0.531445 | − | 0.847093i | \(-0.321649\pi\) | ||||
0.531445 | + | 0.847093i | \(0.321649\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −10136.0 | −0.343448 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 15600.0 | 0.526935 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −18552.0 | −0.624688 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 38853.0 | 1.30419 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −9108.00 | −0.304778 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 20472.0 | 0.682919 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 45780.0 | 1.52243 | 0.761213 | − | 0.648502i | \(-0.224604\pi\) | ||||
0.761213 | + | 0.648502i | \(0.224604\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3762.00 | −0.124719 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −51220.0 | −1.69282 | −0.846410 | − | 0.532532i | \(-0.821241\pi\) | ||||
−0.846410 | + | 0.532532i | \(0.821241\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −30096.0 | −0.991607 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 13080.0 | 0.429636 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −53954.0 | −1.76678 | −0.883389 | − | 0.468641i | \(-0.844744\pi\) | ||||
−0.883389 | + | 0.468641i | \(0.844744\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 25200.0 | 0.822672 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5292.00 | −0.172233 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −45552.0 | −1.47801 | −0.739005 | − | 0.673700i | \(-0.764704\pi\) | ||||
−0.739005 | + | 0.673700i | \(0.764704\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1312.00 | 0.0424404 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 19512.0 | 0.629254 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 16072.0 | 0.516744 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −34510.0 | −1.10620 | −0.553101 | − | 0.833114i | \(-0.686556\pi\) | ||||
−0.553101 | + | 0.833114i | \(0.686556\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −10320.0 | −0.329804 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5392.00 | 0.171797 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −6902.00 | −0.219246 | −0.109623 | − | 0.993973i | \(-0.534964\pi\) | ||||
−0.109623 | + | 0.993973i | \(0.534964\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7992.00 | −0.253109 |
(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 | 912.4.a.h.1.1 | 1 | ||
4.3 | odd | 2 | 228.4.a.b.1.1 | ✓ | 1 | ||
12.11 | even | 2 | 684.4.a.b.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
228.4.a.b.1.1 | ✓ | 1 | 4.3 | odd | 2 | ||
684.4.a.b.1.1 | 1 | 12.11 | even | 2 | |||
912.4.a.h.1.1 | 1 | 1.1 | even | 1 | trivial |