Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [896,2,Mod(225,896)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(896, base_ring=CyclotomicField(4))
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("896.225");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 896 = 2^{7} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 896.m (of order \(4\), degree \(2\), 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: | \(7.15459602111\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 112) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 225.1 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 896.225 |
Dual form | 896.2.m.a.673.1 |
$q$-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 \(\left(\mathbb{Z}/896\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(645\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
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 | ||||||||
\(3\) | −2.00000 | + | 2.00000i | −1.15470 | + | 1.15470i | −0.169102 | + | 0.985599i | \(0.554087\pi\) |
−0.985599 | + | 0.169102i | \(0.945913\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.00000 | + | 2.00000i | 0.894427 | + | 0.894427i | 0.994936 | − | 0.100509i | \(-0.0320471\pi\) |
−0.100509 | + | 0.994936i | \(0.532047\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 5.00000i | − | 1.66667i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.00000 | − | 3.00000i | −0.904534 | − | 0.904534i | 0.0912903 | − | 0.995824i | \(-0.470901\pi\) |
−0.995824 | + | 0.0912903i | \(0.970901\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −8.00000 | −2.06559 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.00000 | −1.45521 | −0.727607 | − | 0.685994i | \(-0.759367\pi\) | ||||
−0.727607 | + | 0.685994i | \(0.759367\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.00000 | + | 4.00000i | −0.917663 | + | 0.917663i | −0.996859 | − | 0.0791961i | \(-0.974765\pi\) |
0.0791961 | + | 0.996859i | \(0.474765\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.00000 | + | 2.00000i | 0.436436 | + | 0.436436i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 2.00000i | − | 0.417029i | −0.978019 | − | 0.208514i | \(-0.933137\pi\) | ||
0.978019 | − | 0.208514i | \(-0.0668628\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.00000i | 0.600000i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.00000 | + | 4.00000i | 0.769800 | + | 0.769800i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.00000 | − | 1.00000i | 0.185695 | − | 0.185695i | −0.608137 | − | 0.793832i | \(-0.708083\pi\) |
0.793832 | + | 0.608137i | \(0.208083\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.00000 | −0.718421 | −0.359211 | − | 0.933257i | \(-0.616954\pi\) | ||||
−0.359211 | + | 0.933257i | \(0.616954\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 12.0000 | 2.08893 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.00000 | − | 2.00000i | 0.338062 | − | 0.338062i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.00000 | − | 3.00000i | −0.493197 | − | 0.493197i | 0.416115 | − | 0.909312i | \(-0.363391\pi\) |
−0.909312 | + | 0.416115i | \(0.863391\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.00000i | 0.312348i | 0.987730 | + | 0.156174i | \(0.0499160\pi\) | ||||
−0.987730 | + | 0.156174i | \(0.950084\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.00000 | − | 5.00000i | −0.762493 | − | 0.762493i | 0.214280 | − | 0.976772i | \(-0.431260\pi\) |
−0.976772 | + | 0.214280i | \(0.931260\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 10.0000 | − | 10.0000i | 1.49071 | − | 1.49071i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.00000 | 1.16692 | 0.583460 | − | 0.812142i | \(-0.301699\pi\) | ||||
0.583460 | + | 0.812142i | \(0.301699\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 12.0000 | − | 12.0000i | 1.68034 | − | 1.68034i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.00000 | − | 7.00000i | −0.961524 | − | 0.961524i | 0.0377628 | − | 0.999287i | \(-0.487977\pi\) |
−0.999287 | + | 0.0377628i | \(0.987977\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 12.0000i | − | 1.61808i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 16.0000i | − | 2.11925i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.00000 | + | 2.00000i | 0.260378 | + | 0.260378i | 0.825208 | − | 0.564830i | \(-0.191058\pi\) |
−0.564830 | + | 0.825208i | \(0.691058\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.00000 | + | 6.00000i | −0.768221 | + | 0.768221i | −0.977793 | − | 0.209572i | \(-0.932793\pi\) |
0.209572 | + | 0.977793i | \(0.432793\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −5.00000 | −0.629941 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.00000 | + | 5.00000i | −0.610847 | + | 0.610847i | −0.943167 | − | 0.332320i | \(-0.892169\pi\) |
0.332320 | + | 0.943167i | \(0.392169\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.00000 | + | 4.00000i | 0.481543 | + | 0.481543i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.00000i | 0.949425i | 0.880141 | + | 0.474713i | \(0.157448\pi\) | ||||
−0.880141 | + | 0.474713i | \(0.842552\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 10.0000i | − | 1.17041i | −0.810885 | − | 0.585206i | \(-0.801014\pi\) | ||
0.810885 | − | 0.585206i | \(-0.198986\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −6.00000 | − | 6.00000i | −0.692820 | − | 0.692820i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.00000 | + | 3.00000i | −0.341882 | + | 0.341882i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.0000 | 1.57512 | 0.787562 | − | 0.616236i | \(-0.211343\pi\) | ||||
0.787562 | + | 0.616236i | \(0.211343\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −12.0000 | − | 12.0000i | −1.30158 | − | 1.30158i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.00000i | 0.428845i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.00000i | 0.635999i | 0.948091 | + | 0.317999i | \(0.103011\pi\) | ||||
−0.948091 | + | 0.317999i | \(0.896989\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.00000 | − | 8.00000i | 0.829561 | − | 0.829561i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −16.0000 | −1.64157 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.00000 | −0.609208 | −0.304604 | − | 0.952479i | \(-0.598524\pi\) | ||||
−0.304604 | + | 0.952479i | \(0.598524\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −15.0000 | + | 15.0000i | −1.50756 | + | 1.50756i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.00000 | − | 2.00000i | −0.199007 | − | 0.199007i | 0.600567 | − | 0.799574i | \(-0.294942\pi\) |
−0.799574 | + | 0.600567i | \(0.794942\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 8.00000i | 0.780720i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.00000 | + | 5.00000i | 0.483368 | + | 0.483368i | 0.906206 | − | 0.422837i | \(-0.138966\pi\) |
−0.422837 | + | 0.906206i | \(0.638966\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.00000 | − | 3.00000i | 0.287348 | − | 0.287348i | −0.548683 | − | 0.836031i | \(-0.684871\pi\) |
0.836031 | + | 0.548683i | \(0.184871\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 12.0000 | 1.13899 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −12.0000 | −1.12887 | −0.564433 | − | 0.825479i | \(-0.690905\pi\) | ||||
−0.564433 | + | 0.825479i | \(0.690905\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.00000 | − | 4.00000i | 0.373002 | − | 0.373002i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.00000i | 0.550019i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.00000i | 0.636364i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.00000 | − | 4.00000i | −0.360668 | − | 0.360668i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.00000 | − | 4.00000i | 0.357771 | − | 0.357771i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.00000 | −0.709885 | −0.354943 | − | 0.934888i | \(-0.615500\pi\) | ||||
−0.354943 | + | 0.934888i | \(0.615500\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 20.0000 | 1.76090 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.0000 | − | 12.0000i | 1.04844 | − | 1.04844i | 0.0496797 | − | 0.998765i | \(-0.484180\pi\) |
0.998765 | − | 0.0496797i | \(-0.0158200\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.00000 | + | 4.00000i | 0.346844 | + | 0.346844i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 16.0000i | 1.37706i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.0000i | 1.02523i | 0.858619 | + | 0.512615i | \(0.171323\pi\) | ||||
−0.858619 | + | 0.512615i | \(0.828677\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.0000 | − | 12.0000i | −1.01783 | − | 1.01783i | −0.999838 | − | 0.0179885i | \(-0.994274\pi\) |
−0.0179885 | − | 0.999838i | \(-0.505726\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −16.0000 | + | 16.0000i | −1.34744 | + | 1.34744i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.00000 | 0.332182 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.00000 | − | 2.00000i | 0.164957 | − | 0.164957i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.0000 | + | 13.0000i | 1.06500 | + | 1.06500i | 0.997735 | + | 0.0672664i | \(0.0214278\pi\) |
0.0672664 | + | 0.997735i | \(0.478572\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.00000i | 0.488273i | 0.969741 | + | 0.244137i | \(0.0785045\pi\) | ||||
−0.969741 | + | 0.244137i | \(0.921495\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 30.0000i | 2.42536i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.00000 | − | 8.00000i | −0.642575 | − | 0.642575i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 28.0000 | 2.22054 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.00000 | −0.157622 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.00000 | + | 5.00000i | −0.391630 | + | 0.391630i | −0.875268 | − | 0.483638i | \(-0.839315\pi\) |
0.483638 | + | 0.875268i | \(0.339315\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 24.0000 | + | 24.0000i | 1.86840 | + | 1.86840i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 13.0000i | 1.00000i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 20.0000 | + | 20.0000i | 1.52944 | + | 1.52944i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −16.0000 | + | 16.0000i | −1.21646 | + | 1.21646i | −0.247593 | + | 0.968864i | \(0.579640\pi\) |
−0.968864 | + | 0.247593i | \(0.920360\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.00000 | 0.226779 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −8.00000 | −0.601317 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.00000 | − | 5.00000i | 0.373718 | − | 0.373718i | −0.495112 | − | 0.868829i | \(-0.664873\pi\) |
0.868829 | + | 0.495112i | \(0.164873\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.00000 | − | 4.00000i | −0.297318 | − | 0.297318i | 0.542645 | − | 0.839962i | \(-0.317423\pi\) |
−0.839962 | + | 0.542645i | \(0.817423\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 24.0000i | − | 1.77413i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 12.0000i | − | 0.882258i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 18.0000 | + | 18.0000i | 1.31629 | + | 1.31629i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.00000 | − | 4.00000i | 0.290957 | − | 0.290957i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −22.0000 | −1.59186 | −0.795932 | − | 0.605386i | \(-0.793019\pi\) | ||||
−0.795932 | + | 0.605386i | \(0.793019\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −24.0000 | −1.72756 | −0.863779 | − | 0.503871i | \(-0.831909\pi\) | ||||
−0.863779 | + | 0.503871i | \(0.831909\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.0000 | + | 11.0000i | 0.783718 | + | 0.783718i | 0.980456 | − | 0.196738i | \(-0.0630350\pi\) |
−0.196738 | + | 0.980456i | \(0.563035\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.0000i | 1.41776i | 0.705328 | + | 0.708881i | \(0.250800\pi\) | ||||
−0.705328 | + | 0.708881i | \(0.749200\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 20.0000i | − | 1.41069i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.00000 | − | 1.00000i | −0.0701862 | − | 0.0701862i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.00000 | + | 4.00000i | −0.279372 | + | 0.279372i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −10.0000 | −0.695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 24.0000 | 1.66011 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.00000 | + | 9.00000i | −0.619586 | + | 0.619586i | −0.945425 | − | 0.325840i | \(-0.894353\pi\) |
0.325840 | + | 0.945425i | \(0.394353\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −16.0000 | − | 16.0000i | −1.09630 | − | 1.09630i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 20.0000i | − | 1.36399i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.00000i | 0.271538i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 20.0000 | + | 20.0000i | 1.35147 | + | 1.35147i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.00000 | −0.267860 | −0.133930 | − | 0.990991i | \(-0.542760\pi\) | ||||
−0.133930 | + | 0.990991i | \(0.542760\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 15.0000 | 1.00000 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.00000 | − | 4.00000i | 0.265489 | − | 0.265489i | −0.561790 | − | 0.827280i | \(-0.689887\pi\) |
0.827280 | + | 0.561790i | \(0.189887\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.0000 | − | 12.0000i | −0.792982 | − | 0.792982i | 0.188996 | − | 0.981978i | \(-0.439477\pi\) |
−0.981978 | + | 0.188996i | \(0.939477\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 12.0000i | − | 0.789542i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 8.00000i | − | 0.524097i | −0.965055 | − | 0.262049i | \(-0.915602\pi\) | ||
0.965055 | − | 0.262049i | \(-0.0843981\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 16.0000 | + | 16.0000i | 1.04372 | + | 1.04372i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −28.0000 | + | 28.0000i | −1.81880 | + | 1.81880i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.00000 | 0.517477 | 0.258738 | − | 0.965947i | \(-0.416693\pi\) | ||||
0.258738 | + | 0.965947i | \(0.416693\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −22.0000 | −1.41714 | −0.708572 | − | 0.705638i | \(-0.750660\pi\) | ||||
−0.708572 | + | 0.705638i | \(0.750660\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −10.0000 | + | 10.0000i | −0.641500 | + | 0.641500i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.00000 | − | 2.00000i | −0.127775 | − | 0.127775i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.00000 | + | 4.00000i | 0.252478 | + | 0.252478i | 0.821986 | − | 0.569508i | \(-0.192866\pi\) |
−0.569508 | + | 0.821986i | \(0.692866\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.00000 | + | 6.00000i | −0.377217 | + | 0.377217i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 48.0000 | 3.00588 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −10.0000 | −0.623783 | −0.311891 | − | 0.950118i | \(-0.600963\pi\) | ||||
−0.311891 | + | 0.950118i | \(0.600963\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.00000 | + | 3.00000i | −0.186411 | + | 0.186411i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.00000 | − | 5.00000i | −0.309492 | − | 0.309492i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 24.0000i | − | 1.47990i | −0.672660 | − | 0.739952i | \(-0.734848\pi\) | ||
0.672660 | − | 0.739952i | \(-0.265152\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 28.0000i | − | 1.72003i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −12.0000 | − | 12.0000i | −0.734388 | − | 0.734388i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 16.0000 | − | 16.0000i | 0.975537 | − | 0.975537i | −0.0241706 | − | 0.999708i | \(-0.507694\pi\) |
0.999708 | + | 0.0241706i | \(0.00769450\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.0000 | −0.971931 | −0.485965 | − | 0.873978i | \(-0.661532\pi\) | ||||
−0.485965 | + | 0.873978i | \(0.661532\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 9.00000 | − | 9.00000i | 0.542720 | − | 0.542720i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.00000 | − | 1.00000i | −0.0600842 | − | 0.0600842i | 0.676426 | − | 0.736510i | \(-0.263528\pi\) |
−0.736510 | + | 0.676426i | \(0.763528\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 20.0000i | 1.19737i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.0000i | 1.43172i | 0.698244 | + | 0.715860i | \(0.253965\pi\) | ||||
−0.698244 | + | 0.715860i | \(0.746035\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.00000 | − | 6.00000i | −0.356663 | − | 0.356663i | 0.505918 | − | 0.862581i | \(-0.331154\pi\) |
−0.862581 | + | 0.505918i | \(0.831154\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 32.0000 | − | 32.0000i | 1.89552 | − | 1.89552i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.00000 | 0.118056 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 19.0000 | 1.11765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.0000 | − | 12.0000i | 0.703452 | − | 0.703452i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.0000 | + | 10.0000i | 0.584206 | + | 0.584206i | 0.936056 | − | 0.351850i | \(-0.114447\pi\) |
−0.351850 | + | 0.936056i | \(0.614447\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.00000i | 0.465778i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 24.0000i | − | 1.39262i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.00000 | + | 5.00000i | −0.288195 | + | 0.288195i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 8.00000 | 0.459588 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −24.0000 | −1.37424 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.00000 | + | 8.00000i | −0.456584 | + | 0.456584i | −0.897532 | − | 0.440948i | \(-0.854642\pi\) |
0.440948 | + | 0.897532i | \(0.354642\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.00000i | 0.226819i | 0.993548 | + | 0.113410i | \(0.0361772\pi\) | ||||
−0.993548 | + | 0.113410i | \(0.963823\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 2.00000i | − | 0.113047i | −0.998401 | − | 0.0565233i | \(-0.981998\pi\) | ||
0.998401 | − | 0.0565233i | \(-0.0180015\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −10.0000 | − | 10.0000i | −0.563436 | − | 0.563436i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 15.0000 | − | 15.0000i | 0.842484 | − | 0.842484i | −0.146697 | − | 0.989181i | \(-0.546864\pi\) |
0.989181 | + | 0.146697i | \(0.0468644\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.00000 | −0.335936 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −20.0000 | −1.11629 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 24.0000 | − | 24.0000i | 1.33540 | − | 1.33540i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 12.0000i | 0.663602i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 8.00000i | − | 0.441054i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −15.0000 | − | 15.0000i | −0.824475 | − | 0.824475i | 0.162272 | − | 0.986746i | \(-0.448118\pi\) |
−0.986746 | + | 0.162272i | \(0.948118\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −15.0000 | + | 15.0000i | −0.821995 | + | 0.821995i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −20.0000 | −1.09272 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.00000 | −0.435788 | −0.217894 | − | 0.975972i | \(-0.569919\pi\) | ||||
−0.217894 | + | 0.975972i | \(0.569919\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 24.0000 | − | 24.0000i | 1.30350 | − | 1.30350i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12.0000 | + | 12.0000i | 0.649836 | + | 0.649836i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 16.0000i | 0.861411i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −13.0000 | − | 13.0000i | −0.697877 | − | 0.697877i | 0.266076 | − | 0.963952i | \(-0.414273\pi\) |
−0.963952 | + | 0.266076i | \(0.914273\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.0000 | + | 16.0000i | −0.856460 | + | 0.856460i | −0.990919 | − | 0.134459i | \(-0.957070\pi\) |
0.134459 | + | 0.990919i | \(0.457070\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 18.0000 | 0.958043 | 0.479022 | − | 0.877803i | \(-0.340992\pi\) | ||||
0.479022 | + | 0.877803i | \(0.340992\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −16.0000 | + | 16.0000i | −0.849192 | + | 0.849192i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −12.0000 | − | 12.0000i | −0.635107 | − | 0.635107i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 22.0000i | − | 1.16112i | −0.814219 | − | 0.580558i | \(-0.802835\pi\) | ||
0.814219 | − | 0.580558i | \(-0.197165\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 13.0000i | − | 0.684211i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −14.0000 | − | 14.0000i | −0.734809 | − | 0.734809i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 20.0000 | − | 20.0000i | 1.04685 | − | 1.04685i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.0000 | 0.835193 | 0.417597 | − | 0.908633i | \(-0.362873\pi\) | ||||
0.417597 | + | 0.908633i | \(0.362873\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 10.0000 | 0.520579 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.00000 | + | 7.00000i | −0.363422 | + | 0.363422i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.00000 | − | 5.00000i | −0.258890 | − | 0.258890i | 0.565712 | − | 0.824603i | \(-0.308601\pi\) |
−0.824603 | + | 0.565712i | \(0.808601\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 16.0000i | 0.826236i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 17.0000 | + | 17.0000i | 0.873231 | + | 0.873231i | 0.992823 | − | 0.119592i | \(-0.0381586\pi\) |
−0.119592 | + | 0.992823i | \(0.538159\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 16.0000 | − | 16.0000i | 0.819705 | − | 0.819705i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 16.0000 | 0.817562 | 0.408781 | − | 0.912633i | \(-0.365954\pi\) | ||||
0.408781 | + | 0.912633i | \(0.365954\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −12.0000 | −0.611577 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −25.0000 | + | 25.0000i | −1.27082 | + | 1.27082i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −19.0000 | − | 19.0000i | −0.963338 | − | 0.963338i | 0.0360131 | − | 0.999351i | \(-0.488534\pi\) |
−0.999351 | + | 0.0360131i | \(0.988534\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12.0000i | 0.606866i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 48.0000i | 2.42128i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 28.0000 | + | 28.0000i | 1.40883 | + | 1.40883i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −16.0000 | −0.801002 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.00000 | −0.199750 | −0.0998752 | − | 0.995000i | \(-0.531844\pi\) | ||||
−0.0998752 | + | 0.995000i | \(0.531844\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.00000 | − | 2.00000i | −0.0993808 | − | 0.0993808i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 18.0000i | 0.892227i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.0000i | 0.494468i | 0.968956 | + | 0.247234i | \(0.0795217\pi\) | ||||
−0.968956 | + | 0.247234i | \(0.920478\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −24.0000 | − | 24.0000i | −1.18383 | − | 1.18383i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.00000 | − | 2.00000i | 0.0984136 | − | 0.0984136i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 48.0000 | 2.35057 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10.0000 | + | 10.0000i | −0.488532 | + | 0.488532i | −0.907843 | − | 0.419311i | \(-0.862272\pi\) |
0.419311 | + | 0.907843i | \(0.362272\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 25.0000 | + | 25.0000i | 1.21843 | + | 1.21843i | 0.968183 | + | 0.250242i | \(0.0805102\pi\) |
0.250242 | + | 0.968183i | \(0.419490\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 40.0000i | − | 1.94487i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 18.0000i | − | 0.873128i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.00000 | + | 6.00000i | 0.290360 | + | 0.290360i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.00000 | −0.0961139 | −0.0480569 | − | 0.998845i | \(-0.515303\pi\) | ||||
−0.0480569 | + | 0.998845i | \(0.515303\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −8.00000 | + | 8.00000i | −0.383571 | + | 0.383571i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.00000 | + | 8.00000i | 0.382692 | + | 0.382692i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 24.0000i | 1.14546i | 0.819745 | + | 0.572729i | \(0.194115\pi\) | ||||
−0.819745 | + | 0.572729i | \(0.805885\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.00000i | 0.238095i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −17.0000 | − | 17.0000i | −0.807694 | − | 0.807694i | 0.176590 | − | 0.984284i | \(-0.443493\pi\) |
−0.984284 | + | 0.176590i | \(0.943493\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −12.0000 | + | 12.0000i | −0.568855 | + | 0.568855i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −52.0000 | −2.45952 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 34.0000 | 1.60456 | 0.802280 | − | 0.596948i | \(-0.203620\pi\) | ||||
0.802280 | + | 0.596948i | \(0.203620\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.00000 | − | 6.00000i | 0.282529 | − | 0.282529i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −12.0000 | − | 12.0000i | −0.563809 | − | 0.563809i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 26.0000i | − | 1.21623i | −0.793849 | − | 0.608114i | \(-0.791926\pi\) | ||
0.793849 | − | 0.608114i | \(-0.208074\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −24.0000 | − | 24.0000i | −1.12022 | − | 1.12022i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 28.0000 | − | 28.0000i | 1.30409 | − | 1.30409i | 0.378481 | − | 0.925609i | \(-0.376447\pi\) |
0.925609 | − | 0.378481i | \(-0.123553\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.0000 | −0.650635 | −0.325318 | − | 0.945605i | \(-0.605471\pi\) | ||||
−0.325318 | + | 0.945605i | \(0.605471\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 32.0000 | 1.48396 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −16.0000 | + | 16.0000i | −0.740392 | + | 0.740392i | −0.972653 | − | 0.232262i | \(-0.925387\pi\) |
0.232262 | + | 0.972653i | \(0.425387\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.00000 | + | 5.00000i | 0.230879 | + | 0.230879i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 30.0000i | 1.37940i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −12.0000 | − | 12.0000i | −0.550598 | − | 0.550598i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −35.0000 | + | 35.0000i | −1.60254 | + | 1.60254i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8.00000 | 0.365529 | 0.182765 | − | 0.983157i | \(-0.441495\pi\) | ||||
0.182765 | + | 0.983157i | \(0.441495\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.00000 | − | 4.00000i | 0.182006 | − | 0.182006i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −12.0000 | − | 12.0000i | −0.544892 | − | 0.544892i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.00000i | 0.0906287i | 0.998973 | + | 0.0453143i | \(0.0144289\pi\) | ||||
−0.998973 | + | 0.0453143i | \(0.985571\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 20.0000i | − | 0.904431i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11.0000 | − | 11.0000i | −0.496423 | − | 0.496423i | 0.413900 | − | 0.910323i | \(-0.364166\pi\) |
−0.910323 | + | 0.413900i | \(0.864166\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.00000 | + | 6.00000i | −0.270226 | + | 0.270226i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −60.0000 | −2.69680 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.00000 | 0.358849 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15.0000 | + | 15.0000i | −0.671492 | + | 0.671492i | −0.958060 | − | 0.286568i | \(-0.907486\pi\) |
0.286568 | + | 0.958060i | \(0.407486\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 8.00000i | − | 0.356702i | −0.983967 | − | 0.178351i | \(-0.942924\pi\) | ||
0.983967 | − | 0.178351i | \(-0.0570763\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 8.00000i | − | 0.355995i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −26.0000 | − | 26.0000i | −1.15470 | − | 1.15470i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12.0000 | − | 12.0000i | 0.531891 | − | 0.531891i | −0.389244 | − | 0.921135i | \(-0.627264\pi\) |
0.921135 | + | 0.389244i | \(0.127264\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.0000 | −0.442374 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −32.0000 | −1.41283 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −24.0000 | − | 24.0000i | −1.05552 | − | 1.05552i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 64.0000i | − | 2.80929i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.00000i | 0.262865i | 0.991325 | + | 0.131432i | \(0.0419576\pi\) | ||||
−0.991325 | + | 0.131432i | \(0.958042\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 26.0000 | + | 26.0000i | 1.13690 | + | 1.13690i | 0.989003 | + | 0.147898i | \(0.0472507\pi\) |
0.147898 | + | 0.989003i | \(0.452749\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −6.00000 | + | 6.00000i | −0.261861 | + | 0.261861i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 24.0000 | 1.04546 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.0000 | 0.826087 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10.0000 | − | 10.0000i | 0.433963 | − | 0.433963i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 20.0000i | 0.864675i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 20.0000i | 0.863064i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.00000 | + | 3.00000i | 0.129219 | + | 0.129219i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 29.0000 | − | 29.0000i | 1.24681 | − | 1.24681i | 0.289685 | − | 0.957122i | \(-0.406449\pi\) |
0.957122 | − | 0.289685i | \(-0.0935507\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 16.0000 | 0.686626 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 12.0000 | 0.514024 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.0000 | − | 19.0000i | 0.812381 | − | 0.812381i | −0.172609 | − | 0.984990i | \(-0.555220\pi\) |
0.984990 | + | 0.172609i | \(0.0552197\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 30.0000 | + | 30.0000i | 1.28037 | + | 1.28037i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.00000i | 0.340811i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 14.0000i | − | 0.595341i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 24.0000 | + | 24.0000i | 1.01874 | + | 1.01874i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −15.0000 | + | 15.0000i | −0.635570 | + | 0.635570i | −0.949460 | − | 0.313889i | \(-0.898368\pi\) |
0.313889 | + | 0.949460i | \(0.398368\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −72.0000 | −3.03984 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −22.0000 | + | 22.0000i | −0.927189 | + | 0.927189i | −0.997523 | − | 0.0703340i | \(-0.977593\pi\) |
0.0703340 | + | 0.997523i | \(0.477593\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −24.0000 | − | 24.0000i | −1.00969 | − | 1.00969i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.00000i | 0.0419961i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 46.0000i | − | 1.92842i | −0.265139 | − | 0.964210i | \(-0.585418\pi\) | ||
0.265139 | − | 0.964210i | \(-0.414582\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21.0000 | − | 21.0000i | −0.878823 | − | 0.878823i | 0.114590 | − | 0.993413i | \(-0.463445\pi\) |
−0.993413 | + | 0.114590i | \(0.963445\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 44.0000 | − | 44.0000i | 1.83813 | − | 1.83813i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.00000 | 0.250217 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −26.0000 | −1.08239 | −0.541197 | − | 0.840896i | \(-0.682029\pi\) | ||||
−0.541197 | + | 0.840896i | \(0.682029\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 48.0000 | − | 48.0000i | 1.99481 | − | 1.99481i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 42.0000i | 1.73946i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8.00000 | + | 8.00000i | 0.330195 | + | 0.330195i | 0.852661 | − | 0.522465i | \(-0.174988\pi\) |
−0.522465 | + | 0.852661i | \(0.674988\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.0000 | − | 16.0000i | 0.659269 | − | 0.659269i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −44.0000 | −1.80992 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −22.0000 | −0.903432 | −0.451716 | − | 0.892162i | \(-0.649188\pi\) | ||||
−0.451716 | + | 0.892162i | \(0.649188\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −12.0000 | + | 12.0000i | −0.491952 | + | 0.491952i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −40.0000 | − | 40.0000i | −1.63709 | − | 1.63709i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.00000i | 0.326871i | 0.986554 | + | 0.163436i | \(0.0522576\pi\) | ||||
−0.986554 | + | 0.163436i | \(0.947742\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 10.0000i | − | 0.407909i | −0.978980 | − | 0.203954i | \(-0.934621\pi\) | ||
0.978980 | − | 0.203954i | \(-0.0653794\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 25.0000 | + | 25.0000i | 1.01808 | + | 1.01808i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −14.0000 | + | 14.0000i | −0.569181 | + | 0.569181i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −20.0000 | −0.811775 | −0.405887 | − | 0.913923i | \(-0.633038\pi\) | ||||
−0.405887 | + | 0.913923i | \(0.633038\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.00000 | 0.162088 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15.0000 | + | 15.0000i | 0.605844 | + | 0.605844i | 0.941857 | − | 0.336013i | \(-0.109079\pi\) |
−0.336013 | + | 0.941857i | \(0.609079\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 16.0000i | − | 0.645182i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 6.00000i | − | 0.241551i | −0.992680 | − | 0.120775i | \(-0.961462\pi\) | ||
0.992680 | − | 0.120775i | \(-0.0385381\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18.0000 | + | 18.0000i | 0.723481 | + | 0.723481i | 0.969313 | − | 0.245831i | \(-0.0790610\pi\) |
−0.245831 | + | 0.969313i | \(0.579061\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.00000 | − | 8.00000i | 0.321029 | − | 0.321029i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.00000 | 0.240385 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 31.0000 | 1.24000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −48.0000 | + | 48.0000i | −1.91694 | + | 1.91694i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 18.0000 | + | 18.0000i | 0.717707 | + | 0.717707i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 36.0000i | − | 1.43087i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −16.0000 | − | 16.0000i | −0.634941 | − | 0.634941i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 40.0000 | 1.58238 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 44.0000 | 1.73790 | 0.868948 | − | 0.494904i | \(-0.164797\pi\) | ||||
0.868948 | + | 0.494904i | \(0.164797\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 26.0000 | − | 26.0000i | 1.02534 | − | 1.02534i | 0.0256694 | − | 0.999670i | \(-0.491828\pi\) |
0.999670 | − | 0.0256694i | \(-0.00817173\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 40.0000 | + | 40.0000i | 1.57500 | + | 1.57500i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 24.0000i | 0.943537i | 0.881722 | + | 0.471769i | \(0.156384\pi\) | ||||
−0.881722 | + | 0.471769i | \(0.843616\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 12.0000i | − | 0.471041i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.00000 | − | 8.00000i | −0.313545 | − | 0.313545i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −25.0000 | + | 25.0000i | −0.978326 | + | 0.978326i | −0.999770 | − | 0.0214444i | \(-0.993173\pi\) |
0.0214444 | + | 0.999770i | \(0.493173\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 48.0000 | 1.87552 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −50.0000 | −1.95069 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 17.0000 | − | 17.0000i | 0.662226 | − | 0.662226i | −0.293678 | − | 0.955904i | \(-0.594879\pi\) |
0.955904 | + | 0.293678i | \(0.0948794\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −30.0000 | − | 30.0000i | −1.16686 | − | 1.16686i | −0.982940 | − | 0.183924i | \(-0.941120\pi\) |
−0.183924 | − | 0.982940i | \(-0.558880\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 16.0000i | 0.620453i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.00000 | − | 2.00000i | −0.0774403 | − | 0.0774403i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 8.00000 | − | 8.00000i | 0.309298 | − | 0.309298i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 36.0000 | 1.38976 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 26.0000 | 1.00223 | 0.501113 | − | 0.865382i | \(-0.332924\pi\) | ||||
0.501113 | + | 0.865382i | \(0.332924\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −12.0000 | + | 12.0000i | −0.461880 | + | 0.461880i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −8.00000 | − | 8.00000i | −0.307465 | − | 0.307465i | 0.536460 | − | 0.843925i | \(-0.319761\pi\) |
−0.843925 | + | 0.536460i | \(0.819761\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.00000i | 0.230259i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 16.0000i | 0.613121i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.00000 | + | 5.00000i | 0.191320 | + | 0.191320i | 0.796266 | − | 0.604946i | \(-0.206805\pi\) |
−0.604946 | + | 0.796266i | \(0.706805\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −24.0000 | + | 24.0000i | −0.916993 | + | 0.916993i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 48.0000 | 1.83131 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.0000 | − | 12.0000i | 0.456502 | − | 0.456502i | −0.441004 | − | 0.897505i | \(-0.645377\pi\) |
0.897505 | + | 0.441004i | \(0.145377\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 15.0000 | + | 15.0000i | 0.569803 | + | 0.569803i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 48.0000i | − | 1.82074i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 12.0000i | − | 0.454532i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 16.0000 | + | 16.0000i | 0.605176 | + | 0.605176i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −13.0000 | + | 13.0000i | −0.491003 | + | 0.491003i | −0.908622 | − | 0.417619i | \(-0.862865\pi\) |
0.417619 | + | 0.908622i | \(0.362865\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 24.0000 | 0.905177 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −64.0000 | −2.41038 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.00000 | + | 2.00000i | −0.0752177 | + | 0.0752177i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 31.0000 | + | 31.0000i | 1.16423 | + | 1.16423i | 0.983540 | + | 0.180689i | \(0.0578328\pi\) |
0.180689 | + | 0.983540i | \(0.442167\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 70.0000i | − | 2.62521i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.00000i | 0.299602i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −16.0000 | + | 16.0000i | −0.597531 | + | 0.597531i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8.00000 | 0.298350 | 0.149175 | − | 0.988811i | \(-0.452338\pi\) | ||||
0.149175 | + | 0.988811i | \(0.452338\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 44.0000 | − | 44.0000i | 1.63638 | − | 1.63638i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.00000 | + | 3.00000i | 0.111417 | + | 0.111417i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 44.0000i | − | 1.63187i | −0.578144 | − | 0.815935i | \(-0.696223\pi\) | ||
0.578144 | − | 0.815935i | \(-0.303777\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 43.0000i | − | 1.59259i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 30.0000 | + | 30.0000i | 1.10959 | + | 1.10959i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.00000 | − | 2.00000i | 0.0738717 | − | 0.0738717i | −0.669206 | − | 0.743077i | \(-0.733365\pi\) |
0.743077 | + | 0.669206i | \(0.233365\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 8.00000 | 0.295084 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 30.0000 | 1.10506 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.00000 | + | 5.00000i | −0.183928 | + | 0.183928i | −0.793065 | − | 0.609137i | \(-0.791516\pi\) |
0.609137 | + | 0.793065i | \(0.291516\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.00000i | 0.220119i | 0.993925 | + | 0.110059i | \(0.0351041\pi\) | ||||
−0.993925 | + | 0.110059i | \(0.964896\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 52.0000i | 1.90513i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.00000 | − | 5.00000i | 0.182696 | − | 0.182696i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −40.0000 | −1.45962 | −0.729810 | − | 0.683650i | \(-0.760392\pi\) | ||||
−0.729810 | + | 0.683650i | \(0.760392\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −16.0000 | −0.583072 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −12.0000 | + | 12.0000i | −0.436725 | + | 0.436725i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −33.0000 | − | 33.0000i | −1.19941 | − | 1.19941i | −0.974345 | − | 0.225061i | \(-0.927742\pi\) |
−0.225061 | − | 0.974345i | \(-0.572258\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 24.0000i | − | 0.871145i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 18.0000i | 0.652499i | 0.945284 | + | 0.326250i | \(0.105785\pi\) | ||||
−0.945284 | + | 0.326250i | \(0.894215\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.00000 | − | 3.00000i | −0.108607 | − | 0.108607i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −60.0000 | + | 60.0000i | −2.16930 | + | 2.16930i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −30.0000 | −1.08183 | −0.540914 | − | 0.841078i | \(-0.681921\pi\) | ||||
−0.540914 | + | 0.841078i | \(0.681921\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 20.0000 | − | 20.0000i | 0.720282 | − | 0.720282i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 30.0000 | + | 30.0000i | 1.07903 | + | 1.07903i | 0.996597 | + | 0.0824280i | \(0.0262674\pi\) |
0.0824280 | + | 0.996597i | \(0.473733\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 12.0000i | − | 0.431053i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 12.0000i | − | 0.430498i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8.00000 | − | 8.00000i | −0.286630 | − | 0.286630i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 24.0000 | − | 24.0000i | 0.858788 | − | 0.858788i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.00000 | 0.285897 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12.0000 | + | 12.0000i | −0.427754 | + | 0.427754i | −0.887863 | − | 0.460109i | \(-0.847810\pi\) |
0.460109 | + | 0.887863i | \(0.347810\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 48.0000 | + | 48.0000i | 1.70885 | + | 1.70885i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 12.0000i | 0.426671i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 56.0000 | + | 56.0000i | 1.98612 | + | 1.98612i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −8.00000 | + | 8.00000i | −0.283375 | + | 0.283375i | −0.834453 | − | 0.551079i | \(-0.814216\pi\) |
0.551079 | + | 0.834453i | \(0.314216\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −48.0000 | −1.69812 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 30.0000 | 1.06000 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −30.0000 | + | 30.0000i | −1.05868 | + | 1.05868i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.00000 | − | 4.00000i | −0.140981 | − | 0.140981i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 64.0000i | 2.25291i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 38.0000i | 1.33601i | 0.744157 | + | 0.668004i | \(0.232851\pi\) | ||||
−0.744157 | + | 0.668004i | \(0.767149\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30.0000 | + | 30.0000i | 1.05344 | + | 1.05344i | 0.998489 | + | 0.0549536i | \(0.0175011\pi\) |
0.0549536 | + | 0.998489i | \(0.482499\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 32.0000 | − | 32.0000i | 1.12229 | − | 1.12229i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −20.0000 | −0.700569 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 40.0000 | 1.39942 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.00000 | + | 7.00000i | 0.244302 | + | 0.244302i | 0.818627 | − | 0.574325i | \(-0.194736\pi\) |
−0.574325 | + | 0.818627i | \(0.694736\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 40.0000i | 1.39431i | 0.716919 | + | 0.697156i | \(0.245552\pi\) | ||||
−0.716919 | + | 0.697156i | \(0.754448\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 36.0000i | 1.25336i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −13.0000 | − | 13.0000i | −0.452054 | − | 0.452054i | 0.443982 | − | 0.896036i | \(-0.353566\pi\) |
−0.896036 | + | 0.443982i | \(0.853566\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.00000 | − | 2.00000i | 0.0694629 | − | 0.0694629i | −0.671522 | − | 0.740985i | \(-0.734359\pi\) |
0.740985 | + | 0.671522i | \(0.234359\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.00000 | 0.138758 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.00000 | 0.207888 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −16.0000 | − | 16.0000i | −0.553041 | − | 0.553041i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 24.0000i | 0.828572i | 0.910147 | + | 0.414286i | \(0.135969\pi\) | ||||
−0.910147 | + | 0.414286i | \(0.864031\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.0000i | 0.931034i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −48.0000 | − | 48.0000i | −1.65321 | − | 1.65321i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −26.0000 | + | 26.0000i | −0.894427 | + | 0.894427i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.00000 | 0.240523 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 24.0000 | 0.823678 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.00000 | + | 6.00000i | −0.205677 | + | 0.205677i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.00000 | + | 4.00000i | 0.136957 | + | 0.136957i | 0.772262 | − | 0.635304i | \(-0.219125\pi\) |
−0.635304 | + | 0.772262i | \(0.719125\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 80.0000i | 2.73594i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 18.0000i | − | 0.614868i | −0.951569 | − | 0.307434i | \(-0.900530\pi\) | ||
0.951569 | − | 0.307434i | \(-0.0994704\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.00000 | − | 4.00000i | −0.136478 | − | 0.136478i | 0.635567 | − | 0.772046i | \(-0.280766\pi\) |
−0.772046 | + | 0.635567i | \(0.780766\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.00000 | + | 4.00000i | −0.136320 | + | 0.136320i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −6.00000 | −0.204242 | −0.102121 | − | 0.994772i | \(-0.532563\pi\) | ||||
−0.102121 | + | 0.994772i | \(0.532563\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −64.0000 | −2.17607 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −38.0000 | + | 38.0000i | −1.29055 | + | 1.29055i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −42.0000 | − | 42.0000i | −1.42475 | − | 1.42475i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 30.0000i | 1.01535i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.00000 | − | 4.00000i | −0.135225 | − | 0.135225i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 21.0000 | − | 21.0000i | 0.709120 | − | 0.709120i | −0.257230 | − | 0.966350i | \(-0.582810\pi\) |
0.966350 | + | 0.257230i | \(0.0828100\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −40.0000 | −1.34917 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 30.0000 | 1.01073 | 0.505363 | − | 0.862907i | \(-0.331359\pi\) | ||||
0.505363 | + | 0.862907i | \(0.331359\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −17.0000 | + | 17.0000i | −0.572096 | + | 0.572096i | −0.932714 | − | 0.360618i | \(-0.882566\pi\) |
0.360618 | + | 0.932714i | \(0.382566\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −16.0000 | − | 16.0000i | −0.537834 | − | 0.537834i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 24.0000i | 0.805841i | 0.915235 | + | 0.402921i | \(0.132005\pi\) | ||||
−0.915235 | + | 0.402921i | \(0.867995\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.00000i | 0.268311i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.00000 | + | 3.00000i | 0.100504 | + | 0.100504i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −32.0000 | + | 32.0000i | −1.07084 | + | 1.07084i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 20.0000 | 0.668526 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4.00000 | + | 4.00000i | −0.133407 | + | 0.133407i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 42.0000 | + | 42.0000i | 1.39922 | + | 1.39922i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 20.0000i | − | 0.665558i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 16.0000i | − | 0.531858i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −9.00000 | − | 9.00000i | −0.298840 | − | 0.298840i | 0.541719 | − | 0.840559i | \(-0.317774\pi\) |
−0.840559 | + | 0.541719i | \(0.817774\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −10.0000 | + | 10.0000i | −0.331679 | + | 0.331679i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 48.0000 | − | 48.0000i | 1.58683 | − | 1.58683i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −12.0000 | − | 12.0000i | −0.396275 | − | 0.396275i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 56.0000i | − | 1.84727i | −0.383274 | − | 0.923635i | \(-0.625203\pi\) | ||
0.383274 | − | 0.923635i | \(-0.374797\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 32.0000i | − | 1.05444i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.00000 | − | 9.00000i | 0.295918 | − | 0.295918i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −30.0000 | −0.984268 | −0.492134 | − | 0.870519i | \(-0.663783\pi\) | ||||
−0.492134 | + | 0.870519i | \(0.663783\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.00000 | − | 4.00000i | 0.131095 | − | 0.131095i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −8.00000 | − | 8.00000i | −0.261908 | − | 0.261908i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 72.0000i | 2.35465i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 50.0000i | 1.63343i | 0.577042 | + | 0.816714i | \(0.304207\pi\) | ||||
−0.577042 | + | 0.816714i | \(0.695793\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.00000 | + | 4.00000i | 0.130535 | + | 0.130535i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −26.0000 | + | 26.0000i | −0.847576 | + | 0.847576i | −0.989830 | − | 0.142254i | \(-0.954565\pi\) |
0.142254 | + | 0.989830i | \(0.454565\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.00000 | 0.130258 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 16.0000 | 0.520480 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 13.0000 | − | 13.0000i | 0.422443 | − | 0.422443i | −0.463601 | − | 0.886044i | \(-0.653443\pi\) |
0.886044 | + | 0.463601i | \(0.153443\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 60.0000i | 1.94563i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 16.0000i | − | 0.518291i | −0.965838 | − | 0.259145i | \(-0.916559\pi\) | ||
0.965838 | − | 0.259145i | \(-0.0834409\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −44.0000 | − | 44.0000i | −1.42381 | − | 1.42381i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 12.0000 | − | 12.0000i | 0.387905 | − | 0.387905i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 12.0000 | 0.387500 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 25.0000 | − | 25.0000i | 0.805614 | − | 0.805614i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −48.0000 | − | 48.0000i | −1.54517 | − | 1.54517i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 38.0000i | 1.22200i | 0.791632 | + | 0.610999i | \(0.209232\pi\) | ||||
−0.791632 | + | 0.610999i | \(0.790768\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 96.0000i | 3.08396i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 26.0000 | + | 26.0000i | 0.834380 | + | 0.834380i | 0.988112 | − | 0.153733i | \(-0.0491295\pi\) |
−0.153733 | + | 0.988112i | \(0.549129\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12.0000 | + | 12.0000i | −0.384702 | + | 0.384702i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −34.0000 | −1.08776 | −0.543878 | − | 0.839164i | \(-0.683045\pi\) | ||||
−0.543878 | + | 0.839164i | \(0.683045\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 18.0000 | − | 18.0000i | 0.575282 | − | 0.575282i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −15.0000 | − | 15.0000i | −0.478913 | − | 0.478913i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 48.0000i | − | 1.53096i | −0.643458 | − | 0.765481i | \(-0.722501\pi\) | ||
0.643458 | − | 0.765481i | \(-0.277499\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 44.0000i | 1.40196i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 16.0000 | + | 16.0000i | 0.509286 | + | 0.509286i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −10.0000 | + | 10.0000i | −0.317982 | + | 0.317982i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.0000 | 0.317660 | 0.158830 | − | 0.987306i | \(-0.449228\pi\) | ||||
0.158830 | + | 0.987306i | \(0.449228\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 60.0000 | 1.90404 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −40.0000 | + | 40.0000i | −1.26809 | + | 1.26809i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −30.0000 | − | 30.0000i | −0.950110 | − | 0.950110i | 0.0487037 | − | 0.998813i | \(-0.484491\pi\) |
−0.998813 | + | 0.0487037i | \(0.984491\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 24.0000i | − | 0.759326i |
(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 | 896.2.m.a.225.1 | 2 | ||
4.3 | odd | 2 | 896.2.m.d.225.1 | 2 | |||
8.3 | odd | 2 | 112.2.m.a.85.1 | yes | 2 | ||
8.5 | even | 2 | 448.2.m.b.113.1 | 2 | |||
16.3 | odd | 4 | 896.2.m.d.673.1 | 2 | |||
16.5 | even | 4 | 448.2.m.b.337.1 | 2 | |||
16.11 | odd | 4 | 112.2.m.a.29.1 | ✓ | 2 | ||
16.13 | even | 4 | inner | 896.2.m.a.673.1 | 2 | ||
32.3 | odd | 8 | 7168.2.a.q.1.2 | 2 | |||
32.13 | even | 8 | 7168.2.a.i.1.2 | 2 | |||
32.19 | odd | 8 | 7168.2.a.q.1.1 | 2 | |||
32.29 | even | 8 | 7168.2.a.i.1.1 | 2 | |||
56.3 | even | 6 | 784.2.x.b.373.1 | 4 | |||
56.11 | odd | 6 | 784.2.x.g.373.1 | 4 | |||
56.19 | even | 6 | 784.2.x.b.165.1 | 4 | |||
56.27 | even | 2 | 784.2.m.c.197.1 | 2 | |||
56.51 | odd | 6 | 784.2.x.g.165.1 | 4 | |||
112.11 | odd | 12 | 784.2.x.g.765.1 | 4 | |||
112.27 | even | 4 | 784.2.m.c.589.1 | 2 | |||
112.59 | even | 12 | 784.2.x.b.765.1 | 4 | |||
112.75 | even | 12 | 784.2.x.b.557.1 | 4 | |||
112.107 | odd | 12 | 784.2.x.g.557.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
112.2.m.a.29.1 | ✓ | 2 | 16.11 | odd | 4 | ||
112.2.m.a.85.1 | yes | 2 | 8.3 | odd | 2 | ||
448.2.m.b.113.1 | 2 | 8.5 | even | 2 | |||
448.2.m.b.337.1 | 2 | 16.5 | even | 4 | |||
784.2.m.c.197.1 | 2 | 56.27 | even | 2 | |||
784.2.m.c.589.1 | 2 | 112.27 | even | 4 | |||
784.2.x.b.165.1 | 4 | 56.19 | even | 6 | |||
784.2.x.b.373.1 | 4 | 56.3 | even | 6 | |||
784.2.x.b.557.1 | 4 | 112.75 | even | 12 | |||
784.2.x.b.765.1 | 4 | 112.59 | even | 12 | |||
784.2.x.g.165.1 | 4 | 56.51 | odd | 6 | |||
784.2.x.g.373.1 | 4 | 56.11 | odd | 6 | |||
784.2.x.g.557.1 | 4 | 112.107 | odd | 12 | |||
784.2.x.g.765.1 | 4 | 112.11 | odd | 12 | |||
896.2.m.a.225.1 | 2 | 1.1 | even | 1 | trivial | ||
896.2.m.a.673.1 | 2 | 16.13 | even | 4 | inner | ||
896.2.m.d.225.1 | 2 | 4.3 | odd | 2 | |||
896.2.m.d.673.1 | 2 | 16.3 | odd | 4 | |||
7168.2.a.i.1.1 | 2 | 32.29 | even | 8 | |||
7168.2.a.i.1.2 | 2 | 32.13 | even | 8 | |||
7168.2.a.q.1.1 | 2 | 32.19 | odd | 8 | |||
7168.2.a.q.1.2 | 2 | 32.3 | odd | 8 |