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: | \(0\) |
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 | 673.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 896.673 |
Dual form | 896.2.m.d.225.1 |
$q$-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 \(\left(\mathbb{Z}/896\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(645\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 | 0.985599 | + | 0.169102i | \(0.0540867\pi\) |
0.169102 | + | 0.985599i | \(0.445913\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.00000 | − | 2.00000i | 0.894427 | − | 0.894427i | −0.100509 | − | 0.994936i | \(-0.532047\pi\) |
0.994936 | + | 0.100509i | \(0.0320471\pi\) | |||||||
\(6\) | 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 | \(-0.529099\pi\) |
0.995824 | + | 0.0912903i | \(0.0290991\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(14\) | 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 | \(-0.0252353\pi\) |
−0.0791961 | + | 0.996859i | \(0.525235\pi\) | |||||||
\(20\) | 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 | 0.793832 | − | 0.608137i | \(-0.208083\pi\) |
−0.608137 | + | 0.793832i | \(0.708083\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.00000 | 0.718421 | 0.359211 | − | 0.933257i | \(-0.383046\pi\) | ||||
0.359211 | + | 0.933257i | \(0.383046\pi\) | |||||||
\(32\) | 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 | −0.909312 | − | 0.416115i | \(-0.863391\pi\) |
0.416115 | + | 0.909312i | \(0.363391\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 2.00000i | − | 0.312348i | −0.987730 | − | 0.156174i | \(-0.950084\pi\) | ||
0.987730 | − | 0.156174i | \(-0.0499160\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.00000 | − | 5.00000i | 0.762493 | − | 0.762493i | −0.214280 | − | 0.976772i | \(-0.568740\pi\) |
0.976772 | + | 0.214280i | \(0.0687403\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 10.0000 | + | 10.0000i | 1.49071 | + | 1.49071i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.00000 | −1.16692 | −0.583460 | − | 0.812142i | \(-0.698301\pi\) | ||||
−0.583460 | + | 0.812142i | \(0.698301\pi\) | |||||||
\(48\) | 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 | −0.999287 | − | 0.0377628i | \(-0.987977\pi\) |
0.0377628 | + | 0.999287i | \(0.487977\pi\) | |||||||
\(54\) | 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 | \(-0.808942\pi\) |
0.564830 | + | 0.825208i | \(0.308942\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.00000 | − | 6.00000i | −0.768221 | − | 0.768221i | 0.209572 | − | 0.977793i | \(-0.432793\pi\) |
−0.977793 | + | 0.209572i | \(0.932793\pi\) | |||||||
\(62\) | 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 | \(-0.107831\pi\) |
−0.332320 | + | 0.943167i | \(0.607831\pi\) | |||||||
\(68\) | 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 | \(0.198986\pi\) | ||||
−0.810885 | + | 0.585206i | \(0.801014\pi\) | |||||||
\(74\) | 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 | \(-0.788657\pi\) | ||||
−0.787562 | + | 0.616236i | \(0.788657\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(84\) | 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 | \(-0.896989\pi\) | ||
0.948091 | − | 0.317999i | \(-0.103011\pi\) | |||||||
\(90\) | 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 | −0.799574 | − | 0.600567i | \(-0.794942\pi\) |
0.600567 | + | 0.799574i | \(0.294942\pi\) | |||||||
\(102\) | 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 | \(-0.861034\pi\) |
0.422837 | + | 0.906206i | \(0.361034\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.00000 | + | 3.00000i | 0.287348 | + | 0.287348i | 0.836031 | − | 0.548683i | \(-0.184871\pi\) |
−0.548683 | + | 0.836031i | \(0.684871\pi\) | |||||||
\(110\) | 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 | \(-0.384500\pi\) | ||||
0.354943 | + | 0.934888i | \(0.384500\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 20.0000 | 1.76090 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.0000 | − | 12.0000i | −1.04844 | − | 1.04844i | −0.998765 | − | 0.0496797i | \(-0.984180\pi\) |
−0.0496797 | − | 0.998765i | \(-0.515820\pi\) | |||||||
\(132\) | 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 | \(-0.828677\pi\) | ||
0.858619 | − | 0.512615i | \(-0.171323\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.0000 | − | 12.0000i | 1.01783 | − | 1.01783i | 0.0179885 | − | 0.999838i | \(-0.494274\pi\) |
0.999838 | − | 0.0179885i | \(-0.00572623\pi\) | |||||||
\(140\) | 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 | 0.0672664 | − | 0.997735i | \(-0.478572\pi\) |
0.997735 | − | 0.0672664i | \(-0.0214278\pi\) | |||||||
\(150\) | 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 | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(158\) | 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 | \(-0.160685\pi\) |
−0.483638 | + | 0.875268i | \(0.660685\pi\) | |||||||
\(164\) | 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 | −0.968864 | − | 0.247593i | \(-0.920360\pi\) |
−0.247593 | − | 0.968864i | \(-0.579640\pi\) | |||||||
\(174\) | 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 | \(-0.335127\pi\) |
−0.868829 | + | 0.495112i | \(0.835127\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.00000 | + | 4.00000i | −0.297318 | + | 0.297318i | −0.839962 | − | 0.542645i | \(-0.817423\pi\) |
0.542645 | + | 0.839962i | \(0.317423\pi\) | |||||||
\(182\) | 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 | \(-0.206981\pi\) | ||||
0.795932 | + | 0.605386i | \(0.206981\pi\) | |||||||
\(192\) | 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 | −0.196738 | − | 0.980456i | \(-0.563035\pi\) |
0.980456 | + | 0.196738i | \(0.0630350\pi\) | |||||||
\(198\) | 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 | \(-0.105647\pi\) |
−0.325840 | + | 0.945425i | \(0.605647\pi\) | |||||||
\(212\) | 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 | \(-0.457240\pi\) | ||||
0.133930 | + | 0.990991i | \(0.457240\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 15.0000 | 1.00000 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.00000 | − | 4.00000i | −0.265489 | − | 0.265489i | 0.561790 | − | 0.827280i | \(-0.310113\pi\) |
−0.827280 | + | 0.561790i | \(0.810113\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.0000 | + | 12.0000i | −0.792982 | + | 0.792982i | −0.981978 | − | 0.188996i | \(-0.939477\pi\) |
0.188996 | + | 0.981978i | \(0.439477\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 12.0000i | − | 0.789542i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.00000i | 0.524097i | 0.965055 | + | 0.262049i | \(0.0843981\pi\) | ||||
−0.965055 | + | 0.262049i | \(0.915602\pi\) | |||||||
\(234\) | 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 | \(-0.583307\pi\) | ||||
−0.258738 | + | 0.965947i | \(0.583307\pi\) | |||||||
\(240\) | 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 | \(-0.807134\pi\) |
0.569508 | + | 0.821986i | \(0.307134\pi\) | |||||||
\(252\) | 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 | 0.999708 | − | 0.0241706i | \(-0.00769450\pi\) |
−0.0241706 | + | 0.999708i | \(0.507694\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.0000 | 0.971931 | 0.485965 | − | 0.873978i | \(-0.338468\pi\) | ||||
0.485965 | + | 0.873978i | \(0.338468\pi\) | |||||||
\(272\) | 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 | −0.736510 | − | 0.676426i | \(-0.763528\pi\) |
0.676426 | + | 0.736510i | \(0.263528\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 20.0000i | 1.19737i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 24.0000i | − | 1.43172i | −0.698244 | − | 0.715860i | \(-0.746035\pi\) | ||
0.698244 | − | 0.715860i | \(-0.253965\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.00000 | − | 6.00000i | 0.356663 | − | 0.356663i | −0.505918 | − | 0.862581i | \(-0.668846\pi\) |
0.862581 | + | 0.505918i | \(0.168846\pi\) | |||||||
\(284\) | 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 | −0.351850 | − | 0.936056i | \(-0.614447\pi\) |
0.936056 | + | 0.351850i | \(0.114447\pi\) | |||||||
\(294\) | 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 | \(-0.145358\pi\) |
−0.440948 | + | 0.897532i | \(0.645358\pi\) | |||||||
\(308\) | 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 | \(0.0180015\pi\) | ||||
−0.998401 | + | 0.0565233i | \(0.981998\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 10.0000 | − | 10.0000i | 0.563436 | − | 0.563436i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 15.0000 | + | 15.0000i | 0.842484 | + | 0.842484i | 0.989181 | − | 0.146697i | \(-0.0468644\pi\) |
−0.146697 | + | 0.989181i | \(0.546864\pi\) | |||||||
\(318\) | 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 | \(-0.551882\pi\) |
0.986746 | + | 0.162272i | \(0.0518821\pi\) | |||||||
\(332\) | 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 | \(-0.585727\pi\) |
0.963952 | + | 0.266076i | \(0.0857271\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.0000 | − | 16.0000i | −0.856460 | − | 0.856460i | 0.134459 | − | 0.990919i | \(-0.457070\pi\) |
−0.990919 | + | 0.134459i | \(0.957070\pi\) | |||||||
\(350\) | 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 | \(-0.637127\pi\) | ||||
−0.417597 | + | 0.908633i | \(0.637127\pi\) | |||||||
\(368\) | 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 | −0.824603 | − | 0.565712i | \(-0.808601\pi\) |
0.565712 | + | 0.824603i | \(0.308601\pi\) | |||||||
\(374\) | 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 | \(-0.961841\pi\) |
0.119592 | + | 0.992823i | \(0.461841\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 16.0000 | + | 16.0000i | 0.819705 | + | 0.819705i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −16.0000 | −0.817562 | −0.408781 | − | 0.912633i | \(-0.634046\pi\) | ||||
−0.408781 | + | 0.912633i | \(0.634046\pi\) | |||||||
\(384\) | 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 | −0.999351 | − | 0.0360131i | \(-0.988534\pi\) |
0.0360131 | + | 0.999351i | \(0.488534\pi\) | |||||||
\(390\) | 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 | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(398\) | 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 | \(-0.920478\pi\) | ||
0.968956 | − | 0.247234i | \(-0.0795217\pi\) | |||||||
\(410\) | 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 | \(-0.137728\pi\) |
−0.419311 | + | 0.907843i | \(0.637728\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 25.0000 | − | 25.0000i | 1.21843 | − | 1.21843i | 0.250242 | − | 0.968183i | \(-0.419490\pi\) |
0.968183 | − | 0.250242i | \(-0.0805102\pi\) | |||||||
\(422\) | 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 | \(-0.556507\pi\) |
0.984284 | + | 0.176590i | \(0.0565067\pi\) | |||||||
\(444\) | 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 | \(0.208074\pi\) | ||||
−0.793849 | + | 0.608114i | \(0.791926\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 24.0000 | − | 24.0000i | 1.12022 | − | 1.12022i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 28.0000 | + | 28.0000i | 1.30409 | + | 1.30409i | 0.925609 | + | 0.378481i | \(0.123553\pi\) |
0.378481 | + | 0.925609i | \(0.376447\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.0000 | 0.650635 | 0.325318 | − | 0.945605i | \(-0.394529\pi\) | ||||
0.325318 | + | 0.945605i | \(0.394529\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 32.0000 | 1.48396 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 16.0000 | + | 16.0000i | 0.740392 | + | 0.740392i | 0.972653 | − | 0.232262i | \(-0.0746126\pi\) |
−0.232262 | + | 0.972653i | \(0.574613\pi\) | |||||||
\(468\) | 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 | \(-0.558505\pi\) | ||||
−0.182765 | + | 0.983157i | \(0.558505\pi\) | |||||||
\(480\) | 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 | \(-0.635834\pi\) |
0.910323 | + | 0.413900i | \(0.135834\pi\) | |||||||
\(492\) | 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 | \(-0.0925144\pi\) |
−0.286568 | + | 0.958060i | \(0.592514\pi\) | |||||||
\(500\) | 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 | 0.921135 | − | 0.389244i | \(-0.127264\pi\) |
−0.389244 | + | 0.921135i | \(0.627264\pi\) | |||||||
\(510\) | 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 | \(-0.958042\pi\) | ||
0.991325 | − | 0.131432i | \(-0.0419576\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −26.0000 | + | 26.0000i | −1.13690 | + | 1.13690i | −0.147898 | + | 0.989003i | \(0.547251\pi\) |
−0.989003 | + | 0.147898i | \(0.952749\pi\) | |||||||
\(524\) | 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 | 0.957122 | + | 0.289685i | \(0.0935507\pi\) |
0.289685 | + | 0.957122i | \(0.406449\pi\) | |||||||
\(542\) | 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 | \(-0.444780\pi\) |
−0.984990 | + | 0.172609i | \(0.944780\pi\) | |||||||
\(548\) | 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 | 0.313889 | − | 0.949460i | \(-0.398368\pi\) |
−0.949460 | + | 0.313889i | \(0.898368\pi\) | |||||||
\(558\) | 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 | \(-0.0224065\pi\) |
−0.0703340 | + | 0.997523i | \(0.522407\pi\) | |||||||
\(564\) | 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 | \(0.414582\pi\) | ||||
−0.265139 | + | 0.964210i | \(0.585418\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21.0000 | − | 21.0000i | 0.878823 | − | 0.878823i | −0.114590 | − | 0.993413i | \(-0.536555\pi\) |
0.993413 | + | 0.114590i | \(0.0365555\pi\) | |||||||
\(572\) | 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 | \(-0.825012\pi\) |
0.522465 | + | 0.852661i | \(0.325012\pi\) | |||||||
\(588\) | 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 | \(0.0653794\pi\) | ||||
−0.978980 | + | 0.203954i | \(0.934621\pi\) | |||||||
\(602\) | 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 | \(-0.366962\pi\) | ||||
0.405887 | + | 0.913923i | \(0.366962\pi\) | |||||||
\(608\) | 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 | −0.336013 | − | 0.941857i | \(-0.609079\pi\) |
0.941857 | + | 0.336013i | \(0.109079\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 16.0000i | − | 0.645182i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.00000i | 0.241551i | 0.992680 | + | 0.120775i | \(0.0385381\pi\) | ||||
−0.992680 | + | 0.120775i | \(0.961462\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −18.0000 | + | 18.0000i | −0.723481 | + | 0.723481i | −0.969313 | − | 0.245831i | \(-0.920939\pi\) |
0.245831 | + | 0.969313i | \(0.420939\pi\) | |||||||
\(620\) | 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 | −0.999670 | − | 0.0256694i | \(-0.991828\pi\) |
−0.0256694 | − | 0.999670i | \(-0.508172\pi\) | |||||||
\(644\) | 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 | 0.0214444 | − | 0.999770i | \(-0.493173\pi\) |
−0.999770 | + | 0.0214444i | \(0.993173\pi\) | |||||||
\(654\) | 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 | \(-0.405121\pi\) |
−0.955904 | + | 0.293678i | \(0.905121\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −30.0000 | + | 30.0000i | −1.16686 | + | 1.16686i | −0.183924 | + | 0.982940i | \(0.558880\pi\) |
−0.982940 | + | 0.183924i | \(0.941120\pi\) | |||||||
\(662\) | 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 | −0.843925 | − | 0.536460i | \(-0.819761\pi\) |
0.536460 | + | 0.843925i | \(0.319761\pi\) | |||||||
\(678\) | 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 | \(-0.793195\pi\) |
0.604946 | + | 0.796266i | \(0.293195\pi\) | |||||||
\(684\) | 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 | \(-0.354623\pi\) |
−0.897505 | + | 0.441004i | \(0.854623\pi\) | |||||||
\(692\) | 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 | 0.417619 | − | 0.908622i | \(-0.362865\pi\) |
−0.908622 | + | 0.417619i | \(0.862865\pi\) | |||||||
\(702\) | 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 | 0.180689 | − | 0.983540i | \(-0.442167\pi\) |
0.983540 | − | 0.180689i | \(-0.0578328\pi\) | |||||||
\(710\) | 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 | \(-0.547662\pi\) | ||||
−0.149175 | + | 0.988811i | \(0.547662\pi\) | |||||||
\(720\) | 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 | 0.743077 | − | 0.669206i | \(-0.233365\pi\) |
−0.669206 | + | 0.743077i | \(0.733365\pi\) | |||||||
\(734\) | 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 | \(-0.208484\pi\) |
−0.609137 | + | 0.793065i | \(0.708484\pi\) | |||||||
\(740\) | 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 | \(-0.239608\pi\) | ||||
0.729810 | + | 0.683650i | \(0.239608\pi\) | |||||||
\(752\) | 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 | −0.225061 | + | 0.974345i | \(0.572258\pi\) |
−0.974345 | + | 0.225061i | \(0.927742\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 24.0000i | − | 0.871145i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 18.0000i | − | 0.652499i | −0.945284 | − | 0.326250i | \(-0.894215\pi\) | ||
0.945284 | − | 0.326250i | \(-0.105785\pi\) | |||||||
\(762\) | 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 | 0.0824280 | − | 0.996597i | \(-0.473733\pi\) |
0.996597 | − | 0.0824280i | \(-0.0262674\pi\) | |||||||
\(774\) | 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 | \(-0.152190\pi\) |
−0.460109 | + | 0.887863i | \(0.652190\pi\) | |||||||
\(788\) | 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 | 0.551079 | − | 0.834453i | \(-0.314216\pi\) |
−0.834453 | + | 0.551079i | \(0.814216\pi\) | |||||||
\(798\) | 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 | \(-0.767149\pi\) | ||
0.744157 | − | 0.668004i | \(-0.232851\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −30.0000 | + | 30.0000i | −1.05344 | + | 1.05344i | −0.0549536 | + | 0.998489i | \(0.517501\pi\) |
−0.998489 | + | 0.0549536i | \(0.982499\pi\) | |||||||
\(812\) | 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 | −0.574325 | − | 0.818627i | \(-0.694736\pi\) |
0.818627 | + | 0.574325i | \(0.194736\pi\) | |||||||
\(822\) | 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 | \(-0.646434\pi\) |
0.896036 | + | 0.443982i | \(0.146434\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.00000 | + | 2.00000i | 0.0694629 | + | 0.0694629i | 0.740985 | − | 0.671522i | \(-0.234359\pi\) |
−0.671522 | + | 0.740985i | \(0.734359\pi\) | |||||||
\(830\) | 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 | −0.635304 | − | 0.772262i | \(-0.719125\pi\) |
0.772262 | + | 0.635304i | \(0.219125\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 80.0000i | 2.73594i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 18.0000i | 0.614868i | 0.951569 | + | 0.307434i | \(0.0994704\pi\) | ||||
−0.951569 | + | 0.307434i | \(0.900530\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.00000 | − | 4.00000i | 0.136478 | − | 0.136478i | −0.635567 | − | 0.772046i | \(-0.719234\pi\) |
0.772046 | + | 0.635567i | \(0.219234\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.00000 | − | 4.00000i | −0.136320 | − | 0.136320i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6.00000 | 0.204242 | 0.102121 | − | 0.994772i | \(-0.467437\pi\) | ||||
0.102121 | + | 0.994772i | \(0.467437\pi\) | |||||||
\(864\) | 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 | 0.966350 | − | 0.257230i | \(-0.0828100\pi\) |
−0.257230 | + | 0.966350i | \(0.582810\pi\) | |||||||
\(878\) | 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 | \(-0.117434\pi\) |
−0.360618 | + | 0.932714i | \(0.617434\pi\) | |||||||
\(884\) | 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 | \(-0.682226\pi\) |
0.840559 | + | 0.541719i | \(0.182226\pi\) | |||||||
\(908\) | 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 | \(-0.695793\pi\) | ||
0.577042 | − | 0.816714i | \(-0.304207\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −4.00000 | + | 4.00000i | −0.130535 | + | 0.130535i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −26.0000 | − | 26.0000i | −0.847576 | − | 0.847576i | 0.142254 | − | 0.989830i | \(-0.454565\pi\) |
−0.989830 | + | 0.142254i | \(0.954565\pi\) | |||||||
\(942\) | 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 | \(-0.346557\pi\) |
−0.886044 | + | 0.463601i | \(0.846557\pi\) | |||||||
\(948\) | 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 | \(0.0834409\pi\) | ||||
−0.965838 | + | 0.259145i | \(0.916559\pi\) | |||||||
\(954\) | 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 | \(-0.950871\pi\) |
0.153733 | + | 0.988112i | \(0.450871\pi\) | |||||||
\(972\) | 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 | \(-0.550772\pi\) | ||||
−0.158830 | + | 0.987306i | \(0.550772\pi\) | |||||||
\(992\) | 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 | −0.998813 | − | 0.0487037i | \(-0.984491\pi\) |
0.0487037 | + | 0.998813i | \(0.484491\pi\) | |||||||
\(998\) | 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.d.673.1 | 2 | ||
4.3 | odd | 2 | 896.2.m.a.673.1 | 2 | |||
8.3 | odd | 2 | 448.2.m.b.337.1 | 2 | |||
8.5 | even | 2 | 112.2.m.a.29.1 | ✓ | 2 | ||
16.3 | odd | 4 | 448.2.m.b.113.1 | 2 | |||
16.5 | even | 4 | inner | 896.2.m.d.225.1 | 2 | ||
16.11 | odd | 4 | 896.2.m.a.225.1 | 2 | |||
16.13 | even | 4 | 112.2.m.a.85.1 | yes | 2 | ||
32.5 | even | 8 | 7168.2.a.q.1.1 | 2 | |||
32.11 | odd | 8 | 7168.2.a.i.1.1 | 2 | |||
32.21 | even | 8 | 7168.2.a.q.1.2 | 2 | |||
32.27 | odd | 8 | 7168.2.a.i.1.2 | 2 | |||
56.5 | odd | 6 | 784.2.x.b.557.1 | 4 | |||
56.13 | odd | 2 | 784.2.m.c.589.1 | 2 | |||
56.37 | even | 6 | 784.2.x.g.557.1 | 4 | |||
56.45 | odd | 6 | 784.2.x.b.765.1 | 4 | |||
56.53 | even | 6 | 784.2.x.g.765.1 | 4 | |||
112.13 | odd | 4 | 784.2.m.c.197.1 | 2 | |||
112.45 | odd | 12 | 784.2.x.b.373.1 | 4 | |||
112.61 | odd | 12 | 784.2.x.b.165.1 | 4 | |||
112.93 | even | 12 | 784.2.x.g.165.1 | 4 | |||
112.109 | even | 12 | 784.2.x.g.373.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
112.2.m.a.29.1 | ✓ | 2 | 8.5 | even | 2 | ||
112.2.m.a.85.1 | yes | 2 | 16.13 | even | 4 | ||
448.2.m.b.113.1 | 2 | 16.3 | odd | 4 | |||
448.2.m.b.337.1 | 2 | 8.3 | odd | 2 | |||
784.2.m.c.197.1 | 2 | 112.13 | odd | 4 | |||
784.2.m.c.589.1 | 2 | 56.13 | odd | 2 | |||
784.2.x.b.165.1 | 4 | 112.61 | odd | 12 | |||
784.2.x.b.373.1 | 4 | 112.45 | odd | 12 | |||
784.2.x.b.557.1 | 4 | 56.5 | odd | 6 | |||
784.2.x.b.765.1 | 4 | 56.45 | odd | 6 | |||
784.2.x.g.165.1 | 4 | 112.93 | even | 12 | |||
784.2.x.g.373.1 | 4 | 112.109 | even | 12 | |||
784.2.x.g.557.1 | 4 | 56.37 | even | 6 | |||
784.2.x.g.765.1 | 4 | 56.53 | even | 6 | |||
896.2.m.a.225.1 | 2 | 16.11 | odd | 4 | |||
896.2.m.a.673.1 | 2 | 4.3 | odd | 2 | |||
896.2.m.d.225.1 | 2 | 16.5 | even | 4 | inner | ||
896.2.m.d.673.1 | 2 | 1.1 | even | 1 | trivial | ||
7168.2.a.i.1.1 | 2 | 32.11 | odd | 8 | |||
7168.2.a.i.1.2 | 2 | 32.27 | odd | 8 | |||
7168.2.a.q.1.1 | 2 | 32.5 | even | 8 | |||
7168.2.a.q.1.2 | 2 | 32.21 | even | 8 |