Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [950,2,Mod(493,950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(950, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("950.493");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 950 = 2 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 950.f (of order \(4\), degree \(2\), 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: | \(7.58578819202\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 190) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 493.2 | ||
Root | \(-0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 950.493 |
Dual form | 950.2.f.a.607.2 |
$q$-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 \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | + | 0.707107i | 0.500000 | + | 0.500000i | ||||
\(3\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | − | 1.00000i | 0.377964 | − | 0.377964i | −0.492403 | − | 0.870367i | \(-0.663881\pi\) |
0.870367 | + | 0.492403i | \(0.163881\pi\) | |||||||
\(8\) | −0.707107 | + | 0.707107i | −0.250000 | + | 0.250000i | ||||
\(9\) | 3.00000i | 1.00000i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.00000 | 0.603023 | 0.301511 | − | 0.953463i | \(-0.402509\pi\) | ||||
0.301511 | + | 0.953463i | \(0.402509\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.24264 | − | 4.24264i | 1.17670 | − | 1.17670i | 0.196116 | − | 0.980581i | \(-0.437167\pi\) |
0.980581 | − | 0.196116i | \(-0.0628330\pi\) | |||||||
\(14\) | 1.41421 | 0.377964 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −3.00000 | + | 3.00000i | −0.727607 | + | 0.727607i | −0.970143 | − | 0.242536i | \(-0.922021\pi\) |
0.242536 | + | 0.970143i | \(0.422021\pi\) | |||||||
\(18\) | −2.12132 | + | 2.12132i | −0.500000 | + | 0.500000i | ||||
\(19\) | 4.24264 | + | 1.00000i | 0.973329 | + | 0.229416i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.41421 | + | 1.41421i | 0.301511 | + | 0.301511i | ||||
\(23\) | −1.00000 | − | 1.00000i | −0.208514 | − | 0.208514i | 0.595121 | − | 0.803636i | \(-0.297104\pi\) |
−0.803636 | + | 0.595121i | \(0.797104\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 6.00000 | 1.17670 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.00000 | + | 1.00000i | 0.188982 | + | 0.188982i | ||||
\(29\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.48528i | 1.52400i | 0.647576 | + | 0.762001i | \(0.275783\pi\) | ||||
−0.647576 | + | 0.762001i | \(0.724217\pi\) | |||||||
\(32\) | −0.707107 | − | 0.707107i | −0.125000 | − | 0.125000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.24264 | −0.727607 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −3.00000 | −0.500000 | ||||||||
\(37\) | 4.24264 | + | 4.24264i | 0.697486 | + | 0.697486i | 0.963868 | − | 0.266382i | \(-0.0858282\pi\) |
−0.266382 | + | 0.963868i | \(0.585828\pi\) | |||||||
\(38\) | 2.29289 | + | 3.70711i | 0.371956 | + | 0.601372i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 8.48528i | − | 1.32518i | −0.748983 | − | 0.662589i | \(-0.769458\pi\) | ||
0.748983 | − | 0.662589i | \(-0.230542\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.00000 | + | 5.00000i | 0.762493 | + | 0.762493i | 0.976772 | − | 0.214280i | \(-0.0687403\pi\) |
−0.214280 | + | 0.976772i | \(0.568740\pi\) | |||||||
\(44\) | 2.00000i | 0.301511i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | − | 1.41421i | − | 0.208514i | ||||||
\(47\) | −7.00000 | + | 7.00000i | −1.02105 | + | 1.02105i | −0.0212814 | + | 0.999774i | \(0.506775\pi\) |
−0.999774 | + | 0.0212814i | \(0.993225\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.00000i | 0.714286i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4.24264 | + | 4.24264i | 0.588348 | + | 0.588348i | ||||
\(53\) | 4.24264 | − | 4.24264i | 0.582772 | − | 0.582772i | −0.352892 | − | 0.935664i | \(-0.614802\pi\) |
0.935664 | + | 0.352892i | \(0.114802\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.41421i | 0.188982i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.00000 | 1.02430 | 0.512148 | − | 0.858898i | \(-0.328850\pi\) | ||||
0.512148 | + | 0.858898i | \(0.328850\pi\) | |||||||
\(62\) | −6.00000 | + | 6.00000i | −0.762001 | + | 0.762001i | ||||
\(63\) | 3.00000 | + | 3.00000i | 0.377964 | + | 0.377964i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.48528 | − | 8.48528i | −1.03664 | − | 1.03664i | −0.999303 | − | 0.0373395i | \(-0.988112\pi\) |
−0.0373395 | − | 0.999303i | \(-0.511888\pi\) | |||||||
\(68\) | −3.00000 | − | 3.00000i | −0.363803 | − | 0.363803i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 8.48528i | − | 1.00702i | −0.863990 | − | 0.503509i | \(-0.832042\pi\) | ||
0.863990 | − | 0.503509i | \(-0.167958\pi\) | |||||||
\(72\) | −2.12132 | − | 2.12132i | −0.250000 | − | 0.250000i | ||||
\(73\) | 1.00000 | + | 1.00000i | 0.117041 | + | 0.117041i | 0.763202 | − | 0.646160i | \(-0.223626\pi\) |
−0.646160 | + | 0.763202i | \(0.723626\pi\) | |||||||
\(74\) | 6.00000i | 0.697486i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.00000 | + | 4.24264i | −0.114708 | + | 0.486664i | ||||
\(77\) | 2.00000 | − | 2.00000i | 0.227921 | − | 0.227921i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.48528 | 0.954669 | 0.477334 | − | 0.878722i | \(-0.341603\pi\) | ||||
0.477334 | + | 0.878722i | \(0.341603\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.00000 | −1.00000 | ||||||||
\(82\) | 6.00000 | − | 6.00000i | 0.662589 | − | 0.662589i | ||||
\(83\) | −9.00000 | − | 9.00000i | −0.987878 | − | 0.987878i | 0.0120491 | − | 0.999927i | \(-0.496165\pi\) |
−0.999927 | + | 0.0120491i | \(0.996165\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 7.07107i | 0.762493i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.41421 | + | 1.41421i | −0.150756 | + | 0.150756i | ||||
\(89\) | 8.48528 | 0.899438 | 0.449719 | − | 0.893170i | \(-0.351524\pi\) | ||||
0.449719 | + | 0.893170i | \(0.351524\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 8.48528i | − | 0.889499i | ||||||
\(92\) | 1.00000 | − | 1.00000i | 0.104257 | − | 0.104257i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −9.89949 | −1.02105 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.24264 | − | 4.24264i | −0.430775 | − | 0.430775i | 0.458117 | − | 0.888892i | \(-0.348524\pi\) |
−0.888892 | + | 0.458117i | \(0.848524\pi\) | |||||||
\(98\) | −3.53553 | + | 3.53553i | −0.357143 | + | 0.357143i | ||||
\(99\) | 6.00000i | 0.603023i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.00000 | 0.398015 | 0.199007 | − | 0.979998i | \(-0.436228\pi\) | ||||
0.199007 | + | 0.979998i | \(0.436228\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.48528 | + | 8.48528i | −0.836080 | + | 0.836080i | −0.988340 | − | 0.152261i | \(-0.951345\pi\) |
0.152261 | + | 0.988340i | \(0.451345\pi\) | |||||||
\(104\) | 6.00000i | 0.588348i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.00000 | 0.582772 | ||||||||
\(107\) | −8.48528 | − | 8.48528i | −0.820303 | − | 0.820303i | 0.165848 | − | 0.986151i | \(-0.446964\pi\) |
−0.986151 | + | 0.165848i | \(0.946964\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.48528 | −0.812743 | −0.406371 | − | 0.913708i | \(-0.633206\pi\) | ||||
−0.406371 | + | 0.913708i | \(0.633206\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.00000 | + | 1.00000i | −0.0944911 | + | 0.0944911i | ||||
\(113\) | −4.24264 | + | 4.24264i | −0.399114 | + | 0.399114i | −0.877920 | − | 0.478806i | \(-0.841070\pi\) |
0.478806 | + | 0.877920i | \(0.341070\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 12.7279 | + | 12.7279i | 1.17670 | + | 1.17670i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.00000i | 0.550019i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | 5.65685 | + | 5.65685i | 0.512148 | + | 0.512148i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −8.48528 | −0.762001 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 4.24264i | 0.377964i | ||||||||
\(127\) | −8.48528 | − | 8.48528i | −0.752947 | − | 0.752947i | 0.222081 | − | 0.975028i | \(-0.428715\pi\) |
−0.975028 | + | 0.222081i | \(0.928715\pi\) | |||||||
\(128\) | 0.707107 | − | 0.707107i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.00000 | 0.349482 | 0.174741 | − | 0.984614i | \(-0.444091\pi\) | ||||
0.174741 | + | 0.984614i | \(0.444091\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.24264 | − | 3.24264i | 0.454595 | − | 0.281173i | ||||
\(134\) | − | 12.0000i | − | 1.03664i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 4.24264i | − | 0.363803i | ||||||
\(137\) | 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 | ||||||||
\(139\) | − | 12.0000i | − | 1.01783i | −0.860818 | − | 0.508913i | \(-0.830047\pi\) | ||
0.860818 | − | 0.508913i | \(-0.169953\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 6.00000 | − | 6.00000i | 0.503509 | − | 0.503509i | ||||
\(143\) | 8.48528 | − | 8.48528i | 0.709575 | − | 0.709575i | ||||
\(144\) | − | 3.00000i | − | 0.250000i | ||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.41421i | 0.117041i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.24264 | + | 4.24264i | −0.348743 | + | 0.348743i | ||||
\(149\) | − | 10.0000i | − | 0.819232i | −0.912258 | − | 0.409616i | \(-0.865663\pi\) | ||
0.912258 | − | 0.409616i | \(-0.134337\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 16.9706i | − | 1.38104i | −0.723311 | − | 0.690522i | \(-0.757381\pi\) | ||
0.723311 | − | 0.690522i | \(-0.242619\pi\) | |||||||
\(152\) | −3.70711 | + | 2.29289i | −0.300686 | + | 0.185978i | ||||
\(153\) | −9.00000 | − | 9.00000i | −0.727607 | − | 0.727607i | ||||
\(154\) | 2.82843 | 0.227921 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.0000 | − | 11.0000i | 0.877896 | − | 0.877896i | −0.115421 | − | 0.993317i | \(-0.536822\pi\) |
0.993317 | + | 0.115421i | \(0.0368217\pi\) | |||||||
\(158\) | 6.00000 | + | 6.00000i | 0.477334 | + | 0.477334i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.00000 | −0.157622 | ||||||||
\(162\) | −6.36396 | − | 6.36396i | −0.500000 | − | 0.500000i | ||||
\(163\) | 7.00000 | + | 7.00000i | 0.548282 | + | 0.548282i | 0.925944 | − | 0.377661i | \(-0.123272\pi\) |
−0.377661 | + | 0.925944i | \(0.623272\pi\) | |||||||
\(164\) | 8.48528 | 0.662589 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 12.7279i | − | 0.987878i | ||||||
\(167\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 23.0000i | − | 1.76923i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.00000 | + | 12.7279i | −0.229416 | + | 0.973329i | ||||
\(172\) | −5.00000 | + | 5.00000i | −0.381246 | + | 0.381246i | ||||
\(173\) | 12.7279 | − | 12.7279i | 0.967686 | − | 0.967686i | −0.0318080 | − | 0.999494i | \(-0.510127\pi\) |
0.999494 | + | 0.0318080i | \(0.0101265\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.00000 | −0.150756 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 6.00000 | + | 6.00000i | 0.449719 | + | 0.449719i | ||||
\(179\) | −16.9706 | −1.26844 | −0.634220 | − | 0.773153i | \(-0.718679\pi\) | ||||
−0.634220 | + | 0.773153i | \(0.718679\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 25.4558i | 1.89212i | 0.323994 | + | 0.946059i | \(0.394974\pi\) | ||||
−0.323994 | + | 0.946059i | \(0.605026\pi\) | |||||||
\(182\) | 6.00000 | − | 6.00000i | 0.444750 | − | 0.444750i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.41421 | 0.104257 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.00000 | + | 6.00000i | −0.438763 | + | 0.438763i | ||||
\(188\) | −7.00000 | − | 7.00000i | −0.510527 | − | 0.510527i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.0000 | −1.15772 | −0.578860 | − | 0.815427i | \(-0.696502\pi\) | ||||
−0.578860 | + | 0.815427i | \(0.696502\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.24264 | + | 4.24264i | −0.305392 | + | 0.305392i | −0.843119 | − | 0.537727i | \(-0.819283\pi\) |
0.537727 | + | 0.843119i | \(0.319283\pi\) | |||||||
\(194\) | − | 6.00000i | − | 0.430775i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.00000 | −0.357143 | ||||||||
\(197\) | −5.00000 | + | 5.00000i | −0.356235 | + | 0.356235i | −0.862423 | − | 0.506188i | \(-0.831054\pi\) |
0.506188 | + | 0.862423i | \(0.331054\pi\) | |||||||
\(198\) | −4.24264 | + | 4.24264i | −0.301511 | + | 0.301511i | ||||
\(199\) | − | 18.0000i | − | 1.27599i | −0.770042 | − | 0.637993i | \(-0.779765\pi\) | ||
0.770042 | − | 0.637993i | \(-0.220235\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.82843 | + | 2.82843i | 0.199007 | + | 0.199007i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −12.0000 | −0.836080 | ||||||||
\(207\) | 3.00000 | − | 3.00000i | 0.208514 | − | 0.208514i | ||||
\(208\) | −4.24264 | + | 4.24264i | −0.294174 | + | 0.294174i | ||||
\(209\) | 8.48528 | + | 2.00000i | 0.586939 | + | 0.138343i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 8.48528i | − | 0.584151i | −0.956395 | − | 0.292075i | \(-0.905654\pi\) | ||
0.956395 | − | 0.292075i | \(-0.0943458\pi\) | |||||||
\(212\) | 4.24264 | + | 4.24264i | 0.291386 | + | 0.291386i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | − | 12.0000i | − | 0.820303i | ||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.48528 | + | 8.48528i | 0.576018 | + | 0.576018i | ||||
\(218\) | −6.00000 | − | 6.00000i | −0.406371 | − | 0.406371i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 25.4558i | 1.71235i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(224\) | −1.41421 | −0.0944911 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.00000 | −0.399114 | ||||||||
\(227\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.00000i | 0.396491i | 0.980152 | + | 0.198246i | \(0.0635244\pi\) | ||||
−0.980152 | + | 0.198246i | \(0.936476\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.00000 | − | 5.00000i | −0.327561 | − | 0.327561i | 0.524097 | − | 0.851658i | \(-0.324403\pi\) |
−0.851658 | + | 0.524097i | \(0.824403\pi\) | |||||||
\(234\) | 18.0000i | 1.17670i | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −4.24264 | + | 4.24264i | −0.275010 | + | 0.275010i | ||||
\(239\) | 10.0000i | 0.646846i | 0.946254 | + | 0.323423i | \(0.104834\pi\) | ||||
−0.946254 | + | 0.323423i | \(0.895166\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.48528i | 0.546585i | 0.961931 | + | 0.273293i | \(0.0881127\pi\) | ||||
−0.961931 | + | 0.273293i | \(0.911887\pi\) | |||||||
\(242\) | −4.94975 | − | 4.94975i | −0.318182 | − | 0.318182i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 8.00000i | 0.512148i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 22.2426 | − | 13.7574i | 1.41527 | − | 0.875360i | ||||
\(248\) | −6.00000 | − | 6.00000i | −0.381000 | − | 0.381000i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −20.0000 | −1.26239 | −0.631194 | − | 0.775625i | \(-0.717435\pi\) | ||||
−0.631194 | + | 0.775625i | \(0.717435\pi\) | |||||||
\(252\) | −3.00000 | + | 3.00000i | −0.188982 | + | 0.188982i | ||||
\(253\) | −2.00000 | − | 2.00000i | −0.125739 | − | 0.125739i | ||||
\(254\) | − | 12.0000i | − | 0.752947i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 4.24264 | + | 4.24264i | 0.264649 | + | 0.264649i | 0.826940 | − | 0.562291i | \(-0.190080\pi\) |
−0.562291 | + | 0.826940i | \(0.690080\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.48528 | 0.527250 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2.82843 | + | 2.82843i | 0.174741 | + | 0.174741i | ||||
\(263\) | −3.00000 | − | 3.00000i | −0.184988 | − | 0.184988i | 0.608537 | − | 0.793525i | \(-0.291757\pi\) |
−0.793525 | + | 0.608537i | \(0.791757\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 6.00000 | + | 1.41421i | 0.367884 | + | 0.0867110i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 8.48528 | − | 8.48528i | 0.518321 | − | 0.518321i | ||||
\(269\) | 8.48528 | 0.517357 | 0.258678 | − | 0.965964i | \(-0.416713\pi\) | ||||
0.258678 | + | 0.965964i | \(0.416713\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 30.0000 | 1.82237 | 0.911185 | − | 0.411997i | \(-0.135169\pi\) | ||||
0.911185 | + | 0.411997i | \(0.135169\pi\) | |||||||
\(272\) | 3.00000 | − | 3.00000i | 0.181902 | − | 0.181902i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4.24264 | 0.256307 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.00000 | − | 7.00000i | 0.420589 | − | 0.420589i | −0.464817 | − | 0.885407i | \(-0.653880\pi\) |
0.885407 | + | 0.464817i | \(0.153880\pi\) | |||||||
\(278\) | 8.48528 | − | 8.48528i | 0.508913 | − | 0.508913i | ||||
\(279\) | −25.4558 | −1.52400 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 25.4558i | − | 1.51857i | −0.650759 | − | 0.759284i | \(-0.725549\pi\) | ||
0.650759 | − | 0.759284i | \(-0.274451\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −19.0000 | − | 19.0000i | −1.12943 | − | 1.12943i | −0.990269 | − | 0.139163i | \(-0.955559\pi\) |
−0.139163 | − | 0.990269i | \(-0.544441\pi\) | |||||||
\(284\) | 8.48528 | 0.503509 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 12.0000 | 0.709575 | ||||||||
\(287\) | −8.48528 | − | 8.48528i | −0.500870 | − | 0.500870i | ||||
\(288\) | 2.12132 | − | 2.12132i | 0.125000 | − | 0.125000i | ||||
\(289\) | − | 1.00000i | − | 0.0588235i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.00000 | + | 1.00000i | −0.0585206 | + | 0.0585206i | ||||
\(293\) | −4.24264 | + | 4.24264i | −0.247858 | + | 0.247858i | −0.820091 | − | 0.572233i | \(-0.806077\pi\) |
0.572233 | + | 0.820091i | \(0.306077\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −6.00000 | −0.348743 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 7.07107 | − | 7.07107i | 0.409616 | − | 0.409616i | ||||
\(299\) | −8.48528 | −0.490716 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.0000 | 0.576390 | ||||||||
\(302\) | 12.0000 | − | 12.0000i | 0.690522 | − | 0.690522i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −4.24264 | − | 1.00000i | −0.243332 | − | 0.0573539i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | − | 12.7279i | − | 0.727607i | ||||||
\(307\) | 8.48528 | + | 8.48528i | 0.484281 | + | 0.484281i | 0.906496 | − | 0.422215i | \(-0.138747\pi\) |
−0.422215 | + | 0.906496i | \(0.638747\pi\) | |||||||
\(308\) | 2.00000 | + | 2.00000i | 0.113961 | + | 0.113961i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −22.0000 | −1.24751 | −0.623753 | − | 0.781622i | \(-0.714393\pi\) | ||||
−0.623753 | + | 0.781622i | \(0.714393\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.00000 | − | 1.00000i | −0.0565233 | − | 0.0565233i | 0.678280 | − | 0.734803i | \(-0.262726\pi\) |
−0.734803 | + | 0.678280i | \(0.762726\pi\) | |||||||
\(314\) | 15.5563 | 0.877896 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.48528i | 0.477334i | ||||||||
\(317\) | −4.24264 | − | 4.24264i | −0.238290 | − | 0.238290i | 0.577851 | − | 0.816142i | \(-0.303891\pi\) |
−0.816142 | + | 0.577851i | \(0.803891\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.41421 | − | 1.41421i | −0.0788110 | − | 0.0788110i | ||||
\(323\) | −15.7279 | + | 9.72792i | −0.875125 | + | 0.541276i | ||||
\(324\) | − | 9.00000i | − | 0.500000i | ||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 9.89949i | 0.548282i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 6.00000 | + | 6.00000i | 0.331295 | + | 0.331295i | ||||
\(329\) | 14.0000i | 0.771845i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 8.48528i | − | 0.466393i | −0.972430 | − | 0.233197i | \(-0.925081\pi\) | ||
0.972430 | − | 0.233197i | \(-0.0749186\pi\) | |||||||
\(332\) | 9.00000 | − | 9.00000i | 0.493939 | − | 0.493939i | ||||
\(333\) | −12.7279 | + | 12.7279i | −0.697486 | + | 0.697486i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.24264 | + | 4.24264i | 0.231111 | + | 0.231111i | 0.813156 | − | 0.582045i | \(-0.197747\pi\) |
−0.582045 | + | 0.813156i | \(0.697747\pi\) | |||||||
\(338\) | 16.2635 | − | 16.2635i | 0.884615 | − | 0.884615i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 16.9706i | 0.919007i | ||||||||
\(342\) | −11.1213 | + | 6.87868i | −0.601372 | + | 0.371956i | ||||
\(343\) | 12.0000 | + | 12.0000i | 0.647939 | + | 0.647939i | ||||
\(344\) | −7.07107 | −0.381246 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 18.0000 | 0.967686 | ||||||||
\(347\) | 15.0000 | − | 15.0000i | 0.805242 | − | 0.805242i | −0.178667 | − | 0.983910i | \(-0.557179\pi\) |
0.983910 | + | 0.178667i | \(0.0571786\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.41421 | − | 1.41421i | −0.0753778 | − | 0.0753778i | ||||
\(353\) | 25.0000 | + | 25.0000i | 1.33062 | + | 1.33062i | 0.904819 | + | 0.425797i | \(0.140006\pi\) |
0.425797 | + | 0.904819i | \(0.359994\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 8.48528i | 0.449719i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −12.0000 | − | 12.0000i | −0.634220 | − | 0.634220i | ||||
\(359\) | − | 8.00000i | − | 0.422224i | −0.977462 | − | 0.211112i | \(-0.932292\pi\) | ||
0.977462 | − | 0.211112i | \(-0.0677085\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.0000 | + | 8.48528i | 0.894737 | + | 0.446594i | ||||
\(362\) | −18.0000 | + | 18.0000i | −0.946059 | + | 0.946059i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 8.48528 | 0.444750 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −17.0000 | + | 17.0000i | −0.887393 | + | 0.887393i | −0.994272 | − | 0.106879i | \(-0.965914\pi\) |
0.106879 | + | 0.994272i | \(0.465914\pi\) | |||||||
\(368\) | 1.00000 | + | 1.00000i | 0.0521286 | + | 0.0521286i | ||||
\(369\) | 25.4558 | 1.32518 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 8.48528i | − | 0.440534i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.24264 | + | 4.24264i | −0.219676 | + | 0.219676i | −0.808362 | − | 0.588686i | \(-0.799645\pi\) |
0.588686 | + | 0.808362i | \(0.299645\pi\) | |||||||
\(374\) | −8.48528 | −0.438763 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 9.89949i | − | 0.510527i | ||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −25.4558 | −1.30758 | −0.653789 | − | 0.756677i | \(-0.726822\pi\) | ||||
−0.653789 | + | 0.756677i | \(0.726822\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −11.3137 | − | 11.3137i | −0.578860 | − | 0.578860i | ||||
\(383\) | −25.4558 | + | 25.4558i | −1.30073 | + | 1.30073i | −0.372835 | + | 0.927898i | \(0.621614\pi\) |
−0.927898 | + | 0.372835i | \(0.878386\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −6.00000 | −0.305392 | ||||||||
\(387\) | −15.0000 | + | 15.0000i | −0.762493 | + | 0.762493i | ||||
\(388\) | 4.24264 | − | 4.24264i | 0.215387 | − | 0.215387i | ||||
\(389\) | 4.00000i | 0.202808i | 0.994845 | + | 0.101404i | \(0.0323335\pi\) | ||||
−0.994845 | + | 0.101404i | \(0.967667\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.00000 | 0.303433 | ||||||||
\(392\) | −3.53553 | − | 3.53553i | −0.178571 | − | 0.178571i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −7.07107 | −0.356235 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −6.00000 | −0.301511 | ||||||||
\(397\) | −25.0000 | + | 25.0000i | −1.25471 | + | 1.25471i | −0.301131 | + | 0.953583i | \(0.597364\pi\) |
−0.953583 | + | 0.301131i | \(0.902636\pi\) | |||||||
\(398\) | 12.7279 | − | 12.7279i | 0.637993 | − | 0.637993i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 33.9411i | − | 1.69494i | −0.530844 | − | 0.847469i | \(-0.678125\pi\) | ||
0.530844 | − | 0.847469i | \(-0.321875\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 36.0000 | + | 36.0000i | 1.79329 | + | 1.79329i | ||||
\(404\) | 4.00000i | 0.199007i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.48528 | + | 8.48528i | 0.420600 | + | 0.420600i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16.9706 | 0.839140 | 0.419570 | − | 0.907723i | \(-0.362181\pi\) | ||||
0.419570 | + | 0.907723i | \(0.362181\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −8.48528 | − | 8.48528i | −0.418040 | − | 0.418040i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 4.24264 | 0.208514 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −6.00000 | −0.294174 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 4.58579 | + | 7.41421i | 0.224298 | + | 0.362641i | ||||
\(419\) | 2.00000i | 0.0977064i | 0.998806 | + | 0.0488532i | \(0.0155566\pi\) | ||||
−0.998806 | + | 0.0488532i | \(0.984443\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 33.9411i | 1.65419i | 0.562063 | + | 0.827095i | \(0.310008\pi\) | ||||
−0.562063 | + | 0.827095i | \(0.689992\pi\) | |||||||
\(422\) | 6.00000 | − | 6.00000i | 0.292075 | − | 0.292075i | ||||
\(423\) | −21.0000 | − | 21.0000i | −1.02105 | − | 1.02105i | ||||
\(424\) | 6.00000i | 0.291386i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.00000 | − | 8.00000i | 0.387147 | − | 0.387147i | ||||
\(428\) | 8.48528 | − | 8.48528i | 0.410152 | − | 0.410152i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 16.9706i | − | 0.817443i | −0.912659 | − | 0.408722i | \(-0.865975\pi\) | ||
0.912659 | − | 0.408722i | \(-0.134025\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 21.2132 | − | 21.2132i | 1.01944 | − | 1.01944i | 0.0196343 | − | 0.999807i | \(-0.493750\pi\) |
0.999807 | − | 0.0196343i | \(-0.00625018\pi\) | |||||||
\(434\) | 12.0000i | 0.576018i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | − | 8.48528i | − | 0.406371i | ||||||
\(437\) | −3.24264 | − | 5.24264i | −0.155117 | − | 0.250790i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −25.4558 | −1.21494 | −0.607471 | − | 0.794342i | \(-0.707816\pi\) | ||||
−0.607471 | + | 0.794342i | \(0.707816\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −15.0000 | −0.714286 | ||||||||
\(442\) | −18.0000 | + | 18.0000i | −0.856173 | + | 0.856173i | ||||
\(443\) | 7.00000 | + | 7.00000i | 0.332580 | + | 0.332580i | 0.853566 | − | 0.520985i | \(-0.174435\pi\) |
−0.520985 | + | 0.853566i | \(0.674435\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.00000 | − | 1.00000i | −0.0472456 | − | 0.0472456i | ||||
\(449\) | 16.9706 | 0.800890 | 0.400445 | − | 0.916321i | \(-0.368855\pi\) | ||||
0.400445 | + | 0.916321i | \(0.368855\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 16.9706i | − | 0.799113i | ||||||
\(452\) | −4.24264 | − | 4.24264i | −0.199557 | − | 0.199557i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.00000 | − | 7.00000i | 0.327446 | − | 0.327446i | −0.524168 | − | 0.851615i | \(-0.675624\pi\) |
0.851615 | + | 0.524168i | \(0.175624\pi\) | |||||||
\(458\) | −4.24264 | + | 4.24264i | −0.198246 | + | 0.198246i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −14.0000 | −0.652045 | −0.326023 | − | 0.945362i | \(-0.605709\pi\) | ||||
−0.326023 | + | 0.945362i | \(0.605709\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.00000 | − | 5.00000i | −0.232370 | − | 0.232370i | 0.581311 | − | 0.813681i | \(-0.302540\pi\) |
−0.813681 | + | 0.581311i | \(0.802540\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | − | 7.07107i | − | 0.327561i | ||||||
\(467\) | −13.0000 | + | 13.0000i | −0.601568 | + | 0.601568i | −0.940729 | − | 0.339160i | \(-0.889857\pi\) |
0.339160 | + | 0.940729i | \(0.389857\pi\) | |||||||
\(468\) | −12.7279 | + | 12.7279i | −0.588348 | + | 0.588348i | ||||
\(469\) | −16.9706 | −0.783628 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 10.0000 | + | 10.0000i | 0.459800 | + | 0.459800i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −6.00000 | −0.275010 | ||||||||
\(477\) | 12.7279 | + | 12.7279i | 0.582772 | + | 0.582772i | ||||
\(478\) | −7.07107 | + | 7.07107i | −0.323423 | + | 0.323423i | ||||
\(479\) | 32.0000i | 1.46212i | 0.682315 | + | 0.731059i | \(0.260973\pi\) | ||||
−0.682315 | + | 0.731059i | \(0.739027\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 36.0000 | 1.64146 | ||||||||
\(482\) | −6.00000 | + | 6.00000i | −0.273293 | + | 0.273293i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | − | 7.00000i | − | 0.318182i | ||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 25.4558 | + | 25.4558i | 1.15351 | + | 1.15351i | 0.985843 | + | 0.167671i | \(0.0536248\pi\) |
0.167671 | + | 0.985843i | \(0.446375\pi\) | |||||||
\(488\) | −5.65685 | + | 5.65685i | −0.256074 | + | 0.256074i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 28.0000 | 1.26362 | 0.631811 | − | 0.775122i | \(-0.282312\pi\) | ||||
0.631811 | + | 0.775122i | \(0.282312\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 25.4558 | + | 6.00000i | 1.14531 | + | 0.269953i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 8.48528i | − | 0.381000i | ||||||
\(497\) | −8.48528 | − | 8.48528i | −0.380617 | − | 0.380617i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 36.0000i | 1.61158i | 0.592200 | + | 0.805791i | \(0.298259\pi\) | ||||
−0.592200 | + | 0.805791i | \(0.701741\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −14.1421 | − | 14.1421i | −0.631194 | − | 0.631194i | ||||
\(503\) | 15.0000 | + | 15.0000i | 0.668817 | + | 0.668817i | 0.957442 | − | 0.288625i | \(-0.0931982\pi\) |
−0.288625 | + | 0.957442i | \(0.593198\pi\) | |||||||
\(504\) | −4.24264 | −0.188982 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 2.82843i | − | 0.125739i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 8.48528 | − | 8.48528i | 0.376473 | − | 0.376473i | ||||
\(509\) | −33.9411 | −1.50441 | −0.752207 | − | 0.658927i | \(-0.771011\pi\) | ||||
−0.752207 | + | 0.658927i | \(0.771011\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.00000 | 0.0884748 | ||||||||
\(512\) | 0.707107 | + | 0.707107i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 6.00000i | 0.264649i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −14.0000 | + | 14.0000i | −0.615719 | + | 0.615719i | ||||
\(518\) | 6.00000 | + | 6.00000i | 0.263625 | + | 0.263625i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 33.9411i | 1.48699i | 0.668743 | + | 0.743494i | \(0.266833\pi\) | ||||
−0.668743 | + | 0.743494i | \(0.733167\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16.9706 | + | 16.9706i | −0.742071 | + | 0.742071i | −0.972976 | − | 0.230905i | \(-0.925831\pi\) |
0.230905 | + | 0.972976i | \(0.425831\pi\) | |||||||
\(524\) | 4.00000i | 0.174741i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | − | 4.24264i | − | 0.184988i | ||||||
\(527\) | −25.4558 | − | 25.4558i | −1.10887 | − | 1.10887i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 21.0000i | − | 0.913043i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 3.24264 | + | 5.24264i | 0.140586 | + | 0.227297i | ||||
\(533\) | −36.0000 | − | 36.0000i | −1.55933 | − | 1.55933i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 12.0000 | 0.518321 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 6.00000 | + | 6.00000i | 0.258678 | + | 0.258678i | ||||
\(539\) | 10.0000i | 0.430730i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.0000 | 0.515920 | 0.257960 | − | 0.966156i | \(-0.416950\pi\) | ||||
0.257960 | + | 0.966156i | \(0.416950\pi\) | |||||||
\(542\) | 21.2132 | + | 21.2132i | 0.911185 | + | 0.911185i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4.24264 | 0.181902 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.48528 | − | 8.48528i | −0.362804 | − | 0.362804i | 0.502040 | − | 0.864844i | \(-0.332583\pi\) |
−0.864844 | + | 0.502040i | \(0.832583\pi\) | |||||||
\(548\) | 3.00000 | + | 3.00000i | 0.128154 | + | 0.128154i | ||||
\(549\) | 24.0000i | 1.02430i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.48528 | − | 8.48528i | 0.360831 | − | 0.360831i | ||||
\(554\) | 9.89949 | 0.420589 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 12.0000 | 0.508913 | ||||||||
\(557\) | 23.0000 | − | 23.0000i | 0.974541 | − | 0.974541i | −0.0251426 | − | 0.999684i | \(-0.508004\pi\) |
0.999684 | + | 0.0251426i | \(0.00800398\pi\) | |||||||
\(558\) | −18.0000 | − | 18.0000i | −0.762001 | − | 0.762001i | ||||
\(559\) | 42.4264 | 1.79445 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 18.0000 | − | 18.0000i | 0.759284 | − | 0.759284i | ||||
\(563\) | −25.4558 | + | 25.4558i | −1.07284 | + | 1.07284i | −0.0757057 | + | 0.997130i | \(0.524121\pi\) |
−0.997130 | + | 0.0757057i | \(0.975879\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 26.8701i | − | 1.12943i | ||||||
\(567\) | −9.00000 | + | 9.00000i | −0.377964 | + | 0.377964i | ||||
\(568\) | 6.00000 | + | 6.00000i | 0.251754 | + | 0.251754i | ||||
\(569\) | 16.9706 | 0.711443 | 0.355722 | − | 0.934592i | \(-0.384235\pi\) | ||||
0.355722 | + | 0.934592i | \(0.384235\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.00000 | −0.251092 | −0.125546 | − | 0.992088i | \(-0.540068\pi\) | ||||
−0.125546 | + | 0.992088i | \(0.540068\pi\) | |||||||
\(572\) | 8.48528 | + | 8.48528i | 0.354787 | + | 0.354787i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − | 12.0000i | − | 0.500870i | ||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 3.00000 | 0.125000 | ||||||||
\(577\) | 23.0000 | − | 23.0000i | 0.957503 | − | 0.957503i | −0.0416305 | − | 0.999133i | \(-0.513255\pi\) |
0.999133 | + | 0.0416305i | \(0.0132552\pi\) | |||||||
\(578\) | 0.707107 | − | 0.707107i | 0.0294118 | − | 0.0294118i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −18.0000 | −0.746766 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.48528 | − | 8.48528i | 0.351424 | − | 0.351424i | ||||
\(584\) | −1.41421 | −0.0585206 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6.00000 | −0.247858 | ||||||||
\(587\) | −11.0000 | + | 11.0000i | −0.454019 | + | 0.454019i | −0.896686 | − | 0.442667i | \(-0.854032\pi\) |
0.442667 | + | 0.896686i | \(0.354032\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.48528 | + | 36.0000i | −0.349630 | + | 1.48335i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.24264 | − | 4.24264i | −0.174371 | − | 0.174371i | ||||
\(593\) | −21.0000 | − | 21.0000i | −0.862367 | − | 0.862367i | 0.129246 | − | 0.991613i | \(-0.458744\pi\) |
−0.991613 | + | 0.129246i | \(0.958744\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 10.0000 | 0.409616 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −6.00000 | − | 6.00000i | −0.245358 | − | 0.245358i | ||||
\(599\) | −25.4558 | −1.04010 | −0.520049 | − | 0.854137i | \(-0.674086\pi\) | ||||
−0.520049 | + | 0.854137i | \(0.674086\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 8.48528i | − | 0.346122i | −0.984911 | − | 0.173061i | \(-0.944634\pi\) | ||
0.984911 | − | 0.173061i | \(-0.0553658\pi\) | |||||||
\(602\) | 7.07107 | + | 7.07107i | 0.288195 | + | 0.288195i | ||||
\(603\) | 25.4558 | − | 25.4558i | 1.03664 | − | 1.03664i | ||||
\(604\) | 16.9706 | 0.690522 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −25.4558 | − | 25.4558i | −1.03322 | − | 1.03322i | −0.999429 | − | 0.0337920i | \(-0.989242\pi\) |
−0.0337920 | − | 0.999429i | \(-0.510758\pi\) | |||||||
\(608\) | −2.29289 | − | 3.70711i | −0.0929891 | − | 0.150343i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 59.3970i | 2.40294i | ||||||||
\(612\) | 9.00000 | − | 9.00000i | 0.363803 | − | 0.363803i | ||||
\(613\) | 17.0000 | + | 17.0000i | 0.686624 | + | 0.686624i | 0.961484 | − | 0.274861i | \(-0.0886317\pi\) |
−0.274861 | + | 0.961484i | \(0.588632\pi\) | |||||||
\(614\) | 12.0000i | 0.484281i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.82843i | 0.113961i | ||||||||
\(617\) | −27.0000 | + | 27.0000i | −1.08698 | + | 1.08698i | −0.0911411 | + | 0.995838i | \(0.529051\pi\) |
−0.995838 | + | 0.0911411i | \(0.970949\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12.0000i | 0.482321i | 0.970485 | + | 0.241160i | \(0.0775280\pi\) | ||||
−0.970485 | + | 0.241160i | \(0.922472\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −15.5563 | − | 15.5563i | −0.623753 | − | 0.623753i | ||||
\(623\) | 8.48528 | − | 8.48528i | 0.339956 | − | 0.339956i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 1.41421i | − | 0.0565233i | ||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 11.0000 | + | 11.0000i | 0.438948 | + | 0.438948i | ||||
\(629\) | −25.4558 | −1.01499 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.00000 | −0.0796187 | −0.0398094 | − | 0.999207i | \(-0.512675\pi\) | ||||
−0.0398094 | + | 0.999207i | \(0.512675\pi\) | |||||||
\(632\) | −6.00000 | + | 6.00000i | −0.238667 | + | 0.238667i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | − | 6.00000i | − | 0.238290i | ||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 21.2132 | + | 21.2132i | 0.840498 | + | 0.840498i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 25.4558 | 1.00702 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 25.4558i | − | 1.00545i | −0.864448 | − | 0.502723i | \(-0.832332\pi\) | ||
0.864448 | − | 0.502723i | \(-0.167668\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −11.0000 | − | 11.0000i | −0.433798 | − | 0.433798i | 0.456120 | − | 0.889918i | \(-0.349239\pi\) |
−0.889918 | + | 0.456120i | \(0.849239\pi\) | |||||||
\(644\) | − | 2.00000i | − | 0.0788110i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −18.0000 | − | 4.24264i | −0.708201 | − | 0.166924i | ||||
\(647\) | −9.00000 | + | 9.00000i | −0.353827 | + | 0.353827i | −0.861531 | − | 0.507705i | \(-0.830494\pi\) |
0.507705 | + | 0.861531i | \(0.330494\pi\) | |||||||
\(648\) | 6.36396 | − | 6.36396i | 0.250000 | − | 0.250000i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −7.00000 | + | 7.00000i | −0.274141 | + | 0.274141i | ||||
\(653\) | 9.00000 | + | 9.00000i | 0.352197 | + | 0.352197i | 0.860927 | − | 0.508729i | \(-0.169885\pi\) |
−0.508729 | + | 0.860927i | \(0.669885\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 8.48528i | 0.331295i | ||||||||
\(657\) | −3.00000 | + | 3.00000i | −0.117041 | + | 0.117041i | ||||
\(658\) | −9.89949 | + | 9.89949i | −0.385922 | + | 0.385922i | ||||
\(659\) | 16.9706 | 0.661079 | 0.330540 | − | 0.943792i | \(-0.392769\pi\) | ||||
0.330540 | + | 0.943792i | \(0.392769\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 33.9411i | − | 1.32016i | −0.751197 | − | 0.660078i | \(-0.770523\pi\) | ||
0.751197 | − | 0.660078i | \(-0.229477\pi\) | |||||||
\(662\) | 6.00000 | − | 6.00000i | 0.233197 | − | 0.233197i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 12.7279 | 0.493939 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −18.0000 | −0.697486 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 16.0000 | 0.617673 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.24264 | − | 4.24264i | 0.163542 | − | 0.163542i | −0.620592 | − | 0.784134i | \(-0.713108\pi\) |
0.784134 | + | 0.620592i | \(0.213108\pi\) | |||||||
\(674\) | 6.00000i | 0.231111i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 23.0000 | 0.884615 | ||||||||
\(677\) | 29.6985 | + | 29.6985i | 1.14141 | + | 1.14141i | 0.988193 | + | 0.153212i | \(0.0489618\pi\) |
0.153212 | + | 0.988193i | \(0.451038\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.48528 | −0.325635 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −12.0000 | + | 12.0000i | −0.459504 | + | 0.459504i | ||||
\(683\) | 8.48528 | − | 8.48528i | 0.324680 | − | 0.324680i | −0.525879 | − | 0.850559i | \(-0.676264\pi\) |
0.850559 | + | 0.525879i | \(0.176264\pi\) | |||||||
\(684\) | −12.7279 | − | 3.00000i | −0.486664 | − | 0.114708i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 16.9706i | 0.647939i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −5.00000 | − | 5.00000i | −0.190623 | − | 0.190623i | ||||
\(689\) | − | 36.0000i | − | 1.37149i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 30.0000 | 1.14125 | 0.570627 | − | 0.821209i | \(-0.306700\pi\) | ||||
0.570627 | + | 0.821209i | \(0.306700\pi\) | |||||||
\(692\) | 12.7279 | + | 12.7279i | 0.483843 | + | 0.483843i | ||||
\(693\) | 6.00000 | + | 6.00000i | 0.227921 | + | 0.227921i | ||||
\(694\) | 21.2132 | 0.805242 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 25.4558 | + | 25.4558i | 0.964209 | + | 0.964209i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −32.0000 | −1.20862 | −0.604312 | − | 0.796748i | \(-0.706552\pi\) | ||||
−0.604312 | + | 0.796748i | \(0.706552\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13.7574 | + | 22.2426i | 0.518869 | + | 0.838897i | ||||
\(704\) | − | 2.00000i | − | 0.0753778i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 35.3553i | 1.33062i | ||||||||
\(707\) | 4.00000 | − | 4.00000i | 0.150435 | − | 0.150435i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 24.0000i | − | 0.901339i | −0.892691 | − | 0.450669i | \(-0.851185\pi\) | ||
0.892691 | − | 0.450669i | \(-0.148815\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 25.4558i | 0.954669i | ||||||||
\(712\) | −6.00000 | + | 6.00000i | −0.224860 | + | 0.224860i | ||||
\(713\) | 8.48528 | − | 8.48528i | 0.317776 | − | 0.317776i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 16.9706i | − | 0.634220i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 5.65685 | − | 5.65685i | 0.211112 | − | 0.211112i | ||||
\(719\) | − | 16.0000i | − | 0.596699i | −0.954457 | − | 0.298350i | \(-0.903564\pi\) | ||
0.954457 | − | 0.298350i | \(-0.0964361\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16.9706i | 0.632017i | ||||||||
\(722\) | 6.02082 | + | 18.0208i | 0.224072 | + | 0.670665i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −25.4558 | −0.946059 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11.0000 | − | 11.0000i | 0.407967 | − | 0.407967i | −0.473062 | − | 0.881029i | \(-0.656851\pi\) |
0.881029 | + | 0.473062i | \(0.156851\pi\) | |||||||
\(728\) | 6.00000 | + | 6.00000i | 0.222375 | + | 0.222375i | ||||
\(729\) | − | 27.0000i | − | 1.00000i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −30.0000 | −1.10959 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 17.0000 | + | 17.0000i | 0.627909 | + | 0.627909i | 0.947542 | − | 0.319632i | \(-0.103559\pi\) |
−0.319632 | + | 0.947542i | \(0.603559\pi\) | |||||||
\(734\) | −24.0416 | −0.887393 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.41421i | 0.0521286i | ||||||||
\(737\) | −16.9706 | − | 16.9706i | −0.625119 | − | 0.625119i | ||||
\(738\) | 18.0000 | + | 18.0000i | 0.662589 | + | 0.662589i | ||||
\(739\) | − | 38.0000i | − | 1.39785i | −0.715194 | − | 0.698926i | \(-0.753662\pi\) | ||
0.715194 | − | 0.698926i | \(-0.246338\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 6.00000 | − | 6.00000i | 0.220267 | − | 0.220267i | ||||
\(743\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −6.00000 | −0.219676 | ||||||||
\(747\) | 27.0000 | − | 27.0000i | 0.987878 | − | 0.987878i | ||||
\(748\) | −6.00000 | − | 6.00000i | −0.219382 | − | 0.219382i | ||||
\(749\) | −16.9706 | −0.620091 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 16.9706i | − | 0.619265i | −0.950856 | − | 0.309632i | \(-0.899794\pi\) | ||
0.950856 | − | 0.309632i | \(-0.100206\pi\) | |||||||
\(752\) | 7.00000 | − | 7.00000i | 0.255264 | − | 0.255264i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 23.0000 | − | 23.0000i | 0.835949 | − | 0.835949i | −0.152374 | − | 0.988323i | \(-0.548692\pi\) |
0.988323 | + | 0.152374i | \(0.0486917\pi\) | |||||||
\(758\) | −18.0000 | − | 18.0000i | −0.653789 | − | 0.653789i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 20.0000 | 0.724999 | 0.362500 | − | 0.931984i | \(-0.381923\pi\) | ||||
0.362500 | + | 0.931984i | \(0.381923\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.48528 | + | 8.48528i | −0.307188 | + | 0.307188i | ||||
\(764\) | − | 16.0000i | − | 0.578860i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −36.0000 | −1.30073 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 30.0000i | 1.08183i | 0.841078 | + | 0.540914i | \(0.181921\pi\) | ||||
−0.841078 | + | 0.540914i | \(0.818079\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −4.24264 | − | 4.24264i | −0.152696 | − | 0.152696i | ||||
\(773\) | −29.6985 | + | 29.6985i | −1.06818 | + | 1.06818i | −0.0706813 | + | 0.997499i | \(0.522517\pi\) |
−0.997499 | + | 0.0706813i | \(0.977483\pi\) | |||||||
\(774\) | −21.2132 | −0.762493 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 6.00000 | 0.215387 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2.82843 | + | 2.82843i | −0.101404 | + | 0.101404i | ||||
\(779\) | 8.48528 | − | 36.0000i | 0.304017 | − | 1.28983i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 16.9706i | − | 0.607254i | ||||||
\(782\) | 4.24264 | + | 4.24264i | 0.151717 | + | 0.151717i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 5.00000i | − | 0.178571i | ||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −25.4558 | − | 25.4558i | −0.907403 | − | 0.907403i | 0.0886592 | − | 0.996062i | \(-0.471742\pi\) |
−0.996062 | + | 0.0886592i | \(0.971742\pi\) | |||||||
\(788\) | −5.00000 | − | 5.00000i | −0.178118 | − | 0.178118i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.48528i | 0.301702i | ||||||||
\(792\) | −4.24264 | − | 4.24264i | −0.150756 | − | 0.150756i | ||||
\(793\) | 33.9411 | − | 33.9411i | 1.20528 | − | 1.20528i | ||||
\(794\) | −35.3553 | −1.25471 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 18.0000 | 0.637993 | ||||||||
\(797\) | 4.24264 | + | 4.24264i | 0.150282 | + | 0.150282i | 0.778244 | − | 0.627962i | \(-0.216111\pi\) |
−0.627962 | + | 0.778244i | \(0.716111\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 42.0000i | − | 1.48585i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 25.4558i | 0.899438i | ||||||||
\(802\) | 24.0000 | − | 24.0000i | 0.847469 | − | 0.847469i | ||||
\(803\) | 2.00000 | + | 2.00000i | 0.0705785 | + | 0.0705785i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 50.9117i | 1.79329i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −2.82843 | + | 2.82843i | −0.0995037 | + | 0.0995037i | ||||
\(809\) | 8.00000i | 0.281265i | 0.990062 | + | 0.140633i | \(0.0449136\pi\) | ||||
−0.990062 | + | 0.140633i | \(0.955086\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 50.9117i | − | 1.78775i | −0.448315 | − | 0.893876i | \(-0.647976\pi\) | ||
0.448315 | − | 0.893876i | \(-0.352024\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 12.0000i | 0.420600i | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 16.2132 | + | 26.2132i | 0.567228 | + | 0.917084i | ||||
\(818\) | 12.0000 | + | 12.0000i | 0.419570 | + | 0.419570i | ||||
\(819\) | 25.4558 | 0.889499 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 34.0000 | 1.18661 | 0.593304 | − | 0.804978i | \(-0.297823\pi\) | ||||
0.593304 | + | 0.804978i | \(0.297823\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −23.0000 | − | 23.0000i | −0.801730 | − | 0.801730i | 0.181636 | − | 0.983366i | \(-0.441861\pi\) |
−0.983366 | + | 0.181636i | \(0.941861\pi\) | |||||||
\(824\) | − | 12.0000i | − | 0.418040i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 8.48528 | + | 8.48528i | 0.295062 | + | 0.295062i | 0.839076 | − | 0.544014i | \(-0.183096\pi\) |
−0.544014 | + | 0.839076i | \(0.683096\pi\) | |||||||
\(828\) | 3.00000 | + | 3.00000i | 0.104257 | + | 0.104257i | ||||
\(829\) | 8.48528 | 0.294706 | 0.147353 | − | 0.989084i | \(-0.452925\pi\) | ||||
0.147353 | + | 0.989084i | \(0.452925\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −4.24264 | − | 4.24264i | −0.147087 | − | 0.147087i | ||||
\(833\) | −15.0000 | − | 15.0000i | −0.519719 | − | 0.519719i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −2.00000 | + | 8.48528i | −0.0691714 | + | 0.293470i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1.41421 | + | 1.41421i | −0.0488532 | + | 0.0488532i | ||||
\(839\) | 42.4264 | 1.46472 | 0.732361 | − | 0.680916i | \(-0.238418\pi\) | ||||
0.732361 | + | 0.680916i | \(0.238418\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −29.0000 | −1.00000 | ||||||||
\(842\) | −24.0000 | + | 24.0000i | −0.827095 | + | 0.827095i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 8.48528 | 0.292075 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | − | 29.6985i | − | 1.02105i | ||||||
\(847\) | −7.00000 | + | 7.00000i | −0.240523 | + | 0.240523i | ||||
\(848\) | −4.24264 | + | 4.24264i | −0.145693 | + | 0.145693i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 8.48528i | − | 0.290872i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.00000 | + | 1.00000i | 0.0342393 | + | 0.0342393i | 0.724019 | − | 0.689780i | \(-0.242293\pi\) |
−0.689780 | + | 0.724019i | \(0.742293\pi\) | |||||||
\(854\) | 11.3137 | 0.387147 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 12.0000 | 0.410152 | ||||||||
\(857\) | −29.6985 | − | 29.6985i | −1.01448 | − | 1.01448i | −0.999894 | − | 0.0145873i | \(-0.995357\pi\) |
−0.0145873 | − | 0.999894i | \(-0.504643\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 22.0000i | − | 0.750630i | −0.926897 | − | 0.375315i | \(-0.877534\pi\) | ||
0.926897 | − | 0.375315i | \(-0.122466\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 12.0000 | − | 12.0000i | 0.408722 | − | 0.408722i | ||||
\(863\) | 16.9706 | − | 16.9706i | 0.577685 | − | 0.577685i | −0.356580 | − | 0.934265i | \(-0.616057\pi\) |
0.934265 | + | 0.356580i | \(0.116057\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 30.0000 | 1.01944 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −8.48528 | + | 8.48528i | −0.288009 | + | 0.288009i | ||||
\(869\) | 16.9706 | 0.575687 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −72.0000 | −2.43963 | ||||||||
\(872\) | 6.00000 | − | 6.00000i | 0.203186 | − | 0.203186i | ||||
\(873\) | 12.7279 | − | 12.7279i | 0.430775 | − | 0.430775i | ||||
\(874\) | 1.41421 | − | 6.00000i | 0.0478365 | − | 0.202953i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −12.7279 | − | 12.7279i | −0.429791 | − | 0.429791i | 0.458766 | − | 0.888557i | \(-0.348292\pi\) |
−0.888557 | + | 0.458766i | \(0.848292\pi\) | |||||||
\(878\) | −18.0000 | − | 18.0000i | −0.607471 | − | 0.607471i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −8.00000 | −0.269527 | −0.134763 | − | 0.990878i | \(-0.543027\pi\) | ||||
−0.134763 | + | 0.990878i | \(0.543027\pi\) | |||||||
\(882\) | −10.6066 | − | 10.6066i | −0.357143 | − | 0.357143i | ||||
\(883\) | −13.0000 | − | 13.0000i | −0.437485 | − | 0.437485i | 0.453680 | − | 0.891165i | \(-0.350111\pi\) |
−0.891165 | + | 0.453680i | \(0.850111\pi\) | |||||||
\(884\) | −25.4558 | −0.856173 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 9.89949i | 0.332580i | ||||||||
\(887\) | −8.48528 | − | 8.48528i | −0.284908 | − | 0.284908i | 0.550155 | − | 0.835063i | \(-0.314569\pi\) |
−0.835063 | + | 0.550155i | \(0.814569\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −16.9706 | −0.569174 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −18.0000 | −0.603023 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −36.6985 | + | 22.6985i | −1.22807 | + | 0.759576i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 1.41421i | − | 0.0472456i | ||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 12.0000 | + | 12.0000i | 0.400445 | + | 0.400445i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 25.4558i | 0.848057i | ||||||||
\(902\) | 12.0000 | − | 12.0000i | 0.399556 | − | 0.399556i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 6.00000i | − | 0.199557i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.48528 | + | 8.48528i | 0.281749 | + | 0.281749i | 0.833806 | − | 0.552057i | \(-0.186157\pi\) |
−0.552057 | + | 0.833806i | \(0.686157\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 12.0000i | 0.398015i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −18.0000 | − | 18.0000i | −0.595713 | − | 0.595713i | ||||
\(914\) | 9.89949 | 0.327446 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6.00000 | −0.198246 | ||||||||
\(917\) | 4.00000 | − | 4.00000i | 0.132092 | − | 0.132092i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 38.0000i | 1.25350i | 0.779219 | + | 0.626752i | \(0.215616\pi\) | ||||
−0.779219 | + | 0.626752i | \(0.784384\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −9.89949 | − | 9.89949i | −0.326023 | − | 0.326023i | ||||
\(923\) | −36.0000 | − | 36.0000i | −1.18495 | − | 1.18495i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 7.07107i | − | 0.232370i | ||||||
\(927\) | −25.4558 | − | 25.4558i | −0.836080 | − | 0.836080i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 28.0000i | 0.918650i | 0.888268 | + | 0.459325i | \(0.151909\pi\) | ||||
−0.888268 | + | 0.459325i | \(0.848091\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.00000 | + | 21.2132i | −0.163868 | + | 0.695235i | ||||
\(932\) | 5.00000 | − | 5.00000i | 0.163780 | − | 0.163780i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −18.3848 | −0.601568 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −18.0000 | −0.588348 | ||||||||
\(937\) | 25.0000 | − | 25.0000i | 0.816714 | − | 0.816714i | −0.168916 | − | 0.985630i | \(-0.554027\pi\) |
0.985630 | + | 0.168916i | \(0.0540267\pi\) | |||||||
\(938\) | −12.0000 | − | 12.0000i | −0.391814 | − | 0.391814i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 25.4558i | − | 0.829837i | −0.909859 | − | 0.414918i | \(-0.863810\pi\) | ||
0.909859 | − | 0.414918i | \(-0.136190\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.48528 | + | 8.48528i | −0.276319 | + | 0.276319i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 14.1421i | 0.459800i | ||||||||
\(947\) | −15.0000 | + | 15.0000i | −0.487435 | + | 0.487435i | −0.907496 | − | 0.420061i | \(-0.862009\pi\) |
0.420061 | + | 0.907496i | \(0.362009\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.48528 | 0.275444 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −4.24264 | − | 4.24264i | −0.137505 | − | 0.137505i | ||||
\(953\) | 12.7279 | − | 12.7279i | 0.412298 | − | 0.412298i | −0.470240 | − | 0.882538i | \(-0.655833\pi\) |
0.882538 | + | 0.470240i | \(0.155833\pi\) | |||||||
\(954\) | 18.0000i | 0.582772i | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −10.0000 | −0.323423 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −22.6274 | + | 22.6274i | −0.731059 | + | 0.731059i | ||||
\(959\) | − | 6.00000i | − | 0.193750i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −41.0000 | −1.32258 | ||||||||
\(962\) | 25.4558 | + | 25.4558i | 0.820729 | + | 0.820729i | ||||
\(963\) | 25.4558 | − | 25.4558i | 0.820303 | − | 0.820303i | ||||
\(964\) | −8.48528 | −0.273293 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 13.0000 | − | 13.0000i | 0.418052 | − | 0.418052i | −0.466480 | − | 0.884532i | \(-0.654478\pi\) |
0.884532 | + | 0.466480i | \(0.154478\pi\) | |||||||
\(968\) | 4.94975 | − | 4.94975i | 0.159091 | − | 0.159091i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 50.9117i | − | 1.63383i | −0.576755 | − | 0.816917i | \(-0.695681\pi\) | ||
0.576755 | − | 0.816917i | \(-0.304319\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12.0000 | − | 12.0000i | −0.384702 | − | 0.384702i | ||||
\(974\) | 36.0000i | 1.15351i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8.00000 | −0.256074 | ||||||||
\(977\) | 4.24264 | + | 4.24264i | 0.135734 | + | 0.135734i | 0.771709 | − | 0.635975i | \(-0.219402\pi\) |
−0.635975 | + | 0.771709i | \(0.719402\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 16.9706 | 0.542382 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 25.4558i | − | 0.812743i | ||||||
\(982\) | 19.7990 | + | 19.7990i | 0.631811 | + | 0.631811i | ||||
\(983\) | −16.9706 | + | 16.9706i | −0.541277 | + | 0.541277i | −0.923903 | − | 0.382626i | \(-0.875020\pi\) |
0.382626 | + | 0.923903i | \(0.375020\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 13.7574 | + | 22.2426i | 0.437680 | + | 0.707633i | ||||
\(989\) | − | 10.0000i | − | 0.317982i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 33.9411i | 1.07818i | 0.842250 | + | 0.539088i | \(0.181231\pi\) | ||||
−0.842250 | + | 0.539088i | \(0.818769\pi\) | |||||||
\(992\) | 6.00000 | − | 6.00000i | 0.190500 | − | 0.190500i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | − | 12.0000i | − | 0.380617i | ||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −11.0000 | + | 11.0000i | −0.348373 | + | 0.348373i | −0.859503 | − | 0.511130i | \(-0.829227\pi\) |
0.511130 | + | 0.859503i | \(0.329227\pi\) | |||||||
\(998\) | −25.4558 | + | 25.4558i | −0.805791 | + | 0.805791i | ||||
\(999\) | 0 | 0 |
(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 | 950.2.f.a.493.2 | 4 | ||
5.2 | odd | 4 | inner | 950.2.f.a.607.1 | 4 | ||
5.3 | odd | 4 | 190.2.f.a.37.2 | yes | 4 | ||
5.4 | even | 2 | 190.2.f.a.113.1 | yes | 4 | ||
15.8 | even | 4 | 1710.2.p.a.37.1 | 4 | |||
15.14 | odd | 2 | 1710.2.p.a.1063.2 | 4 | |||
19.18 | odd | 2 | inner | 950.2.f.a.493.1 | 4 | ||
95.18 | even | 4 | 190.2.f.a.37.1 | ✓ | 4 | ||
95.37 | even | 4 | inner | 950.2.f.a.607.2 | 4 | ||
95.94 | odd | 2 | 190.2.f.a.113.2 | yes | 4 | ||
285.113 | odd | 4 | 1710.2.p.a.37.2 | 4 | |||
285.284 | even | 2 | 1710.2.p.a.1063.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
190.2.f.a.37.1 | ✓ | 4 | 95.18 | even | 4 | ||
190.2.f.a.37.2 | yes | 4 | 5.3 | odd | 4 | ||
190.2.f.a.113.1 | yes | 4 | 5.4 | even | 2 | ||
190.2.f.a.113.2 | yes | 4 | 95.94 | odd | 2 | ||
950.2.f.a.493.1 | 4 | 19.18 | odd | 2 | inner | ||
950.2.f.a.493.2 | 4 | 1.1 | even | 1 | trivial | ||
950.2.f.a.607.1 | 4 | 5.2 | odd | 4 | inner | ||
950.2.f.a.607.2 | 4 | 95.37 | even | 4 | inner | ||
1710.2.p.a.37.1 | 4 | 15.8 | even | 4 | |||
1710.2.p.a.37.2 | 4 | 285.113 | odd | 4 | |||
1710.2.p.a.1063.1 | 4 | 285.284 | even | 2 | |||
1710.2.p.a.1063.2 | 4 | 15.14 | odd | 2 |