Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1216,3,Mod(1025,1216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1216, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1216.1025");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1216 = 2^{6} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1216.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: | \(33.1336001462\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{-2}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 152) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1025.2 | ||
Root | \(1.41421i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1216.1025 |
Dual form | 1216.3.e.d.1025.1 |
$q$-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 \(\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(705\) | \(837\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 5.65685i | 1.88562i | 0.333333 | + | 0.942809i | \(0.391827\pi\) | ||||
−0.333333 | + | 0.942809i | \(0.608173\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −7.00000 | −1.40000 | −0.700000 | − | 0.714143i | \(-0.746817\pi\) | ||||
−0.700000 | + | 0.714143i | \(0.746817\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 11.0000 | 1.57143 | 0.785714 | − | 0.618590i | \(-0.212296\pi\) | ||||
0.785714 | + | 0.618590i | \(0.212296\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −23.0000 | −2.55556 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.00000 | −0.272727 | −0.136364 | − | 0.990659i | \(-0.543542\pi\) | ||||
−0.136364 | + | 0.990659i | \(0.543542\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 11.3137i | − 0.870285i | −0.900362 | − | 0.435143i | \(-0.856698\pi\) | ||||
0.900362 | − | 0.435143i | \(-0.143302\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − 39.5980i | − 2.63987i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −17.0000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 19.0000 | 1.00000 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 62.2254i | 2.96311i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.00000 | 0.0869565 | 0.0434783 | − | 0.999054i | \(-0.486156\pi\) | ||||
0.0434783 | + | 0.999054i | \(0.486156\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 24.0000 | 0.960000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 79.1960i | − 2.93318i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 39.5980i | − 1.36545i | −0.730677 | − | 0.682724i | \(-0.760795\pi\) | ||||
0.730677 | − | 0.682724i | \(-0.239205\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 5.65685i | − 0.182479i | −0.995829 | − | 0.0912396i | \(-0.970917\pi\) | ||||
0.995829 | − | 0.0912396i | \(-0.0290829\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 16.9706i | − 0.514259i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −77.0000 | −2.20000 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 39.5980i | − 1.07022i | −0.844784 | − | 0.535108i | \(-0.820271\pi\) | ||||
0.844784 | − | 0.535108i | \(-0.179729\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 64.0000 | 1.64103 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 39.5980i | − 0.965804i | −0.875674 | − | 0.482902i | \(-0.839583\pi\) | ||||
0.875674 | − | 0.482902i | \(-0.160417\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 21.0000 | 0.488372 | 0.244186 | − | 0.969728i | \(-0.421479\pi\) | ||||
0.244186 | + | 0.969728i | \(0.421479\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 161.000 | 3.57778 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.00000 | −0.106383 | −0.0531915 | − | 0.998584i | \(-0.516939\pi\) | ||||
−0.0531915 | + | 0.998584i | \(0.516939\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 72.0000 | 1.46939 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 96.1665i | − 1.88562i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.65685i | 0.106733i | 0.998575 | + | 0.0533665i | \(0.0169952\pi\) | ||||
−0.998575 | + | 0.0533665i | \(0.983005\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 21.0000 | 0.381818 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 107.480i | 1.88562i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 33.9411i | 0.575273i | 0.957740 | + | 0.287637i | \(0.0928695\pi\) | ||||
−0.957740 | + | 0.287637i | \(0.907130\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −23.0000 | −0.377049 | −0.188525 | − | 0.982068i | \(-0.560371\pi\) | ||||
−0.188525 | + | 0.982068i | \(0.560371\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −253.000 | −4.01587 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 79.1960i | 1.21840i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 39.5980i | 0.591015i | 0.955340 | + | 0.295507i | \(0.0954887\pi\) | ||||
−0.955340 | + | 0.295507i | \(0.904511\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 11.3137i | 0.163967i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 90.5097i | − 1.27478i | −0.770540 | − | 0.637392i | \(-0.780013\pi\) | ||||
0.770540 | − | 0.637392i | \(-0.219987\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 39.0000 | 0.534247 | 0.267123 | − | 0.963662i | \(-0.413927\pi\) | ||||
0.267123 | + | 0.963662i | \(0.413927\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 135.765i | 1.81019i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −33.0000 | −0.428571 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 96.1665i | 1.21730i | 0.793440 | + | 0.608649i | \(0.208288\pi\) | ||||
−0.793440 | + | 0.608649i | \(0.791712\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 241.000 | 2.97531 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.00000 | 0.0722892 | 0.0361446 | − | 0.999347i | \(-0.488492\pi\) | ||||
0.0361446 | + | 0.999347i | \(0.488492\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 119.000 | 1.40000 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 224.000 | 2.57471 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 118.794i | − 1.33476i | −0.744716 | − | 0.667382i | \(-0.767415\pi\) | ||||
0.744716 | − | 0.667382i | \(-0.232585\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 124.451i | − 1.36759i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 32.0000 | 0.344086 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −133.000 | −1.40000 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 169.706i | 1.74954i | 0.484536 | + | 0.874771i | \(0.338988\pi\) | ||||
−0.484536 | + | 0.874771i | \(0.661012\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 69.0000 | 0.696970 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −122.000 | −1.20792 | −0.603960 | − | 0.797014i | \(-0.706411\pi\) | ||||
−0.603960 | + | 0.797014i | \(0.706411\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 101.823i | − 0.988576i | −0.869298 | − | 0.494288i | \(-0.835429\pi\) | ||||
0.869298 | − | 0.494288i | \(-0.164571\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − 435.578i | − 4.14836i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 158.392i | 1.48030i | 0.672443 | + | 0.740149i | \(0.265245\pi\) | ||||
−0.672443 | + | 0.740149i | \(0.734755\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 118.794i | − 1.08985i | −0.838484 | − | 0.544926i | \(-0.816558\pi\) | ||||
0.838484 | − | 0.544926i | \(-0.183442\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 224.000 | 2.01802 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 50.9117i | − 0.450546i | −0.974296 | − | 0.225273i | \(-0.927673\pi\) | ||||
0.974296 | − | 0.225273i | \(-0.0723274\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −14.0000 | −0.121739 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 260.215i | 2.22406i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −187.000 | −1.57143 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −112.000 | −0.925620 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 224.000 | 1.82114 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 7.00000 | 0.0560000 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 39.5980i | 0.311795i | 0.987773 | + | 0.155898i | \(0.0498270\pi\) | ||||
−0.987773 | + | 0.155898i | \(0.950173\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 118.794i | 0.920883i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 149.000 | 1.13740 | 0.568702 | − | 0.822543i | \(-0.307446\pi\) | ||||
0.568702 | + | 0.822543i | \(0.307446\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 209.000 | 1.57143 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 554.372i | 4.10646i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 95.0000 | 0.693431 | 0.346715 | − | 0.937970i | \(-0.387297\pi\) | ||||
0.346715 | + | 0.937970i | \(0.387297\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −155.000 | −1.11511 | −0.557554 | − | 0.830141i | \(-0.688260\pi\) | ||||
−0.557554 | + | 0.830141i | \(0.688260\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 28.2843i | − 0.200598i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 33.9411i | 0.237351i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 277.186i | 1.91163i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 407.294i | 2.77070i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −63.0000 | −0.422819 | −0.211409 | − | 0.977398i | \(-0.567805\pi\) | ||||
−0.211409 | + | 0.977398i | \(0.567805\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 124.451i | 0.824177i | 0.911144 | + | 0.412089i | \(0.135201\pi\) | ||||
−0.911144 | + | 0.412089i | \(0.864799\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 391.000 | 2.55556 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 39.5980i | 0.255471i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 150.000 | 0.955414 | 0.477707 | − | 0.878519i | \(-0.341468\pi\) | ||||
0.477707 | + | 0.878519i | \(0.341468\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −32.0000 | −0.201258 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 22.0000 | 0.136646 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 166.000 | 1.01840 | 0.509202 | − | 0.860647i | \(-0.329940\pi\) | ||||
0.509202 | + | 0.860647i | \(0.329940\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 118.794i | 0.719963i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 209.304i | − 1.25332i | −0.779295 | − | 0.626658i | \(-0.784423\pi\) | ||||
0.779295 | − | 0.626658i | \(-0.215577\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 41.0000 | 0.242604 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −437.000 | −2.55556 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 56.5685i | 0.326986i | 0.986545 | + | 0.163493i | \(0.0522761\pi\) | ||||
−0.986545 | + | 0.163493i | \(0.947724\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 264.000 | 1.50857 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −192.000 | −1.08475 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 73.5391i | − 0.410833i | −0.978675 | − | 0.205416i | \(-0.934145\pi\) | ||||
0.978675 | − | 0.205416i | \(-0.0658549\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 79.1960i | − 0.437547i | −0.975776 | − | 0.218773i | \(-0.929794\pi\) | ||||
0.975776 | − | 0.218773i | \(-0.0702055\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 130.108i | − 0.710971i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 277.186i | 1.49830i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 51.0000 | 0.272727 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 871.156i | − 4.60929i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −301.000 | −1.57592 | −0.787958 | − | 0.615729i | \(-0.788862\pi\) | ||||
−0.787958 | + | 0.615729i | \(0.788862\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 152.735i | − 0.791373i | −0.918386 | − | 0.395687i | \(-0.870507\pi\) | ||||
0.918386 | − | 0.395687i | \(-0.129493\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −448.000 | −2.29744 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −90.0000 | −0.456853 | −0.228426 | − | 0.973561i | \(-0.573358\pi\) | ||||
−0.228426 | + | 0.973561i | \(0.573358\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 147.000 | 0.738693 | 0.369347 | − | 0.929292i | \(-0.379581\pi\) | ||||
0.369347 | + | 0.929292i | \(0.379581\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −224.000 | −1.11443 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 435.578i | − 2.14570i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 277.186i | 1.35213i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −46.0000 | −0.222222 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −57.0000 | −0.272727 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 328.098i | − 1.55496i | −0.628905 | − | 0.777482i | \(-0.716496\pi\) | ||||
0.628905 | − | 0.777482i | \(-0.283504\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 512.000 | 2.40376 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −147.000 | −0.683721 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 62.2254i | − 0.286753i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 220.617i | 1.00739i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 192.333i | 0.870285i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 356.382i | − 1.59812i | −0.601248 | − | 0.799062i | \(-0.705330\pi\) | ||||
0.601248 | − | 0.799062i | \(-0.294670\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −552.000 | −2.45333 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 316.784i | − 1.39552i | −0.716330 | − | 0.697762i | \(-0.754179\pi\) | ||||
0.716330 | − | 0.697762i | \(-0.245821\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 257.000 | 1.12227 | 0.561135 | − | 0.827724i | \(-0.310365\pi\) | ||||
0.561135 | + | 0.827724i | \(0.310365\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − 186.676i | − 0.808122i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −177.000 | −0.759657 | −0.379828 | − | 0.925057i | \(-0.624017\pi\) | ||||
−0.379828 | + | 0.925057i | \(0.624017\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 35.0000 | 0.148936 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −544.000 | −2.29536 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 363.000 | 1.51883 | 0.759414 | − | 0.650607i | \(-0.225486\pi\) | ||||
0.759414 | + | 0.650607i | \(0.225486\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − 356.382i | − 1.47876i | −0.673287 | − | 0.739381i | \(-0.735118\pi\) | ||||
0.673287 | − | 0.739381i | \(-0.264882\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 650.538i | 2.67711i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −504.000 | −2.05714 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 214.960i | − 0.870285i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 33.9411i | 0.136310i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 133.000 | 0.529880 | 0.264940 | − | 0.964265i | \(-0.414648\pi\) | ||||
0.264940 | + | 0.964265i | \(0.414648\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.00000 | −0.0237154 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 673.166i | 2.63987i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 135.765i | 0.528267i | 0.964486 | + | 0.264133i | \(0.0850859\pi\) | ||||
−0.964486 | + | 0.264133i | \(0.914914\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 435.578i | − 1.68177i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 910.754i | 3.48948i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −101.000 | −0.384030 | −0.192015 | − | 0.981392i | \(-0.561502\pi\) | ||||
−0.192015 | + | 0.981392i | \(0.561502\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − 39.5980i | − 0.149426i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 672.000 | 2.51685 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 356.382i | 1.32484i | 0.749133 | + | 0.662420i | \(0.230470\pi\) | ||||
−0.749133 | + | 0.662420i | \(0.769530\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −142.000 | −0.523985 | −0.261993 | − | 0.965070i | \(-0.584380\pi\) | ||||
−0.261993 | + | 0.965070i | \(0.584380\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 704.000 | 2.57875 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −72.0000 | −0.261818 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −199.000 | −0.718412 | −0.359206 | − | 0.933258i | \(-0.616952\pi\) | ||||
−0.359206 | + | 0.933258i | \(0.616952\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 130.108i | 0.466336i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 463.862i | − 1.65075i | −0.564582 | − | 0.825377i | \(-0.690962\pi\) | ||||
0.564582 | − | 0.825377i | \(-0.309038\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −427.000 | −1.50883 | −0.754417 | − | 0.656395i | \(-0.772080\pi\) | ||||
−0.754417 | + | 0.656395i | \(0.772080\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 752.362i | − 2.63987i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 435.578i | − 1.51769i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −960.000 | −3.29897 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 237.588i | − 0.810880i | −0.914122 | − | 0.405440i | \(-0.867118\pi\) | ||||
0.914122 | − | 0.405440i | \(-0.132882\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 237.588i | − 0.805383i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 237.588i | 0.799959i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 22.6274i | − 0.0756770i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 231.000 | 0.767442 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 690.136i | − 2.27768i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 161.000 | 0.527869 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 526.087i | − 1.71364i | −0.515616 | − | 0.856820i | \(-0.672437\pi\) | ||||
0.515616 | − | 0.856820i | \(-0.327563\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 576.000 | 1.86408 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 235.000 | 0.755627 | 0.377814 | − | 0.925882i | \(-0.376676\pi\) | ||||
0.377814 | + | 0.925882i | \(0.376676\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 530.000 | 1.69329 | 0.846645 | − | 0.532158i | \(-0.178619\pi\) | ||||
0.846645 | + | 0.532158i | \(0.178619\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1771.00 | 5.62222 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 214.960i | − 0.678109i | −0.940767 | − | 0.339054i | \(-0.889893\pi\) | ||||
0.940767 | − | 0.339054i | \(-0.110107\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 118.794i | 0.372395i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −896.000 | −2.79128 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −323.000 | −1.00000 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 271.529i | − 0.835474i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 672.000 | 2.05505 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −55.0000 | −0.167173 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 96.1665i | 0.290533i | 0.989393 | + | 0.145267i | \(0.0464040\pi\) | ||||
−0.989393 | + | 0.145267i | \(0.953596\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 910.754i | 2.73500i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 277.186i | − 0.827420i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 169.706i | 0.503578i | 0.967782 | + | 0.251789i | \(0.0810188\pi\) | ||||
−0.967782 | + | 0.251789i | \(0.918981\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 288.000 | 0.849558 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 16.9706i | 0.0497670i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 253.000 | 0.737609 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − 79.1960i | − 0.229554i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 253.000 | 0.729107 | 0.364553 | − | 0.931183i | \(-0.381222\pi\) | ||||
0.364553 | + | 0.931183i | \(0.381222\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −351.000 | −1.00573 | −0.502865 | − | 0.864365i | \(-0.667721\pi\) | ||||
−0.502865 | + | 0.864365i | \(0.667721\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −896.000 | −2.55271 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 98.0000 | 0.277620 | 0.138810 | − | 0.990319i | \(-0.455672\pi\) | ||||
0.138810 | + | 0.990319i | \(0.455672\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 633.568i | 1.78470i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 1057.83i | − 2.96311i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −61.0000 | −0.169916 | −0.0849582 | − | 0.996385i | \(-0.527076\pi\) | ||||
−0.0849582 | + | 0.996385i | \(0.527076\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 361.000 | 1.00000 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 633.568i | − 1.74537i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −273.000 | −0.747945 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −686.000 | −1.86921 | −0.934605 | − | 0.355688i | \(-0.884247\pi\) | ||||
−0.934605 | + | 0.355688i | \(0.884247\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 910.754i | 2.46817i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 62.2254i | 0.167723i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 135.765i | 0.363980i | 0.983300 | + | 0.181990i | \(0.0582538\pi\) | ||||
−0.983300 | + | 0.181990i | \(0.941746\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 39.5980i | 0.105595i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −448.000 | −1.18833 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 79.1960i | 0.208960i | 0.994527 | + | 0.104480i | \(0.0333179\pi\) | ||||
−0.994527 | + | 0.104480i | \(0.966682\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −224.000 | −0.587927 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 16.9706i | 0.0443096i | 0.999755 | + | 0.0221548i | \(0.00705266\pi\) | ||||
−0.999755 | + | 0.0221548i | \(0.992947\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 231.000 | 0.600000 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −483.000 | −1.24806 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −599.000 | −1.53985 | −0.769923 | − | 0.638137i | \(-0.779705\pi\) | ||||
−0.769923 | + | 0.638137i | \(0.779705\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −34.0000 | −0.0869565 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 842.871i | 2.14471i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 673.166i | − 1.70422i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 569.000 | 1.43325 | 0.716625 | − | 0.697459i | \(-0.245686\pi\) | ||||
0.716625 | + | 0.697459i | \(0.245686\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1182.28i | 2.96311i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 16.9706i | 0.0423206i | 0.999776 | + | 0.0211603i | \(0.00673604\pi\) | ||||
−0.999776 | + | 0.0211603i | \(0.993264\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −64.0000 | −0.158809 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1687.00 | −4.16543 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 118.794i | 0.291877i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − 593.970i | − 1.45225i | −0.687563 | − | 0.726124i | \(-0.741320\pi\) | ||||
0.687563 | − | 0.726124i | \(-0.258680\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 537.401i | 1.30755i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 373.352i | 0.904001i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −42.0000 | −0.101205 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − 876.812i | − 2.10267i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 230.000 | 0.548926 | 0.274463 | − | 0.961598i | \(-0.411500\pi\) | ||||
0.274463 | + | 0.961598i | \(0.411500\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 593.970i | − 1.41085i | −0.708782 | − | 0.705427i | \(-0.750755\pi\) | ||||
0.708782 | − | 0.705427i | \(-0.249245\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 115.000 | 0.271868 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −408.000 | −0.960000 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −253.000 | −0.592506 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −192.000 | −0.447552 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 475.176i | 1.10250i | 0.834341 | + | 0.551248i | \(0.185848\pi\) | ||||
−0.834341 | + | 0.551248i | \(0.814152\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 593.970i | − 1.37175i | −0.727717 | − | 0.685877i | \(-0.759419\pi\) | ||||
0.727717 | − | 0.685877i | \(-0.240581\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1568.00 | −3.60460 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 38.0000 | 0.0869565 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 118.794i | − 0.270601i | −0.990805 | − | 0.135301i | \(-0.956800\pi\) | ||||
0.990805 | − | 0.135301i | \(-0.0432000\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1656.00 | −3.75510 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 653.000 | 1.47404 | 0.737020 | − | 0.675871i | \(-0.236232\pi\) | ||||
0.737020 | + | 0.675871i | \(0.236232\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 831.558i | 1.86867i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 356.382i | − 0.797275i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 147.078i | 0.327568i | 0.986496 | + | 0.163784i | \(0.0523701\pi\) | ||||
−0.986496 | + | 0.163784i | \(0.947630\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 118.794i | 0.263401i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −704.000 | −1.55408 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 871.156i | 1.91463i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −817.000 | −1.78775 | −0.893873 | − | 0.448320i | \(-0.852022\pi\) | ||||
−0.893873 | + | 0.448320i | \(0.852022\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1346.33i | 2.93318i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −463.000 | −1.00434 | −0.502169 | − | 0.864769i | \(-0.667465\pi\) | ||||
−0.502169 | + | 0.864769i | \(0.667465\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −29.0000 | −0.0626350 | −0.0313175 | − | 0.999509i | \(-0.509970\pi\) | ||||
−0.0313175 | + | 0.999509i | \(0.509970\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −224.000 | −0.481720 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −19.0000 | −0.0406852 | −0.0203426 | − | 0.999793i | \(-0.506476\pi\) | ||||
−0.0203426 | + | 0.999793i | \(0.506476\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 435.578i | 0.928737i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 848.528i | 1.80155i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −63.0000 | −0.133192 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 456.000 | 0.960000 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 130.108i | − 0.272762i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −206.000 | −0.430063 | −0.215031 | − | 0.976607i | \(-0.568985\pi\) | ||||
−0.215031 | + | 0.976607i | \(0.568985\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −448.000 | −0.931393 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 124.451i | 0.257662i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 1187.94i | − 2.44936i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 45.2548i | − 0.0929257i | −0.998920 | − | 0.0464629i | \(-0.985205\pi\) | ||||
0.998920 | − | 0.0464629i | \(-0.0147949\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 939.038i | 1.92032i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 246.000 | 0.501018 | 0.250509 | − | 0.968114i | \(-0.419402\pi\) | ||||
0.250509 | + | 0.968114i | \(0.419402\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 673.166i | 1.36545i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −483.000 | −0.975758 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 995.606i | − 2.00323i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 21.0000 | 0.0420842 | 0.0210421 | − | 0.999779i | \(-0.493302\pi\) | ||||
0.0210421 | + | 0.999779i | \(0.493302\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1184.00 | 2.36327 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 386.000 | 0.767396 | 0.383698 | − | 0.923459i | \(-0.374650\pi\) | ||||
0.383698 | + | 0.923459i | \(0.374650\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 854.000 | 1.69109 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 231.931i | 0.457458i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 475.176i | − 0.933548i | −0.884377 | − | 0.466774i | \(-0.845416\pi\) | ||||
0.884377 | − | 0.466774i | \(-0.154584\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 429.000 | 0.839530 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − 1504.72i | − 2.93318i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 712.764i | 1.38401i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 15.0000 | 0.0290135 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −320.000 | −0.616570 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 786.303i | 1.50922i | 0.656175 | + | 0.754609i | \(0.272174\pi\) | ||||
−0.656175 | + | 0.754609i | \(0.727826\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 395.980i | 0.757132i | 0.925574 | + | 0.378566i | \(0.123583\pi\) | ||||
−0.925574 | + | 0.378566i | \(0.876417\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1493.41i | 2.84459i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 96.1665i | 0.182479i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −525.000 | −0.992439 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 780.646i | − 1.47014i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −448.000 | −0.840525 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 1108.74i | − 2.07242i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 416.000 | 0.774674 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −216.000 | −0.400742 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.00000 | −0.0129390 | −0.00646950 | − | 0.999979i | \(-0.502059\pi\) | ||||
−0.00646950 | + | 0.999979i | \(0.502059\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 448.000 | 0.825046 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 831.558i | 1.52579i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 712.764i | 1.30304i | 0.758631 | + | 0.651521i | \(0.225869\pi\) | ||||
−0.758631 | + | 0.651521i | \(0.774131\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 529.000 | 0.963570 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 752.362i | − 1.36545i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1057.83i | 1.91290i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1568.00 | −2.82523 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1001.00 | 1.79713 | 0.898564 | − | 0.438843i | \(-0.144612\pi\) | ||||
0.898564 | + | 0.438843i | \(0.144612\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 237.588i | − 0.425023i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 288.500i | 0.514259i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 322.441i | − 0.572719i | −0.958122 | − | 0.286359i | \(-0.907555\pi\) | ||||
0.958122 | − | 0.286359i | \(-0.0924451\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 356.382i | 0.630764i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2651.00 | 4.67549 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 712.764i | 1.25266i | 0.779558 | + | 0.626330i | \(0.215444\pi\) | ||||
−0.779558 | + | 0.626330i | \(0.784556\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −746.000 | −1.30648 | −0.653240 | − | 0.757151i | \(-0.726591\pi\) | ||||
−0.653240 | + | 0.757151i | \(0.726591\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 1702.71i | − 2.97158i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 48.0000 | 0.0834783 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −25.0000 | −0.0433276 | −0.0216638 | − | 0.999765i | \(-0.506896\pi\) | ||||
−0.0216638 | + | 0.999765i | \(0.506896\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 864.000 | 1.49223 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 66.0000 | 0.113597 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 16.9706i | − 0.0291090i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − 1821.51i | − 3.11369i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 869.000 | 1.48041 | 0.740204 | − | 0.672382i | \(-0.234729\pi\) | ||||
0.740204 | + | 0.672382i | \(0.234729\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 107.480i | − 0.182479i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − 509.117i | − 0.861450i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 898.000 | 1.51433 | 0.757167 | − | 0.653221i | \(-0.226583\pi\) | ||||
0.757167 | + | 0.653221i | \(0.226583\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1309.00 | 2.20000 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 831.558i | 1.39289i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 277.186i | 0.462748i | 0.972865 | + | 0.231374i | \(0.0743220\pi\) | ||||
−0.972865 | + | 0.231374i | \(0.925678\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 475.176i | 0.790642i | 0.918543 | + | 0.395321i | \(0.129367\pi\) | ||||
−0.918543 | + | 0.395321i | \(0.870633\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 910.754i | − 1.51037i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 784.000 | 1.29587 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 452.548i | 0.745549i | 0.927922 | + | 0.372775i | \(0.121594\pi\) | ||||
−0.927922 | + | 0.372775i | \(0.878406\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2464.00 | 4.04598 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 56.5685i | 0.0925835i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 585.000 | 0.954323 | 0.477162 | − | 0.878816i | \(-0.341666\pi\) | ||||
0.477162 | + | 0.878816i | \(0.341666\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1568.00 | −2.54959 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −873.000 | −1.41491 | −0.707455 | − | 0.706758i | \(-0.750157\pi\) | ||||
−0.707455 | + | 0.706758i | \(0.750157\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −970.000 | −1.56704 | −0.783522 | − | 0.621364i | \(-0.786579\pi\) | ||||
−0.783522 | + | 0.621364i | \(0.786579\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 158.392i | − 0.255059i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 1306.73i | − 2.09749i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −649.000 | −1.03840 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 322.441i | − 0.514259i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 673.166i | 1.07022i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 259.000 | 0.410460 | 0.205230 | − | 0.978714i | \(-0.434206\pi\) | ||||
0.205230 | + | 0.978714i | \(0.434206\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1856.00 | 2.93207 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 277.186i | − 0.436513i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 814.587i | − 1.27879i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2081.72i | 3.25778i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 1063.49i | − 1.65911i | −0.558426 | − | 0.829554i | \(-0.688595\pi\) | ||||
0.558426 | − | 0.829554i | \(-0.311405\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 645.000 | 1.00311 | 0.501555 | − | 0.865126i | \(-0.332761\pi\) | ||||
0.501555 | + | 0.865126i | \(0.332761\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 831.558i | − 1.28924i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −29.0000 | −0.0448223 | −0.0224111 | − | 0.999749i | \(-0.507134\pi\) | ||||
−0.0224111 | + | 0.999749i | \(0.507134\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − 101.823i | − 0.156893i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 352.000 | 0.540707 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −135.000 | −0.206738 | −0.103369 | − | 0.994643i | \(-0.532962\pi\) | ||||
−0.103369 | + | 0.994643i | \(0.532962\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1043.00 | −1.59237 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −897.000 | −1.36530 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 780.646i | 1.18459i | 0.805721 | + | 0.592296i | \(0.201778\pi\) | ||||
−0.805721 | + | 0.592296i | \(0.798222\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 995.606i | − 1.50621i | −0.657899 | − | 0.753106i | \(-0.728555\pi\) | ||||
0.657899 | − | 0.753106i | \(-0.271445\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1088.00 | −1.64103 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1463.00 | −2.20000 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 79.1960i | − 0.118735i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2016.00 | 3.01345 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 69.0000 | 0.102832 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 395.980i | 0.588380i | 0.955747 | + | 0.294190i | \(0.0950499\pi\) | ||||
−0.955747 | + | 0.294190i | \(0.904950\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 1900.70i | − 2.81586i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 356.382i | 0.526413i | 0.964739 | + | 0.263207i | \(0.0847801\pi\) | ||||
−0.964739 | + | 0.263207i | \(0.915220\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1866.76i | 2.74928i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1792.00 | 2.63142 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 520.431i | 0.761977i | 0.924580 | + | 0.380989i | \(0.124416\pi\) | ||||
−0.924580 | + | 0.380989i | \(0.875584\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −665.000 | −0.970803 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1453.81i | 2.11617i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 64.0000 | 0.0928882 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −835.000 | −1.20839 | −0.604197 | − | 0.796835i | \(-0.706506\pi\) | ||||
−0.604197 | + | 0.796835i | \(0.706506\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 759.000 | 1.09524 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1085.00 | 1.56115 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 673.166i | 0.965804i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 1001.26i | − 1.43242i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1002.00 | −1.42939 | −0.714693 | − | 0.699438i | \(-0.753434\pi\) | ||||
−0.714693 | + | 0.699438i | \(0.753434\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 752.362i | − 1.07022i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 197.990i | 0.280837i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1342.00 | −1.89816 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −250.000 | −0.352609 | −0.176305 | − | 0.984336i | \(-0.556414\pi\) | ||||
−0.176305 | + | 0.984336i | \(0.556414\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − 2211.83i | − 3.11087i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 11.3137i | − 0.0158678i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 237.588i | − 0.332291i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2053.44i | 2.86393i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1171.00 | 1.62865 | 0.814325 | − | 0.580409i | \(-0.197107\pi\) | ||||
0.814325 | + | 0.580409i | \(0.197107\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − 1120.06i | − 1.55348i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2016.00 | 2.78838 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 950.352i | − 1.31083i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 91.0000 | 0.125172 | 0.0625860 | − | 0.998040i | \(-0.480065\pi\) | ||||
0.0625860 | + | 0.998040i | \(0.480065\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1511.00 | −2.07270 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −357.000 | −0.488372 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −682.000 | −0.930423 | −0.465211 | − | 0.885200i | \(-0.654022\pi\) | ||||
−0.465211 | + | 0.885200i | \(0.654022\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − 2851.05i | − 3.87899i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 118.794i | − 0.161186i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 221.000 | 0.299053 | 0.149526 | − | 0.988758i | \(-0.452225\pi\) | ||||
0.149526 | + | 0.988758i | \(0.452225\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1216.00 | 1.64103 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 288.500i | 0.388290i | 0.980973 | + | 0.194145i | \(0.0621933\pi\) | ||||
−0.980973 | + | 0.194145i | \(0.937807\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 441.000 | 0.591946 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −138.000 | −0.184739 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1742.31i | 2.32618i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 927.724i | − 1.23532i | −0.786446 | − | 0.617659i | \(-0.788081\pi\) | ||||
0.786446 | − | 0.617659i | \(-0.211919\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 752.362i | 0.999152i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 871.156i | − 1.15385i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −895.000 | −1.18230 | −0.591149 | − | 0.806562i | \(-0.701326\pi\) | ||||
−0.591149 | + | 0.806562i | \(0.701326\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − 33.9411i | − 0.0447182i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 95.0000 | 0.124836 | 0.0624179 | − | 0.998050i | \(-0.480119\pi\) | ||||
0.0624179 | + | 0.998050i | \(0.480119\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 1306.73i | − 1.71263i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2737.00 | −3.57778 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 384.000 | 0.500652 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 679.000 | 0.882965 | 0.441482 | − | 0.897270i | \(-0.354453\pi\) | ||||
0.441482 | + | 0.897270i | \(0.354453\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −768.000 | −0.996109 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 135.765i | − 0.175180i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2464.00 | 3.17117 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 752.362i | − 0.965804i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 271.529i | 0.347668i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3136.00 | −4.00511 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1050.00 | −1.33758 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 1391.59i | − 1.76822i | −0.467282 | − | 0.884108i | \(-0.654767\pi\) | ||||
0.467282 | − | 0.884108i | \(-0.345233\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 571.342i | − 0.724135i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 560.029i | − 0.708001i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 260.215i | 0.328140i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 224.000 | 0.281761 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 356.382i | − 0.447154i | −0.974686 | − | 0.223577i | \(-0.928227\pi\) | ||||
0.974686 | − | 0.223577i | \(-0.0717734\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 85.0000 | 0.106383 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2732.26i | 3.41106i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −117.000 | −0.145704 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −154.000 | −0.191304 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2016.00 | −2.49814 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 455.000 | 0.562423 | 0.281211 | − | 0.959646i | \(-0.409264\pi\) | ||||
0.281211 | + | 0.959646i | \(0.409264\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 475.176i | 0.585913i | 0.956126 | + | 0.292957i | \(0.0946392\pi\) | ||||
−0.956126 | + | 0.292957i | \(0.905361\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 803.273i | − 0.988036i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1162.00 | −1.42577 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 399.000 | 0.488372 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2862.37i | 3.49496i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −831.000 | −1.01218 | −0.506090 | − | 0.862481i | \(-0.668910\pi\) | ||||
−0.506090 | + | 0.862481i | \(0.668910\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −109.000 | −0.132442 | −0.0662211 | − | 0.997805i | \(-0.521094\pi\) | ||||
−0.0662211 | + | 0.997805i | \(0.521094\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − 407.294i | − 0.493689i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1238.85i | 1.49801i | 0.662567 | + | 0.749003i | \(0.269467\pi\) | ||||
−0.662567 | + | 0.749003i | \(0.730533\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 667.509i | − 0.805198i | −0.915377 | − | 0.402599i | \(-0.868107\pi\) | ||||
0.915377 | − | 0.402599i | \(-0.131893\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − 1125.71i | − 1.35465i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1224.00 | −1.46939 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1465.13i | 1.75464i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −448.000 | −0.535245 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 316.784i | − 0.377573i | −0.982018 | − | 0.188787i | \(-0.939545\pi\) | ||||
0.982018 | − | 0.188787i | \(-0.0604554\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −727.000 | −0.864447 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2624.00 | 3.11269 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −287.000 | −0.339645 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1232.00 | −1.45455 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − 2415.48i | − 2.84508i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 79.1960i | − 0.0930622i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1126.00 | 1.32005 | 0.660023 | − | 0.751245i | \(-0.270546\pi\) | ||||
0.660023 | + | 0.751245i | \(0.270546\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3059.00 | 3.57778 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 203.647i | 0.237627i | 0.992917 | + | 0.118814i | \(0.0379091\pi\) | ||||
−0.992917 | + | 0.118814i | \(0.962091\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −651.000 | −0.757858 | −0.378929 | − | 0.925426i | \(-0.623708\pi\) | ||||
−0.378929 | + | 0.925426i | \(0.623708\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2464.00 | 2.86179 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 39.5980i | − 0.0458841i | −0.999737 | − | 0.0229421i | \(-0.992697\pi\) | ||||
0.999737 | − | 0.0229421i | \(-0.00730332\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − 395.980i | − 0.457780i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 288.500i | − 0.331990i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 448.000 | 0.514351 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 3903.23i | − 4.47105i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 77.0000 | 0.0880000 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1029.55i | 1.17394i | 0.809608 | + | 0.586971i | \(0.199680\pi\) | ||||
−0.809608 | + | 0.586971i | \(0.800320\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1344.00 | 1.52901 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 391.000 | 0.443814 | 0.221907 | − | 0.975068i | \(-0.428772\pi\) | ||||
0.221907 | + | 0.975068i | \(0.428772\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −995.000 | −1.12684 | −0.563420 | − | 0.826171i | \(-0.690515\pi\) | ||||
−0.563420 | + | 0.826171i | \(0.690515\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1344.00 | 1.51864 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 475.176i | 0.535711i | 0.963459 | + | 0.267856i | \(0.0863150\pi\) | ||||
−0.963459 | + | 0.267856i | \(0.913685\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 435.578i | 0.489964i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −723.000 | −0.811448 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −95.0000 | −0.106383 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 514.774i | 0.575166i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 128.000 | 0.142698 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −224.000 | −0.249166 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 96.1665i | − 0.106733i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1306.73i | 1.44710i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 554.372i | 0.612565i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 627.911i | − 0.692294i | −0.938180 | − | 0.346147i | \(-0.887490\pi\) | ||||
0.938180 | − | 0.346147i | \(-0.112510\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2806.00 | 3.08691 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 803.273i | 0.881749i | 0.897569 | + | 0.440874i | \(0.145332\pi\) | ||||
−0.897569 | + | 0.440874i | \(0.854668\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −18.0000 | −0.0197152 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 910.754i | 0.995359i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1639.00 | 1.78735 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1090.00 | 1.18607 | 0.593036 | − | 0.805176i | \(-0.297929\pi\) | ||||
0.593036 | + | 0.805176i | \(0.297929\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2976.00 | 3.23127 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1024.00 | −1.10943 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 950.352i | − 1.02741i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2341.94i | 2.52636i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 226.000 | 0.243272 | 0.121636 | − | 0.992575i | \(-0.461186\pi\) | ||||
0.121636 | + | 0.992575i | \(0.461186\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1368.00 | 1.46939 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1329.36i | 1.42482i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −357.000 | −0.381818 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 623.000 | 0.664888 | 0.332444 | − | 0.943123i | \(-0.392127\pi\) | ||||
0.332444 | + | 0.943123i | \(0.392127\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2998.13i | 3.19290i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 1549.98i | − 1.64716i | −0.567200 | − | 0.823580i | \(-0.691973\pi\) | ||||
0.567200 | − | 0.823580i | \(-0.308027\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 79.1960i | − 0.0839830i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 6098.09i | 6.45300i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −602.000 | −0.635692 | −0.317846 | − | 0.948142i | \(-0.602959\pi\) | ||||
−0.317846 | + | 0.948142i | \(0.602959\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 441.235i | − 0.464947i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1216.00 | 1.27865 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 277.186i | − 0.290856i | −0.989369 | − | 0.145428i | \(-0.953544\pi\) | ||||
0.989369 | − | 0.145428i | \(-0.0464559\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2107.00 | 2.20628 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −672.000 | −0.702194 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1045.00 | 1.08968 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 929.000 | 0.966701 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 3643.01i | − 3.78298i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1069.15i | 1.10792i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 770.000 | 0.796277 | 0.398139 | − | 0.917325i | \(-0.369656\pi\) | ||||
0.398139 | + | 0.917325i | \(0.369656\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − 1827.16i | − 1.88562i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 712.764i | − 0.734051i | −0.930211 | − | 0.367026i | \(-0.880376\pi\) | ||||
0.930211 | − | 0.367026i | \(-0.119624\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1705.00 | −1.75231 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1536.00 | 1.57538 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 1340.67i | − 1.37224i | −0.727490 | − | 0.686118i | \(-0.759313\pi\) | ||||
0.727490 | − | 0.686118i | \(-0.240687\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 356.382i | 0.364026i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2732.26i | 2.78518i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 554.372i | − 0.563959i | −0.959420 | − | 0.281980i | \(-0.909009\pi\) | ||||
0.959420 | − | 0.281980i | \(-0.0909910\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 630.000 | 0.639594 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 311.127i | − 0.315225i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 42.0000 | 0.0424671 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 639.225i | 0.645030i | 0.946564 | + | 0.322515i | \(0.104528\pi\) | ||||
−0.946564 | + | 0.322515i | \(0.895472\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −544.000 | −0.547835 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1029.00 | −1.03417 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 473.000 | 0.474423 | 0.237212 | − | 0.971458i | \(-0.423767\pi\) | ||||
0.237212 | + | 0.971458i | \(0.423767\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3136.00 | −3.13914 |
(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 | 1216.3.e.d.1025.2 | 2 | ||
4.3 | odd | 2 | 1216.3.e.c.1025.1 | 2 | |||
8.3 | odd | 2 | 304.3.e.f.113.2 | 2 | |||
8.5 | even | 2 | 152.3.e.a.113.1 | ✓ | 2 | ||
19.18 | odd | 2 | inner | 1216.3.e.d.1025.1 | 2 | ||
24.5 | odd | 2 | 1368.3.o.a.721.2 | 2 | |||
24.11 | even | 2 | 2736.3.o.b.721.2 | 2 | |||
76.75 | even | 2 | 1216.3.e.c.1025.2 | 2 | |||
152.37 | odd | 2 | 152.3.e.a.113.2 | yes | 2 | ||
152.75 | even | 2 | 304.3.e.f.113.1 | 2 | |||
456.227 | odd | 2 | 2736.3.o.b.721.1 | 2 | |||
456.341 | even | 2 | 1368.3.o.a.721.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
152.3.e.a.113.1 | ✓ | 2 | 8.5 | even | 2 | ||
152.3.e.a.113.2 | yes | 2 | 152.37 | odd | 2 | ||
304.3.e.f.113.1 | 2 | 152.75 | even | 2 | |||
304.3.e.f.113.2 | 2 | 8.3 | odd | 2 | |||
1216.3.e.c.1025.1 | 2 | 4.3 | odd | 2 | |||
1216.3.e.c.1025.2 | 2 | 76.75 | even | 2 | |||
1216.3.e.d.1025.1 | 2 | 19.18 | odd | 2 | inner | ||
1216.3.e.d.1025.2 | 2 | 1.1 | even | 1 | trivial | ||
1368.3.o.a.721.1 | 2 | 456.341 | even | 2 | |||
1368.3.o.a.721.2 | 2 | 24.5 | odd | 2 | |||
2736.3.o.b.721.1 | 2 | 456.227 | odd | 2 | |||
2736.3.o.b.721.2 | 2 | 24.11 | even | 2 |