Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1080,4,Mod(1,1080)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1080, 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("1080.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1080.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: | \(63.7220628062\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.985.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 6x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{3}\cdot 3^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.93080\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1080.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −7.95278 | −0.429410 | −0.214705 | − | 0.976679i | \(-0.568879\pi\) | ||||
−0.214705 | + | 0.976679i | \(0.568879\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 37.1224 | 1.01753 | 0.508765 | − | 0.860906i | \(-0.330102\pi\) | ||||
0.508765 | + | 0.860906i | \(0.330102\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −35.1224 | −0.749323 | −0.374662 | − | 0.927162i | \(-0.622241\pi\) | ||||
−0.374662 | + | 0.927162i | \(0.622241\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 99.1976 | 1.41523 | 0.707616 | − | 0.706597i | \(-0.249771\pi\) | ||||
0.707616 | + | 0.706597i | \(0.249771\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −44.6505 | −0.539133 | −0.269567 | − | 0.962982i | \(-0.586880\pi\) | ||||
−0.269567 | + | 0.962982i | \(0.586880\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −102.603 | −0.930186 | −0.465093 | − | 0.885262i | \(-0.653979\pi\) | ||||
−0.465093 | + | 0.885262i | \(0.653979\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −285.404 | −1.82752 | −0.913762 | − | 0.406249i | \(-0.866837\pi\) | ||||
−0.913762 | + | 0.406249i | \(0.866837\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 238.593 | 1.38234 | 0.691171 | − | 0.722692i | \(-0.257095\pi\) | ||||
0.691171 | + | 0.722692i | \(0.257095\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 39.7639 | 0.192038 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 339.168 | 1.50700 | 0.753498 | − | 0.657450i | \(-0.228365\pi\) | ||||
0.753498 | + | 0.657450i | \(0.228365\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 423.799 | 1.61430 | 0.807150 | − | 0.590346i | \(-0.201009\pi\) | ||||
0.807150 | + | 0.590346i | \(0.201009\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 144.330 | 0.511863 | 0.255931 | − | 0.966695i | \(-0.417618\pi\) | ||||
0.255931 | + | 0.966695i | \(0.417618\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −418.414 | −1.29855 | −0.649276 | − | 0.760553i | \(-0.724928\pi\) | ||||
−0.649276 | + | 0.760553i | \(0.724928\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −279.753 | −0.815607 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −186.933 | −0.484476 | −0.242238 | − | 0.970217i | \(-0.577882\pi\) | ||||
−0.242238 | + | 0.970217i | \(0.577882\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −185.612 | −0.455053 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −293.783 | −0.648259 | −0.324129 | − | 0.946013i | \(-0.605071\pi\) | ||||
−0.324129 | + | 0.946013i | \(0.605071\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −701.657 | −1.47275 | −0.736377 | − | 0.676571i | \(-0.763465\pi\) | ||||
−0.736377 | + | 0.676571i | \(0.763465\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 175.612 | 0.335107 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −292.697 | −0.533710 | −0.266855 | − | 0.963737i | \(-0.585984\pi\) | ||||
−0.266855 | + | 0.963737i | \(0.585984\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −738.742 | −1.23482 | −0.617412 | − | 0.786640i | \(-0.711819\pi\) | ||||
−0.617412 | + | 0.786640i | \(0.711819\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 453.214 | 0.726639 | 0.363320 | − | 0.931665i | \(-0.381643\pi\) | ||||
0.363320 | + | 0.931665i | \(0.381643\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −295.226 | −0.436937 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 892.759 | 1.27143 | 0.635717 | − | 0.771922i | \(-0.280705\pi\) | ||||
0.635717 | + | 0.771922i | \(0.280705\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 66.4113 | 0.0878264 | 0.0439132 | − | 0.999035i | \(-0.486018\pi\) | ||||
0.0439132 | + | 0.999035i | \(0.486018\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −495.988 | −0.632911 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −868.816 | −1.03477 | −0.517384 | − | 0.855753i | \(-0.673094\pi\) | ||||
−0.517384 | + | 0.855753i | \(0.673094\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 279.321 | 0.321767 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 223.253 | 0.241108 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 112.488 | 0.117747 | 0.0588735 | − | 0.998265i | \(-0.481249\pi\) | ||||
0.0588735 | + | 0.998265i | \(0.481249\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1581.13 | −1.55770 | −0.778852 | − | 0.627207i | \(-0.784198\pi\) | ||||
−0.778852 | + | 0.627207i | \(0.784198\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −905.167 | −0.865910 | −0.432955 | − | 0.901416i | \(-0.642529\pi\) | ||||
−0.432955 | + | 0.901416i | \(0.642529\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1127.93 | 1.01908 | 0.509539 | − | 0.860447i | \(-0.329816\pi\) | ||||
0.509539 | + | 0.860447i | \(0.329816\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1947.65 | −1.71148 | −0.855739 | − | 0.517408i | \(-0.826897\pi\) | ||||
−0.855739 | + | 0.517408i | \(0.826897\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1724.52 | −1.43566 | −0.717829 | − | 0.696220i | \(-0.754864\pi\) | ||||
−0.717829 | + | 0.696220i | \(0.754864\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 513.017 | 0.415992 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −788.896 | −0.607714 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 47.0724 | 0.0353662 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 645.720 | 0.451168 | 0.225584 | − | 0.974224i | \(-0.427571\pi\) | ||||
0.225584 | + | 0.974224i | \(0.427571\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2055.92 | −1.37119 | −0.685597 | − | 0.727982i | \(-0.740459\pi\) | ||||
−0.685597 | + | 0.727982i | \(0.740459\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 355.096 | 0.231509 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 244.549 | 0.152505 | 0.0762525 | − | 0.997089i | \(-0.475704\pi\) | ||||
0.0762525 | + | 0.997089i | \(0.475704\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1068.67 | 0.652111 | 0.326056 | − | 0.945351i | \(-0.394280\pi\) | ||||
0.326056 | + | 0.945351i | \(0.394280\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1303.83 | −0.762458 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1427.02 | 0.817294 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1295.84 | 0.712481 | 0.356240 | − | 0.934394i | \(-0.384058\pi\) | ||||
0.356240 | + | 0.934394i | \(0.384058\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2727.32 | −1.46984 | −0.734921 | − | 0.678153i | \(-0.762781\pi\) | ||||
−0.734921 | + | 0.678153i | \(0.762781\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1192.97 | −0.618202 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 867.700 | 0.441083 | 0.220541 | − | 0.975378i | \(-0.429218\pi\) | ||||
0.220541 | + | 0.975378i | \(0.429218\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 815.981 | 0.399431 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1217.40 | 0.584995 | 0.292497 | − | 0.956266i | \(-0.405514\pi\) | ||||
0.292497 | + | 0.956266i | \(0.405514\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3266.76 | −1.51371 | −0.756854 | − | 0.653583i | \(-0.773265\pi\) | ||||
−0.756854 | + | 0.653583i | \(0.773265\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −963.417 | −0.438515 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1421.71 | −0.624802 | −0.312401 | − | 0.949950i | \(-0.601133\pi\) | ||||
−0.312401 | + | 0.949950i | \(0.601133\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −198.819 | −0.0858819 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −949.492 | −0.396471 | −0.198236 | − | 0.980154i | \(-0.563521\pi\) | ||||
−0.198236 | + | 0.980154i | \(0.563521\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1748.25 | 0.717938 | 0.358969 | − | 0.933350i | \(-0.383128\pi\) | ||||
0.358969 | + | 0.933350i | \(0.383128\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1695.84 | −0.673950 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3682.45 | 1.44004 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1418.37 | 0.537327 | 0.268664 | − | 0.963234i | \(-0.413418\pi\) | ||||
0.268664 | + | 0.963234i | \(0.413418\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3733.49 | −1.39245 | −0.696223 | − | 0.717825i | \(-0.745138\pi\) | ||||
−0.696223 | + | 0.717825i | \(0.745138\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2294.67 | −0.829889 | −0.414945 | − | 0.909847i | \(-0.636199\pi\) | ||||
−0.414945 | + | 0.909847i | \(0.636199\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3713.93 | 1.32298 | 0.661492 | − | 0.749952i | \(-0.269924\pi\) | ||||
0.661492 | + | 0.749952i | \(0.269924\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2269.76 | 0.784757 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2119.00 | −0.721937 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1657.53 | −0.548584 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −199.877 | −0.0652139 | −0.0326069 | − | 0.999468i | \(-0.510381\pi\) | ||||
−0.0326069 | + | 0.999468i | \(0.510381\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −721.649 | −0.228912 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1897.48 | −0.593591 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3484.06 | −1.06047 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 879.739 | 0.264178 | 0.132089 | − | 0.991238i | \(-0.457832\pi\) | ||||
0.132089 | + | 0.991238i | \(0.457832\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4331.67 | −1.26653 | −0.633267 | − | 0.773934i | \(-0.718286\pi\) | ||||
−0.633267 | + | 0.773934i | \(0.718286\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2995.80 | −0.864489 | −0.432244 | − | 0.901757i | \(-0.642278\pi\) | ||||
−0.432244 | + | 0.901757i | \(0.642278\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2068.75 | −0.581666 | −0.290833 | − | 0.956774i | \(-0.593932\pi\) | ||||
−0.290833 | + | 0.956774i | \(0.593932\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2092.07 | 0.580730 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −311.612 | −0.0843368 | −0.0421684 | − | 0.999111i | \(-0.513427\pi\) | ||||
−0.0421684 | + | 0.999111i | \(0.513427\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4636.53 | −1.23928 | −0.619638 | − | 0.784888i | \(-0.712720\pi\) | ||||
−0.619638 | + | 0.784888i | \(0.712720\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1398.77 | 0.364751 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1568.23 | 0.403985 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1243.61 | −0.312732 | −0.156366 | − | 0.987699i | \(-0.549978\pi\) | ||||
−0.156366 | + | 0.987699i | \(0.549978\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3808.88 | −0.946491 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 687.895 | 0.166964 | 0.0834819 | − | 0.996509i | \(-0.473396\pi\) | ||||
0.0834819 | + | 0.996509i | \(0.473396\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2697.33 | −0.647119 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2819.20 | 0.660986 | 0.330493 | − | 0.943808i | \(-0.392785\pi\) | ||||
0.330493 | + | 0.943808i | \(0.392785\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 934.666 | 0.216664 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4208.33 | −0.953854 | −0.476927 | − | 0.878943i | \(-0.658249\pi\) | ||||
−0.476927 | + | 0.878943i | \(0.658249\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8395.09 | 1.88179 | 0.940896 | − | 0.338696i | \(-0.109986\pi\) | ||||
0.940896 | + | 0.338696i | \(0.109986\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 928.060 | 0.203506 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1197.24 | −0.259694 | −0.129847 | − | 0.991534i | \(-0.541449\pi\) | ||||
−0.129847 | + | 0.991534i | \(0.541449\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2335.97 | −0.495916 | −0.247958 | − | 0.968771i | \(-0.579759\pi\) | ||||
−0.247958 | + | 0.968771i | \(0.579759\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1028.83 | −0.216104 | −0.108052 | − | 0.994145i | \(-0.534461\pi\) | ||||
−0.108052 | + | 0.994145i | \(0.534461\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3370.38 | −0.693196 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4927.16 | 1.00288 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3375.36 | 0.673006 | 0.336503 | − | 0.941682i | \(-0.390756\pi\) | ||||
0.336503 | + | 0.941682i | \(0.390756\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1468.91 | 0.289910 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3603.67 | 0.697010 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1147.82 | −0.219799 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3508.29 | 0.658636 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6518.27 | 1.21178 | 0.605892 | − | 0.795547i | \(-0.292816\pi\) | ||||
0.605892 | + | 0.795547i | \(0.292816\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7327.27 | 1.33598 | 0.667992 | − | 0.744168i | \(-0.267154\pi\) | ||||
0.667992 | + | 0.744168i | \(0.267154\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1834.06 | 0.331206 | 0.165603 | − | 0.986193i | \(-0.447043\pi\) | ||||
0.165603 | + | 0.986193i | \(0.447043\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3431.64 | −0.608013 | −0.304006 | − | 0.952670i | \(-0.598324\pi\) | ||||
−0.304006 | + | 0.952670i | \(0.598324\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −10594.9 | −1.85956 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4429.22 | −0.762999 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −878.060 | −0.149865 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3327.55 | 0.557611 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7488.66 | 1.24355 | 0.621773 | − | 0.783197i | \(-0.286412\pi\) | ||||
0.621773 | + | 0.783197i | \(0.286412\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1463.48 | 0.238682 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6037.63 | −0.975936 | −0.487968 | − | 0.872862i | \(-0.662262\pi\) | ||||
−0.487968 | + | 0.872862i | \(0.662262\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8857.15 | 1.40657 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4952.62 | 0.779639 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4374.17 | 0.676708 | 0.338354 | − | 0.941019i | \(-0.390130\pi\) | ||||
0.338354 | + | 0.941019i | \(0.390130\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11777.8 | −1.80645 | −0.903223 | − | 0.429172i | \(-0.858805\pi\) | ||||
−0.903223 | + | 0.429172i | \(0.858805\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1548.39 | 0.233463 | 0.116732 | − | 0.993163i | \(-0.462758\pi\) | ||||
0.116732 | + | 0.993163i | \(0.462758\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3693.71 | 0.552230 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4793.75 | 0.704748 | 0.352374 | − | 0.935859i | \(-0.385374\pi\) | ||||
0.352374 | + | 0.935859i | \(0.385374\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4865.33 | −0.709335 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2266.07 | −0.324963 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7183.40 | 1.02172 | 0.510859 | − | 0.859665i | \(-0.329327\pi\) | ||||
0.510859 | + | 0.859665i | \(0.329327\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1486.64 | 0.208039 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6359.09 | −0.882738 | −0.441369 | − | 0.897326i | \(-0.645507\pi\) | ||||
−0.441369 | + | 0.897326i | \(0.645507\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10024.1 | 1.36941 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7598.86 | −1.02989 | −0.514944 | − | 0.857224i | \(-0.672187\pi\) | ||||
−0.514944 | + | 0.857224i | \(0.672187\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11674.6 | −1.55756 | −0.778778 | − | 0.627300i | \(-0.784160\pi\) | ||||
−0.778778 | + | 0.627300i | \(0.784160\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1476.13 | 0.195404 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4324.51 | 0.563653 | 0.281827 | − | 0.959465i | \(-0.409060\pi\) | ||||
0.281827 | + | 0.959465i | \(0.409060\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10178.0 | −1.31643 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4463.80 | −0.568602 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9834.45 | 1.24327 | 0.621633 | − | 0.783308i | \(-0.286469\pi\) | ||||
0.621633 | + | 0.783308i | \(0.286469\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2593.68 | −0.322998 | −0.161499 | − | 0.986873i | \(-0.551633\pi\) | ||||
−0.161499 | + | 0.986873i | \(0.551633\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8379.96 | −1.03582 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 12590.7 | 1.53341 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12202.2 | −1.47520 | −0.737602 | − | 0.675236i | \(-0.764042\pi\) | ||||
−0.737602 | + | 0.675236i | \(0.764042\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2336.39 | 0.278369 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −332.057 | −0.0392771 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13107.9 | −1.52831 | −0.764155 | − | 0.645033i | \(-0.776844\pi\) | ||||
−0.764155 | + | 0.645033i | \(0.776844\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 624.409 | 0.0722846 | 0.0361423 | − | 0.999347i | \(-0.488493\pi\) | ||||
0.0361423 | + | 0.999347i | \(0.488493\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2479.94 | 0.283046 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5580.13 | 0.632415 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6376.30 | −0.712612 | −0.356306 | − | 0.934369i | \(-0.615964\pi\) | ||||
−0.356306 | + | 0.934369i | \(0.615964\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11244.7 | 1.24800 | 0.624000 | − | 0.781424i | \(-0.285506\pi\) | ||||
0.624000 | + | 0.781424i | \(0.285506\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4581.29 | 0.501494 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11262.2 | 1.22441 | 0.612204 | − | 0.790700i | \(-0.290283\pi\) | ||||
0.612204 | + | 0.790700i | \(0.290283\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14404.2 | 1.54485 | 0.772423 | − | 0.635109i | \(-0.219045\pi\) | ||||
0.772423 | + | 0.635109i | \(0.219045\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4344.08 | 0.462762 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11709.3 | 1.23073 | 0.615365 | − | 0.788242i | \(-0.289008\pi\) | ||||
0.615365 | + | 0.788242i | \(0.289008\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 15732.4 | 1.64260 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1396.60 | −0.143898 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15784.8 | 1.61572 | 0.807858 | − | 0.589377i | \(-0.200627\pi\) | ||||
0.807858 | + | 0.589377i | \(0.200627\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3956.19 | −0.399692 | −0.199846 | − | 0.979827i | \(-0.564044\pi\) | ||||
−0.199846 | + | 0.979827i | \(0.564044\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9252.50 | 0.928726 | 0.464363 | − | 0.885645i | \(-0.346283\pi\) | ||||
0.464363 | + | 0.885645i | \(0.346283\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9116.74 | 0.903367 | 0.451684 | − | 0.892178i | \(-0.350824\pi\) | ||||
0.451684 | + | 0.892178i | \(0.350824\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2327.75 | 0.229180 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5357.87 | 0.520835 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1116.26 | −0.107827 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2236.33 | −0.213321 | −0.106660 | − | 0.994296i | \(-0.534016\pi\) | ||||
−0.106660 | + | 0.994296i | \(0.534016\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11912.4 | −1.12923 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −562.441 | −0.0526580 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14371.9 | 1.33728 | 0.668638 | − | 0.743588i | \(-0.266878\pi\) | ||||
0.668638 | + | 0.743588i | \(0.266878\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5423.17 | 0.498461 | 0.249230 | − | 0.968444i | \(-0.419822\pi\) | ||||
0.249230 | + | 0.968444i | \(0.419822\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −28311.4 | −2.58637 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5875.05 | 0.530246 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4920.24 | −0.441403 | −0.220701 | − | 0.975341i | \(-0.570835\pi\) | ||||
−0.220701 | + | 0.975341i | \(0.570835\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16004.1 | 1.41866 | 0.709330 | − | 0.704876i | \(-0.248998\pi\) | ||||
0.709330 | + | 0.704876i | \(0.248998\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7905.64 | 0.696627 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12973.0 | 1.12970 | 0.564852 | − | 0.825192i | \(-0.308933\pi\) | ||||
0.564852 | + | 0.825192i | \(0.308933\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3604.31 | −0.312026 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4525.83 | 0.387247 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −15532.5 | −1.32132 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1933.35 | −0.162575 | −0.0812877 | − | 0.996691i | \(-0.525903\pi\) | ||||
−0.0812877 | + | 0.996691i | \(0.525903\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12275.0 | 1.02629 | 0.513144 | − | 0.858303i | \(-0.328481\pi\) | ||||
0.513144 | + | 0.858303i | \(0.328481\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 23667.9 | 1.95633 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1639.56 | −0.134755 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −14884.8 | −1.20963 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5639.67 | −0.455746 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −10385.1 | −0.829904 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6956.43 | 0.552829 | 0.276414 | − | 0.961039i | \(-0.410854\pi\) | ||||
0.276414 | + | 0.961039i | \(0.410854\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9738.25 | 0.765396 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16829.2 | −1.31547 | −0.657737 | − | 0.753247i | \(-0.728486\pi\) | ||||
−0.657737 | + | 0.753247i | \(0.728486\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12743.4 | 0.985280 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7099.92 | −0.545966 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1687.87 | −0.128398 | −0.0641988 | − | 0.997937i | \(-0.520449\pi\) | ||||
−0.0641988 | + | 0.997937i | \(0.520449\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5069.21 | −0.383551 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 19706.4 | 1.47518 | 0.737590 | − | 0.675249i | \(-0.235964\pi\) | ||||
0.737590 | + | 0.675249i | \(0.235964\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8622.61 | 0.642046 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −19640.8 | −1.44707 | −0.723537 | − | 0.690286i | \(-0.757485\pi\) | ||||
−0.723537 | + | 0.690286i | \(0.757485\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5247.74 | −0.384608 | −0.192304 | − | 0.981335i | \(-0.561596\pi\) | ||||
−0.192304 | + | 0.981335i | \(0.561596\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2565.08 | −0.186037 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 25474.3 | 1.83797 | 0.918985 | − | 0.394293i | \(-0.129011\pi\) | ||||
0.918985 | + | 0.394293i | \(0.129011\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −528.154 | −0.0377135 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6939.41 | −0.492969 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −22502.7 | −1.58226 | −0.791129 | − | 0.611650i | \(-0.790506\pi\) | ||||
−0.791129 | + | 0.611650i | \(0.790506\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10653.3 | −0.745266 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4175.65 | 0.289163 | 0.144581 | − | 0.989493i | \(-0.453816\pi\) | ||||
0.144581 | + | 0.989493i | \(0.453816\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3944.48 | 0.271778 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7096.57 | 0.484070 | 0.242035 | − | 0.970267i | \(-0.422185\pi\) | ||||
0.242035 | + | 0.970267i | \(0.422185\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9677.83 | 0.656850 | 0.328425 | − | 0.944530i | \(-0.393482\pi\) | ||||
0.328425 | + | 0.944530i | \(0.393482\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −235.362 | −0.0158162 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 24557.7 | 1.64212 | 0.821060 | − | 0.570842i | \(-0.193383\pi\) | ||||
0.821060 | + | 0.570842i | \(0.193383\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 14695.7 | 0.973035 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −22514.3 | −1.48343 | −0.741715 | − | 0.670716i | \(-0.765987\pi\) | ||||
−0.741715 | + | 0.670716i | \(0.765987\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14144.1 | −0.922882 | −0.461441 | − | 0.887171i | \(-0.652667\pi\) | ||||
−0.461441 | + | 0.887171i | \(0.652667\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −24650.9 | −1.60065 | −0.800324 | − | 0.599567i | \(-0.795339\pi\) | ||||
−0.800324 | + | 0.599567i | \(0.795339\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6909.50 | 0.444339 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 33644.6 | 2.13275 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21513.3 | −1.35726 | −0.678630 | − | 0.734481i | \(-0.737426\pi\) | ||||
−0.678630 | + | 0.734481i | \(0.737426\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3228.60 | −0.201769 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9825.61 | 0.611153 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 17483.0 | 1.07728 | 0.538640 | − | 0.842536i | \(-0.318938\pi\) | ||||
0.538640 | + | 0.842536i | \(0.318938\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −25464.1 | −1.56175 | −0.780877 | − | 0.624685i | \(-0.785227\pi\) | ||||
−0.780877 | + | 0.624685i | \(0.785227\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −25974.4 | −1.57830 | −0.789148 | − | 0.614203i | \(-0.789477\pi\) | ||||
−0.789148 | + | 0.614203i | \(0.789477\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10905.9 | −0.659622 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3532.46 | 0.211694 | 0.105847 | − | 0.994382i | \(-0.466245\pi\) | ||||
0.105847 | + | 0.994382i | \(0.466245\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10279.6 | 0.613216 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 29558.1 | 1.74723 | 0.873613 | − | 0.486622i | \(-0.161771\pi\) | ||||
0.873613 | + | 0.486622i | \(0.161771\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17632.5 | −1.03755 | −0.518777 | − | 0.854910i | \(-0.673612\pi\) | ||||
−0.518777 | + | 0.854910i | \(0.673612\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1775.48 | −0.103534 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 29283.4 | 1.69994 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −26047.2 | −1.49857 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16119.9 | 0.923296 | 0.461648 | − | 0.887063i | \(-0.347258\pi\) | ||||
0.461648 | + | 0.887063i | \(0.347258\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −8987.07 | −0.510194 | −0.255097 | − | 0.966915i | \(-0.582107\pi\) | ||||
−0.255097 | + | 0.966915i | \(0.582107\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −894.594 | −0.0505617 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −16085.7 | −0.901173 | −0.450586 | − | 0.892733i | \(-0.648785\pi\) | ||||
−0.450586 | + | 0.892733i | \(0.648785\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1222.74 | −0.0682023 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6565.54 | 0.363029 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2781.12 | 0.153109 | 0.0765547 | − | 0.997065i | \(-0.475608\pi\) | ||||
0.0765547 | + | 0.997065i | \(0.475608\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5343.35 | −0.291633 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 42039.9 | 2.28461 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19690.3 | 1.06090 | 0.530450 | − | 0.847716i | \(-0.322023\pi\) | ||||
0.530450 | + | 0.847716i | \(0.322023\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −15144.0 | −0.812472 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 12574.4 | 0.668894 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14455.3 | −0.765699 | −0.382849 | − | 0.923811i | \(-0.625057\pi\) | ||||
−0.382849 | + | 0.923811i | \(0.625057\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −24480.4 | −1.28583 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6519.14 | 0.340982 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −20466.1 | −1.06155 | −0.530776 | − | 0.847512i | \(-0.678100\pi\) | ||||
−0.530776 | + | 0.847512i | \(0.678100\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7198.59 | 0.371830 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7135.10 | −0.365505 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14551.8 | 0.742362 | 0.371181 | − | 0.928561i | \(-0.378953\pi\) | ||||
0.371181 | + | 0.928561i | \(0.378953\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 14317.2 | 0.724405 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7253.87 | −0.365522 | −0.182761 | − | 0.983157i | \(-0.558503\pi\) | ||||
−0.182761 | + | 0.983157i | \(0.558503\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −10865.6 | −0.543066 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19673.1 | 0.979281 | 0.489640 | − | 0.871925i | \(-0.337128\pi\) | ||||
0.489640 | + | 0.871925i | \(0.337128\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −16033.8 | −0.791686 | −0.395843 | − | 0.918318i | \(-0.629547\pi\) | ||||
−0.395843 | + | 0.918318i | \(0.629547\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6479.22 | −0.318631 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −8970.20 | −0.437602 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4848.93 | −0.235606 | −0.117803 | − | 0.993037i | \(-0.537585\pi\) | ||||
−0.117803 | + | 0.993037i | \(0.537585\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 13636.6 | 0.657333 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 31534.6 | 1.51406 | 0.757030 | − | 0.653380i | \(-0.226650\pi\) | ||||
0.757030 | + | 0.653380i | \(0.226650\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7873.75 | −0.375063 | −0.187532 | − | 0.982259i | \(-0.560049\pi\) | ||||
−0.187532 | + | 0.982259i | \(0.560049\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 15489.2 | 0.734925 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 10318.4 | 0.485755 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7134.10 | −0.334541 | −0.167271 | − | 0.985911i | \(-0.553495\pi\) | ||||
−0.167271 | + | 0.985911i | \(0.553495\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −9224.32 | −0.429205 | −0.214603 | − | 0.976701i | \(-0.568846\pi\) | ||||
−0.214603 | + | 0.976701i | \(0.568846\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5964.83 | 0.276468 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −18922.9 | −0.870323 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −27423.9 | −1.25647 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4338.50 | −0.197258 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −30384.7 | −1.37623 | −0.688117 | − | 0.725599i | \(-0.741563\pi\) | ||||
−0.688117 | + | 0.725599i | \(0.741563\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 13714.7 | 0.616485 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 24643.9 | 1.10357 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 9064.89 | 0.402879 | 0.201440 | − | 0.979501i | \(-0.435438\pi\) | ||||
0.201440 | + | 0.979501i | \(0.435438\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −41505.7 | −1.83775 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 16824.4 | 0.739377 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4079.91 | −0.178631 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 11430.1 | 0.496737 | 0.248368 | − | 0.968666i | \(-0.420106\pi\) | ||||
0.248368 | + | 0.968666i | \(0.420106\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −27003.1 | −1.16918 | −0.584591 | − | 0.811328i | \(-0.698745\pi\) | ||||
−0.584591 | + | 0.811328i | \(0.698745\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6087.00 | −0.261618 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6444.40 | −0.275962 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −32910.1 | −1.39899 | −0.699494 | − | 0.714638i | \(-0.746591\pi\) | ||||
−0.699494 | + | 0.714638i | \(0.746591\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −29489.1 | −1.24900 | −0.624499 | − | 0.781026i | \(-0.714697\pi\) | ||||
−0.624499 | + | 0.781026i | \(0.714697\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −18645.6 | −0.784002 | −0.392001 | − | 0.919965i | \(-0.628217\pi\) | ||||
−0.392001 | + | 0.919965i | \(0.628217\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4919.89 | −0.206122 | −0.103061 | − | 0.994675i | \(-0.532864\pi\) | ||||
−0.103061 | + | 0.994675i | \(0.532864\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −27750.9 | −1.15427 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 16333.8 | 0.676951 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −45795.6 | −1.88444 | −0.942218 | − | 0.335001i | \(-0.891263\pi\) | ||||
−0.942218 | + | 0.335001i | \(0.891263\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 57066.5 | 2.33985 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4817.09 | 0.196110 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −374.356 | −0.0151866 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −34799.8 | −1.40179 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 42136.7 | 1.69136 | 0.845681 | − | 0.533688i | \(-0.179194\pi\) | ||||
0.845681 | + | 0.533688i | \(0.179194\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −27884.1 | −1.11144 | −0.555720 | − | 0.831370i | \(-0.687557\pi\) | ||||
−0.555720 | + | 0.831370i | \(0.687557\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −28863.7 | −1.14647 | −0.573234 | − | 0.819392i | \(-0.694311\pi\) | ||||
−0.573234 | + | 0.819392i | \(0.694311\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 13061.5 | 0.515203 | 0.257601 | − | 0.966251i | \(-0.417068\pi\) | ||||
0.257601 | + | 0.966251i | \(0.417068\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7108.56 | 0.279420 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 33141.4 | 1.29372 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10280.2 | 0.399921 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 994.097 | 0.0384076 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6501.20 | 0.250319 | 0.125160 | − | 0.992137i | \(-0.460056\pi\) | ||||
0.125160 | + | 0.992137i | \(0.460056\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −45486.0 | −1.73946 | −0.869729 | − | 0.493529i | \(-0.835707\pi\) | ||||
−0.869729 | + | 0.493529i | \(0.835707\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5963.30 | −0.227272 | −0.113636 | − | 0.993522i | \(-0.536250\pi\) | ||||
−0.113636 | + | 0.993522i | \(0.536250\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −14524.3 | −0.549807 | −0.274903 | − | 0.961472i | \(-0.588646\pi\) | ||||
−0.274903 | + | 0.961472i | \(0.588646\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5135.27 | −0.193736 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 18682.4 | 0.700093 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4747.46 | 0.177307 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −68095.5 | −2.52626 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −18543.3 | −0.685646 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −8741.27 | −0.321072 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 25024.4 | 0.916119 | 0.458060 | − | 0.888921i | \(-0.348545\pi\) | ||||
0.458060 | + | 0.888921i | \(0.348545\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 27898.0 | 1.01460 | 0.507300 | − | 0.861770i | \(-0.330644\pi\) | ||||
0.507300 | + | 0.861770i | \(0.330644\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2465.35 | 0.0893659 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 16350.3 | 0.588804 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −19703.7 | −0.707253 | −0.353627 | − | 0.935387i | \(-0.615052\pi\) | ||||
−0.353627 | + | 0.935387i | \(0.615052\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 25946.4 | 0.925283 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8479.20 | 0.301399 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 17982.7 | 0.635083 | 0.317542 | − | 0.948244i | \(-0.397143\pi\) | ||||
0.317542 | + | 0.948244i | \(0.397143\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12491.1 | 0.439721 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −18412.3 | −0.644006 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 25616.7 | 0.893128 | 0.446564 | − | 0.894752i | \(-0.352647\pi\) | ||||
0.446564 | + | 0.894752i | \(0.352647\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −18854.2 | −0.653166 | −0.326583 | − | 0.945169i | \(-0.605897\pi\) | ||||
−0.326583 | + | 0.945169i | \(0.605897\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −43483.2 | −1.50160 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 24298.8 | 0.833798 | 0.416899 | − | 0.908953i | \(-0.363117\pi\) | ||||
0.416899 | + | 0.908953i | \(0.363117\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −15918.0 | −0.544487 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 10472.4 | 0.355963 | 0.177982 | − | 0.984034i | \(-0.443043\pi\) | ||||
0.177982 | + | 0.984034i | \(0.443043\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7091.84 | −0.240300 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1944.84 | −0.0654871 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 27135.6 | 0.910867 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 18667.4 | 0.622721 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 56840.3 | 1.89024 | 0.945120 | − | 0.326723i | \(-0.105944\pi\) | ||||
0.945120 | + | 0.326723i | \(0.105944\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −52095.6 | −1.72176 | −0.860879 | − | 0.508810i | \(-0.830086\pi\) | ||||
−0.860879 | + | 0.508810i | \(0.830086\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8498.90 | −0.280023 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 24247.8 | 0.794017 | 0.397008 | − | 0.917815i | \(-0.370048\pi\) | ||||
0.397008 | + | 0.917815i | \(0.370048\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −32252.5 | −1.05291 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3529.10 | 0.114508 | 0.0572538 | − | 0.998360i | \(-0.481766\pi\) | ||||
0.0572538 | + | 0.998360i | \(0.481766\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11473.3 | 0.371138 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −14808.7 | −0.476127 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2131.22 | 0.0683151 | 0.0341576 | − | 0.999416i | \(-0.489125\pi\) | ||||
0.0341576 | + | 0.999416i | \(0.489125\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −18569.7 | −0.591656 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20296.8 | 0.644739 | 0.322370 | − | 0.946614i | \(-0.395521\pi\) | ||||
0.322370 | + | 0.946614i | \(0.395521\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1080.4.a.g.1.2 | ✓ | 3 | |
3.2 | odd | 2 | 1080.4.a.m.1.2 | yes | 3 | ||
4.3 | odd | 2 | 2160.4.a.bg.1.2 | 3 | |||
12.11 | even | 2 | 2160.4.a.bo.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1080.4.a.g.1.2 | ✓ | 3 | 1.1 | even | 1 | trivial | |
1080.4.a.m.1.2 | yes | 3 | 3.2 | odd | 2 | ||
2160.4.a.bg.1.2 | 3 | 4.3 | odd | 2 | |||
2160.4.a.bo.1.2 | 3 | 12.11 | even | 2 |