Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,3,Mod(145,1008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.145");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.cg (of order \(6\), 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: | \(27.4660106475\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3 \) |
Twist minimal: | no (minimal twist has level 126) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 577.2 | ||
Root | \(0.707107 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1008.577 |
Dual form | 1008.3.cg.i.145.2 |
$q$-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 \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.24264 | − | 2.44949i | 0.848528 | − | 0.489898i | −0.0116258 | − | 0.999932i | \(-0.503701\pi\) |
0.860154 | + | 0.510034i | \(0.170367\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.50000 | − | 6.06218i | −0.500000 | − | 0.866025i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −8.48528 | + | 14.6969i | −0.771389 | + | 1.33609i | 0.165412 | + | 0.986224i | \(0.447104\pi\) |
−0.936802 | + | 0.349861i | \(0.886229\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 1.73205i | − | 0.133235i | −0.997779 | − | 0.0666173i | \(-0.978779\pi\) | ||
0.997779 | − | 0.0666173i | \(-0.0212207\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.24264 | − | 2.44949i | −0.249567 | − | 0.144088i | 0.369999 | − | 0.929032i | \(-0.379358\pi\) |
−0.619566 | + | 0.784945i | \(0.712691\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −25.5000 | + | 14.7224i | −1.34211 | + | 0.774865i | −0.987116 | − | 0.160006i | \(-0.948849\pi\) |
−0.354989 | + | 0.934870i | \(0.615515\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.24264 | − | 7.34847i | −0.184463 | − | 0.319499i | 0.758933 | − | 0.651169i | \(-0.225721\pi\) |
−0.943395 | + | 0.331670i | \(0.892388\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −33.9411 | −1.17038 | −0.585192 | − | 0.810895i | \(-0.698981\pi\) | ||||
−0.585192 | + | 0.810895i | \(0.698981\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.5000 | + | 6.06218i | 0.338710 | + | 0.195554i | 0.659701 | − | 0.751528i | \(-0.270683\pi\) |
−0.320992 | + | 0.947082i | \(0.604016\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −29.6985 | − | 17.1464i | −0.848528 | − | 0.489898i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 23.5000 | + | 40.7032i | 0.635135 | + | 1.10009i | 0.986486 | + | 0.163843i | \(0.0523889\pi\) |
−0.351351 | + | 0.936244i | \(0.614278\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 68.5857i | 1.67282i | 0.548103 | + | 0.836411i | \(0.315350\pi\) | ||||
−0.548103 | + | 0.836411i | \(0.684650\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −31.0000 | −0.720930 | −0.360465 | − | 0.932773i | \(-0.617382\pi\) | ||||
−0.360465 | + | 0.932773i | \(0.617382\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 72.1249 | − | 41.6413i | 1.53457 | − | 0.885986i | 0.535430 | − | 0.844580i | \(-0.320150\pi\) |
0.999142 | − | 0.0414059i | \(-0.0131837\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −24.5000 | + | 42.4352i | −0.500000 | + | 0.866025i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 38.1838 | − | 66.1362i | 0.720448 | − | 1.24785i | −0.240372 | − | 0.970681i | \(-0.577269\pi\) |
0.960820 | − | 0.277172i | \(-0.0893973\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 83.1384i | 1.51161i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 72.1249 | + | 41.6413i | 1.22246 | + | 0.705785i | 0.965441 | − | 0.260622i | \(-0.0839277\pi\) |
0.257015 | + | 0.966407i | \(0.417261\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −72.0000 | + | 41.5692i | −1.18033 | + | 0.681463i | −0.956090 | − | 0.293072i | \(-0.905322\pi\) |
−0.224237 | + | 0.974535i | \(0.571989\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.24264 | − | 7.34847i | −0.0652714 | − | 0.113053i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −15.5000 | + | 26.8468i | −0.231343 | + | 0.400698i | −0.958204 | − | 0.286087i | \(-0.907645\pi\) |
0.726860 | + | 0.686785i | \(0.240979\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −59.3970 | −0.836577 | −0.418289 | − | 0.908314i | \(-0.637370\pi\) | ||||
−0.418289 | + | 0.908314i | \(0.637370\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −70.5000 | − | 40.7032i | −0.965753 | − | 0.557578i | −0.0678144 | − | 0.997698i | \(-0.521603\pi\) |
−0.897939 | + | 0.440120i | \(0.854936\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 118.794 | 1.54278 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 20.5000 | + | 35.5070i | 0.259494 | + | 0.449456i | 0.966106 | − | 0.258144i | \(-0.0831110\pi\) |
−0.706613 | + | 0.707601i | \(0.749778\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.89898i | 0.0590238i | 0.999564 | + | 0.0295119i | \(0.00939530\pi\) | ||||
−0.999564 | + | 0.0295119i | \(0.990605\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −24.0000 | −0.282353 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 50.9117 | − | 29.3939i | 0.572041 | − | 0.330268i | −0.185923 | − | 0.982564i | \(-0.559527\pi\) |
0.757964 | + | 0.652296i | \(0.226194\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.5000 | + | 6.06218i | −0.115385 | + | 0.0666173i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −72.1249 | + | 124.924i | −0.759209 | + | 1.31499i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 41.5692i | 0.428549i | 0.976774 | + | 0.214274i | \(0.0687387\pi\) | ||||
−0.976774 | + | 0.214274i | \(0.931261\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −152.735 | − | 88.1816i | −1.51223 | − | 0.873085i | −0.999898 | − | 0.0142971i | \(-0.995449\pi\) |
−0.512331 | − | 0.858788i | \(-0.671218\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 25.5000 | − | 14.7224i | 0.247573 | − | 0.142936i | −0.371080 | − | 0.928601i | \(-0.621012\pi\) |
0.618652 | + | 0.785665i | \(0.287679\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −72.1249 | − | 124.924i | −0.674064 | − | 1.16751i | −0.976741 | − | 0.214421i | \(-0.931214\pi\) |
0.302677 | − | 0.953093i | \(-0.402120\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −84.5000 | + | 146.358i | −0.775229 | + | 1.34274i | 0.159436 | + | 0.987208i | \(0.449032\pi\) |
−0.934665 | + | 0.355528i | \(0.884301\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −59.3970 | −0.525637 | −0.262818 | − | 0.964845i | \(-0.584652\pi\) | ||||
−0.262818 | + | 0.964845i | \(0.584652\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −36.0000 | − | 20.7846i | −0.313043 | − | 0.180736i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 34.2929i | 0.288175i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −83.5000 | − | 144.626i | −0.690083 | − | 1.19526i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 127.373i | 1.01899i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −209.000 | −1.64567 | −0.822835 | − | 0.568281i | \(-0.807609\pi\) | ||||
−0.822835 | + | 0.568281i | \(0.807609\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 50.9117 | − | 29.3939i | 0.388639 | − | 0.224381i | −0.292931 | − | 0.956133i | \(-0.594631\pi\) |
0.681570 | + | 0.731753i | \(0.261297\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 178.500 | + | 103.057i | 1.34211 | + | 0.774865i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −76.3675 | + | 132.272i | −0.557427 | + | 0.965492i | 0.440283 | + | 0.897859i | \(0.354878\pi\) |
−0.997710 | + | 0.0676333i | \(0.978455\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 195.722i | 1.40807i | 0.710165 | + | 0.704035i | \(0.248620\pi\) | ||||
−0.710165 | + | 0.704035i | \(0.751380\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 25.4558 | + | 14.6969i | 0.178013 | + | 0.102776i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −144.000 | + | 83.1384i | −0.993103 | + | 0.573369i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −25.4558 | − | 44.0908i | −0.170845 | − | 0.295912i | 0.767871 | − | 0.640605i | \(-0.221316\pi\) |
−0.938715 | + | 0.344693i | \(0.887983\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.00000 | − | 8.66025i | 0.0331126 | − | 0.0573527i | −0.848994 | − | 0.528402i | \(-0.822791\pi\) |
0.882107 | + | 0.471049i | \(0.156125\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 59.3970 | 0.383206 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 36.0000 | + | 20.7846i | 0.229299 | + | 0.132386i | 0.610249 | − | 0.792210i | \(-0.291069\pi\) |
−0.380949 | + | 0.924596i | \(0.624403\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −29.6985 | + | 51.4393i | −0.184463 | + | 0.319499i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 43.0000 | + | 74.4782i | 0.263804 | + | 0.456921i | 0.967250 | − | 0.253828i | \(-0.0816896\pi\) |
−0.703446 | + | 0.710749i | \(0.748356\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 181.262i | − | 1.08540i | −0.839926 | − | 0.542701i | \(-0.817402\pi\) | ||
0.839926 | − | 0.542701i | \(-0.182598\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 166.000 | 0.982249 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −38.1838 | + | 22.0454i | −0.220715 | + | 0.127430i | −0.606281 | − | 0.795250i | \(-0.707340\pi\) |
0.385566 | + | 0.922680i | \(0.374006\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.00000 | 0.0400000 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.24264 | + | 7.34847i | −0.0237019 | + | 0.0410529i | −0.877633 | − | 0.479333i | \(-0.840879\pi\) |
0.853931 | + | 0.520386i | \(0.174212\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 43.3013i | 0.239234i | 0.992820 | + | 0.119617i | \(0.0381666\pi\) | ||||
−0.992820 | + | 0.119617i | \(0.961833\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 199.404 | + | 115.126i | 1.07786 | + | 0.622303i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 72.0000 | − | 41.5692i | 0.385027 | − | 0.222295i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 38.1838 | + | 66.1362i | 0.199915 | + | 0.346263i | 0.948501 | − | 0.316775i | \(-0.102600\pi\) |
−0.748586 | + | 0.663038i | \(0.769267\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 143.500 | − | 248.549i | 0.743523 | − | 1.28782i | −0.207358 | − | 0.978265i | \(-0.566487\pi\) |
0.950882 | − | 0.309555i | \(-0.100180\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 127.279 | 0.646087 | 0.323044 | − | 0.946384i | \(-0.395294\pi\) | ||||
0.323044 | + | 0.946384i | \(0.395294\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −180.000 | − | 103.923i | −0.904523 | − | 0.522226i | −0.0258579 | − | 0.999666i | \(-0.508232\pi\) |
−0.878665 | + | 0.477439i | \(0.841565\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 118.794 | + | 205.757i | 0.585192 | + | 1.01358i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 168.000 | + | 290.985i | 0.819512 | + | 1.41944i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 499.696i | − | 2.39089i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −82.0000 | −0.388626 | −0.194313 | − | 0.980940i | \(-0.562248\pi\) | ||||
−0.194313 | + | 0.980940i | \(0.562248\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −131.522 | + | 75.9342i | −0.611730 | + | 0.353182i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 84.8705i | − | 0.391108i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.24264 | + | 7.34847i | −0.0191975 | + | 0.0332510i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 41.5692i | 0.186409i | 0.995647 | + | 0.0932045i | \(0.0297110\pi\) | ||||
−0.995647 | + | 0.0932045i | \(0.970289\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −330.926 | − | 191.060i | −1.45782 | − | 0.841675i | −0.458920 | − | 0.888478i | \(-0.651763\pi\) |
−0.998904 | + | 0.0468029i | \(0.985097\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −70.5000 | + | 40.7032i | −0.307860 | + | 0.177743i | −0.645969 | − | 0.763364i | \(-0.723546\pi\) |
0.338108 | + | 0.941107i | \(0.390213\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −114.551 | − | 198.409i | −0.491636 | − | 0.851539i | 0.508317 | − | 0.861170i | \(-0.330268\pi\) |
−0.999954 | + | 0.00963059i | \(0.996934\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 204.000 | − | 353.338i | 0.868085 | − | 1.50357i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 67.8823 | 0.284026 | 0.142013 | − | 0.989865i | \(-0.454642\pi\) | ||||
0.142013 | + | 0.989865i | \(0.454642\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −396.000 | − | 228.631i | −1.64315 | − | 0.948675i | −0.979703 | − | 0.200455i | \(-0.935758\pi\) |
−0.663451 | − | 0.748220i | \(-0.730909\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 240.050i | 0.979796i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 25.5000 | + | 44.1673i | 0.103239 | + | 0.178815i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 347.828i | 1.38577i | 0.721050 | + | 0.692884i | \(0.243660\pi\) | ||||
−0.721050 | + | 0.692884i | \(0.756340\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 144.000 | 0.569170 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 140.007 | − | 80.8332i | 0.544775 | − | 0.314526i | −0.202237 | − | 0.979337i | \(-0.564821\pi\) |
0.747012 | + | 0.664811i | \(0.231488\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 164.500 | − | 284.922i | 0.635135 | − | 1.10009i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 127.279 | − | 220.454i | 0.483951 | − | 0.838228i | −0.515879 | − | 0.856662i | \(-0.672534\pi\) |
0.999830 | + | 0.0184332i | \(0.00586781\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 374.123i | − | 1.41178i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 16.9706 | + | 9.79796i | 0.0630876 | + | 0.0364236i | 0.531212 | − | 0.847239i | \(-0.321737\pi\) |
−0.468124 | + | 0.883663i | \(0.655070\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −36.0000 | + | 20.7846i | −0.132841 | + | 0.0766960i | −0.564948 | − | 0.825127i | \(-0.691104\pi\) |
0.432107 | + | 0.901823i | \(0.357770\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −8.48528 | − | 14.6969i | −0.0308556 | − | 0.0534434i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 168.500 | − | 291.851i | 0.608303 | − | 1.05361i | −0.383217 | − | 0.923658i | \(-0.625184\pi\) |
0.991520 | − | 0.129954i | \(-0.0414829\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 246.073 | 0.875705 | 0.437853 | − | 0.899047i | \(-0.355739\pi\) | ||||
0.437853 | + | 0.899047i | \(0.355739\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 169.500 | + | 97.8609i | 0.598940 | + | 0.345798i | 0.768624 | − | 0.639700i | \(-0.220942\pi\) |
−0.169685 | + | 0.985498i | \(0.554275\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 415.779 | − | 240.050i | 1.44871 | − | 0.836411i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −132.500 | − | 229.497i | −0.458478 | − | 0.794106i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 97.9796i | 0.334401i | 0.985923 | + | 0.167201i | \(0.0534728\pi\) | ||||
−0.985923 | + | 0.167201i | \(0.946527\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 408.000 | 1.38305 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −12.7279 | + | 7.34847i | −0.0425683 | + | 0.0245768i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 108.500 | + | 187.928i | 0.360465 | + | 0.624344i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −203.647 | + | 352.727i | −0.667694 | + | 1.15648i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 71.0141i | 0.231316i | 0.993289 | + | 0.115658i | \(0.0368977\pi\) | ||||
−0.993289 | + | 0.115658i | \(0.963102\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −186.676 | − | 107.778i | −0.600245 | − | 0.346552i | 0.168893 | − | 0.985634i | \(-0.445981\pi\) |
−0.769138 | + | 0.639083i | \(0.779314\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 253.500 | − | 146.358i | 0.809904 | − | 0.467598i | −0.0370184 | − | 0.999315i | \(-0.511786\pi\) |
0.846923 | + | 0.531716i | \(0.178453\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 118.794 | + | 205.757i | 0.374744 | + | 0.649076i | 0.990289 | − | 0.139026i | \(-0.0443972\pi\) |
−0.615544 | + | 0.788102i | \(0.711064\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 288.000 | − | 498.831i | 0.902821 | − | 1.56373i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 144.250 | 0.446594 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.50000 | + | 0.866025i | 0.00461538 | + | 0.00266469i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −504.874 | − | 291.489i | −1.53457 | − | 0.885986i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −92.5000 | − | 160.215i | −0.279456 | − | 0.484032i | 0.691794 | − | 0.722095i | \(-0.256821\pi\) |
−0.971250 | + | 0.238063i | \(0.923488\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 151.868i | 0.453338i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −359.000 | −1.06528 | −0.532641 | − | 0.846341i | \(-0.678800\pi\) | ||||
−0.532641 | + | 0.846341i | \(0.678800\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −178.191 | + | 102.879i | −0.522554 | + | 0.301697i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000 | 1.00000 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 233.345 | − | 404.166i | 0.672465 | − | 1.16474i | −0.304738 | − | 0.952436i | \(-0.598569\pi\) |
0.977203 | − | 0.212307i | \(-0.0680976\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 581.969i | 1.66753i | 0.552117 | + | 0.833767i | \(0.313820\pi\) | ||||
−0.552117 | + | 0.833767i | \(0.686180\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 250.316 | + | 144.520i | 0.709110 | + | 0.409405i | 0.810731 | − | 0.585418i | \(-0.199070\pi\) |
−0.101621 | + | 0.994823i | \(0.532403\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −252.000 | + | 145.492i | −0.709859 | + | 0.409837i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 169.706 | + | 293.939i | 0.472718 | + | 0.818771i | 0.999512 | − | 0.0312215i | \(-0.00993973\pi\) |
−0.526795 | + | 0.849992i | \(0.676606\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 253.000 | − | 438.209i | 0.700831 | − | 1.21387i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −398.808 | −1.09263 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −133.500 | − | 77.0763i | −0.363760 | − | 0.210017i | 0.306969 | − | 0.951720i | \(-0.400685\pi\) |
−0.670729 | + | 0.741703i | \(0.734019\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −534.573 | −1.44090 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 144.500 | + | 250.281i | 0.387399 | + | 0.670996i | 0.992099 | − | 0.125458i | \(-0.0400401\pi\) |
−0.604699 | + | 0.796454i | \(0.706707\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 58.7878i | 0.155936i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.00000 | −0.0184697 | −0.00923483 | − | 0.999957i | \(-0.502940\pi\) | ||||
−0.00923483 | + | 0.999957i | \(0.502940\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −428.507 | + | 247.398i | −1.11882 | + | 0.645949i | −0.941099 | − | 0.338132i | \(-0.890205\pi\) |
−0.177718 | + | 0.984081i | \(0.556871\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 504.000 | − | 290.985i | 1.30909 | − | 0.755804i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 114.551 | − | 198.409i | 0.294476 | − | 0.510048i | −0.680387 | − | 0.732853i | \(-0.738188\pi\) |
0.974863 | + | 0.222805i | \(0.0715214\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 41.5692i | 0.106315i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 173.948 | + | 100.429i | 0.440375 | + | 0.254251i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 70.5000 | − | 40.7032i | 0.177582 | − | 0.102527i | −0.408574 | − | 0.912725i | \(-0.633974\pi\) |
0.586156 | + | 0.810198i | \(0.300641\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 46.6690 | + | 80.8332i | 0.116382 | + | 0.201579i | 0.918331 | − | 0.395813i | \(-0.129537\pi\) |
−0.801950 | + | 0.597392i | \(0.796204\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.5000 | − | 18.1865i | 0.0260546 | − | 0.0451279i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −797.616 | −1.95975 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −361.500 | − | 208.712i | −0.883863 | − | 0.510299i | −0.0119329 | − | 0.999929i | \(-0.503798\pi\) |
−0.871930 | + | 0.489630i | \(0.837132\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 582.979i | − | 1.41157i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12.0000 | + | 20.7846i | 0.0289157 | + | 0.0500834i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 19.5959i | − | 0.0467683i | −0.999727 | − | 0.0233842i | \(-0.992556\pi\) | ||
0.999727 | − | 0.0233842i | \(-0.00744408\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 407.000 | 0.966746 | 0.483373 | − | 0.875415i | \(-0.339412\pi\) | ||||
0.483373 | + | 0.875415i | \(0.339412\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.24264 | − | 2.44949i | 0.00998268 | − | 0.00576351i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 504.000 | + | 290.985i | 1.18033 | + | 0.681463i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −80.6102 | + | 139.621i | −0.187031 | + | 0.323946i | −0.944259 | − | 0.329204i | \(-0.893220\pi\) |
0.757228 | + | 0.653150i | \(0.226553\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 168.009i | − | 0.388011i | −0.981000 | − | 0.194006i | \(-0.937852\pi\) | ||
0.981000 | − | 0.194006i | \(-0.0621480\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 216.375 | + | 124.924i | 0.495137 | + | 0.285867i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 468.000 | − | 270.200i | 1.06606 | − | 0.615490i | 0.138957 | − | 0.990298i | \(-0.455625\pi\) |
0.927102 | + | 0.374809i | \(0.122292\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 63.6396 | + | 110.227i | 0.143656 | + | 0.248819i | 0.928871 | − | 0.370404i | \(-0.120781\pi\) |
−0.785215 | + | 0.619224i | \(0.787447\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 144.000 | − | 249.415i | 0.323596 | − | 0.560484i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 110.309 | 0.245676 | 0.122838 | − | 0.992427i | \(-0.460800\pi\) | ||||
0.122838 | + | 0.992427i | \(0.460800\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1008.00 | − | 581.969i | −2.23503 | − | 1.29040i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −29.6985 | + | 51.4393i | −0.0652714 | + | 0.113053i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12.5000 | − | 21.6506i | −0.0273523 | − | 0.0473756i | 0.852025 | − | 0.523501i | \(-0.175374\pi\) |
−0.879378 | + | 0.476125i | \(0.842041\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 78.3837i | − | 0.170030i | −0.996380 | − | 0.0850148i | \(-0.972906\pi\) | ||
0.996380 | − | 0.0850148i | \(-0.0270938\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −521.000 | −1.12527 | −0.562635 | − | 0.826705i | \(-0.690212\pi\) | ||||
−0.562635 | + | 0.826705i | \(0.690212\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 190.919 | − | 110.227i | 0.408820 | − | 0.236032i | −0.281463 | − | 0.959572i | \(-0.590820\pi\) |
0.690283 | + | 0.723540i | \(0.257486\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 217.000 | 0.462687 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 263.044 | − | 455.605i | 0.556118 | − | 0.963224i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 29.4449i | − | 0.0619892i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 759.433 | + | 438.459i | 1.58545 | + | 0.915363i | 0.994043 | + | 0.108993i | \(0.0347626\pi\) |
0.591412 | + | 0.806370i | \(0.298571\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 70.5000 | − | 40.7032i | 0.146570 | − | 0.0846220i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 101.823 | + | 176.363i | 0.209945 | + | 0.363636i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 63.5000 | − | 109.985i | 0.130390 | − | 0.225842i | −0.793437 | − | 0.608653i | \(-0.791710\pi\) |
0.923827 | + | 0.382810i | \(0.125044\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 627.911 | 1.27884 | 0.639420 | − | 0.768857i | \(-0.279174\pi\) | ||||
0.639420 | + | 0.768857i | \(0.279174\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 144.000 | + | 83.1384i | 0.292089 | + | 0.168638i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 207.889 | + | 360.075i | 0.418289 | + | 0.724497i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −116.500 | − | 201.784i | −0.233467 | − | 0.404377i | 0.725359 | − | 0.688371i | \(-0.241674\pi\) |
−0.958826 | + | 0.283994i | \(0.908340\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 538.888i | − | 1.07135i | −0.844425 | − | 0.535674i | \(-0.820058\pi\) | ||
0.844425 | − | 0.535674i | \(-0.179942\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −864.000 | −1.71089 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 275.772 | − | 159.217i | 0.541791 | − | 0.312803i | −0.204013 | − | 0.978968i | \(-0.565399\pi\) |
0.745805 | + | 0.666165i | \(0.232065\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 569.845i | 1.11516i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 72.1249 | − | 124.924i | 0.140048 | − | 0.242571i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1413.35i | 2.73376i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −492.146 | − | 284.141i | −0.944619 | − | 0.545376i | −0.0532135 | − | 0.998583i | \(-0.516946\pi\) |
−0.891405 | + | 0.453207i | \(0.850280\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −457.500 | + | 264.138i | −0.874761 | + | 0.505043i | −0.868927 | − | 0.494939i | \(-0.835190\pi\) |
−0.00583355 | + | 0.999983i | \(0.501857\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −29.6985 | − | 51.4393i | −0.0563539 | − | 0.0976078i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 228.500 | − | 395.774i | 0.431947 | − | 0.748154i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 118.794 | 0.222878 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −612.000 | − | 353.338i | −1.14393 | − | 0.660446i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −415.779 | − | 720.150i | −0.771389 | − | 1.33609i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −167.500 | − | 290.119i | −0.309612 | − | 0.536263i | 0.668666 | − | 0.743563i | \(-0.266866\pi\) |
−0.978277 | + | 0.207300i | \(0.933532\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 827.928i | 1.51913i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 658.000 | 1.20293 | 0.601463 | − | 0.798901i | \(-0.294585\pi\) | ||||
0.601463 | + | 0.798901i | \(0.294585\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 865.499 | − | 499.696i | 1.57078 | − | 0.906889i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 143.500 | − | 248.549i | 0.259494 | − | 0.449456i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 135.765 | − | 235.151i | 0.243742 | − | 0.422174i | −0.718035 | − | 0.696007i | \(-0.754958\pi\) |
0.961777 | + | 0.273833i | \(0.0882915\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 53.6936i | 0.0960529i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 12.7279 | + | 7.34847i | 0.0226073 | + | 0.0130523i | 0.511261 | − | 0.859425i | \(-0.329179\pi\) |
−0.488654 | + | 0.872478i | \(0.662512\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −252.000 | + | 145.492i | −0.446018 | + | 0.257508i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 424.264 | + | 734.847i | 0.745631 | + | 1.29147i | 0.949899 | + | 0.312556i | \(0.101185\pi\) |
−0.204268 | + | 0.978915i | \(0.565481\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 224.500 | − | 388.845i | 0.393170 | − | 0.680990i | −0.599696 | − | 0.800228i | \(-0.704712\pi\) |
0.992866 | + | 0.119238i | \(0.0380451\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.48528 | 0.0147570 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −253.500 | − | 146.358i | −0.439341 | − | 0.253654i | 0.263977 | − | 0.964529i | \(-0.414966\pi\) |
−0.703318 | + | 0.710875i | \(0.748299\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 29.6985 | − | 17.1464i | 0.0511162 | − | 0.0295119i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 648.000 | + | 1122.37i | 1.11149 | + | 1.92516i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 529.090i | 0.901345i | 0.892689 | + | 0.450673i | \(0.148816\pi\) | ||||
−0.892689 | + | 0.450673i | \(0.851184\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −357.000 | −0.606112 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −907.925 | + | 524.191i | −1.53107 | + | 0.883964i | −0.531758 | + | 0.846896i | \(0.678469\pi\) |
−0.999313 | + | 0.0370681i | \(0.988198\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 84.0000 | + | 145.492i | 0.141176 | + | 0.244525i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −322.441 | + | 558.484i | −0.538298 | + | 0.932360i | 0.460698 | + | 0.887557i | \(0.347599\pi\) |
−0.998996 | + | 0.0448028i | \(0.985734\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 458.993i | 0.763716i | 0.924221 | + | 0.381858i | \(0.124716\pi\) | ||||
−0.924221 | + | 0.381858i | \(0.875284\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −708.521 | − | 409.065i | −1.17111 | − | 0.676140i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −910.500 | + | 525.677i | −1.50000 | + | 0.866025i | −0.500000 | + | 0.866025i | \(0.666667\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −72.1249 | − | 124.924i | −0.118044 | − | 0.204458i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −145.000 | + | 251.147i | −0.236542 | + | 0.409702i | −0.959720 | − | 0.280960i | \(-0.909347\pi\) |
0.723178 | + | 0.690662i | \(0.242681\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −729.734 | −1.18271 | −0.591357 | − | 0.806410i | \(-0.701407\pi\) | ||||
−0.591357 | + | 0.806410i | \(0.701407\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 709.500 | + | 409.630i | 1.14620 | + | 0.661761i | 0.947959 | − | 0.318392i | \(-0.103143\pi\) |
0.198244 | + | 0.980153i | \(0.436476\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −356.382 | − | 205.757i | −0.572041 | − | 0.330268i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 299.500 | + | 518.749i | 0.479200 | + | 0.829999i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 230.252i | − | 0.366060i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 58.0000 | 0.0919176 | 0.0459588 | − | 0.998943i | \(-0.485366\pi\) | ||||
0.0459588 | + | 0.998943i | \(0.485366\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −886.712 | + | 511.943i | −1.39640 | + | 0.806210i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 73.5000 | + | 42.4352i | 0.115385 | + | 0.0666173i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 479.418 | − | 830.377i | 0.747923 | − | 1.29544i | −0.200894 | − | 0.979613i | \(-0.564385\pi\) |
0.948817 | − | 0.315827i | \(-0.102282\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 760.370i | 1.18254i | 0.806475 | + | 0.591268i | \(0.201372\pi\) | ||||
−0.806475 | + | 0.591268i | \(0.798628\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −305.470 | − | 176.363i | −0.472133 | − | 0.272586i | 0.244999 | − | 0.969523i | \(-0.421212\pi\) |
−0.717132 | + | 0.696937i | \(0.754546\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1224.00 | + | 706.677i | −1.88598 | + | 1.08887i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −220.617 | − | 382.120i | −0.337852 | − | 0.585177i | 0.646177 | − | 0.763188i | \(-0.276367\pi\) |
−0.984028 | + | 0.178011i | \(0.943034\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 144.000 | − | 249.415i | 0.219847 | − | 0.380787i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 161.220 | 0.244644 | 0.122322 | − | 0.992490i | \(-0.460966\pi\) | ||||
0.122322 | + | 0.992490i | \(0.460966\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −721.500 | − | 416.558i | −1.09153 | − | 0.630194i | −0.157545 | − | 0.987512i | \(-0.550358\pi\) |
−0.933983 | + | 0.357318i | \(0.883691\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1009.75 | 1.51842 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 144.000 | + | 249.415i | 0.215892 | + | 0.373936i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 1410.91i | − | 2.10269i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −263.000 | −0.390788 | −0.195394 | − | 0.980725i | \(-0.562598\pi\) | ||||
−0.195394 | + | 0.980725i | \(0.562598\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −432.749 | + | 249.848i | −0.639216 | + | 0.369052i | −0.784313 | − | 0.620366i | \(-0.786984\pi\) |
0.145096 | + | 0.989418i | \(0.453651\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 252.000 | − | 145.492i | 0.371134 | − | 0.214274i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −479.418 | + | 830.377i | −0.701930 | + | 1.21578i | 0.265858 | + | 0.964012i | \(0.414345\pi\) |
−0.967788 | + | 0.251767i | \(0.918988\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 748.246i | 1.09233i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −114.551 | − | 66.1362i | −0.166257 | − | 0.0959887i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1069.50 | + | 617.476i | −1.54776 | + | 0.893598i | −0.549444 | + | 0.835530i | \(0.685161\pi\) |
−0.998313 | + | 0.0580674i | \(0.981506\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 479.418 | + | 830.377i | 0.689811 | + | 1.19479i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 168.000 | − | 290.985i | 0.241033 | − | 0.417481i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 975.807 | 1.39202 | 0.696011 | − | 0.718031i | \(-0.254956\pi\) | ||||
0.696011 | + | 0.718031i | \(0.254956\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1198.50 | − | 691.954i | −1.70484 | − | 0.984288i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1234.54i | 1.74617i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 553.000 | + | 957.824i | 0.779972 | + | 1.35095i | 0.931957 | + | 0.362568i | \(0.118100\pi\) |
−0.151986 | + | 0.988383i | \(0.548567\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 102.879i | − | 0.144290i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 144.000 | 0.201399 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −593.970 | + | 342.929i | −0.826105 | + | 0.476952i | −0.852517 | − | 0.522699i | \(-0.824925\pi\) |
0.0264120 | + | 0.999651i | \(0.491592\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −178.500 | − | 103.057i | −0.247573 | − | 0.142936i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 16.9706 | − | 29.3939i | 0.0234077 | − | 0.0405433i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 427.817i | 0.588468i | 0.955733 | + | 0.294234i | \(0.0950646\pi\) | ||||
−0.955733 | + | 0.294234i | \(0.904935\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 131.522 | + | 75.9342i | 0.179920 | + | 0.103877i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 34.5000 | − | 19.9186i | 0.0470668 | − | 0.0271741i | −0.476282 | − | 0.879293i | \(-0.658016\pi\) |
0.523349 | + | 0.852119i | \(0.324682\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −263.044 | − | 455.605i | −0.356911 | − | 0.618189i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −243.500 | + | 421.754i | −0.329499 | + | 0.570710i | −0.982413 | − | 0.186723i | \(-0.940213\pi\) |
0.652913 | + | 0.757433i | \(0.273547\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 509.117 | 0.685218 | 0.342609 | − | 0.939478i | \(-0.388689\pi\) | ||||
0.342609 | + | 0.939478i | \(0.388689\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −216.000 | − | 124.708i | −0.289933 | − | 0.167393i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −504.874 | + | 874.468i | −0.674064 | + | 1.16751i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −272.500 | − | 471.984i | −0.362850 | − | 0.628474i | 0.625579 | − | 0.780161i | \(-0.284863\pi\) |
−0.988429 | + | 0.151687i | \(0.951529\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 48.9898i | − | 0.0648871i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −770.000 | −1.01717 | −0.508587 | − | 0.861011i | \(-0.669832\pi\) | ||||
−0.508587 | + | 0.861011i | \(0.669832\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 148.492 | − | 85.7321i | 0.195128 | − | 0.112657i | −0.399253 | − | 0.916841i | \(-0.630730\pi\) |
0.594381 | + | 0.804184i | \(0.297397\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1183.00 | 1.55046 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 72.1249 | − | 124.924i | 0.0940351 | − | 0.162874i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 704.945i | 0.916703i | 0.888771 | + | 0.458352i | \(0.151560\pi\) | ||||
−0.888771 | + | 0.458352i | \(0.848440\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 797.616 | + | 460.504i | 1.03185 | + | 0.595736i | 0.917513 | − | 0.397706i | \(-0.130194\pi\) |
0.114333 | + | 0.993443i | \(0.463527\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −10.5000 | + | 6.06218i | −0.0135484 | + | 0.00782216i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1009.75 | − | 1748.94i | −1.29621 | − | 2.24510i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 504.000 | − | 872.954i | 0.645327 | − | 1.11774i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 203.647 | 0.259423 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −396.000 | − | 228.631i | −0.503177 | − | 0.290509i | 0.226848 | − | 0.973930i | \(-0.427158\pi\) |
−0.730024 | + | 0.683421i | \(0.760491\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 207.889 | + | 360.075i | 0.262818 | + | 0.455215i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 72.0000 | + | 124.708i | 0.0907945 | + | 0.157261i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 14.6969i | − | 0.0184403i | −0.999957 | − | 0.00922016i | \(-0.997065\pi\) | ||
0.999957 | − | 0.00922016i | \(-0.00293491\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −408.000 | −0.510638 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1196.42 | − | 690.756i | 1.48994 | − | 0.860219i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 290.985i | 0.361471i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −470.933 | + | 815.680i | −0.582118 | + | 1.00826i | 0.413110 | + | 0.910681i | \(0.364442\pi\) |
−0.995228 | + | 0.0975763i | \(0.968891\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 498.831i | 0.615081i | 0.951535 | + | 0.307540i | \(0.0995059\pi\) | ||||
−0.951535 | + | 0.307540i | \(0.900494\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 364.867 | + | 210.656i | 0.447690 | + | 0.258474i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 790.500 | − | 456.395i | 0.967564 | − | 0.558623i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −301.227 | − | 521.741i | −0.366903 | − | 0.635495i | 0.622176 | − | 0.782877i | \(-0.286249\pi\) |
−0.989080 | + | 0.147382i | \(0.952915\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 19.0000 | − | 32.9090i | 0.0230863 | − | 0.0399866i | −0.854251 | − | 0.519860i | \(-0.825984\pi\) |
0.877338 | + | 0.479873i | \(0.159317\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 687.308 | 0.831086 | 0.415543 | − | 0.909574i | \(-0.363592\pi\) | ||||
0.415543 | + | 0.909574i | \(0.363592\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −721.500 | − | 416.558i | −0.870326 | − | 0.502483i | −0.00286924 | − | 0.999996i | \(-0.500913\pi\) |
−0.867456 | + | 0.497513i | \(0.834247\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 207.889 | − | 120.025i | 0.249567 | − | 0.144088i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −444.000 | − | 769.031i | −0.531737 | − | 0.920995i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 244.949i | 0.291953i | 0.989288 | + | 0.145977i | \(0.0466325\pi\) | ||||
−0.989288 | + | 0.145977i | \(0.953368\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 311.000 | 0.369798 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 704.278 | − | 406.615i | 0.833466 | − | 0.481202i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −584.500 | + | 1012.38i | −0.690083 | + | 1.19526i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 199.404 | − | 345.378i | 0.234317 | − | 0.405850i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 1245.34i | − | 1.45996i | −0.683469 | − | 0.729979i | \(-0.739530\pi\) | ||
0.683469 | − | 0.729979i | \(-0.260470\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1060.66 | − | 612.372i | −1.23764 | − | 0.714554i | −0.269031 | − | 0.963131i | \(-0.586703\pi\) |
−0.968612 | + | 0.248578i | \(0.920037\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −216.000 | + | 124.708i | −0.251455 | + | 0.145178i | −0.620430 | − | 0.784262i | \(-0.713042\pi\) |
0.368975 | + | 0.929439i | \(0.379709\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −330.926 | − | 573.181i | −0.383460 | − | 0.664172i | 0.608094 | − | 0.793865i | \(-0.291934\pi\) |
−0.991554 | + | 0.129693i | \(0.958601\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −108.000 | + | 187.061i | −0.124855 | + | 0.216256i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −695.793 | −0.800682 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 46.5000 | + | 26.8468i | 0.0533869 | + | 0.0308229i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 772.161 | − | 445.807i | 0.882469 | − | 0.509494i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 287.000 | + | 497.099i | 0.327252 | + | 0.566817i | 0.981966 | − | 0.189060i | \(-0.0605441\pi\) |
−0.654714 | + | 0.755877i | \(0.727211\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 161.666i | − | 0.183503i | −0.995782 | − | 0.0917516i | \(-0.970753\pi\) | ||
0.995782 | − | 0.0917516i | \(-0.0292466\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1735.00 | −1.96489 | −0.982446 | − | 0.186546i | \(-0.940271\pi\) | ||||
−0.982446 | + | 0.186546i | \(0.940271\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −169.706 | + | 97.9796i | −0.191325 | + | 0.110462i | −0.592603 | − | 0.805495i | \(-0.701900\pi\) |
0.401277 | + | 0.915957i | \(0.368566\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 731.500 | + | 1267.00i | 0.822835 | + | 1.42519i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1226.12 | + | 2123.71i | −1.37304 | + | 2.37817i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 41.5692i | 0.0464461i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −356.382 | − | 205.757i | −0.396420 | − | 0.228873i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −324.000 | + | 187.061i | −0.359600 | + | 0.207615i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 106.066 | + | 183.712i | 0.117200 | + | 0.202996i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 375.500 | − | 650.385i | 0.414002 | − | 0.717073i | −0.581321 | − | 0.813674i | \(-0.697464\pi\) |
0.995323 | + | 0.0966015i | \(0.0307972\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1247.34 | −1.36919 | −0.684597 | − | 0.728921i | \(-0.740022\pi\) | ||||
−0.684597 | + | 0.728921i | \(0.740022\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −72.0000 | − | 41.5692i | −0.0788609 | − | 0.0455304i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −356.382 | − | 205.757i | −0.388639 | − | 0.224381i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 507.500 | + | 879.016i | 0.552231 | + | 0.956492i | 0.998113 | + | 0.0614001i | \(0.0195566\pi\) |
−0.445883 | + | 0.895091i | \(0.647110\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 102.879i | 0.111461i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −47.0000 | −0.0508108 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 946.109 | − | 546.236i | 1.01842 | − | 0.587983i | 0.104772 | − | 0.994496i | \(-0.466589\pi\) |
0.913645 | + | 0.406513i | \(0.133256\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 1442.80i | − | 1.54973i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 203.647 | − | 352.727i | 0.217804 | − | 0.377248i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1747.64i | 1.86514i | 0.360985 | + | 0.932572i | \(0.382441\pi\) | ||||
−0.360985 | + | 0.932572i | \(0.617559\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1073.39 | + | 619.721i | 1.14069 | + | 0.658577i | 0.946601 | − | 0.322407i | \(-0.104492\pi\) |
0.194088 | + | 0.980984i | \(0.437825\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 504.000 | − | 290.985i | 0.534464 | − | 0.308573i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 602.455 | + | 1043.48i | 0.636172 | + | 1.10188i | 0.986266 | + | 0.165168i | \(0.0528165\pi\) |
−0.350093 | + | 0.936715i | \(0.613850\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −70.5000 | + | 122.110i | −0.0742887 | + | 0.128672i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1026.72 | 1.07735 | 0.538677 | − | 0.842512i | \(-0.318924\pi\) | ||||
0.538677 | + | 0.842512i | \(0.318924\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 324.000 | + | 187.061i | 0.339267 | + | 0.195876i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1069.15 | 1.11485 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −407.000 | − | 704.945i | −0.423517 | − | 0.733553i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 1406.01i | − | 1.45700i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 895.000 | 0.925543 | 0.462771 | − | 0.886478i | \(-0.346855\pi\) | ||||
0.462771 | + | 0.886478i | \(0.346855\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 182.434 | − | 105.328i | 0.187882 | − | 0.108474i | −0.403109 | − | 0.915152i | \(-0.632070\pi\) |
0.590991 | + | 0.806678i | \(0.298737\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1186.50 | − | 685.026i | 1.21942 | − | 0.704035i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 627.911 | − | 1087.57i | 0.642693 | − | 1.11318i | −0.342136 | − | 0.939650i | \(-0.611151\pi\) |
0.984829 | − | 0.173526i | \(-0.0555161\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 997.661i | 1.01906i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1022.48 | − | 590.327i | −1.04016 | − | 0.600536i | −0.120281 | − | 0.992740i | \(-0.538379\pi\) |
−0.919878 | + | 0.392204i | \(0.871713\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 540.000 | − | 311.769i | 0.548223 | − | 0.316517i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 131.522 | + | 227.803i | 0.132985 | + | 0.230336i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 327.500 | − | 567.247i | 0.330474 | − | 0.572398i | −0.652131 | − | 0.758107i | \(-0.726125\pi\) |
0.982605 | + | 0.185708i | \(0.0594580\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1018.23 | −1.02335 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 397.500 | + | 229.497i | 0.398696 | + | 0.230187i | 0.685921 | − | 0.727676i | \(-0.259399\pi\) |
−0.287225 | + | 0.957863i | \(0.592733\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1008.3.cg.i.577.2 | 4 | ||
3.2 | odd | 2 | inner | 1008.3.cg.i.577.1 | 4 | ||
4.3 | odd | 2 | 126.3.n.b.73.1 | yes | 4 | ||
7.5 | odd | 6 | inner | 1008.3.cg.i.145.2 | 4 | ||
12.11 | even | 2 | 126.3.n.b.73.2 | yes | 4 | ||
21.5 | even | 6 | inner | 1008.3.cg.i.145.1 | 4 | ||
28.3 | even | 6 | 882.3.c.c.685.3 | 4 | |||
28.11 | odd | 6 | 882.3.c.c.685.4 | 4 | |||
28.19 | even | 6 | 126.3.n.b.19.1 | ✓ | 4 | ||
28.23 | odd | 6 | 882.3.n.c.19.1 | 4 | |||
28.27 | even | 2 | 882.3.n.c.325.1 | 4 | |||
84.11 | even | 6 | 882.3.c.c.685.1 | 4 | |||
84.23 | even | 6 | 882.3.n.c.19.2 | 4 | |||
84.47 | odd | 6 | 126.3.n.b.19.2 | yes | 4 | ||
84.59 | odd | 6 | 882.3.c.c.685.2 | 4 | |||
84.83 | odd | 2 | 882.3.n.c.325.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
126.3.n.b.19.1 | ✓ | 4 | 28.19 | even | 6 | ||
126.3.n.b.19.2 | yes | 4 | 84.47 | odd | 6 | ||
126.3.n.b.73.1 | yes | 4 | 4.3 | odd | 2 | ||
126.3.n.b.73.2 | yes | 4 | 12.11 | even | 2 | ||
882.3.c.c.685.1 | 4 | 84.11 | even | 6 | |||
882.3.c.c.685.2 | 4 | 84.59 | odd | 6 | |||
882.3.c.c.685.3 | 4 | 28.3 | even | 6 | |||
882.3.c.c.685.4 | 4 | 28.11 | odd | 6 | |||
882.3.n.c.19.1 | 4 | 28.23 | odd | 6 | |||
882.3.n.c.19.2 | 4 | 84.23 | even | 6 | |||
882.3.n.c.325.1 | 4 | 28.27 | even | 2 | |||
882.3.n.c.325.2 | 4 | 84.83 | odd | 2 | |||
1008.3.cg.i.145.1 | 4 | 21.5 | even | 6 | inner | ||
1008.3.cg.i.145.2 | 4 | 7.5 | odd | 6 | inner | ||
1008.3.cg.i.577.1 | 4 | 3.2 | odd | 2 | inner | ||
1008.3.cg.i.577.2 | 4 | 1.1 | even | 1 | trivial |