Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1600,2,Mod(401,1600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1600, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1600.401");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1600 = 2^{6} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1600.l (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: | \(12.7760643234\) |
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 80) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1201.1 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1600.1201 |
Dual form | 1600.2.l.c.401.1 |
$q$-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 \(\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1151\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
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 | 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 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000i | 0.333333i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.00000 | + | 3.00000i | 0.904534 | + | 0.904534i | 0.995824 | − | 0.0912903i | \(-0.0290991\pi\) |
−0.0912903 | + | 0.995824i | \(0.529099\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.00000 | + | 3.00000i | −0.832050 | + | 0.832050i | −0.987797 | − | 0.155747i | \(-0.950222\pi\) |
0.155747 | + | 0.987797i | \(0.450222\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.00000 | −0.970143 | −0.485071 | − | 0.874475i | \(-0.661206\pi\) | ||||
−0.485071 | + | 0.874475i | \(0.661206\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | + | 1.00000i | −0.229416 | + | 0.229416i | −0.812449 | − | 0.583033i | \(-0.801866\pi\) |
0.583033 | + | 0.812449i | \(0.301866\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.00000i | 1.66812i | 0.551677 | + | 0.834058i | \(0.313988\pi\) | ||||
−0.551677 | + | 0.834058i | \(0.686012\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.00000 | + | 4.00000i | 0.769800 | + | 0.769800i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.00000 | + | 3.00000i | −0.557086 | + | 0.557086i | −0.928477 | − | 0.371391i | \(-0.878881\pi\) |
0.371391 | + | 0.928477i | \(0.378881\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.00000 | 1.04447 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.00000 | − | 3.00000i | −0.493197 | − | 0.493197i | 0.416115 | − | 0.909312i | \(-0.363391\pi\) |
−0.909312 | + | 0.416115i | \(0.863391\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.00000i | 0.960769i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.00000 | − | 3.00000i | −0.457496 | − | 0.457496i | 0.440337 | − | 0.897833i | \(-0.354859\pi\) |
−0.897833 | + | 0.440337i | \(0.854859\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.00000 | 0.291730 | 0.145865 | − | 0.989305i | \(-0.453403\pi\) | ||||
0.145865 | + | 0.989305i | \(0.453403\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.00000 | 1.00000 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.00000 | + | 4.00000i | −0.560112 | + | 0.560112i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.00000 | − | 9.00000i | −1.23625 | − | 1.23625i | −0.961524 | − | 0.274721i | \(-0.911414\pi\) |
−0.274721 | − | 0.961524i | \(-0.588586\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.00000i | 0.264906i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.00000 | + | 9.00000i | 1.17170 | + | 1.17170i | 0.981804 | + | 0.189896i | \(0.0608151\pi\) |
0.189896 | + | 0.981804i | \(0.439185\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.00000 | + | 5.00000i | −0.640184 | + | 0.640184i | −0.950601 | − | 0.310416i | \(-0.899532\pi\) |
0.310416 | + | 0.950601i | \(0.399532\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.00000 | − | 3.00000i | 0.366508 | − | 0.366508i | −0.499694 | − | 0.866202i | \(-0.666554\pi\) |
0.866202 | + | 0.499694i | \(0.166554\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.00000 | + | 8.00000i | 0.963087 | + | 0.963087i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 6.00000i | − | 0.712069i | −0.934473 | − | 0.356034i | \(-0.884129\pi\) | ||
0.934473 | − | 0.356034i | \(-0.115871\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.00000i | 0.702247i | 0.936329 | + | 0.351123i | \(0.114200\pi\) | ||||
−0.936329 | + | 0.351123i | \(0.885800\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.00000 | 0.900070 | 0.450035 | − | 0.893011i | \(-0.351411\pi\) | ||||
0.450035 | + | 0.893011i | \(0.351411\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.00000 | 0.555556 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.00000 | − | 9.00000i | 0.987878 | − | 0.987878i | −0.0120491 | − | 0.999927i | \(-0.503835\pi\) |
0.999927 | + | 0.0120491i | \(0.00383543\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.00000i | 0.643268i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.0000i | 1.27200i | 0.771690 | + | 0.635999i | \(0.219412\pi\) | ||||
−0.771690 | + | 0.635999i | \(0.780588\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.0000 | 1.21842 | 0.609208 | − | 0.793011i | \(-0.291488\pi\) | ||||
0.609208 | + | 0.793011i | \(0.291488\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.00000 | + | 3.00000i | −0.301511 | + | 0.301511i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.00000 | + | 3.00000i | 0.298511 | + | 0.298511i | 0.840431 | − | 0.541919i | \(-0.182302\pi\) |
−0.541919 | + | 0.840431i | \(0.682302\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.00000 | − | 9.00000i | −0.870063 | − | 0.870063i | 0.122416 | − | 0.992479i | \(-0.460936\pi\) |
−0.992479 | + | 0.122416i | \(0.960936\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.00000 | − | 1.00000i | 0.0957826 | − | 0.0957826i | −0.657592 | − | 0.753374i | \(-0.728425\pi\) |
0.753374 | + | 0.657592i | \(0.228425\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.00000 | −0.569495 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.00000 | 0.752577 | 0.376288 | − | 0.926503i | \(-0.377200\pi\) | ||||
0.376288 | + | 0.926503i | \(0.377200\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.00000 | − | 3.00000i | −0.277350 | − | 0.277350i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.00000i | 0.636364i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.00000 | −0.532414 | −0.266207 | − | 0.963916i | \(-0.585770\pi\) | ||||
−0.266207 | + | 0.963916i | \(0.585770\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.00000 | −0.528271 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.00000 | − | 9.00000i | 0.786334 | − | 0.786334i | −0.194557 | − | 0.980891i | \(-0.562327\pi\) |
0.980891 | + | 0.194557i | \(0.0623271\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 2.00000i | − | 0.170872i | −0.996344 | − | 0.0854358i | \(-0.972772\pi\) | ||
0.996344 | − | 0.0854358i | \(-0.0272282\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.00000 | − | 7.00000i | −0.593732 | − | 0.593732i | 0.344905 | − | 0.938638i | \(-0.387911\pi\) |
−0.938638 | + | 0.344905i | \(0.887911\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.00000 | − | 2.00000i | 0.168430 | − | 0.168430i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −18.0000 | −1.50524 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 7.00000 | − | 7.00000i | 0.577350 | − | 0.577350i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.00000 | − | 3.00000i | −0.245770 | − | 0.245770i | 0.573462 | − | 0.819232i | \(-0.305600\pi\) |
−0.819232 | + | 0.573462i | \(0.805600\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.0000i | 1.46482i | 0.680864 | + | 0.732410i | \(0.261604\pi\) | ||||
−0.680864 | + | 0.732410i | \(0.738396\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 4.00000i | − | 0.323381i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.00000 | + | 9.00000i | −0.718278 | + | 0.718278i | −0.968252 | − | 0.249974i | \(-0.919578\pi\) |
0.249974 | + | 0.968252i | \(0.419578\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −18.0000 | −1.42749 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 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 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.00000i | 0.619059i | 0.950890 | + | 0.309529i | \(0.100171\pi\) | ||||
−0.950890 | + | 0.309529i | \(0.899829\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 5.00000i | − | 0.384615i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.00000 | − | 1.00000i | −0.0764719 | − | 0.0764719i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.00000 | − | 9.00000i | 0.684257 | − | 0.684257i | −0.276699 | − | 0.960957i | \(-0.589241\pi\) |
0.960957 | + | 0.276699i | \(0.0892406\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 18.0000 | 1.35296 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.00000 | − | 3.00000i | 0.224231 | − | 0.224231i | −0.586047 | − | 0.810277i | \(-0.699317\pi\) |
0.810277 | + | 0.586047i | \(0.199317\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.00000 | − | 1.00000i | −0.0743294 | − | 0.0743294i | 0.668965 | − | 0.743294i | \(-0.266738\pi\) |
−0.743294 | + | 0.668965i | \(0.766738\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 10.0000i | 0.739221i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12.0000 | − | 12.0000i | −0.877527 | − | 0.877527i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 24.0000 | 1.73658 | 0.868290 | − | 0.496058i | \(-0.165220\pi\) | ||||
0.868290 | + | 0.496058i | \(0.165220\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.0000 | 0.863779 | 0.431889 | − | 0.901927i | \(-0.357847\pi\) | ||||
0.431889 | + | 0.901927i | \(0.357847\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.00000 | + | 5.00000i | 0.356235 | + | 0.356235i | 0.862423 | − | 0.506188i | \(-0.168946\pi\) |
−0.506188 | + | 0.862423i | \(0.668946\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 2.00000i | − | 0.141776i | −0.997484 | − | 0.0708881i | \(-0.977417\pi\) | ||
0.997484 | − | 0.0708881i | \(-0.0225833\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 6.00000i | − | 0.423207i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −8.00000 | −0.556038 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.00000 | −0.415029 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.0000 | + | 11.0000i | −0.757271 | + | 0.757271i | −0.975825 | − | 0.218554i | \(-0.929866\pi\) |
0.218554 | + | 0.975825i | \(0.429866\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.00000 | − | 6.00000i | −0.411113 | − | 0.411113i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.00000 | + | 6.00000i | 0.405442 | + | 0.405442i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.0000 | − | 12.0000i | 0.807207 | − | 0.807207i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.00000 | 0.401790 | 0.200895 | − | 0.979613i | \(-0.435615\pi\) | ||||
0.200895 | + | 0.979613i | \(0.435615\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.00000 | + | 9.00000i | −0.597351 | + | 0.597351i | −0.939607 | − | 0.342256i | \(-0.888809\pi\) |
0.342256 | + | 0.939607i | \(0.388809\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.00000 | − | 7.00000i | −0.462573 | − | 0.462573i | 0.436925 | − | 0.899498i | \(-0.356068\pi\) |
−0.899498 | + | 0.436925i | \(0.856068\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 22.0000i | 1.44127i | 0.693316 | + | 0.720634i | \(0.256149\pi\) | ||||
−0.693316 | + | 0.720634i | \(0.743851\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 8.00000 | − | 8.00000i | 0.519656 | − | 0.519656i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 24.0000 | 1.55243 | 0.776215 | − | 0.630468i | \(-0.217137\pi\) | ||||
0.776215 | + | 0.630468i | \(0.217137\pi\) | |||||||
\(240\) | 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 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 6.00000i | − | 0.381771i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 18.0000i | − | 1.14070i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.00000 | − | 9.00000i | −0.568075 | − | 0.568075i | 0.363514 | − | 0.931589i | \(-0.381577\pi\) |
−0.931589 | + | 0.363514i | \(0.881577\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −24.0000 | + | 24.0000i | −1.50887 | + | 1.50887i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −8.00000 | −0.499026 | −0.249513 | − | 0.968371i | \(-0.580271\pi\) | ||||
−0.249513 | + | 0.968371i | \(0.580271\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.00000 | − | 3.00000i | −0.185695 | − | 0.185695i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 16.0000i | 0.986602i | 0.869859 | + | 0.493301i | \(0.164210\pi\) | ||||
−0.869859 | + | 0.493301i | \(0.835790\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12.0000 | + | 12.0000i | 0.734388 | + | 0.734388i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.00000 | − | 9.00000i | 0.548740 | − | 0.548740i | −0.377337 | − | 0.926076i | \(-0.623160\pi\) |
0.926076 | + | 0.377337i | \(0.123160\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.0000 | −0.971931 | −0.485965 | − | 0.873978i | \(-0.661532\pi\) | ||||
−0.485965 | + | 0.873978i | \(0.661532\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.00000 | − | 3.00000i | −0.180253 | − | 0.180253i | 0.611213 | − | 0.791466i | \(-0.290682\pi\) |
−0.791466 | + | 0.611213i | \(0.790682\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 12.0000i | − | 0.715860i | −0.933748 | − | 0.357930i | \(-0.883483\pi\) | ||
0.933748 | − | 0.357930i | \(-0.116517\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.0000 | − | 15.0000i | −0.891657 | − | 0.891657i | 0.103022 | − | 0.994679i | \(-0.467149\pi\) |
−0.994679 | + | 0.103022i | \(0.967149\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.00000 | −0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.0000 | − | 12.0000i | 0.703452 | − | 0.703452i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −9.00000 | − | 9.00000i | −0.525786 | − | 0.525786i | 0.393527 | − | 0.919313i | \(-0.371255\pi\) |
−0.919313 | + | 0.393527i | \(0.871255\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 24.0000i | 1.39262i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −24.0000 | − | 24.0000i | −1.38796 | − | 1.38796i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 6.00000 | 0.344691 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.00000 | − | 3.00000i | 0.171219 | − | 0.171219i | −0.616296 | − | 0.787515i | \(-0.711367\pi\) |
0.787515 | + | 0.616296i | \(0.211367\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 6.00000i | − | 0.340229i | −0.985424 | − | 0.170114i | \(-0.945586\pi\) | ||
0.985424 | − | 0.170114i | \(-0.0544137\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 6.00000i | − | 0.339140i | −0.985518 | − | 0.169570i | \(-0.945762\pi\) | ||
0.985518 | − | 0.169570i | \(-0.0542379\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7.00000 | − | 7.00000i | 0.393159 | − | 0.393159i | −0.482653 | − | 0.875812i | \(-0.660327\pi\) |
0.875812 | + | 0.482653i | \(0.160327\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −18.0000 | −1.00781 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −18.0000 | −1.00466 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.00000 | − | 4.00000i | 0.222566 | − | 0.222566i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 2.00000i | − | 0.110600i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.00000 | − | 5.00000i | −0.274825 | − | 0.274825i | 0.556214 | − | 0.831039i | \(-0.312253\pi\) |
−0.831039 | + | 0.556214i | \(0.812253\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.00000 | − | 3.00000i | 0.164399 | − | 0.164399i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −24.0000 | −1.30736 | −0.653682 | − | 0.756770i | \(-0.726776\pi\) | ||||
−0.653682 | + | 0.756770i | \(0.726776\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 8.00000 | − | 8.00000i | 0.434500 | − | 0.434500i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 19.0000 | + | 19.0000i | 1.01997 | + | 1.01997i | 0.999796 | + | 0.0201770i | \(0.00642298\pi\) |
0.0201770 | + | 0.999796i | \(0.493577\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.00000 | − | 5.00000i | 0.267644 | − | 0.267644i | −0.560506 | − | 0.828150i | \(-0.689393\pi\) |
0.828150 | + | 0.560506i | \(0.189393\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −24.0000 | −1.28103 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 16.0000 | 0.851594 | 0.425797 | − | 0.904819i | \(-0.359994\pi\) | ||||
0.425797 | + | 0.904819i | \(0.359994\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 18.0000i | − | 0.950004i | −0.879985 | − | 0.475002i | \(-0.842447\pi\) | ||
0.879985 | − | 0.475002i | \(-0.157553\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.0000i | 0.894737i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 7.00000 | + | 7.00000i | 0.367405 | + | 0.367405i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 18.0000 | 0.939592 | 0.469796 | − | 0.882775i | \(-0.344327\pi\) | ||||
0.469796 | + | 0.882775i | \(0.344327\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 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 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 18.0000i | − | 0.927047i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.00000 | + | 1.00000i | 0.0513665 | + | 0.0513665i | 0.732323 | − | 0.680957i | \(-0.238436\pi\) |
−0.680957 | + | 0.732323i | \(0.738436\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.00000 | + | 6.00000i | −0.307389 | + | 0.307389i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10.0000 | −0.510976 | −0.255488 | − | 0.966812i | \(-0.582236\pi\) | ||||
−0.255488 | + | 0.966812i | \(0.582236\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.00000 | − | 3.00000i | 0.152499 | − | 0.152499i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −15.0000 | − | 15.0000i | −0.760530 | − | 0.760530i | 0.215888 | − | 0.976418i | \(-0.430735\pi\) |
−0.976418 | + | 0.215888i | \(0.930735\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 32.0000i | − | 1.61831i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 18.0000i | − | 0.907980i | ||||||
\(394\) | 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 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 30.0000 | 1.49813 | 0.749064 | − | 0.662497i | \(-0.230503\pi\) | ||||
0.749064 | + | 0.662497i | \(0.230503\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 18.0000i | − | 0.892227i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.00000 | − | 2.00000i | −0.0986527 | − | 0.0986527i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −14.0000 | −0.685583 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15.0000 | − | 15.0000i | 0.732798 | − | 0.732798i | −0.238375 | − | 0.971173i | \(-0.576615\pi\) |
0.971173 | + | 0.238375i | \(0.0766148\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.00000 | − | 5.00000i | −0.243685 | − | 0.243685i | 0.574688 | − | 0.818373i | \(-0.305124\pi\) |
−0.818373 | + | 0.574688i | \(0.805124\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.00000i | 0.0972433i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −18.0000 | + | 18.0000i | −0.869048 | + | 0.869048i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 24.0000 | 1.15604 | 0.578020 | − | 0.816023i | \(-0.303826\pi\) | ||||
0.578020 | + | 0.816023i | \(0.303826\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −36.0000 | −1.73005 | −0.865025 | − | 0.501729i | \(-0.832697\pi\) | ||||
−0.865025 | + | 0.501729i | \(0.832697\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −8.00000 | − | 8.00000i | −0.382692 | − | 0.382692i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 10.0000i | − | 0.477274i | −0.971109 | − | 0.238637i | \(-0.923299\pi\) | ||
0.971109 | − | 0.238637i | \(-0.0767006\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.00000i | 0.333333i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.00000 | + | 9.00000i | 0.427603 | + | 0.427603i | 0.887811 | − | 0.460208i | \(-0.152225\pi\) |
−0.460208 | + | 0.887811i | \(0.652225\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −6.00000 | −0.283790 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.0000 | 0.849473 | 0.424736 | − | 0.905317i | \(-0.360367\pi\) | ||||
0.424736 | + | 0.905317i | \(0.360367\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 18.0000 | + | 18.0000i | 0.845714 | + | 0.845714i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 18.0000i | − | 0.842004i | −0.907060 | − | 0.421002i | \(-0.861678\pi\) | ||
0.907060 | − | 0.421002i | \(-0.138322\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −16.0000 | − | 16.0000i | −0.746816 | − | 0.746816i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.00000 | − | 3.00000i | 0.139724 | − | 0.139724i | −0.633785 | − | 0.773509i | \(-0.718500\pi\) |
0.773509 | + | 0.633785i | \(0.218500\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 30.0000 | 1.39422 | 0.697109 | − | 0.716965i | \(-0.254469\pi\) | ||||
0.697109 | + | 0.716965i | \(0.254469\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.00000 | + | 5.00000i | −0.231372 | + | 0.231372i | −0.813265 | − | 0.581893i | \(-0.802312\pi\) |
0.581893 | + | 0.813265i | \(0.302312\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 18.0000i | 0.829396i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 18.0000i | − | 0.827641i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.00000 | − | 9.00000i | 0.412082 | − | 0.412082i | ||||
\(478\) | 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 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 24.0000i | 1.08754i | 0.839233 | + | 0.543772i | \(0.183004\pi\) | ||||
−0.839233 | + | 0.543772i | \(0.816996\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 18.0000i | − | 0.813988i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.0000 | + | 15.0000i | 0.676941 | + | 0.676941i | 0.959307 | − | 0.282366i | \(-0.0911193\pi\) |
−0.282366 | + | 0.959307i | \(0.591119\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.0000 | − | 12.0000i | 0.540453 | − | 0.540453i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −29.0000 | + | 29.0000i | −1.29822 | + | 1.29822i | −0.368650 | + | 0.929568i | \(0.620180\pi\) |
−0.929568 | + | 0.368650i | \(0.879820\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.00000 | + | 8.00000i | 0.357414 | + | 0.357414i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 32.0000i | − | 1.42681i | −0.700752 | − | 0.713405i | \(-0.747152\pi\) | ||
0.700752 | − | 0.713405i | \(-0.252848\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5.00000 | − | 5.00000i | −0.222058 | − | 0.222058i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9.00000 | − | 9.00000i | 0.398918 | − | 0.398918i | −0.478933 | − | 0.877851i | \(-0.658976\pi\) |
0.877851 | + | 0.478933i | \(0.158976\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −8.00000 | −0.353209 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.00000 | + | 6.00000i | 0.263880 | + | 0.263880i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 18.0000i | − | 0.790112i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 24.0000i | − | 1.05146i | −0.850652 | − | 0.525730i | \(-0.823792\pi\) | ||
0.850652 | − | 0.525730i | \(-0.176208\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.00000 | + | 9.00000i | 0.393543 | + | 0.393543i | 0.875948 | − | 0.482405i | \(-0.160237\pi\) |
−0.482405 | + | 0.875948i | \(0.660237\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −41.0000 | −1.78261 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −9.00000 | + | 9.00000i | −0.390567 | + | 0.390567i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 6.00000i | − | 0.258919i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 21.0000 | + | 21.0000i | 0.904534 | + | 0.904534i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.00000 | + | 1.00000i | −0.0429934 | + | 0.0429934i | −0.728277 | − | 0.685283i | \(-0.759678\pi\) |
0.685283 | + | 0.728277i | \(0.259678\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.00000 | −0.0858282 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.00000 | − | 3.00000i | 0.128271 | − | 0.128271i | −0.640057 | − | 0.768328i | \(-0.721089\pi\) |
0.768328 | + | 0.640057i | \(0.221089\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.00000 | − | 5.00000i | −0.213395 | − | 0.213395i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 6.00000i | − | 0.255609i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −9.00000 | + | 9.00000i | −0.381342 | + | 0.381342i | −0.871586 | − | 0.490243i | \(-0.836908\pi\) |
0.490243 | + | 0.871586i | \(0.336908\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 18.0000 | 0.761319 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −24.0000 | −1.01328 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −19.0000 | + | 19.0000i | −0.800755 | + | 0.800755i | −0.983213 | − | 0.182459i | \(-0.941594\pi\) |
0.182459 | + | 0.983213i | \(0.441594\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 24.0000i | − | 1.00613i | −0.864248 | − | 0.503066i | \(-0.832205\pi\) | ||
0.864248 | − | 0.503066i | \(-0.167795\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.0000 | + | 11.0000i | 0.460336 | + | 0.460336i | 0.898765 | − | 0.438430i | \(-0.144465\pi\) |
−0.438430 | + | 0.898765i | \(0.644465\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 24.0000 | − | 24.0000i | 1.00261 | − | 1.00261i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 24.0000 | 0.999133 | 0.499567 | − | 0.866276i | \(-0.333493\pi\) | ||||
0.499567 | + | 0.866276i | \(0.333493\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 12.0000 | − | 12.0000i | 0.498703 | − | 0.498703i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 54.0000i | − | 2.23645i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −9.00000 | − | 9.00000i | −0.371470 | − | 0.371470i | 0.496543 | − | 0.868012i | \(-0.334603\pi\) |
−0.868012 | + | 0.496543i | \(0.834603\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 10.0000 | 0.411345 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −32.0000 | −1.31408 | −0.657041 | − | 0.753855i | \(-0.728192\pi\) | ||||
−0.657041 | + | 0.753855i | \(0.728192\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.00000 | − | 2.00000i | −0.0818546 | − | 0.0818546i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 30.0000i | 1.22577i | 0.790173 | + | 0.612883i | \(0.209990\pi\) | ||||
−0.790173 | + | 0.612883i | \(0.790010\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 36.0000i | − | 1.46847i | −0.678895 | − | 0.734235i | \(-0.737541\pi\) | ||
0.678895 | − | 0.734235i | \(-0.262459\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.00000 | + | 3.00000i | 0.122169 | + | 0.122169i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 42.0000 | 1.70473 | 0.852364 | − | 0.522949i | \(-0.175168\pi\) | ||||
0.852364 | + | 0.522949i | \(0.175168\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.00000 | + | 6.00000i | −0.242734 | + | 0.242734i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 27.0000 | + | 27.0000i | 1.09052 | + | 1.09052i | 0.995473 | + | 0.0950469i | \(0.0303001\pi\) |
0.0950469 | + | 0.995473i | \(0.469700\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10.0000i | 0.402585i | 0.979531 | + | 0.201292i | \(0.0645141\pi\) | ||||
−0.979531 | + | 0.201292i | \(0.935486\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 13.0000 | + | 13.0000i | 0.522514 | + | 0.522514i | 0.918330 | − | 0.395816i | \(-0.129538\pi\) |
−0.395816 | + | 0.918330i | \(0.629538\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −32.0000 | + | 32.0000i | −1.28412 | + | 1.28412i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.00000 | + | 6.00000i | −0.239617 | + | 0.239617i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 12.0000 | + | 12.0000i | 0.478471 | + | 0.478471i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.00000i | 0.0796187i | 0.999207 | + | 0.0398094i | \(0.0126751\pi\) | ||||
−0.999207 | + | 0.0398094i | \(0.987325\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 22.0000i | 0.874421i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −21.0000 | + | 21.0000i | −0.832050 | + | 0.832050i | ||||
\(638\) | 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 | ||||||||
\(643\) | −27.0000 | + | 27.0000i | −1.06478 | + | 1.06478i | −0.0670247 | + | 0.997751i | \(0.521351\pi\) |
−0.997751 | + | 0.0670247i | \(0.978649\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 32.0000i | − | 1.25805i | −0.777385 | − | 0.629025i | \(-0.783454\pi\) | ||
0.777385 | − | 0.629025i | \(-0.216546\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 54.0000i | 2.11969i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.00000 | − | 9.00000i | 0.352197 | − | 0.352197i | −0.508729 | − | 0.860927i | \(-0.669885\pi\) |
0.860927 | + | 0.508729i | \(0.169885\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −6.00000 | −0.234082 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −21.0000 | + | 21.0000i | −0.818044 | + | 0.818044i | −0.985824 | − | 0.167781i | \(-0.946340\pi\) |
0.167781 | + | 0.985824i | \(0.446340\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −29.0000 | − | 29.0000i | −1.12797 | − | 1.12797i | −0.990507 | − | 0.137462i | \(-0.956105\pi\) |
−0.137462 | − | 0.990507i | \(-0.543895\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 24.0000i | − | 0.932083i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −24.0000 | − | 24.0000i | −0.929284 | − | 0.929284i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6.00000 | − | 6.00000i | 0.231973 | − | 0.231973i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −30.0000 | −1.15814 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12.0000 | −0.462566 | −0.231283 | − | 0.972887i | \(-0.574292\pi\) | ||||
−0.231283 | + | 0.972887i | \(0.574292\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9.00000 | + | 9.00000i | 0.345898 | + | 0.345898i | 0.858579 | − | 0.512681i | \(-0.171348\pi\) |
−0.512681 | + | 0.858579i | \(0.671348\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 18.0000i | 0.689761i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 13.0000 | + | 13.0000i | 0.497431 | + | 0.497431i | 0.910637 | − | 0.413206i | \(-0.135591\pi\) |
−0.413206 | + | 0.910637i | \(0.635591\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −14.0000 | −0.534133 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 54.0000 | 2.05724 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.00000 | − | 5.00000i | 0.190209 | − | 0.190209i | −0.605577 | − | 0.795786i | \(-0.707058\pi\) |
0.795786 | + | 0.605577i | \(0.207058\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 22.0000 | + | 22.0000i | 0.832116 | + | 0.832116i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.00000 | − | 3.00000i | 0.113308 | − | 0.113308i | −0.648179 | − | 0.761488i | \(-0.724469\pi\) |
0.761488 | + | 0.648179i | \(0.224469\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.00000 | 0.226294 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13.0000 | + | 13.0000i | 0.488225 | + | 0.488225i | 0.907746 | − | 0.419521i | \(-0.137802\pi\) |
−0.419521 | + | 0.907746i | \(0.637802\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.00000i | 0.300023i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 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 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −18.0000 | + | 18.0000i | −0.669427 | + | 0.669427i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24.0000i | 0.890111i | 0.895503 | + | 0.445055i | \(0.146816\pi\) | ||||
−0.895503 | + | 0.445055i | \(0.853184\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.0000i | 1.07407i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 12.0000 | + | 12.0000i | 0.443836 | + | 0.443836i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.00000 | + | 3.00000i | −0.110808 | + | 0.110808i | −0.760337 | − | 0.649529i | \(-0.774966\pi\) |
0.649529 | + | 0.760337i | \(0.274966\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 18.0000 | 0.663039 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19.0000 | − | 19.0000i | 0.698926 | − | 0.698926i | −0.265253 | − | 0.964179i | \(-0.585455\pi\) |
0.964179 | + | 0.265253i | \(0.0854554\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6.00000 | − | 6.00000i | −0.220416 | − | 0.220416i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8.00000i | 0.293492i | 0.989174 | + | 0.146746i | \(0.0468799\pi\) | ||||
−0.989174 | + | 0.146746i | \(0.953120\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 9.00000 | + | 9.00000i | 0.329293 | + | 0.329293i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −18.0000 | −0.655956 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 33.0000 | + | 33.0000i | 1.19941 | + | 1.19941i | 0.974345 | + | 0.225061i | \(0.0722580\pi\) |
0.225061 | + | 0.974345i | \(0.427742\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 48.0000i | 1.74229i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 48.0000i | 1.74000i | 0.493053 | + | 0.869999i | \(0.335881\pi\) | ||||
−0.493053 | + | 0.869999i | \(0.664119\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −54.0000 | −1.94983 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18.0000 | 0.649097 | 0.324548 | − | 0.945869i | \(-0.394788\pi\) | ||||
0.324548 | + | 0.945869i | \(0.394788\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.00000 | + | 8.00000i | −0.288113 | + | 0.288113i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 23.0000 | + | 23.0000i | 0.827253 | + | 0.827253i | 0.987136 | − | 0.159883i | \(-0.0511118\pi\) |
−0.159883 | + | 0.987136i | \(0.551112\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 18.0000 | − | 18.0000i | 0.644091 | − | 0.644091i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −24.0000 | −0.857690 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −33.0000 | + | 33.0000i | −1.17632 | + | 1.17632i | −0.195649 | + | 0.980674i | \(0.562681\pi\) |
−0.980674 | + | 0.195649i | \(0.937319\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 16.0000 | + | 16.0000i | 0.569615 | + | 0.569615i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 30.0000i | − | 1.06533i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 19.0000 | − | 19.0000i | 0.673015 | − | 0.673015i | −0.285395 | − | 0.958410i | \(-0.592125\pi\) |
0.958410 | + | 0.285395i | \(0.0921249\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.00000 | −0.283020 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −12.0000 | −0.423999 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −18.0000 | + | 18.0000i | −0.635206 | + | 0.635206i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 18.0000i | − | 0.633630i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −37.0000 | − | 37.0000i | −1.29925 | − | 1.29925i | −0.928890 | − | 0.370356i | \(-0.879236\pi\) |
−0.370356 | − | 0.928890i | \(-0.620764\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −16.0000 | + | 16.0000i | −0.561144 | + | 0.561144i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.00000 | 0.209913 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 39.0000 | + | 39.0000i | 1.36111 | + | 1.36111i | 0.872506 | + | 0.488603i | \(0.162493\pi\) |
0.488603 | + | 0.872506i | \(0.337507\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.0000i | 0.836587i | 0.908312 | + | 0.418294i | \(0.137372\pi\) | ||||
−0.908312 | + | 0.418294i | \(0.862628\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 31.0000 | + | 31.0000i | 1.07798 | + | 1.07798i | 0.996691 | + | 0.0812847i | \(0.0259023\pi\) |
0.0812847 | + | 0.996691i | \(0.474098\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −35.0000 | + | 35.0000i | −1.21560 | + | 1.21560i | −0.246443 | + | 0.969157i | \(0.579262\pi\) |
−0.969157 | + | 0.246443i | \(0.920738\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6.00000 | −0.208138 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −28.0000 | −0.970143 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 42.0000i | − | 1.45000i | −0.688748 | − | 0.725001i | \(-0.741839\pi\) | ||
0.688748 | − | 0.725001i | \(-0.258161\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.0000i | 0.379310i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −12.0000 | − | 12.0000i | −0.413302 | − | 0.413302i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −30.0000 | −1.02960 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 24.0000 | − | 24.0000i | 0.822709 | − | 0.822709i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15.0000 | + | 15.0000i | 0.513590 | + | 0.513590i | 0.915625 | − | 0.402034i | \(-0.131697\pi\) |
−0.402034 | + | 0.915625i | \(0.631697\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 38.0000i | 1.29806i | 0.760765 | + | 0.649028i | \(0.224824\pi\) | ||||
−0.760765 | + | 0.649028i | \(0.775176\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.00000 | − | 7.00000i | −0.238837 | − | 0.238837i | 0.577531 | − | 0.816368i | \(-0.304016\pi\) |
−0.816368 | + | 0.577531i | \(0.804016\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 22.0000 | 0.748889 | 0.374444 | − | 0.927249i | \(-0.377833\pi\) | ||||
0.374444 | + | 0.927249i | \(0.377833\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.00000 | + | 1.00000i | −0.0339618 | + | 0.0339618i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 24.0000 | + | 24.0000i | 0.814144 | + | 0.814144i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 18.0000i | 0.609907i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 12.0000i | 0.406138i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.00000 | − | 3.00000i | 0.101303 | − | 0.101303i | −0.654639 | − | 0.755942i | \(-0.727179\pi\) |
0.755942 | + | 0.654639i | \(0.227179\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −18.0000 | −0.607125 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −6.00000 | −0.202145 | −0.101073 | − | 0.994879i | \(-0.532227\pi\) | ||||
−0.101073 | + | 0.994879i | \(0.532227\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21.0000 | − | 21.0000i | 0.706706 | − | 0.706706i | −0.259135 | − | 0.965841i | \(-0.583437\pi\) |
0.965841 | + | 0.259135i | \(0.0834374\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 8.00000i | − | 0.268614i | −0.990940 | − | 0.134307i | \(-0.957119\pi\) | ||
0.990940 | − | 0.134307i | \(-0.0428808\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 15.0000 | + | 15.0000i | 0.502519 | + | 0.502519i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.00000 | + | 2.00000i | −0.0669274 | + | 0.0669274i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −48.0000 | −1.60267 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 36.0000 | + | 36.0000i | 1.19933 | + | 1.19933i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −21.0000 | − | 21.0000i | −0.697294 | − | 0.697294i | 0.266532 | − | 0.963826i | \(-0.414122\pi\) |
−0.963826 | + | 0.266532i | \(0.914122\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.00000 | + | 3.00000i | −0.0995037 | + | 0.0995037i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 48.0000 | 1.59031 | 0.795155 | − | 0.606406i | \(-0.207389\pi\) | ||||
0.795155 | + | 0.606406i | \(0.207389\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 54.0000 | 1.78714 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 54.0000i | 1.78130i | 0.454694 | + | 0.890648i | \(0.349749\pi\) | ||||
−0.454694 | + | 0.890648i | \(0.650251\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 6.00000i | − | 0.197707i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 18.0000 | + | 18.0000i | 0.592477 | + | 0.592477i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −30.0000 | −0.984268 | −0.492134 | − | 0.870519i | \(-0.663783\pi\) | ||||
−0.492134 | + | 0.870519i | \(0.663783\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.00000 | + | 7.00000i | −0.229416 | + | 0.229416i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −6.00000 | − | 6.00000i | −0.196431 | − | 0.196431i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 54.0000i | − | 1.76410i | −0.471153 | − | 0.882052i | \(-0.656162\pi\) | ||
0.471153 | − | 0.882052i | \(-0.343838\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.00000 | − | 6.00000i | −0.195803 | − | 0.195803i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 27.0000 | − | 27.0000i | 0.880175 | − | 0.880175i | −0.113377 | − | 0.993552i | \(-0.536167\pi\) |
0.993552 | + | 0.113377i | \(0.0361668\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 27.0000 | − | 27.0000i | 0.877382 | − | 0.877382i | −0.115881 | − | 0.993263i | \(-0.536969\pi\) |
0.993263 | + | 0.115881i | \(0.0369691\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −18.0000 | − | 18.0000i | −0.584305 | − | 0.584305i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 14.0000i | − | 0.453981i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 22.0000i | − | 0.712650i | −0.934362 | − | 0.356325i | \(-0.884030\pi\) | ||
0.934362 | − | 0.356325i | \(-0.115970\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −18.0000 | + | 18.0000i | −0.581857 | + | 0.581857i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 9.00000 | − | 9.00000i | 0.290021 | − | 0.290021i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 48.0000i | − | 1.54358i | −0.635880 | − | 0.771788i | \(-0.719363\pi\) | ||
0.635880 | − | 0.771788i | \(-0.280637\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 8.00000i | − | 0.256997i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −9.00000 | − | 9.00000i | −0.288824 | − | 0.288824i | 0.547791 | − | 0.836615i | \(-0.315469\pi\) |
−0.836615 | + | 0.547791i | \(0.815469\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −28.0000 | −0.895799 | −0.447900 | − | 0.894084i | \(-0.647828\pi\) | ||||
−0.447900 | + | 0.894084i | \(0.647828\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −36.0000 | + | 36.0000i | −1.15056 | + | 1.15056i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.00000 | + | 1.00000i | 0.0319275 | + | 0.0319275i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 16.0000i | − | 0.510321i | −0.966899 | − | 0.255160i | \(-0.917872\pi\) | ||
0.966899 | − | 0.255160i | \(-0.0821283\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 24.0000 | − | 24.0000i | 0.763156 | − | 0.763156i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.0000 | 0.508257 | 0.254128 | − | 0.967170i | \(-0.418211\pi\) | ||||
0.254128 | + | 0.967170i | \(0.418211\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −10.0000 | −0.317340 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.00000 | + | 9.00000i | 0.285033 | + | 0.285033i | 0.835112 | − | 0.550079i | \(-0.185403\pi\) |
−0.550079 | + | 0.835112i | \(0.685403\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 24.0000i | − | 0.759326i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1600.2.l.c.1201.1 | 2 | ||
4.3 | odd | 2 | 400.2.l.a.101.1 | 2 | |||
5.2 | odd | 4 | 320.2.q.a.49.1 | 2 | |||
5.3 | odd | 4 | 320.2.q.b.49.1 | 2 | |||
5.4 | even | 2 | 1600.2.l.b.1201.1 | 2 | |||
16.3 | odd | 4 | 400.2.l.a.301.1 | 2 | |||
16.13 | even | 4 | inner | 1600.2.l.c.401.1 | 2 | ||
20.3 | even | 4 | 80.2.q.b.69.1 | yes | 2 | ||
20.7 | even | 4 | 80.2.q.a.69.1 | yes | 2 | ||
20.19 | odd | 2 | 400.2.l.b.101.1 | 2 | |||
40.3 | even | 4 | 640.2.q.c.609.1 | 2 | |||
40.13 | odd | 4 | 640.2.q.a.609.1 | 2 | |||
40.27 | even | 4 | 640.2.q.b.609.1 | 2 | |||
40.37 | odd | 4 | 640.2.q.d.609.1 | 2 | |||
60.23 | odd | 4 | 720.2.bm.a.469.1 | 2 | |||
60.47 | odd | 4 | 720.2.bm.b.469.1 | 2 | |||
80.3 | even | 4 | 80.2.q.a.29.1 | ✓ | 2 | ||
80.13 | odd | 4 | 320.2.q.a.209.1 | 2 | |||
80.19 | odd | 4 | 400.2.l.b.301.1 | 2 | |||
80.27 | even | 4 | 640.2.q.c.289.1 | 2 | |||
80.29 | even | 4 | 1600.2.l.b.401.1 | 2 | |||
80.37 | odd | 4 | 640.2.q.a.289.1 | 2 | |||
80.43 | even | 4 | 640.2.q.b.289.1 | 2 | |||
80.53 | odd | 4 | 640.2.q.d.289.1 | 2 | |||
80.67 | even | 4 | 80.2.q.b.29.1 | yes | 2 | ||
80.77 | odd | 4 | 320.2.q.b.209.1 | 2 | |||
240.83 | odd | 4 | 720.2.bm.b.109.1 | 2 | |||
240.227 | odd | 4 | 720.2.bm.a.109.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
80.2.q.a.29.1 | ✓ | 2 | 80.3 | even | 4 | ||
80.2.q.a.69.1 | yes | 2 | 20.7 | even | 4 | ||
80.2.q.b.29.1 | yes | 2 | 80.67 | even | 4 | ||
80.2.q.b.69.1 | yes | 2 | 20.3 | even | 4 | ||
320.2.q.a.49.1 | 2 | 5.2 | odd | 4 | |||
320.2.q.a.209.1 | 2 | 80.13 | odd | 4 | |||
320.2.q.b.49.1 | 2 | 5.3 | odd | 4 | |||
320.2.q.b.209.1 | 2 | 80.77 | odd | 4 | |||
400.2.l.a.101.1 | 2 | 4.3 | odd | 2 | |||
400.2.l.a.301.1 | 2 | 16.3 | odd | 4 | |||
400.2.l.b.101.1 | 2 | 20.19 | odd | 2 | |||
400.2.l.b.301.1 | 2 | 80.19 | odd | 4 | |||
640.2.q.a.289.1 | 2 | 80.37 | odd | 4 | |||
640.2.q.a.609.1 | 2 | 40.13 | odd | 4 | |||
640.2.q.b.289.1 | 2 | 80.43 | even | 4 | |||
640.2.q.b.609.1 | 2 | 40.27 | even | 4 | |||
640.2.q.c.289.1 | 2 | 80.27 | even | 4 | |||
640.2.q.c.609.1 | 2 | 40.3 | even | 4 | |||
640.2.q.d.289.1 | 2 | 80.53 | odd | 4 | |||
640.2.q.d.609.1 | 2 | 40.37 | odd | 4 | |||
720.2.bm.a.109.1 | 2 | 240.227 | odd | 4 | |||
720.2.bm.a.469.1 | 2 | 60.23 | odd | 4 | |||
720.2.bm.b.109.1 | 2 | 240.83 | odd | 4 | |||
720.2.bm.b.469.1 | 2 | 60.47 | odd | 4 | |||
1600.2.l.b.401.1 | 2 | 80.29 | even | 4 | |||
1600.2.l.b.1201.1 | 2 | 5.4 | even | 2 | |||
1600.2.l.c.401.1 | 2 | 16.13 | even | 4 | inner | ||
1600.2.l.c.1201.1 | 2 | 1.1 | even | 1 | trivial |