Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1152,3,Mod(449,1152)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1152, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1152.449");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1152 = 2^{7} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1152.h (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(31.3897264543\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.5473632256.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 49x^{4} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{14} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 449.6 | ||
Root | \(-1.81129 - 1.81129i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1152.449 |
Dual form | 1152.3.h.f.449.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(641\) | \(901\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5.83095 | 1.16619 | 0.583095 | − | 0.812404i | \(-0.301841\pi\) | ||||
0.583095 | + | 0.812404i | \(0.301841\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.82843 | −0.404061 | −0.202031 | − | 0.979379i | \(-0.564754\pi\) | ||||
−0.202031 | + | 0.979379i | \(0.564754\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −16.4924 | −1.49931 | −0.749656 | − | 0.661828i | \(-0.769781\pi\) | ||||
−0.749656 | + | 0.661828i | \(0.769781\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 8.24621i | 0.634324i | 0.948371 | + | 0.317162i | \(0.102730\pi\) | ||||
−0.948371 | + | 0.317162i | \(0.897270\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.07107i | 0.415945i | 0.978135 | + | 0.207973i | \(0.0666865\pi\) | ||||
−0.978135 | + | 0.207973i | \(0.933314\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 23.3238i | − 1.22757i | −0.789474 | − | 0.613784i | \(-0.789646\pi\) | ||||
0.789474 | − | 0.613784i | \(-0.210354\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 20.0000i | − 0.869565i | −0.900535 | − | 0.434783i | \(-0.856825\pi\) | ||||
0.900535 | − | 0.434783i | \(-0.143175\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 9.00000 | 0.360000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −29.1548 | −1.00534 | −0.502668 | − | 0.864479i | \(-0.667648\pi\) | ||||
−0.502668 | + | 0.864479i | \(0.667648\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −42.4264 | −1.36859 | −0.684297 | − | 0.729204i | \(-0.739891\pi\) | ||||
−0.684297 | + | 0.729204i | \(0.739891\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −16.4924 | −0.471212 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 49.4773i | − 1.33722i | −0.743612 | − | 0.668612i | \(-0.766889\pi\) | ||||
0.743612 | − | 0.668612i | \(-0.233111\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 26.8701i | − 0.655367i | −0.944788 | − | 0.327684i | \(-0.893732\pi\) | ||||
0.944788 | − | 0.327684i | \(-0.106268\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 44.0000i | − 0.936170i | −0.883683 | − | 0.468085i | \(-0.844944\pi\) | ||||
0.883683 | − | 0.468085i | \(-0.155056\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −41.0000 | −0.836735 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 29.1548 | 0.550090 | 0.275045 | − | 0.961431i | \(-0.411307\pi\) | ||||
0.275045 | + | 0.961431i | \(0.411307\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −96.1665 | −1.74848 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 65.9697 | 1.11813 | 0.559065 | − | 0.829124i | \(-0.311160\pi\) | ||||
0.559065 | + | 0.829124i | \(0.311160\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 82.4621i | 1.35184i | 0.736976 | + | 0.675919i | \(0.236253\pi\) | ||||
−0.736976 | + | 0.675919i | \(0.763747\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 48.0833i | 0.739742i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 116.619i | 1.74058i | 0.492537 | + | 0.870291i | \(0.336070\pi\) | ||||
−0.492537 | + | 0.870291i | \(0.663930\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 100.000i | − 1.40845i | −0.709977 | − | 0.704225i | \(-0.751294\pi\) | ||||
0.709977 | − | 0.704225i | \(-0.248706\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 40.0000 | 0.547945 | 0.273973 | − | 0.961737i | \(-0.411662\pi\) | ||||
0.273973 | + | 0.961737i | \(0.411662\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 46.6476 | 0.605813 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −127.279 | −1.61113 | −0.805565 | − | 0.592508i | \(-0.798138\pi\) | ||||
−0.805565 | + | 0.592508i | \(0.798138\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 82.4621 | 0.993519 | 0.496760 | − | 0.867888i | \(-0.334523\pi\) | ||||
0.496760 | + | 0.867888i | \(0.334523\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 41.2311i | 0.485071i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 114.551i | − 1.28709i | −0.765407 | − | 0.643547i | \(-0.777462\pi\) | ||||
0.765407 | − | 0.643547i | \(-0.222538\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 23.3238i | − 0.256306i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 136.000i | − 1.43158i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −40.0000 | −0.412371 | −0.206186 | − | 0.978513i | \(-0.566105\pi\) | ||||
−0.206186 | + | 0.978513i | \(0.566105\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −29.1548 | −0.288661 | −0.144330 | − | 0.989530i | \(-0.546103\pi\) | ||||
−0.144330 | + | 0.989530i | \(0.546103\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −166.877 | −1.62017 | −0.810083 | − | 0.586315i | \(-0.800578\pi\) | ||||
−0.810083 | + | 0.586315i | \(0.800578\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 206.155i | − 1.89133i | −0.325138 | − | 0.945666i | \(-0.605411\pi\) | ||||
0.325138 | − | 0.945666i | \(-0.394589\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 205.061i | 1.81470i | 0.420377 | + | 0.907349i | \(0.361898\pi\) | ||||
−0.420377 | + | 0.907349i | \(0.638102\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 116.619i | − 1.01408i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 20.0000i | − 0.168067i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 151.000 | 1.24793 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −93.2952 | −0.746362 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −144.250 | −1.13583 | −0.567913 | − | 0.823089i | \(-0.692249\pi\) | ||||
−0.567913 | + | 0.823089i | \(0.692249\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −98.9545 | −0.755378 | −0.377689 | − | 0.925932i | \(-0.623281\pi\) | ||||
−0.377689 | + | 0.925932i | \(0.623281\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 65.9697i | 0.496013i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 120.208i | − 0.877432i | −0.898626 | − | 0.438716i | \(-0.855433\pi\) | ||||
0.898626 | − | 0.438716i | \(-0.144567\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 116.619i | 0.838986i | 0.907759 | + | 0.419493i | \(0.137792\pi\) | ||||
−0.907759 | + | 0.419493i | \(0.862208\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 136.000i | − 0.951049i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −170.000 | −1.17241 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −145.774 | −0.978348 | −0.489174 | − | 0.872186i | \(-0.662702\pi\) | ||||
−0.489174 | + | 0.872186i | \(0.662702\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −127.279 | −0.842909 | −0.421454 | − | 0.906850i | \(-0.638480\pi\) | ||||
−0.421454 | + | 0.906850i | \(0.638480\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −247.386 | −1.59604 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 49.4773i | 0.315142i | 0.987508 | + | 0.157571i | \(0.0503663\pi\) | ||||
−0.987508 | + | 0.157571i | \(0.949634\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 56.5685i | 0.351357i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 233.238i | − 1.43091i | −0.698660 | − | 0.715454i | \(-0.746220\pi\) | ||||
0.698660 | − | 0.715454i | \(-0.253780\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 160.000i | − 0.958084i | −0.877792 | − | 0.479042i | \(-0.840984\pi\) | ||||
0.877792 | − | 0.479042i | \(-0.159016\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 101.000 | 0.597633 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 320.702 | 1.85377 | 0.926885 | − | 0.375344i | \(-0.122476\pi\) | ||||
0.926885 | + | 0.375344i | \(0.122476\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −25.4558 | −0.145462 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −98.9545 | −0.552819 | −0.276409 | − | 0.961040i | \(-0.589145\pi\) | ||||
−0.276409 | + | 0.961040i | \(0.589145\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 206.155i | 1.13898i | 0.821998 | + | 0.569490i | \(0.192859\pi\) | ||||
−0.821998 | + | 0.569490i | \(0.807141\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 288.500i | − 1.55946i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 116.619i | − 0.623631i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 160.000i | 0.837696i | 0.908056 | + | 0.418848i | \(0.137566\pi\) | ||||
−0.908056 | + | 0.418848i | \(0.862434\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −150.000 | −0.777202 | −0.388601 | − | 0.921406i | \(-0.627042\pi\) | ||||
−0.388601 | + | 0.921406i | \(0.627042\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 157.436 | 0.799166 | 0.399583 | − | 0.916697i | \(-0.369155\pi\) | ||||
0.399583 | + | 0.916697i | \(0.369155\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 70.7107 | 0.355330 | 0.177665 | − | 0.984091i | \(-0.443146\pi\) | ||||
0.177665 | + | 0.984091i | \(0.443146\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 82.4621 | 0.406217 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 156.678i | − 0.764283i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 384.666i | 1.84051i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 349.857i | 1.65809i | 0.559181 | + | 0.829045i | \(0.311116\pi\) | ||||
−0.559181 | + | 0.829045i | \(0.688884\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 120.000 | 0.552995 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −58.3095 | −0.263844 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.82843 | 0.0126835 | 0.00634176 | − | 0.999980i | \(-0.497981\pi\) | ||||
0.00634176 | + | 0.999980i | \(0.497981\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 247.386 | 1.08981 | 0.544904 | − | 0.838499i | \(-0.316566\pi\) | ||||
0.544904 | + | 0.838499i | \(0.316566\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 206.155i | − 0.900241i | −0.892968 | − | 0.450121i | \(-0.851381\pi\) | ||||
0.892968 | − | 0.450121i | \(-0.148619\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 190.919i | − 0.819394i | −0.912222 | − | 0.409697i | \(-0.865634\pi\) | ||||
0.912222 | − | 0.409697i | \(-0.134366\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 256.562i | − 1.09175i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 40.0000i | 0.167364i | 0.996493 | + | 0.0836820i | \(0.0266680\pi\) | ||||
−0.996493 | + | 0.0836820i | \(0.973332\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −240.000 | −0.995851 | −0.497925 | − | 0.867220i | \(-0.665905\pi\) | ||||
−0.497925 | + | 0.867220i | \(0.665905\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −239.069 | −0.975792 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 192.333 | 0.778676 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 346.341 | 1.37984 | 0.689922 | − | 0.723884i | \(-0.257645\pi\) | ||||
0.689922 | + | 0.723884i | \(0.257645\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 329.848i | 1.30375i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 21.2132i | 0.0825416i | 0.999148 | + | 0.0412708i | \(0.0131406\pi\) | ||||
−0.999148 | + | 0.0412708i | \(0.986859\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 139.943i | 0.540320i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 360.000i | 1.36882i | 0.729097 | + | 0.684411i | \(0.239940\pi\) | ||||
−0.729097 | + | 0.684411i | \(0.760060\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 170.000 | 0.641509 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −437.321 | −1.62573 | −0.812865 | − | 0.582452i | \(-0.802093\pi\) | ||||
−0.812865 | + | 0.582452i | \(0.802093\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 240.416 | 0.887145 | 0.443573 | − | 0.896238i | \(-0.353711\pi\) | ||||
0.443573 | + | 0.896238i | \(0.353711\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −148.432 | −0.539752 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 321.602i | − 1.16102i | −0.814254 | − | 0.580509i | \(-0.802853\pi\) | ||||
0.814254 | − | 0.580509i | \(-0.197147\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 227.688i | − 0.810279i | −0.914255 | − | 0.405139i | \(-0.867223\pi\) | ||||
0.914255 | − | 0.405139i | \(-0.132777\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 466.476i | 1.64833i | 0.566353 | + | 0.824163i | \(0.308354\pi\) | ||||
−0.566353 | + | 0.824163i | \(0.691646\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 76.0000i | 0.264808i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 239.000 | 0.826990 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 215.745 | 0.736332 | 0.368166 | − | 0.929760i | \(-0.379986\pi\) | ||||
0.368166 | + | 0.929760i | \(0.379986\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 384.666 | 1.30395 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 164.924 | 0.551586 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 480.833i | 1.57650i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 116.619i | 0.379867i | 0.981797 | + | 0.189933i | \(0.0608272\pi\) | ||||
−0.981797 | + | 0.189933i | \(0.939173\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 40.0000i | − 0.128617i | −0.997930 | − | 0.0643087i | \(-0.979516\pi\) | ||||
0.997930 | − | 0.0643087i | \(-0.0204842\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 250.000 | 0.798722 | 0.399361 | − | 0.916794i | \(-0.369232\pi\) | ||||
0.399361 | + | 0.916794i | \(0.369232\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −17.4929 | −0.0551825 | −0.0275913 | − | 0.999619i | \(-0.508784\pi\) | ||||
−0.0275913 | + | 0.999619i | \(0.508784\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 480.833 | 1.50731 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 164.924 | 0.510601 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 74.2159i | 0.228357i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 124.451i | 0.378270i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 23.3238i | 0.0704647i | 0.999379 | + | 0.0352323i | \(0.0112171\pi\) | ||||
−0.999379 | + | 0.0352323i | \(0.988783\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 680.000i | 2.02985i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −520.000 | −1.54303 | −0.771513 | − | 0.636213i | \(-0.780500\pi\) | ||||
−0.771513 | + | 0.636213i | \(0.780500\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 699.714 | 2.05195 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 254.558 | 0.742153 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −247.386 | −0.712929 | −0.356464 | − | 0.934309i | \(-0.616018\pi\) | ||||
−0.356464 | + | 0.934309i | \(0.616018\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 82.4621i | 0.236281i | 0.992997 | + | 0.118141i | \(0.0376933\pi\) | ||||
−0.992997 | + | 0.118141i | \(0.962307\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 360.624i | − 1.02160i | −0.859700 | − | 0.510800i | \(-0.829349\pi\) | ||||
0.859700 | − | 0.510800i | \(-0.170651\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 583.095i | − 1.64252i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 340.000i | 0.947075i | 0.880774 | + | 0.473538i | \(0.157023\pi\) | ||||
−0.880774 | + | 0.473538i | \(0.842977\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −183.000 | −0.506925 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 233.238 | 0.639008 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 364.867 | 0.994188 | 0.497094 | − | 0.867697i | \(-0.334400\pi\) | ||||
0.497094 | + | 0.867697i | \(0.334400\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −82.4621 | −0.222270 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 49.4773i | 0.132647i | 0.997798 | + | 0.0663234i | \(0.0211269\pi\) | ||||
−0.997798 | + | 0.0663234i | \(0.978873\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 240.416i | − 0.637709i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 116.619i | − 0.307702i | −0.988094 | − | 0.153851i | \(-0.950832\pi\) | ||||
0.988094 | − | 0.153851i | \(-0.0491676\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 184.000i | − 0.480418i | −0.970721 | − | 0.240209i | \(-0.922784\pi\) | ||||
0.970721 | − | 0.240209i | \(-0.0772159\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 272.000 | 0.706494 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −379.012 | −0.974324 | −0.487162 | − | 0.873312i | \(-0.661968\pi\) | ||||
−0.487162 | + | 0.873312i | \(0.661968\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 141.421 | 0.361691 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −742.159 | −1.87888 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 544.250i | 1.37091i | 0.728117 | + | 0.685453i | \(0.240396\pi\) | ||||
−0.728117 | + | 0.685453i | \(0.759604\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 267.286i | 0.666550i | 0.942830 | + | 0.333275i | \(0.108154\pi\) | ||||
−0.942830 | + | 0.333275i | \(0.891846\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 349.857i | − 0.868132i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 816.000i | 2.00491i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 232.000 | 0.567237 | 0.283619 | − | 0.958937i | \(-0.408465\pi\) | ||||
0.283619 | + | 0.958937i | \(0.408465\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −186.590 | −0.451793 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 480.833 | 1.15863 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 16.4924 | 0.0393614 | 0.0196807 | − | 0.999806i | \(-0.493735\pi\) | ||||
0.0196807 | + | 0.999806i | \(0.493735\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 123.693i | − 0.293808i | −0.989151 | − | 0.146904i | \(-0.953069\pi\) | ||||
0.989151 | − | 0.146904i | \(-0.0469308\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 63.6396i | 0.149740i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 233.238i | − 0.546225i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 140.000i | − 0.324826i | −0.986723 | − | 0.162413i | \(-0.948072\pi\) | ||||
0.986723 | − | 0.162413i | \(-0.0519277\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −190.000 | −0.438799 | −0.219400 | − | 0.975635i | \(-0.570410\pi\) | ||||
−0.219400 | + | 0.975635i | \(0.570410\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −466.476 | −1.06745 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 664.680 | 1.51408 | 0.757039 | − | 0.653370i | \(-0.226645\pi\) | ||||
0.757039 | + | 0.653370i | \(0.226645\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −82.4621 | −0.186145 | −0.0930724 | − | 0.995659i | \(-0.529669\pi\) | ||||
−0.0930724 | + | 0.995659i | \(0.529669\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 667.943i | − 1.50100i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 436.992i | − 0.973256i | −0.873609 | − | 0.486628i | \(-0.838227\pi\) | ||||
0.873609 | − | 0.486628i | \(-0.161773\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 443.152i | 0.982599i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 136.000i | − 0.298901i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −600.000 | −1.31291 | −0.656455 | − | 0.754365i | \(-0.727945\pi\) | ||||
−0.656455 | + | 0.754365i | \(0.727945\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −87.4643 | −0.189727 | −0.0948636 | − | 0.995490i | \(-0.530242\pi\) | ||||
−0.0948636 | + | 0.995490i | \(0.530242\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 53.7401 | 0.116069 | 0.0580347 | − | 0.998315i | \(-0.481517\pi\) | ||||
0.0580347 | + | 0.998315i | \(0.481517\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −82.4621 | −0.176578 | −0.0882892 | − | 0.996095i | \(-0.528140\pi\) | ||||
−0.0882892 | + | 0.996095i | \(0.528140\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 329.848i | − 0.703302i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 209.914i | − 0.441925i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 860.000i | 1.79541i | 0.440600 | + | 0.897704i | \(0.354766\pi\) | ||||
−0.440600 | + | 0.897704i | \(0.645234\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 408.000 | 0.848233 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −233.238 | −0.480903 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −31.1127 | −0.0638864 | −0.0319432 | − | 0.999490i | \(-0.510170\pi\) | ||||
−0.0319432 | + | 0.999490i | \(0.510170\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 428.803 | 0.873326 | 0.436663 | − | 0.899625i | \(-0.356160\pi\) | ||||
0.436663 | + | 0.899625i | \(0.356160\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 206.155i | − 0.418165i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 282.843i | 0.569100i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 93.2952i | − 0.186964i | −0.995621 | − | 0.0934822i | \(-0.970200\pi\) | ||||
0.995621 | − | 0.0934822i | \(-0.0297998\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 556.000i | − 1.10537i | −0.833391 | − | 0.552684i | \(-0.813604\pi\) | ||||
0.833391 | − | 0.552684i | \(-0.186396\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −170.000 | −0.336634 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 670.559 | 1.31741 | 0.658703 | − | 0.752403i | \(-0.271105\pi\) | ||||
0.658703 | + | 0.752403i | \(0.271105\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −113.137 | −0.221403 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −973.053 | −1.88942 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 725.667i | 1.40361i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 920.653i | 1.76709i | 0.468348 | + | 0.883544i | \(0.344849\pi\) | ||||
−0.468348 | + | 0.883544i | \(0.655151\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 583.095i | 1.11490i | 0.830209 | + | 0.557452i | \(0.188221\pi\) | ||||
−0.830209 | + | 0.557452i | \(0.811779\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 300.000i | − 0.569260i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 129.000 | 0.243856 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 221.576 | 0.415715 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 676.189 | 1.25453 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 865.852i | − 1.60047i | −0.599689 | − | 0.800233i | \(-0.704709\pi\) | ||||
0.599689 | − | 0.800233i | \(-0.295291\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 1202.08i | − 2.20565i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 932.952i | 1.70558i | 0.522254 | + | 0.852790i | \(0.325091\pi\) | ||||
−0.522254 | + | 0.852790i | \(0.674909\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 680.000i | 1.23412i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 360.000 | 0.650995 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −87.4643 | −0.157027 | −0.0785137 | − | 0.996913i | \(-0.525017\pi\) | ||||
−0.0785137 | + | 0.996913i | \(0.525017\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1072.01 | 1.90410 | 0.952049 | − | 0.305945i | \(-0.0989723\pi\) | ||||
0.952049 | + | 0.305945i | \(0.0989723\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1195.70i | 2.11628i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 72.1249i | 0.126757i | 0.997990 | + | 0.0633786i | \(0.0201876\pi\) | ||||
−0.997990 | + | 0.0633786i | \(0.979812\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 793.009i | − 1.38881i | −0.719585 | − | 0.694404i | \(-0.755668\pi\) | ||||
0.719585 | − | 0.694404i | \(-0.244332\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 180.000i | − 0.313043i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 890.000 | 1.54246 | 0.771231 | − | 0.636556i | \(-0.219642\pi\) | ||||
0.771231 | + | 0.636556i | \(0.219642\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −233.238 | −0.401442 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −480.833 | −0.824756 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 989.545 | 1.68577 | 0.842884 | − | 0.538096i | \(-0.180856\pi\) | ||||
0.842884 | + | 0.538096i | \(0.180856\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 989.545i | 1.68004i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 473.762i | 0.798923i | 0.916750 | + | 0.399462i | \(0.130803\pi\) | ||||
−0.916750 | + | 0.399462i | \(0.869197\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 116.619i | − 0.195998i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 740.000i | − 1.23539i | −0.786417 | − | 0.617696i | \(-0.788066\pi\) | ||||
0.786417 | − | 0.617696i | \(-0.211934\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −310.000 | −0.515807 | −0.257903 | − | 0.966171i | \(-0.583032\pi\) | ||||
−0.257903 | + | 0.966171i | \(0.583032\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 880.474 | 1.45533 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −370.524 | −0.610418 | −0.305209 | − | 0.952285i | \(-0.598726\pi\) | ||||
−0.305209 | + | 0.952285i | \(0.598726\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 362.833 | 0.593835 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 280.371i | − 0.457376i | −0.973500 | − | 0.228688i | \(-0.926557\pi\) | ||||
0.973500 | − | 0.228688i | \(-0.0734435\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 586.899i | 0.951213i | 0.879658 | + | 0.475607i | \(0.157771\pi\) | ||||
−0.879658 | + | 0.475607i | \(0.842229\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 699.714i | 1.13039i | 0.824956 | + | 0.565197i | \(0.191200\pi\) | ||||
−0.824956 | + | 0.565197i | \(0.808800\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 324.000i | 0.520064i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −769.000 | −1.23040 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 349.857 | 0.556212 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −381.838 | −0.605131 | −0.302566 | − | 0.953129i | \(-0.597843\pi\) | ||||
−0.302566 | + | 0.953129i | \(0.597843\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −841.114 | −1.32459 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 338.095i | − 0.530761i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 1203.50i | − 1.87753i | −0.344560 | − | 0.938764i | \(-0.611972\pi\) | ||||
0.344560 | − | 0.938764i | \(-0.388028\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 233.238i | − 0.362734i | −0.983415 | − | 0.181367i | \(-0.941948\pi\) | ||||
0.983415 | − | 0.181367i | \(-0.0580522\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 844.000i | − 1.30448i | −0.758012 | − | 0.652241i | \(-0.773829\pi\) | ||||
0.758012 | − | 0.652241i | \(-0.226171\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1088.00 | −1.67643 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1032.08 | −1.58052 | −0.790259 | − | 0.612773i | \(-0.790054\pi\) | ||||
−0.790259 | + | 0.612773i | \(0.790054\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −576.999 | −0.880915 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 263.879 | 0.400423 | 0.200212 | − | 0.979753i | \(-0.435837\pi\) | ||||
0.200212 | + | 0.979753i | \(0.435837\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 907.083i | − 1.37229i | −0.727465 | − | 0.686145i | \(-0.759302\pi\) | ||||
0.727465 | − | 0.686145i | \(-0.240698\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 384.666i | 0.578445i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 583.095i | 0.874206i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 1360.00i | − 2.02683i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1070.00 | 1.58990 | 0.794948 | − | 0.606678i | \(-0.207498\pi\) | ||||
0.794948 | + | 0.606678i | \(0.207498\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −40.8167 | −0.0602905 | −0.0301452 | − | 0.999546i | \(-0.509597\pi\) | ||||
−0.0301452 | + | 0.999546i | \(0.509597\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 113.137 | 0.166623 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1072.01 | −1.56956 | −0.784779 | − | 0.619776i | \(-0.787223\pi\) | ||||
−0.784779 | + | 0.619776i | \(0.787223\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 700.928i | − 1.02325i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 240.416i | 0.348935i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 326.533i | − 0.472552i | −0.971686 | − | 0.236276i | \(-0.924073\pi\) | ||||
0.971686 | − | 0.236276i | \(-0.0759269\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 680.000i | 0.978417i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 190.000 | 0.272597 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −495.631 | −0.707034 | −0.353517 | − | 0.935428i | \(-0.615014\pi\) | ||||
−0.353517 | + | 0.935428i | \(0.615014\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1154.00 | −1.64153 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 82.4621 | 0.116637 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 123.693i | 0.174461i | 0.996188 | + | 0.0872307i | \(0.0278017\pi\) | ||||
−0.996188 | + | 0.0872307i | \(0.972198\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 848.528i | 1.19008i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 793.009i | − 1.10910i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 300.000i | − 0.417246i | −0.977996 | − | 0.208623i | \(-0.933102\pi\) | ||||
0.977996 | − | 0.208623i | \(-0.0668982\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 472.000 | 0.654646 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −262.393 | −0.361921 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1298.25 | −1.78576 | −0.892880 | − | 0.450294i | \(-0.851319\pi\) | ||||
−0.892880 | + | 0.450294i | \(0.851319\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 74.2159i | 0.101250i | 0.998718 | + | 0.0506248i | \(0.0161213\pi\) | ||||
−0.998718 | + | 0.0506248i | \(0.983879\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 1923.33i | − 2.60967i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 139.943i | − 0.189368i | −0.995507 | − | 0.0946839i | \(-0.969816\pi\) | ||||
0.995507 | − | 0.0946839i | \(-0.0301840\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 1264.00i | − 1.70121i | −0.525804 | − | 0.850606i | \(-0.676236\pi\) | ||||
0.525804 | − | 0.850606i | \(-0.323764\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −850.000 | −1.14094 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −664.680 | −0.885060 | −0.442530 | − | 0.896754i | \(-0.645919\pi\) | ||||
−0.442530 | + | 0.896754i | \(0.645919\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −742.159 | −0.982992 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 733.913i | − 0.969502i | −0.874652 | − | 0.484751i | \(-0.838910\pi\) | ||||
0.874652 | − | 0.484751i | \(-0.161090\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 72.1249i | − 0.0947765i | −0.998877 | − | 0.0473882i | \(-0.984910\pi\) | ||||
0.998877 | − | 0.0473882i | \(-0.0150898\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 583.095i | 0.764214i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 544.000i | 0.709257i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −10.0000 | −0.0130039 | −0.00650195 | − | 0.999979i | \(-0.502070\pi\) | ||||
−0.00650195 | + | 0.999979i | \(0.502070\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −250.731 | −0.324361 | −0.162180 | − | 0.986761i | \(-0.551853\pi\) | ||||
−0.162180 | + | 0.986761i | \(0.551853\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −381.838 | −0.492694 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −626.712 | −0.804508 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1649.24i | 2.11171i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 288.500i | 0.367515i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 816.333i | − 1.03727i | −0.854995 | − | 0.518636i | \(-0.826440\pi\) | ||||
0.854995 | − | 0.518636i | \(-0.173560\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 580.000i | − 0.733249i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −680.000 | −0.857503 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 320.702 | 0.402387 | 0.201193 | − | 0.979552i | \(-0.435518\pi\) | ||||
0.201193 | + | 0.979552i | \(0.435518\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 311.127 | 0.389395 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −659.697 | −0.821540 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 329.848i | 0.409750i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 550.129i | 0.680011i | 0.940423 | + | 0.340006i | \(0.110429\pi\) | ||||
−0.940423 | + | 0.340006i | \(0.889571\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 116.619i | − 0.143797i | −0.997412 | − | 0.0718983i | \(-0.977094\pi\) | ||||
0.997412 | − | 0.0718983i | \(-0.0229057\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 1360.00i | − 1.66871i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 204.083 | 0.248579 | 0.124289 | − | 0.992246i | \(-0.460335\pi\) | ||||
0.124289 | + | 0.992246i | \(0.460335\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1439.67 | −1.74929 | −0.874647 | − | 0.484760i | \(-0.838907\pi\) | ||||
−0.874647 | + | 0.484760i | \(0.838907\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 494.773 | 0.598274 | 0.299137 | − | 0.954210i | \(-0.403301\pi\) | ||||
0.299137 | + | 0.954210i | \(0.403301\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1113.24i | 1.34287i | 0.741064 | + | 0.671435i | \(0.234322\pi\) | ||||
−0.741064 | + | 0.671435i | \(0.765678\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 289.914i | − 0.348036i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 932.952i | − 1.11731i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 820.000i | 0.977354i | 0.872465 | + | 0.488677i | \(0.162520\pi\) | ||||
−0.872465 | + | 0.488677i | \(0.837480\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.00000 | 0.0107015 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 588.926 | 0.696954 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −427.092 | −0.504241 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −989.545 | −1.16280 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 1104.99i | − 1.29542i | −0.761887 | − | 0.647709i | \(-0.775727\pi\) | ||||
0.761887 | − | 0.647709i | \(-0.224273\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 742.462i | 0.866350i | 0.901310 | + | 0.433175i | \(0.142607\pi\) | ||||
−0.901310 | + | 0.433175i | \(0.857393\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 932.952i | − 1.08609i | −0.839703 | − | 0.543046i | \(-0.817271\pi\) | ||||
0.839703 | − | 0.543046i | \(-0.182729\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 1360.00i | − 1.57590i | −0.615740 | − | 0.787949i | \(-0.711143\pi\) | ||||
0.615740 | − | 0.787949i | \(-0.288857\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1870.00 | 2.16185 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2099.14 | 2.41558 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −961.665 | −1.10409 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 263.879 | 0.301576 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 379.326i | − 0.432526i | −0.976335 | − | 0.216263i | \(-0.930613\pi\) | ||||
0.976335 | − | 0.216263i | \(-0.0693869\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 111.723i | 0.126814i | 0.997988 | + | 0.0634069i | \(0.0201966\pi\) | ||||
−0.997988 | + | 0.0634069i | \(0.979803\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1399.43i | 1.58486i | 0.609965 | + | 0.792428i | \(0.291183\pi\) | ||||
−0.609965 | + | 0.792428i | \(0.708817\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 840.000i | − 0.947012i | −0.880790 | − | 0.473506i | \(-0.842988\pi\) | ||||
0.880790 | − | 0.473506i | \(-0.157012\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 408.000 | 0.458943 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1026.25 | −1.14921 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −576.999 | −0.644692 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1236.93 | 1.37590 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 206.155i | 0.228807i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1202.08i | 1.32827i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 932.952i | − 1.02861i | −0.857606 | − | 0.514307i | \(-0.828049\pi\) | ||||
0.857606 | − | 0.514307i | \(-0.171951\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 560.000i | 0.614709i | 0.951595 | + | 0.307355i | \(0.0994438\pi\) | ||||
−0.951595 | + | 0.307355i | \(0.900556\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1360.00 | −1.48959 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 279.886 | 0.305219 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 777.817 | 0.846374 | 0.423187 | − | 0.906042i | \(-0.360911\pi\) | ||||
0.423187 | + | 0.906042i | \(0.360911\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 824.621 | 0.893414 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 445.295i | − 0.481400i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 1497.65i | − 1.61211i | −0.591839 | − | 0.806056i | \(-0.701598\pi\) | ||||
0.591839 | − | 0.806056i | \(-0.298402\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 956.276i | 1.02715i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 680.000i | − 0.727273i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −510.000 | −0.544290 | −0.272145 | − | 0.962256i | \(-0.587733\pi\) | ||||
−0.272145 | + | 0.962256i | \(0.587733\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −553.940 | −0.588672 | −0.294336 | − | 0.955702i | \(-0.595098\pi\) | ||||
−0.294336 | + | 0.955702i | \(0.595098\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −537.401 | −0.569885 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 329.848i | 0.347575i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 912.168i | − 0.957154i | −0.878046 | − | 0.478577i | \(-0.841153\pi\) | ||||
0.878046 | − | 0.478577i | \(-0.158847\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 932.952i | 0.976913i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 340.000i | 0.354536i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 839.000 | 0.873049 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −874.643 | −0.906366 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 285.671 | 0.295420 | 0.147710 | − | 0.989031i | \(-0.452810\pi\) | ||||
0.147710 | + | 0.989031i | \(0.452810\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 643.204 | 0.662414 | 0.331207 | − | 0.943558i | \(-0.392544\pi\) | ||||
0.331207 | + | 0.943558i | \(0.392544\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 329.848i | − 0.339001i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 388.909i | 0.398064i | 0.979993 | + | 0.199032i | \(0.0637798\pi\) | ||||
−0.979993 | + | 0.199032i | \(0.936220\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1889.23i | 1.92975i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 984.000i | 1.00102i | 0.865732 | + | 0.500509i | \(0.166854\pi\) | ||||
−0.865732 | + | 0.500509i | \(0.833146\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 918.000 | 0.931980 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −890.955 | −0.899046 | −0.449523 | − | 0.893269i | \(-0.648406\pi\) | ||||
−0.449523 | + | 0.893269i | \(0.648406\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 412.311 | 0.414382 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 940.068i | − 0.942897i | −0.881894 | − | 0.471448i | \(-0.843731\pi\) | ||||
0.881894 | − | 0.471448i | \(-0.156269\pi\) | |||||||
\(998\) | 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 | 1152.3.h.f.449.6 | yes | 8 | |
3.2 | odd | 2 | inner | 1152.3.h.f.449.2 | yes | 8 | |
4.3 | odd | 2 | inner | 1152.3.h.f.449.8 | yes | 8 | |
8.3 | odd | 2 | inner | 1152.3.h.f.449.3 | yes | 8 | |
8.5 | even | 2 | inner | 1152.3.h.f.449.1 | ✓ | 8 | |
12.11 | even | 2 | inner | 1152.3.h.f.449.4 | yes | 8 | |
16.3 | odd | 4 | 2304.3.e.m.1025.1 | 8 | |||
16.5 | even | 4 | 2304.3.e.m.1025.8 | 8 | |||
16.11 | odd | 4 | 2304.3.e.m.1025.6 | 8 | |||
16.13 | even | 4 | 2304.3.e.m.1025.3 | 8 | |||
24.5 | odd | 2 | inner | 1152.3.h.f.449.5 | yes | 8 | |
24.11 | even | 2 | inner | 1152.3.h.f.449.7 | yes | 8 | |
48.5 | odd | 4 | 2304.3.e.m.1025.4 | 8 | |||
48.11 | even | 4 | 2304.3.e.m.1025.2 | 8 | |||
48.29 | odd | 4 | 2304.3.e.m.1025.7 | 8 | |||
48.35 | even | 4 | 2304.3.e.m.1025.5 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1152.3.h.f.449.1 | ✓ | 8 | 8.5 | even | 2 | inner | |
1152.3.h.f.449.2 | yes | 8 | 3.2 | odd | 2 | inner | |
1152.3.h.f.449.3 | yes | 8 | 8.3 | odd | 2 | inner | |
1152.3.h.f.449.4 | yes | 8 | 12.11 | even | 2 | inner | |
1152.3.h.f.449.5 | yes | 8 | 24.5 | odd | 2 | inner | |
1152.3.h.f.449.6 | yes | 8 | 1.1 | even | 1 | trivial | |
1152.3.h.f.449.7 | yes | 8 | 24.11 | even | 2 | inner | |
1152.3.h.f.449.8 | yes | 8 | 4.3 | odd | 2 | inner | |
2304.3.e.m.1025.1 | 8 | 16.3 | odd | 4 | |||
2304.3.e.m.1025.2 | 8 | 48.11 | even | 4 | |||
2304.3.e.m.1025.3 | 8 | 16.13 | even | 4 | |||
2304.3.e.m.1025.4 | 8 | 48.5 | odd | 4 | |||
2304.3.e.m.1025.5 | 8 | 48.35 | even | 4 | |||
2304.3.e.m.1025.6 | 8 | 16.11 | odd | 4 | |||
2304.3.e.m.1025.7 | 8 | 48.29 | odd | 4 | |||
2304.3.e.m.1025.8 | 8 | 16.5 | even | 4 |