Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1792,2,Mod(897,1792)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1792, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1792.897");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1792 = 2^{8} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1792.b (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: | \(14.3091920422\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 3x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 224) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 897.1 | ||
Root | \(-1.61803i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1792.897 |
Dual form | 1792.2.b.m.897.4 |
$q$-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 \(\left(\mathbb{Z}/1792\mathbb{Z}\right)^\times\).
\(n\) | \(1023\) | \(1025\) | \(1541\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | − 3.23607i | − 1.86834i | −0.356822 | − | 0.934172i | \(-0.616140\pi\) | ||||
0.356822 | − | 0.934172i | \(-0.383860\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 1.23607i | − 0.552786i | −0.961045 | − | 0.276393i | \(-0.910861\pi\) | ||||
0.961045 | − | 0.276393i | \(-0.0891392\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −7.47214 | −2.49071 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 2.47214i | − 0.745377i | −0.927957 | − | 0.372689i | \(-0.878436\pi\) | ||||
0.927957 | − | 0.372689i | \(-0.121564\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 5.23607i | − 1.45222i | −0.687576 | − | 0.726112i | \(-0.741325\pi\) | ||||
0.687576 | − | 0.726112i | \(-0.258675\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.00000 | −1.03280 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.47214 | −1.08465 | −0.542326 | − | 0.840168i | \(-0.682456\pi\) | ||||
−0.542326 | + | 0.840168i | \(0.682456\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.23607i | 0.742405i | 0.928552 | + | 0.371202i | \(0.121054\pi\) | ||||
−0.928552 | + | 0.371202i | \(0.878946\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 3.23607i | − 0.706168i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.00000 | 0.834058 | 0.417029 | − | 0.908893i | \(-0.363071\pi\) | ||||
0.417029 | + | 0.908893i | \(0.363071\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.47214 | 0.694427 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 14.4721i | 2.78516i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 4.47214i | − 0.830455i | −0.909718 | − | 0.415227i | \(-0.863702\pi\) | ||||
0.909718 | − | 0.415227i | \(-0.136298\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.47214 | −1.16243 | −0.581215 | − | 0.813750i | \(-0.697422\pi\) | ||||
−0.581215 | + | 0.813750i | \(0.697422\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −8.00000 | −1.39262 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 1.23607i | − 0.208934i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.47214i | 0.735215i | 0.929981 | + | 0.367607i | \(0.119823\pi\) | ||||
−0.929981 | + | 0.367607i | \(0.880177\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −16.9443 | −2.71325 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.472136 | −0.0737352 | −0.0368676 | − | 0.999320i | \(-0.511738\pi\) | ||||
−0.0368676 | + | 0.999320i | \(0.511738\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.47214i | 0.376997i | 0.982073 | + | 0.188499i | \(0.0603621\pi\) | ||||
−0.982073 | + | 0.188499i | \(0.939638\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 9.23607i | 1.37683i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.52786 | −0.222862 | −0.111431 | − | 0.993772i | \(-0.535543\pi\) | ||||
−0.111431 | + | 0.993772i | \(0.535543\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 14.4721i | 2.02650i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 10.0000i | − 1.37361i | −0.726844 | − | 0.686803i | \(-0.759014\pi\) | ||||
0.726844 | − | 0.686803i | \(-0.240986\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.05573 | −0.412034 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 10.4721 | 1.38707 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.76393i | 0.620211i | 0.950702 | + | 0.310106i | \(0.100364\pi\) | ||||
−0.950702 | + | 0.310106i | \(0.899636\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 6.76393i | − 0.866033i | −0.901386 | − | 0.433016i | \(-0.857449\pi\) | ||||
0.901386 | − | 0.433016i | \(-0.142551\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −7.47214 | −0.941401 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.47214 | −0.802770 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.00000i | 0.488678i | 0.969690 | + | 0.244339i | \(0.0785709\pi\) | ||||
−0.969690 | + | 0.244339i | \(0.921429\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 12.9443i | − 1.55831i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.9443 | 1.53620 | 0.768101 | − | 0.640328i | \(-0.221202\pi\) | ||||
0.768101 | + | 0.640328i | \(0.221202\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −14.9443 | −1.74909 | −0.874547 | − | 0.484940i | \(-0.838841\pi\) | ||||
−0.874547 | + | 0.484940i | \(0.838841\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 11.2361i | − 1.29743i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 2.47214i | − 0.281726i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.94427 | 0.556274 | 0.278137 | − | 0.960541i | \(-0.410283\pi\) | ||||
0.278137 | + | 0.960541i | \(0.410283\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 24.4164 | 2.71293 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 4.76393i | − 0.522909i | −0.965216 | − | 0.261455i | \(-0.915798\pi\) | ||||
0.965216 | − | 0.261455i | \(-0.0842022\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.52786i | 0.599581i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −14.4721 | −1.55158 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.00000 | 0.635999 | 0.317999 | − | 0.948091i | \(-0.396989\pi\) | ||||
0.317999 | + | 0.948091i | \(0.396989\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 5.23607i | − 0.548889i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 20.9443i | 2.17182i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.00000 | 0.410391 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.52786 | 0.358200 | 0.179100 | − | 0.983831i | \(-0.442681\pi\) | ||||
0.179100 | + | 0.983831i | \(0.442681\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 18.4721i | 1.85652i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.7082i | 1.16501i | 0.812827 | + | 0.582505i | \(0.197927\pi\) | ||||
−0.812827 | + | 0.582505i | \(0.802073\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.4721 | −1.42598 | −0.712991 | − | 0.701173i | \(-0.752660\pi\) | ||||
−0.712991 | + | 0.701173i | \(0.752660\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.00000 | −0.390360 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.94427i | 0.864675i | 0.901712 | + | 0.432338i | \(0.142311\pi\) | ||||
−0.901712 | + | 0.432338i | \(0.857689\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.472136i | 0.0452224i | 0.999744 | + | 0.0226112i | \(0.00719799\pi\) | ||||
−0.999744 | + | 0.0226112i | \(0.992802\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 14.4721 | 1.37363 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.52786 | −0.331874 | −0.165937 | − | 0.986136i | \(-0.553065\pi\) | ||||
−0.165937 | + | 0.986136i | \(0.553065\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 4.94427i | − 0.461056i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 39.1246i | 3.61707i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.47214 | −0.409960 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.88854 | 0.444413 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.52786i | 0.137763i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 10.4721i | − 0.936656i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.94427 | 0.793676 | 0.396838 | − | 0.917889i | \(-0.370108\pi\) | ||||
0.396838 | + | 0.917889i | \(0.370108\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.00000 | 0.704361 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 1.70820i | − 0.149246i | −0.997212 | − | 0.0746232i | \(-0.976225\pi\) | ||||
0.997212 | − | 0.0746232i | \(-0.0237754\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.23607i | 0.280603i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 17.8885 | 1.53960 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.94427 | 0.251546 | 0.125773 | − | 0.992059i | \(-0.459859\pi\) | ||||
0.125773 | + | 0.992059i | \(0.459859\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.23607i | 0.274480i | 0.990538 | + | 0.137240i | \(0.0438231\pi\) | ||||
−0.990538 | + | 0.137240i | \(0.956177\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.94427i | 0.416383i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −12.9443 | −1.08245 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.52786 | −0.459064 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 3.23607i | − 0.266906i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 14.9443i | − 1.22428i | −0.790748 | − | 0.612141i | \(-0.790308\pi\) | ||||
0.790748 | − | 0.612141i | \(-0.209692\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.94427 | 0.727875 | 0.363937 | − | 0.931423i | \(-0.381432\pi\) | ||||
0.363937 | + | 0.931423i | \(0.381432\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 33.4164 | 2.70156 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.00000i | 0.642575i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 5.23607i | − 0.417884i | −0.977928 | − | 0.208942i | \(-0.932998\pi\) | ||||
0.977928 | − | 0.208942i | \(-0.0670019\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −32.3607 | −2.56637 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.00000 | 0.315244 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 23.4164i | 1.83411i | 0.398755 | + | 0.917057i | \(0.369442\pi\) | ||||
−0.398755 | + | 0.917057i | \(0.630558\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 9.88854i | 0.769822i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.41641 | −0.264370 | −0.132185 | − | 0.991225i | \(-0.542199\pi\) | ||||
−0.132185 | + | 0.991225i | \(0.542199\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −14.4164 | −1.10895 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 24.1803i | − 1.84912i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.70820i | 0.586044i | 0.956106 | + | 0.293022i | \(0.0946609\pi\) | ||||
−0.956106 | + | 0.293022i | \(0.905339\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.47214 | 0.262469 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 15.4164 | 1.15877 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 24.9443i | − 1.86442i | −0.361915 | − | 0.932211i | \(-0.617877\pi\) | ||||
0.361915 | − | 0.932211i | \(-0.382123\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.1803i | 0.756699i | 0.925663 | + | 0.378349i | \(0.123508\pi\) | ||||
−0.925663 | + | 0.378349i | \(0.876492\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −21.8885 | −1.61805 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.52786 | 0.406417 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 11.0557i | 0.808475i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 14.4721i | 1.05269i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.9443 | 0.936615 | 0.468307 | − | 0.883566i | \(-0.344864\pi\) | ||||
0.468307 | + | 0.883566i | \(0.344864\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.47214 | −0.609838 | −0.304919 | − | 0.952378i | \(-0.598629\pi\) | ||||
−0.304919 | + | 0.952378i | \(0.598629\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 20.9443i | 1.49985i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 6.94427i | − 0.494759i | −0.968919 | − | 0.247379i | \(-0.920431\pi\) | ||||
0.968919 | − | 0.247379i | \(-0.0795694\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.4164 | −0.809288 | −0.404644 | − | 0.914474i | \(-0.632605\pi\) | ||||
−0.404644 | + | 0.914474i | \(0.632605\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 12.9443 | 0.913019 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 4.47214i | − 0.313882i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.583592i | 0.0407598i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −29.8885 | −2.07740 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.00000 | 0.553372 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 12.0000i | − 0.826114i | −0.910705 | − | 0.413057i | \(-0.864461\pi\) | ||||
0.910705 | − | 0.413057i | \(-0.135539\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 41.8885i | − 2.87016i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.05573 | 0.208399 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.47214 | −0.439357 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 48.3607i | 3.26791i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 23.4164i | 1.57516i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.94427 | 0.331093 | 0.165546 | − | 0.986202i | \(-0.447061\pi\) | ||||
0.165546 | + | 0.986202i | \(0.447061\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −25.9443 | −1.72962 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 12.7639i | − 0.847172i | −0.905856 | − | 0.423586i | \(-0.860771\pi\) | ||||
0.905856 | − | 0.423586i | \(-0.139229\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 25.5967i | − 1.69148i | −0.533595 | − | 0.845740i | \(-0.679159\pi\) | ||||
0.533595 | − | 0.845740i | \(-0.320841\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.00000 | −0.526361 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −19.8885 | −1.30294 | −0.651471 | − | 0.758674i | \(-0.725848\pi\) | ||||
−0.651471 | + | 0.758674i | \(0.725848\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.88854i | 0.123195i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 16.0000i | − 1.03931i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −21.8885 | −1.41585 | −0.707926 | − | 0.706287i | \(-0.750369\pi\) | ||||
−0.707926 | + | 0.706287i | \(0.750369\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.52786 | 0.227250 | 0.113625 | − | 0.993524i | \(-0.463754\pi\) | ||||
0.113625 | + | 0.993524i | \(0.463754\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 35.5967i | − 2.28353i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 1.23607i | − 0.0789695i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 16.9443 | 1.07814 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −15.4164 | −0.976975 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 17.7082i | − 1.11773i | −0.829258 | − | 0.558866i | \(-0.811237\pi\) | ||||
0.829258 | − | 0.558866i | \(-0.188763\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 9.88854i | − 0.621687i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 17.8885 | 1.12022 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −14.0000 | −0.873296 | −0.436648 | − | 0.899632i | \(-0.643834\pi\) | ||||
−0.436648 | + | 0.899632i | \(0.643834\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.47214i | 0.277885i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 33.4164i | 2.06842i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 28.9443 | 1.78478 | 0.892390 | − | 0.451265i | \(-0.149027\pi\) | ||||
0.892390 | + | 0.451265i | \(0.149027\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.3607 | −0.759311 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 19.4164i | − 1.18826i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 18.1803i | − 1.10847i | −0.832359 | − | 0.554237i | \(-0.813010\pi\) | ||||
0.832359 | − | 0.554237i | \(-0.186990\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 24.0000 | 1.45790 | 0.728948 | − | 0.684569i | \(-0.240010\pi\) | ||||
0.728948 | + | 0.684569i | \(0.240010\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −16.9443 | −1.02551 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 8.58359i | − 0.517610i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 27.8885i | − 1.67566i | −0.545931 | − | 0.837830i | \(-0.683824\pi\) | ||||
0.545931 | − | 0.837830i | \(-0.316176\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 48.3607 | 2.89528 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −26.0000 | −1.55103 | −0.775515 | − | 0.631329i | \(-0.782510\pi\) | ||||
−0.775515 | + | 0.631329i | \(0.782510\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 16.1803i | − 0.961821i | −0.876770 | − | 0.480911i | \(-0.840306\pi\) | ||||
0.876770 | − | 0.480911i | \(-0.159694\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 12.9443i | − 0.766752i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.472136 | −0.0278693 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.00000 | 0.176471 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 11.4164i | − 0.669242i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 17.2361i | − 1.00694i | −0.864012 | − | 0.503471i | \(-0.832056\pi\) | ||||
0.864012 | − | 0.503471i | \(-0.167944\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.88854 | 0.342844 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 35.7771 | 2.07600 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 20.9443i | − 1.21124i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.47214i | 0.142492i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 37.8885 | 2.17664 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −8.36068 | −0.478731 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 24.1803i | 1.38004i | 0.723788 | + | 0.690022i | \(0.242399\pi\) | ||||
−0.723788 | + | 0.690022i | \(0.757601\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 46.8328i | 2.66423i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.00000 | 0.453638 | 0.226819 | − | 0.973937i | \(-0.427167\pi\) | ||||
0.226819 | + | 0.973937i | \(0.427167\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.472136 | −0.0266867 | −0.0133434 | − | 0.999911i | \(-0.504247\pi\) | ||||
−0.0133434 | + | 0.999911i | \(0.504247\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 9.23607i | 0.520393i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 26.9443i | − 1.51334i | −0.653796 | − | 0.756671i | \(-0.726825\pi\) | ||||
0.653796 | − | 0.756671i | \(-0.273175\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −11.0557 | −0.619002 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 28.9443 | 1.61551 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 14.4721i | − 0.805251i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 18.1803i | − 1.00846i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.52786 | 0.0844911 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.52786 | −0.0842339 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 13.5279i | − 0.743559i | −0.928321 | − | 0.371779i | \(-0.878748\pi\) | ||||
0.928321 | − | 0.371779i | \(-0.121252\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 33.4164i | − 1.83121i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.94427 | 0.270134 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −34.3607 | −1.87175 | −0.935873 | − | 0.352338i | \(-0.885387\pi\) | ||||
−0.935873 | + | 0.352338i | \(0.885387\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 11.4164i | 0.620054i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 16.0000i | 0.866449i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −16.0000 | −0.861411 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.47214i | 0.132711i | 0.997796 | + | 0.0663556i | \(0.0211372\pi\) | ||||
−0.997796 | + | 0.0663556i | \(0.978863\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.65248i | 0.249041i | 0.992217 | + | 0.124521i | \(0.0397393\pi\) | ||||
−0.992217 | + | 0.124521i | \(0.960261\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 75.7771 | 4.04468 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 19.8885 | 1.05856 | 0.529280 | − | 0.848447i | \(-0.322462\pi\) | ||||
0.529280 | + | 0.848447i | \(0.322462\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 16.0000i | − 0.849192i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 14.4721i | 0.765947i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0.944272 | 0.0498368 | 0.0249184 | − | 0.999689i | \(-0.492067\pi\) | ||||
0.0249184 | + | 0.999689i | \(0.492067\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.52786 | 0.448835 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 15.8197i | − 0.830317i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 18.4721i | 0.966876i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −30.8328 | −1.60946 | −0.804730 | − | 0.593641i | \(-0.797690\pi\) | ||||
−0.804730 | + | 0.593641i | \(0.797690\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.52786 | 0.183653 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 10.0000i | − 0.519174i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 14.9443i | − 0.773785i | −0.922125 | − | 0.386893i | \(-0.873548\pi\) | ||||
0.922125 | − | 0.386893i | \(-0.126452\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −33.8885 | −1.75000 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −23.4164 | −1.20601 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 31.4164i | 1.61375i | 0.590721 | + | 0.806876i | \(0.298844\pi\) | ||||
−0.590721 | + | 0.806876i | \(0.701156\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 28.9443i | − 1.48286i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11.4164 | −0.583351 | −0.291676 | − | 0.956517i | \(-0.594213\pi\) | ||||
−0.291676 | + | 0.956517i | \(0.594213\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.05573 | −0.155734 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 18.4721i | − 0.938991i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.47214i | 0.226746i | 0.993552 | + | 0.113373i | \(0.0361656\pi\) | ||||
−0.993552 | + | 0.113373i | \(0.963834\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −17.8885 | −0.904663 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.52786 | −0.278844 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 6.11146i | − 0.307501i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.7639i | 0.540226i | 0.962829 | + | 0.270113i | \(0.0870611\pi\) | ||||
−0.962829 | + | 0.270113i | \(0.912939\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 10.4721 | 0.524263 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −32.4721 | −1.62158 | −0.810791 | − | 0.585336i | \(-0.800962\pi\) | ||||
−0.810791 | + | 0.585336i | \(0.800962\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 33.8885i | 1.68811i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 30.1803i | − 1.49967i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11.0557 | 0.548012 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.41641 | −0.267824 | −0.133912 | − | 0.990993i | \(-0.542754\pi\) | ||||
−0.133912 | + | 0.990993i | \(0.542754\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 9.52786i | − 0.469975i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.76393i | 0.234418i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.88854 | −0.289057 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 10.4721 | 0.512823 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 0.180340i | − 0.00881018i | −0.999990 | − | 0.00440509i | \(-0.998598\pi\) | ||||
0.999990 | − | 0.00440509i | \(-0.00140219\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 2.00000i | − 0.0974740i | −0.998812 | − | 0.0487370i | \(-0.984480\pi\) | ||||
0.998812 | − | 0.0487370i | \(-0.0155196\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 11.4164 | 0.555085 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −15.5279 | −0.753212 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 6.76393i | − 0.327330i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 41.8885i | 2.02240i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 28.0000 | 1.34871 | 0.674356 | − | 0.738406i | \(-0.264421\pi\) | ||||
0.674356 | + | 0.738406i | \(0.264421\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −17.4164 | −0.836979 | −0.418490 | − | 0.908222i | \(-0.637440\pi\) | ||||
−0.418490 | + | 0.908222i | \(0.637440\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 17.8885i | 0.857690i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 12.9443i | 0.619208i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −32.0000 | −1.52728 | −0.763638 | − | 0.645644i | \(-0.776589\pi\) | ||||
−0.763638 | + | 0.645644i | \(0.776589\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7.47214 | −0.355816 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 21.8885i | − 1.03996i | −0.854180 | − | 0.519978i | \(-0.825940\pi\) | ||||
0.854180 | − | 0.519978i | \(-0.174060\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 7.41641i | − 0.351571i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −48.3607 | −2.28738 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 27.8885 | 1.31614 | 0.658071 | − | 0.752956i | \(-0.271373\pi\) | ||||
0.658071 | + | 0.752956i | \(0.271373\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.16718i | 0.0549606i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 28.9443i | − 1.35992i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.47214 | −0.303418 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16.4721 | 0.770534 | 0.385267 | − | 0.922805i | \(-0.374109\pi\) | ||||
0.385267 | + | 0.922805i | \(0.374109\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 64.7214i | − 3.02093i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 8.29180i | − 0.386187i | −0.981180 | − | 0.193094i | \(-0.938148\pi\) | ||||
0.981180 | − | 0.193094i | \(-0.0618521\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −35.7771 | −1.66270 | −0.831351 | − | 0.555748i | \(-0.812432\pi\) | ||||
−0.831351 | + | 0.555748i | \(0.812432\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 25.8885 | 1.20055 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 26.0689i | 1.20632i | 0.797619 | + | 0.603162i | \(0.206093\pi\) | ||||
−0.797619 | + | 0.603162i | \(0.793907\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.00000i | 0.184703i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −16.9443 | −0.780751 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.11146 | 0.281005 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 11.2361i | 0.515546i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 74.7214i | 3.42126i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 35.4164 | 1.61822 | 0.809108 | − | 0.587659i | \(-0.199950\pi\) | ||||
0.809108 | + | 0.587659i | \(0.199950\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 23.4164 | 1.06770 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 12.9443i | − 0.588985i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 4.36068i | − 0.198008i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.0000 | 0.906287 | 0.453143 | − | 0.891438i | \(-0.350303\pi\) | ||||
0.453143 | + | 0.891438i | \(0.350303\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 75.7771 | 3.42676 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 2.11146i | − 0.0952887i | −0.998864 | − | 0.0476443i | \(-0.984829\pi\) | ||||
0.998864 | − | 0.0476443i | \(-0.0151714\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 20.0000i | 0.900755i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 22.8328 | 1.02626 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 12.9443 | 0.580630 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 13.8885i | − 0.621737i | −0.950453 | − | 0.310868i | \(-0.899380\pi\) | ||||
0.950453 | − | 0.310868i | \(-0.100620\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 11.0557i | 0.493934i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12.9443 | 0.577157 | 0.288578 | − | 0.957456i | \(-0.406817\pi\) | ||||
0.288578 | + | 0.957456i | \(0.406817\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14.4721 | 0.644002 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 46.6525i | 2.07191i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0.875388i | 0.0388009i | 0.999812 | + | 0.0194004i | \(0.00617574\pi\) | ||||
−0.999812 | + | 0.0194004i | \(0.993824\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14.9443 | −0.661096 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −46.8328 | −2.06772 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 17.8885i | 0.788263i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.77709i | 0.166116i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 24.9443 | 1.09493 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 33.4164 | 1.46400 | 0.732000 | − | 0.681305i | \(-0.238587\pi\) | ||||
0.732000 | + | 0.681305i | \(0.238587\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17.7082i | 0.774326i | 0.922011 | + | 0.387163i | \(0.126545\pi\) | ||||
−0.922011 | + | 0.387163i | \(0.873455\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 11.2361i | − 0.490382i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 28.9443 | 1.26083 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 35.5967i | − 1.54477i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.47214i | 0.107080i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 11.0557 | 0.477981 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −80.7214 | −3.48338 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 2.47214i | − 0.106482i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22.9443i | 0.986451i | 0.869901 | + | 0.493226i | \(0.164182\pi\) | ||||
−0.869901 | + | 0.493226i | \(0.835818\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 32.9443 | 1.41377 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.583592 | 0.0249983 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 31.4164i | − 1.34327i | −0.740883 | − | 0.671634i | \(-0.765593\pi\) | ||||
0.740883 | − | 0.671634i | \(-0.234407\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 50.5410i | 2.15704i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 14.4721 | 0.616534 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.94427 | 0.210252 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 17.8885i | − 0.759326i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 26.9443i | − 1.14167i | −0.821066 | − | 0.570833i | \(-0.806620\pi\) | ||||
0.821066 | − | 0.570833i | \(-0.193380\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12.9443 | 0.547484 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 35.7771 | 1.51051 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 40.1803i | − 1.69340i | −0.532071 | − | 0.846700i | \(-0.678586\pi\) | ||||
0.532071 | − | 0.846700i | \(-0.321414\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.36068i | 0.183455i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 24.4164 | 1.02539 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 18.3607 | 0.769720 | 0.384860 | − | 0.922975i | \(-0.374250\pi\) | ||||
0.384860 | + | 0.922975i | \(0.374250\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.52786i | 0.231334i | 0.993288 | + | 0.115667i | \(0.0369005\pi\) | ||||
−0.993288 | + | 0.115667i | \(0.963099\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 41.8885i | − 1.74992i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 13.8885 | 0.579192 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.00000 | −0.249783 | −0.124892 | − | 0.992170i | \(-0.539858\pi\) | ||||
−0.124892 | + | 0.992170i | \(0.539858\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 27.4164i | 1.13939i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 4.76393i | − 0.197641i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −24.7214 | −1.02385 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 48.3607 | 1.99947 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 9.70820i | − 0.400700i | −0.979724 | − | 0.200350i | \(-0.935792\pi\) | ||||
0.979724 | − | 0.200350i | \(-0.0642080\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 20.9443i | − 0.862994i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −22.4721 | −0.924380 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −20.8328 | −0.855501 | −0.427751 | − | 0.903897i | \(-0.640694\pi\) | ||||
−0.427751 | + | 0.903897i | \(0.640694\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.52786i | 0.226620i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 36.9443i | 1.51203i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −17.8885 | −0.730906 | −0.365453 | − | 0.930830i | \(-0.619086\pi\) | ||||
−0.365453 | + | 0.930830i | \(0.619086\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 41.7771 | 1.70412 | 0.852061 | − | 0.523442i | \(-0.175352\pi\) | ||||
0.852061 | + | 0.523442i | \(0.175352\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 29.8885i | − 1.21716i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 6.04257i | − 0.245666i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 25.8885 | 1.05078 | 0.525392 | − | 0.850860i | \(-0.323919\pi\) | ||||
0.525392 | + | 0.850860i | \(0.323919\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −14.4721 | −0.586441 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.00000i | 0.323645i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.58359i | 0.104350i | 0.998638 | + | 0.0521752i | \(0.0166154\pi\) | ||||
−0.998638 | + | 0.0521752i | \(0.983385\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.88854 | 0.0761534 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10.3607 | 0.417105 | 0.208553 | − | 0.978011i | \(-0.433125\pi\) | ||||
0.208553 | + | 0.978011i | \(0.433125\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 10.0689i | − 0.404703i | −0.979313 | − | 0.202351i | \(-0.935142\pi\) | ||||
0.979313 | − | 0.202351i | \(-0.0648583\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 57.8885i | 2.32299i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.00000 | 0.240385 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.41641 | 0.176656 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 25.8885i | − 1.03389i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 20.0000i | − 0.797452i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −27.0557 | −1.07707 | −0.538536 | − | 0.842603i | \(-0.681022\pi\) | ||||
−0.538536 | + | 0.842603i | \(0.681022\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −38.8328 | −1.54347 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 11.0557i | − 0.438733i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 5.23607i | − 0.207461i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −96.7214 | −3.82624 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 41.4164 | 1.63585 | 0.817925 | − | 0.575325i | \(-0.195124\pi\) | ||||
0.817925 | + | 0.575325i | \(0.195124\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 30.2918i | − 1.19459i | −0.802021 | − | 0.597296i | \(-0.796242\pi\) | ||||
0.802021 | − | 0.597296i | \(-0.203758\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 9.88854i | − 0.389361i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 24.3607 | 0.957717 | 0.478859 | − | 0.877892i | \(-0.341051\pi\) | ||||
0.478859 | + | 0.877892i | \(0.341051\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11.7771 | 0.462291 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 20.9443i | 0.820871i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 17.4164i | − 0.681557i | −0.940144 | − | 0.340778i | \(-0.889309\pi\) | ||||
0.940144 | − | 0.340778i | \(-0.110691\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.11146 | −0.0825014 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 111.666 | 4.35649 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 25.3050i | − 0.985741i | −0.870103 | − | 0.492870i | \(-0.835948\pi\) | ||||
0.870103 | − | 0.492870i | \(-0.164052\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.65248i | 0.336542i | 0.985741 | + | 0.168271i | \(0.0538184\pi\) | ||||
−0.985741 | + | 0.168271i | \(0.946182\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 75.7771 | 2.94294 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.00000 | 0.155113 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 17.8885i | − 0.692647i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 16.0000i | − 0.618596i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −16.7214 | −0.645521 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14.9443 | 0.576059 | 0.288030 | − | 0.957621i | \(-0.407000\pi\) | ||||
0.288030 | + | 0.957621i | \(0.407000\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 50.2492i | 1.93409i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 42.1803i | 1.62112i | 0.585654 | + | 0.810561i | \(0.300838\pi\) | ||||
−0.585654 | + | 0.810561i | \(0.699162\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.52786 | 0.135387 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −41.3050 | −1.58281 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 47.7771i | 1.82814i | 0.405557 | + | 0.914070i | \(0.367078\pi\) | ||||
−0.405557 | + | 0.914070i | \(0.632922\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 3.63932i | − 0.139051i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −82.8328 | −3.16027 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −52.3607 | −1.99478 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.18034i | 0.311195i | 0.987821 | + | 0.155597i | \(0.0497302\pi\) | ||||
−0.987821 | + | 0.155597i | \(0.950270\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 18.4721i | 0.701698i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.00000 | 0.151729 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.11146 | 0.0799771 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 64.3607i | 2.43434i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14.5836i | 0.550815i | 0.961328 | + | 0.275407i | \(0.0888127\pi\) | ||||
−0.961328 | + | 0.275407i | \(0.911187\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −14.4721 | −0.545827 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6.11146 | 0.230171 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 11.7082i | 0.440332i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 46.3607i | 1.74111i | 0.492069 | + | 0.870556i | \(0.336241\pi\) | ||||
−0.492069 | + | 0.870556i | \(0.663759\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −36.9443 | −1.38552 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −25.8885 | −0.969534 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 16.0000i | 0.598366i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 70.8328i | 2.64530i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 47.1935 | 1.76002 | 0.880010 | − | 0.474955i | \(-0.157536\pi\) | ||||
0.880010 | + | 0.474955i | \(0.157536\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.4721 | −0.538971 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 11.4164i | − 0.424581i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 15.5279i | − 0.576690i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −32.3607 | −1.20019 | −0.600096 | − | 0.799928i | \(-0.704871\pi\) | ||||
−0.600096 | + | 0.799928i | \(0.704871\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −41.9443 | −1.55349 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 11.0557i | − 0.408911i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.23607i | 0.341142i | 0.985345 | + | 0.170571i | \(0.0545612\pi\) | ||||
−0.985345 | + | 0.170571i | \(0.945439\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −4.00000 | −0.147542 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 9.88854 | 0.364249 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 23.4164i | 0.861386i | 0.902498 | + | 0.430693i | \(0.141731\pi\) | ||||
−0.902498 | + | 0.430693i | \(0.858269\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 54.8328i | − 2.01433i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 7.05573 | 0.258850 | 0.129425 | − | 0.991589i | \(-0.458687\pi\) | ||||
0.129425 | + | 0.991589i | \(0.458687\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −18.4721 | −0.676767 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 35.5967i | 1.30242i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.94427i | 0.326817i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −36.0000 | −1.31366 | −0.656829 | − | 0.754039i | \(-0.728103\pi\) | ||||
−0.656829 | + | 0.754039i | \(0.728103\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −57.3050 | −2.08831 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 11.0557i | − 0.402359i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 23.3050i | − 0.847033i | −0.905888 | − | 0.423516i | \(-0.860796\pi\) | ||||
0.905888 | − | 0.423516i | \(-0.139204\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −32.0000 | −1.16153 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12.4721 | 0.452115 | 0.226057 | − | 0.974114i | \(-0.427416\pi\) | ||||
0.226057 | + | 0.974114i | \(0.427416\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.472136i | 0.0170925i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 41.3050i | − 1.49338i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 24.9443 | 0.900685 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 26.3607 | 0.950590 | 0.475295 | − | 0.879826i | \(-0.342341\pi\) | ||||
0.475295 | + | 0.879826i | \(0.342341\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 45.3050i | 1.63162i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 17.8197i | 0.640929i | 0.947261 | + | 0.320464i | \(0.103839\pi\) | ||||
−0.947261 | + | 0.320464i | \(0.896161\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −22.4721 | −0.807223 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 14.4721 | 0.519185 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 1.52786i | − 0.0547414i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 32.0000i | − 1.14505i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 64.7214 | 2.31295 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.47214 | −0.231000 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 25.7082i | − 0.916399i | −0.888850 | − | 0.458199i | \(-0.848495\pi\) | ||||
0.888850 | − | 0.458199i | \(-0.151505\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 93.6656i | − 3.33458i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.52786 | −0.125436 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −35.4164 | −1.25767 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 40.0000i | 1.41865i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 29.8197i | 1.05627i | 0.849161 | + | 0.528133i | \(0.177108\pi\) | ||||
−0.849161 | + | 0.528133i | \(0.822892\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.83282 | 0.241728 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −44.8328 | −1.58409 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 36.9443i | 1.30374i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 4.94427i | − 0.174263i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −58.8328 | −2.07101 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −9.41641 | −0.331063 | −0.165532 | − | 0.986204i | \(-0.552934\pi\) | ||||
−0.165532 | + | 0.986204i | \(0.552934\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 23.0132i | − 0.808101i | −0.914737 | − | 0.404051i | \(-0.867602\pi\) | ||||
0.914737 | − | 0.404051i | \(-0.132398\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 77.6656i | − 2.72385i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 28.9443 | 1.01387 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.00000 | −0.279885 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 39.1246i | 1.36712i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 39.8885i | 1.39212i | 0.717984 | + | 0.696060i | \(0.245065\pi\) | ||||
−0.717984 | + | 0.696060i | \(0.754935\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 51.7771 | 1.80484 | 0.902418 | − | 0.430862i | \(-0.141790\pi\) | ||||
0.902418 | + | 0.430862i | \(0.141790\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −27.7771 | −0.967074 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 32.9443i | − 1.14558i | −0.819701 | − | 0.572792i | \(-0.805860\pi\) | ||||
0.819701 | − | 0.572792i | \(-0.194140\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 6.76393i | − 0.234921i | −0.993078 | − | 0.117461i | \(-0.962525\pi\) | ||||
0.993078 | − | 0.117461i | \(-0.0374754\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −90.2492 | −3.13071 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.47214 | −0.154950 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.22291i | 0.146140i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 93.6656i | − 3.23756i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −30.4721 | −1.05201 | −0.526007 | − | 0.850480i | \(-0.676312\pi\) | ||||
−0.526007 | + | 0.850480i | \(0.676312\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.00000 | 0.310345 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 84.1378i | 2.89786i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 17.8197i | 0.613015i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.88854 | 0.167972 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −52.3607 | −1.79701 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 17.8885i | 0.613211i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.291796i | 0.00999091i | 0.999988 | + | 0.00499545i | \(0.00159011\pi\) | ||||
−0.999988 | + | 0.00499545i | \(0.998410\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −29.8885 | −1.02217 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 36.4721 | 1.24586 | 0.622932 | − | 0.782276i | \(-0.285941\pi\) | ||||
0.622932 | + | 0.782276i | \(0.285941\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 56.1803i | 1.91685i | 0.285347 | + | 0.958424i | \(0.407891\pi\) | ||||
−0.285347 | + | 0.958424i | \(0.592109\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.52786i | 0.0520695i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.05573 | 0.104018 | 0.0520091 | − | 0.998647i | \(-0.483438\pi\) | ||||
0.0520091 | + | 0.998647i | \(0.483438\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.52786 | 0.323957 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 9.70820i | − 0.329708i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 12.2229i | − 0.414634i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 20.9443 | 0.709670 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −26.3607 | −0.892174 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 10.4721i | − 0.354023i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 13.4164i | 0.453040i | 0.974007 | + | 0.226520i | \(0.0727348\pi\) | ||||
−0.974007 | + | 0.226520i | \(0.927265\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −55.7771 | −1.88131 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −28.8328 | −0.971402 | −0.485701 | − | 0.874125i | \(-0.661436\pi\) | ||||
−0.485701 | + | 0.874125i | \(0.661436\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 40.9443i | 1.37788i | 0.724816 | + | 0.688942i | \(0.241925\pi\) | ||||
−0.724816 | + | 0.688942i | \(0.758075\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 19.0557i | − 0.640551i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 29.3050 | 0.983964 | 0.491982 | − | 0.870605i | \(-0.336273\pi\) | ||||
0.491982 | + | 0.870605i | \(0.336273\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.94427 | 0.299981 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 60.3607i | − 2.02216i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 4.94427i | − 0.165454i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −30.8328 | −1.03063 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −67.7771 | −2.26301 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 28.9443i | 0.965346i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 44.7214i | 1.48988i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 8.00000 | 0.266223 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 12.5836 | 0.418293 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 16.9443i | 0.562625i | 0.959616 | + | 0.281313i | \(0.0907698\pi\) | ||||
−0.959616 | + | 0.281313i | \(0.909230\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 87.4853i | − 2.90170i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18.8328 | −0.623959 | −0.311980 | − | 0.950089i | \(-0.600992\pi\) | ||||
−0.311980 | + | 0.950089i | \(0.600992\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11.7771 | −0.389765 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 27.0557i | 0.894435i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 1.70820i | − 0.0564099i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 35.7771 | 1.18018 | 0.590089 | − | 0.807338i | \(-0.299093\pi\) | ||||
0.590089 | + | 0.807338i | \(0.299093\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 78.2492 | 2.57840 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 67.7771i | − 2.23091i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 15.5279i | 0.510553i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 108.138 | 3.55171 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 15.3050 | 0.502139 | 0.251070 | − | 0.967969i | \(-0.419218\pi\) | ||||
0.251070 | + | 0.967969i | \(0.419218\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.23607i | 0.106058i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 25.8885i | − 0.847553i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 13.6656 | 0.446914 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 26.9443 | 0.880231 | 0.440115 | − | 0.897941i | \(-0.354937\pi\) | ||||
0.440115 | + | 0.897941i | \(0.354937\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.52786i | 0.0498600i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 13.5967i | − 0.443241i | −0.975133 | − | 0.221621i | \(-0.928865\pi\) | ||||
0.975133 | − | 0.221621i | \(-0.0711347\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.88854 | −0.0614994 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 17.8885 | 0.581914 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 31.4164i | − 1.02090i | −0.859909 | − | 0.510448i | \(-0.829480\pi\) | ||||
0.859909 | − | 0.510448i | \(-0.170520\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 78.2492i | 2.54008i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −87.1935 | −2.82744 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −16.1115 | −0.521901 | −0.260951 | − | 0.965352i | \(-0.584036\pi\) | ||||
−0.260951 | + | 0.965352i | \(0.584036\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 16.0000i | − 0.517748i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 35.7771i | 1.15651i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.94427 | 0.0950755 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10.8885 | 0.351243 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 66.8328i | − 2.15366i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 10.4721i | 0.337110i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.88854 | −0.189363 | −0.0946814 | − | 0.995508i | \(-0.530183\pi\) | ||||
−0.0946814 | + | 0.995508i | \(0.530183\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −46.8328 | −1.50449 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 27.2361i | − 0.874047i | −0.899450 | − | 0.437024i | \(-0.856033\pi\) | ||||
0.899450 | − | 0.437024i | \(-0.143967\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.23607i | 0.103744i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −58.8328 | −1.88416 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 40.8328 | 1.30636 | 0.653179 | − | 0.757204i | \(-0.273435\pi\) | ||||
0.653179 | + | 0.757204i | \(0.273435\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 14.8328i | − 0.474059i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 3.52786i | − 0.112636i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −14.4721 | −0.461589 | −0.230795 | − | 0.973002i | \(-0.574133\pi\) | ||||
−0.230795 | + | 0.973002i | \(0.574133\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.58359 | −0.273496 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4.94427i | 0.157378i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9.88854i | 0.314437i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24.0000 | 0.762385 | 0.381193 | − | 0.924496i | \(-0.375513\pi\) | ||||
0.381193 | + | 0.924496i | \(0.375513\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −43.7771 | −1.38922 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 14.1115i | 0.447363i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 40.0689i | − 1.26899i | −0.772925 | − | 0.634497i | \(-0.781207\pi\) | ||||
0.772925 | − | 0.634497i | \(-0.218793\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −64.7214 | −2.04769 |
(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 | 1792.2.b.m.897.1 | 4 | ||
4.3 | odd | 2 | 1792.2.b.k.897.4 | 4 | |||
8.3 | odd | 2 | 1792.2.b.k.897.1 | 4 | |||
8.5 | even | 2 | inner | 1792.2.b.m.897.4 | 4 | ||
16.3 | odd | 4 | 224.2.a.c.1.1 | ✓ | 2 | ||
16.5 | even | 4 | 448.2.a.i.1.1 | 2 | |||
16.11 | odd | 4 | 448.2.a.j.1.2 | 2 | |||
16.13 | even | 4 | 224.2.a.d.1.2 | yes | 2 | ||
48.5 | odd | 4 | 4032.2.a.bv.1.1 | 2 | |||
48.11 | even | 4 | 4032.2.a.bw.1.1 | 2 | |||
48.29 | odd | 4 | 2016.2.a.o.1.2 | 2 | |||
48.35 | even | 4 | 2016.2.a.r.1.2 | 2 | |||
80.19 | odd | 4 | 5600.2.a.bk.1.2 | 2 | |||
80.29 | even | 4 | 5600.2.a.z.1.1 | 2 | |||
112.3 | even | 12 | 1568.2.i.n.961.1 | 4 | |||
112.13 | odd | 4 | 1568.2.a.k.1.1 | 2 | |||
112.19 | even | 12 | 1568.2.i.n.1537.1 | 4 | |||
112.27 | even | 4 | 3136.2.a.bf.1.1 | 2 | |||
112.45 | odd | 12 | 1568.2.i.w.961.2 | 4 | |||
112.51 | odd | 12 | 1568.2.i.v.1537.2 | 4 | |||
112.61 | odd | 12 | 1568.2.i.w.1537.2 | 4 | |||
112.67 | odd | 12 | 1568.2.i.v.961.2 | 4 | |||
112.69 | odd | 4 | 3136.2.a.by.1.2 | 2 | |||
112.83 | even | 4 | 1568.2.a.v.1.2 | 2 | |||
112.93 | even | 12 | 1568.2.i.m.1537.1 | 4 | |||
112.109 | even | 12 | 1568.2.i.m.961.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
224.2.a.c.1.1 | ✓ | 2 | 16.3 | odd | 4 | ||
224.2.a.d.1.2 | yes | 2 | 16.13 | even | 4 | ||
448.2.a.i.1.1 | 2 | 16.5 | even | 4 | |||
448.2.a.j.1.2 | 2 | 16.11 | odd | 4 | |||
1568.2.a.k.1.1 | 2 | 112.13 | odd | 4 | |||
1568.2.a.v.1.2 | 2 | 112.83 | even | 4 | |||
1568.2.i.m.961.1 | 4 | 112.109 | even | 12 | |||
1568.2.i.m.1537.1 | 4 | 112.93 | even | 12 | |||
1568.2.i.n.961.1 | 4 | 112.3 | even | 12 | |||
1568.2.i.n.1537.1 | 4 | 112.19 | even | 12 | |||
1568.2.i.v.961.2 | 4 | 112.67 | odd | 12 | |||
1568.2.i.v.1537.2 | 4 | 112.51 | odd | 12 | |||
1568.2.i.w.961.2 | 4 | 112.45 | odd | 12 | |||
1568.2.i.w.1537.2 | 4 | 112.61 | odd | 12 | |||
1792.2.b.k.897.1 | 4 | 8.3 | odd | 2 | |||
1792.2.b.k.897.4 | 4 | 4.3 | odd | 2 | |||
1792.2.b.m.897.1 | 4 | 1.1 | even | 1 | trivial | ||
1792.2.b.m.897.4 | 4 | 8.5 | even | 2 | inner | ||
2016.2.a.o.1.2 | 2 | 48.29 | odd | 4 | |||
2016.2.a.r.1.2 | 2 | 48.35 | even | 4 | |||
3136.2.a.bf.1.1 | 2 | 112.27 | even | 4 | |||
3136.2.a.by.1.2 | 2 | 112.69 | odd | 4 | |||
4032.2.a.bv.1.1 | 2 | 48.5 | odd | 4 | |||
4032.2.a.bw.1.1 | 2 | 48.11 | even | 4 | |||
5600.2.a.z.1.1 | 2 | 80.29 | even | 4 | |||
5600.2.a.bk.1.2 | 2 | 80.19 | odd | 4 |