Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [882,3,Mod(685,882)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(882, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("882.685");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 882.c (of order \(2\), degree \(1\), 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: | \(24.0327593166\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
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: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 126) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 685.1 | ||
Root | \(-0.707107 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 882.685 |
Dual form | 882.3.c.c.685.2 |
$q$-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 \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(785\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.41421 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | − 4.89898i | − 0.979796i | −0.871780 | − | 0.489898i | \(-0.837034\pi\) | ||||
0.871780 | − | 0.489898i | \(-0.162966\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.82843 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 6.92820i | 0.692820i | ||||||||
\(11\) | 16.9706 | 1.54278 | 0.771389 | − | 0.636364i | \(-0.219562\pi\) | ||||
0.771389 | + | 0.636364i | \(0.219562\pi\) | |||||||
\(12\) | 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 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | − 4.89898i | − 0.288175i | −0.989565 | − | 0.144088i | \(-0.953975\pi\) | ||||
0.989565 | − | 0.144088i | \(-0.0460247\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 29.4449i | 1.54973i | 0.632127 | + | 0.774865i | \(0.282182\pi\) | ||||
−0.632127 | + | 0.774865i | \(0.717818\pi\) | |||||||
\(20\) | − 9.79796i | − 0.489898i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −24.0000 | −1.09091 | ||||||||
\(23\) | 8.48528 | 0.368925 | 0.184463 | − | 0.982840i | \(-0.440946\pi\) | ||||
0.184463 | + | 0.982840i | \(0.440946\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.0400000 | ||||||||
\(26\) | 2.44949i | 0.0942111i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 33.9411 | 1.17038 | 0.585192 | − | 0.810895i | \(-0.301019\pi\) | ||||
0.585192 | + | 0.810895i | \(0.301019\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 12.1244i | 0.391108i | 0.980693 | + | 0.195554i | \(0.0626505\pi\) | ||||
−0.980693 | + | 0.195554i | \(0.937349\pi\) | |||||||
\(32\) | −5.65685 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.92820i | 0.203771i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −47.0000 | −1.27027 | −0.635135 | − | 0.772401i | \(-0.719056\pi\) | ||||
−0.635135 | + | 0.772401i | \(0.719056\pi\) | |||||||
\(38\) | − 41.6413i | − 1.09582i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 13.8564i | 0.346410i | ||||||||
\(41\) | − 68.5857i | − 1.67282i | −0.548103 | − | 0.836411i | \(-0.684650\pi\) | ||||
0.548103 | − | 0.836411i | \(-0.315350\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 31.0000 | 0.720930 | 0.360465 | − | 0.932773i | \(-0.382618\pi\) | ||||
0.360465 | + | 0.932773i | \(0.382618\pi\) | |||||||
\(44\) | 33.9411 | 0.771389 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −12.0000 | −0.260870 | ||||||||
\(47\) | 83.2827i | 1.77197i | 0.463713 | + | 0.885986i | \(0.346517\pi\) | ||||
−0.463713 | + | 0.885986i | \(0.653483\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −1.41421 | −0.0282843 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − 3.46410i | − 0.0666173i | ||||||||
\(53\) | 76.3675 | 1.44090 | 0.720448 | − | 0.693509i | \(-0.243936\pi\) | ||||
0.720448 | + | 0.693509i | \(0.243936\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 83.1384i | − 1.51161i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −48.0000 | −0.827586 | ||||||||
\(59\) | − 83.2827i | − 1.41157i | −0.708426 | − | 0.705785i | \(-0.750594\pi\) | ||||
0.708426 | − | 0.705785i | \(-0.249406\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 83.1384i | − 1.36293i | −0.731853 | − | 0.681463i | \(-0.761344\pi\) | ||||
0.731853 | − | 0.681463i | \(-0.238656\pi\) | |||||||
\(62\) | − 17.1464i | − 0.276555i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | −8.48528 | −0.130543 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −31.0000 | −0.462687 | −0.231343 | − | 0.972872i | \(-0.574312\pi\) | ||||
−0.231343 | + | 0.972872i | \(0.574312\pi\) | |||||||
\(68\) | − 9.79796i | − 0.144088i | ||||||||
\(69\) | 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 | ||||||||
\(73\) | 81.4064i | 1.11516i | 0.830125 | + | 0.557578i | \(0.188269\pi\) | ||||
−0.830125 | + | 0.557578i | \(0.811731\pi\) | |||||||
\(74\) | 66.4680 | 0.898217 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 58.8897i | 0.774865i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 41.0000 | 0.518987 | 0.259494 | − | 0.965745i | \(-0.416444\pi\) | ||||
0.259494 | + | 0.965745i | \(0.416444\pi\) | |||||||
\(80\) | − 19.5959i | − 0.244949i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 96.9948i | 1.18286i | ||||||||
\(83\) | 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 | ||||||||
\(86\) | −43.8406 | −0.509775 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −48.0000 | −0.545455 | ||||||||
\(89\) | − 58.7878i | − 0.660537i | −0.943887 | − | 0.330268i | \(-0.892861\pi\) | ||||
0.943887 | − | 0.330268i | \(-0.107139\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 16.9706 | 0.184463 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − 117.779i | − 1.25297i | ||||||||
\(95\) | 144.250 | 1.51842 | ||||||||
\(96\) | 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 | ||||||||
\(100\) | 2.00000 | 0.0200000 | ||||||||
\(101\) | − 176.363i | − 1.74617i | −0.487567 | − | 0.873085i | \(-0.662116\pi\) | ||||
0.487567 | − | 0.873085i | \(-0.337884\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 29.4449i | − 0.285872i | −0.989732 | − | 0.142936i | \(-0.954346\pi\) | ||||
0.989732 | − | 0.142936i | \(-0.0456544\pi\) | |||||||
\(104\) | 4.89898i | 0.0471056i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −108.000 | −1.01887 | ||||||||
\(107\) | 144.250 | 1.34813 | 0.674064 | − | 0.738673i | \(-0.264547\pi\) | ||||
0.674064 | + | 0.738673i | \(0.264547\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 169.000 | 1.55046 | 0.775229 | − | 0.631680i | \(-0.217634\pi\) | ||||
0.775229 | + | 0.631680i | \(0.217634\pi\) | |||||||
\(110\) | 117.576i | 1.06887i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 59.3970 | 0.525637 | 0.262818 | − | 0.964845i | \(-0.415348\pi\) | ||||
0.262818 | + | 0.964845i | \(0.415348\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 41.5692i | − 0.361471i | ||||||||
\(116\) | 67.8823 | 0.585192 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 117.779i | 0.998131i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 167.000 | 1.38017 | ||||||||
\(122\) | 117.576i | 0.963734i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 24.2487i | 0.195554i | ||||||||
\(125\) | − 127.373i | − 1.01899i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 209.000 | 1.64567 | 0.822835 | − | 0.568281i | \(-0.192391\pi\) | ||||
0.822835 | + | 0.568281i | \(0.192391\pi\) | |||||||
\(128\) | −11.3137 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 12.0000 | 0.0923077 | ||||||||
\(131\) | 58.7878i | 0.448761i | 0.974502 | + | 0.224381i | \(0.0720359\pi\) | ||||
−0.974502 | + | 0.224381i | \(0.927964\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 43.8406 | 0.327169 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 13.8564i | 0.101885i | ||||||||
\(137\) | −152.735 | −1.11485 | −0.557427 | − | 0.830226i | \(-0.688211\pi\) | ||||
−0.557427 | + | 0.830226i | \(0.688211\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 195.722i | − 1.40807i | −0.710165 | − | 0.704035i | \(-0.751380\pi\) | ||||
0.710165 | − | 0.704035i | \(-0.248620\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 84.0000 | 0.591549 | ||||||||
\(143\) | − 29.3939i | − 0.205552i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − 166.277i | − 1.14674i | ||||||||
\(146\) | − 115.126i | − 0.788534i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −94.0000 | −0.635135 | ||||||||
\(149\) | −50.9117 | −0.341689 | −0.170845 | − | 0.985298i | \(-0.554650\pi\) | ||||
−0.170845 | + | 0.985298i | \(0.554650\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.0000 | 0.0662252 | 0.0331126 | − | 0.999452i | \(-0.489458\pi\) | ||||
0.0331126 | + | 0.999452i | \(0.489458\pi\) | |||||||
\(152\) | − 83.2827i | − 0.547912i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 59.3970 | 0.383206 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 41.5692i | − 0.264772i | −0.991198 | − | 0.132386i | \(-0.957736\pi\) | ||||
0.991198 | − | 0.132386i | \(-0.0422639\pi\) | |||||||
\(158\) | −57.9828 | −0.366979 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 27.7128i | 0.173205i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 86.0000 | 0.527607 | 0.263804 | − | 0.964576i | \(-0.415023\pi\) | ||||
0.263804 | + | 0.964576i | \(0.415023\pi\) | |||||||
\(164\) | − 137.171i | − 0.836411i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − 6.92820i | − 0.0417362i | ||||||||
\(167\) | − 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 | ||||||||
\(170\) | 33.9411 | 0.199654 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 62.0000 | 0.360465 | ||||||||
\(173\) | 44.0908i | 0.254860i | 0.991848 | + | 0.127430i | \(0.0406728\pi\) | ||||
−0.991848 | + | 0.127430i | \(0.959327\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 67.8823 | 0.385695 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 83.1384i | 0.467070i | ||||||||
\(179\) | 8.48528 | 0.0474038 | 0.0237019 | − | 0.999719i | \(-0.492455\pi\) | ||||
0.0237019 | + | 0.999719i | \(0.492455\pi\) | |||||||
\(180\) | 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 | ||||||||
\(184\) | −24.0000 | −0.130435 | ||||||||
\(185\) | 230.252i | 1.24461i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 83.1384i | − 0.444591i | ||||||||
\(188\) | 166.565i | 0.885986i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −204.000 | −1.07368 | ||||||||
\(191\) | −76.3675 | −0.399830 | −0.199915 | − | 0.979813i | \(-0.564067\pi\) | ||||
−0.199915 | + | 0.979813i | \(0.564067\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −287.000 | −1.48705 | −0.743523 | − | 0.668710i | \(-0.766847\pi\) | ||||
−0.743523 | + | 0.668710i | \(0.766847\pi\) | |||||||
\(194\) | − 58.7878i | − 0.303030i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −127.279 | −0.646087 | −0.323044 | − | 0.946384i | \(-0.604706\pi\) | ||||
−0.323044 | + | 0.946384i | \(0.604706\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 207.846i | − 1.04445i | −0.852807 | − | 0.522226i | \(-0.825102\pi\) | ||||
0.852807 | − | 0.522226i | \(-0.174898\pi\) | |||||||
\(200\) | −2.82843 | −0.0141421 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 249.415i | 1.23473i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −336.000 | −1.63902 | ||||||||
\(206\) | 41.6413i | 0.202142i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − 6.92820i | − 0.0333087i | ||||||||
\(209\) | 499.696i | 2.39089i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 82.0000 | 0.388626 | 0.194313 | − | 0.980940i | \(-0.437752\pi\) | ||||
0.194313 | + | 0.980940i | \(0.437752\pi\) | |||||||
\(212\) | 152.735 | 0.720448 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −204.000 | −0.953271 | ||||||||
\(215\) | − 151.868i | − 0.706364i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −239.002 | −1.09634 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | − 166.277i | − 0.755804i | ||||||||
\(221\) | −8.48528 | −0.0383949 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 41.5692i | − 0.186409i | −0.995647 | − | 0.0932045i | \(-0.970289\pi\) | ||||
0.995647 | − | 0.0932045i | \(-0.0297110\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −84.0000 | −0.371681 | ||||||||
\(227\) | 382.120i | 1.68335i | 0.539985 | + | 0.841675i | \(0.318430\pi\) | ||||
−0.539985 | + | 0.841675i | \(0.681570\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 81.4064i | − 0.355486i | −0.984077 | − | 0.177743i | \(-0.943120\pi\) | ||||
0.984077 | − | 0.177743i | \(-0.0568796\pi\) | |||||||
\(230\) | 58.7878i | 0.255599i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −96.0000 | −0.413793 | ||||||||
\(233\) | −229.103 | −0.983273 | −0.491636 | − | 0.870801i | \(-0.663601\pi\) | ||||
−0.491636 | + | 0.870801i | \(0.663601\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 408.000 | 1.73617 | ||||||||
\(236\) | − 166.565i | − 0.705785i | ||||||||
\(237\) | 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 | ||||||||
\(241\) | 457.261i | 1.89735i | 0.316252 | + | 0.948675i | \(0.397575\pi\) | ||||
−0.316252 | + | 0.948675i | \(0.602425\pi\) | |||||||
\(242\) | −236.174 | −0.975924 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − 166.277i | − 0.681463i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 51.0000 | 0.206478 | ||||||||
\(248\) | − 34.2929i | − 0.138278i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 180.133i | 0.720533i | ||||||||
\(251\) | 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 | ||||||||
\(254\) | −295.571 | −1.16366 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | − 161.666i | − 0.629052i | −0.949249 | − | 0.314526i | \(-0.898154\pi\) | ||||
0.949249 | − | 0.314526i | \(-0.101846\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −16.9706 | −0.0652714 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − 83.1384i | − 0.317322i | ||||||||
\(263\) | −254.558 | −0.967903 | −0.483951 | − | 0.875095i | \(-0.660799\pi\) | ||||
−0.483951 | + | 0.875095i | \(0.660799\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − 374.123i | − 1.41178i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −62.0000 | −0.231343 | ||||||||
\(269\) | 19.5959i | 0.0728473i | 0.999336 | + | 0.0364236i | \(0.0115966\pi\) | ||||
−0.999336 | + | 0.0364236i | \(0.988403\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 41.5692i | 0.153392i | 0.997055 | + | 0.0766960i | \(0.0244371\pi\) | ||||
−0.997055 | + | 0.0766960i | \(0.975563\pi\) | |||||||
\(272\) | − 19.5959i | − 0.0720438i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 216.000 | 0.788321 | ||||||||
\(275\) | 16.9706 | 0.0617111 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −337.000 | −1.21661 | −0.608303 | − | 0.793705i | \(-0.708150\pi\) | ||||
−0.608303 | + | 0.793705i | \(0.708150\pi\) | |||||||
\(278\) | 276.792i | 0.995656i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −246.073 | −0.875705 | −0.437853 | − | 0.899047i | \(-0.644261\pi\) | ||||
−0.437853 | + | 0.899047i | \(0.644261\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 195.722i | 0.691596i | 0.938309 | + | 0.345798i | \(0.112392\pi\) | ||||
−0.938309 | + | 0.345798i | \(0.887608\pi\) | |||||||
\(284\) | −118.794 | −0.418289 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 41.5692i | 0.145347i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 265.000 | 0.916955 | ||||||||
\(290\) | 235.151i | 0.810866i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 162.813i | 0.557578i | ||||||||
\(293\) | − 97.9796i | − 0.334401i | −0.985923 | − | 0.167201i | \(-0.946527\pi\) | ||||
0.985923 | − | 0.167201i | \(-0.0534728\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −408.000 | −1.38305 | ||||||||
\(296\) | 132.936 | 0.449108 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 72.0000 | 0.241611 | ||||||||
\(299\) | − 14.6969i | − 0.0491536i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −14.1421 | −0.0468283 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 117.779i | 0.387432i | ||||||||
\(305\) | −407.294 | −1.33539 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 71.0141i | − 0.231316i | −0.993289 | − | 0.115658i | \(-0.963102\pi\) | ||||
0.993289 | − | 0.115658i | \(-0.0368977\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −84.0000 | −0.270968 | ||||||||
\(311\) | 215.555i | 0.693103i | 0.938031 | + | 0.346552i | \(0.112647\pi\) | ||||
−0.938031 | + | 0.346552i | \(0.887353\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 292.717i | 0.935197i | 0.883941 | + | 0.467598i | \(0.154881\pi\) | ||||
−0.883941 | + | 0.467598i | \(0.845119\pi\) | |||||||
\(314\) | 58.7878i | 0.187222i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 82.0000 | 0.259494 | ||||||||
\(317\) | 237.588 | 0.749489 | 0.374744 | − | 0.927128i | \(-0.377731\pi\) | ||||
0.374744 | + | 0.927128i | \(0.377731\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 576.000 | 1.80564 | ||||||||
\(320\) | − 39.1918i | − 0.122474i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 144.250 | 0.446594 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 1.73205i | − 0.00532939i | ||||||||
\(326\) | −121.622 | −0.373075 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 193.990i | 0.591432i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −185.000 | −0.558912 | −0.279456 | − | 0.960158i | \(-0.590154\pi\) | ||||
−0.279456 | + | 0.960158i | \(0.590154\pi\) | |||||||
\(332\) | 9.79796i | 0.0295119i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 256.344i | 0.767496i | ||||||||
\(335\) | 151.868i | 0.453338i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −359.000 | −1.06528 | −0.532641 | − | 0.846341i | \(-0.678800\pi\) | ||||
−0.532641 | + | 0.846341i | \(0.678800\pi\) | |||||||
\(338\) | −234.759 | −0.694555 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −48.0000 | −0.141176 | ||||||||
\(341\) | 205.757i | 0.603393i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −87.6812 | −0.254887 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − 62.3538i | − 0.180213i | ||||||||
\(347\) | −466.690 | −1.34493 | −0.672465 | − | 0.740129i | \(-0.734764\pi\) | ||||
−0.672465 | + | 0.740129i | \(0.734764\pi\) | |||||||
\(348\) | 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 | ||||||||
\(352\) | −96.0000 | −0.272727 | ||||||||
\(353\) | 289.040i | 0.818810i | 0.912353 | + | 0.409405i | \(0.134264\pi\) | ||||
−0.912353 | + | 0.409405i | \(0.865736\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 290.985i | 0.819675i | ||||||||
\(356\) | − 117.576i | − 0.330268i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −12.0000 | −0.0335196 | ||||||||
\(359\) | −339.411 | −0.945435 | −0.472718 | − | 0.881214i | \(-0.656727\pi\) | ||||
−0.472718 | + | 0.881214i | \(0.656727\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −506.000 | −1.40166 | ||||||||
\(362\) | − 61.2372i | − 0.169164i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 398.808 | 1.09263 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 154.153i | − 0.420034i | −0.977698 | − | 0.210017i | \(-0.932648\pi\) | ||||
0.977698 | − | 0.210017i | \(-0.0673520\pi\) | |||||||
\(368\) | 33.9411 | 0.0922313 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − 325.626i | − 0.880069i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −289.000 | −0.774799 | −0.387399 | − | 0.921912i | \(-0.626627\pi\) | ||||
−0.387399 | + | 0.921912i | \(0.626627\pi\) | |||||||
\(374\) | 117.576i | 0.314373i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − 235.559i | − 0.626486i | ||||||||
\(377\) | − 58.7878i | − 0.155936i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.00000 | 0.0184697 | 0.00923483 | − | 0.999957i | \(-0.497060\pi\) | ||||
0.00923483 | + | 0.999957i | \(0.497060\pi\) | |||||||
\(380\) | 288.500 | 0.759209 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 108.000 | 0.282723 | ||||||||
\(383\) | − 494.797i | − 1.29190i | −0.763381 | − | 0.645949i | \(-0.776462\pi\) | ||||
0.763381 | − | 0.645949i | \(-0.223538\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 405.879 | 1.05150 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 83.1384i | 0.214274i | ||||||||
\(389\) | 229.103 | 0.588953 | 0.294476 | − | 0.955659i | \(-0.404855\pi\) | ||||
0.294476 | + | 0.955659i | \(0.404855\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 41.5692i | − 0.106315i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 180.000 | 0.456853 | ||||||||
\(395\) | − 200.858i | − 0.508502i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 81.4064i | 0.205054i | 0.994730 | + | 0.102527i | \(0.0326928\pi\) | ||||
−0.994730 | + | 0.102527i | \(0.967307\pi\) | |||||||
\(398\) | 293.939i | 0.738540i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.00000 | 0.0100000 | ||||||||
\(401\) | 93.3381 | 0.232763 | 0.116382 | − | 0.993205i | \(-0.462870\pi\) | ||||
0.116382 | + | 0.993205i | \(0.462870\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 21.0000 | 0.0521092 | ||||||||
\(404\) | − 352.727i | − 0.873085i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −797.616 | −1.95975 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 417.424i | 1.02060i | 0.859997 | + | 0.510299i | \(0.170465\pi\) | ||||
−0.859997 | + | 0.510299i | \(0.829535\pi\) | |||||||
\(410\) | 475.176 | 1.15897 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − 58.8897i | − 0.142936i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 24.0000 | 0.0578313 | ||||||||
\(416\) | 9.79796i | 0.0235528i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − 706.677i | − 1.69061i | ||||||||
\(419\) | − 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 | \(0.339412\pi\) | |||||||
\(422\) | −115.966 | −0.274800 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −216.000 | −0.509434 | ||||||||
\(425\) | − 4.89898i | − 0.0115270i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 288.500 | 0.674064 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 214.774i | 0.499475i | ||||||||
\(431\) | 161.220 | 0.374061 | 0.187031 | − | 0.982354i | \(-0.440114\pi\) | ||||
0.187031 | + | 0.982354i | \(0.440114\pi\) | |||||||
\(432\) | 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 | ||||||||
\(436\) | 338.000 | 0.775229 | ||||||||
\(437\) | 249.848i | 0.571734i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 540.400i | − 1.23098i | −0.788145 | − | 0.615490i | \(-0.788958\pi\) | ||||
0.788145 | − | 0.615490i | \(-0.211042\pi\) | |||||||
\(440\) | 235.151i | 0.534434i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 12.0000 | 0.0271493 | ||||||||
\(443\) | −127.279 | −0.287312 | −0.143656 | − | 0.989628i | \(-0.545886\pi\) | ||||
−0.143656 | + | 0.989628i | \(0.545886\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −288.000 | −0.647191 | ||||||||
\(446\) | 58.7878i | 0.131811i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −110.309 | −0.245676 | −0.122838 | − | 0.992427i | \(-0.539200\pi\) | ||||
−0.122838 | + | 0.992427i | \(0.539200\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 1163.94i | − 2.58079i | ||||||||
\(452\) | 118.794 | 0.262818 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − 540.400i | − 1.19031i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 25.0000 | 0.0547046 | 0.0273523 | − | 0.999626i | \(-0.491292\pi\) | ||||
0.0273523 | + | 0.999626i | \(0.491292\pi\) | |||||||
\(458\) | 115.126i | 0.251367i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − 83.1384i | − 0.180736i | ||||||||
\(461\) | 78.3837i | 0.170030i | 0.996380 | + | 0.0850148i | \(0.0270938\pi\) | ||||
−0.996380 | + | 0.0850148i | \(0.972906\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 521.000 | 1.12527 | 0.562635 | − | 0.826705i | \(-0.309788\pi\) | ||||
0.562635 | + | 0.826705i | \(0.309788\pi\) | |||||||
\(464\) | 135.765 | 0.292596 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 324.000 | 0.695279 | ||||||||
\(467\) | 220.454i | 0.472064i | 0.971745 | + | 0.236032i | \(0.0758471\pi\) | ||||
−0.971745 | + | 0.236032i | \(0.924153\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −576.999 | −1.22766 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 235.559i | 0.499065i | ||||||||
\(473\) | 526.087 | 1.11224 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 29.4449i | 0.0619892i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −96.0000 | −0.200837 | ||||||||
\(479\) | − 876.917i | − 1.83073i | −0.402631 | − | 0.915363i | \(-0.631904\pi\) | ||||
0.402631 | − | 0.915363i | \(-0.368096\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 81.4064i | 0.169244i | ||||||||
\(482\) | − 646.665i | − 1.34163i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 334.000 | 0.690083 | ||||||||
\(485\) | 203.647 | 0.419890 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 127.000 | 0.260780 | 0.130390 | − | 0.991463i | \(-0.458377\pi\) | ||||
0.130390 | + | 0.991463i | \(0.458377\pi\) | |||||||
\(488\) | 235.151i | 0.481867i | ||||||||
\(489\) | 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 | ||||||||
\(493\) | − 166.277i | − 0.337276i | ||||||||
\(494\) | −72.1249 | −0.146002 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 48.4974i | 0.0977771i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −233.000 | −0.466934 | −0.233467 | − | 0.972365i | \(-0.575007\pi\) | ||||
−0.233467 | + | 0.972365i | \(0.575007\pi\) | |||||||
\(500\) | − 254.747i | − 0.509494i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − 491.902i | − 0.979885i | ||||||||
\(503\) | − 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 | ||||||||
\(506\) | −203.647 | −0.402464 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 418.000 | 0.822835 | ||||||||
\(509\) | − 318.434i | − 0.625606i | −0.949818 | − | 0.312803i | \(-0.898732\pi\) | ||||
0.949818 | − | 0.312803i | \(-0.101268\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −22.6274 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 228.631i | 0.444807i | ||||||||
\(515\) | −144.250 | −0.280097 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1413.35i | 2.73376i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 24.0000 | 0.0461538 | ||||||||
\(521\) | − 568.282i | − 1.09075i | −0.838192 | − | 0.545376i | \(-0.816387\pi\) | ||||
0.838192 | − | 0.545376i | \(-0.183613\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 528.275i | 1.01009i | 0.863094 | + | 0.505043i | \(0.168524\pi\) | ||||
−0.863094 | + | 0.505043i | \(0.831476\pi\) | |||||||
\(524\) | 117.576i | 0.224381i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 360.000 | 0.684411 | ||||||||
\(527\) | 59.3970 | 0.112708 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −457.000 | −0.863894 | ||||||||
\(530\) | 529.090i | 0.998283i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −118.794 | −0.222878 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 706.677i | − 1.32089i | ||||||||
\(536\) | 87.6812 | 0.163584 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − 27.7128i | − 0.0515108i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 335.000 | 0.619224 | 0.309612 | − | 0.950863i | \(-0.399801\pi\) | ||||
0.309612 | + | 0.950863i | \(0.399801\pi\) | |||||||
\(542\) | − 58.7878i | − 0.108464i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 27.7128i | 0.0509427i | ||||||||
\(545\) | − 827.928i | − 1.51913i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −658.000 | −1.20293 | −0.601463 | − | 0.798901i | \(-0.705415\pi\) | ||||
−0.601463 | + | 0.798901i | \(0.705415\pi\) | |||||||
\(548\) | −305.470 | −0.557427 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −24.0000 | −0.0436364 | ||||||||
\(551\) | 999.392i | 1.81378i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 476.590 | 0.860271 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − 391.443i | − 0.704035i | ||||||||
\(557\) | 271.529 | 0.487485 | 0.243742 | − | 0.969840i | \(-0.421625\pi\) | ||||
0.243742 | + | 0.969840i | \(0.421625\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 53.6936i | − 0.0960529i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 348.000 | 0.619217 | ||||||||
\(563\) | − 14.6969i | − 0.0261047i | −0.999915 | − | 0.0130523i | \(-0.995845\pi\) | ||||
0.999915 | − | 0.0130523i | \(-0.00415481\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 290.985i | − 0.515017i | ||||||||
\(566\) | − 276.792i | − 0.489032i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 168.000 | 0.295775 | ||||||||
\(569\) | 848.528 | 1.49126 | 0.745631 | − | 0.666359i | \(-0.232148\pi\) | ||||
0.745631 | + | 0.666359i | \(0.232148\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 449.000 | 0.786340 | 0.393170 | − | 0.919466i | \(-0.371378\pi\) | ||||
0.393170 | + | 0.919466i | \(0.371378\pi\) | |||||||
\(572\) | − 58.7878i | − 0.102776i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.48528 | 0.0147570 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 292.717i | 0.507308i | 0.967295 | + | 0.253654i | \(0.0816324\pi\) | ||||
−0.967295 | + | 0.253654i | \(0.918368\pi\) | |||||||
\(578\) | −374.767 | −0.648385 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − 332.554i | − 0.573369i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1296.00 | 2.22298 | ||||||||
\(584\) | − 230.252i | − 0.394267i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 138.564i | 0.236457i | ||||||||
\(587\) | 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 | ||||||||
\(590\) | 576.999 | 0.977965 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −188.000 | −0.317568 | ||||||||
\(593\) | 1048.38i | 1.76793i | 0.467554 | + | 0.883964i | \(0.345135\pi\) | ||||
−0.467554 | + | 0.883964i | \(0.654865\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −101.823 | −0.170845 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 20.7846i | 0.0347569i | ||||||||
\(599\) | 644.881 | 1.07660 | 0.538298 | − | 0.842754i | \(-0.319067\pi\) | ||||
0.538298 | + | 0.842754i | \(0.319067\pi\) | |||||||
\(600\) | 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 | ||||||||
\(604\) | 20.0000 | 0.0331126 | ||||||||
\(605\) | − 818.130i | − 1.35228i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1051.35i | 1.73205i | 0.500000 | + | 0.866025i | \(0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(608\) | − 166.565i | − 0.273956i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 576.000 | 0.944262 | ||||||||
\(611\) | 144.250 | 0.236088 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 290.000 | 0.473083 | 0.236542 | − | 0.971621i | \(-0.423986\pi\) | ||||
0.236542 | + | 0.971621i | \(0.423986\pi\) | |||||||
\(614\) | 100.429i | 0.163565i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 729.734 | 1.18271 | 0.591357 | − | 0.806410i | \(-0.298593\pi\) | ||||
0.591357 | + | 0.806410i | \(0.298593\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 819.260i | 1.32352i | 0.749715 | + | 0.661761i | \(0.230191\pi\) | ||||
−0.749715 | + | 0.661761i | \(0.769809\pi\) | |||||||
\(620\) | 118.794 | 0.191603 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − 304.841i | − 0.490098i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −599.000 | −0.958400 | ||||||||
\(626\) | − 413.964i | − 0.661284i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − 83.1384i | − 0.132386i | ||||||||
\(629\) | 230.252i | 0.366060i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −58.0000 | −0.0919176 | −0.0459588 | − | 0.998943i | \(-0.514634\pi\) | ||||
−0.0459588 | + | 0.998943i | \(0.514634\pi\) | |||||||
\(632\) | −115.966 | −0.183490 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −336.000 | −0.529968 | ||||||||
\(635\) | − 1023.89i | − 1.61242i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −814.587 | −1.27678 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 55.4256i | 0.0866025i | ||||||||
\(641\) | 958.837 | 1.49585 | 0.747923 | − | 0.663786i | \(-0.231051\pi\) | ||||
0.747923 | + | 0.663786i | \(0.231051\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 760.370i | − 1.18254i | −0.806475 | − | 0.591268i | \(-0.798628\pi\) | ||||
0.806475 | − | 0.591268i | \(-0.201372\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −204.000 | −0.315789 | ||||||||
\(647\) | 352.727i | 0.545172i | 0.962131 | + | 0.272586i | \(0.0878790\pi\) | ||||
−0.962131 | + | 0.272586i | \(0.912121\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − 1413.35i | − 2.17774i | ||||||||
\(650\) | 2.44949i | 0.00376845i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 172.000 | 0.263804 | ||||||||
\(653\) | −441.235 | −0.675704 | −0.337852 | − | 0.941199i | \(-0.609700\pi\) | ||||
−0.337852 | + | 0.941199i | \(0.609700\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 288.000 | 0.439695 | ||||||||
\(656\) | − 274.343i | − 0.418206i | ||||||||
\(657\) | 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 | ||||||||
\(661\) | 833.116i | 1.26039i | 0.776438 | + | 0.630194i | \(0.217025\pi\) | ||||
−0.776438 | + | 0.630194i | \(0.782975\pi\) | |||||||
\(662\) | 261.630 | 0.395211 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − 13.8564i | − 0.0208681i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 288.000 | 0.431784 | ||||||||
\(668\) | − 362.524i | − 0.542701i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | − 214.774i | − 0.320559i | ||||||||
\(671\) | − 1410.91i | − 2.10269i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −263.000 | −0.390788 | −0.195394 | − | 0.980725i | \(-0.562598\pi\) | ||||
−0.195394 | + | 0.980725i | \(0.562598\pi\) | |||||||
\(674\) | 507.703 | 0.753268 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 332.000 | 0.491124 | ||||||||
\(677\) | 499.696i | 0.738103i | 0.929409 | + | 0.369052i | \(0.120317\pi\) | ||||
−0.929409 | + | 0.369052i | \(0.879683\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 67.8823 | 0.0998268 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − 290.985i | − 0.426664i | ||||||||
\(683\) | 958.837 | 1.40386 | 0.701930 | − | 0.712246i | \(-0.252322\pi\) | ||||
0.701930 | + | 0.712246i | \(0.252322\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 748.246i | 1.09233i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 124.000 | 0.180233 | ||||||||
\(689\) | − 132.272i | − 0.191977i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1234.95i | 1.78720i | 0.448868 | + | 0.893598i | \(0.351827\pi\) | ||||
−0.448868 | + | 0.893598i | \(0.648173\pi\) | |||||||
\(692\) | 88.1816i | 0.127430i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 660.000 | 0.951009 | ||||||||
\(695\) | −958.837 | −1.37962 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −336.000 | −0.482066 | ||||||||
\(698\) | − 823.029i | − 1.17912i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −975.807 | −1.39202 | −0.696011 | − | 0.718031i | \(-0.745044\pi\) | ||||
−0.696011 | + | 0.718031i | \(0.745044\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 1383.91i | − 1.96858i | ||||||||
\(704\) | 135.765 | 0.192847 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − 408.764i | − 0.578986i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1106.00 | −1.55994 | −0.779972 | − | 0.625815i | \(-0.784767\pi\) | ||||
−0.779972 | + | 0.625815i | \(0.784767\pi\) | |||||||
\(710\) | − 411.514i | − 0.579598i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 166.277i | 0.233535i | ||||||||
\(713\) | 102.879i | 0.144290i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −144.000 | −0.201399 | ||||||||
\(716\) | 16.9706 | 0.0237019 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 480.000 | 0.668524 | ||||||||
\(719\) | − 685.857i | − 0.953904i | −0.878929 | − | 0.476952i | \(-0.841742\pi\) | ||||
0.878929 | − | 0.476952i | \(-0.158258\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 715.592 | 0.991125 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 86.6025i | 0.119617i | ||||||||
\(725\) | 33.9411 | 0.0468153 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 427.817i | − 0.588468i | −0.955733 | − | 0.294234i | \(-0.904935\pi\) | ||||
0.955733 | − | 0.294234i | \(-0.0950646\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −564.000 | −0.772603 | ||||||||
\(731\) | − 151.868i | − 0.207754i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 39.8372i | 0.0543481i | 0.999631 | + | 0.0271741i | \(0.00865084\pi\) | ||||
−0.999631 | + | 0.0271741i | \(0.991349\pi\) | |||||||
\(734\) | 218.005i | 0.297009i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −48.0000 | −0.0652174 | ||||||||
\(737\) | −526.087 | −0.713823 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −487.000 | −0.658999 | −0.329499 | − | 0.944156i | \(-0.606880\pi\) | ||||
−0.329499 | + | 0.944156i | \(0.606880\pi\) | |||||||
\(740\) | 460.504i | 0.622303i | ||||||||
\(741\) | 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 | ||||||||
\(745\) | 249.415i | 0.334786i | ||||||||
\(746\) | 408.708 | 0.547866 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − 166.277i | − 0.222295i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −545.000 | −0.725699 | −0.362850 | − | 0.931848i | \(-0.618196\pi\) | ||||
−0.362850 | + | 0.931848i | \(0.618196\pi\) | |||||||
\(752\) | 333.131i | 0.442993i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 83.1384i | 0.110263i | ||||||||
\(755\) | − 48.9898i | − 0.0648871i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −770.000 | −1.01717 | −0.508587 | − | 0.861011i | \(-0.669832\pi\) | ||||
−0.508587 | + | 0.861011i | \(0.669832\pi\) | |||||||
\(758\) | −9.89949 | −0.0130600 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −408.000 | −0.536842 | ||||||||
\(761\) | − 171.464i | − 0.225314i | −0.993634 | − | 0.112657i | \(-0.964064\pi\) | ||||
0.993634 | − | 0.112657i | \(-0.0359362\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −152.735 | −0.199915 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 699.749i | 0.913510i | ||||||||
\(767\) | −144.250 | −0.188070 | ||||||||
\(768\) | 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 | ||||||||
\(772\) | −574.000 | −0.743523 | ||||||||
\(773\) | 921.008i | 1.19147i | 0.803180 | + | 0.595736i | \(0.203140\pi\) | ||||
−0.803180 | + | 0.595736i | \(0.796860\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 12.1244i | 0.0156443i | ||||||||
\(776\) | − 117.576i | − 0.151515i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −324.000 | −0.416452 | ||||||||
\(779\) | 2019.50 | 2.59242 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1008.00 | −1.29065 | ||||||||
\(782\) | 58.7878i | 0.0751762i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −203.647 | −0.259423 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 457.261i | − 0.581018i | −0.956872 | − | 0.290509i | \(-0.906175\pi\) | ||||
0.956872 | − | 0.290509i | \(-0.0938247\pi\) | |||||||
\(788\) | −254.558 | −0.323044 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 284.056i | 0.359565i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −144.000 | −0.181589 | ||||||||
\(794\) | − 115.126i | − 0.144995i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − 415.692i | − 0.522226i | ||||||||
\(797\) | 14.6969i | 0.0184403i | 0.999957 | + | 0.00922016i | \(0.00293491\pi\) | ||||
−0.999957 | + | 0.00922016i | \(0.997065\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 408.000 | 0.510638 | ||||||||
\(800\) | −5.65685 | −0.00707107 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −132.000 | −0.164589 | ||||||||
\(803\) | 1381.51i | 1.72044i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −29.6985 | −0.0368468 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 498.831i | 0.617365i | ||||||||
\(809\) | −941.866 | −1.16424 | −0.582118 | − | 0.813105i | \(-0.697776\pi\) | ||||
−0.582118 | + | 0.813105i | \(0.697776\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 498.831i | − 0.615081i | −0.951535 | − | 0.307540i | \(-0.900494\pi\) | ||||
0.951535 | − | 0.307540i | \(-0.0995059\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1128.00 | 1.38575 | ||||||||
\(815\) | − 421.312i | − 0.516948i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 912.791i | 1.11725i | ||||||||
\(818\) | − 590.327i | − 0.721671i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −672.000 | −0.819512 | ||||||||
\(821\) | −602.455 | −0.733806 | −0.366903 | − | 0.930259i | \(-0.619582\pi\) | ||||
−0.366903 | + | 0.930259i | \(0.619582\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 38.0000 | 0.0461725 | 0.0230863 | − | 0.999733i | \(-0.492651\pi\) | ||||
0.0230863 | + | 0.999733i | \(0.492651\pi\) | |||||||
\(824\) | 83.2827i | 0.101071i | ||||||||
\(825\) | 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 | ||||||||
\(829\) | 833.116i | 1.00497i | 0.864587 | + | 0.502483i | \(0.167580\pi\) | ||||
−0.864587 | + | 0.502483i | \(0.832420\pi\) | |||||||
\(830\) | −33.9411 | −0.0408929 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − 13.8564i | − 0.0166543i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −888.000 | −1.06347 | ||||||||
\(836\) | 999.392i | 1.19544i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 27.7128i | 0.0330702i | ||||||||
\(839\) | 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 | ||||||||
\(842\) | −575.585 | −0.683593 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 164.000 | 0.194313 | ||||||||
\(845\) | − 813.231i | − 0.962403i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 305.470 | 0.360224 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 6.92820i | 0.00815083i | ||||||||
\(851\) | −398.808 | −0.468635 | ||||||||
\(852\) | 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 | ||||||||
\(856\) | −408.000 | −0.476636 | ||||||||
\(857\) | − 1224.74i | − 1.42911i | −0.699581 | − | 0.714554i | \(-0.746630\pi\) | ||||
0.699581 | − | 0.714554i | \(-0.253370\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 249.415i | 0.290355i | 0.989406 | + | 0.145178i | \(0.0463754\pi\) | ||||
−0.989406 | + | 0.145178i | \(0.953625\pi\) | |||||||
\(860\) | − 303.737i | − 0.353182i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −228.000 | −0.264501 | ||||||||
\(863\) | 661.852 | 0.766920 | 0.383460 | − | 0.923557i | \(-0.374732\pi\) | ||||
0.383460 | + | 0.923557i | \(0.374732\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 216.000 | 0.249711 | ||||||||
\(866\) | 237.601i | 0.274365i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 695.793 | 0.800682 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 53.6936i | 0.0616459i | ||||||||
\(872\) | −478.004 | −0.548170 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − 353.338i | − 0.404277i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −574.000 | −0.654504 | −0.327252 | − | 0.944937i | \(-0.606123\pi\) | ||||
−0.327252 | + | 0.944937i | \(0.606123\pi\) | |||||||
\(878\) | 764.241i | 0.870434i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | − 332.554i | − 0.377902i | ||||||||
\(881\) | 161.666i | 0.183503i | 0.995782 | + | 0.0917516i | \(0.0292466\pi\) | ||||
−0.995782 | + | 0.0917516i | \(0.970753\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1735.00 | 1.96489 | 0.982446 | − | 0.186546i | \(-0.0597294\pi\) | ||||
0.982446 | + | 0.186546i | \(0.0597294\pi\) | |||||||
\(884\) | −16.9706 | −0.0191975 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 180.000 | 0.203160 | ||||||||
\(887\) | − 195.959i | − 0.220924i | −0.993880 | − | 0.110462i | \(-0.964767\pi\) | ||||
0.993880 | − | 0.110462i | \(-0.0352330\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 407.294 | 0.457633 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − 83.1384i | − 0.0932045i | ||||||||
\(893\) | −2452.25 | −2.74608 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 41.5692i | − 0.0464461i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 156.000 | 0.173719 | ||||||||
\(899\) | 411.514i | 0.457747i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 374.123i | − 0.415231i | ||||||||
\(902\) | 1646.06i | 1.82490i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −168.000 | −0.185841 | ||||||||
\(905\) | 212.132 | 0.234400 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 751.000 | 0.828004 | 0.414002 | − | 0.910276i | \(-0.364131\pi\) | ||||
0.414002 | + | 0.910276i | \(0.364131\pi\) | |||||||
\(908\) | 764.241i | 0.841675i | ||||||||
\(909\) | 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 | ||||||||
\(913\) | 83.1384i | 0.0910607i | ||||||||
\(914\) | −35.3553 | −0.0386820 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − 162.813i | − 0.177743i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1015.00 | 1.10446 | 0.552231 | − | 0.833691i | \(-0.313777\pi\) | ||||
0.552231 | + | 0.833691i | \(0.313777\pi\) | |||||||
\(920\) | 117.576i | 0.127799i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − 110.851i | − 0.120229i | ||||||||
\(923\) | 102.879i | 0.111461i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −47.0000 | −0.0508108 | ||||||||
\(926\) | −736.805 | −0.795686 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −192.000 | −0.206897 | ||||||||
\(929\) | − 1092.47i | − 1.17597i | −0.808873 | − | 0.587983i | \(-0.799922\pi\) | ||||
0.808873 | − | 0.587983i | \(-0.200078\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −458.205 | −0.491636 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − 311.769i | − 0.333800i | ||||||||
\(935\) | −407.294 | −0.435608 | ||||||||
\(936\) | 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 | ||||||||
\(940\) | 816.000 | 0.868085 | ||||||||
\(941\) | 1239.44i | 1.31715i | 0.752513 | + | 0.658577i | \(0.228841\pi\) | ||||
−0.752513 | + | 0.658577i | \(0.771159\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 581.969i | − 0.617146i | ||||||||
\(944\) | − 333.131i | − 0.352893i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −744.000 | −0.786469 | ||||||||
\(947\) | −1204.91 | −1.27234 | −0.636172 | − | 0.771547i | \(-0.719483\pi\) | ||||
−0.636172 | + | 0.771547i | \(0.719483\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 141.000 | 0.148577 | ||||||||
\(950\) | − 41.6413i | − 0.0438330i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1026.72 | −1.07735 | −0.538677 | − | 0.842512i | \(-0.681076\pi\) | ||||
−0.538677 | + | 0.842512i | \(0.681076\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 374.123i | 0.391752i | ||||||||
\(956\) | 135.765 | 0.142013 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1240.15i | 1.29452i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 814.000 | 0.847034 | ||||||||
\(962\) | − 115.126i | − 0.119674i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 914.523i | 0.948675i | ||||||||
\(965\) | 1406.01i | 1.45700i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −895.000 | −0.925543 | −0.462771 | − | 0.886478i | \(-0.653145\pi\) | ||||
−0.462771 | + | 0.886478i | \(0.653145\pi\) | |||||||
\(968\) | −472.347 | −0.487962 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −288.000 | −0.296907 | ||||||||
\(971\) | 210.656i | 0.216948i | 0.994099 | + | 0.108474i | \(0.0345964\pi\) | ||||
−0.994099 | + | 0.108474i | \(0.965404\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −179.605 | −0.184400 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − 332.554i | − 0.340731i | ||||||||
\(977\) | 1255.82 | 1.28539 | 0.642693 | − | 0.766124i | \(-0.277817\pi\) | ||||
0.642693 | + | 0.766124i | \(0.277817\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 997.661i | − 1.01906i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −888.000 | −0.904277 | ||||||||
\(983\) | 1180.65i | 1.20107i | 0.799598 | + | 0.600536i | \(0.205046\pi\) | ||||
−0.799598 | + | 0.600536i | \(0.794954\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 623.538i | 0.633034i | ||||||||
\(986\) | 235.151i | 0.238490i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 102.000 | 0.103239 | ||||||||
\(989\) | 263.044 | 0.265969 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 655.000 | 0.660949 | 0.330474 | − | 0.943815i | \(-0.392791\pi\) | ||||
0.330474 | + | 0.943815i | \(0.392791\pi\) | |||||||
\(992\) | − 68.5857i | − 0.0691388i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1018.23 | −1.02335 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 458.993i | − 0.460375i | −0.973146 | − | 0.230187i | \(-0.926066\pi\) | ||||
0.973146 | − | 0.230187i | \(-0.0739339\pi\) | |||||||
\(998\) | 329.512 | 0.330172 | ||||||||
\(999\) | 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 | 882.3.c.c.685.1 | 4 | ||
3.2 | odd | 2 | inner | 882.3.c.c.685.4 | 4 | ||
7.2 | even | 3 | 126.3.n.b.73.2 | yes | 4 | ||
7.3 | odd | 6 | 126.3.n.b.19.2 | yes | 4 | ||
7.4 | even | 3 | 882.3.n.c.19.2 | 4 | |||
7.5 | odd | 6 | 882.3.n.c.325.2 | 4 | |||
7.6 | odd | 2 | inner | 882.3.c.c.685.2 | 4 | ||
21.2 | odd | 6 | 126.3.n.b.73.1 | yes | 4 | ||
21.5 | even | 6 | 882.3.n.c.325.1 | 4 | |||
21.11 | odd | 6 | 882.3.n.c.19.1 | 4 | |||
21.17 | even | 6 | 126.3.n.b.19.1 | ✓ | 4 | ||
21.20 | even | 2 | inner | 882.3.c.c.685.3 | 4 | ||
28.3 | even | 6 | 1008.3.cg.i.145.1 | 4 | |||
28.23 | odd | 6 | 1008.3.cg.i.577.1 | 4 | |||
84.23 | even | 6 | 1008.3.cg.i.577.2 | 4 | |||
84.59 | odd | 6 | 1008.3.cg.i.145.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
126.3.n.b.19.1 | ✓ | 4 | 21.17 | even | 6 | ||
126.3.n.b.19.2 | yes | 4 | 7.3 | odd | 6 | ||
126.3.n.b.73.1 | yes | 4 | 21.2 | odd | 6 | ||
126.3.n.b.73.2 | yes | 4 | 7.2 | even | 3 | ||
882.3.c.c.685.1 | 4 | 1.1 | even | 1 | trivial | ||
882.3.c.c.685.2 | 4 | 7.6 | odd | 2 | inner | ||
882.3.c.c.685.3 | 4 | 21.20 | even | 2 | inner | ||
882.3.c.c.685.4 | 4 | 3.2 | odd | 2 | inner | ||
882.3.n.c.19.1 | 4 | 21.11 | odd | 6 | |||
882.3.n.c.19.2 | 4 | 7.4 | even | 3 | |||
882.3.n.c.325.1 | 4 | 21.5 | even | 6 | |||
882.3.n.c.325.2 | 4 | 7.5 | odd | 6 | |||
1008.3.cg.i.145.1 | 4 | 28.3 | even | 6 | |||
1008.3.cg.i.145.2 | 4 | 84.59 | odd | 6 | |||
1008.3.cg.i.577.1 | 4 | 28.23 | odd | 6 | |||
1008.3.cg.i.577.2 | 4 | 84.23 | even | 6 |