Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1600,2,Mod(49,1600)]
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, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1600.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1600 = 2^{6} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1600.q (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: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(i, \sqrt{11})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 5x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 400) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 849.2 | ||
Root | \(1.65831 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1600.849 |
Dual form | 1600.2.q.c.49.2 |
$q$-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 \(\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1151\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
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 | 0 | ||||||||
\(3\) | 1.15831 | − | 1.15831i | 0.668752 | − | 0.668752i | −0.288675 | − | 0.957427i | \(-0.593215\pi\) |
0.957427 | + | 0.288675i | \(0.0932147\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.31662 | 1.63153 | 0.815765 | − | 0.578383i | \(-0.196316\pi\) | ||||
0.815765 | + | 0.578383i | \(0.196316\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.316625i | 0.105542i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.158312 | − | 0.158312i | 0.0477330 | − | 0.0477330i | −0.682837 | − | 0.730570i | \(-0.739254\pi\) |
0.730570 | + | 0.682837i | \(0.239254\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.31662 | − | 2.31662i | 0.642516 | − | 0.642516i | −0.308657 | − | 0.951173i | \(-0.599880\pi\) |
0.951173 | + | 0.308657i | \(0.0998796\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 5.31662i | − | 1.28947i | −0.764406 | − | 0.644735i | \(-0.776968\pi\) | ||
0.764406 | − | 0.644735i | \(-0.223032\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.15831 | + | 3.15831i | 0.724567 | + | 0.724567i | 0.969532 | − | 0.244965i | \(-0.0787766\pi\) |
−0.244965 | + | 0.969532i | \(0.578777\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.00000 | − | 5.00000i | 1.09109 | − | 1.09109i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.31662 | −1.31711 | −0.658554 | − | 0.752534i | \(-0.728831\pi\) | ||||
−0.658554 | + | 0.752534i | \(0.728831\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.84169 | + | 3.84169i | 0.739333 | + | 0.739333i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.00000 | − | 2.00000i | −0.371391 | − | 0.371391i | 0.496593 | − | 0.867984i | \(-0.334584\pi\) |
−0.867984 | + | 0.496593i | \(0.834584\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.31662 | −0.775289 | −0.387644 | − | 0.921809i | \(-0.626711\pi\) | ||||
−0.387644 | + | 0.921809i | \(0.626711\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 0.366750i | − | 0.0638431i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.31662 | + | 7.31662i | 1.20285 | + | 1.20285i | 0.973297 | + | 0.229548i | \(0.0737249\pi\) |
0.229548 | + | 0.973297i | \(0.426275\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 5.36675i | − | 0.859368i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 5.00000i | − | 0.780869i | −0.920631 | − | 0.390434i | \(-0.872325\pi\) | ||
0.920631 | − | 0.390434i | \(-0.127675\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.63325 | + | 5.63325i | 0.859063 | + | 0.859063i | 0.991228 | − | 0.132165i | \(-0.0421929\pi\) |
−0.132165 | + | 0.991228i | \(0.542193\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.00000i | 1.16692i | 0.812142 | + | 0.583460i | \(0.198301\pi\) | ||||
−0.812142 | + | 0.583460i | \(0.801699\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 11.6332 | 1.66189 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.15831 | − | 6.15831i | −0.862336 | − | 0.862336i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.31662 | − | 3.31662i | −0.455573 | − | 0.455573i | 0.441626 | − | 0.897199i | \(-0.354402\pi\) |
−0.897199 | + | 0.441626i | \(0.854402\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.31662 | 0.969111 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.31662 | − | 5.31662i | 0.692166 | − | 0.692166i | −0.270542 | − | 0.962708i | \(-0.587203\pi\) |
0.962708 | + | 0.270542i | \(0.0872030\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.63325 | − | 3.63325i | −0.465190 | − | 0.465190i | 0.435162 | − | 0.900352i | \(-0.356691\pi\) |
−0.900352 | + | 0.435162i | \(0.856691\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.36675i | 0.172194i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.84169 | − | 5.84169i | 0.713676 | − | 0.713676i | −0.253626 | − | 0.967302i | \(-0.581623\pi\) |
0.967302 | + | 0.253626i | \(0.0816234\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −7.31662 | + | 7.31662i | −0.880818 | + | 0.880818i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.63325i | 0.549866i | 0.961463 | + | 0.274933i | \(0.0886556\pi\) | ||||
−0.961463 | + | 0.274933i | \(0.911344\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −13.3166 | −1.55859 | −0.779297 | − | 0.626655i | \(-0.784423\pi\) | ||||
−0.779297 | + | 0.626655i | \(0.784423\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.683375 | − | 0.683375i | 0.0778778 | − | 0.0778778i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.31662 | −0.260641 | −0.130320 | − | 0.991472i | \(-0.541601\pi\) | ||||
−0.130320 | + | 0.991472i | \(0.541601\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.94987 | 0.883319 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.84169 | − | 3.84169i | 0.421680 | − | 0.421680i | −0.464102 | − | 0.885782i | \(-0.653623\pi\) |
0.885782 | + | 0.464102i | \(0.153623\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.63325 | −0.496736 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 15.9499i | − | 1.69068i | −0.534226 | − | 0.845342i | \(-0.679397\pi\) | ||
0.534226 | − | 0.845342i | \(-0.320603\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.0000 | − | 10.0000i | 1.04828 | − | 1.04828i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.00000 | + | 5.00000i | −0.518476 | + | 0.518476i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.63325i | 0.673504i | 0.941593 | + | 0.336752i | \(0.109328\pi\) | ||||
−0.941593 | + | 0.336752i | \(0.890672\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.0501256 | + | 0.0501256i | 0.00503782 | + | 0.00503782i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.31662 | + | 1.31662i | −0.131009 | + | 0.131009i | −0.769571 | − | 0.638562i | \(-0.779530\pi\) |
0.638562 | + | 0.769571i | \(0.279530\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.63325 | −0.850659 | −0.425330 | − | 0.905038i | \(-0.639842\pi\) | ||||
−0.425330 | + | 0.905038i | \(0.639842\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.15831 | + | 6.15831i | 0.595347 | + | 0.595347i | 0.939071 | − | 0.343724i | \(-0.111689\pi\) |
−0.343724 | + | 0.939071i | \(0.611689\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.9499 | − | 13.9499i | −1.33616 | − | 1.33616i | −0.899750 | − | 0.436406i | \(-0.856251\pi\) |
−0.436406 | − | 0.899750i | \(-0.643749\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 16.9499 | 1.60881 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 15.6332i | − | 1.47065i | −0.677713 | − | 0.735326i | \(-0.737029\pi\) | ||
0.677713 | − | 0.735326i | \(-0.262971\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.733501 | + | 0.733501i | 0.0678122 | + | 0.0678122i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 22.9499i | − | 2.10381i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.9499i | 0.995443i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −5.79156 | − | 5.79156i | −0.522208 | − | 0.522208i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.316625i | 0.0280959i | 0.999901 | + | 0.0140480i | \(0.00447175\pi\) | ||||
−0.999901 | + | 0.0140480i | \(0.995528\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 13.0501 | 1.14900 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.00000 | − | 1.00000i | −0.0873704 | − | 0.0873704i | 0.662071 | − | 0.749441i | \(-0.269678\pi\) |
−0.749441 | + | 0.662071i | \(0.769678\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 13.6332 | + | 13.6332i | 1.18215 | + | 1.18215i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.63325 | −0.139538 | −0.0697690 | − | 0.997563i | \(-0.522226\pi\) | ||||
−0.0697690 | + | 0.997563i | \(0.522226\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.84169 | + | 5.84169i | −0.495485 | + | 0.495485i | −0.910029 | − | 0.414544i | \(-0.863941\pi\) |
0.414544 | + | 0.910029i | \(0.363941\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.26650 | + | 9.26650i | 0.780380 | + | 0.780380i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 0.733501i | − | 0.0613384i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 13.4749 | − | 13.4749i | 1.11139 | − | 1.11139i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.36675 | + | 3.36675i | −0.275815 | + | 0.275815i | −0.831436 | − | 0.555621i | \(-0.812481\pi\) |
0.555621 | + | 0.831436i | \(0.312481\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 2.31662i | − | 0.188524i | −0.995547 | − | 0.0942621i | \(-0.969951\pi\) | ||
0.995547 | − | 0.0942621i | \(-0.0300492\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.68338 | 0.136093 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.68338 | + | 4.68338i | −0.373774 | + | 0.373774i | −0.868850 | − | 0.495076i | \(-0.835140\pi\) |
0.495076 | + | 0.868850i | \(0.335140\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −7.68338 | −0.609331 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −27.2665 | −2.14890 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.84169 | − | 3.84169i | 0.300904 | − | 0.300904i | −0.540463 | − | 0.841368i | \(-0.681751\pi\) |
0.841368 | + | 0.540463i | \(0.181751\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −18.0000 | −1.39288 | −0.696441 | − | 0.717614i | \(-0.745234\pi\) | ||||
−0.696441 | + | 0.717614i | \(0.745234\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.26650i | 0.174346i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.00000 | + | 1.00000i | −0.0764719 | + | 0.0764719i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.94987 | + | 6.94987i | −0.528389 | + | 0.528389i | −0.920092 | − | 0.391703i | \(-0.871886\pi\) |
0.391703 | + | 0.920092i | \(0.371886\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 12.3166i | − | 0.925774i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 7.79156 | + | 7.79156i | 0.582369 | + | 0.582369i | 0.935554 | − | 0.353185i | \(-0.114901\pi\) |
−0.353185 | + | 0.935554i | \(0.614901\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.31662 | − | 3.31662i | 0.246523 | − | 0.246523i | −0.573019 | − | 0.819542i | \(-0.694228\pi\) |
0.819542 | + | 0.573019i | \(0.194228\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.41688 | −0.622193 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.841688 | − | 0.841688i | −0.0615503 | − | 0.0615503i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 16.5831 | + | 16.5831i | 1.20624 | + | 1.20624i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.05013 | 0.0759844 | 0.0379922 | − | 0.999278i | \(-0.487904\pi\) | ||||
0.0379922 | + | 0.999278i | \(0.487904\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.3166i | 0.814588i | 0.913297 | + | 0.407294i | \(0.133528\pi\) | ||||
−0.913297 | + | 0.407294i | \(0.866472\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.5831 | + | 16.5831i | 1.18150 | + | 1.18150i | 0.979356 | + | 0.202143i | \(0.0647904\pi\) |
0.202143 | + | 0.979356i | \(0.435210\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 0.633250i | − | 0.0448899i | −0.999748 | − | 0.0224449i | \(-0.992855\pi\) | ||
0.999748 | − | 0.0224449i | \(-0.00714505\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 13.5330i | − | 0.954544i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.63325 | − | 8.63325i | −0.605935 | − | 0.605935i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 2.00000i | − | 0.139010i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.00000 | 0.0691714 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.79156 | + | 4.79156i | 0.329865 | + | 0.329865i | 0.852535 | − | 0.522670i | \(-0.175064\pi\) |
−0.522670 | + | 0.852535i | \(0.675064\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.36675 | + | 5.36675i | 0.367724 | + | 0.367724i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −18.6332 | −1.26491 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −15.4248 | + | 15.4248i | −1.04231 | + | 1.04231i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −12.3166 | − | 12.3166i | −0.828506 | − | 0.828506i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.00000i | 0.401790i | 0.979613 | + | 0.200895i | \(0.0643850\pi\) | ||||
−0.979613 | + | 0.200895i | \(0.935615\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −17.6332 | + | 17.6332i | −1.17036 | + | 1.17036i | −0.188236 | + | 0.982124i | \(0.560277\pi\) |
−0.982124 | + | 0.188236i | \(0.939723\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.00000 | − | 2.00000i | 0.132164 | − | 0.132164i | −0.637930 | − | 0.770094i | \(-0.720209\pi\) |
0.770094 | + | 0.637930i | \(0.220209\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 1.58312i | − | 0.104162i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 27.8997 | 1.82777 | 0.913887 | − | 0.405969i | \(-0.133066\pi\) | ||||
0.913887 | + | 0.405969i | \(0.133066\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.68338 | + | 2.68338i | −0.174304 | + | 0.174304i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5.36675 | −0.347146 | −0.173573 | − | 0.984821i | \(-0.555531\pi\) | ||||
−0.173573 | + | 0.984821i | \(0.555531\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.5831 | −0.939382 | −0.469691 | − | 0.882831i | \(-0.655635\pi\) | ||||
−0.469691 | + | 0.882831i | \(0.655635\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2.31662 | + | 2.31662i | −0.148612 | + | 0.148612i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 14.6332 | 0.931091 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 8.89975i | − | 0.563999i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −14.1082 | + | 14.1082i | −0.890501 | + | 0.890501i | −0.994570 | − | 0.104069i | \(-0.966814\pi\) |
0.104069 | + | 0.994570i | \(0.466814\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.00000 | + | 1.00000i | −0.0628695 | + | 0.0628695i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 3.36675i | − | 0.210012i | −0.994472 | − | 0.105006i | \(-0.966514\pi\) | ||
0.994472 | − | 0.105006i | \(-0.0334862\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 31.5831 | + | 31.5831i | 1.96248 | + | 1.96248i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.633250 | − | 0.633250i | 0.0391972 | − | 0.0391972i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 17.5831 | 1.08422 | 0.542111 | − | 0.840307i | \(-0.317625\pi\) | ||||
0.542111 | + | 0.840307i | \(0.317625\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −18.4749 | − | 18.4749i | −1.13065 | − | 1.13065i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.316625 | + | 0.316625i | 0.0193050 | + | 0.0193050i | 0.716693 | − | 0.697388i | \(-0.245655\pi\) |
−0.697388 | + | 0.716693i | \(0.745655\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −18.9499 | −1.15112 | −0.575561 | − | 0.817759i | \(-0.695216\pi\) | ||||
−0.575561 | + | 0.817759i | \(0.695216\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 23.1662i | − | 1.40209i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.68338 | − | 7.68338i | −0.461649 | − | 0.461649i | 0.437547 | − | 0.899196i | \(-0.355848\pi\) |
−0.899196 | + | 0.437547i | \(0.855848\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 1.36675i | − | 0.0818252i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 19.2665i | 1.14934i | 0.818384 | + | 0.574671i | \(0.194870\pi\) | ||||
−0.818384 | + | 0.574671i | \(0.805130\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.15831 | + | 7.15831i | 0.425518 | + | 0.425518i | 0.887098 | − | 0.461581i | \(-0.152718\pi\) |
−0.461581 | + | 0.887098i | \(0.652718\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 21.5831i | − | 1.27401i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.2665 | −0.662735 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.68338 | + | 7.68338i | 0.450407 | + | 0.450407i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.26650 | + | 8.26650i | 0.482934 | + | 0.482934i | 0.906067 | − | 0.423133i | \(-0.139070\pi\) |
−0.423133 | + | 0.906067i | \(0.639070\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.21637 | 0.0705812 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −14.6332 | + | 14.6332i | −0.846263 | + | 0.846263i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 24.3166 | + | 24.3166i | 1.40159 | + | 1.40159i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.05013i | 0.175225i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.8417 | − | 10.8417i | 0.618768 | − | 0.618768i | −0.326448 | − | 0.945215i | \(-0.605852\pi\) |
0.945215 | + | 0.326448i | \(0.105852\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −10.0000 | + | 10.0000i | −0.568880 | + | 0.568880i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 6.94987i | − | 0.394091i | −0.980394 | − | 0.197046i | \(-0.936865\pi\) | ||
0.980394 | − | 0.197046i | \(-0.0631347\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −16.0000 | −0.904373 | −0.452187 | − | 0.891923i | \(-0.649356\pi\) | ||||
−0.452187 | + | 0.891923i | \(0.649356\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.94987 | − | 4.94987i | 0.278013 | − | 0.278013i | −0.554303 | − | 0.832315i | \(-0.687015\pi\) |
0.832315 | + | 0.554303i | \(0.187015\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.633250 | −0.0354552 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 14.2665 | 0.796278 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 16.7916 | − | 16.7916i | 0.934308 | − | 0.934308i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −32.3166 | −1.78711 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 34.5330i | 1.90387i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.15831 | + | 2.15831i | −0.118632 | + | 0.118632i | −0.763930 | − | 0.645299i | \(-0.776733\pi\) |
0.645299 | + | 0.763930i | \(0.276733\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.31662 | + | 2.31662i | −0.126950 | + | 0.126950i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 16.8997i | − | 0.920588i | −0.887767 | − | 0.460294i | \(-0.847744\pi\) | ||
0.887767 | − | 0.460294i | \(-0.152256\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −18.1082 | − | 18.1082i | −0.983502 | − | 0.983502i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.683375 | + | 0.683375i | −0.0370068 | + | 0.0370068i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.0000 | 1.07990 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 15.4248 | + | 15.4248i | 0.828047 | + | 0.828047i | 0.987246 | − | 0.159199i | \(-0.0508912\pi\) |
−0.159199 | + | 0.987246i | \(0.550891\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.26650 | + | 2.26650i | 0.121323 | + | 0.121323i | 0.765161 | − | 0.643838i | \(-0.222659\pi\) |
−0.643838 | + | 0.765161i | \(0.722659\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 17.7995 | 0.950067 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 6.73350i | − | 0.358388i | −0.983814 | − | 0.179194i | \(-0.942651\pi\) | ||
0.983814 | − | 0.179194i | \(-0.0573490\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −26.5831 | − | 26.5831i | −1.40693 | − | 1.40693i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 16.3166i | 0.861159i | 0.902553 | + | 0.430579i | \(0.141691\pi\) | ||||
−0.902553 | + | 0.430579i | \(0.858309\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.949874i | 0.0499934i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 12.6834 | + | 12.6834i | 0.665705 | + | 0.665705i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.3668i | 0.697739i | 0.937171 | + | 0.348869i | \(0.113434\pi\) | ||||
−0.937171 | + | 0.348869i | \(0.886566\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.58312 | 0.0824141 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −14.3166 | − | 14.3166i | −0.743282 | − | 0.743282i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −15.6332 | − | 15.6332i | −0.809459 | − | 0.809459i | 0.175093 | − | 0.984552i | \(-0.443977\pi\) |
−0.984552 | + | 0.175093i | \(0.943977\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.26650 | −0.477249 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.4248 | − | 18.4248i | 0.946419 | − | 0.946419i | −0.0522168 | − | 0.998636i | \(-0.516629\pi\) |
0.998636 | + | 0.0522168i | \(0.0166287\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.366750 | + | 0.366750i | 0.0187892 | + | 0.0187892i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.94987i | 0.150732i | 0.997156 | + | 0.0753658i | \(0.0240124\pi\) | ||||
−0.997156 | + | 0.0753658i | \(0.975988\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.78363 | + | 1.78363i | −0.0906668 | + | 0.0906668i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −22.2665 | + | 22.2665i | −1.12896 | + | 1.12896i | −0.138609 | + | 0.990347i | \(0.544263\pi\) |
−0.990347 | + | 0.138609i | \(0.955737\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 33.5831i | 1.69837i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.31662 | −0.116858 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.26650 | + | 1.26650i | −0.0635638 | + | 0.0635638i | −0.738174 | − | 0.674610i | \(-0.764312\pi\) |
0.674610 | + | 0.738174i | \(0.264312\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 31.5831 | 1.58113 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.31662 | 0.465250 | 0.232625 | − | 0.972567i | \(-0.425269\pi\) | ||||
0.232625 | + | 0.972567i | \(0.425269\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10.0000 | + | 10.0000i | −0.498135 | + | 0.498135i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.31662 | 0.114831 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.36675i | 0.314816i | 0.987534 | + | 0.157408i | \(0.0503137\pi\) | ||||
−0.987534 | + | 0.157408i | \(0.949686\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.89181 | + | 1.89181i | −0.0933163 | + | 0.0933163i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 22.9499 | − | 22.9499i | 1.12929 | − | 1.12929i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 13.5330i | 0.662714i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −21.4749 | − | 21.4749i | −1.04912 | − | 1.04912i | −0.998730 | − | 0.0503897i | \(-0.983954\pi\) |
−0.0503897 | − | 0.998730i | \(-0.516046\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.63325 | + | 8.63325i | −0.420759 | + | 0.420759i | −0.885465 | − | 0.464706i | \(-0.846160\pi\) |
0.464706 | + | 0.885465i | \(0.346160\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.53300 | −0.123159 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −15.6834 | − | 15.6834i | −0.758972 | − | 0.758972i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.849623 | − | 0.849623i | −0.0410202 | − | 0.0410202i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.94987 | −0.431100 | −0.215550 | − | 0.976493i | \(-0.569154\pi\) | ||||
−0.215550 | + | 0.976493i | \(0.569154\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 20.5831i | 0.989162i | 0.869132 | + | 0.494581i | \(0.164678\pi\) | ||||
−0.869132 | + | 0.494581i | \(0.835322\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −19.9499 | − | 19.9499i | −0.954332 | − | 0.954332i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.6332i | 0.889316i | 0.895700 | + | 0.444658i | \(0.146675\pi\) | ||||
−0.895700 | + | 0.444658i | \(0.853325\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.68338i | 0.175399i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.10819 | + | 4.10819i | 0.195186 | + | 0.195186i | 0.797933 | − | 0.602747i | \(-0.205927\pi\) |
−0.602747 | + | 0.797933i | \(0.705927\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 7.79950i | 0.368904i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −27.3166 | −1.28915 | −0.644576 | − | 0.764541i | \(-0.722966\pi\) | ||||
−0.644576 | + | 0.764541i | \(0.722966\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.791562 | − | 0.791562i | −0.0372732 | − | 0.0372732i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.68338 | − | 2.68338i | −0.126076 | − | 0.126076i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.0000 | −0.795226 | −0.397613 | − | 0.917553i | \(-0.630161\pi\) | ||||
−0.397613 | + | 0.917553i | \(0.630161\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 20.4248 | − | 20.4248i | 0.953349 | − | 0.953349i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −26.3166 | − | 26.3166i | −1.22569 | − | 1.22569i | −0.965580 | − | 0.260108i | \(-0.916242\pi\) |
−0.260108 | − | 0.965580i | \(-0.583758\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.3668i | 0.528258i | 0.964487 | + | 0.264129i | \(0.0850844\pi\) | ||||
−0.964487 | + | 0.264129i | \(0.914916\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −12.2665 | + | 12.2665i | −0.567626 | + | 0.567626i | −0.931463 | − | 0.363837i | \(-0.881467\pi\) |
0.363837 | + | 0.931463i | \(0.381467\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 25.2164 | − | 25.2164i | 1.16438 | − | 1.16438i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 10.8496i | 0.499924i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.78363 | 0.0820112 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.05013 | − | 1.05013i | 0.0480819 | − | 0.0480819i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −36.2164 | −1.65477 | −0.827384 | − | 0.561636i | \(-0.810172\pi\) | ||||
−0.827384 | + | 0.561636i | \(0.810172\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 33.8997 | 1.54570 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −31.5831 | + | 31.5831i | −1.43708 | + | 1.43708i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −14.2164 | −0.644205 | −0.322103 | − | 0.946705i | \(-0.604390\pi\) | ||||
−0.322103 | + | 0.946705i | \(0.604390\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 8.89975i | − | 0.402461i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16.3668 | + | 16.3668i | −0.738621 | + | 0.738621i | −0.972311 | − | 0.233690i | \(-0.924920\pi\) |
0.233690 | + | 0.972311i | \(0.424920\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.6332 | + | 10.6332i | −0.478897 | + | 0.478897i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 20.0000i | 0.897123i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.8997 | − | 16.8997i | −0.756537 | − | 0.756537i | 0.219154 | − | 0.975690i | \(-0.429670\pi\) |
−0.975690 | + | 0.219154i | \(0.929670\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −20.8496 | + | 20.8496i | −0.931492 | + | 0.931492i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7.89975 | −0.352232 | −0.176116 | − | 0.984369i | \(-0.556353\pi\) | ||||
−0.176116 | + | 0.984369i | \(0.556353\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.62531 | + | 2.62531i | 0.116594 | + | 0.116594i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.26650 | − | 6.26650i | −0.277758 | − | 0.277758i | 0.554456 | − | 0.832213i | \(-0.312927\pi\) |
−0.832213 | + | 0.554456i | \(0.812927\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −57.4829 | −2.54289 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 24.2665i | 1.07139i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.26650 | + | 1.26650i | 0.0557006 | + | 0.0557006i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 16.1003i | 0.706723i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0.366750i | 0.0160676i | 0.999968 | + | 0.00803381i | \(0.00255727\pi\) | ||||
−0.999968 | + | 0.00803381i | \(0.997443\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.47494 | − | 2.47494i | −0.108221 | − | 0.108221i | 0.650923 | − | 0.759144i | \(-0.274382\pi\) |
−0.759144 | + | 0.650923i | \(0.774382\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 22.9499i | 0.999712i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 16.8997 | 0.734772 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.68338 | + | 1.68338i | 0.0730523 | + | 0.0730523i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −11.5831 | − | 11.5831i | −0.501721 | − | 0.501721i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 18.0501 | 0.778920 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.84169 | − | 1.84169i | 0.0793271 | − | 0.0793271i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.3166 | + | 18.3166i | 0.787493 | + | 0.787493i | 0.981083 | − | 0.193589i | \(-0.0620130\pi\) |
−0.193589 | + | 0.981083i | \(0.562013\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 7.68338i | − | 0.329725i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −20.7414 | + | 20.7414i | −0.886840 | + | 0.886840i | −0.994218 | − | 0.107378i | \(-0.965754\pi\) |
0.107378 | + | 0.994218i | \(0.465754\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.15038 | − | 1.15038i | 0.0490969 | − | 0.0490969i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 12.6332i | − | 0.538195i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10.0000 | −0.425243 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −19.6834 | + | 19.6834i | −0.834011 | + | 0.834011i | −0.988063 | − | 0.154051i | \(-0.950768\pi\) |
0.154051 | + | 0.988063i | \(0.450768\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 26.1003 | 1.10392 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.94987 | −0.0823238 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.94987 | − | 1.94987i | 0.0821774 | − | 0.0821774i | −0.664823 | − | 0.747001i | \(-0.731493\pi\) |
0.747001 | + | 0.664823i | \(0.231493\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 34.3166 | 1.44116 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 9.00000i | − | 0.377300i | −0.982044 | − | 0.188650i | \(-0.939589\pi\) | ||
0.982044 | − | 0.188650i | \(-0.0604111\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 28.2665 | − | 28.2665i | 1.18292 | − | 1.18292i | 0.203931 | − | 0.978985i | \(-0.434628\pi\) |
0.978985 | − | 0.203931i | \(-0.0653718\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.21637 | − | 1.21637i | 0.0508147 | − | 0.0508147i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.36675i | 0.0985291i | 0.998786 | + | 0.0492646i | \(0.0156877\pi\) | ||||
−0.998786 | + | 0.0492646i | \(0.984312\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 13.1082 | + | 13.1082i | 0.544758 | + | 0.544758i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 16.5831 | − | 16.5831i | 0.687984 | − | 0.687984i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.05013 | −0.0434918 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −20.4248 | − | 20.4248i | −0.843022 | − | 0.843022i | 0.146229 | − | 0.989251i | \(-0.453286\pi\) |
−0.989251 | + | 0.146229i | \(0.953286\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −13.6332 | − | 13.6332i | −0.561748 | − | 0.561748i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 38.4169 | 1.58026 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 17.5330i | 0.719994i | 0.932953 | + | 0.359997i | \(0.117222\pi\) | ||||
−0.932953 | + | 0.359997i | \(0.882778\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.733501 | − | 0.733501i | −0.0300202 | − | 0.0300202i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10.2164i | 0.417430i | 0.977977 | + | 0.208715i | \(0.0669281\pi\) | ||||
−0.977977 | + | 0.208715i | \(0.933072\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 41.9499i | − | 1.71117i | −0.517661 | − | 0.855586i | \(-0.673197\pi\) | ||
0.517661 | − | 0.855586i | \(-0.326803\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.84962 | + | 1.84962i | 0.0753225 | + | 0.0753225i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 45.1662i | − | 1.83324i | −0.399758 | − | 0.916621i | \(-0.630906\pi\) | ||
0.399758 | − | 0.916621i | \(-0.369094\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −20.0000 | −0.810441 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 18.5330 | + | 18.5330i | 0.749765 | + | 0.749765i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10.2665 | − | 10.2665i | −0.414660 | − | 0.414660i | 0.468698 | − | 0.883358i | \(-0.344723\pi\) |
−0.883358 | + | 0.468698i | \(0.844723\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 27.2665 | 1.09771 | 0.548854 | − | 0.835918i | \(-0.315064\pi\) | ||||
0.548854 | + | 0.835918i | \(0.315064\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −21.6332 | + | 21.6332i | −0.869514 | + | 0.869514i | −0.992418 | − | 0.122905i | \(-0.960779\pi\) |
0.122905 | + | 0.992418i | \(0.460779\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −24.2665 | − | 24.2665i | −0.973781 | − | 0.973781i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 68.8496i | − | 2.75840i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.15831 | − | 1.15831i | 0.0462585 | − | 0.0462585i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 38.8997 | − | 38.8997i | 1.55103 | − | 1.55103i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 17.6834i | − | 0.703964i | −0.936007 | − | 0.351982i | \(-0.885508\pi\) | ||
0.936007 | − | 0.351982i | \(-0.114492\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 11.1003 | 0.441195 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 26.9499 | − | 26.9499i | 1.06779 | − | 1.06779i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.46700 | −0.0580337 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15.8997 | 0.628002 | 0.314001 | − | 0.949423i | \(-0.398330\pi\) | ||||
0.314001 | + | 0.949423i | \(0.398330\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 24.2665 | − | 24.2665i | 0.956977 | − | 0.956977i | −0.0421346 | − | 0.999112i | \(-0.513416\pi\) |
0.999112 | + | 0.0421346i | \(0.0134158\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 45.1662 | 1.77567 | 0.887834 | − | 0.460163i | \(-0.152209\pi\) | ||||
0.887834 | + | 0.460163i | \(0.152209\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 1.68338i | − | 0.0660783i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −21.5831 | + | 21.5831i | −0.845909 | + | 0.845909i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 29.6332 | − | 29.6332i | 1.15964 | − | 1.15964i | 0.175085 | − | 0.984553i | \(-0.443980\pi\) |
0.984553 | − | 0.175085i | \(-0.0560202\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 4.21637i | − | 0.164496i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −21.8417 | − | 21.8417i | −0.850831 | − | 0.850831i | 0.139404 | − | 0.990236i | \(-0.455481\pi\) |
−0.990236 | + | 0.139404i | \(0.955481\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.41688 | + | 2.41688i | −0.0940056 | + | 0.0940056i | −0.752546 | − | 0.658540i | \(-0.771174\pi\) |
0.658540 | + | 0.752546i | \(0.271174\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −28.5330 | −1.10813 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12.6332 | + | 12.6332i | 0.489161 | + | 0.489161i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6.94987 | + | 6.94987i | 0.268698 | + | 0.268698i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.15038 | −0.0444098 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 29.3668i | 1.13201i | 0.824404 | + | 0.566003i | \(0.191511\pi\) | ||||
−0.824404 | + | 0.566003i | \(0.808489\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 24.6332 | + | 24.6332i | 0.946733 | + | 0.946733i | 0.998651 | − | 0.0519186i | \(-0.0165336\pi\) |
−0.0519186 | + | 0.998651i | \(0.516534\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 28.6332i | 1.09884i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 40.8496i | 1.56536i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.47494 | + | 4.47494i | 0.171229 | + | 0.171229i | 0.787519 | − | 0.616290i | \(-0.211365\pi\) |
−0.616290 | + | 0.787519i | \(0.711365\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 4.63325i | − | 0.176769i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −15.3668 | −0.585427 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22.8417 | + | 22.8417i | 0.868939 | + | 0.868939i | 0.992355 | − | 0.123416i | \(-0.0393850\pi\) |
−0.123416 | + | 0.992355i | \(0.539385\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.216374 | + | 0.216374i | 0.00821935 | + | 0.00821935i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −26.5831 | −1.00691 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 32.3166 | − | 32.3166i | 1.22233 | − | 1.22233i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.26650 | + | 5.26650i | 0.198913 | + | 0.198913i | 0.799534 | − | 0.600621i | \(-0.205080\pi\) |
−0.600621 | + | 0.799534i | \(0.705080\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 46.2164i | 1.74308i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −5.68338 | + | 5.68338i | −0.213745 | + | 0.213745i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 22.0000 | − | 22.0000i | 0.826227 | − | 0.826227i | −0.160765 | − | 0.986993i | \(-0.551396\pi\) |
0.986993 | + | 0.160765i | \(0.0513962\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 0.733501i | − | 0.0275084i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 27.2665 | 1.02114 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −6.21637 | + | 6.21637i | −0.232155 | + | 0.232155i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −16.9499 | −0.632124 | −0.316062 | − | 0.948739i | \(-0.602361\pi\) | ||||
−0.316062 | + | 0.948739i | \(0.602361\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −37.2665 | −1.38788 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −16.8918 | + | 16.8918i | −0.628213 | + | 0.628213i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 50.5330 | 1.87417 | 0.937083 | − | 0.349108i | \(-0.113515\pi\) | ||||
0.937083 | + | 0.349108i | \(0.113515\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.2164i | 1.08209i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 29.9499 | − | 29.9499i | 1.10774 | − | 1.10774i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12.3166 | − | 12.3166i | 0.454925 | − | 0.454925i | −0.442060 | − | 0.896985i | \(-0.645752\pi\) |
0.896985 | + | 0.442060i | \(0.145752\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 1.84962i | − | 0.0681317i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −27.6332 | − | 27.6332i | −1.01651 | − | 1.01651i | −0.999861 | − | 0.0166440i | \(-0.994702\pi\) |
−0.0166440 | − | 0.999861i | \(-0.505298\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 16.9499 | − | 16.9499i | 0.622669 | − | 0.622669i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 13.6834 | 0.501994 | 0.250997 | − | 0.967988i | \(-0.419242\pi\) | ||||
0.250997 | + | 0.967988i | \(0.419242\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.21637 | + | 1.21637i | 0.0445048 | + | 0.0445048i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 26.5831 | + | 26.5831i | 0.971326 | + | 0.971326i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 50.4327 | 1.84032 | 0.920159 | − | 0.391546i | \(-0.128060\pi\) | ||||
0.920159 | + | 0.391546i | \(0.128060\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 32.6834i | 1.19105i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 27.6834 | + | 27.6834i | 1.00617 | + | 1.00617i | 0.999981 | + | 0.00618854i | \(0.00196988\pi\) |
0.00618854 | + | 0.999981i | \(0.498030\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.31662i | 0.0840882i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 5.73350i | − | 0.207839i | −0.994586 | − | 0.103920i | \(-0.966862\pi\) | ||
0.994586 | − | 0.103920i | \(-0.0331385\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −60.2164 | − | 60.2164i | −2.17998 | − | 2.17998i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 24.6332i | − | 0.889455i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −40.4829 | −1.45985 | −0.729925 | − | 0.683527i | \(-0.760445\pi\) | ||||
−0.729925 | + | 0.683527i | \(0.760445\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.89975 | − | 3.89975i | −0.140446 | − | 0.140446i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −30.6332 | − | 30.6332i | −1.10180 | − | 1.10180i | −0.994193 | − | 0.107608i | \(-0.965681\pi\) |
−0.107608 | − | 0.994193i | \(-0.534319\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 73.1662 | 2.62482 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 15.7916 | − | 15.7916i | 0.565791 | − | 0.565791i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.733501 | + | 0.733501i | 0.0262467 | + | 0.0262467i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 15.3668i | − | 0.549163i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.00000 | − | 7.00000i | 0.249523 | − | 0.249523i | −0.571252 | − | 0.820775i | \(-0.693542\pi\) |
0.820775 | + | 0.571252i | \(0.193542\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 20.3668 | − | 20.3668i | 0.725076 | − | 0.725076i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 67.4829i | − | 2.39941i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −16.8338 | −0.597784 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.36675 | + | 2.36675i | −0.0838346 | + | 0.0838346i | −0.747781 | − | 0.663946i | \(-0.768880\pi\) |
0.663946 | + | 0.747781i | \(0.268880\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 42.5330 | 1.50471 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.05013 | 0.178437 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.10819 | + | 2.10819i | −0.0743963 | + | 0.0743963i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.733501 | 0.0258205 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 14.5330i | 0.510953i | 0.966815 | + | 0.255477i | \(0.0822323\pi\) | ||||
−0.966815 | + | 0.255477i | \(0.917768\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24.3668 | − | 24.3668i | 0.855632 | − | 0.855632i | −0.135188 | − | 0.990820i | \(-0.543164\pi\) |
0.990820 | + | 0.135188i | \(0.0431637\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −21.9499 | + | 21.9499i | −0.769816 | + | 0.769816i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 35.5831i | 1.24490i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.16625 | + | 3.16625i | 0.110638 | + | 0.110638i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −28.2665 | + | 28.2665i | −0.986508 | + | 0.986508i | −0.999910 | − | 0.0134026i | \(-0.995734\pi\) |
0.0134026 | + | 0.999910i | \(0.495734\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 29.8997 | 1.04224 | 0.521120 | − | 0.853484i | \(-0.325514\pi\) | ||||
0.521120 | + | 0.853484i | \(0.325514\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 11.1583 | + | 11.1583i | 0.388013 | + | 0.388013i | 0.873978 | − | 0.485965i | \(-0.161532\pi\) |
−0.485965 | + | 0.873978i | \(0.661532\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 27.2665 | + | 27.2665i | 0.947005 | + | 0.947005i | 0.998665 | − | 0.0516601i | \(-0.0164512\pi\) |
−0.0516601 | + | 0.998665i | \(0.516451\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −17.7995 | −0.617458 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 61.8496i | − | 2.14296i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −16.5831 | − | 16.5831i | −0.573197 | − | 0.573197i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 10.6332i | − | 0.367101i | −0.983010 | − | 0.183550i | \(-0.941241\pi\) | ||
0.983010 | − | 0.183550i | \(-0.0587590\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 21.0000i | − | 0.724138i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 22.3166 | + | 22.3166i | 0.768625 | + | 0.768625i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 47.2665i | 1.62410i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 16.5831 | 0.569131 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −46.2164 | − | 46.2164i | −1.58428 | − | 1.58428i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 33.6332 | + | 33.6332i | 1.15158 | + | 1.15158i | 0.986236 | + | 0.165345i | \(0.0528737\pi\) |
0.165345 | + | 0.986236i | \(0.447126\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 8.36675 | 0.285803 | 0.142901 | − | 0.989737i | \(-0.454357\pi\) | ||||
0.142901 | + | 0.989737i | \(0.454357\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.42481 | + | 7.42481i | −0.253331 | + | 0.253331i | −0.822335 | − | 0.569004i | \(-0.807329\pi\) |
0.569004 | + | 0.822335i | \(0.307329\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −25.0000 | − | 25.0000i | −0.851998 | − | 0.851998i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 32.5330i | − | 1.10744i | −0.832704 | − | 0.553718i | \(-0.813209\pi\) | ||
0.832704 | − | 0.553718i | \(-0.186791\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −13.0501 | + | 13.0501i | −0.443206 | + | 0.443206i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.366750 | + | 0.366750i | −0.0124412 | + | 0.0124412i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 27.0660i | − | 0.917096i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.10025 | −0.0710827 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 39.5831 | − | 39.5831i | 1.33663 | − | 1.33663i | 0.437322 | − | 0.899305i | \(-0.355927\pi\) |
0.899305 | − | 0.437322i | \(-0.144073\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 19.1504 | 0.645926 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.89975 | −0.0640042 | −0.0320021 | − | 0.999488i | \(-0.510188\pi\) | ||||
−0.0320021 | + | 0.999488i | \(0.510188\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −18.8417 | + | 18.8417i | −0.634073 | + | 0.634073i | −0.949087 | − | 0.315014i | \(-0.897991\pi\) |
0.315014 | + | 0.949087i | \(0.397991\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −6.53300 | −0.219357 | −0.109678 | − | 0.993967i | \(-0.534982\pi\) | ||||
−0.109678 | + | 0.993967i | \(0.534982\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.36675i | 0.0458393i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.25856 | − | 1.25856i | 0.0421635 | − | 0.0421635i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −25.2665 | + | 25.2665i | −0.845511 | + | 0.845511i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 33.8997i | 1.13188i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8.63325 | + | 8.63325i | 0.287935 | + | 0.287935i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −17.6332 | + | 17.6332i | −0.587449 | + | 0.587449i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 56.3325 | 1.87463 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.366750 | − | 0.366750i | −0.0121777 | − | 0.0121777i | 0.700992 | − | 0.713169i | \(-0.252741\pi\) |
−0.713169 | + | 0.700992i | \(0.752741\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.416876 | − | 0.416876i | −0.0138269 | − | 0.0138269i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −25.1662 | −0.833795 | −0.416897 | − | 0.908954i | \(-0.636883\pi\) | ||||
−0.416897 | + | 0.908954i | \(0.636883\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 1.21637i | − | 0.0402561i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.31662 | − | 4.31662i | −0.142548 | − | 0.142548i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 37.5831i | − | 1.23975i | −0.784699 | − | 0.619876i | \(-0.787183\pi\) | ||
0.784699 | − | 0.619876i | \(-0.212817\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 25.1161i | − | 0.827604i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 10.7335 | + | 10.7335i | 0.353297 | + | 0.353297i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 2.73350i | − | 0.0897799i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 20.0000 | 0.656179 | 0.328089 | − | 0.944647i | \(-0.393595\pi\) | ||||
0.328089 | + | 0.944647i | \(0.393595\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 36.7414 | + | 36.7414i | 1.20415 | + | 1.20415i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −8.05013 | − | 8.05013i | −0.263549 | − | 0.263549i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 16.0501 | 0.524335 | 0.262167 | − | 0.965022i | \(-0.415563\pi\) | ||||
0.262167 | + | 0.965022i | \(0.415563\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −18.5330 | + | 18.5330i | −0.604802 | + | 0.604802i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −10.9499 | − | 10.9499i | −0.356956 | − | 0.356956i | 0.505734 | − | 0.862690i | \(-0.331222\pi\) |
−0.862690 | + | 0.505734i | \(0.831222\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 31.5831i | 1.02849i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 38.5831 | − | 38.5831i | 1.25378 | − | 1.25378i | 0.299772 | − | 0.954011i | \(-0.403089\pi\) |
0.954011 | − | 0.299772i | \(-0.0969107\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −30.8496 | + | 30.8496i | −1.00142 | + | 1.00142i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 11.4670i | − | 0.371843i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −15.6332 | −0.506411 | −0.253205 | − | 0.967413i | \(-0.581485\pi\) | ||||
−0.253205 | + | 0.967413i | \(0.581485\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.733501 | + | 0.733501i | −0.0237107 | + | 0.0237107i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −7.05013 | −0.227660 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.3668 | −0.398927 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.94987 | + | 1.94987i | −0.0628338 | + | 0.0628338i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −13.3668 | −0.429846 | −0.214923 | − | 0.976631i | \(-0.568950\pi\) | ||||
−0.214923 | + | 0.976631i | \(0.568950\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 38.8997i | − | 1.24964i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −27.5251 | + | 27.5251i | −0.883321 | + | 0.883321i | −0.993871 | − | 0.110549i | \(-0.964739\pi\) |
0.110549 | + | 0.993871i | \(0.464739\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −25.2164 | + | 25.2164i | −0.808400 | + | 0.808400i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 56.3826i | 1.80384i | 0.431903 | + | 0.901920i | \(0.357842\pi\) | ||||
−0.431903 | + | 0.901920i | \(0.642158\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.52506 | − | 2.52506i | −0.0807014 | − | 0.0807014i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.41688 | − | 4.41688i | 0.141020 | − | 0.141020i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −21.6834 | −0.691592 | −0.345796 | − | 0.938310i | \(-0.612391\pi\) | ||||
−0.345796 | + | 0.938310i | \(0.612391\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 40.0000 | + | 40.0000i | 1.27321 | + | 1.27321i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −35.5831 | − | 35.5831i | −1.13148 | − | 1.13148i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 23.4829 | 0.745958 | 0.372979 | − | 0.927840i | \(-0.378336\pi\) | ||||
0.372979 | + | 0.927840i | \(0.378336\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 5.00000i | 0.158670i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −16.9499 | − | 16.9499i | −0.536808 | − | 0.536808i | 0.385782 | − | 0.922590i | \(-0.373932\pi\) |
−0.922590 | + | 0.385782i | \(0.873932\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 56.2164i | 1.77861i |
(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.q.c.849.2 | 4 | ||
4.3 | odd | 2 | 400.2.q.c.349.1 | 4 | |||
5.2 | odd | 4 | 1600.2.l.e.401.1 | 4 | |||
5.3 | odd | 4 | 1600.2.l.d.401.2 | 4 | |||
5.4 | even | 2 | 1600.2.q.d.849.1 | 4 | |||
16.5 | even | 4 | 1600.2.q.d.49.1 | 4 | |||
16.11 | odd | 4 | 400.2.q.d.149.2 | 4 | |||
20.3 | even | 4 | 400.2.l.e.301.1 | yes | 4 | ||
20.7 | even | 4 | 400.2.l.d.301.2 | yes | 4 | ||
20.19 | odd | 2 | 400.2.q.d.349.2 | 4 | |||
80.27 | even | 4 | 400.2.l.d.101.2 | ✓ | 4 | ||
80.37 | odd | 4 | 1600.2.l.e.1201.1 | 4 | |||
80.43 | even | 4 | 400.2.l.e.101.1 | yes | 4 | ||
80.53 | odd | 4 | 1600.2.l.d.1201.2 | 4 | |||
80.59 | odd | 4 | 400.2.q.c.149.1 | 4 | |||
80.69 | even | 4 | inner | 1600.2.q.c.49.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
400.2.l.d.101.2 | ✓ | 4 | 80.27 | even | 4 | ||
400.2.l.d.301.2 | yes | 4 | 20.7 | even | 4 | ||
400.2.l.e.101.1 | yes | 4 | 80.43 | even | 4 | ||
400.2.l.e.301.1 | yes | 4 | 20.3 | even | 4 | ||
400.2.q.c.149.1 | 4 | 80.59 | odd | 4 | |||
400.2.q.c.349.1 | 4 | 4.3 | odd | 2 | |||
400.2.q.d.149.2 | 4 | 16.11 | odd | 4 | |||
400.2.q.d.349.2 | 4 | 20.19 | odd | 2 | |||
1600.2.l.d.401.2 | 4 | 5.3 | odd | 4 | |||
1600.2.l.d.1201.2 | 4 | 80.53 | odd | 4 | |||
1600.2.l.e.401.1 | 4 | 5.2 | odd | 4 | |||
1600.2.l.e.1201.1 | 4 | 80.37 | odd | 4 | |||
1600.2.q.c.49.2 | 4 | 80.69 | even | 4 | inner | ||
1600.2.q.c.849.2 | 4 | 1.1 | even | 1 | trivial | ||
1600.2.q.d.49.1 | 4 | 16.5 | even | 4 | |||
1600.2.q.d.849.1 | 4 | 5.4 | even | 2 |