Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1280,2,Mod(767,1280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1280, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1280.767");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1280 = 2^{8} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1280.n (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: | \(10.2208514587\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 320) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1023.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1280.1023 |
Dual form | 1280.2.n.j.767.1 |
$q$-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 \(\left(\mathbb{Z}/1280\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(261\) | \(511\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | − | 1.00000i | 0.577350 | − | 0.577350i | −0.356822 | − | 0.934172i | \(-0.616140\pi\) |
0.934172 | + | 0.356822i | \(0.116140\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.00000 | + | 1.00000i | 0.894427 | + | 0.447214i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | + | 1.00000i | 0.377964 | + | 0.377964i | 0.870367 | − | 0.492403i | \(-0.163881\pi\) |
−0.492403 | + | 0.870367i | \(0.663881\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000i | 0.333333i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.00000i | 1.20605i | 0.797724 | + | 0.603023i | \(0.206037\pi\) | ||||
−0.797724 | + | 0.603023i | \(0.793963\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.00000 | − | 3.00000i | −0.832050 | − | 0.832050i | 0.155747 | − | 0.987797i | \(-0.450222\pi\) |
−0.987797 | + | 0.155747i | \(0.950222\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.00000 | − | 1.00000i | 0.774597 | − | 0.258199i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.00000 | + | 3.00000i | −0.727607 | + | 0.727607i | −0.970143 | − | 0.242536i | \(-0.922021\pi\) |
0.242536 | + | 0.970143i | \(0.422021\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.00000 | 1.37649 | 0.688247 | − | 0.725476i | \(-0.258380\pi\) | ||||
0.688247 | + | 0.725476i | \(0.258380\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.00000 | 0.436436 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.00000 | − | 3.00000i | 0.625543 | − | 0.625543i | −0.321400 | − | 0.946943i | \(-0.604153\pi\) |
0.946943 | + | 0.321400i | \(0.104153\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.00000 | + | 4.00000i | 0.600000 | + | 0.800000i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.00000 | + | 4.00000i | 0.769800 | + | 0.769800i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.00000i | 0.371391i | 0.982607 | + | 0.185695i | \(0.0594537\pi\) | ||||
−0.982607 | + | 0.185695i | \(0.940546\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.00000i | 1.07763i | 0.842424 | + | 0.538816i | \(0.181128\pi\) | ||||
−0.842424 | + | 0.538816i | \(0.818872\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.00000 | + | 4.00000i | 0.696311 | + | 0.696311i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.00000 | + | 3.00000i | 0.169031 | + | 0.507093i | ||||
\(36\) | 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 | ||||||||
\(39\) | −6.00000 | −0.960769 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.00000 | −0.937043 | −0.468521 | − | 0.883452i | \(-0.655213\pi\) | ||||
−0.468521 | + | 0.883452i | \(0.655213\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.00000 | − | 3.00000i | 0.457496 | − | 0.457496i | −0.440337 | − | 0.897833i | \(-0.645141\pi\) |
0.897833 | + | 0.440337i | \(0.145141\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | + | 2.00000i | −0.149071 | + | 0.298142i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.00000 | − | 9.00000i | −1.31278 | − | 1.31278i | −0.919354 | − | 0.393431i | \(-0.871288\pi\) |
−0.393431 | − | 0.919354i | \(-0.628712\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 5.00000i | − | 0.714286i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.00000i | 0.840168i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.00000 | − | 5.00000i | −0.686803 | − | 0.686803i | 0.274721 | − | 0.961524i | \(-0.411414\pi\) |
−0.961524 | + | 0.274721i | \(0.911414\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.00000 | + | 8.00000i | −0.539360 | + | 1.07872i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.00000 | − | 6.00000i | 0.794719 | − | 0.794719i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.0000 | 1.30189 | 0.650945 | − | 0.759125i | \(-0.274373\pi\) | ||||
0.650945 | + | 0.759125i | \(0.274373\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.0000 | 1.53644 | 0.768221 | − | 0.640184i | \(-0.221142\pi\) | ||||
0.768221 | + | 0.640184i | \(0.221142\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.00000 | + | 1.00000i | −0.125988 | + | 0.125988i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.00000 | − | 9.00000i | −0.372104 | − | 1.11631i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.00000 | + | 9.00000i | 1.09952 | + | 1.09952i | 0.994466 | + | 0.105059i | \(0.0335031\pi\) |
0.105059 | + | 0.994466i | \(0.466497\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 6.00000i | − | 0.722315i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 6.00000i | − | 0.712069i | −0.934473 | − | 0.356034i | \(-0.884129\pi\) | ||
0.934473 | − | 0.356034i | \(-0.115871\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.00000 | − | 5.00000i | −0.585206 | − | 0.585206i | 0.351123 | − | 0.936329i | \(-0.385800\pi\) |
−0.936329 | + | 0.351123i | \(0.885800\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 7.00000 | + | 1.00000i | 0.808290 | + | 0.115470i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.00000 | + | 4.00000i | −0.455842 | + | 0.455842i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.00000 | 0.555556 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.00000 | + | 3.00000i | −0.329293 | + | 0.329293i | −0.852318 | − | 0.523025i | \(-0.824804\pi\) |
0.523025 | + | 0.852318i | \(0.324804\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.00000 | + | 3.00000i | −0.976187 | + | 0.325396i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.00000 | + | 2.00000i | 0.214423 | + | 0.214423i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 6.00000i | − | 0.628971i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.00000 | + | 6.00000i | 0.622171 | + | 0.622171i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 12.0000 | + | 6.00000i | 1.23117 | + | 0.615587i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.00000 | + | 7.00000i | −0.710742 | + | 0.710742i | −0.966691 | − | 0.255948i | \(-0.917612\pi\) |
0.255948 | + | 0.966691i | \(0.417612\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.00000 | −0.402015 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.00000 | 0.796030 | 0.398015 | − | 0.917379i | \(-0.369699\pi\) | ||||
0.398015 | + | 0.917379i | \(0.369699\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.0000 | − | 11.0000i | 1.08386 | − | 1.08386i | 0.0877167 | − | 0.996145i | \(-0.472043\pi\) |
0.996145 | − | 0.0877167i | \(-0.0279570\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.00000 | + | 2.00000i | 0.390360 | + | 0.195180i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.00000 | + | 3.00000i | 0.290021 | + | 0.290021i | 0.837088 | − | 0.547068i | \(-0.184256\pi\) |
−0.547068 | + | 0.837088i | \(0.684256\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 18.0000i | − | 1.72409i | −0.506834 | − | 0.862044i | \(-0.669184\pi\) | ||
0.506834 | − | 0.862044i | \(-0.330816\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.00000i | 0.569495i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.00000 | − | 3.00000i | −0.282216 | − | 0.282216i | 0.551776 | − | 0.833992i | \(-0.313950\pi\) |
−0.833992 | + | 0.551776i | \(0.813950\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.00000 | − | 3.00000i | 0.839254 | − | 0.279751i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.00000 | − | 3.00000i | 0.277350 | − | 0.277350i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.00000 | −0.550019 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.00000 | −0.454545 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6.00000 | + | 6.00000i | −0.541002 | + | 0.541002i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.00000 | + | 11.0000i | 0.178885 | + | 0.983870i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.00000 | − | 5.00000i | −0.443678 | − | 0.443678i | 0.449568 | − | 0.893246i | \(-0.351578\pi\) |
−0.893246 | + | 0.449568i | \(0.851578\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 6.00000i | − | 0.528271i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 4.00000i | − | 0.349482i | −0.984614 | − | 0.174741i | \(-0.944091\pi\) | ||
0.984614 | − | 0.174741i | \(-0.0559088\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.00000 | + | 6.00000i | 0.520266 | + | 0.520266i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.00000 | + | 12.0000i | 0.344265 | + | 1.03280i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.00000 | − | 3.00000i | 0.256307 | − | 0.256307i | −0.567243 | − | 0.823550i | \(-0.691990\pi\) |
0.823550 | + | 0.567243i | \(0.191990\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.00000 | −0.508913 | −0.254457 | − | 0.967084i | \(-0.581897\pi\) | ||||
−0.254457 | + | 0.967084i | \(0.581897\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −18.0000 | −1.51587 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 12.0000 | − | 12.0000i | 1.00349 | − | 1.00349i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.00000 | + | 4.00000i | −0.166091 | + | 0.332182i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5.00000 | − | 5.00000i | −0.412393 | − | 0.412393i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.00000i | 0.163846i | 0.996639 | + | 0.0819232i | \(0.0261062\pi\) | ||||
−0.996639 | + | 0.0819232i | \(0.973894\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.0000i | 0.813788i | 0.913475 | + | 0.406894i | \(0.133388\pi\) | ||||
−0.913475 | + | 0.406894i | \(0.866612\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.00000 | − | 3.00000i | −0.242536 | − | 0.242536i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.00000 | + | 12.0000i | −0.481932 | + | 0.963863i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.00000 | − | 3.00000i | 0.239426 | − | 0.239426i | −0.577186 | − | 0.816612i | \(-0.695849\pi\) |
0.816612 | + | 0.577186i | \(0.195849\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −10.0000 | −0.793052 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.00000 | 0.472866 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.00000 | − | 9.00000i | 0.704934 | − | 0.704934i | −0.260531 | − | 0.965465i | \(-0.583898\pi\) |
0.965465 | + | 0.260531i | \(0.0838976\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.00000 | + | 12.0000i | 0.311400 | + | 0.934199i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.00000 | − | 3.00000i | −0.232147 | − | 0.232147i | 0.581441 | − | 0.813588i | \(-0.302489\pi\) |
−0.813588 | + | 0.581441i | \(0.802489\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.00000i | 0.384615i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.00000i | 0.458831i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −15.0000 | − | 15.0000i | −1.14043 | − | 1.14043i | −0.988372 | − | 0.152057i | \(-0.951410\pi\) |
−0.152057 | − | 0.988372i | \(-0.548590\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.00000 | + | 7.00000i | −0.0755929 | + | 0.529150i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 10.0000 | − | 10.0000i | 0.751646 | − | 0.751646i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.00000 | −0.149487 | −0.0747435 | − | 0.997203i | \(-0.523814\pi\) | ||||
−0.0747435 | + | 0.997203i | \(0.523814\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 12.0000 | − | 12.0000i | 0.887066 | − | 0.887066i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −9.00000 | + | 3.00000i | −0.661693 | + | 0.220564i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12.0000 | − | 12.0000i | −0.877527 | − | 0.877527i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 8.00000i | 0.581914i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.00000i | 0.434145i | 0.976156 | + | 0.217072i | \(0.0696508\pi\) | ||||
−0.976156 | + | 0.217072i | \(0.930349\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.00000 | + | 5.00000i | 0.359908 | + | 0.359908i | 0.863779 | − | 0.503871i | \(-0.168091\pi\) |
−0.503871 | + | 0.863779i | \(0.668091\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −12.0000 | − | 6.00000i | −0.859338 | − | 0.429669i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.00000 | − | 5.00000i | 0.356235 | − | 0.356235i | −0.506188 | − | 0.862423i | \(-0.668946\pi\) |
0.862423 | + | 0.506188i | \(0.168946\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.0000 | −1.13421 | −0.567105 | − | 0.823646i | \(-0.691937\pi\) | ||||
−0.567105 | + | 0.823646i | \(0.691937\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 18.0000 | 1.26962 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.00000 | + | 2.00000i | −0.140372 | + | 0.140372i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −12.0000 | − | 6.00000i | −0.838116 | − | 0.419058i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.00000 | + | 3.00000i | 0.208514 | + | 0.208514i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 24.0000i | 1.66011i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 12.0000i | − | 0.826114i | −0.910705 | − | 0.413057i | \(-0.864461\pi\) | ||
0.910705 | − | 0.413057i | \(-0.135539\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.00000 | − | 6.00000i | −0.411113 | − | 0.411113i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 9.00000 | − | 3.00000i | 0.613795 | − | 0.204598i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.00000 | + | 6.00000i | −0.407307 | + | 0.407307i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −10.0000 | −0.675737 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 18.0000 | 1.21081 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.0000 | − | 13.0000i | 0.870544 | − | 0.870544i | −0.121987 | − | 0.992532i | \(-0.538927\pi\) |
0.992532 | + | 0.121987i | \(0.0389267\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.00000 | + | 3.00000i | −0.266667 | + | 0.200000i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.0000 | − | 11.0000i | −0.730096 | − | 0.730096i | 0.240543 | − | 0.970639i | \(-0.422675\pi\) |
−0.970639 | + | 0.240543i | \(0.922675\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.00000i | 0.396491i | 0.980152 | + | 0.198246i | \(0.0635244\pi\) | ||||
−0.980152 | + | 0.198246i | \(0.936476\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.00000i | 0.526361i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 15.0000 | + | 15.0000i | 0.982683 | + | 0.982683i | 0.999853 | − | 0.0171699i | \(-0.00546562\pi\) |
−0.0171699 | + | 0.999853i | \(0.505466\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.00000 | − | 27.0000i | −0.587095 | − | 1.76129i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −24.0000 | −1.55243 | −0.776215 | − | 0.630468i | \(-0.782863\pi\) | ||||
−0.776215 | + | 0.630468i | \(0.782863\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −18.0000 | −1.15948 | −0.579741 | − | 0.814801i | \(-0.696846\pi\) | ||||
−0.579741 | + | 0.814801i | \(0.696846\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −7.00000 | + | 7.00000i | −0.449050 | + | 0.449050i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.00000 | − | 10.0000i | 0.319438 | − | 0.638877i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −18.0000 | − | 18.0000i | −1.14531 | − | 1.14531i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.00000i | 0.380235i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 4.00000i | − | 0.252478i | −0.992000 | − | 0.126239i | \(-0.959709\pi\) | ||
0.992000 | − | 0.126239i | \(-0.0402906\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.0000 | + | 12.0000i | 0.754434 | + | 0.754434i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −6.00000 | + | 12.0000i | −0.375735 | + | 0.751469i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.00000 | + | 3.00000i | −0.187135 | + | 0.187135i | −0.794456 | − | 0.607321i | \(-0.792244\pi\) |
0.607321 | + | 0.794456i | \(0.292244\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.00000 | −0.372822 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.00000 | −0.123797 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −9.00000 | + | 9.00000i | −0.554964 | + | 0.554964i | −0.927869 | − | 0.372906i | \(-0.878362\pi\) |
0.372906 | + | 0.927869i | \(0.378362\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.00000 | − | 15.0000i | −0.307148 | − | 0.921443i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 14.0000i | 0.853595i | 0.904347 | + | 0.426798i | \(0.140358\pi\) | ||||
−0.904347 | + | 0.426798i | \(0.859642\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 2.00000i | − | 0.121491i | −0.998153 | − | 0.0607457i | \(-0.980652\pi\) | ||
0.998153 | − | 0.0607457i | \(-0.0193479\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −6.00000 | − | 6.00000i | −0.363137 | − | 0.363137i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −16.0000 | + | 12.0000i | −0.964836 | + | 0.723627i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −15.0000 | + | 15.0000i | −0.901263 | + | 0.901263i | −0.995545 | − | 0.0942828i | \(-0.969944\pi\) |
0.0942828 | + | 0.995545i | \(0.469944\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.00000 | −0.359211 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.00000 | −0.357930 | −0.178965 | − | 0.983855i | \(-0.557275\pi\) | ||||
−0.178965 | + | 0.983855i | \(0.557275\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.0000 | − | 15.0000i | 0.891657 | − | 0.891657i | −0.103022 | − | 0.994679i | \(-0.532851\pi\) |
0.994679 | + | 0.103022i | \(0.0328511\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 18.0000 | − | 6.00000i | 1.06623 | − | 0.355409i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.00000 | − | 6.00000i | −0.354169 | − | 0.354169i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 1.00000i | − | 0.0588235i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 14.0000i | 0.820695i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.00000 | − | 1.00000i | −0.0584206 | − | 0.0584206i | 0.677293 | − | 0.735714i | \(-0.263153\pi\) |
−0.735714 | + | 0.677293i | \(0.763153\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 20.0000 | + | 10.0000i | 1.16445 | + | 0.582223i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −16.0000 | + | 16.0000i | −0.928414 | + | 0.928414i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −18.0000 | −1.04097 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.00000 | 0.345834 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 8.00000 | − | 8.00000i | 0.459588 | − | 0.459588i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 24.0000 | + | 12.0000i | 1.37424 | + | 0.687118i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −15.0000 | − | 15.0000i | −0.856095 | − | 0.856095i | 0.134780 | − | 0.990876i | \(-0.456967\pi\) |
−0.990876 | + | 0.134780i | \(0.956967\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 22.0000i | − | 1.25154i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 18.0000i | 1.02069i | 0.859971 | + | 0.510343i | \(0.170482\pi\) | ||||
−0.859971 | + | 0.510343i | \(0.829518\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.00000 | − | 1.00000i | −0.0565233 | − | 0.0565233i | 0.678280 | − | 0.734803i | \(-0.262726\pi\) |
−0.734803 | + | 0.678280i | \(0.762726\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.00000 | + | 1.00000i | −0.169031 | + | 0.0563436i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.00000 | − | 3.00000i | 0.168497 | − | 0.168497i | −0.617822 | − | 0.786318i | \(-0.711985\pi\) |
0.786318 | + | 0.617822i | \(0.211985\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.00000 | −0.447914 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.00000 | 0.334887 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −18.0000 | + | 18.0000i | −1.00155 | + | 1.00155i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.00000 | − | 21.0000i | 0.166410 | − | 1.16487i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −18.0000 | − | 18.0000i | −0.995402 | − | 0.995402i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 18.0000i | − | 0.992372i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 12.0000i | − | 0.659580i | −0.944054 | − | 0.329790i | \(-0.893022\pi\) | ||
0.944054 | − | 0.329790i | \(-0.106978\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.00000 | − | 3.00000i | −0.164399 | − | 0.164399i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 9.00000 | + | 27.0000i | 0.491723 | + | 1.47517i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 25.0000 | − | 25.0000i | 1.36184 | − | 1.36184i | 0.490261 | − | 0.871576i | \(-0.336901\pi\) |
0.871576 | − | 0.490261i | \(-0.163099\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.00000 | −0.325875 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −24.0000 | −1.29967 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.0000 | − | 12.0000i | 0.647939 | − | 0.647939i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 6.00000 | − | 12.0000i | 0.323029 | − | 0.646058i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −17.0000 | − | 17.0000i | −0.912608 | − | 0.912608i | 0.0838690 | − | 0.996477i | \(-0.473272\pi\) |
−0.996477 | + | 0.0838690i | \(0.973272\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 18.0000i | 0.963518i | 0.876304 | + | 0.481759i | \(0.160002\pi\) | ||||
−0.876304 | + | 0.481759i | \(0.839998\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 24.0000i | − | 1.28103i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −15.0000 | − | 15.0000i | −0.798369 | − | 0.798369i | 0.184469 | − | 0.982838i | \(-0.440943\pi\) |
−0.982838 | + | 0.184469i | \(0.940943\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.00000 | − | 12.0000i | 0.318447 | − | 0.636894i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.00000 | + | 6.00000i | −0.317554 | + | 0.317554i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 24.0000 | 1.26667 | 0.633336 | − | 0.773877i | \(-0.281685\pi\) | ||||
0.633336 | + | 0.773877i | \(0.281685\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.0000 | 0.894737 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −5.00000 | + | 5.00000i | −0.262432 | + | 0.262432i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.00000 | − | 15.0000i | −0.261712 | − | 0.785136i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.0000 | + | 11.0000i | 0.574195 | + | 0.574195i | 0.933298 | − | 0.359103i | \(-0.116917\pi\) |
−0.359103 | + | 0.933298i | \(0.616917\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 6.00000i | − | 0.312348i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 10.0000i | − | 0.519174i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.00000 | + | 3.00000i | 0.155334 | + | 0.155334i | 0.780496 | − | 0.625161i | \(-0.214967\pi\) |
−0.625161 | + | 0.780496i | \(0.714967\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 13.0000 | + | 9.00000i | 0.671317 | + | 0.464758i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.00000 | − | 6.00000i | 0.309016 | − | 0.309016i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.0000 | 0.924598 | 0.462299 | − | 0.886724i | \(-0.347025\pi\) | ||||
0.462299 | + | 0.886724i | \(0.347025\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −10.0000 | −0.512316 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 21.0000 | − | 21.0000i | 1.07305 | − | 1.07305i | 0.0759373 | − | 0.997113i | \(-0.475805\pi\) |
0.997113 | − | 0.0759373i | \(-0.0241949\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −12.0000 | + | 4.00000i | −0.611577 | + | 0.203859i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.00000 | + | 3.00000i | 0.152499 | + | 0.152499i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 26.0000i | 1.31825i | 0.752032 | + | 0.659126i | \(0.229074\pi\) | ||||
−0.752032 | + | 0.659126i | \(0.770926\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.0000i | 0.910299i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.00000 | − | 4.00000i | −0.201773 | − | 0.201773i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.00000 | + | 9.00000i | −0.451697 | + | 0.451697i | −0.895918 | − | 0.444220i | \(-0.853481\pi\) |
0.444220 | + | 0.895918i | \(0.353481\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 12.0000 | 0.600751 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −30.0000 | −1.49813 | −0.749064 | − | 0.662497i | \(-0.769497\pi\) | ||||
−0.749064 | + | 0.662497i | \(0.769497\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 18.0000 | − | 18.0000i | 0.896644 | − | 0.896644i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 10.0000 | + | 5.00000i | 0.496904 | + | 0.248452i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −12.0000 | − | 12.0000i | −0.594818 | − | 0.594818i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 12.0000i | − | 0.593362i | −0.954977 | − | 0.296681i | \(-0.904120\pi\) | ||
0.954977 | − | 0.296681i | \(-0.0958798\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 6.00000i | − | 0.295958i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 10.0000 | + | 10.0000i | 0.492068 | + | 0.492068i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.00000 | + | 3.00000i | −0.441793 | + | 0.147264i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.00000 | + | 6.00000i | −0.293821 | + | 0.293821i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10.0000 | −0.488532 | −0.244266 | − | 0.969708i | \(-0.578547\pi\) | ||||
−0.244266 | + | 0.969708i | \(0.578547\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.0000 | 0.584844 | 0.292422 | − | 0.956289i | \(-0.405539\pi\) | ||||
0.292422 | + | 0.956289i | \(0.405539\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 9.00000 | − | 9.00000i | 0.437595 | − | 0.437595i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −21.0000 | − | 3.00000i | −1.01865 | − | 0.145521i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.0000 | + | 12.0000i | 0.580721 | + | 0.580721i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 24.0000i | − | 1.15873i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 30.0000i | 1.44505i | 0.691345 | + | 0.722525i | \(0.257018\pi\) | ||||
−0.691345 | + | 0.722525i | \(0.742982\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.00000 | − | 7.00000i | −0.336399 | − | 0.336399i | 0.518611 | − | 0.855010i | \(-0.326449\pi\) |
−0.855010 | + | 0.518611i | \(0.826449\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.00000 | + | 6.00000i | 0.0958927 | + | 0.287678i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 18.0000 | − | 18.0000i | 0.861057 | − | 0.861057i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.00000 | −0.381819 | −0.190910 | − | 0.981608i | \(-0.561144\pi\) | ||||
−0.190910 | + | 0.981608i | \(0.561144\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.00000 | 0.238095 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −25.0000 | + | 25.0000i | −1.18779 | + | 1.18779i | −0.210108 | + | 0.977678i | \(0.567381\pi\) |
−0.977678 | + | 0.210108i | \(0.932619\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.00000 | + | 2.00000i | 0.0945968 | + | 0.0945968i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 12.0000i | − | 0.566315i | −0.959073 | − | 0.283158i | \(-0.908618\pi\) | ||
0.959073 | − | 0.283158i | \(-0.0913819\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 24.0000i | − | 1.13012i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 10.0000 | + | 10.0000i | 0.469841 | + | 0.469841i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.00000 | − | 12.0000i | 0.281284 | − | 0.562569i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.0000 | + | 17.0000i | −0.795226 | + | 0.795226i | −0.982339 | − | 0.187112i | \(-0.940087\pi\) |
0.187112 | + | 0.982339i | \(0.440087\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −24.0000 | −1.12022 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −40.0000 | −1.86299 | −0.931493 | − | 0.363760i | \(-0.881493\pi\) | ||||
−0.931493 | + | 0.363760i | \(0.881493\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.00000 | − | 1.00000i | 0.0464739 | − | 0.0464739i | −0.683488 | − | 0.729962i | \(-0.739538\pi\) |
0.729962 | + | 0.683488i | \(0.239538\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6.00000 | + | 18.0000i | 0.278243 | + | 0.834730i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 21.0000 | + | 21.0000i | 0.971764 | + | 0.971764i | 0.999612 | − | 0.0278481i | \(-0.00886546\pi\) |
−0.0278481 | + | 0.999612i | \(0.508865\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 18.0000i | 0.831163i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 6.00000i | − | 0.276465i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 12.0000 | + | 12.0000i | 0.551761 | + | 0.551761i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 18.0000 | + | 24.0000i | 0.825897 | + | 1.10120i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.00000 | − | 5.00000i | 0.228934 | − | 0.228934i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −24.0000 | −1.09659 | −0.548294 | − | 0.836286i | \(-0.684723\pi\) | ||||
−0.548294 | + | 0.836286i | \(0.684723\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.0000 | 0.820729 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6.00000 | − | 6.00000i | 0.273009 | − | 0.273009i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −21.0000 | + | 7.00000i | −0.953561 | + | 0.317854i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.00000 | + | 1.00000i | 0.0453143 | + | 0.0453143i | 0.729401 | − | 0.684087i | \(-0.239799\pi\) |
−0.684087 | + | 0.729401i | \(0.739799\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 18.0000i | − | 0.813988i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20.0000i | 0.902587i | 0.892375 | + | 0.451294i | \(0.149037\pi\) | ||||
−0.892375 | + | 0.451294i | \(0.850963\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.00000 | − | 6.00000i | −0.270226 | − | 0.270226i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −8.00000 | − | 4.00000i | −0.359573 | − | 0.179787i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.00000 | − | 6.00000i | 0.269137 | − | 0.269137i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.00000 | 0.268597 | 0.134298 | − | 0.990941i | \(-0.457122\pi\) | ||||
0.134298 | + | 0.990941i | \(0.457122\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.00000 | −0.268060 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −21.0000 | + | 21.0000i | −0.936344 | + | 0.936344i | −0.998092 | − | 0.0617480i | \(-0.980332\pi\) |
0.0617480 | + | 0.998092i | \(0.480332\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 16.0000 | + | 8.00000i | 0.711991 | + | 0.355995i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.00000 | + | 5.00000i | 0.222058 | + | 0.222058i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 14.0000i | − | 0.620539i | −0.950649 | − | 0.310270i | \(-0.899581\pi\) | ||
0.950649 | − | 0.310270i | \(-0.100419\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 10.0000i | − | 0.442374i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 24.0000 | + | 24.0000i | 1.05963 | + | 1.05963i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 33.0000 | − | 11.0000i | 1.45415 | − | 0.484718i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 36.0000 | − | 36.0000i | 1.58328 | − | 1.58328i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −30.0000 | −1.31685 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −18.0000 | −0.788594 | −0.394297 | − | 0.918983i | \(-0.629012\pi\) | ||||
−0.394297 | + | 0.918983i | \(0.629012\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.0000 | − | 15.0000i | 0.655904 | − | 0.655904i | −0.298504 | − | 0.954408i | \(-0.596488\pi\) |
0.954408 | + | 0.298504i | \(0.0964877\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6.00000 | + | 8.00000i | 0.261861 | + | 0.349149i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −18.0000 | − | 18.0000i | −0.784092 | − | 0.784092i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.00000i | 0.217391i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10.0000i | 0.433963i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 18.0000 | + | 18.0000i | 0.779667 | + | 0.779667i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.00000 | + | 9.00000i | 0.129701 | + | 0.389104i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.00000 | + | 2.00000i | −0.0863064 | + | 0.0863064i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 20.0000 | 0.861461 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −24.0000 | −1.03184 | −0.515920 | − | 0.856637i | \(-0.672550\pi\) | ||||
−0.515920 | + | 0.856637i | \(0.672550\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 18.0000 | − | 36.0000i | 0.771035 | − | 1.54207i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.00000 | − | 3.00000i | −0.128271 | − | 0.128271i | 0.640057 | − | 0.768328i | \(-0.278911\pi\) |
−0.768328 | + | 0.640057i | \(0.778911\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 12.0000i | 0.512148i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.0000i | 0.511217i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −6.00000 | + | 12.0000i | −0.254686 | + | 0.509372i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 31.0000 | − | 31.0000i | 1.31351 | − | 1.31351i | 0.394704 | − | 0.918808i | \(-0.370847\pi\) |
0.918808 | − | 0.394704i | \(-0.129153\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −18.0000 | −0.761319 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −24.0000 | −1.01328 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.00000 | − | 1.00000i | 0.0421450 | − | 0.0421450i | −0.685720 | − | 0.727865i | \(-0.740513\pi\) |
0.727865 | + | 0.685720i | \(0.240513\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.00000 | − | 9.00000i | −0.126211 | − | 0.378633i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 5.00000 | + | 5.00000i | 0.209980 | + | 0.209980i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 12.0000i | 0.503066i | 0.967849 | + | 0.251533i | \(0.0809347\pi\) | ||||
−0.967849 | + | 0.251533i | \(0.919065\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 12.0000i | − | 0.502184i | −0.967963 | − | 0.251092i | \(-0.919210\pi\) | ||
0.967963 | − | 0.251092i | \(-0.0807897\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.00000 | + | 6.00000i | 0.250654 | + | 0.250654i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 21.0000 | + | 3.00000i | 0.875761 | + | 0.125109i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −19.0000 | + | 19.0000i | −0.790980 | + | 0.790980i | −0.981654 | − | 0.190673i | \(-0.938933\pi\) |
0.190673 | + | 0.981654i | \(0.438933\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 10.0000 | 0.415586 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.00000 | −0.248922 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 20.0000 | − | 20.0000i | 0.828315 | − | 0.828315i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 9.00000 | − | 3.00000i | 0.372104 | − | 0.124035i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 15.0000 | + | 15.0000i | 0.619116 | + | 0.619116i | 0.945305 | − | 0.326188i | \(-0.105764\pi\) |
−0.326188 | + | 0.945305i | \(0.605764\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 36.0000i | 1.48335i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 10.0000i | − | 0.411345i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −15.0000 | − | 15.0000i | −0.615976 | − | 0.615976i | 0.328521 | − | 0.944497i | \(-0.393450\pi\) |
−0.944497 | + | 0.328521i | \(0.893450\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −12.0000 | − | 6.00000i | −0.491952 | − | 0.245976i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −16.0000 | + | 16.0000i | −0.654836 | + | 0.654836i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.0000 | 0.407909 | 0.203954 | − | 0.978980i | \(-0.434621\pi\) | ||||
0.203954 | + | 0.978980i | \(0.434621\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −9.00000 | + | 9.00000i | −0.366508 | + | 0.366508i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −10.0000 | − | 5.00000i | −0.406558 | − | 0.203279i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.00000 | + | 7.00000i | 0.284121 | + | 0.284121i | 0.834750 | − | 0.550629i | \(-0.185612\pi\) |
−0.550629 | + | 0.834750i | \(0.685612\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.00000i | 0.162088i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 54.0000i | 2.18461i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.00000 | − | 9.00000i | −0.363507 | − | 0.363507i | 0.501596 | − | 0.865102i | \(-0.332747\pi\) |
−0.865102 | + | 0.501596i | \(0.832747\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −18.0000 | + | 6.00000i | −0.725830 | + | 0.241943i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15.0000 | − | 15.0000i | 0.603877 | − | 0.603877i | −0.337462 | − | 0.941339i | \(-0.609568\pi\) |
0.941339 | + | 0.337462i | \(0.109568\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 42.0000 | 1.68812 | 0.844061 | − | 0.536247i | \(-0.180158\pi\) | ||||
0.844061 | + | 0.536247i | \(0.180158\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 24.0000 | 0.963087 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.00000 | + | 24.0000i | −0.280000 | + | 0.960000i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 24.0000 | + | 24.0000i | 0.958468 | + | 0.958468i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 18.0000i | − | 0.717707i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 30.0000i | − | 1.19428i | −0.802137 | − | 0.597141i | \(-0.796303\pi\) | ||
0.802137 | − | 0.597141i | \(-0.203697\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −12.0000 | − | 12.0000i | −0.476957 | − | 0.476957i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.00000 | − | 15.0000i | −0.198419 | − | 0.595257i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −15.0000 | + | 15.0000i | −0.594322 | + | 0.594322i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.00000 | 0.237356 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 30.0000 | 1.18493 | 0.592464 | − | 0.805597i | \(-0.298155\pi\) | ||||
0.592464 | + | 0.805597i | \(0.298155\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.00000 | + | 3.00000i | −0.118308 | + | 0.118308i | −0.763782 | − | 0.645474i | \(-0.776660\pi\) |
0.645474 | + | 0.763782i | \(0.276660\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.00000 | − | 12.0000i | 0.236250 | − | 0.472500i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9.00000 | + | 9.00000i | 0.353827 | + | 0.353827i | 0.861531 | − | 0.507705i | \(-0.169506\pi\) |
−0.507705 | + | 0.861531i | \(0.669506\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 40.0000i | 1.57014i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 12.0000i | 0.470317i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 33.0000 | + | 33.0000i | 1.29139 | + | 1.29139i | 0.933928 | + | 0.357462i | \(0.116358\pi\) |
0.357462 | + | 0.933928i | \(0.383642\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.00000 | − | 8.00000i | 0.156293 | − | 0.312586i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5.00000 | − | 5.00000i | 0.195069 | − | 0.195069i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 22.0000 | 0.856998 | 0.428499 | − | 0.903542i | \(-0.359042\pi\) | ||||
0.428499 | + | 0.903542i | \(0.359042\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.0000 | −0.466746 | −0.233373 | − | 0.972387i | \(-0.574976\pi\) | ||||
−0.233373 | + | 0.972387i | \(0.574976\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 18.0000 | − | 18.0000i | 0.699062 | − | 0.699062i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 6.00000 | + | 18.0000i | 0.232670 | + | 0.698010i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.00000 | + | 6.00000i | 0.232321 | + | 0.232321i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 26.0000i | − | 1.00522i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 48.0000i | 1.85302i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 25.0000 | + | 25.0000i | 0.963679 | + | 0.963679i | 0.999363 | − | 0.0356839i | \(-0.0113610\pi\) |
−0.0356839 | + | 0.999363i | \(0.511361\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.00000 | + | 28.0000i | −0.153960 | + | 1.07772i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −27.0000 | + | 27.0000i | −1.03769 | + | 1.03769i | −0.0384331 | + | 0.999261i | \(0.512237\pi\) |
−0.999261 | + | 0.0384331i | \(0.987763\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −14.0000 | −0.537271 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −22.0000 | −0.843042 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 27.0000 | − | 27.0000i | 1.03313 | − | 1.03313i | 0.0336941 | − | 0.999432i | \(-0.489273\pi\) |
0.999432 | − | 0.0336941i | \(-0.0107272\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.00000 | − | 3.00000i | 0.343872 | − | 0.114624i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.00000 | + | 6.00000i | 0.228914 | + | 0.228914i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 30.0000i | 1.14291i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 12.0000i | − | 0.456502i | −0.973602 | − | 0.228251i | \(-0.926699\pi\) | ||
0.973602 | − | 0.228251i | \(-0.0733006\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.00000 | − | 4.00000i | −0.151947 | − | 0.151947i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −12.0000 | − | 6.00000i | −0.455186 | − | 0.227593i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 18.0000 | − | 18.0000i | 0.681799 | − | 0.681799i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 30.0000 | 1.13470 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 20.0000 | 0.755390 | 0.377695 | − | 0.925930i | \(-0.376717\pi\) | ||||
0.377695 | + | 0.925930i | \(0.376717\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −18.0000 | + | 18.0000i | −0.678883 | + | 0.678883i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −36.0000 | − | 18.0000i | −1.35584 | − | 0.677919i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.00000 | + | 8.00000i | 0.300871 | + | 0.300871i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 42.0000i | − | 1.57734i | −0.614815 | − | 0.788672i | \(-0.710769\pi\) | ||
0.614815 | − | 0.788672i | \(-0.289231\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 18.0000 | + | 18.0000i | 0.674105 | + | 0.674105i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 36.0000 | − | 12.0000i | 1.34632 | − | 0.448775i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −24.0000 | + | 24.0000i | −0.896296 | + | 0.896296i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 24.0000 | 0.895049 | 0.447524 | − | 0.894272i | \(-0.352306\pi\) | ||||
0.447524 | + | 0.894272i | \(0.352306\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 22.0000 | 0.819323 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −18.0000 | + | 18.0000i | −0.669427 | + | 0.669427i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −8.00000 | + | 6.00000i | −0.297113 | + | 0.222834i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 25.0000 | + | 25.0000i | 0.927199 | + | 0.927199i | 0.997524 | − | 0.0703254i | \(-0.0224038\pi\) |
−0.0703254 | + | 0.997524i | \(0.522404\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.0000i | 1.07407i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 18.0000i | 0.665754i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −15.0000 | − | 15.0000i | −0.554038 | − | 0.554038i | 0.373566 | − | 0.927604i | \(-0.378135\pi\) |
−0.927604 | + | 0.373566i | \(0.878135\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5.00000 | − | 15.0000i | −0.184428 | − | 0.553283i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −36.0000 | + | 36.0000i | −1.32608 | + | 1.32608i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 30.0000 | 1.10357 | 0.551784 | − | 0.833987i | \(-0.313947\pi\) | ||||
0.551784 | + | 0.833987i | \(0.313947\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −36.0000 | −1.32249 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −9.00000 | + | 9.00000i | −0.330178 | + | 0.330178i | −0.852654 | − | 0.522476i | \(-0.825008\pi\) |
0.522476 | + | 0.852654i | \(0.325008\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.00000 | + | 4.00000i | −0.0732743 | + | 0.146549i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.00000 | − | 3.00000i | −0.109764 | − | 0.109764i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.00000i | 0.219235i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 42.0000i | − | 1.53260i | −0.642482 | − | 0.766301i | \(-0.722095\pi\) | ||
0.642482 | − | 0.766301i | \(-0.277905\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4.00000 | − | 4.00000i | −0.145768 | − | 0.145768i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −10.0000 | + | 20.0000i | −0.363937 | + | 0.727875i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.00000 | − | 9.00000i | 0.327111 | − | 0.327111i | −0.524376 | − | 0.851487i | \(-0.675701\pi\) |
0.851487 | + | 0.524376i | \(0.175701\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 24.0000 | 0.871145 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18.0000 | −0.652499 | −0.326250 | − | 0.945284i | \(-0.605785\pi\) | ||||
−0.326250 | + | 0.945284i | \(0.605785\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 18.0000 | − | 18.0000i | 0.651644 | − | 0.651644i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.00000 | − | 9.00000i | −0.108465 | − | 0.325396i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −30.0000 | − | 30.0000i | −1.08324 | − | 1.08324i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 40.0000i | − | 1.44244i | −0.692708 | − | 0.721218i | \(-0.743582\pi\) | ||
0.692708 | − | 0.721218i | \(-0.256418\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.00000i | 0.216085i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −9.00000 | − | 9.00000i | −0.323708 | − | 0.323708i | 0.526480 | − | 0.850188i | \(-0.323511\pi\) |
−0.850188 | + | 0.526480i | \(0.823511\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −24.0000 | + | 18.0000i | −0.862105 | + | 0.646579i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −6.00000 | + | 6.00000i | −0.215249 | + | 0.215249i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −36.0000 | −1.28983 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 24.0000 | 0.858788 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −8.00000 | + | 8.00000i | −0.285897 | + | 0.285897i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9.00000 | − | 3.00000i | 0.321224 | − | 0.107075i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −15.0000 | − | 15.0000i | −0.534692 | − | 0.534692i | 0.387273 | − | 0.921965i | \(-0.373417\pi\) |
−0.921965 | + | 0.387273i | \(0.873417\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 18.0000i | 0.640817i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 6.00000i | − | 0.213335i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −36.0000 | − | 36.0000i | −1.27840 | − | 1.27840i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −20.0000 | − | 10.0000i | −0.709327 | − | 0.354663i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.00000 | − | 3.00000i | 0.106265 | − | 0.106265i | −0.651975 | − | 0.758240i | \(-0.726059\pi\) |
0.758240 | + | 0.651975i | \(0.226059\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 54.0000 | 1.91038 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 20.0000 | − | 20.0000i | 0.705785 | − | 0.705785i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 12.0000 | + | 6.00000i | 0.422944 | + | 0.211472i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 14.0000 | + | 14.0000i | 0.492823 | + | 0.492823i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 48.0000i | − | 1.68759i | −0.536666 | − | 0.843795i | \(-0.680316\pi\) | ||
0.536666 | − | 0.843795i | \(-0.319684\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12.0000i | 0.421377i | 0.977553 | + | 0.210688i | \(0.0675706\pi\) | ||||
−0.977553 | + | 0.210688i | \(0.932429\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.00000 | − | 2.00000i | −0.0701431 | − | 0.0701431i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 27.0000 | − | 9.00000i | 0.945769 | − | 0.315256i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 18.0000 | − | 18.0000i | 0.629740 | − | 0.629740i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.00000 | 0.209657 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 52.0000 | 1.81481 | 0.907406 | − | 0.420255i | \(-0.138059\pi\) | ||||
0.907406 | + | 0.420255i | \(0.138059\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.00000 | + | 5.00000i | −0.174289 | + | 0.174289i | −0.788861 | − | 0.614572i | \(-0.789329\pi\) |
0.614572 | + | 0.788861i | \(0.289329\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.00000 | + | 28.0000i | −0.139262 | + | 0.974835i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 23.0000 | + | 23.0000i | 0.799788 | + | 0.799788i | 0.983062 | − | 0.183274i | \(-0.0586694\pi\) |
−0.183274 | + | 0.983062i | \(0.558669\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 30.0000i | 1.04194i | 0.853574 | + | 0.520972i | \(0.174430\pi\) | ||||
−0.853574 | + | 0.520972i | \(0.825570\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 30.0000i | 1.04069i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 15.0000 | + | 15.0000i | 0.519719 | + | 0.519719i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.00000 | − | 9.00000i | −0.103819 | − | 0.311458i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −24.0000 | + | 24.0000i | −0.829561 | + | 0.829561i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 48.0000 | 1.65714 | 0.828572 | − | 0.559883i | \(-0.189154\pi\) | ||||
0.828572 | + | 0.559883i | \(0.189154\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25.0000 | 0.862069 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −6.00000 | + | 6.00000i | −0.206651 | + | 0.206651i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −5.00000 | + | 10.0000i | −0.172005 | + | 0.344010i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.00000 | − | 5.00000i | −0.171802 | − | 0.171802i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 30.0000i | − | 1.02960i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 18.0000i | 0.617032i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −9.00000 | − | 9.00000i | −0.308154 | − | 0.308154i | 0.536039 | − | 0.844193i | \(-0.319920\pi\) |
−0.844193 | + | 0.536039i | \(0.819920\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −6.00000 | + | 12.0000i | −0.205196 | + | 0.410391i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 27.0000 | − | 27.0000i | 0.922302 | − | 0.922302i | −0.0748894 | − | 0.997192i | \(-0.523860\pi\) |
0.997192 | + | 0.0748894i | \(0.0238604\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.00000 | −0.204717 | −0.102359 | − | 0.994748i | \(-0.532639\pi\) | ||||
−0.102359 | + | 0.994748i | \(0.532639\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −12.0000 | −0.408959 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −15.0000 | + | 15.0000i | −0.510606 | + | 0.510606i | −0.914712 | − | 0.404106i | \(-0.867583\pi\) |
0.404106 | + | 0.914712i | \(0.367583\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −15.0000 | − | 45.0000i | −0.510015 | − | 1.53005i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.00000 | − | 1.00000i | −0.0339618 | − | 0.0339618i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 54.0000i | − | 1.82972i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −7.00000 | − | 7.00000i | −0.236914 | − | 0.236914i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −9.00000 | + | 13.0000i | −0.304256 | + | 0.439480i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 27.0000 | − | 27.0000i | 0.911725 | − | 0.911725i | −0.0846827 | − | 0.996408i | \(-0.526988\pi\) |
0.996408 | + | 0.0846827i | \(0.0269877\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.00000 | −0.0674583 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 30.0000 | 1.01073 | 0.505363 | − | 0.862907i | \(-0.331359\pi\) | ||||
0.505363 | + | 0.862907i | \(0.331359\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9.00000 | − | 9.00000i | 0.302874 | − | 0.302874i | −0.539263 | − | 0.842137i | \(-0.681297\pi\) |
0.842137 | + | 0.539263i | \(0.181297\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 30.0000 | − | 10.0000i | 1.00844 | − | 0.336146i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 9.00000 | + | 9.00000i | 0.302190 | + | 0.302190i | 0.841870 | − | 0.539680i | \(-0.181455\pi\) |
−0.539680 | + | 0.841870i | \(0.681455\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 10.0000i | − | 0.335389i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 20.0000i | 0.670025i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −54.0000 | − | 54.0000i | −1.80704 | − | 1.80704i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.00000 | − | 2.00000i | −0.133705 | − | 0.0668526i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −18.0000 | + | 18.0000i | −0.601003 | + | 0.601003i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −12.0000 | −0.400222 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 30.0000 | 0.999445 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6.00000 | − | 6.00000i | 0.199667 | − | 0.199667i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.00000 | + | 3.00000i | 0.0996134 | + | 0.0996134i | 0.755157 | − | 0.655544i | \(-0.227561\pi\) |
−0.655544 | + | 0.755157i | \(0.727561\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 8.00000i | 0.265343i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.00000i | 0.198789i | 0.995048 | + | 0.0993944i | \(0.0316906\pi\) | ||||
−0.995048 | + | 0.0993944i | \(0.968309\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −12.0000 | − | 12.0000i | −0.397142 | − | 0.397142i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 36.0000 | − | 12.0000i | 1.19012 | − | 0.396708i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.00000 | − | 4.00000i | 0.132092 | − | 0.132092i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −48.0000 | −1.58337 | −0.791687 | − | 0.610927i | \(-0.790797\pi\) | ||||
−0.791687 | + | 0.610927i | \(0.790797\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −30.0000 | −0.988534 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −18.0000 | + | 18.0000i | −0.592477 | + | 0.592477i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −21.0000 | − | 3.00000i | −0.690476 | − | 0.0986394i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 11.0000 | + | 11.0000i | 0.361287 | + | 0.361287i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 12.0000i | 0.393707i | 0.980433 | + | 0.196854i | \(0.0630724\pi\) | ||||
−0.980433 | + | 0.196854i | \(0.936928\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 30.0000i | − | 0.983210i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 18.0000 | + | 18.0000i | 0.589294 | + | 0.589294i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −12.0000 | − | 36.0000i | −0.392442 | − | 1.17733i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 23.0000 | − | 23.0000i | 0.751377 | − | 0.751377i | −0.223359 | − | 0.974736i | \(-0.571702\pi\) |
0.974736 | + | 0.223359i | \(0.0717022\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.00000 | −0.0652675 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 32.0000 | 1.04317 | 0.521585 | − | 0.853199i | \(-0.325341\pi\) | ||||
0.521585 | + | 0.853199i | \(0.325341\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −18.0000 | + | 18.0000i | −0.586161 | + | 0.586161i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −8.00000 | + | 16.0000i | −0.260240 | + | 0.520480i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −7.00000 | − | 7.00000i | −0.227469 | − | 0.227469i | 0.584165 | − | 0.811635i | \(-0.301422\pi\) |
−0.811635 | + | 0.584165i | \(0.801422\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 30.0000i | 0.973841i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 6.00000i | − | 0.194563i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −9.00000 | − | 9.00000i | −0.291539 | − | 0.291539i | 0.546149 | − | 0.837688i | \(-0.316093\pi\) |
−0.837688 | + | 0.546149i | \(0.816093\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.00000 | + | 12.0000i | −0.194155 | + | 0.388311i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −8.00000 | + | 8.00000i | −0.258603 | + | 0.258603i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.00000 | 0.193750 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.00000 | −0.161290 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.00000 | + | 3.00000i | −0.0966736 | + | 0.0966736i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.00000 | + | 15.0000i | 0.160956 | + | 0.482867i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.00000 | + | 5.00000i | 0.160789 | + | 0.160789i | 0.782916 | − | 0.622127i | \(-0.213731\pi\) |
−0.622127 | + | 0.782916i | \(0.713731\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 36.0000i | 1.15649i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 20.0000i | − | 0.641831i | −0.947108 | − | 0.320915i | \(-0.896010\pi\) | ||
0.947108 | − | 0.320915i | \(-0.103990\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.00000 | − | 6.00000i | −0.192351 | − | 0.192351i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −18.0000 | − | 24.0000i | −0.576461 | − | 0.768615i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 9.00000 | − | 9.00000i | 0.287936 | − | 0.287936i | −0.548328 | − | 0.836263i | \(-0.684735\pi\) |
0.836263 | + | 0.548328i | \(0.184735\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 18.0000 | 0.574696 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −33.0000 | + | 33.0000i | −1.05254 | + | 1.05254i | −0.0539954 | + | 0.998541i | \(0.517196\pi\) |
−0.998541 | + | 0.0539954i | \(0.982804\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 15.0000 | − | 5.00000i | 0.477940 | − | 0.159313i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −18.0000 | − | 18.0000i | −0.572946 | − | 0.572946i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 18.0000i | − | 0.572367i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 2.00000i | − | 0.0635321i | −0.999495 | − | 0.0317660i | \(-0.989887\pi\) | ||
0.999495 | − | 0.0317660i | \(-0.0101131\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −12.0000 | − | 12.0000i | −0.380808 | − | 0.380808i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −32.0000 | − | 16.0000i | −1.01447 | − | 0.507234i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.00000 | − | 9.00000i | 0.285033 | − | 0.285033i | −0.550079 | − | 0.835112i | \(-0.685403\pi\) |
0.835112 | + | 0.550079i | \(0.185403\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −24.0000 | −0.759326 |
(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 | 1280.2.n.j.1023.1 | 2 | ||
4.3 | odd | 2 | 1280.2.n.d.1023.1 | 2 | |||
5.2 | odd | 4 | 1280.2.n.d.767.1 | 2 | |||
8.3 | odd | 2 | 1280.2.n.i.1023.1 | 2 | |||
8.5 | even | 2 | 1280.2.n.c.1023.1 | 2 | |||
16.3 | odd | 4 | 320.2.o.b.223.1 | yes | 2 | ||
16.5 | even | 4 | 320.2.o.a.223.1 | ✓ | 2 | ||
16.11 | odd | 4 | 320.2.o.c.223.1 | yes | 2 | ||
16.13 | even | 4 | 320.2.o.d.223.1 | yes | 2 | ||
20.7 | even | 4 | inner | 1280.2.n.j.767.1 | 2 | ||
40.27 | even | 4 | 1280.2.n.c.767.1 | 2 | |||
40.37 | odd | 4 | 1280.2.n.i.767.1 | 2 | |||
80.3 | even | 4 | 1600.2.o.d.607.1 | 2 | |||
80.13 | odd | 4 | 1600.2.o.a.607.1 | 2 | |||
80.19 | odd | 4 | 1600.2.o.c.543.1 | 2 | |||
80.27 | even | 4 | 320.2.o.d.287.1 | yes | 2 | ||
80.29 | even | 4 | 1600.2.o.b.543.1 | 2 | |||
80.37 | odd | 4 | 320.2.o.b.287.1 | yes | 2 | ||
80.43 | even | 4 | 1600.2.o.b.607.1 | 2 | |||
80.53 | odd | 4 | 1600.2.o.c.607.1 | 2 | |||
80.59 | odd | 4 | 1600.2.o.a.543.1 | 2 | |||
80.67 | even | 4 | 320.2.o.a.287.1 | yes | 2 | ||
80.69 | even | 4 | 1600.2.o.d.543.1 | 2 | |||
80.77 | odd | 4 | 320.2.o.c.287.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
320.2.o.a.223.1 | ✓ | 2 | 16.5 | even | 4 | ||
320.2.o.a.287.1 | yes | 2 | 80.67 | even | 4 | ||
320.2.o.b.223.1 | yes | 2 | 16.3 | odd | 4 | ||
320.2.o.b.287.1 | yes | 2 | 80.37 | odd | 4 | ||
320.2.o.c.223.1 | yes | 2 | 16.11 | odd | 4 | ||
320.2.o.c.287.1 | yes | 2 | 80.77 | odd | 4 | ||
320.2.o.d.223.1 | yes | 2 | 16.13 | even | 4 | ||
320.2.o.d.287.1 | yes | 2 | 80.27 | even | 4 | ||
1280.2.n.c.767.1 | 2 | 40.27 | even | 4 | |||
1280.2.n.c.1023.1 | 2 | 8.5 | even | 2 | |||
1280.2.n.d.767.1 | 2 | 5.2 | odd | 4 | |||
1280.2.n.d.1023.1 | 2 | 4.3 | odd | 2 | |||
1280.2.n.i.767.1 | 2 | 40.37 | odd | 4 | |||
1280.2.n.i.1023.1 | 2 | 8.3 | odd | 2 | |||
1280.2.n.j.767.1 | 2 | 20.7 | even | 4 | inner | ||
1280.2.n.j.1023.1 | 2 | 1.1 | even | 1 | trivial | ||
1600.2.o.a.543.1 | 2 | 80.59 | odd | 4 | |||
1600.2.o.a.607.1 | 2 | 80.13 | odd | 4 | |||
1600.2.o.b.543.1 | 2 | 80.29 | even | 4 | |||
1600.2.o.b.607.1 | 2 | 80.43 | even | 4 | |||
1600.2.o.c.543.1 | 2 | 80.19 | odd | 4 | |||
1600.2.o.c.607.1 | 2 | 80.53 | odd | 4 | |||
1600.2.o.d.543.1 | 2 | 80.69 | even | 4 | |||
1600.2.o.d.607.1 | 2 | 80.3 | even | 4 |