Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [93,2,Mod(11,93)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(93, base_ring=CyclotomicField(30))
chi = DirichletCharacter(H, H._module([15, 23]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("93.11");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 93 = 3 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 93.p (of order \(30\), degree \(8\), 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: | \(0.742608738798\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{15})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{30}]$ |
Embedding invariants
Embedding label | 44.1 | ||
Root | \(-0.978148 + 0.207912i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 93.44 |
Dual form | 93.2.p.a.74.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/93\mathbb{Z}\right)^\times\).
\(n\) | \(32\) | \(34\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{11}{30}\right)\) |
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 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(3\) | 0.704489 | + | 1.58231i | 0.406737 | + | 0.913545i | ||||
\(4\) | 0.618034 | − | 1.90211i | 0.309017 | − | 0.951057i | ||||
\(5\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.802903 | + | 0.891714i | 0.303469 | + | 0.337036i | 0.875520 | − | 0.483181i | \(-0.160519\pi\) |
−0.572051 | + | 0.820218i | \(0.693852\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.00739 | + | 2.22943i | −0.669131 | + | 0.743145i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | −0.207912 | − | 0.978148i | \(-0.566667\pi\) | ||||
0.207912 | + | 0.978148i | \(0.433333\pi\) | |||||||
\(12\) | 3.44512 | − | 0.362097i | 0.994522 | − | 0.104528i | ||||
\(13\) | −3.13233 | − | 0.329221i | −0.868752 | − | 0.0913095i | −0.340345 | − | 0.940301i | \(-0.610544\pi\) |
−0.528407 | + | 0.848991i | \(0.677210\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.23607 | − | 2.35114i | −0.809017 | − | 0.587785i | ||||
\(17\) | 0 | 0 | 0.207912 | − | 0.978148i | \(-0.433333\pi\) | ||||
−0.207912 | + | 0.978148i | \(0.566667\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.742670 | − | 7.06603i | −0.170380 | − | 1.62106i | −0.661485 | − | 0.749958i | \(-0.730073\pi\) |
0.491105 | − | 0.871100i | \(-0.336593\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.845330 | + | 1.89864i | −0.184466 | + | 0.414318i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.50000 | + | 4.33013i | −0.500000 | + | 0.866025i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.94183 | − | 1.60570i | −0.951057 | − | 0.309017i | ||||
\(28\) | 2.19236 | − | 0.976103i | 0.414318 | − | 0.184466i | ||||
\(29\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.67226 | + | 3.02821i | −0.839162 | + | 0.543882i | ||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.00000 | + | 5.19615i | 0.500000 | + | 0.866025i | ||||
\(37\) | 9.23998 | + | 5.33471i | 1.51904 | + | 0.877020i | 0.999749 | + | 0.0224255i | \(0.00713887\pi\) |
0.519295 | + | 0.854595i | \(0.326194\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.68576 | − | 5.18824i | −0.269938 | − | 0.830783i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | −0.913545 | − | 0.406737i | \(-0.866667\pi\) | ||||
0.913545 | + | 0.406737i | \(0.133333\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 12.6779 | − | 1.33250i | 1.93336 | − | 0.203205i | 0.942121 | − | 0.335272i | \(-0.108828\pi\) |
0.991241 | + | 0.132068i | \(0.0421616\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(48\) | 1.44045 | − | 6.77681i | 0.207912 | − | 0.978148i | ||||
\(49\) | 0.581198 | − | 5.52973i | 0.0830283 | − | 0.789962i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.56210 | + | 5.75457i | −0.355300 | + | 0.798016i | ||||
\(53\) | 0 | 0 | −0.743145 | − | 0.669131i | \(-0.766667\pi\) | ||||
0.743145 | + | 0.669131i | \(0.233333\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 10.6574 | − | 6.15307i | 1.41161 | − | 0.814994i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 0.913545 | − | 0.406737i | \(-0.133333\pi\) | ||||
−0.913545 | + | 0.406737i | \(0.866667\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 15.4557i | 1.97890i | 0.144866 | + | 0.989451i | \(0.453725\pi\) | ||||
−0.144866 | + | 0.989451i | \(0.546275\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.59976 | −0.453527 | ||||||||
\(64\) | −6.47214 | + | 4.70228i | −0.809017 | + | 0.587785i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.824858 | − | 1.42870i | −0.100772 | − | 0.174543i | 0.811231 | − | 0.584726i | \(-0.198798\pi\) |
−0.912003 | + | 0.410183i | \(0.865465\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 0.669131 | − | 0.743145i | \(-0.266667\pi\) | ||||
−0.669131 | + | 0.743145i | \(0.733333\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.78619 | + | 8.40335i | 0.209058 | + | 0.983538i | 0.950068 | + | 0.312044i | \(0.101014\pi\) |
−0.741010 | + | 0.671494i | \(0.765653\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −8.61281 | − | 0.905243i | −0.994522 | − | 0.104528i | ||||
\(76\) | −13.8994 | − | 2.95441i | −1.59437 | − | 0.338894i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.90376 | − | 8.95646i | 0.214189 | − | 1.00768i | −0.731307 | − | 0.682048i | \(-0.761089\pi\) |
0.945496 | − | 0.325633i | \(-0.105577\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.940756 | − | 8.95070i | −0.104528 | − | 0.994522i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | 0.406737 | − | 0.913545i | \(-0.366667\pi\) | ||||
−0.406737 | + | 0.913545i | \(0.633333\pi\) | |||||||
\(84\) | 3.08899 | + | 2.78134i | 0.337036 | + | 0.303469i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.22139 | − | 3.05748i | −0.232865 | − | 0.320511i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.08310 | − | 5.25961i | −0.838179 | − | 0.545396i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.07686 | − | 18.7027i | 0.617012 | − | 1.89897i | 0.253837 | − | 0.967247i | \(-0.418307\pi\) |
0.363176 | − | 0.931721i | \(-0.381693\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 6.69131 | + | 7.43145i | 0.669131 | + | 0.743145i | ||||
\(101\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −17.9785 | − | 8.00453i | −1.77147 | − | 0.788710i | −0.985329 | − | 0.170664i | \(-0.945409\pi\) |
−0.786142 | − | 0.618046i | \(-0.787925\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | −0.978148 | − | 0.207912i | \(-0.933333\pi\) | ||||
0.978148 | + | 0.207912i | \(0.0666667\pi\) | |||||||
\(108\) | −6.10844 | + | 8.40755i | −0.587785 | + | 0.809017i | ||||
\(109\) | 16.8921 | + | 12.2728i | 1.61797 | + | 1.17553i | 0.814152 | + | 0.580651i | \(0.197202\pi\) |
0.803819 | + | 0.594874i | \(0.202798\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.93168 | + | 18.3787i | −0.183347 | + | 1.74443i | ||||
\(112\) | −0.501703 | − | 4.77339i | −0.0474065 | − | 0.451043i | ||||
\(113\) | 0 | 0 | 0.978148 | − | 0.207912i | \(-0.0666667\pi\) | ||||
−0.978148 | + | 0.207912i | \(0.933333\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 7.02179 | − | 6.32245i | 0.649165 | − | 0.584510i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.0490 | + | 4.47410i | −0.913545 | + | 0.406737i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.87238 | + | 10.7587i | 0.257947 | + | 0.966159i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.44326 | − | 5.48764i | −0.216804 | − | 0.486950i | 0.772101 | − | 0.635500i | \(-0.219206\pi\) |
−0.988905 | + | 0.148550i | \(0.952539\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 11.0399 | + | 19.1216i | 0.972006 | + | 1.68356i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | −0.669131 | − | 0.743145i | \(-0.733333\pi\) | ||||
0.669131 | + | 0.743145i | \(0.266667\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.70459 | − | 6.33559i | 0.494651 | − | 0.549365i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | −0.994522 | − | 0.104528i | \(-0.966667\pi\) | ||||
0.994522 | + | 0.104528i | \(0.0333333\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.7643 | − | 18.9449i | 1.16747 | − | 1.60688i | 0.488918 | − | 0.872330i | \(-0.337392\pi\) |
0.678551 | − | 0.734553i | \(-0.262608\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 11.7378 | − | 2.49494i | 0.978148 | − | 0.207912i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 9.15918 | − | 2.97600i | 0.755437 | − | 0.245456i | ||||
\(148\) | 15.8578 | − | 14.2785i | 1.30351 | − | 1.17368i | ||||
\(149\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.19401 | − | 2.01256i | −0.504061 | − | 0.163779i | 0.0459384 | − | 0.998944i | \(-0.485372\pi\) |
−0.550000 | + | 0.835165i | \(0.685372\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −10.9105 | −0.873537 | ||||||||
\(157\) | −14.5748 | + | 10.5892i | −1.16319 | + | 0.845110i | −0.990179 | − | 0.139808i | \(-0.955351\pi\) |
−0.173016 | + | 0.984919i | \(0.555351\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.19381 | + | 22.1403i | 0.563462 | + | 1.73416i | 0.672476 | + | 0.740119i | \(0.265231\pi\) |
−0.109014 | + | 0.994040i | \(0.534769\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 0.994522 | − | 0.104528i | \(-0.0333333\pi\) | ||||
−0.994522 | + | 0.104528i | \(0.966667\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.01282 | − | 0.640394i | −0.231755 | − | 0.0492611i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 17.2441 | + | 12.5286i | 1.31869 | + | 0.958083i | ||||
\(172\) | 5.30081 | − | 24.9383i | 0.404183 | − | 1.90153i | ||||
\(173\) | 0 | 0 | 0.104528 | − | 0.994522i | \(-0.466667\pi\) | ||||
−0.104528 | + | 0.994522i | \(0.533333\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.86850 | + | 1.24739i | −0.443617 | + | 0.0942936i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | 0.743145 | − | 0.669131i | \(-0.233333\pi\) | ||||
−0.743145 | + | 0.669131i | \(0.766667\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.6396 | + | 8.45219i | −1.08815 | + | 0.628246i | −0.933085 | − | 0.359657i | \(-0.882894\pi\) |
−0.155070 | + | 0.987903i | \(0.549560\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −24.4557 | + | 10.8884i | −1.80782 | + | 0.804892i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.53599 | − | 5.69593i | −0.184466 | − | 0.414318i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(192\) | −12.0000 | − | 6.92820i | −0.866025 | − | 0.500000i | ||||
\(193\) | −2.54639 | − | 2.82805i | −0.183293 | − | 0.203568i | 0.644495 | − | 0.764609i | \(-0.277068\pi\) |
−0.827788 | + | 0.561041i | \(0.810401\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −10.1590 | − | 4.52307i | −0.725641 | − | 0.323076i | ||||
\(197\) | 0 | 0 | −0.207912 | − | 0.978148i | \(-0.566667\pi\) | ||||
0.207912 | + | 0.978148i | \(0.433333\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −19.1550 | − | 2.01327i | −1.35786 | − | 0.142717i | −0.602549 | − | 0.798082i | \(-0.705848\pi\) |
−0.755312 | + | 0.655365i | \(0.772515\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.67953 | − | 2.31168i | 0.118465 | − | 0.163053i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 9.36239 | + | 8.42993i | 0.649165 | + | 0.584510i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.2398 | − | 21.1999i | 0.842621 | − | 1.45946i | −0.0450495 | − | 0.998985i | \(-0.514345\pi\) |
0.887671 | − | 0.460478i | \(-0.152322\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.45166 | − | 1.73496i | −0.437967 | − | 0.117777i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −12.0383 | + | 8.74637i | −0.813476 | + | 0.591025i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 24.0425 | + | 13.8809i | 1.61000 | + | 0.929536i | 0.989367 | + | 0.145437i | \(0.0464589\pi\) |
0.620636 | + | 0.784099i | \(0.286874\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.63525 | − | 14.2658i | −0.309017 | − | 0.951057i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | −0.913545 | − | 0.406737i | \(-0.866667\pi\) | ||||
0.913545 | + | 0.406737i | \(0.133333\pi\) | |||||||
\(228\) | −5.11718 | − | 24.0744i | −0.338894 | − | 1.59437i | ||||
\(229\) | −24.7680 | + | 2.60323i | −1.63672 | + | 0.172026i | −0.877756 | − | 0.479108i | \(-0.840960\pi\) |
−0.758963 | + | 0.651134i | \(0.774293\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 15.5131 | − | 3.29740i | 1.00768 | − | 0.214189i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | −0.743145 | − | 0.669131i | \(-0.766667\pi\) | ||||
0.743145 | + | 0.669131i | \(0.233333\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.28716 | + | 1.15897i | −0.0829136 | + | 0.0746557i | −0.709545 | − | 0.704660i | \(-0.751100\pi\) |
0.626632 | + | 0.779315i | \(0.284433\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.5000 | − | 7.79423i | 0.866025 | − | 0.500000i | ||||
\(244\) | 29.3985 | + | 9.55216i | 1.88205 | + | 0.611515i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 22.3776i | 1.42386i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | −0.406737 | − | 0.913545i | \(-0.633333\pi\) | ||||
0.406737 | + | 0.913545i | \(0.366667\pi\) | |||||||
\(252\) | −2.22477 | + | 6.84715i | −0.140148 | + | 0.431330i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4.94427 | + | 15.2169i | 0.309017 | + | 0.951057i | ||||
\(257\) | 0 | 0 | 0.669131 | − | 0.743145i | \(-0.266667\pi\) | ||||
−0.669131 | + | 0.743145i | \(0.733333\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.66178 | + | 12.5227i | 0.165395 | + | 0.778121i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3.22733 | + | 0.685990i | −0.197141 | + | 0.0419035i | ||||
\(269\) | 0 | 0 | 0.406737 | − | 0.913545i | \(-0.366667\pi\) | ||||
−0.406737 | + | 0.913545i | \(0.633333\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.21741 | − | 1.37032i | 0.256189 | − | 0.0832410i | −0.178107 | − | 0.984011i | \(-0.556997\pi\) |
0.434296 | + | 0.900770i | \(0.356997\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.27293 | − | 5.66887i | 0.198086 | − | 0.343096i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.12652 | − | 9.80881i | −0.428191 | − | 0.589354i | 0.539346 | − | 0.842084i | \(-0.318672\pi\) |
−0.967537 | + | 0.252730i | \(0.918672\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.62786 | − | 16.4953i | 0.157326 | − | 0.987547i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.22744 | + | 13.0107i | −0.251295 | + | 0.773407i | 0.743242 | + | 0.669023i | \(0.233287\pi\) |
−0.994537 | + | 0.104384i | \(0.966713\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.5303 | − | 6.91452i | −0.913545 | − | 0.406737i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 33.8744 | − | 3.56035i | 1.98575 | − | 0.208711i | ||||
\(292\) | 17.0881 | + | 1.79603i | 1.00000 | + | 0.105105i | ||||
\(293\) | 0 | 0 | −0.978148 | − | 0.207912i | \(-0.933333\pi\) | ||||
0.978148 | + | 0.207912i | \(0.0666667\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −7.04489 | + | 15.8231i | −0.406737 | + | 0.913545i | ||||
\(301\) | 11.3673 | + | 10.2352i | 0.655203 | + | 0.589947i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −14.2099 | + | 24.6123i | −0.814994 | + | 1.41161i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 30.9464 | − | 13.7782i | 1.76620 | − | 0.786365i | 0.778976 | − | 0.627054i | \(-0.215739\pi\) |
0.987228 | − | 0.159311i | \(-0.0509273\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 34.0866i | − | 1.93912i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.72096 | + | 17.3416i | 0.436415 | + | 0.980203i | 0.989158 | + | 0.146852i | \(0.0469141\pi\) |
−0.552744 | + | 0.833351i | \(0.686419\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −15.8596 | − | 9.15656i | −0.892173 | − | 0.515097i | ||||
\(317\) | 0 | 0 | −0.669131 | − | 0.743145i | \(-0.733333\pi\) | ||||
0.669131 | + | 0.743145i | \(0.266667\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −17.6067 | − | 3.74241i | −0.978148 | − | 0.207912i | ||||
\(325\) | 9.25639 | − | 12.7403i | 0.513452 | − | 0.706706i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −7.51910 | + | 35.3746i | −0.415807 | + | 1.95622i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.74937 | − | 17.4054i | 0.425944 | − | 0.956686i | −0.565329 | − | 0.824865i | \(-0.691251\pi\) |
0.991274 | − | 0.131821i | \(-0.0420824\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −30.4416 | + | 9.89109i | −1.66819 | + | 0.542028i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 7.19952 | − | 4.15665i | 0.392766 | − | 0.226764i | ||||
\(337\) | −26.6810 | − | 8.66918i | −1.45341 | − | 0.472240i | −0.527357 | − | 0.849644i | \(-0.676817\pi\) |
−0.926049 | + | 0.377403i | \(0.876817\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.1929 | − | 8.85864i | 0.658354 | − | 0.478322i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.30619 | − | 25.5638i | −0.444620 | − | 1.36840i | −0.882900 | − | 0.469562i | \(-0.844412\pi\) |
0.438279 | − | 0.898839i | \(-0.355588\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 14.9508 | + | 6.65654i | 0.798016 | + | 0.355300i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | 0.994522 | − | 0.104528i | \(-0.0333333\pi\) | ||||
−0.994522 | + | 0.104528i | \(0.966667\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 0.104528 | − | 0.994522i | \(-0.466667\pi\) | ||||
−0.104528 | + | 0.994522i | \(0.533333\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −30.7924 | + | 6.54514i | −1.62065 | + | 0.344481i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −14.1588 | − | 12.7487i | −0.743145 | − | 0.669131i | ||||
\(364\) | −7.18856 | + | 2.33570i | −0.376783 | + | 0.122424i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −19.5000 | + | 11.2583i | −1.01789 | + | 0.587680i | −0.913493 | − | 0.406855i | \(-0.866625\pi\) |
−0.104399 | + | 0.994535i | \(0.533292\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −15.0000 | + | 12.1244i | −0.777714 | + | 0.628619i | ||||
\(373\) | 30.5756 | 1.58315 | 0.791573 | − | 0.611075i | \(-0.209263\pi\) | ||||
0.791573 | + | 0.611075i | \(0.209263\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.3663 | − | 17.0660i | −0.789314 | − | 0.876622i | 0.205466 | − | 0.978664i | \(-0.434129\pi\) |
−0.994780 | + | 0.102042i | \(0.967462\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.96189 | − | 7.73196i | 0.356669 | − | 0.396121i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.207912 | − | 0.978148i | \(-0.566667\pi\) | ||||
0.207912 | + | 0.978148i | \(0.433333\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −22.4788 | + | 30.9394i | −1.14266 | + | 1.57274i | ||||
\(388\) | −31.8189 | − | 23.1178i | −1.61536 | − | 1.17363i | ||||
\(389\) | 0 | 0 | 0.207912 | − | 0.978148i | \(-0.433333\pi\) | ||||
−0.207912 | + | 0.978148i | \(0.566667\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.63038 | + | 8.02005i | −0.232392 | + | 0.402515i | −0.958512 | − | 0.285054i | \(-0.907989\pi\) |
0.726119 | + | 0.687569i | \(0.241322\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 14.0437 | + | 4.56306i | 0.703063 | + | 0.228439i | ||||
\(400\) | 18.2709 | − | 8.13473i | 0.913545 | − | 0.406737i | ||||
\(401\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 15.6320 | − | 7.94713i | 0.778685 | − | 0.395875i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 22.5000 | + | 12.9904i | 1.11255 | + | 0.642333i | 0.939490 | − | 0.342578i | \(-0.111300\pi\) |
0.173064 | + | 0.984911i | \(0.444633\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −26.3368 | + | 29.2500i | −1.29752 | + | 1.44104i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 39.6734 | + | 8.43283i | 1.94281 | + | 0.412958i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.98879 | − | 37.9508i | 0.194402 | − | 1.84961i | −0.268600 | − | 0.963252i | \(-0.586561\pi\) |
0.463002 | − | 0.886357i | \(-0.346772\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −13.7821 | + | 12.4095i | −0.666962 | + | 0.600535i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 0.913545 | − | 0.406737i | \(-0.133333\pi\) | ||||
−0.913545 | + | 0.406737i | \(0.866667\pi\) | |||||||
\(432\) | 12.2169 | + | 16.8151i | 0.587785 | + | 0.809017i | ||||
\(433\) | 2.35612i | 0.113228i | 0.998396 | + | 0.0566140i | \(0.0180304\pi\) | ||||
−0.998396 | + | 0.0566140i | \(0.981970\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 33.7842 | − | 24.5457i | 1.61797 | − | 1.17553i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14.0397 | − | 24.3174i | −0.670077 | − | 1.16061i | −0.977882 | − | 0.209157i | \(-0.932928\pi\) |
0.307805 | − | 0.951449i | \(-0.400405\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 11.1615 | + | 12.3961i | 0.531499 | + | 0.590290i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | 0.669131 | − | 0.743145i | \(-0.266667\pi\) | ||||
−0.669131 | + | 0.743145i | \(0.733333\pi\) | |||||||
\(444\) | 33.7646 | + | 15.0330i | 1.60240 | + | 0.713433i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −9.38959 | − | 1.99582i | −0.443617 | − | 0.0942936i | ||||
\(449\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.17913 | − | 11.2186i | −0.0554002 | − | 0.527098i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 28.0037 | − | 9.09896i | 1.30996 | − | 0.425632i | 0.430924 | − | 0.902388i | \(-0.358188\pi\) |
0.879035 | + | 0.476757i | \(0.158188\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 23.7231 | + | 32.6521i | 1.10251 | + | 1.51747i | 0.832018 | + | 0.554748i | \(0.187185\pi\) |
0.270489 | + | 0.962723i | \(0.412815\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(468\) | −7.68631 | − | 17.2637i | −0.355300 | − | 0.798016i | ||||
\(469\) | 0.611707 | − | 1.88264i | 0.0282460 | − | 0.0869323i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −27.0231 | − | 15.6018i | −1.24516 | − | 0.718894i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 32.4535 | + | 14.4492i | 1.48907 | + | 0.662976i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.978148 | − | 0.207912i | \(-0.933333\pi\) | ||||
0.978148 | + | 0.207912i | \(0.0666667\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −27.1864 | − | 19.7521i | −1.23959 | − | 0.900616i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.29963 | + | 21.8795i | 0.104528 | + | 0.994522i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −15.6514 | − | 14.0926i | −0.709232 | − | 0.638596i | 0.233418 | − | 0.972376i | \(-0.425009\pi\) |
−0.942651 | + | 0.333781i | \(0.891675\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −29.9647 | + | 26.9804i | −1.35505 | + | 1.22009i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 22.2395 | + | 1.18565i | 0.998582 | + | 0.0532375i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.2971 | + | 36.6039i | 0.729560 | + | 1.63862i | 0.768882 | + | 0.639391i | \(0.220813\pi\) |
−0.0393222 | + | 0.999227i | \(0.512520\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | −0.669131 | − | 0.743145i | \(-0.733333\pi\) | ||||
0.669131 | + | 0.743145i | \(0.266667\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.10920 | − | 5.21835i | −0.0492611 | − | 0.231755i | ||||
\(508\) | −11.9481 | + | 1.25580i | −0.530113 | + | 0.0557171i | ||||
\(509\) | 0 | 0 | −0.994522 | − | 0.104528i | \(-0.966667\pi\) | ||||
0.994522 | + | 0.104528i | \(0.0333333\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.05926 | + | 8.33985i | −0.268046 | + | 0.368933i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −7.67577 | + | 36.1117i | −0.338894 | + | 1.59437i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 43.1945 | − | 9.18127i | 1.90153 | − | 0.404183i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −30.1774 | − | 9.80525i | −1.31957 | − | 0.428753i | −0.437221 | − | 0.899354i | \(-0.644037\pi\) |
−0.882346 | + | 0.470601i | \(0.844037\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −6.10804 | − | 8.40699i | −0.266577 | − | 0.366911i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 18.6074 | − | 13.5191i | 0.809017 | − | 0.587785i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −8.52538 | − | 14.7664i | −0.369622 | − | 0.640204i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 45.4205 | + | 9.65443i | 1.95278 | + | 0.415076i | 0.988847 | + | 0.148933i | \(0.0475840\pi\) |
0.963934 | + | 0.266143i | \(0.0857493\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −23.6874 | − | 17.2099i | −1.01652 | − | 0.738548i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −43.8069 | + | 9.31143i | −1.87305 | + | 0.398128i | −0.996529 | − | 0.0832432i | \(-0.973472\pi\) |
−0.876517 | + | 0.481371i | \(0.840139\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −34.4575 | − | 31.0257i | −1.47061 | − | 1.32414i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.51514 | − | 5.49357i | 0.404625 | − | 0.233610i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −27.5285 | − | 37.8897i | −1.16747 | − | 1.60688i | ||||
\(557\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −40.1501 | −1.69817 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 7.22613 | − | 8.02543i | 0.303469 | − | 0.337036i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | −0.207912 | − | 0.978148i | \(-0.566667\pi\) | ||||
0.207912 | + | 0.978148i | \(0.433333\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 36.1738 | + | 3.80202i | 1.51383 | + | 0.159110i | 0.824716 | − | 0.565547i | \(-0.191335\pi\) |
0.689111 | + | 0.724656i | \(0.258001\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 2.50868 | − | 23.8685i | 0.104528 | − | 0.994522i | ||||
\(577\) | 4.74135 | + | 45.1109i | 0.197385 | + | 1.87799i | 0.426353 | + | 0.904557i | \(0.359798\pi\) |
−0.228968 | + | 0.973434i | \(0.573535\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.68095 | − | 6.02151i | 0.111416 | − | 0.250245i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(588\) | − | 19.2611i | − | 0.794313i | ||||||
\(589\) | 24.8673 | + | 30.7654i | 1.02464 | + | 1.26766i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −17.3586 | − | 38.9880i | −0.713433 | − | 1.60240i | ||||
\(593\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −10.3089 | − | 31.7274i | −0.421914 | − | 1.29852i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | −0.913545 | − | 0.406737i | \(-0.866667\pi\) | ||||
0.913545 | + | 0.406737i | \(0.133333\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −48.6447 | + | 5.11276i | −1.98426 | + | 0.208554i | −0.984882 | + | 0.173228i | \(0.944580\pi\) |
−0.999376 | + | 0.0353259i | \(0.988753\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.84100 | + | 1.02899i | 0.197141 | + | 0.0419035i | ||||
\(604\) | −7.65622 | + | 10.5379i | −0.311527 | + | 0.428780i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.02358 | + | 28.7674i | −0.122723 | + | 1.16763i | 0.743766 | + | 0.668440i | \(0.233038\pi\) |
−0.866490 | + | 0.499195i | \(0.833629\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −36.7981 | + | 33.1332i | −1.48626 | + | 1.33824i | −0.739054 | + | 0.673646i | \(0.764727\pi\) |
−0.747208 | + | 0.664590i | \(0.768606\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 0.913545 | − | 0.406737i | \(-0.133333\pi\) | ||||
−0.913545 | + | 0.406737i | \(0.866667\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 30.6193i | − | 1.23069i | −0.788257 | − | 0.615346i | \(-0.789016\pi\) | ||
0.788257 | − | 0.615346i | \(-0.210984\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −6.74305 | + | 20.7530i | −0.269938 | + | 0.830783i | ||||
\(625\) | −12.5000 | − | 21.6506i | −0.500000 | − | 0.866025i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 11.1341 | + | 34.2674i | 0.444301 | + | 1.36742i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.14244 | + | 33.6025i | 0.284336 | + | 1.33770i | 0.855901 | + | 0.517139i | \(0.173003\pi\) |
−0.571566 | + | 0.820556i | \(0.693664\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 42.1676 | + | 4.43199i | 1.67601 | + | 0.176156i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.64101 | + | 17.1296i | −0.144262 | + | 0.678699i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | 0.406737 | − | 0.913545i | \(-0.366667\pi\) | ||||
−0.406737 | + | 0.913545i | \(0.633333\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.43051 | − | 2.73924i | 0.332467 | − | 0.108025i | −0.138027 | − | 0.990429i | \(-0.544076\pi\) |
0.470493 | + | 0.882403i | \(0.344076\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.79988 | − | 11.4308i | −0.0705429 | − | 0.448007i | ||||
\(652\) | 46.5593 | 1.82340 | ||||||||
\(653\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −22.3203 | − | 12.8866i | −0.870798 | − | 0.502756i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 27.8441 | + | 12.3970i | 1.08301 | + | 0.482187i | 0.869085 | − | 0.494663i | \(-0.164708\pi\) |
0.213925 | + | 0.976850i | \(0.431375\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5.02625 | + | 47.8215i | −0.194326 | + | 1.84889i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 30.1712 | + | 27.1663i | 1.16301 | + | 1.04718i | 0.998146 | + | 0.0608665i | \(0.0193864\pi\) |
0.164868 | + | 0.986316i | \(0.447280\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 19.3075 | − | 17.3845i | 0.743145 | − | 0.669131i | ||||
\(676\) | −3.08013 | + | 5.33493i | −0.118466 | + | 0.205190i | ||||
\(677\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 21.5566 | − | 9.59760i | 0.827265 | − | 0.368322i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(684\) | 34.4882 | − | 25.0571i | 1.31869 | − | 0.958083i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −21.5679 | − | 37.3567i | −0.822867 | − | 1.42525i | ||||
\(688\) | −44.1595 | − | 25.4955i | −1.68356 | − | 0.972006i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 34.7215 | − | 38.5621i | 1.32087 | − | 1.46697i | 0.541012 | − | 0.841015i | \(-0.318041\pi\) |
0.779857 | − | 0.625958i | \(-0.215292\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.25426 | + | 11.9335i | −0.0474065 | + | 0.451043i | ||||
\(701\) | 0 | 0 | −0.104528 | − | 0.994522i | \(-0.533333\pi\) | ||||
0.104528 | + | 0.994522i | \(0.466667\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 30.8330 | − | 69.2519i | 1.16289 | − | 2.61189i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 41.1820 | + | 13.3808i | 1.54662 | + | 0.502528i | 0.953194 | − | 0.302360i | \(-0.0977745\pi\) |
0.593427 | + | 0.804888i | \(0.297775\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 16.1463 | + | 22.2234i | 0.605532 | + | 0.833444i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.29722 | − | 22.4585i | −0.271763 | − | 0.836399i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.74064 | − | 1.22021i | −0.101925 | − | 0.0453801i | ||||
\(724\) | 7.02924 | + | 33.0700i | 0.261240 | + | 1.22904i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.89074 | − | 1.03956i | −0.181387 | − | 0.0385551i | 0.116322 | − | 0.993212i | \(-0.462889\pi\) |
−0.297710 | + | 0.954656i | \(0.596223\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 21.8435 | + | 15.8702i | 0.809017 | + | 0.587785i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 5.59647 | + | 53.2469i | 0.206852 | + | 1.96806i | ||||
\(733\) | −6.84703 | + | 1.45538i | −0.252901 | + | 0.0537558i | −0.332618 | − | 0.943062i | \(-0.607932\pi\) |
0.0797166 | + | 0.996818i | \(0.474598\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −40.4082 | + | 23.3297i | −1.48644 | + | 0.858196i | −0.999881 | − | 0.0154516i | \(-0.995081\pi\) |
−0.486559 | + | 0.873648i | \(0.661748\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −35.4083 | + | 15.7648i | −1.30076 | + | 0.579134i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.36044 | − | 8.17459i | −0.268586 | − | 0.298295i | 0.593731 | − | 0.804664i | \(-0.297654\pi\) |
−0.862317 | + | 0.506368i | \(0.830988\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −12.4016 | + | 1.30346i | −0.451043 | + | 0.0474065i | ||||
\(757\) | 9.68758 | + | 1.01821i | 0.352101 | + | 0.0370073i | 0.278928 | − | 0.960312i | \(-0.410021\pi\) |
0.0731729 | + | 0.997319i | \(0.476688\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.207912 | − | 0.978148i | \(-0.433333\pi\) | ||||
−0.207912 | + | 0.978148i | \(0.566667\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.61887 | + | 24.9169i | 0.0948093 | + | 0.902051i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −20.5946 | + | 18.5435i | −0.743145 | + | 0.669131i | ||||
\(769\) | 15.4802 | − | 26.8124i | 0.558229 | − | 0.966881i | −0.439415 | − | 0.898284i | \(-0.644814\pi\) |
0.997644 | − | 0.0685971i | \(-0.0218523\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −6.95304 | + | 3.09569i | −0.250245 | + | 0.111416i | ||||
\(773\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.43187 | − | 27.8020i | −0.0514344 | − | 0.998676i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −17.9395 | + | 13.0338i | −0.643577 | + | 0.467586i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −14.8820 | + | 16.5281i | −0.531499 | + | 0.590290i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −46.5092 | + | 4.88831i | −1.65787 | + | 0.174250i | −0.886690 | − | 0.462364i | \(-0.847001\pi\) |
−0.771183 | + | 0.636613i | \(0.780335\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.08835 | − | 48.4124i | 0.180693 | − | 1.71918i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −15.6679 | + | 35.1907i | −0.555334 | + | 1.24730i | ||||
\(797\) | 0 | 0 | −0.743145 | − | 0.669131i | \(-0.766667\pi\) | ||||
0.743145 | + | 0.669131i | \(0.233333\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −3.35906 | − | 4.62336i | −0.118465 | − | 0.163053i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | −0.406737 | − | 0.913545i | \(-0.633333\pi\) | ||||
0.406737 | + | 0.913545i | \(0.366667\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9.50000 | − | 16.4545i | −0.333590 | − | 0.577795i | 0.649623 | − | 0.760257i | \(-0.274927\pi\) |
−0.983213 | + | 0.182462i | \(0.941593\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5.13938 | + | 5.70786i | 0.180246 | + | 0.200183i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −18.8310 | − | 88.5929i | −0.658813 | − | 3.09947i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 11.2756 | + | 1.18512i | 0.394003 | + | 0.0414113i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.27605 | + | 10.7080i | −0.0793382 | + | 0.373257i | −0.999847 | − | 0.0174637i | \(-0.994441\pi\) |
0.920509 | + | 0.390721i | \(0.127774\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | 0.406737 | − | 0.913545i | \(-0.366667\pi\) | ||||
−0.406737 | + | 0.913545i | \(0.633333\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −23.1298 | + | 7.51532i | −0.803330 | + | 0.261018i | −0.681770 | − | 0.731566i | \(-0.738790\pi\) |
−0.121560 | + | 0.992584i | \(0.538790\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 10.5000 | − | 18.1865i | 0.364241 | − | 0.630884i | ||||
\(832\) | 21.8210 | − | 12.5983i | 0.756505 | − | 0.436769i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 27.9519 | − | 7.46265i | 0.966159 | − | 0.257947i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.96149 | + | 27.5806i | −0.309017 | + | 0.951057i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −32.7601 | − | 36.3837i | −1.12765 | − | 1.25238i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −12.0580 | − | 5.36857i | −0.414318 | − | 0.184466i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −23.5651 | + | 2.47680i | −0.808754 | + | 0.0850034i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18.6074 | + | 13.5191i | 0.637105 | + | 0.462884i | 0.858854 | − | 0.512220i | \(-0.171177\pi\) |
−0.221749 | + | 0.975104i | \(0.571177\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | 0.978148 | − | 0.207912i | \(-0.0666667\pi\) | ||||
−0.978148 | + | 0.207912i | \(0.933333\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −42.7336 | − | 38.4775i | −1.45805 | − | 1.31284i | −0.858840 | − | 0.512244i | \(-0.828814\pi\) |
−0.599211 | − | 0.800591i | \(-0.704519\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 29.4449i | − | 1.00000i | ||||||
\(868\) | −7.28744 | + | 11.1995i | −0.247352 | + | 0.380137i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.11337 | + | 4.74671i | 0.0716088 | + | 0.160836i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 29.4977 | + | 51.0915i | 0.998346 | + | 1.72919i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 9.19647 | + | 28.3038i | 0.310720 | + | 0.956298i | ||||
\(877\) | 16.7283 | − | 18.5786i | 0.564873 | − | 0.627355i | −0.391262 | − | 0.920279i | \(-0.627962\pi\) |
0.956136 | + | 0.292924i | \(0.0946282\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | −0.994522 | − | 0.104528i | \(-0.966667\pi\) | ||||
0.994522 | + | 0.104528i | \(0.0333333\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.05832 | + | 1.45665i | −0.0356153 | + | 0.0490203i | −0.826453 | − | 0.563005i | \(-0.809645\pi\) |
0.790838 | + | 0.612026i | \(0.209645\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.104528 | − | 0.994522i | \(-0.533333\pi\) | ||||
0.104528 | + | 0.994522i | \(0.466667\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.93171 | − | 6.58473i | 0.0983265 | − | 0.220845i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 41.2622 | − | 37.1526i | 1.38156 | − | 1.24396i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −30.0000 | −1.00000 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8.18707 | + | 25.1972i | −0.272449 | + | 0.838510i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 17.0546 | + | 52.4887i | 0.566289 | + | 1.74286i | 0.664089 | + | 0.747653i | \(0.268820\pi\) |
−0.0977997 | + | 0.995206i | \(0.531180\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 0.994522 | − | 0.104528i | \(-0.0333333\pi\) | ||||
−0.994522 | + | 0.104528i | \(0.966667\pi\) | |||||||
\(912\) | −48.9549 | − | 5.14537i | −1.62106 | − | 0.170380i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −10.3559 | + | 48.7205i | −0.342167 | + | 1.60977i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 56.0926 | − | 11.9228i | 1.85032 | − | 0.393298i | 0.857661 | − | 0.514216i | \(-0.171917\pi\) |
0.992663 | + | 0.120917i | \(0.0385836\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 43.6028 | + | 39.2601i | 1.43676 | + | 1.29366i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −46.1999 | + | 26.6735i | −1.51904 | + | 0.877020i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 53.9354 | − | 24.0136i | 1.77147 | − | 0.788710i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −39.5049 | −1.29472 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 38.7023 | + | 42.9833i | 1.26435 | + | 1.40420i | 0.875727 | + | 0.482807i | \(0.160383\pi\) |
0.388623 | + | 0.921397i | \(0.372951\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −22.0004 | + | 24.4339i | −0.717954 | + | 0.797369i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | −0.207912 | − | 0.978148i | \(-0.566667\pi\) | ||||
0.207912 | + | 0.978148i | \(0.433333\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | 0.207912 | − | 0.978148i | \(-0.433333\pi\) | ||||
−0.207912 | + | 0.978148i | \(0.566667\pi\) | |||||||
\(948\) | 3.31556 | − | 31.5455i | 0.107685 | − | 1.02455i | ||||
\(949\) | −2.82837 | − | 26.9101i | −0.0918127 | − | 0.873540i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.6599 | − | 28.2971i | 0.408385 | − | 0.912810i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.40898 | + | 3.16461i | 0.0453801 | + | 0.101925i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 31.0791 | + | 17.9435i | 0.999437 | + | 0.577025i | 0.908082 | − | 0.418793i | \(-0.137547\pi\) |
0.0913556 | + | 0.995818i | \(0.470880\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | −0.913545 | − | 0.406737i | \(-0.866667\pi\) | ||||
0.913545 | + | 0.406737i | \(0.133333\pi\) | |||||||
\(972\) | −6.48205 | − | 30.4956i | −0.207912 | − | 0.978148i | ||||
\(973\) | 27.9448 | − | 2.93711i | 0.895869 | − | 0.0941596i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 26.6801 | + | 5.67104i | 0.854448 | + | 0.181619i | ||||
\(976\) | 36.3386 | − | 50.0158i | 1.16317 | − | 1.60097i | ||||
\(977\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −61.2706 | + | 13.0235i | −1.95622 | + | 0.415807i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | −0.743145 | − | 0.669131i | \(-0.766667\pi\) | ||||
0.743145 | + | 0.669131i | \(0.233333\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 42.5648 | + | 13.8301i | 1.35417 | + | 0.439995i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.56520i | 0.0814862i | 0.999170 | + | 0.0407431i | \(0.0129725\pi\) | ||||
−0.999170 | + | 0.0407431i | \(0.987027\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 33.0000 | 1.04722 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 14.2802 | + | 24.7341i | 0.452260 | + | 0.783337i | 0.998526 | − | 0.0542745i | \(-0.0172846\pi\) |
−0.546266 | + | 0.837612i | \(0.683951\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −37.0965 | − | 41.1999i | −1.17368 | − | 1.30351i |
(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 | 93.2.p.a.44.1 | ✓ | 8 | |
3.2 | odd | 2 | CM | 93.2.p.a.44.1 | ✓ | 8 | |
31.12 | odd | 30 | inner | 93.2.p.a.74.1 | yes | 8 | |
93.74 | even | 30 | inner | 93.2.p.a.74.1 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
93.2.p.a.44.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
93.2.p.a.44.1 | ✓ | 8 | 3.2 | odd | 2 | CM | |
93.2.p.a.74.1 | yes | 8 | 31.12 | odd | 30 | inner | |
93.2.p.a.74.1 | yes | 8 | 93.74 | even | 30 | inner |