Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1600,3,Mod(799,1600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1600, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 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("1600.799");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1600 = 2^{6} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1600.e (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(43.5968422976\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{31}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | no (minimal twist has level 64) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 799.1 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1600.799 |
Dual form | 1600.3.e.a.799.3 |
$q$-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 \(\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1151\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | − 3.46410i | − 1.15470i | −0.816497 | − | 0.577350i | \(-0.804087\pi\) | ||||
0.816497 | − | 0.577350i | \(-0.195913\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −8.00000 | −1.14286 | −0.571429 | − | 0.820652i | \(-0.693611\pi\) | ||||
−0.571429 | + | 0.820652i | \(0.693611\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.46410 | −0.314918 | −0.157459 | − | 0.987525i | \(-0.550330\pi\) | ||||
−0.157459 | + | 0.987525i | \(0.550330\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.92820 | −0.532939 | −0.266469 | − | 0.963843i | \(-0.585857\pi\) | ||||
−0.266469 | + | 0.963843i | \(0.585857\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.00000i | 0.352941i | 0.984306 | + | 0.176471i | \(0.0564680\pi\) | ||||
−0.984306 | + | 0.176471i | \(0.943532\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −24.2487 | −1.27625 | −0.638124 | − | 0.769934i | \(-0.720289\pi\) | ||||
−0.638124 | + | 0.769934i | \(0.720289\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 27.7128i | 1.31966i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 24.0000 | 1.04348 | 0.521739 | − | 0.853105i | \(-0.325283\pi\) | ||||
0.521739 | + | 0.853105i | \(0.325283\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 20.7846i | − 0.769800i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 20.7846i | 0.716711i | 0.933585 | + | 0.358355i | \(0.116662\pi\) | ||||
−0.933585 | + | 0.358355i | \(0.883338\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 32.0000i | 1.03226i | 0.856511 | + | 0.516129i | \(0.172628\pi\) | ||||
−0.856511 | + | 0.516129i | \(0.827372\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 12.0000i | 0.363636i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.92820 | −0.187249 | −0.0936244 | − | 0.995608i | \(-0.529845\pi\) | ||||
−0.0936244 | + | 0.995608i | \(0.529845\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 24.0000i | 0.615385i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 66.0000 | 1.60976 | 0.804878 | − | 0.593440i | \(-0.202231\pi\) | ||||
0.804878 | + | 0.593440i | \(0.202231\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 31.1769i | − 0.725045i | −0.931975 | − | 0.362522i | \(-0.881916\pi\) | ||||
0.931975 | − | 0.362522i | \(-0.118084\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −48.0000 | −1.02128 | −0.510638 | − | 0.859796i | \(-0.670591\pi\) | ||||
−0.510638 | + | 0.859796i | \(0.670591\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 15.0000 | 0.306122 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 20.7846 | 0.407541 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 90.0666 | 1.69937 | 0.849685 | − | 0.527290i | \(-0.176792\pi\) | ||||
0.849685 | + | 0.527290i | \(0.176792\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 84.0000i | 1.47368i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 31.1769 | 0.528422 | 0.264211 | − | 0.964465i | \(-0.414888\pi\) | ||||
0.264211 | + | 0.964465i | \(0.414888\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 90.0666i | 1.47650i | 0.674526 | + | 0.738251i | \(0.264348\pi\) | ||||
−0.674526 | + | 0.738251i | \(0.735652\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 24.0000 | 0.380952 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 79.6743i | − 1.18917i | −0.804033 | − | 0.594585i | \(-0.797317\pi\) | ||||
0.804033 | − | 0.594585i | \(-0.202683\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 83.1384i | − 1.20490i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 120.000i | 1.69014i | 0.534655 | + | 0.845070i | \(0.320442\pi\) | ||||
−0.534655 | + | 0.845070i | \(0.679558\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 58.0000i | 0.794521i | 0.917706 | + | 0.397260i | \(0.130039\pi\) | ||||
−0.917706 | + | 0.397260i | \(0.869961\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 27.7128 | 0.359907 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 16.0000i | 0.202532i | 0.994859 | + | 0.101266i | \(0.0322893\pi\) | ||||
−0.994859 | + | 0.101266i | \(0.967711\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −99.0000 | −1.22222 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 58.8897i | − 0.709515i | −0.934958 | − | 0.354757i | \(-0.884563\pi\) | ||||
0.934958 | − | 0.354757i | \(-0.115437\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 72.0000 | 0.827586 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 102.000 | 1.14607 | 0.573034 | − | 0.819532i | \(-0.305766\pi\) | ||||
0.573034 | + | 0.819532i | \(0.305766\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 55.4256 | 0.609073 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 110.851 | 1.19195 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 26.0000i | − 0.268041i | −0.990979 | − | 0.134021i | \(-0.957211\pi\) | ||||
0.990979 | − | 0.134021i | \(-0.0427888\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 10.3923 | 0.104973 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 6.92820i | − 0.0685961i | −0.999412 | − | 0.0342980i | \(-0.989080\pi\) | ||||
0.999412 | − | 0.0342980i | \(-0.0109195\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 40.0000 | 0.388350 | 0.194175 | − | 0.980967i | \(-0.437797\pi\) | ||||
0.194175 | + | 0.980967i | \(0.437797\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 58.8897i | 0.550371i | 0.961391 | + | 0.275186i | \(0.0887393\pi\) | ||||
−0.961391 | + | 0.275186i | \(0.911261\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 103.923i | 0.953422i | 0.879060 | + | 0.476711i | \(0.158171\pi\) | ||||
−0.879060 | + | 0.476711i | \(0.841829\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 24.0000i | 0.216216i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 66.0000i | 0.584071i | 0.956408 | + | 0.292035i | \(0.0943325\pi\) | ||||
−0.956408 | + | 0.292035i | \(0.905667\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 20.7846 | 0.177646 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 48.0000i | − 0.403361i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −109.000 | −0.900826 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 228.631i | − 1.85879i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 64.0000 | 0.503937 | 0.251969 | − | 0.967735i | \(-0.418922\pi\) | ||||
0.251969 | + | 0.967735i | \(0.418922\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −108.000 | −0.837209 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 245.951 | 1.87749 | 0.938745 | − | 0.344612i | \(-0.111990\pi\) | ||||
0.938745 | + | 0.344612i | \(0.111990\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 193.990 | 1.45857 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 30.0000i | 0.218978i | 0.993988 | + | 0.109489i | \(0.0349215\pi\) | ||||
−0.993988 | + | 0.109489i | \(0.965079\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −79.6743 | −0.573197 | −0.286598 | − | 0.958051i | \(-0.592525\pi\) | ||||
−0.286598 | + | 0.958051i | \(0.592525\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 166.277i | 1.17927i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 24.0000 | 0.167832 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 51.9615i | − 0.353480i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 131.636i | − 0.883462i | −0.897148 | − | 0.441731i | \(-0.854365\pi\) | ||||
0.897148 | − | 0.441731i | \(-0.145635\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 152.000i | − 1.00662i | −0.864105 | − | 0.503311i | \(-0.832115\pi\) | ||||
0.864105 | − | 0.503311i | \(-0.167885\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 18.0000i | − 0.117647i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 145.492 | 0.926702 | 0.463351 | − | 0.886175i | \(-0.346647\pi\) | ||||
0.463351 | + | 0.886175i | \(0.346647\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − 312.000i | − 1.96226i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −192.000 | −1.19255 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 169.741i | − 1.04136i | −0.853753 | − | 0.520678i | \(-0.825679\pi\) | ||||
0.853753 | − | 0.520678i | \(-0.174321\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 216.000 | 1.29341 | 0.646707 | − | 0.762739i | \(-0.276146\pi\) | ||||
0.646707 | + | 0.762739i | \(0.276146\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −121.000 | −0.715976 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 72.7461 | 0.425416 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −173.205 | −1.00119 | −0.500593 | − | 0.865683i | \(-0.666885\pi\) | ||||
−0.500593 | + | 0.865683i | \(0.666885\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − 108.000i | − 0.610169i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −107.387 | −0.599928 | −0.299964 | − | 0.953950i | \(-0.596975\pi\) | ||||
−0.299964 | + | 0.953950i | \(0.596975\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 76.2102i | 0.421051i | 0.977588 | + | 0.210526i | \(0.0675175\pi\) | ||||
−0.977588 | + | 0.210526i | \(0.932482\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 312.000 | 1.70492 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 20.7846i | − 0.111148i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 166.277i | 0.879772i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 218.000i | 1.12953i | 0.825251 | + | 0.564767i | \(0.191034\pi\) | ||||
−0.825251 | + | 0.564767i | \(0.808966\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 214.774 | 1.09022 | 0.545112 | − | 0.838363i | \(-0.316487\pi\) | ||||
0.545112 | + | 0.838363i | \(0.316487\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 328.000i | 1.64824i | 0.566414 | + | 0.824121i | \(0.308330\pi\) | ||||
−0.566414 | + | 0.824121i | \(0.691670\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −276.000 | −1.37313 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 166.277i | − 0.819098i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −72.0000 | −0.347826 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 84.0000 | 0.401914 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 107.387 | 0.508944 | 0.254472 | − | 0.967080i | \(-0.418098\pi\) | ||||
0.254472 | + | 0.967080i | \(0.418098\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 415.692 | 1.95161 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 256.000i | − 1.17972i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 200.918 | 0.917433 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 41.5692i | − 0.188096i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 32.0000 | 0.143498 | 0.0717489 | − | 0.997423i | \(-0.477142\pi\) | ||||
0.0717489 | + | 0.997423i | \(0.477142\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 114.315i | 0.503592i | 0.967780 | + | 0.251796i | \(0.0810212\pi\) | ||||
−0.967780 | + | 0.251796i | \(0.918979\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 270.200i | − 1.17991i | −0.807435 | − | 0.589956i | \(-0.799145\pi\) | ||||
0.807435 | − | 0.589956i | \(-0.200855\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − 96.0000i | − 0.415584i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 186.000i | 0.798283i | 0.916889 | + | 0.399142i | \(0.130692\pi\) | ||||
−0.916889 | + | 0.399142i | \(0.869308\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 55.4256 | 0.233863 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 48.0000i | 0.200837i | 0.994945 | + | 0.100418i | \(0.0320181\pi\) | ||||
−0.994945 | + | 0.100418i | \(0.967982\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 250.000 | 1.03734 | 0.518672 | − | 0.854973i | \(-0.326427\pi\) | ||||
0.518672 | + | 0.854973i | \(0.326427\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 155.885i | 0.641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 168.000 | 0.680162 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −204.000 | −0.819277 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 301.377 | 1.20070 | 0.600352 | − | 0.799736i | \(-0.295027\pi\) | ||||
0.600352 | + | 0.799736i | \(0.295027\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −83.1384 | −0.328610 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 222.000i | 0.863813i | 0.901918 | + | 0.431907i | \(0.142159\pi\) | ||||
−0.901918 | + | 0.431907i | \(0.857841\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 55.4256 | 0.213999 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 62.3538i | − 0.238904i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −312.000 | −1.18631 | −0.593156 | − | 0.805088i | \(-0.702118\pi\) | ||||
−0.593156 | + | 0.805088i | \(0.702118\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 353.338i | − 1.32336i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 62.3538i | − 0.231799i | −0.993261 | − | 0.115899i | \(-0.963025\pi\) | ||||
0.993261 | − | 0.115899i | \(-0.0369750\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 112.000i | 0.413284i | 0.978417 | + | 0.206642i | \(0.0662536\pi\) | ||||
−0.978417 | + | 0.206642i | \(0.933746\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − 192.000i | − 0.703297i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −145.492 | −0.525243 | −0.262621 | − | 0.964899i | \(-0.584587\pi\) | ||||
−0.262621 | + | 0.964899i | \(0.584587\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − 96.0000i | − 0.344086i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 90.0000 | 0.320285 | 0.160142 | − | 0.987094i | \(-0.448805\pi\) | ||||
0.160142 | + | 0.987094i | \(0.448805\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 218.238i | 0.771160i | 0.922674 | + | 0.385580i | \(0.125999\pi\) | ||||
−0.922674 | + | 0.385580i | \(0.874001\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −528.000 | −1.83972 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 253.000 | 0.875433 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −90.0666 | −0.309507 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 62.3538 | 0.212812 | 0.106406 | − | 0.994323i | \(-0.466066\pi\) | ||||
0.106406 | + | 0.994323i | \(0.466066\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 72.0000i | 0.242424i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −166.277 | −0.556110 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 249.415i | 0.828622i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −24.0000 | −0.0792079 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 135.100i | − 0.440065i | −0.975493 | − | 0.220033i | \(-0.929384\pi\) | ||||
0.975493 | − | 0.220033i | \(-0.0706163\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 138.564i | − 0.448427i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 264.000i | 0.848875i | 0.905457 | + | 0.424437i | \(0.139528\pi\) | ||||
−0.905457 | + | 0.424437i | \(0.860472\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 226.000i | 0.722045i | 0.932557 | + | 0.361022i | \(0.117572\pi\) | ||||
−0.932557 | + | 0.361022i | \(0.882428\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −408.764 | −1.28948 | −0.644738 | − | 0.764404i | \(-0.723034\pi\) | ||||
−0.644738 | + | 0.764404i | \(0.723034\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 72.0000i | − 0.225705i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 204.000 | 0.635514 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 145.492i | − 0.450440i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 360.000 | 1.10092 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 384.000 | 1.16717 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −502.295 | −1.51751 | −0.758753 | − | 0.651378i | \(-0.774191\pi\) | ||||
−0.758753 | + | 0.651378i | \(0.774191\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 20.7846 | 0.0624162 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 382.000i | 1.13353i | 0.823879 | + | 0.566766i | \(0.191805\pi\) | ||||
−0.823879 | + | 0.566766i | \(0.808195\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 228.631 | 0.674427 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 110.851i | − 0.325077i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 272.000 | 0.793003 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 640.859i | 1.84686i | 0.383773 | + | 0.923428i | \(0.374625\pi\) | ||||
−0.383773 | + | 0.923428i | \(0.625375\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 464.190i | 1.33006i | 0.746818 | + | 0.665028i | \(0.231580\pi\) | ||||
−0.746818 | + | 0.665028i | \(0.768420\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 144.000i | 0.410256i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 318.000i | − 0.900850i | −0.892814 | − | 0.450425i | \(-0.851272\pi\) | ||||
0.892814 | − | 0.450425i | \(-0.148728\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −166.277 | −0.465762 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 552.000i | 1.53760i | 0.639487 | + | 0.768802i | \(0.279147\pi\) | ||||
−0.639487 | + | 0.768802i | \(0.720853\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 227.000 | 0.628809 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 377.587i | 1.04018i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −496.000 | −1.35150 | −0.675749 | − | 0.737132i | \(-0.736180\pi\) | ||||
−0.675749 | + | 0.737132i | \(0.736180\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −198.000 | −0.536585 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −720.533 | −1.94214 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −575.041 | −1.54166 | −0.770832 | − | 0.637038i | \(-0.780159\pi\) | ||||
−0.770832 | + | 0.637038i | \(0.780159\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 144.000i | − 0.381963i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −245.951 | −0.648948 | −0.324474 | − | 0.945895i | \(-0.605187\pi\) | ||||
−0.324474 | + | 0.945895i | \(0.605187\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 221.703i | − 0.581896i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −384.000 | −1.00261 | −0.501305 | − | 0.865270i | \(-0.667147\pi\) | ||||
−0.501305 | + | 0.865270i | \(0.667147\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 93.5307i | 0.241682i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 284.056i | 0.730222i | 0.930964 | + | 0.365111i | \(0.118969\pi\) | ||||
−0.930964 | + | 0.365111i | \(0.881031\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 144.000i | 0.368286i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 852.000i | − 2.16794i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 394.908 | 0.994729 | 0.497365 | − | 0.867542i | \(-0.334301\pi\) | ||||
0.497365 | + | 0.867542i | \(0.334301\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − 672.000i | − 1.68421i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 378.000 | 0.942643 | 0.471322 | − | 0.881961i | \(-0.343777\pi\) | ||||
0.471322 | + | 0.881961i | \(0.343777\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 221.703i | − 0.550130i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 24.0000 | 0.0589681 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −34.0000 | −0.0831296 | −0.0415648 | − | 0.999136i | \(-0.513234\pi\) | ||||
−0.0415648 | + | 0.999136i | \(0.513234\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 103.923 | 0.252854 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −249.415 | −0.603911 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 276.000i | 0.661871i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −301.377 | −0.719276 | −0.359638 | − | 0.933092i | \(-0.617100\pi\) | ||||
−0.359638 | + | 0.933092i | \(0.617100\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 48.4974i | 0.115196i | 0.998340 | + | 0.0575979i | \(0.0183441\pi\) | ||||
−0.998340 | + | 0.0575979i | \(0.981656\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 144.000 | 0.340426 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 720.533i | − 1.68743i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 83.1384i | − 0.193796i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 144.000i | 0.334107i | 0.985948 | + | 0.167053i | \(0.0534252\pi\) | ||||
−0.985948 | + | 0.167053i | \(0.946575\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 134.000i | − 0.309469i | −0.987956 | − | 0.154734i | \(-0.950548\pi\) | ||||
0.987956 | − | 0.154734i | \(-0.0494522\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −581.969 | −1.33174 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 376.000i | 0.856492i | 0.903662 | + | 0.428246i | \(0.140868\pi\) | ||||
−0.903662 | + | 0.428246i | \(0.859132\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −45.0000 | −0.102041 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 384.515i | 0.867980i | 0.900918 | + | 0.433990i | \(0.142895\pi\) | ||||
−0.900918 | + | 0.433990i | \(0.857105\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −456.000 | −1.02013 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 102.000 | 0.227171 | 0.113586 | − | 0.993528i | \(-0.463766\pi\) | ||||
0.113586 | + | 0.993528i | \(0.463766\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −228.631 | −0.506942 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −526.543 | −1.16235 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 254.000i | 0.555799i | 0.960610 | + | 0.277899i | \(0.0896382\pi\) | ||||
−0.960610 | + | 0.277899i | \(0.910362\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 124.708 | 0.271694 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 48.4974i | − 0.105200i | −0.998616 | − | 0.0526002i | \(-0.983249\pi\) | ||||
0.998616 | − | 0.0526002i | \(-0.0167509\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −880.000 | −1.90065 | −0.950324 | − | 0.311263i | \(-0.899248\pi\) | ||||
−0.950324 | + | 0.311263i | \(0.899248\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 142.028i | 0.304129i | 0.988371 | + | 0.152064i | \(0.0485921\pi\) | ||||
−0.988371 | + | 0.152064i | \(0.951408\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 637.395i | 1.35905i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − 504.000i | − 1.07006i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 108.000i | 0.228330i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −270.200 | −0.566457 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 480.000i | − 1.00209i | −0.865422 | − | 0.501044i | \(-0.832950\pi\) | ||||
0.865422 | − | 0.501044i | \(-0.167050\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 48.0000 | 0.0997921 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 665.108i | 1.37703i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 280.000 | 0.574949 | 0.287474 | − | 0.957788i | \(-0.407184\pi\) | ||||
0.287474 | + | 0.957788i | \(0.407184\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −588.000 | −1.20245 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −751.710 | −1.53098 | −0.765489 | − | 0.643449i | \(-0.777503\pi\) | ||||
−0.765489 | + | 0.643449i | \(0.777503\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −124.708 | −0.252957 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 960.000i | − 1.93159i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 280.592 | 0.562309 | 0.281155 | − | 0.959663i | \(-0.409283\pi\) | ||||
0.281155 | + | 0.959663i | \(0.409283\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 748.246i | − 1.49350i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 120.000 | 0.238569 | 0.119284 | − | 0.992860i | \(-0.461940\pi\) | ||||
0.119284 | + | 0.992860i | \(0.461940\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 419.156i | 0.826738i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 533.472i | − 1.04808i | −0.851694 | − | 0.524039i | \(-0.824425\pi\) | ||||
0.851694 | − | 0.524039i | \(-0.175575\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 464.000i | − 0.908023i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 504.000i | 0.982456i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 166.277 | 0.321619 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 600.000i | 1.15607i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 354.000 | 0.679463 | 0.339731 | − | 0.940523i | \(-0.389664\pi\) | ||||
0.339731 | + | 0.940523i | \(0.389664\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 162.813i | 0.311305i | 0.987812 | + | 0.155653i | \(0.0497481\pi\) | ||||
−0.987812 | + | 0.155653i | \(0.950252\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −192.000 | −0.364326 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 47.0000 | 0.0888469 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −93.5307 | −0.176141 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −457.261 | −0.857901 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 372.000i | 0.692737i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −51.9615 | −0.0964036 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 1073.87i | − 1.98498i | −0.122346 | − | 0.992488i | \(-0.539042\pi\) | ||||
0.122346 | − | 0.992488i | \(-0.460958\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 264.000 | 0.486188 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 917.987i | 1.67822i | 0.543961 | + | 0.839111i | \(0.316924\pi\) | ||||
−0.543961 | + | 0.839111i | \(0.683076\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 270.200i | − 0.492167i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 504.000i | − 0.914701i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 128.000i | − 0.231465i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −381.051 | −0.684113 | −0.342057 | − | 0.939679i | \(-0.611123\pi\) | ||||
−0.342057 | + | 0.939679i | \(0.611123\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 216.000i | 0.386404i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −72.0000 | −0.128342 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 911.059i | 1.61822i | 0.587656 | + | 0.809111i | \(0.300051\pi\) | ||||
−0.587656 | + | 0.809111i | \(0.699949\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 792.000 | 1.39683 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 702.000 | 1.23374 | 0.616872 | − | 0.787064i | \(-0.288400\pi\) | ||||
0.616872 | + | 0.787064i | \(0.288400\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 938.772 | 1.64408 | 0.822042 | − | 0.569427i | \(-0.192835\pi\) | ||||
0.822042 | + | 0.569427i | \(0.192835\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 802.000i | − 1.38995i | −0.719035 | − | 0.694974i | \(-0.755416\pi\) | ||||
0.719035 | − | 0.694974i | \(-0.244584\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 755.174 | 1.30427 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 471.118i | 0.810874i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −312.000 | −0.535163 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 107.387i | − 0.182942i | −0.995808 | − | 0.0914712i | \(-0.970843\pi\) | ||||
0.995808 | − | 0.0914712i | \(-0.0291569\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 775.959i | − 1.31742i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − 744.000i | − 1.25888i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 798.000i | − 1.34570i | −0.739779 | − | 0.672850i | \(-0.765070\pi\) | ||||
0.739779 | − | 0.672850i | \(-0.234930\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1136.23 | 1.90323 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 24.0000i | 0.0400668i | 0.999799 | + | 0.0200334i | \(0.00637725\pi\) | ||||
−0.999799 | + | 0.0200334i | \(0.993623\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 218.000 | 0.362729 | 0.181364 | − | 0.983416i | \(-0.441949\pi\) | ||||
0.181364 | + | 0.983416i | \(0.441949\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 239.023i | 0.396390i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −608.000 | −1.00165 | −0.500824 | − | 0.865549i | \(-0.666970\pi\) | ||||
−0.500824 | + | 0.865549i | \(0.666970\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −576.000 | −0.945813 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 332.554 | 0.544278 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −381.051 | −0.621617 | −0.310808 | − | 0.950473i | \(-0.600600\pi\) | ||||
−0.310808 | + | 0.950473i | \(0.600600\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 954.000i | − 1.54619i | −0.634289 | − | 0.773096i | \(-0.718707\pi\) | ||||
0.634289 | − | 0.773096i | \(-0.281293\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 225.167 | 0.363759 | 0.181879 | − | 0.983321i | \(-0.441782\pi\) | ||||
0.181879 | + | 0.983321i | \(0.441782\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 498.831i | − 0.803270i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −816.000 | −1.30979 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 290.985i | − 0.464090i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 41.5692i | − 0.0660878i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 248.000i | − 0.393027i | −0.980501 | − | 0.196513i | \(-0.937038\pi\) | ||||
0.980501 | − | 0.196513i | \(-0.0629619\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 372.000i | − 0.587678i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −103.923 | −0.163145 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − 360.000i | − 0.563380i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1062.00 | −1.65679 | −0.828393 | − | 0.560147i | \(-0.810745\pi\) | ||||
−0.828393 | + | 0.560147i | \(0.810745\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 301.377i | 0.468704i | 0.972152 | + | 0.234352i | \(0.0752969\pi\) | ||||
−0.972152 | + | 0.234352i | \(0.924703\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 696.000 | 1.07573 | 0.537867 | − | 0.843030i | \(-0.319230\pi\) | ||||
0.537867 | + | 0.843030i | \(0.319230\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −108.000 | −0.166410 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −886.810 | −1.36223 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −505.759 | −0.774516 | −0.387258 | − | 0.921971i | \(-0.626578\pi\) | ||||
−0.387258 | + | 0.921971i | \(0.626578\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 174.000i | − 0.264840i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −938.772 | −1.42454 | −0.712270 | − | 0.701906i | \(-0.752333\pi\) | ||||
−0.712270 | + | 0.701906i | \(0.752333\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 200.918i | − 0.303961i | −0.988384 | − | 0.151980i | \(-0.951435\pi\) | ||||
0.988384 | − | 0.151980i | \(-0.0485650\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −144.000 | −0.217195 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 498.831i | 0.747872i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 110.851i | − 0.165697i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 312.000i | − 0.464978i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 730.000i | 1.08470i | 0.840154 | + | 0.542348i | \(0.182464\pi\) | ||||
−0.840154 | + | 0.542348i | \(0.817536\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −893.738 | −1.32015 | −0.660073 | − | 0.751202i | \(-0.729474\pi\) | ||||
−0.660073 | + | 0.751202i | \(0.729474\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 208.000i | 0.306333i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 396.000 | 0.581498 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 467.654i | 0.684705i | 0.939572 | + | 0.342353i | \(0.111224\pi\) | ||||
−0.939572 | + | 0.342353i | \(0.888776\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −936.000 | −1.36245 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −624.000 | −0.905660 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −446.869 | −0.646699 | −0.323350 | − | 0.946280i | \(-0.604809\pi\) | ||||
−0.323350 | + | 0.946280i | \(0.604809\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −83.1384 | −0.119969 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 396.000i | 0.568149i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 644.323 | 0.921778 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 131.636i | − 0.187783i | −0.995582 | − | 0.0938915i | \(-0.970069\pi\) | ||||
0.995582 | − | 0.0938915i | \(-0.0299307\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 168.000 | 0.238976 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 55.4256i | 0.0783955i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1281.72i | 1.80778i | 0.427763 | + | 0.903891i | \(0.359302\pi\) | ||||
−0.427763 | + | 0.903891i | \(0.640698\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − 48.0000i | − 0.0675105i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 768.000i | 1.07714i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 166.277 | 0.231906 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 1008.00i | − 1.40195i | −0.713187 | − | 0.700974i | \(-0.752749\pi\) | ||||
0.713187 | − | 0.700974i | \(-0.247251\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −320.000 | −0.443828 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 866.025i | − 1.19782i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1384.00 | 1.90371 | 0.951857 | − | 0.306543i | \(-0.0991722\pi\) | ||||
0.951857 | + | 0.306543i | \(0.0991722\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −351.000 | −0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 187.061 | 0.255898 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1018.45 | 1.38942 | 0.694711 | − | 0.719289i | \(-0.255532\pi\) | ||||
0.694711 | + | 0.719289i | \(0.255532\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 276.000i | 0.374491i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 446.869 | 0.604694 | 0.302347 | − | 0.953198i | \(-0.402230\pi\) | ||||
0.302347 | + | 0.953198i | \(0.402230\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 581.969i | − 0.785383i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 744.000 | 1.00135 | 0.500673 | − | 0.865637i | \(-0.333086\pi\) | ||||
0.500673 | + | 0.865637i | \(0.333086\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 176.669i | 0.236505i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 471.118i | − 0.628996i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 848.000i | 1.12916i | 0.825378 | + | 0.564581i | \(0.190962\pi\) | ||||
−0.825378 | + | 0.564581i | \(0.809038\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − 1044.00i | − 1.38645i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 297.913 | 0.393544 | 0.196772 | − | 0.980449i | \(-0.436954\pi\) | ||||
0.196772 | + | 0.980449i | \(0.436954\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 288.000i | 0.379447i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −414.000 | −0.544021 | −0.272011 | − | 0.962294i | \(-0.587689\pi\) | ||||
−0.272011 | + | 0.962294i | \(0.587689\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 831.384i | − 1.08963i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −216.000 | −0.281617 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 358.000 | 0.465540 | 0.232770 | − | 0.972532i | \(-0.425221\pi\) | ||||
0.232770 | + | 0.972532i | \(0.425221\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 769.031 | 0.997446 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1267.86 | −1.64018 | −0.820091 | − | 0.572233i | \(-0.806077\pi\) | ||||
−0.820091 | + | 0.572233i | \(0.806077\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − 192.000i | − 0.247104i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1600.41 | −2.05445 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 415.692i | − 0.532256i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 432.000 | 0.551724 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 772.495i | − 0.981569i | −0.871281 | − | 0.490784i | \(-0.836710\pi\) | ||||
0.871281 | − | 0.490784i | \(-0.163290\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1080.80i | 1.36983i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 528.000i | − 0.667509i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 624.000i | − 0.786885i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −76.2102 | −0.0956214 | −0.0478107 | − | 0.998856i | \(-0.515224\pi\) | ||||
−0.0478107 | + | 0.998856i | \(0.515224\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 288.000i | − 0.360451i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −306.000 | −0.382022 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 200.918i | − 0.250209i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −216.000 | −0.267658 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 702.000 | 0.867738 | 0.433869 | − | 0.900976i | \(-0.357148\pi\) | ||||
0.433869 | + | 0.900976i | \(0.357148\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −446.869 | −0.551010 | −0.275505 | − | 0.961300i | \(-0.588845\pi\) | ||||
−0.275505 | + | 0.961300i | \(0.588845\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 387.979 | 0.477219 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 756.000i | 0.925337i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −166.277 | −0.203024 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1351.00i | 1.64555i | 0.568365 | + | 0.822777i | \(0.307576\pi\) | ||||
−0.568365 | + | 0.822777i | \(0.692424\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −520.000 | −0.631835 | −0.315917 | − | 0.948787i | \(-0.602312\pi\) | ||||
−0.315917 | + | 0.948787i | \(0.602312\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1111.98i | 1.34459i | 0.740283 | + | 0.672295i | \(0.234692\pi\) | ||||
−0.740283 | + | 0.672295i | \(0.765308\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 200.918i | − 0.242362i | −0.992630 | − | 0.121181i | \(-0.961332\pi\) | ||||
0.992630 | − | 0.121181i | \(-0.0386681\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 504.000i | 0.606498i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 90.0000i | 0.108043i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 665.108 | 0.794633 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 72.0000i | 0.0858164i | 0.999079 | + | 0.0429082i | \(0.0136623\pi\) | ||||
−0.999079 | + | 0.0429082i | \(0.986338\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 409.000 | 0.486326 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 311.769i | − 0.369833i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 872.000 | 1.02952 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 756.000 | 0.890459 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −166.277 | −0.195390 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 256.344 | 0.300520 | 0.150260 | − | 0.988647i | \(-0.451989\pi\) | ||||
0.150260 | + | 0.988647i | \(0.451989\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 510.000i | 0.595099i | 0.954706 | + | 0.297550i | \(0.0961694\pi\) | ||||
−0.954706 | + | 0.297550i | \(0.903831\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 973.413 | 1.13319 | 0.566596 | − | 0.823995i | \(-0.308260\pi\) | ||||
0.566596 | + | 0.823995i | \(0.308260\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1829.05i | 2.12433i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1248.00 | −1.44612 | −0.723059 | − | 0.690786i | \(-0.757265\pi\) | ||||
−0.723059 | + | 0.690786i | \(0.757265\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 876.418i | − 1.01086i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 55.4256i | − 0.0637809i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 552.000i | 0.633754i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 78.0000i | 0.0893471i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 450.333 | 0.513493 | 0.256746 | − | 0.966479i | \(-0.417349\pi\) | ||||
0.256746 | + | 0.966479i | \(0.417349\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − 216.000i | − 0.245734i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1218.00 | 1.38252 | 0.691260 | − | 0.722606i | \(-0.257056\pi\) | ||||
0.691260 | + | 0.722606i | \(0.257056\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 252.879i | − 0.286387i | −0.989695 | − | 0.143193i | \(-0.954263\pi\) | ||||
0.989695 | − | 0.143193i | \(-0.0457371\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1464.00 | −1.65051 | −0.825254 | − | 0.564762i | \(-0.808968\pi\) | ||||
−0.825254 | + | 0.564762i | \(0.808968\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −512.000 | −0.575928 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 342.946 | 0.384900 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1163.94 | 1.30340 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 576.000i | 0.642140i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −665.108 | −0.739830 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 540.400i | 0.599778i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 864.000 | 0.956811 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 1243.61i | − 1.37113i | −0.728013 | − | 0.685564i | \(-0.759556\pi\) | ||||
0.728013 | − | 0.685564i | \(-0.240444\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 20.7846i | 0.0228654i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 624.000i | 0.684962i | 0.939525 | + | 0.342481i | \(0.111267\pi\) | ||||
−0.939525 | + | 0.342481i | \(0.888733\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 204.000i | 0.223439i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1967.61 | −2.14570 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1304.00i | 1.41893i | 0.704739 | + | 0.709467i | \(0.251064\pi\) | ||||
−0.704739 | + | 0.709467i | \(0.748936\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −468.000 | −0.508143 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 831.384i | − 0.900741i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −120.000 | −0.129450 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 486.000 | 0.523143 | 0.261572 | − | 0.965184i | \(-0.415759\pi\) | ||||
0.261572 | + | 0.965184i | \(0.415759\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −363.731 | −0.390688 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 914.523 | 0.980196 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1094.00i | 1.16756i | 0.811913 | + | 0.583778i | \(0.198426\pi\) | ||||
−0.811913 | + | 0.583778i | \(0.801574\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 782.887 | 0.833745 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 214.774i | − 0.228240i | −0.993467 | − | 0.114120i | \(-0.963595\pi\) | ||||
0.993467 | − | 0.114120i | \(-0.0364049\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1584.00 | 1.67975 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 640.859i | 0.676725i | 0.941016 | + | 0.338363i | \(0.109873\pi\) | ||||
−0.941016 | + | 0.338363i | \(0.890127\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 401.836i | − 0.423431i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1416.00i | 1.48896i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1218.00i | 1.27807i | 0.769178 | + | 0.639035i | \(0.220666\pi\) | ||||
−0.769178 | + | 0.639035i | \(0.779334\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −249.415 | −0.260622 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 240.000i | − 0.250261i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −63.0000 | −0.0655567 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 176.669i | − 0.183457i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 56.0000 | 0.0579111 | 0.0289555 | − | 0.999581i | \(-0.490782\pi\) | ||||
0.0289555 | + | 0.999581i | \(0.490782\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −504.000 | −0.520124 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −86.6025 | −0.0891890 | −0.0445945 | − | 0.999005i | \(-0.514200\pi\) | ||||
−0.0445945 | + | 0.999005i | \(0.514200\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 637.395 | 0.655082 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 570.000i | − 0.583419i | −0.956507 | − | 0.291709i | \(-0.905776\pi\) | ||||
0.956507 | − | 0.291709i | \(-0.0942240\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −353.338 | −0.360918 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 311.769i | − 0.317807i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 792.000 | 0.805697 | 0.402848 | − | 0.915267i | \(-0.368020\pi\) | ||||
0.402848 | + | 0.915267i | \(0.368020\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 1330.22i | − 1.34774i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 748.246i | − 0.756568i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1184.00i | 1.19475i | 0.801961 | + | 0.597376i | \(0.203790\pi\) | ||||
−0.801961 | + | 0.597376i | \(0.796210\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1740.00i | 1.75227i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 769.031 | 0.771345 | 0.385672 | − | 0.922636i | \(-0.373970\pi\) | ||||
0.385672 | + | 0.922636i | \(0.373970\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 144.000i | 0.144144i |
(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 | 1600.3.e.a.799.1 | 4 | ||
4.3 | odd | 2 | 1600.3.e.f.799.4 | 4 | |||
5.2 | odd | 4 | 64.3.d.a.31.1 | ✓ | 4 | ||
5.3 | odd | 4 | 1600.3.g.c.351.4 | 4 | |||
5.4 | even | 2 | 1600.3.e.f.799.3 | 4 | |||
8.3 | odd | 2 | 1600.3.e.f.799.1 | 4 | |||
8.5 | even | 2 | inner | 1600.3.e.a.799.4 | 4 | ||
15.2 | even | 4 | 576.3.b.d.415.3 | 4 | |||
20.3 | even | 4 | 1600.3.g.c.351.1 | 4 | |||
20.7 | even | 4 | 64.3.d.a.31.3 | yes | 4 | ||
20.19 | odd | 2 | inner | 1600.3.e.a.799.2 | 4 | ||
40.3 | even | 4 | 1600.3.g.c.351.3 | 4 | |||
40.13 | odd | 4 | 1600.3.g.c.351.2 | 4 | |||
40.19 | odd | 2 | inner | 1600.3.e.a.799.3 | 4 | ||
40.27 | even | 4 | 64.3.d.a.31.2 | yes | 4 | ||
40.29 | even | 2 | 1600.3.e.f.799.2 | 4 | |||
40.37 | odd | 4 | 64.3.d.a.31.4 | yes | 4 | ||
60.47 | odd | 4 | 576.3.b.d.415.4 | 4 | |||
80.27 | even | 4 | 256.3.c.g.255.2 | 4 | |||
80.37 | odd | 4 | 256.3.c.g.255.4 | 4 | |||
80.67 | even | 4 | 256.3.c.g.255.3 | 4 | |||
80.77 | odd | 4 | 256.3.c.g.255.1 | 4 | |||
120.77 | even | 4 | 576.3.b.d.415.1 | 4 | |||
120.107 | odd | 4 | 576.3.b.d.415.2 | 4 | |||
240.77 | even | 4 | 2304.3.g.u.1279.4 | 4 | |||
240.107 | odd | 4 | 2304.3.g.u.1279.1 | 4 | |||
240.197 | even | 4 | 2304.3.g.u.1279.2 | 4 | |||
240.227 | odd | 4 | 2304.3.g.u.1279.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
64.3.d.a.31.1 | ✓ | 4 | 5.2 | odd | 4 | ||
64.3.d.a.31.2 | yes | 4 | 40.27 | even | 4 | ||
64.3.d.a.31.3 | yes | 4 | 20.7 | even | 4 | ||
64.3.d.a.31.4 | yes | 4 | 40.37 | odd | 4 | ||
256.3.c.g.255.1 | 4 | 80.77 | odd | 4 | |||
256.3.c.g.255.2 | 4 | 80.27 | even | 4 | |||
256.3.c.g.255.3 | 4 | 80.67 | even | 4 | |||
256.3.c.g.255.4 | 4 | 80.37 | odd | 4 | |||
576.3.b.d.415.1 | 4 | 120.77 | even | 4 | |||
576.3.b.d.415.2 | 4 | 120.107 | odd | 4 | |||
576.3.b.d.415.3 | 4 | 15.2 | even | 4 | |||
576.3.b.d.415.4 | 4 | 60.47 | odd | 4 | |||
1600.3.e.a.799.1 | 4 | 1.1 | even | 1 | trivial | ||
1600.3.e.a.799.2 | 4 | 20.19 | odd | 2 | inner | ||
1600.3.e.a.799.3 | 4 | 40.19 | odd | 2 | inner | ||
1600.3.e.a.799.4 | 4 | 8.5 | even | 2 | inner | ||
1600.3.e.f.799.1 | 4 | 8.3 | odd | 2 | |||
1600.3.e.f.799.2 | 4 | 40.29 | even | 2 | |||
1600.3.e.f.799.3 | 4 | 5.4 | even | 2 | |||
1600.3.e.f.799.4 | 4 | 4.3 | odd | 2 | |||
1600.3.g.c.351.1 | 4 | 20.3 | even | 4 | |||
1600.3.g.c.351.2 | 4 | 40.13 | odd | 4 | |||
1600.3.g.c.351.3 | 4 | 40.3 | even | 4 | |||
1600.3.g.c.351.4 | 4 | 5.3 | odd | 4 | |||
2304.3.g.u.1279.1 | 4 | 240.107 | odd | 4 | |||
2304.3.g.u.1279.2 | 4 | 240.197 | even | 4 | |||
2304.3.g.u.1279.3 | 4 | 240.227 | odd | 4 | |||
2304.3.g.u.1279.4 | 4 | 240.77 | even | 4 |