Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1216,2,Mod(577,1216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1216, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1216.577");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1216 = 2^{6} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1216.i (of order \(3\), 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: | \(9.70980888579\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.39075800976.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + 12x^{6} - 13x^{5} + 125x^{4} - 116x^{3} + 232x^{2} + 96x + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 608) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 961.2 | ||
Root | \(1.51772 - 2.62877i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1216.961 |
Dual form | 1216.2.i.p.577.2 |
$q$-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 \(\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(705\) | \(837\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.684999 | + | 1.18645i | −0.395484 | + | 0.684999i | −0.993163 | − | 0.116737i | \(-0.962757\pi\) |
0.597679 | + | 0.801736i | \(0.296090\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.780776 | − | 1.35234i | 0.349174 | − | 0.604787i | −0.636929 | − | 0.770922i | \(-0.719796\pi\) |
0.986103 | + | 0.166136i | \(0.0531289\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.561553 | + | 0.972638i | 0.187184 | + | 0.324213i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.50932 | −1.05810 | −0.529050 | − | 0.848591i | \(-0.677452\pi\) | ||||
−0.529050 | + | 0.848591i | \(0.677452\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.219224 | − | 0.379706i | −0.0608017 | − | 0.105312i | 0.834022 | − | 0.551731i | \(-0.186032\pi\) |
−0.894824 | + | 0.446419i | \(0.852699\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.06966 | + | 1.85271i | 0.276186 | + | 0.478367i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.219224 | − | 0.379706i | 0.0531695 | − | 0.0920923i | −0.838216 | − | 0.545339i | \(-0.816401\pi\) |
0.891385 | + | 0.453247i | \(0.149734\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.12466 | + | 3.03916i | −0.716846 | + | 0.697232i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.43966 | + | 4.22562i | 0.508704 | + | 0.881102i | 0.999949 | + | 0.0100802i | \(0.00320867\pi\) |
−0.491245 | + | 0.871021i | \(0.663458\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.28078 | + | 2.21837i | 0.256155 | + | 0.443674i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.64865 | −1.08708 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.34233 | + | 4.05703i | 0.434960 | + | 0.753372i | 0.997292 | − | 0.0735389i | \(-0.0234293\pi\) |
−0.562333 | + | 0.826911i | \(0.690096\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.74000 | 0.492118 | 0.246059 | − | 0.969255i | \(-0.420864\pi\) | ||||
0.246059 | + | 0.969255i | \(0.420864\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.40388 | − | 4.16365i | 0.418462 | − | 0.724798i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.12311 | 0.184637 | 0.0923187 | − | 0.995730i | \(-0.470572\pi\) | ||||
0.0923187 | + | 0.995730i | \(0.470572\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.600672 | 0.0961845 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.500000 | + | 0.866025i | −0.0780869 | + | 0.135250i | −0.902424 | − | 0.430848i | \(-0.858214\pi\) |
0.824338 | + | 0.566099i | \(0.191548\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.80966 | + | 6.59852i | −0.580967 | + | 1.00627i | 0.414398 | + | 0.910096i | \(0.363992\pi\) |
−0.995365 | + | 0.0961691i | \(0.969341\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.75379 | 0.261439 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.06966 | + | 1.85271i | 0.156026 | + | 0.270245i | 0.933432 | − | 0.358754i | \(-0.116798\pi\) |
−0.777406 | + | 0.628999i | \(0.783465\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7.00000 | −1.00000 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.300336 | + | 0.520197i | 0.0420554 | + | 0.0728421i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.219224 | + | 0.379706i | 0.0301127 | + | 0.0521567i | 0.880689 | − | 0.473695i | \(-0.157080\pi\) |
−0.850576 | + | 0.525852i | \(0.823747\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.74000 | + | 4.74581i | −0.369461 | + | 0.639925i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.46543 | − | 5.78908i | −0.194102 | − | 0.766783i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.684999 | − | 1.18645i | 0.0891793 | − | 0.154463i | −0.817985 | − | 0.575239i | \(-0.804909\pi\) |
0.907164 | + | 0.420776i | \(0.138242\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.21922 | − | 2.11176i | −0.156106 | − | 0.270383i | 0.777355 | − | 0.629062i | \(-0.216561\pi\) |
−0.933461 | + | 0.358679i | \(0.883227\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.684658 | −0.0849214 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.93432 | + | 12.0106i | 0.847162 | + | 1.46733i | 0.883731 | + | 0.467996i | \(0.155024\pi\) |
−0.0365690 | + | 0.999331i | \(0.511643\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.68466 | −0.804738 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.43966 | + | 4.22562i | −0.289534 | + | 0.501488i | −0.973699 | − | 0.227840i | \(-0.926834\pi\) |
0.684164 | + | 0.729328i | \(0.260167\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.623106 | + | 1.07925i | −0.0729290 | + | 0.126317i | −0.900184 | − | 0.435510i | \(-0.856568\pi\) |
0.827255 | + | 0.561827i | \(0.189901\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.50932 | −0.405222 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.06966 | − | 1.85271i | 0.120346 | − | 0.208446i | −0.799558 | − | 0.600589i | \(-0.794933\pi\) |
0.919904 | + | 0.392143i | \(0.128266\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.18466 | − | 3.78394i | 0.242740 | − | 0.420438i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.24932 | 0.685952 | 0.342976 | − | 0.939344i | \(-0.388565\pi\) | ||||
0.342976 | + | 0.939344i | \(0.388565\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.342329 | − | 0.592932i | −0.0371308 | − | 0.0643125i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6.41797 | −0.688079 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.34233 | + | 9.25319i | 0.566286 | + | 0.980836i | 0.996929 | + | 0.0783134i | \(0.0249535\pi\) |
−0.430643 | + | 0.902522i | \(0.641713\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.87689 | + | 3.25088i | −0.194625 | + | 0.337100i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.67033 | + | 6.59852i | 0.171373 | + | 0.676994i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.62311 | + | 9.73950i | −0.570940 | + | 0.988897i | 0.425530 | + | 0.904944i | \(0.360088\pi\) |
−0.996470 | + | 0.0839525i | \(0.973246\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.97067 | − | 3.41330i | −0.198060 | − | 0.343050i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.90388 | − | 13.6899i | −0.786466 | − | 1.36220i | −0.928120 | − | 0.372282i | \(-0.878575\pi\) |
0.141654 | − | 0.989916i | \(-0.454758\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −17.9786 | −1.77149 | −0.885743 | − | 0.464175i | \(-0.846351\pi\) | ||||
−0.885743 | + | 0.464175i | \(0.846351\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.47999 | −0.529771 | −0.264885 | − | 0.964280i | \(-0.585334\pi\) | ||||
−0.264885 | + | 0.964280i | \(0.585334\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.90388 | + | 10.2258i | −0.565489 | + | 0.979456i | 0.431515 | + | 0.902106i | \(0.357979\pi\) |
−0.997004 | + | 0.0773503i | \(0.975354\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.769326 | + | 1.33251i | −0.0730212 | + | 0.126476i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.56155 | −0.617259 | −0.308629 | − | 0.951182i | \(-0.599870\pi\) | ||||
−0.308629 | + | 0.951182i | \(0.599870\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.61932 | 0.710505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.246211 | − | 0.426450i | 0.0227622 | − | 0.0394254i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.31534 | 0.119577 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.684999 | − | 1.18645i | −0.0617643 | − | 0.106979i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.8078 | 1.05612 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.57898 | − | 7.93103i | −0.406319 | − | 0.703765i | 0.588155 | − | 0.808748i | \(-0.299855\pi\) |
−0.994474 | + | 0.104983i | \(0.966521\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.21922 | − | 9.03996i | −0.459527 | − | 0.795924i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.79499 | − | 8.30517i | 0.418940 | − | 0.725626i | −0.576893 | − | 0.816820i | \(-0.695735\pi\) |
0.995833 | + | 0.0911938i | \(0.0290683\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −4.41033 | + | 7.63892i | −0.379581 | + | 0.657453i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.50000 | + | 6.06218i | 0.299025 | + | 0.517927i | 0.975913 | − | 0.218159i | \(-0.0700052\pi\) |
−0.676888 | + | 0.736086i | \(0.736672\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.56432 | + | 9.63768i | 0.471959 | + | 0.817458i | 0.999485 | − | 0.0320813i | \(-0.0102136\pi\) |
−0.527526 | + | 0.849539i | \(0.676880\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.93087 | −0.246824 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.769326 | + | 1.33251i | 0.0643343 | + | 0.111430i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.31534 | 0.607506 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.79499 | − | 8.30517i | 0.395484 | − | 0.684999i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.46543 | + | 7.73436i | −0.365823 | + | 0.633623i | −0.988908 | − | 0.148531i | \(-0.952546\pi\) |
0.623085 | + | 0.782154i | \(0.285879\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.01864 | −0.571169 | −0.285585 | − | 0.958354i | \(-0.592188\pi\) | ||||
−0.285585 | + | 0.958354i | \(0.592188\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.492423 | 0.0398100 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.13932 | − | 3.70542i | 0.171835 | − | 0.297626i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.90388 | − | 17.1540i | 0.790416 | − | 1.36904i | −0.135294 | − | 0.990806i | \(-0.543198\pi\) |
0.925710 | − | 0.378235i | \(-0.123469\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.600672 | −0.0476364 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.50932 | 0.274871 | 0.137436 | − | 0.990511i | \(-0.456114\pi\) | ||||
0.137436 | + | 0.990511i | \(0.456114\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.75379 | − | 6.50175i | −0.292232 | − | 0.506161i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −11.4290 | − | 19.7956i | −0.884401 | − | 1.53183i | −0.846399 | − | 0.532549i | \(-0.821234\pi\) |
−0.0380014 | − | 0.999278i | \(-0.512099\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.40388 | − | 11.0918i | 0.492606 | − | 0.853219i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.71067 | − | 1.33251i | −0.360234 | − | 0.101900i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.90388 | + | 5.02967i | −0.220778 | + | 0.382399i | −0.955044 | − | 0.296463i | \(-0.904193\pi\) |
0.734266 | + | 0.678861i | \(0.237526\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.938447 | + | 1.62544i | 0.0705380 | + | 0.122175i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 17.5466 | 1.31150 | 0.655748 | − | 0.754980i | \(-0.272354\pi\) | ||||
0.655748 | + | 0.754980i | \(0.272354\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.4654 | + | 18.1267i | 0.777890 | + | 1.34734i | 0.933156 | + | 0.359472i | \(0.117043\pi\) |
−0.155266 | + | 0.987873i | \(0.549624\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.34067 | 0.246949 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.876894 | − | 1.51883i | 0.0644706 | − | 0.111666i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.769326 | + | 1.33251i | −0.0562587 | + | 0.0974429i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 24.9973 | 1.80874 | 0.904370 | − | 0.426750i | \(-0.140342\pi\) | ||||
0.904370 | + | 0.426750i | \(0.140342\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.90388 | − | 8.49377i | 0.352989 | − | 0.611395i | −0.633783 | − | 0.773511i | \(-0.718499\pi\) |
0.986772 | + | 0.162116i | \(0.0518319\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.468990 | − | 0.812315i | 0.0335851 | − | 0.0581711i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 19.3693 | 1.38001 | 0.690003 | − | 0.723806i | \(-0.257609\pi\) | ||||
0.690003 | + | 0.723806i | \(0.257609\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.45830 | − | 16.3823i | −0.670481 | − | 1.16131i | −0.977768 | − | 0.209691i | \(-0.932754\pi\) |
0.307286 | − | 0.951617i | \(-0.400579\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −19.0000 | −1.34016 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.780776 | + | 1.35234i | 0.0545318 | + | 0.0944518i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.74000 | + | 4.74581i | −0.190443 | + | 0.329857i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 10.9654 | − | 10.6654i | 0.758495 | − | 0.737741i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.80966 | − | 6.59852i | 0.262268 | − | 0.454261i | −0.704576 | − | 0.709628i | \(-0.748863\pi\) |
0.966844 | + | 0.255367i | \(0.0821963\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.34233 | − | 5.78908i | −0.229013 | − | 0.396662i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.94898 | + | 10.3039i | 0.405717 | + | 0.702723i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.853653 | − | 1.47857i | −0.0576846 | − | 0.0999126i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.192236 | −0.0129312 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.45830 | − | 16.3823i | 0.633375 | − | 1.09704i | −0.353482 | − | 0.935441i | \(-0.615002\pi\) |
0.986857 | − | 0.161596i | \(-0.0516642\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.43845 | + | 2.49146i | −0.0958965 | + | 0.166098i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.5280 | 0.698766 | 0.349383 | − | 0.936980i | \(-0.386391\pi\) | ||||
0.349383 | + | 0.936980i | \(0.386391\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.75379 | 0.644549 | 0.322274 | − | 0.946646i | \(-0.395553\pi\) | ||||
0.322274 | + | 0.946646i | \(0.395553\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.93845 | + | 3.35749i | −0.126992 | + | 0.219956i | −0.922510 | − | 0.385974i | \(-0.873866\pi\) |
0.795518 | + | 0.605930i | \(0.207199\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.34067 | 0.217921 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.46543 | + | 2.53821i | 0.0951902 | + | 0.164874i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 29.2759 | 1.89370 | 0.946851 | − | 0.321673i | \(-0.104245\pi\) | ||||
0.946851 | + | 0.321673i | \(0.104245\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.74621 | + | 16.8809i | 0.627809 | + | 1.08740i | 0.987991 | + | 0.154514i | \(0.0493813\pi\) |
−0.360182 | + | 0.932882i | \(0.617285\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.47999 | − | 9.49162i | −0.351542 | − | 0.608888i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.46543 | + | 9.46641i | −0.349174 | + | 0.604787i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.83899 | + | 0.520197i | 0.117012 | + | 0.0330993i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.28078 | + | 7.41452i | −0.271283 | + | 0.469876i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.4436 | − | 18.0889i | −0.659197 | − | 1.14176i | −0.980824 | − | 0.194896i | \(-0.937563\pi\) |
0.321627 | − | 0.946866i | \(-0.395770\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.56155 | − | 14.8290i | −0.538260 | − | 0.932294i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.937981 | 0.0587386 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.62311 | + | 9.73950i | 0.350760 | + | 0.607534i | 0.986383 | − | 0.164466i | \(-0.0525901\pi\) |
−0.635623 | + | 0.772000i | \(0.719257\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.63068 | + | 4.55648i | −0.162835 | + | 0.282039i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 11.4290 | − | 19.7956i | 0.704741 | − | 1.22065i | −0.262044 | − | 0.965056i | \(-0.584397\pi\) |
0.966785 | − | 0.255591i | \(-0.0822700\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.684658 | 0.0420582 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −14.6380 | −0.895829 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.78078 | + | 15.2088i | −0.535373 | + | 0.927294i | 0.463772 | + | 0.885955i | \(0.346496\pi\) |
−0.999145 | + | 0.0413392i | \(0.986838\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.06966 | + | 1.85271i | −0.0649773 | + | 0.112544i | −0.896684 | − | 0.442671i | \(-0.854031\pi\) |
0.831707 | + | 0.555215i | \(0.187364\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.49466 | − | 7.78497i | −0.271038 | − | 0.469452i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.00000 | 0.240337 | 0.120168 | − | 0.992754i | \(-0.461657\pi\) | ||||
0.120168 | + | 0.992754i | \(0.461657\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.53865 | + | 2.66502i | 0.0921167 | + | 0.159551i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −11.5000 | − | 19.9186i | −0.686032 | − | 1.18824i | −0.973111 | − | 0.230336i | \(-0.926017\pi\) |
0.287079 | − | 0.957907i | \(-0.407316\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.79499 | − | 8.30517i | 0.285033 | − | 0.493691i | −0.687584 | − | 0.726104i | \(-0.741329\pi\) |
0.972617 | + | 0.232413i | \(0.0746622\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −8.97301 | − | 2.53821i | −0.531515 | − | 0.150350i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.40388 | + | 14.5560i | 0.494346 | + | 0.856232i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.70364 | − | 13.3431i | −0.451596 | − | 0.782186i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.00000 | 0.233682 | 0.116841 | − | 0.993151i | \(-0.462723\pi\) | ||||
0.116841 | + | 0.993151i | \(0.462723\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.06966 | − | 1.85271i | −0.0622781 | − | 0.107869i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 19.8229 | 1.15024 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.06966 | − | 1.85271i | 0.0618602 | − | 0.107145i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 21.6566 | 1.24414 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.80776 | −0.218032 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.30431 | + | 14.3835i | −0.473952 | + | 0.820909i | −0.999555 | − | 0.0298205i | \(-0.990506\pi\) |
0.525603 | + | 0.850730i | \(0.323840\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 12.3153 | − | 21.3308i | 0.700595 | − | 1.21347i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.7000 | 0.776855 | 0.388427 | − | 0.921479i | \(-0.373018\pi\) | ||||
0.388427 | + | 0.921479i | \(0.373018\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.62311 | − | 9.73950i | −0.317837 | − | 0.550509i | 0.662200 | − | 0.749327i | \(-0.269623\pi\) |
−0.980036 | + | 0.198818i | \(0.936290\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −15.5885 | − | 27.0001i | −0.875540 | − | 1.51648i | −0.856187 | − | 0.516666i | \(-0.827173\pi\) |
−0.0193529 | − | 0.999813i | \(-0.506161\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.21999 | − | 14.2374i | −0.460231 | − | 0.797143i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.75379 | − | 6.50175i | 0.209516 | − | 0.362892i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.468990 | + | 1.85271i | 0.0260953 | + | 0.103087i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.561553 | − | 0.972638i | 0.0311493 | − | 0.0539522i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −8.08831 | − | 14.0094i | −0.447284 | − | 0.774719i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −21.4879 | −1.18108 | −0.590542 | − | 0.807007i | \(-0.701086\pi\) | ||||
−0.590542 | + | 0.807007i | \(0.701086\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.630683 | + | 1.09238i | 0.0345612 | + | 0.0598618i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 21.6566 | 1.18323 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.06155 | + | 5.30277i | −0.166773 | + | 0.288860i | −0.937284 | − | 0.348568i | \(-0.886668\pi\) |
0.770510 | + | 0.637428i | \(0.220002\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.49466 | − | 7.78497i | 0.244116 | − | 0.422822i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.61553 | −0.520710 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5.21922 | + | 9.03996i | −0.280994 | + | 0.486695i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.79499 | + | 8.30517i | −0.257409 | + | 0.445845i | −0.965547 | − | 0.260229i | \(-0.916202\pi\) |
0.708138 | + | 0.706074i | \(0.249535\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.0000 | 0.642345 | 0.321173 | − | 0.947021i | \(-0.395923\pi\) | ||||
0.321173 | + | 0.947021i | \(0.395923\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.23832 | + | 2.14483i | 0.0660964 | + | 0.114482i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −24.8078 | −1.32038 | −0.660192 | − | 0.751097i | \(-0.729525\pi\) | ||||
−0.660192 | + | 0.751097i | \(0.729525\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.80966 | + | 6.59852i | 0.202196 | + | 0.350213i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.43966 | − | 4.22562i | 0.128760 | − | 0.223019i | −0.794436 | − | 0.607348i | \(-0.792234\pi\) |
0.923197 | + | 0.384328i | \(0.125567\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.526988 | − | 18.9927i | 0.0277362 | − | 0.999615i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.901008 | + | 1.56059i | −0.0472906 | + | 0.0819098i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.973012 | + | 1.68531i | 0.0509298 | + | 0.0882130i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.45830 | − | 16.3823i | −0.493719 | − | 0.855147i | 0.506254 | − | 0.862384i | \(-0.331030\pi\) |
−0.999974 | + | 0.00723702i | \(0.997696\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.12311 | −0.0584665 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −27.6155 | −1.42988 | −0.714939 | − | 0.699187i | \(-0.753546\pi\) | ||||
−0.714939 | + | 0.699187i | \(0.753546\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −8.08831 | + | 14.0094i | −0.417678 | + | 0.723440i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.02699 | − | 1.77879i | 0.0528926 | − | 0.0916126i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.55730 | −0.439559 | −0.219779 | − | 0.975550i | \(-0.570534\pi\) | ||||
−0.219779 | + | 0.975550i | \(0.570534\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 12.5464 | 0.642771 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5.94898 | + | 10.3039i | −0.303979 | + | 0.526507i | −0.977033 | − | 0.213086i | \(-0.931649\pi\) |
0.673055 | + | 0.739593i | \(0.264982\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8.55730 | −0.434992 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 14.1501 | + | 24.5087i | 0.717438 | + | 1.24264i | 0.962012 | + | 0.273009i | \(0.0880188\pi\) |
−0.244573 | + | 0.969631i | \(0.578648\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.13932 | 0.108190 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.56913 | + | 11.3781i | 0.331369 | + | 0.573948i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.67033 | − | 2.89310i | −0.0840436 | − | 0.145568i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.7808 | + | 23.8690i | −0.691637 | + | 1.19795i | 0.279664 | + | 0.960098i | \(0.409777\pi\) |
−0.971301 | + | 0.237853i | \(0.923556\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.50000 | + | 14.7224i | −0.424470 | + | 0.735203i | −0.996371 | − | 0.0851195i | \(-0.972873\pi\) |
0.571901 | + | 0.820323i | \(0.306206\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.600672 | − | 1.04039i | −0.0299216 | − | 0.0518257i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.41146 | − | 5.90882i | −0.169517 | − | 0.293612i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.94134 | −0.195365 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.30776 | + | 16.1215i | 0.460239 | + | 0.797158i | 0.998973 | − | 0.0453185i | \(-0.0144303\pi\) |
−0.538733 | + | 0.842476i | \(0.681097\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.58999 | −0.473039 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.87932 | − | 8.45123i | 0.239516 | − | 0.414855i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −15.2462 | −0.746610 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 30.4773 | 1.48891 | 0.744456 | − | 0.667672i | \(-0.232709\pi\) | ||||
0.744456 | + | 0.667672i | \(0.232709\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.0270 | + | 27.7596i | −0.781108 | + | 1.35292i | 0.150189 | + | 0.988657i | \(0.452012\pi\) |
−0.931297 | + | 0.364261i | \(0.881322\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.20134 | + | 2.08079i | −0.0584113 | + | 0.101171i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.12311 | 0.0544786 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.10795 | −0.101773 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14.9383 | + | 25.8739i | 0.719552 | + | 1.24630i | 0.961177 | + | 0.275932i | \(0.0889863\pi\) |
−0.241625 | + | 0.970370i | \(0.577680\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −15.5885 | − | 27.0001i | −0.749137 | − | 1.29754i | −0.948237 | − | 0.317565i | \(-0.897135\pi\) |
0.199099 | − | 0.979979i | \(-0.436198\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.01100 | + | 8.67931i | −0.240259 | + | 0.416141i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −20.4654 | − | 5.78908i | −0.978995 | − | 0.276929i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.43966 | + | 4.22562i | −0.116439 | + | 0.201678i | −0.918354 | − | 0.395760i | \(-0.870481\pi\) |
0.801915 | + | 0.597438i | \(0.203814\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.93087 | − | 6.80847i | −0.187184 | − | 0.324213i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.05500 | + | 3.55936i | 0.0976359 | + | 0.169110i | 0.910706 | − | 0.413056i | \(-0.135539\pi\) |
−0.813070 | + | 0.582166i | \(0.802205\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 16.6847 | 0.790929 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −6.11764 | − | 10.5961i | −0.289354 | − | 0.501176i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 24.8078 | 1.17075 | 0.585375 | − | 0.810762i | \(-0.300947\pi\) | ||||
0.585375 | + | 0.810762i | \(0.300947\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.75466 | − | 3.03916i | 0.0826238 | − | 0.143109i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.80776 | − | 8.32729i | 0.225888 | − | 0.391250i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −32.5616 | −1.52317 | −0.761583 | − | 0.648068i | \(-0.775577\pi\) | ||||
−0.761583 | + | 0.648068i | \(0.775577\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.23832 | + | 2.14483i | −0.0577997 | + | 0.100112i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.7808 | − | 23.8690i | 0.641835 | − | 1.11169i | −0.343188 | − | 0.939267i | \(-0.611507\pi\) |
0.985023 | − | 0.172424i | \(-0.0551598\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.7773 | −0.779707 | −0.389853 | − | 0.920877i | \(-0.627474\pi\) | ||||
−0.389853 | + | 0.920877i | \(0.627474\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.93087 | + | 5.07642i | 0.135916 | + | 0.235413i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14.4693 | 0.669560 | 0.334780 | − | 0.942296i | \(-0.391338\pi\) | ||||
0.334780 | + | 0.942296i | \(0.391338\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 13.5683 | + | 23.5010i | 0.625194 | + | 1.08287i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 13.3693 | − | 23.1563i | 0.614722 | − | 1.06473i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −10.7440 | − | 3.03916i | −0.492967 | − | 0.139446i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.246211 | + | 0.426450i | −0.0112732 | + | 0.0195258i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.41033 | − | 7.63892i | −0.201513 | − | 0.349031i | 0.747503 | − | 0.664258i | \(-0.231253\pi\) |
−0.949016 | + | 0.315227i | \(0.897919\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.246211 | − | 0.426450i | −0.0112263 | − | 0.0194445i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.78078 | + | 15.2088i | 0.398715 | + | 0.690594i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −32.0159 | −1.45078 | −0.725390 | − | 0.688338i | \(-0.758340\pi\) | ||||
−0.725390 | + | 0.688338i | \(0.758340\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.40388 | + | 4.16365i | −0.108707 | + | 0.188287i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.3083 | − | 28.2468i | 0.735983 | − | 1.27476i | −0.218308 | − | 0.975880i | \(-0.570054\pi\) |
0.954291 | − | 0.298880i | \(-0.0966130\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.05398 | 0.0925064 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.15461 | −0.276629 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.33365 | + | 10.9702i | −0.283533 | + | 0.491093i | −0.972252 | − | 0.233935i | \(-0.924840\pi\) |
0.688719 | + | 0.725028i | \(0.258173\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 31.3153 | 1.39907 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 14.9383 | + | 25.8739i | 0.666066 | + | 1.15366i | 0.978995 | + | 0.203883i | \(0.0653563\pi\) |
−0.312930 | + | 0.949776i | \(0.601310\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −24.6847 | −1.09845 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 8.77331 | + | 15.1958i | 0.389636 | + | 0.674870i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.534565 | − | 0.925894i | −0.0236942 | − | 0.0410395i | 0.853935 | − | 0.520379i | \(-0.174209\pi\) |
−0.877629 | + | 0.479340i | \(0.840876\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 17.6501 | − | 17.1672i | 0.779271 | − | 0.757948i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −14.0373 | + | 24.3133i | −0.618557 | + | 1.07137i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.75379 | − | 6.50175i | −0.165091 | − | 0.285947i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.97831 | − | 6.89064i | −0.174629 | − | 0.302465i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 28.4233 | 1.24525 | 0.622624 | − | 0.782522i | \(-0.286067\pi\) | ||||
0.622624 | + | 0.782522i | \(0.286067\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.94898 | + | 10.3039i | 0.260131 | + | 0.450560i | 0.966276 | − | 0.257507i | \(-0.0829010\pi\) |
−0.706146 | + | 0.708067i | \(0.749568\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.600672 | − | 1.04039i | 0.0261657 | − | 0.0453203i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.403882 | + | 0.699544i | −0.0175601 | + | 0.0304150i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.53865 | 0.0667718 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.438447 | 0.0189913 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.27865 | + | 7.41084i | −0.184982 | + | 0.320398i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −12.0194 | + | 20.8182i | −0.518676 | + | 0.898373i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 24.5653 | 1.05810 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14.1501 | − | 24.5087i | −0.608360 | − | 1.05371i | −0.991511 | − | 0.130025i | \(-0.958494\pi\) |
0.383151 | − | 0.923686i | \(-0.374839\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −28.6752 | −1.23057 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9.21922 | + | 15.9682i | 0.394908 | + | 0.684001i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.94898 | − | 10.3039i | −0.254360 | − | 0.440565i | 0.710361 | − | 0.703837i | \(-0.248532\pi\) |
−0.964722 | + | 0.263272i | \(0.915198\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.36932 | − | 2.37173i | 0.0584410 | − | 0.101223i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −19.6490 | − | 5.55813i | −0.837074 | − | 0.236784i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.20134 | + | 2.08079i | 0.0509942 | + | 0.0883245i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −5.21922 | − | 9.03996i | −0.221146 | − | 0.383035i | 0.734011 | − | 0.679138i | \(-0.237646\pi\) |
−0.955156 | + | 0.296103i | \(0.904313\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.34067 | 0.141295 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.05398 | − | 1.82554i | −0.0444989 | − | 0.0770743i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 32.4479 | 1.36752 | 0.683759 | − | 0.729708i | \(-0.260344\pi\) | ||||
0.683759 | + | 0.729708i | \(0.260344\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.12311 | + | 8.87348i | −0.215531 | + | 0.373310i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0.630683 | 0.0264396 | 0.0132198 | − | 0.999913i | \(-0.495792\pi\) | ||||
0.0132198 | + | 0.999913i | \(0.495792\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.4693 | 0.605522 | 0.302761 | − | 0.953067i | \(-0.402092\pi\) | ||||
0.302761 | + | 0.953067i | \(0.402092\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −17.1231 | + | 29.6581i | −0.715328 | + | 1.23898i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.24932 | + | 10.8241i | −0.260615 | + | 0.451398i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 24.1771 | 1.00651 | 0.503253 | − | 0.864139i | \(-0.332137\pi\) | ||||
0.503253 | + | 0.864139i | \(0.332137\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.71831 | + | 11.6365i | 0.279203 | + | 0.483594i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.769326 | − | 1.33251i | −0.0318622 | − | 0.0551870i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.384472 | − | 0.665925i | −0.0158960 | − | 0.0275326i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −10.2276 | + | 17.7148i | −0.422139 | + | 0.731167i | −0.996149 | − | 0.0876819i | \(-0.972054\pi\) |
0.574009 | + | 0.818849i | \(0.305387\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.56155 | + | 8.32729i | −0.352773 | + | 0.343120i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −13.2680 | + | 22.9808i | −0.545771 | + | 0.945303i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 11.1847 | + | 19.3724i | 0.459299 | + | 0.795529i | 0.998924 | − | 0.0463764i | \(-0.0147674\pi\) |
−0.539625 | + | 0.841905i | \(0.681434\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 25.9157 | 1.06066 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7.91965 | + | 13.7172i | 0.323588 | + | 0.560471i | 0.981226 | − | 0.192863i | \(-0.0617774\pi\) |
−0.657637 | + | 0.753335i | \(0.728444\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 42.4233 | 1.73048 | 0.865241 | − | 0.501356i | \(-0.167165\pi\) | ||||
0.865241 | + | 0.501356i | \(0.167165\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.78797 | + | 13.4892i | −0.317151 | + | 0.549321i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.02699 | − | 1.77879i | 0.0417530 | − | 0.0723183i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −39.0346 | −1.58436 | −0.792182 | − | 0.610285i | \(-0.791055\pi\) | ||||
−0.792182 | + | 0.610285i | \(0.791055\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.468990 | − | 0.812315i | 0.0189733 | − | 0.0328628i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22.9039 | − | 39.6707i | 0.925079 | − | 1.60228i | 0.133645 | − | 0.991029i | \(-0.457332\pi\) |
0.791434 | − | 0.611255i | \(-0.209335\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.13932 | −0.0862659 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −16.1847 | − | 28.0327i | −0.651570 | − | 1.12855i | −0.982742 | − | 0.184982i | \(-0.940777\pi\) |
0.331172 | − | 0.943570i | \(-0.392556\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 19.5173 | 0.784466 | 0.392233 | − | 0.919866i | \(-0.371703\pi\) | ||||
0.392233 | + | 0.919866i | \(0.371703\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −13.7808 | − | 23.8690i | −0.553004 | − | 0.957830i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.81534 | − | 4.87631i | 0.112614 | − | 0.195053i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.14268 | + | 20.3158i | 0.205379 | + | 0.811333i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.246211 | − | 0.426450i | 0.00981709 | − | 0.0170037i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.08831 | + | 14.0094i | 0.321990 | + | 0.557704i | 0.980899 | − | 0.194520i | \(-0.0623148\pi\) |
−0.658908 | + | 0.752223i | \(0.728981\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5.21922 | + | 9.03996i | 0.207446 | + | 0.359306i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −14.3007 | −0.567504 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.53457 | + | 2.65794i | 0.0608017 | + | 0.105312i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.47999 | −0.216785 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.18466 | + | 12.4442i | −0.283777 | + | 0.491516i | −0.972312 | − | 0.233687i | \(-0.924921\pi\) |
0.688535 | + | 0.725203i | \(0.258254\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.28567 | + | 2.22685i | −0.0507019 | + | 0.0878183i | −0.890263 | − | 0.455448i | \(-0.849479\pi\) |
0.839561 | + | 0.543266i | \(0.182813\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −16.3002 | −0.641819 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −28.9386 | −1.13769 | −0.568847 | − | 0.822443i | \(-0.692610\pi\) | ||||
−0.568847 | + | 0.822443i | \(0.692610\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.40388 | + | 4.16365i | −0.0943606 | + | 0.163437i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 40.4924 | 1.58459 | 0.792295 | − | 0.610138i | \(-0.208886\pi\) | ||||
0.792295 | + | 0.610138i | \(0.208886\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.48763 | − | 12.9690i | −0.292566 | − | 0.506739i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.39963 | −0.0546046 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5.94898 | + | 10.3039i | 0.231739 | + | 0.401384i | 0.958320 | − | 0.285697i | \(-0.0922250\pi\) |
−0.726581 | + | 0.687081i | \(0.758892\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.15009 | − | 3.72407i | −0.0836289 | − | 0.144850i | 0.821177 | − | 0.570673i | \(-0.193318\pi\) |
−0.904806 | + | 0.425824i | \(0.859984\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.131681 | − | 0.228079i | 0.00511408 | − | 0.00885785i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −11.4290 | + | 19.7956i | −0.442532 | + | 0.766487i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 12.9579 | + | 22.4437i | 0.500980 | + | 0.867722i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.27865 | + | 7.41084i | 0.165175 | + | 0.286092i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25.6155 | −0.987406 | −0.493703 | − | 0.869631i | \(-0.664357\pi\) | ||||
−0.493703 | + | 0.869631i | \(0.664357\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −7.23465 | − | 12.5308i | −0.278462 | − | 0.482310i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.12311 | −0.0431645 | −0.0215822 | − | 0.999767i | \(-0.506870\pi\) | ||||
−0.0215822 | + | 0.999767i | \(0.506870\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.21165 | + | 12.4909i | −0.276351 | + | 0.478654i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 23.7959 | 0.910526 | 0.455263 | − | 0.890357i | \(-0.349545\pi\) | ||||
0.455263 | + | 0.890357i | \(0.349545\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10.9309 | 0.417647 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.68134 | + | 11.5724i | −0.254909 | + | 0.441515i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.0961180 | − | 0.166481i | 0.00366180 | − | 0.00634243i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −41.4372 | −1.57635 | −0.788174 | − | 0.615453i | \(-0.788973\pi\) | ||||
−0.788174 | + | 0.615453i | \(0.788973\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 17.3780 | 0.659183 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.219224 | + | 0.379706i | 0.00830369 | + | 0.0143824i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.65567 | − | 4.59975i | −0.100447 | − | 0.173979i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −12.7808 | + | 22.1370i | −0.482723 | + | 0.836101i | −0.999803 | − | 0.0198359i | \(-0.993686\pi\) |
0.517080 | + | 0.855937i | \(0.327019\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.50932 | + | 3.41330i | −0.132357 | + | 0.128735i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.28835 | + | 3.96355i | −0.0861844 | + | 0.149276i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12.9039 | − | 22.3502i | −0.484615 | − | 0.839379i | 0.515228 | − | 0.857053i | \(-0.327707\pi\) |
−0.999844 | + | 0.0176744i | \(0.994374\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.40269 | 0.0901078 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.68466 | + | 11.5782i | 0.250342 | + | 0.433606i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.40269 | 0.0898554 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −20.0540 | + | 34.7345i | −0.748929 | + | 1.29718i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −17.0776 | + | 29.5793i | −0.636888 | + | 1.10312i | 0.349224 | + | 0.937039i | \(0.386445\pi\) |
−0.986112 | + | 0.166083i | \(0.946888\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −26.7046 | −0.993154 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6.00000 | + | 10.3923i | −0.222834 | + | 0.385961i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13.5683 | + | 23.5010i | −0.503220 | + | 0.871603i | 0.496773 | + | 0.867881i | \(0.334518\pi\) |
−0.999993 | + | 0.00372251i | \(0.998815\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 28.1231 | 1.04160 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.67033 | + | 2.89310i | 0.0617795 | + | 0.107005i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.36932 | 0.124449 | 0.0622243 | − | 0.998062i | \(-0.480181\pi\) | ||||
0.0622243 | + | 0.998062i | \(0.480181\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −7.48763 | − | 12.9690i | −0.276186 | − | 0.478367i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −24.3348 | − | 42.1490i | −0.896382 | − | 1.55258i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.79499 | + | 8.30517i | −0.176387 | + | 0.305511i | −0.940640 | − | 0.339405i | \(-0.889774\pi\) |
0.764254 | + | 0.644916i | \(0.223108\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.87689 | + | 1.82554i | −0.0689494 | + | 0.0670628i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 14.9383 | − | 25.8739i | 0.548033 | − | 0.949221i | −0.450376 | − | 0.892839i | \(-0.648710\pi\) |
0.998409 | − | 0.0563821i | \(-0.0179565\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.97301 | + | 12.0776i | 0.255471 | + | 0.442489i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.50932 | + | 6.07832i | 0.128399 | + | 0.222394i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.9569 | + | 38.0305i | 0.801220 | + | 1.38775i | 0.918813 | + | 0.394692i | \(0.129149\pi\) |
−0.117593 | + | 0.993062i | \(0.537518\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 28.6155 | 1.04281 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.47999 | + | 9.49162i | −0.199437 | + | 0.345436i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.65767 | + | 8.06732i | −0.169286 | + | 0.293212i | −0.938169 | − | 0.346178i | \(-0.887479\pi\) |
0.768883 | + | 0.639389i | \(0.220813\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 23.4586 | 0.851494 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −21.9309 | −0.794993 | −0.397497 | − | 0.917604i | \(-0.630121\pi\) | ||||
−0.397497 | + | 0.917604i | \(0.630121\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.384472 | − | 0.665925i | 0.0139006 | − | 0.0240766i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.600672 | −0.0216890 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.34233 | − | 9.25319i | −0.192649 | − | 0.333678i | 0.753478 | − | 0.657473i | \(-0.228375\pi\) |
−0.946127 | + | 0.323795i | \(0.895041\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −15.4073 | −0.554880 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −14.3423 | − | 24.8416i | −0.515858 | − | 0.893492i | −0.999831 | − | 0.0184088i | \(-0.994140\pi\) |
0.483973 | − | 0.875083i | \(-0.339193\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.50932 | + | 6.07832i | 0.126059 | + | 0.218340i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.06966 | − | 4.22562i | −0.0383246 | − | 0.151398i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.56155 | − | 14.8290i | 0.306356 | − | 0.530625i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −13.2310 | − | 22.9167i | −0.472837 | − | 0.818978i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −15.4654 | − | 26.7869i | −0.551985 | − | 0.956066i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −21.4879 | −0.765963 | −0.382981 | − | 0.923756i | \(-0.625103\pi\) | ||||
−0.382981 | + | 0.923756i | \(0.625103\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 15.6577 | + | 27.1199i | 0.557428 | + | 0.965493i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.534565 | + | 0.925894i | −0.0189830 | + | 0.0328795i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.468990 | + | 0.812315i | −0.0166334 | + | 0.0288098i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 12.6307 | 0.447402 | 0.223701 | − | 0.974658i | \(-0.428186\pi\) | ||||
0.223701 | + | 0.974658i | \(0.428186\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.937981 | 0.0331834 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.00000 | + | 10.3923i | −0.212000 | + | 0.367194i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.18668 | − | 3.78744i | 0.0771662 | − | 0.133656i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −12.0296 | − | 20.8360i | −0.423464 | − | 0.733460i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −40.1771 | −1.41255 | −0.706275 | − | 0.707937i | \(-0.749626\pi\) | ||||
−0.706275 | + | 0.707937i | \(0.749626\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −26.0669 | − | 45.1493i | −0.915334 | − | 1.58540i | −0.806412 | − | 0.591354i | \(-0.798593\pi\) |
−0.108922 | − | 0.994050i | \(-0.534740\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.46543 | − | 2.53821i | −0.0513950 | − | 0.0890188i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.74000 | − | 4.74581i | 0.0959779 | − | 0.166239i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.15009 | − | 32.1963i | −0.285136 | − | 1.12641i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −8.71165 | − | 15.0890i | −0.304039 | − | 0.526610i | 0.673008 | − | 0.739635i | \(-0.265002\pi\) |
−0.977047 | + | 0.213025i | \(0.931668\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.0963 | + | 41.7360i | 0.839943 | + | 1.45482i | 0.889942 | + | 0.456075i | \(0.150745\pi\) |
−0.0499986 | + | 0.998749i | \(0.515922\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 12.3153 | 0.428765 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3.42499 | − | 5.93227i | −0.119099 | − | 0.206285i | 0.800312 | − | 0.599584i | \(-0.204667\pi\) |
−0.919411 | + | 0.393299i | \(0.871334\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 31.1231 | 1.08095 | 0.540475 | − | 0.841360i | \(-0.318245\pi\) | ||||
0.540475 | + | 0.841360i | \(0.318245\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.74000 | + | 4.74581i | −0.0950494 | + | 0.164630i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.53457 | + | 2.65794i | −0.0531695 | + | 0.0920923i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −35.6939 | −1.23524 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −15.4773 | −0.534973 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 25.4663 | − | 44.1089i | 0.879193 | − | 1.52281i | 0.0269650 | − | 0.999636i | \(-0.491416\pi\) |
0.852228 | − | 0.523171i | \(-0.175251\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.52699 | − | 6.10892i | 0.121620 | − | 0.210652i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 31.5100 | 1.08526 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −10.0000 | − | 17.3205i | −0.344010 | − | 0.595844i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 6.56913 | + | 11.3781i | 0.225452 | + | 0.390494i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.74000 | + | 4.74581i | 0.0939258 | + | 0.162684i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.78078 | + | 3.08440i | −0.0609726 | + | 0.105608i | −0.894900 | − | 0.446266i | \(-0.852754\pi\) |
0.833928 | + | 0.551874i | \(0.186087\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.47999 | + | 5.33005i | −0.187412 | + | 0.182284i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0.815342 | − | 1.41221i | 0.0278515 | − | 0.0482403i | −0.851764 | − | 0.523926i | \(-0.824467\pi\) |
0.879615 | + | 0.475686i | \(0.157800\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 26.4516 | + | 45.8155i | 0.902517 | + | 1.56321i | 0.824216 | + | 0.566275i | \(0.191616\pi\) |
0.0783006 | + | 0.996930i | \(0.475051\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 33.2173 | 1.13073 | 0.565364 | − | 0.824841i | \(-0.308736\pi\) | ||||
0.565364 | + | 0.824841i | \(0.308736\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.53457 | + | 7.85410i | 0.154180 | + | 0.267047i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −23.0266 | −0.782024 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.75379 | + | 6.50175i | −0.127339 | + | 0.220557i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.04033 | − | 5.26601i | 0.103018 | − | 0.178432i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −12.6307 | −0.427484 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −19.6577 | + | 34.0481i | −0.663792 | + | 1.14972i | 0.315819 | + | 0.948820i | \(0.397721\pi\) |
−0.979611 | + | 0.200903i | \(0.935613\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.74000 | + | 4.74581i | −0.0924178 | + | 0.160072i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −11.0540 | −0.372418 | −0.186209 | − | 0.982510i | \(-0.559620\pi\) | ||||
−0.186209 | + | 0.982510i | \(0.559620\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −17.4623 | − | 30.2456i | −0.587653 | − | 1.01784i | −0.994539 | − | 0.104365i | \(-0.966719\pi\) |
0.406886 | − | 0.913479i | \(-0.366614\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.93087 | 0.0985201 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −5.94898 | − | 10.3039i | −0.199747 | − | 0.345972i | 0.748699 | − | 0.662910i | \(-0.230679\pi\) |
−0.948446 | + | 0.316938i | \(0.897345\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −7.66667 | + | 13.2791i | −0.256843 | + | 0.444865i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −8.97301 | − | 2.53821i | −0.300270 | − | 0.0849379i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 13.7000 | − | 23.7291i | 0.457940 | − | 0.793175i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.46543 | + | 2.53821i | 0.0489294 | + | 0.0847483i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.41797 | + | 11.1163i | 0.214051 | + | 0.370748i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.192236 | 0.00640431 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 32.6847 | 1.08647 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6.76566 | + | 11.7185i | −0.224650 | + | 0.389105i | −0.956214 | − | 0.292667i | \(-0.905457\pi\) |
0.731564 | + | 0.681772i | \(0.238791\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 8.87689 | − | 15.3752i | 0.294428 | − | 0.509964i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10.0959 | 0.334494 | 0.167247 | − | 0.985915i | \(-0.446512\pi\) | ||||
0.167247 | + | 0.985915i | \(0.446512\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −21.9309 | −0.725806 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.60831 | − | 4.51773i | 0.0862282 | − | 0.149352i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 57.0132 | 1.88069 | 0.940346 | − | 0.340220i | \(-0.110502\pi\) | ||||
0.940346 | + | 0.340220i | \(0.110502\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −11.3769 | − | 19.7054i | −0.374881 | − | 0.649314i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.13932 | 0.0704167 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.43845 | + | 2.49146i | 0.0472959 | + | 0.0819188i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −10.0959 | − | 17.4867i | −0.331594 | − | 0.574338i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −6.06155 | + | 10.4989i | −0.198873 | + | 0.344458i | −0.948163 | − | 0.317783i | \(-0.897061\pi\) |
0.749290 | + | 0.662242i | \(0.230395\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 21.8726 | − | 21.2741i | 0.716846 | − | 0.697232i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −9.38447 | + | 16.2544i | −0.307234 | + | 0.532145i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.20134 | + | 2.08079i | 0.0392881 | + | 0.0680490i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20.9924 | + | 36.3599i | 0.685793 | + | 1.18783i | 0.973187 | + | 0.230015i | \(0.0738776\pi\) |
−0.287394 | + | 0.957812i | \(0.592789\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 15.4073 | 0.502798 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.78078 | − | 6.54850i | −0.123250 | − | 0.213475i | 0.797798 | − | 0.602925i | \(-0.205998\pi\) |
−0.921047 | + | 0.389450i | \(0.872665\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.87932 | −0.158893 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −23.3269 | + | 40.4034i | −0.758024 | + | 1.31294i | 0.185833 | + | 0.982581i | \(0.440502\pi\) |
−0.943857 | + | 0.330354i | \(0.892832\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.546398 | 0.0177368 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 42.7125 | 1.38505 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −28.3078 | + | 49.0305i | −0.916978 | + | 1.58825i | −0.113000 | + | 0.993595i | \(0.536046\pi\) |
−0.803979 | + | 0.594658i | \(0.797287\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 19.5173 | − | 33.8049i | 0.631564 | − | 1.09390i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 22.5227 | 0.728057 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.4924 | −0.757820 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.07730 | − | 5.33005i | −0.0991648 | − | 0.171758i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −7.65767 | − | 13.2635i | −0.246509 | − | 0.426966i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15.5390 | − | 26.9143i | 0.499700 | − | 0.865505i | −0.500300 | − | 0.865852i | \(-0.666777\pi\) |
1.00000 | 0.000346935i | \(0.000110433\pi\) | ||||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.51941 | − | 0.712669i | −0.0809351 | − | 0.0228942i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.73297 | − | 9.92980i | 0.183980 | − | 0.318662i | −0.759252 | − | 0.650796i | \(-0.774435\pi\) |
0.943232 | + | 0.332134i | \(0.107769\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.769326 | + | 1.33251i | 0.0246382 | + | 0.0426745i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 37.3002 | 1.19334 | 0.596669 | − | 0.802487i | \(-0.296490\pi\) | ||||
0.596669 | + | 0.802487i | \(0.296490\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −18.7480 | − | 32.4724i | −0.599187 | − | 1.03782i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −13.2614 | −0.423403 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 19.0483 | − | 32.9926i | 0.607546 | − | 1.05230i | −0.384097 | − | 0.923293i | \(-0.625487\pi\) |
0.991644 | − | 0.129008i | \(-0.0411793\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 15.1231 | − | 26.1940i | 0.481862 | − | 0.834610i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −37.1771 | −1.18216 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16.9090 | + | 29.2872i | −0.537131 | + | 0.930338i | 0.461926 | + | 0.886919i | \(0.347159\pi\) |
−0.999057 | + | 0.0434197i | \(0.986175\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 14.7192 | − | 25.4944i | 0.467100 | − | 0.809042i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −29.5393 | −0.936458 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −11.4654 | − | 19.8587i | −0.363114 | − | 0.628932i | 0.625358 | − | 0.780338i | \(-0.284953\pi\) |
−0.988472 | + | 0.151406i | \(0.951620\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6.34403 | −0.200716 |
(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 | 1216.2.i.p.961.2 | 8 | ||
4.3 | odd | 2 | inner | 1216.2.i.p.961.3 | 8 | ||
8.3 | odd | 2 | 608.2.i.d.353.2 | ✓ | 8 | ||
8.5 | even | 2 | 608.2.i.d.353.3 | yes | 8 | ||
19.7 | even | 3 | inner | 1216.2.i.p.577.2 | 8 | ||
76.7 | odd | 6 | inner | 1216.2.i.p.577.3 | 8 | ||
152.45 | even | 6 | 608.2.i.d.577.3 | yes | 8 | ||
152.83 | odd | 6 | 608.2.i.d.577.2 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
608.2.i.d.353.2 | ✓ | 8 | 8.3 | odd | 2 | ||
608.2.i.d.353.3 | yes | 8 | 8.5 | even | 2 | ||
608.2.i.d.577.2 | yes | 8 | 152.83 | odd | 6 | ||
608.2.i.d.577.3 | yes | 8 | 152.45 | even | 6 | ||
1216.2.i.p.577.2 | 8 | 19.7 | even | 3 | inner | ||
1216.2.i.p.577.3 | 8 | 76.7 | odd | 6 | inner | ||
1216.2.i.p.961.2 | 8 | 1.1 | even | 1 | trivial | ||
1216.2.i.p.961.3 | 8 | 4.3 | odd | 2 | inner |