Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [784,2,Mod(165,784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(784, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 3, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("784.165");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.x (of order \(12\), degree \(4\), 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: | \(6.26027151847\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 112) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 373.1 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 784.373 |
Dual form | 784.2.x.d.557.1 |
$q$-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 \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(687\) | \(689\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.366025 | − | 1.36603i | −0.258819 | − | 0.965926i | ||||
\(3\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(4\) | −1.73205 | + | 1.00000i | −0.866025 | + | 0.500000i | ||||
\(5\) | −2.73205 | + | 0.732051i | −1.22181 | + | 0.327383i | −0.811386 | − | 0.584511i | \(-0.801286\pi\) |
−0.410425 | + | 0.911894i | \(0.634620\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.00000 | + | 2.00000i | 0.707107 | + | 0.707107i | ||||
\(9\) | −2.59808 | − | 1.50000i | −0.866025 | − | 0.500000i | ||||
\(10\) | 2.00000 | + | 3.46410i | 0.632456 | + | 1.09545i | ||||
\(11\) | 0.366025 | − | 1.36603i | 0.110361 | − | 0.411872i | −0.888537 | − | 0.458804i | \(-0.848278\pi\) |
0.998898 | + | 0.0469323i | \(0.0149445\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.00000 | − | 3.46410i | 0.500000 | − | 0.866025i | ||||
\(17\) | 1.00000 | + | 1.73205i | 0.242536 | + | 0.420084i | 0.961436 | − | 0.275029i | \(-0.0886875\pi\) |
−0.718900 | + | 0.695113i | \(0.755354\pi\) | |||||||
\(18\) | −1.09808 | + | 4.09808i | −0.258819 | + | 0.965926i | ||||
\(19\) | 0.732051 | + | 2.73205i | 0.167944 | + | 0.626775i | 0.997646 | + | 0.0685694i | \(0.0218435\pi\) |
−0.829702 | + | 0.558206i | \(0.811490\pi\) | |||||||
\(20\) | 4.00000 | − | 4.00000i | 0.894427 | − | 0.894427i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.00000 | −0.426401 | ||||||||
\(23\) | 5.19615 | + | 3.00000i | 1.08347 | + | 0.625543i | 0.931831 | − | 0.362892i | \(-0.118211\pi\) |
0.151642 | + | 0.988436i | \(0.451544\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.59808 | − | 1.50000i | 0.519615 | − | 0.300000i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.00000 | − | 7.00000i | 1.29987 | − | 1.29987i | 0.371391 | − | 0.928477i | \(-0.378881\pi\) |
0.928477 | − | 0.371391i | \(-0.121119\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.00000 | + | 6.92820i | 0.718421 | + | 1.24434i | 0.961625 | + | 0.274367i | \(0.0884683\pi\) |
−0.243204 | + | 0.969975i | \(0.578198\pi\) | |||||||
\(32\) | −5.46410 | − | 1.46410i | −0.965926 | − | 0.258819i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.00000 | − | 2.00000i | 0.342997 | − | 0.342997i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 6.00000 | 1.00000 | ||||||||
\(37\) | 6.83013 | − | 1.83013i | 1.12287 | − | 0.300871i | 0.350823 | − | 0.936442i | \(-0.385902\pi\) |
0.772043 | + | 0.635571i | \(0.219235\pi\) | |||||||
\(38\) | 3.46410 | − | 2.00000i | 0.561951 | − | 0.324443i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −6.92820 | − | 4.00000i | −1.09545 | − | 0.632456i | ||||
\(41\) | 10.0000i | 1.56174i | 0.624695 | + | 0.780869i | \(0.285223\pi\) | ||||
−0.624695 | + | 0.780869i | \(0.714777\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.00000 | − | 1.00000i | −0.152499 | − | 0.152499i | 0.626734 | − | 0.779233i | \(-0.284391\pi\) |
−0.779233 | + | 0.626734i | \(0.784391\pi\) | |||||||
\(44\) | 0.732051 | + | 2.73205i | 0.110361 | + | 0.411872i | ||||
\(45\) | 8.19615 | + | 2.19615i | 1.22181 | + | 0.327383i | ||||
\(46\) | 2.19615 | − | 8.19615i | 0.323805 | − | 1.20846i | ||||
\(47\) | 6.00000 | − | 10.3923i | 0.875190 | − | 1.51587i | 0.0186297 | − | 0.999826i | \(-0.494070\pi\) |
0.856560 | − | 0.516047i | \(-0.172597\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −3.00000 | − | 3.00000i | −0.424264 | − | 0.424264i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.366025 | + | 1.36603i | −0.0502775 | + | 0.187638i | −0.986498 | − | 0.163776i | \(-0.947632\pi\) |
0.936220 | + | 0.351414i | \(0.114299\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.00000i | 0.539360i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −12.1244 | − | 7.00000i | −1.59201 | − | 0.919145i | ||||
\(59\) | 2.92820 | − | 10.9282i | 0.381220 | − | 1.42273i | −0.462821 | − | 0.886452i | \(-0.653163\pi\) |
0.844041 | − | 0.536279i | \(-0.180171\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.19615 | + | 8.19615i | 0.281189 | + | 1.04941i | 0.951580 | + | 0.307402i | \(0.0994596\pi\) |
−0.670391 | + | 0.742008i | \(0.733874\pi\) | |||||||
\(62\) | 8.00000 | − | 8.00000i | 1.01600 | − | 1.01600i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000i | 1.00000i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.09808 | − | 1.09808i | −0.500660 | − | 0.134151i | −0.000353546 | − | 1.00000i | \(-0.500113\pi\) |
−0.500306 | + | 0.865849i | \(0.666779\pi\) | |||||||
\(68\) | −3.46410 | − | 2.00000i | −0.420084 | − | 0.242536i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | −2.19615 | − | 8.19615i | −0.258819 | − | 0.965926i | ||||
\(73\) | −5.19615 | + | 3.00000i | −0.608164 | + | 0.351123i | −0.772246 | − | 0.635323i | \(-0.780867\pi\) |
0.164083 | + | 0.986447i | \(0.447534\pi\) | |||||||
\(74\) | −5.00000 | − | 8.66025i | −0.581238 | − | 1.00673i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.00000 | − | 4.00000i | −0.458831 | − | 0.458831i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.00000 | + | 8.66025i | −0.562544 | + | 0.974355i | 0.434730 | + | 0.900561i | \(0.356844\pi\) |
−0.997274 | + | 0.0737937i | \(0.976489\pi\) | |||||||
\(80\) | −2.92820 | + | 10.9282i | −0.327383 | + | 1.22181i | ||||
\(81\) | 4.50000 | + | 7.79423i | 0.500000 | + | 0.866025i | ||||
\(82\) | 13.6603 | − | 3.66025i | 1.50852 | − | 0.404207i | ||||
\(83\) | −10.0000 | + | 10.0000i | −1.09764 | + | 1.09764i | −0.102957 | + | 0.994686i | \(0.532830\pi\) |
−0.994686 | + | 0.102957i | \(0.967170\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.00000 | − | 4.00000i | −0.433861 | − | 0.433861i | ||||
\(86\) | −1.00000 | + | 1.73205i | −0.107833 | + | 0.186772i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.46410 | − | 2.00000i | 0.369274 | − | 0.213201i | ||||
\(89\) | 12.1244 | + | 7.00000i | 1.28518 | + | 0.741999i | 0.977790 | − | 0.209585i | \(-0.0672115\pi\) |
0.307389 | + | 0.951584i | \(0.400545\pi\) | |||||||
\(90\) | − | 12.0000i | − | 1.26491i | ||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −12.0000 | −1.25109 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −16.3923 | − | 4.39230i | −1.69074 | − | 0.453032i | ||||
\(95\) | −4.00000 | − | 6.92820i | −0.410391 | − | 0.710819i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.00000 | −0.203069 | −0.101535 | − | 0.994832i | \(-0.532375\pi\) | ||||
−0.101535 | + | 0.994832i | \(0.532375\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.00000 | + | 3.00000i | −0.301511 | + | 0.301511i | ||||
\(100\) | −3.00000 | + | 5.19615i | −0.300000 | + | 0.519615i | ||||
\(101\) | 2.19615 | − | 8.19615i | 0.218525 | − | 0.815548i | −0.766370 | − | 0.642399i | \(-0.777939\pi\) |
0.984896 | − | 0.173149i | \(-0.0553941\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.46410 | − | 2.00000i | −0.341328 | − | 0.197066i | 0.319531 | − | 0.947576i | \(-0.396475\pi\) |
−0.660859 | + | 0.750510i | \(0.729808\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.00000 | 0.194257 | ||||||||
\(107\) | −6.83013 | + | 1.83013i | −0.660293 | + | 0.176925i | −0.573378 | − | 0.819291i | \(-0.694367\pi\) |
−0.0869149 | + | 0.996216i | \(0.527701\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.09808 | + | 1.09808i | 0.392525 | + | 0.105177i | 0.449682 | − | 0.893189i | \(-0.351537\pi\) |
−0.0571579 | + | 0.998365i | \(0.518204\pi\) | |||||||
\(110\) | 5.46410 | − | 1.46410i | 0.520982 | − | 0.139597i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.00000 | 0.376288 | 0.188144 | − | 0.982141i | \(-0.439753\pi\) | ||||
0.188144 | + | 0.982141i | \(0.439753\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −16.3923 | − | 4.39230i | −1.52859 | − | 0.409585i | ||||
\(116\) | −5.12436 | + | 19.1244i | −0.475784 | + | 1.77565i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −16.0000 | −1.47292 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.79423 | + | 4.50000i | 0.708566 | + | 0.409091i | ||||
\(122\) | 10.3923 | − | 6.00000i | 0.940875 | − | 0.543214i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −13.8564 | − | 8.00000i | −1.24434 | − | 0.718421i | ||||
\(125\) | 4.00000 | − | 4.00000i | 0.357771 | − | 0.357771i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.00000 | 0.709885 | 0.354943 | − | 0.934888i | \(-0.384500\pi\) | ||||
0.354943 | + | 0.934888i | \(0.384500\pi\) | |||||||
\(128\) | 10.9282 | − | 2.92820i | 0.965926 | − | 0.258819i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.12436 | − | 19.1244i | −0.447717 | − | 1.67090i | −0.708661 | − | 0.705549i | \(-0.750701\pi\) |
0.260944 | − | 0.965354i | \(-0.415966\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 6.00000i | 0.518321i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.46410 | + | 5.46410i | −0.125546 | + | 0.468543i | ||||
\(137\) | 10.3923 | − | 6.00000i | 0.887875 | − | 0.512615i | 0.0146279 | − | 0.999893i | \(-0.495344\pi\) |
0.873247 | + | 0.487278i | \(0.162010\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.00000 | − | 2.00000i | −0.169638 | − | 0.169638i | 0.617182 | − | 0.786820i | \(-0.288274\pi\) |
−0.786820 | + | 0.617182i | \(0.788274\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −10.3923 | + | 6.00000i | −0.866025 | + | 0.500000i | ||||
\(145\) | −14.0000 | + | 24.2487i | −1.16264 | + | 2.01375i | ||||
\(146\) | 6.00000 | + | 6.00000i | 0.496564 | + | 0.496564i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −10.0000 | + | 10.0000i | −0.821995 | + | 0.821995i | ||||
\(149\) | −4.09808 | + | 1.09808i | −0.335727 | + | 0.0899579i | −0.422744 | − | 0.906249i | \(-0.638933\pi\) |
0.0870170 | + | 0.996207i | \(0.472267\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.66025 | − | 5.00000i | 0.704761 | − | 0.406894i | −0.104357 | − | 0.994540i | \(-0.533278\pi\) |
0.809118 | + | 0.587646i | \(0.199945\pi\) | |||||||
\(152\) | −4.00000 | + | 6.92820i | −0.324443 | + | 0.561951i | ||||
\(153\) | − | 6.00000i | − | 0.485071i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −16.0000 | − | 16.0000i | −1.28515 | − | 1.28515i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.3923 | + | 4.39230i | 1.30825 | + | 0.350544i | 0.844563 | − | 0.535456i | \(-0.179860\pi\) |
0.463685 | + | 0.886000i | \(0.346527\pi\) | |||||||
\(158\) | 13.6603 | + | 3.66025i | 1.08675 | + | 0.291194i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 16.0000 | 1.26491 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 9.00000 | − | 9.00000i | 0.707107 | − | 0.707107i | ||||
\(163\) | 5.49038 | + | 20.4904i | 0.430040 | + | 1.60493i | 0.752665 | + | 0.658404i | \(0.228768\pi\) |
−0.322625 | + | 0.946527i | \(0.604565\pi\) | |||||||
\(164\) | −10.0000 | − | 17.3205i | −0.780869 | − | 1.35250i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 17.3205 | + | 10.0000i | 1.34433 | + | 0.776151i | ||||
\(167\) | 12.0000i | 0.928588i | 0.885681 | + | 0.464294i | \(0.153692\pi\) | ||||
−0.885681 | + | 0.464294i | \(0.846308\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 13.0000i | 1.00000i | ||||||||
\(170\) | −4.00000 | + | 6.92820i | −0.306786 | + | 0.531369i | ||||
\(171\) | 2.19615 | − | 8.19615i | 0.167944 | − | 0.626775i | ||||
\(172\) | 2.73205 | + | 0.732051i | 0.208317 | + | 0.0558184i | ||||
\(173\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.00000 | − | 4.00000i | −0.301511 | − | 0.301511i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 5.12436 | − | 19.1244i | 0.384087 | − | 1.43343i | ||||
\(179\) | 4.09808 | + | 1.09808i | 0.306305 | + | 0.0820741i | 0.408697 | − | 0.912670i | \(-0.365983\pi\) |
−0.102393 | + | 0.994744i | \(0.532650\pi\) | |||||||
\(180\) | −16.3923 | + | 4.39230i | −1.22181 | + | 0.327383i | ||||
\(181\) | −4.00000 | − | 4.00000i | −0.297318 | − | 0.297318i | 0.542645 | − | 0.839962i | \(-0.317423\pi\) |
−0.839962 | + | 0.542645i | \(0.817423\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 4.39230 | + | 16.3923i | 0.323805 | + | 1.20846i | ||||
\(185\) | −17.3205 | + | 10.0000i | −1.27343 | + | 0.735215i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.73205 | − | 0.732051i | 0.199787 | − | 0.0535329i | ||||
\(188\) | 24.0000i | 1.75038i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −8.00000 | + | 8.00000i | −0.580381 | + | 0.580381i | ||||
\(191\) | 9.00000 | − | 15.5885i | 0.651217 | − | 1.12794i | −0.331611 | − | 0.943416i | \(-0.607592\pi\) |
0.982828 | − | 0.184525i | \(-0.0590746\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.00000 | + | 13.8564i | 0.575853 | + | 0.997406i | 0.995948 | + | 0.0899262i | \(0.0286631\pi\) |
−0.420096 | + | 0.907480i | \(0.638004\pi\) | |||||||
\(194\) | 0.732051 | + | 2.73205i | 0.0525582 | + | 0.196150i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.00000 | + | 5.00000i | 0.356235 | + | 0.356235i | 0.862423 | − | 0.506188i | \(-0.168946\pi\) |
−0.506188 | + | 0.862423i | \(0.668946\pi\) | |||||||
\(198\) | 5.19615 | + | 3.00000i | 0.369274 | + | 0.213201i | ||||
\(199\) | −20.7846 | + | 12.0000i | −1.47338 | + | 0.850657i | −0.999551 | − | 0.0299585i | \(-0.990462\pi\) |
−0.473831 | + | 0.880616i | \(0.657129\pi\) | |||||||
\(200\) | 8.19615 | + | 2.19615i | 0.579555 | + | 0.155291i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −12.0000 | −0.844317 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.32051 | − | 27.3205i | −0.511286 | − | 1.90815i | ||||
\(206\) | −1.46410 | + | 5.46410i | −0.102009 | + | 0.380702i | ||||
\(207\) | −9.00000 | − | 15.5885i | −0.625543 | − | 1.08347i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.00000 | 0.276686 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.00000 | + | 9.00000i | −0.619586 | + | 0.619586i | −0.945425 | − | 0.325840i | \(-0.894353\pi\) |
0.325840 | + | 0.945425i | \(0.394353\pi\) | |||||||
\(212\) | −0.732051 | − | 2.73205i | −0.0502775 | − | 0.187638i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 5.00000 | + | 8.66025i | 0.341793 | + | 0.592003i | ||||
\(215\) | 3.46410 | + | 2.00000i | 0.236250 | + | 0.136399i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − | 6.00000i | − | 0.406371i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −4.00000 | − | 6.92820i | −0.269680 | − | 0.467099i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.00000 | 0.267860 | 0.133930 | − | 0.990991i | \(-0.457240\pi\) | ||||
0.133930 | + | 0.990991i | \(0.457240\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −9.00000 | −0.600000 | ||||||||
\(226\) | −1.46410 | − | 5.46410i | −0.0973906 | − | 0.363467i | ||||
\(227\) | 2.73205 | + | 0.732051i | 0.181333 | + | 0.0485879i | 0.348343 | − | 0.937367i | \(-0.386745\pi\) |
−0.167010 | + | 0.985955i | \(0.553411\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.9282 | + | 2.92820i | −0.722156 | + | 0.193501i | −0.601133 | − | 0.799149i | \(-0.705284\pi\) |
−0.121023 | + | 0.992650i | \(0.538617\pi\) | |||||||
\(230\) | 24.0000i | 1.58251i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 28.0000 | 1.83829 | ||||||||
\(233\) | 13.8564 | + | 8.00000i | 0.907763 | + | 0.524097i | 0.879711 | − | 0.475509i | \(-0.157736\pi\) |
0.0280525 | + | 0.999606i | \(0.491069\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.78461 | + | 32.7846i | −0.573045 | + | 2.13863i | ||||
\(236\) | 5.85641 | + | 21.8564i | 0.381220 | + | 1.42273i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.0000 | − | 19.0526i | −0.708572 | − | 1.22728i | −0.965387 | − | 0.260822i | \(-0.916006\pi\) |
0.256814 | − | 0.966461i | \(-0.417327\pi\) | |||||||
\(242\) | 3.29423 | − | 12.2942i | 0.211761 | − | 0.790303i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −12.0000 | − | 12.0000i | −0.768221 | − | 0.768221i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −5.85641 | + | 21.8564i | −0.371882 | + | 1.38788i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −6.92820 | − | 4.00000i | −0.438178 | − | 0.252982i | ||||
\(251\) | −14.0000 | − | 14.0000i | −0.883672 | − | 0.883672i | 0.110234 | − | 0.993906i | \(-0.464840\pi\) |
−0.993906 | + | 0.110234i | \(0.964840\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.00000 | − | 6.00000i | 0.377217 | − | 0.377217i | ||||
\(254\) | −2.92820 | − | 10.9282i | −0.183732 | − | 0.685696i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | − | 13.8564i | −0.500000 | − | 0.866025i | ||||
\(257\) | 1.00000 | − | 1.73205i | 0.0623783 | − | 0.108042i | −0.833150 | − | 0.553047i | \(-0.813465\pi\) |
0.895528 | + | 0.445005i | \(0.146798\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −28.6865 | + | 7.68653i | −1.77565 | + | 0.475784i | ||||
\(262\) | −24.2487 | + | 14.0000i | −1.49809 | + | 0.864923i | ||||
\(263\) | −13.8564 | + | 8.00000i | −0.854423 | + | 0.493301i | −0.862141 | − | 0.506669i | \(-0.830877\pi\) |
0.00771799 | + | 0.999970i | \(0.497543\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 4.00000i | − | 0.245718i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 8.19615 | − | 2.19615i | 0.500660 | − | 0.134151i | ||||
\(269\) | 10.9282 | + | 2.92820i | 0.666304 | + | 0.178536i | 0.576089 | − | 0.817387i | \(-0.304578\pi\) |
0.0902148 | + | 0.995922i | \(0.471245\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.00000 | − | 6.92820i | 0.242983 | − | 0.420858i | −0.718580 | − | 0.695444i | \(-0.755208\pi\) |
0.961563 | + | 0.274586i | \(0.0885408\pi\) | |||||||
\(272\) | 8.00000 | 0.485071 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −12.0000 | − | 12.0000i | −0.724947 | − | 0.724947i | ||||
\(275\) | −1.09808 | − | 4.09808i | −0.0662165 | − | 0.247123i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.49038 | + | 20.4904i | −0.329885 | + | 1.23115i | 0.579424 | + | 0.815026i | \(0.303278\pi\) |
−0.909309 | + | 0.416121i | \(0.863389\pi\) | |||||||
\(278\) | −2.00000 | + | 3.46410i | −0.119952 | + | 0.207763i | ||||
\(279\) | − | 24.0000i | − | 1.43684i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.46410 | − | 5.46410i | 0.0870318 | − | 0.324807i | −0.908659 | − | 0.417538i | \(-0.862893\pi\) |
0.995691 | + | 0.0927310i | \(0.0295597\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 12.0000 | + | 12.0000i | 0.707107 | + | 0.707107i | ||||
\(289\) | 6.50000 | − | 11.2583i | 0.382353 | − | 0.662255i | ||||
\(290\) | 38.2487 | + | 10.2487i | 2.24604 | + | 0.601825i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 6.00000 | − | 10.3923i | 0.351123 | − | 0.608164i | ||||
\(293\) | 14.0000 | + | 14.0000i | 0.817889 | + | 0.817889i | 0.985802 | − | 0.167913i | \(-0.0537028\pi\) |
−0.167913 | + | 0.985802i | \(0.553703\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 32.0000i | 1.86311i | ||||||||
\(296\) | 17.3205 | + | 10.0000i | 1.00673 | + | 0.581238i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.00000 | + | 5.19615i | 0.173785 | + | 0.301005i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −10.0000 | − | 10.0000i | −0.575435 | − | 0.575435i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 10.9282 | + | 2.92820i | 0.626775 | + | 0.167944i | ||||
\(305\) | −12.0000 | − | 20.7846i | −0.687118 | − | 1.19012i | ||||
\(306\) | −8.19615 | + | 2.19615i | −0.468543 | + | 0.125546i | ||||
\(307\) | 18.0000 | − | 18.0000i | 1.02731 | − | 1.02731i | 0.0276979 | − | 0.999616i | \(-0.491182\pi\) |
0.999616 | − | 0.0276979i | \(-0.00881765\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −16.0000 | + | 27.7128i | −0.908739 | + | 1.57398i | ||||
\(311\) | 17.3205 | − | 10.0000i | 0.982156 | − | 0.567048i | 0.0792356 | − | 0.996856i | \(-0.474752\pi\) |
0.902920 | + | 0.429808i | \(0.141419\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.1244 | − | 7.00000i | −0.685309 | − | 0.395663i | 0.116543 | − | 0.993186i | \(-0.462819\pi\) |
−0.801852 | + | 0.597522i | \(0.796152\pi\) | |||||||
\(314\) | − | 24.0000i | − | 1.35440i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 20.0000i | − | 1.12509i | ||||||
\(317\) | −2.56218 | − | 9.56218i | −0.143906 | − | 0.537065i | −0.999802 | − | 0.0199164i | \(-0.993660\pi\) |
0.855895 | − | 0.517149i | \(-0.173007\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.00000 | − | 12.1244i | −0.391925 | − | 0.678834i | ||||
\(320\) | −5.85641 | − | 21.8564i | −0.327383 | − | 1.22181i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.00000 | + | 4.00000i | −0.222566 | + | 0.222566i | ||||
\(324\) | −15.5885 | − | 9.00000i | −0.866025 | − | 0.500000i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 25.9808 | − | 15.0000i | 1.43894 | − | 0.830773i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −20.0000 | + | 20.0000i | −1.10432 | + | 1.10432i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −28.6865 | + | 7.68653i | −1.57675 | + | 0.422490i | −0.937919 | − | 0.346854i | \(-0.887250\pi\) |
−0.638835 | + | 0.769344i | \(0.720583\pi\) | |||||||
\(332\) | 7.32051 | − | 27.3205i | 0.401765 | − | 1.49941i | ||||
\(333\) | −20.4904 | − | 5.49038i | −1.12287 | − | 0.300871i | ||||
\(334\) | 16.3923 | − | 4.39230i | 0.896947 | − | 0.240336i | ||||
\(335\) | 12.0000 | 0.655630 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.00000 | 0.435788 | 0.217894 | − | 0.975972i | \(-0.430081\pi\) | ||||
0.217894 | + | 0.975972i | \(0.430081\pi\) | |||||||
\(338\) | 17.7583 | − | 4.75833i | 0.965926 | − | 0.258819i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 10.9282 | + | 2.92820i | 0.592665 | + | 0.158804i | ||||
\(341\) | 10.9282 | − | 2.92820i | 0.591795 | − | 0.158571i | ||||
\(342\) | −12.0000 | −0.648886 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − | 4.00000i | − | 0.215666i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.49038 | − | 20.4904i | 0.294739 | − | 1.09998i | −0.646685 | − | 0.762757i | \(-0.723845\pi\) |
0.941424 | − | 0.337224i | \(-0.109488\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.0000 | − | 12.0000i | 0.642345 | − | 0.642345i | −0.308786 | − | 0.951131i | \(-0.599923\pi\) |
0.951131 | + | 0.308786i | \(0.0999228\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4.00000 | + | 6.92820i | −0.213201 | + | 0.369274i | ||||
\(353\) | 3.00000 | + | 5.19615i | 0.159674 | + | 0.276563i | 0.934751 | − | 0.355303i | \(-0.115622\pi\) |
−0.775077 | + | 0.631867i | \(0.782289\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −28.0000 | −1.48400 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 6.00000i | − | 0.317110i | ||||||
\(359\) | −5.19615 | − | 3.00000i | −0.274242 | − | 0.158334i | 0.356572 | − | 0.934268i | \(-0.383946\pi\) |
−0.630814 | + | 0.775934i | \(0.717279\pi\) | |||||||
\(360\) | 12.0000 | + | 20.7846i | 0.632456 | + | 1.09545i | ||||
\(361\) | 9.52628 | − | 5.50000i | 0.501383 | − | 0.289474i | ||||
\(362\) | −4.00000 | + | 6.92820i | −0.210235 | + | 0.364138i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 12.0000 | − | 12.0000i | 0.628109 | − | 0.628109i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.0000 | + | 27.7128i | 0.835193 | + | 1.44660i | 0.893873 | + | 0.448320i | \(0.147978\pi\) |
−0.0586798 | + | 0.998277i | \(0.518689\pi\) | |||||||
\(368\) | 20.7846 | − | 12.0000i | 1.08347 | − | 0.625543i | ||||
\(369\) | 15.0000 | − | 25.9808i | 0.780869 | − | 1.35250i | ||||
\(370\) | 20.0000 | + | 20.0000i | 1.03975 | + | 1.03975i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 15.0263 | − | 4.02628i | 0.778031 | − | 0.208473i | 0.152115 | − | 0.988363i | \(-0.451392\pi\) |
0.625917 | + | 0.779890i | \(0.284725\pi\) | |||||||
\(374\) | −2.00000 | − | 3.46410i | −0.103418 | − | 0.179124i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 32.7846 | − | 8.78461i | 1.69074 | − | 0.453032i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.0000 | + | 13.0000i | 0.667765 | + | 0.667765i | 0.957198 | − | 0.289433i | \(-0.0934668\pi\) |
−0.289433 | + | 0.957198i | \(0.593467\pi\) | |||||||
\(380\) | 13.8564 | + | 8.00000i | 0.710819 | + | 0.410391i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −24.5885 | − | 6.58846i | −1.25805 | − | 0.337095i | ||||
\(383\) | −2.00000 | + | 3.46410i | −0.102195 | + | 0.177007i | −0.912589 | − | 0.408879i | \(-0.865920\pi\) |
0.810394 | + | 0.585886i | \(0.199253\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 16.0000 | − | 16.0000i | 0.814379 | − | 0.814379i | ||||
\(387\) | 1.09808 | + | 4.09808i | 0.0558184 | + | 0.208317i | ||||
\(388\) | 3.46410 | − | 2.00000i | 0.175863 | − | 0.101535i | ||||
\(389\) | 1.09808 | − | 4.09808i | 0.0556747 | − | 0.207781i | −0.932485 | − | 0.361208i | \(-0.882364\pi\) |
0.988160 | + | 0.153427i | \(0.0490311\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12.0000i | 0.606866i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 5.00000 | − | 8.66025i | 0.251896 | − | 0.436297i | ||||
\(395\) | 7.32051 | − | 27.3205i | 0.368335 | − | 1.37464i | ||||
\(396\) | 2.19615 | − | 8.19615i | 0.110361 | − | 0.411872i | ||||
\(397\) | −4.39230 | − | 16.3923i | −0.220443 | − | 0.822706i | −0.984179 | − | 0.177177i | \(-0.943304\pi\) |
0.763736 | − | 0.645529i | \(-0.223363\pi\) | |||||||
\(398\) | 24.0000 | + | 24.0000i | 1.20301 | + | 1.20301i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | − | 12.0000i | − | 0.600000i | ||||||
\(401\) | −6.00000 | + | 10.3923i | −0.299626 | + | 0.518967i | −0.976050 | − | 0.217545i | \(-0.930195\pi\) |
0.676425 | + | 0.736512i | \(0.263528\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 4.39230 | + | 16.3923i | 0.218525 | + | 0.815548i | ||||
\(405\) | −18.0000 | − | 18.0000i | −0.894427 | − | 0.894427i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 10.0000i | − | 0.495682i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12.1244 | + | 7.00000i | −0.599511 | + | 0.346128i | −0.768849 | − | 0.639430i | \(-0.779170\pi\) |
0.169338 | + | 0.985558i | \(0.445837\pi\) | |||||||
\(410\) | −34.6410 | + | 20.0000i | −1.71080 | + | 0.987730i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 8.00000 | 0.394132 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −18.0000 | + | 18.0000i | −0.884652 | + | 0.884652i | ||||
\(415\) | 20.0000 | − | 34.6410i | 0.981761 | − | 1.70046i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.46410 | − | 5.46410i | −0.0716116 | − | 0.267258i | ||||
\(419\) | 12.0000 | − | 12.0000i | 0.586238 | − | 0.586238i | −0.350372 | − | 0.936611i | \(-0.613945\pi\) |
0.936611 | + | 0.350372i | \(0.113945\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.00000 | − | 9.00000i | −0.438633 | − | 0.438633i | 0.452919 | − | 0.891552i | \(-0.350383\pi\) |
−0.891552 | + | 0.452919i | \(0.850383\pi\) | |||||||
\(422\) | 15.5885 | + | 9.00000i | 0.758834 | + | 0.438113i | ||||
\(423\) | −31.1769 | + | 18.0000i | −1.51587 | + | 0.875190i | ||||
\(424\) | −3.46410 | + | 2.00000i | −0.168232 | + | 0.0971286i | ||||
\(425\) | 5.19615 | + | 3.00000i | 0.252050 | + | 0.145521i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 10.0000 | − | 10.0000i | 0.483368 | − | 0.483368i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.46410 | − | 5.46410i | 0.0706052 | − | 0.263502i | ||||
\(431\) | 4.00000 | + | 6.92820i | 0.192673 | + | 0.333720i | 0.946135 | − | 0.323772i | \(-0.104951\pi\) |
−0.753462 | + | 0.657491i | \(0.771618\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.00000 | −0.288342 | −0.144171 | − | 0.989553i | \(-0.546051\pi\) | ||||
−0.144171 | + | 0.989553i | \(0.546051\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −8.19615 | + | 2.19615i | −0.392525 | + | 0.105177i | ||||
\(437\) | −4.39230 | + | 16.3923i | −0.210112 | + | 0.784150i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13.8564 | − | 8.00000i | −0.661330 | − | 0.381819i | 0.131453 | − | 0.991322i | \(-0.458036\pi\) |
−0.792784 | + | 0.609503i | \(0.791369\pi\) | |||||||
\(440\) | −8.00000 | + | 8.00000i | −0.381385 | + | 0.381385i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.36603 | − | 0.366025i | 0.0649018 | − | 0.0173904i | −0.226222 | − | 0.974076i | \(-0.572637\pi\) |
0.291124 | + | 0.956685i | \(0.405971\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −38.2487 | − | 10.2487i | −1.81316 | − | 0.485836i | ||||
\(446\) | −1.46410 | − | 5.46410i | −0.0693272 | − | 0.258733i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −30.0000 | −1.41579 | −0.707894 | − | 0.706319i | \(-0.750354\pi\) | ||||
−0.707894 | + | 0.706319i | \(0.750354\pi\) | |||||||
\(450\) | 3.29423 | + | 12.2942i | 0.155291 | + | 0.579555i | ||||
\(451\) | 13.6603 | + | 3.66025i | 0.643236 | + | 0.172355i | ||||
\(452\) | −6.92820 | + | 4.00000i | −0.325875 | + | 0.188144i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 4.00000i | − | 0.187729i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −19.0526 | − | 11.0000i | −0.891241 | − | 0.514558i | −0.0168929 | − | 0.999857i | \(-0.505377\pi\) |
−0.874348 | + | 0.485299i | \(0.838711\pi\) | |||||||
\(458\) | 8.00000 | + | 13.8564i | 0.373815 | + | 0.647467i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 32.7846 | − | 8.78461i | 1.52859 | − | 0.409585i | ||||
\(461\) | 16.0000 | − | 16.0000i | 0.745194 | − | 0.745194i | −0.228378 | − | 0.973572i | \(-0.573342\pi\) |
0.973572 | + | 0.228378i | \(0.0733423\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.0000 | 0.650635 | 0.325318 | − | 0.945605i | \(-0.394529\pi\) | ||||
0.325318 | + | 0.945605i | \(0.394529\pi\) | |||||||
\(464\) | −10.2487 | − | 38.2487i | −0.475784 | − | 1.77565i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5.85641 | − | 21.8564i | 0.271293 | − | 1.01248i | ||||
\(467\) | 6.58846 | + | 24.5885i | 0.304877 | + | 1.13782i | 0.933051 | + | 0.359745i | \(0.117136\pi\) |
−0.628173 | + | 0.778073i | \(0.716197\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 48.0000 | 2.21407 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 27.7128 | − | 16.0000i | 1.27559 | − | 0.736460i | ||||
\(473\) | −1.73205 | + | 1.00000i | −0.0796398 | + | 0.0459800i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.00000 | + | 6.00000i | 0.275299 | + | 0.275299i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.00000 | − | 3.00000i | 0.137361 | − | 0.137361i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10.0000 | + | 17.3205i | 0.456912 | + | 0.791394i | 0.998796 | − | 0.0490589i | \(-0.0156222\pi\) |
−0.541884 | + | 0.840453i | \(0.682289\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −22.0000 | + | 22.0000i | −1.00207 | + | 1.00207i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −18.0000 | −0.818182 | ||||||||
\(485\) | 5.46410 | − | 1.46410i | 0.248112 | − | 0.0664814i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 19.0526 | − | 11.0000i | 0.863354 | − | 0.498458i | −0.00178012 | − | 0.999998i | \(-0.500567\pi\) |
0.865134 | + | 0.501541i | \(0.167233\pi\) | |||||||
\(488\) | −12.0000 | + | 20.7846i | −0.543214 | + | 0.940875i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19.0000 | − | 19.0000i | −0.857458 | − | 0.857458i | 0.133580 | − | 0.991038i | \(-0.457353\pi\) |
−0.991038 | + | 0.133580i | \(0.957353\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 19.1244 | + | 5.12436i | 0.861318 | + | 0.230789i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6.00000 | − | 10.3923i | 0.269680 | − | 0.467099i | ||||
\(496\) | 32.0000 | 1.43684 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.41858 | − | 31.4186i | −0.376868 | − | 1.40649i | −0.850597 | − | 0.525818i | \(-0.823759\pi\) |
0.473729 | − | 0.880671i | \(-0.342908\pi\) | |||||||
\(500\) | −2.92820 | + | 10.9282i | −0.130953 | + | 0.488724i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −14.0000 | + | 24.2487i | −0.624851 | + | 1.08227i | ||||
\(503\) | − | 16.0000i | − | 0.713405i | −0.934218 | − | 0.356702i | \(-0.883901\pi\) | ||
0.934218 | − | 0.356702i | \(-0.116099\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 24.0000i | 1.06799i | ||||||||
\(506\) | −10.3923 | − | 6.00000i | −0.461994 | − | 0.266733i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −13.8564 | + | 8.00000i | −0.614779 | + | 0.354943i | ||||
\(509\) | −2.92820 | − | 10.9282i | −0.129790 | − | 0.484384i | 0.870175 | − | 0.492743i | \(-0.164006\pi\) |
−0.999965 | + | 0.00835918i | \(0.997339\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −16.0000 | + | 16.0000i | −0.707107 | + | 0.707107i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −2.73205 | − | 0.732051i | −0.120506 | − | 0.0322894i | ||||
\(515\) | 10.9282 | + | 2.92820i | 0.481554 | + | 0.129032i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −12.0000 | − | 12.0000i | −0.527759 | − | 0.527759i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.66025 | + | 5.00000i | −0.379413 | + | 0.219054i | −0.677563 | − | 0.735465i | \(-0.736964\pi\) |
0.298150 | + | 0.954519i | \(0.403630\pi\) | |||||||
\(522\) | 21.0000 | + | 36.3731i | 0.919145 | + | 1.59201i | ||||
\(523\) | −32.7846 | + | 8.78461i | −1.43357 | + | 0.384124i | −0.890277 | − | 0.455419i | \(-0.849490\pi\) |
−0.543293 | + | 0.839543i | \(0.682823\pi\) | |||||||
\(524\) | 28.0000 | + | 28.0000i | 1.22319 | + | 1.22319i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 16.0000 | + | 16.0000i | 0.697633 | + | 0.697633i | ||||
\(527\) | −8.00000 | + | 13.8564i | −0.348485 | + | 0.603595i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.50000 | + | 11.2583i | 0.282609 | + | 0.489493i | ||||
\(530\) | −5.46410 | + | 1.46410i | −0.237345 | + | 0.0635965i | ||||
\(531\) | −24.0000 | + | 24.0000i | −1.04151 | + | 1.04151i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 17.3205 | − | 10.0000i | 0.748831 | − | 0.432338i | ||||
\(536\) | −6.00000 | − | 10.3923i | −0.259161 | − | 0.448879i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 16.0000i | − | 0.689809i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.02628 | + | 15.0263i | 0.173103 | + | 0.646030i | 0.996867 | + | 0.0790969i | \(0.0252036\pi\) |
−0.823764 | + | 0.566933i | \(0.808130\pi\) | |||||||
\(542\) | −10.9282 | − | 2.92820i | −0.469407 | − | 0.125777i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.92820 | − | 10.9282i | −0.125546 | − | 0.468543i | ||||
\(545\) | −12.0000 | −0.514024 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 23.0000 | − | 23.0000i | 0.983409 | − | 0.983409i | −0.0164556 | − | 0.999865i | \(-0.505238\pi\) |
0.999865 | + | 0.0164556i | \(0.00523822\pi\) | |||||||
\(548\) | −12.0000 | + | 20.7846i | −0.512615 | + | 0.887875i | ||||
\(549\) | 6.58846 | − | 24.5885i | 0.281189 | − | 1.04941i | ||||
\(550\) | −5.19615 | + | 3.00000i | −0.221565 | + | 0.127920i | ||||
\(551\) | 24.2487 | + | 14.0000i | 1.03303 | + | 0.596420i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 30.0000 | 1.27458 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.46410 | + | 1.46410i | 0.231730 | + | 0.0620917i | ||||
\(557\) | 23.2224 | + | 6.22243i | 0.983966 | + | 0.263653i | 0.714714 | − | 0.699417i | \(-0.246557\pi\) |
0.269252 | + | 0.963070i | \(0.413224\pi\) | |||||||
\(558\) | −32.7846 | + | 8.78461i | −1.38788 | + | 0.371882i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −27.3205 | − | 7.32051i | −1.15142 | − | 0.308523i | −0.367887 | − | 0.929870i | \(-0.619919\pi\) |
−0.783535 | + | 0.621348i | \(0.786585\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.9282 | + | 2.92820i | −0.459753 | + | 0.123190i | ||||
\(566\) | −8.00000 | −0.336265 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 12.1244 | + | 7.00000i | 0.508279 | + | 0.293455i | 0.732126 | − | 0.681169i | \(-0.238528\pi\) |
−0.223847 | + | 0.974624i | \(0.571861\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.29423 | + | 12.2942i | −0.137859 | + | 0.514497i | 0.862111 | + | 0.506720i | \(0.169142\pi\) |
−0.999970 | + | 0.00777727i | \(0.997524\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 18.0000 | 0.750652 | ||||||||
\(576\) | 12.0000 | − | 20.7846i | 0.500000 | − | 0.866025i | ||||
\(577\) | 1.00000 | + | 1.73205i | 0.0416305 | + | 0.0721062i | 0.886090 | − | 0.463513i | \(-0.153411\pi\) |
−0.844459 | + | 0.535620i | \(0.820078\pi\) | |||||||
\(578\) | −17.7583 | − | 4.75833i | −0.738649 | − | 0.197920i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 56.0000i | − | 2.32527i | ||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.73205 | + | 1.00000i | 0.0717342 | + | 0.0414158i | ||||
\(584\) | −16.3923 | − | 4.39230i | −0.678318 | − | 0.181755i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 14.0000 | − | 24.2487i | 0.578335 | − | 1.00171i | ||||
\(587\) | 10.0000 | + | 10.0000i | 0.412744 | + | 0.412744i | 0.882693 | − | 0.469949i | \(-0.155728\pi\) |
−0.469949 | + | 0.882693i | \(0.655728\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16.0000 | + | 16.0000i | −0.659269 | + | 0.659269i | ||||
\(590\) | 43.7128 | − | 11.7128i | 1.79963 | − | 0.482209i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 7.32051 | − | 27.3205i | 0.300871 | − | 1.12287i | ||||
\(593\) | 3.00000 | − | 5.19615i | 0.123195 | − | 0.213380i | −0.797831 | − | 0.602881i | \(-0.794019\pi\) |
0.921026 | + | 0.389501i | \(0.127353\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6.00000 | − | 6.00000i | 0.245770 | − | 0.245770i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −20.7846 | + | 12.0000i | −0.849236 | + | 0.490307i | −0.860393 | − | 0.509631i | \(-0.829782\pi\) |
0.0111569 | + | 0.999938i | \(0.496449\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.0000i | 0.407909i | 0.978980 | + | 0.203954i | \(0.0653794\pi\) | ||||
−0.978980 | + | 0.203954i | \(0.934621\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9.00000 | + | 9.00000i | 0.366508 | + | 0.366508i | ||||
\(604\) | −10.0000 | + | 17.3205i | −0.406894 | + | 0.704761i | ||||
\(605\) | −24.5885 | − | 6.58846i | −0.999663 | − | 0.267859i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14.0000 | + | 24.2487i | −0.568242 | + | 0.984225i | 0.428497 | + | 0.903543i | \(0.359043\pi\) |
−0.996740 | + | 0.0806818i | \(0.974290\pi\) | |||||||
\(608\) | − | 16.0000i | − | 0.648886i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −24.0000 | + | 24.0000i | −0.971732 | + | 0.971732i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 6.00000 | + | 10.3923i | 0.242536 | + | 0.420084i | ||||
\(613\) | 3.29423 | − | 12.2942i | 0.133053 | − | 0.496559i | −0.866946 | − | 0.498403i | \(-0.833920\pi\) |
0.999998 | + | 0.00184345i | \(0.000586790\pi\) | |||||||
\(614\) | −31.1769 | − | 18.0000i | −1.25820 | − | 0.726421i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 42.0000i | 1.69086i | 0.534089 | + | 0.845428i | \(0.320655\pi\) | ||||
−0.534089 | + | 0.845428i | \(0.679345\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.39230 | + | 16.3923i | −0.176542 | + | 0.658862i | 0.819742 | + | 0.572733i | \(0.194117\pi\) |
−0.996284 | + | 0.0861298i | \(0.972550\pi\) | |||||||
\(620\) | 43.7128 | + | 11.7128i | 1.75555 | + | 0.470398i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −20.0000 | − | 20.0000i | −0.801927 | − | 0.801927i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −15.5000 | + | 26.8468i | −0.620000 | + | 1.07387i | ||||
\(626\) | −5.12436 | + | 19.1244i | −0.204810 | + | 0.764363i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −32.7846 | + | 8.78461i | −1.30825 | + | 0.350544i | ||||
\(629\) | 10.0000 | + | 10.0000i | 0.398726 | + | 0.398726i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 40.0000i | − | 1.59237i | −0.605050 | − | 0.796187i | \(-0.706847\pi\) | ||
0.605050 | − | 0.796187i | \(-0.293153\pi\) | |||||||
\(632\) | −27.3205 | + | 7.32051i | −1.08675 | + | 0.291194i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −12.1244 | + | 7.00000i | −0.481520 | + | 0.278006i | ||||
\(635\) | −21.8564 | + | 5.85641i | −0.867345 | + | 0.232404i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −14.0000 | + | 14.0000i | −0.554265 | + | 0.554265i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −27.7128 | + | 16.0000i | −1.09545 | + | 0.632456i | ||||
\(641\) | −6.00000 | − | 10.3923i | −0.236986 | − | 0.410471i | 0.722862 | − | 0.690992i | \(-0.242826\pi\) |
−0.959848 | + | 0.280521i | \(0.909493\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.92820 | + | 4.00000i | 0.272587 | + | 0.157378i | ||||
\(647\) | 10.3923 | − | 6.00000i | 0.408564 | − | 0.235884i | −0.281609 | − | 0.959529i | \(-0.590868\pi\) |
0.690172 | + | 0.723645i | \(0.257535\pi\) | |||||||
\(648\) | −6.58846 | + | 24.5885i | −0.258819 | + | 0.965926i | ||||
\(649\) | −13.8564 | − | 8.00000i | −0.543912 | − | 0.314027i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −30.0000 | − | 30.0000i | −1.17489 | − | 1.17489i | ||||
\(653\) | 9.15064 | + | 34.1506i | 0.358092 | + | 1.33642i | 0.876548 | + | 0.481314i | \(0.159840\pi\) |
−0.518456 | + | 0.855104i | \(0.673493\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 28.0000 | + | 48.4974i | 1.09405 | + | 1.89495i | ||||
\(656\) | 34.6410 | + | 20.0000i | 1.35250 | + | 0.780869i | ||||
\(657\) | 18.0000 | 0.702247 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.00000 | + | 3.00000i | −0.116863 | + | 0.116863i | −0.763120 | − | 0.646257i | \(-0.776334\pi\) |
0.646257 | + | 0.763120i | \(0.276334\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.51666 | − | 35.5167i | 0.370155 | − | 1.38144i | −0.490141 | − | 0.871643i | \(-0.663055\pi\) |
0.860296 | − | 0.509795i | \(-0.170279\pi\) | |||||||
\(662\) | 21.0000 | + | 36.3731i | 0.816188 | + | 1.41368i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −40.0000 | −1.55230 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 30.0000i | 1.16248i | ||||||||
\(667\) | 57.3731 | − | 15.3731i | 2.22149 | − | 0.595248i | ||||
\(668\) | −12.0000 | − | 20.7846i | −0.464294 | − | 0.804181i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −4.39230 | − | 16.3923i | −0.169690 | − | 0.633290i | ||||
\(671\) | 12.0000 | 0.463255 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 34.0000 | 1.31060 | 0.655302 | − | 0.755367i | \(-0.272541\pi\) | ||||
0.655302 | + | 0.755367i | \(0.272541\pi\) | |||||||
\(674\) | −2.92820 | − | 10.9282i | −0.112790 | − | 0.420939i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −13.0000 | − | 22.5167i | −0.500000 | − | 0.866025i | ||||
\(677\) | 27.3205 | − | 7.32051i | 1.05001 | − | 0.281350i | 0.307756 | − | 0.951465i | \(-0.400422\pi\) |
0.742257 | + | 0.670115i | \(0.233755\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | − | 16.0000i | − | 0.613572i | ||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −8.00000 | − | 13.8564i | −0.306336 | − | 0.530589i | ||||
\(683\) | −4.02628 | + | 15.0263i | −0.154061 | + | 0.574965i | 0.845123 | + | 0.534573i | \(0.179527\pi\) |
−0.999184 | + | 0.0403921i | \(0.987139\pi\) | |||||||
\(684\) | 4.39230 | + | 16.3923i | 0.167944 | + | 0.626775i | ||||
\(685\) | −24.0000 | + | 24.0000i | −0.916993 | + | 0.916993i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −5.46410 | + | 1.46410i | −0.208317 | + | 0.0558184i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.51666 | + | 35.5167i | 0.362031 | + | 1.35112i | 0.871402 | + | 0.490570i | \(0.163212\pi\) |
−0.509371 | + | 0.860547i | \(0.670122\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −30.0000 | −1.13878 | ||||||||
\(695\) | 6.92820 | + | 4.00000i | 0.262802 | + | 0.151729i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −17.3205 | + | 10.0000i | −0.656061 | + | 0.378777i | ||||
\(698\) | −20.7846 | − | 12.0000i | −0.786709 | − | 0.454207i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19.0000 | + | 19.0000i | −0.717620 | + | 0.717620i | −0.968117 | − | 0.250497i | \(-0.919406\pi\) |
0.250497 | + | 0.968117i | \(0.419406\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.0000 | + | 17.3205i | 0.377157 | + | 0.653255i | ||||
\(704\) | 10.9282 | + | 2.92820i | 0.411872 | + | 0.110361i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.00000 | − | 6.00000i | 0.225813 | − | 0.225813i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.56218 | − | 2.56218i | 0.359115 | − | 0.0962246i | −0.0747503 | − | 0.997202i | \(-0.523816\pi\) |
0.433865 | + | 0.900978i | \(0.357149\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 25.9808 | − | 15.0000i | 0.974355 | − | 0.562544i | ||||
\(712\) | 10.2487 | + | 38.2487i | 0.384087 | + | 1.43343i | ||||
\(713\) | 48.0000i | 1.79761i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −8.19615 | + | 2.19615i | −0.306305 | + | 0.0820741i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −2.19615 | + | 8.19615i | −0.0819597 | + | 0.305878i | ||||
\(719\) | −10.0000 | + | 17.3205i | −0.372937 | + | 0.645946i | −0.990016 | − | 0.140955i | \(-0.954983\pi\) |
0.617079 | + | 0.786901i | \(0.288316\pi\) | |||||||
\(720\) | 24.0000 | − | 24.0000i | 0.894427 | − | 0.894427i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −11.0000 | − | 11.0000i | −0.409378 | − | 0.409378i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 10.9282 | + | 2.92820i | 0.406143 | + | 0.108826i | ||||
\(725\) | 7.68653 | − | 28.6865i | 0.285471 | − | 1.06539i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32.0000i | 1.18681i | 0.804902 | + | 0.593407i | \(0.202218\pi\) | ||||
−0.804902 | + | 0.593407i | \(0.797782\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 27.0000i | − | 1.00000i | ||||||
\(730\) | −20.7846 | − | 12.0000i | −0.769273 | − | 0.444140i | ||||
\(731\) | 0.732051 | − | 2.73205i | 0.0270759 | − | 0.101049i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.66025 | − | 13.6603i | −0.135195 | − | 0.504553i | −0.999997 | − | 0.00244074i | \(-0.999223\pi\) |
0.864802 | − | 0.502112i | \(-0.167444\pi\) | |||||||
\(734\) | 32.0000 | − | 32.0000i | 1.18114 | − | 1.18114i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −24.0000 | − | 24.0000i | −0.884652 | − | 0.884652i | ||||
\(737\) | −3.00000 | + | 5.19615i | −0.110506 | + | 0.191403i | ||||
\(738\) | −40.9808 | − | 10.9808i | −1.50852 | − | 0.404207i | ||||
\(739\) | −9.56218 | − | 2.56218i | −0.351750 | − | 0.0942512i | 0.0786174 | − | 0.996905i | \(-0.474949\pi\) |
−0.430368 | + | 0.902654i | \(0.641616\pi\) | |||||||
\(740\) | 20.0000 | − | 34.6410i | 0.735215 | − | 1.27343i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 6.00000i | − | 0.220119i | −0.993925 | − | 0.110059i | \(-0.964896\pi\) | ||
0.993925 | − | 0.110059i | \(-0.0351041\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10.3923 | − | 6.00000i | 0.380745 | − | 0.219823i | ||||
\(746\) | −11.0000 | − | 19.0526i | −0.402739 | − | 0.697564i | ||||
\(747\) | 40.9808 | − | 10.9808i | 1.49941 | − | 0.401765i | ||||
\(748\) | −4.00000 | + | 4.00000i | −0.146254 | + | 0.146254i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −16.0000 | + | 27.7128i | −0.583848 | + | 1.01125i | 0.411170 | + | 0.911559i | \(0.365120\pi\) |
−0.995018 | + | 0.0996961i | \(0.968213\pi\) | |||||||
\(752\) | −24.0000 | − | 41.5692i | −0.875190 | − | 1.51587i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −20.0000 | + | 20.0000i | −0.727875 | + | 0.727875i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.0000 | − | 15.0000i | −0.545184 | − | 0.545184i | 0.379860 | − | 0.925044i | \(-0.375972\pi\) |
−0.925044 | + | 0.379860i | \(0.875972\pi\) | |||||||
\(758\) | 13.0000 | − | 22.5167i | 0.472181 | − | 0.817842i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 5.85641 | − | 21.8564i | 0.212434 | − | 0.792815i | ||||
\(761\) | 25.9808 | + | 15.0000i | 0.941802 | + | 0.543750i | 0.890525 | − | 0.454935i | \(-0.150337\pi\) |
0.0512772 | + | 0.998684i | \(0.483671\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 36.0000i | 1.30243i | ||||||||
\(765\) | 4.39230 | + | 16.3923i | 0.158804 | + | 0.592665i | ||||
\(766\) | 5.46410 | + | 1.46410i | 0.197426 | + | 0.0529001i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −10.0000 | −0.360609 | −0.180305 | − | 0.983611i | \(-0.557708\pi\) | ||||
−0.180305 | + | 0.983611i | \(0.557708\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −27.7128 | − | 16.0000i | −0.997406 | − | 0.575853i | ||||
\(773\) | −2.19615 | + | 8.19615i | −0.0789901 | + | 0.294795i | −0.994108 | − | 0.108390i | \(-0.965430\pi\) |
0.915118 | + | 0.403185i | \(0.132097\pi\) | |||||||
\(774\) | 5.19615 | − | 3.00000i | 0.186772 | − | 0.107833i | ||||
\(775\) | 20.7846 | + | 12.0000i | 0.746605 | + | 0.431053i | ||||
\(776\) | −4.00000 | − | 4.00000i | −0.143592 | − | 0.143592i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −6.00000 | −0.215110 | ||||||||
\(779\) | −27.3205 | + | 7.32051i | −0.978859 | + | 0.262284i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 16.3923 | − | 4.39230i | 0.586188 | − | 0.157069i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −48.0000 | −1.71319 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −24.5885 | − | 6.58846i | −0.876484 | − | 0.234853i | −0.207594 | − | 0.978215i | \(-0.566563\pi\) |
−0.668889 | + | 0.743362i | \(0.733230\pi\) | |||||||
\(788\) | −13.6603 | − | 3.66025i | −0.486626 | − | 0.130391i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −40.0000 | −1.42314 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −12.0000 | −0.426401 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −20.7846 | + | 12.0000i | −0.737618 | + | 0.425864i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 24.0000 | − | 41.5692i | 0.850657 | − | 1.47338i | ||||
\(797\) | −32.0000 | + | 32.0000i | −1.13350 | + | 1.13350i | −0.143907 | + | 0.989591i | \(0.545967\pi\) |
−0.989591 | + | 0.143907i | \(0.954033\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 24.0000 | 0.849059 | ||||||||
\(800\) | −16.3923 | + | 4.39230i | −0.579555 | + | 0.155291i | ||||
\(801\) | −21.0000 | − | 36.3731i | −0.741999 | − | 1.28518i | ||||
\(802\) | 16.3923 | + | 4.39230i | 0.578832 | + | 0.155098i | ||||
\(803\) | 2.19615 | + | 8.19615i | 0.0775005 | + | 0.289236i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 20.7846 | − | 12.0000i | 0.731200 | − | 0.422159i | ||||
\(809\) | 5.19615 | − | 3.00000i | 0.182687 | − | 0.105474i | −0.405868 | − | 0.913932i | \(-0.633031\pi\) |
0.588555 | + | 0.808458i | \(0.299697\pi\) | |||||||
\(810\) | −18.0000 | + | 31.1769i | −0.632456 | + | 1.09545i | ||||
\(811\) | −24.0000 | − | 24.0000i | −0.842754 | − | 0.842754i | 0.146462 | − | 0.989216i | \(-0.453211\pi\) |
−0.989216 | + | 0.146462i | \(0.953211\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −13.6603 | + | 3.66025i | −0.478792 | + | 0.128292i | ||||
\(815\) | −30.0000 | − | 51.9615i | −1.05085 | − | 1.82013i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.00000 | − | 3.46410i | 0.0699711 | − | 0.121194i | ||||
\(818\) | 14.0000 | + | 14.0000i | 0.489499 | + | 0.489499i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 40.0000 | + | 40.0000i | 1.39686 | + | 1.39686i | ||||
\(821\) | −1.36603 | + | 0.366025i | −0.0476746 | + | 0.0127744i | −0.282578 | − | 0.959244i | \(-0.591189\pi\) |
0.234903 | + | 0.972019i | \(0.424523\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20.7846 | − | 12.0000i | 0.724506 | − | 0.418294i | −0.0919029 | − | 0.995768i | \(-0.529295\pi\) |
0.816409 | + | 0.577474i | \(0.195962\pi\) | |||||||
\(824\) | −2.92820 | − | 10.9282i | −0.102009 | − | 0.380702i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −5.00000 | − | 5.00000i | −0.173867 | − | 0.173867i | 0.614809 | − | 0.788676i | \(-0.289233\pi\) |
−0.788676 | + | 0.614809i | \(0.789233\pi\) | |||||||
\(828\) | 31.1769 | + | 18.0000i | 1.08347 | + | 0.625543i | ||||
\(829\) | −2.73205 | − | 0.732051i | −0.0948880 | − | 0.0254252i | 0.211063 | − | 0.977473i | \(-0.432308\pi\) |
−0.305951 | + | 0.952047i | \(0.598974\pi\) | |||||||
\(830\) | −54.6410 | − | 14.6410i | −1.89662 | − | 0.508197i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.78461 | − | 32.7846i | −0.304004 | − | 1.13456i | ||||
\(836\) | −6.92820 | + | 4.00000i | −0.239617 | + | 0.138343i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −20.7846 | − | 12.0000i | −0.717992 | − | 0.414533i | ||||
\(839\) | − | 4.00000i | − | 0.138095i | −0.997613 | − | 0.0690477i | \(-0.978004\pi\) | ||
0.997613 | − | 0.0690477i | \(-0.0219961\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 69.0000i | − | 2.37931i | ||||||
\(842\) | −9.00000 | + | 15.5885i | −0.310160 | + | 0.537214i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 6.58846 | − | 24.5885i | 0.226784 | − | 0.846370i | ||||
\(845\) | −9.51666 | − | 35.5167i | −0.327383 | − | 1.22181i | ||||
\(846\) | 36.0000 | + | 36.0000i | 1.23771 | + | 1.23771i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 4.00000 | + | 4.00000i | 0.137361 | + | 0.137361i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2.19615 | − | 8.19615i | 0.0753274 | − | 0.281126i | ||||
\(851\) | 40.9808 | + | 10.9808i | 1.40480 | + | 0.376416i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 24.0000 | + | 24.0000i | 0.821744 | + | 0.821744i | 0.986358 | − | 0.164614i | \(-0.0526378\pi\) |
−0.164614 | + | 0.986358i | \(0.552638\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 24.0000i | 0.820783i | ||||||||
\(856\) | −17.3205 | − | 10.0000i | −0.592003 | − | 0.341793i | ||||
\(857\) | −15.5885 | + | 9.00000i | −0.532492 | + | 0.307434i | −0.742030 | − | 0.670366i | \(-0.766137\pi\) |
0.209539 | + | 0.977800i | \(0.432804\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.73205 | − | 0.732051i | 0.0932164 | − | 0.0249773i | −0.211909 | − | 0.977289i | \(-0.567968\pi\) |
0.305126 | + | 0.952312i | \(0.401302\pi\) | |||||||
\(860\) | −8.00000 | −0.272798 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 8.00000 | − | 8.00000i | 0.272481 | − | 0.272481i | ||||
\(863\) | −7.00000 | + | 12.1244i | −0.238283 | + | 0.412718i | −0.960222 | − | 0.279239i | \(-0.909918\pi\) |
0.721939 | + | 0.691957i | \(0.243251\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 2.19615 | + | 8.19615i | 0.0746283 | + | 0.278517i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 10.0000 | + | 10.0000i | 0.339227 | + | 0.339227i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 6.00000 | + | 10.3923i | 0.203186 | + | 0.351928i | ||||
\(873\) | 5.19615 | + | 3.00000i | 0.175863 | + | 0.101535i | ||||
\(874\) | 24.0000 | 0.811812 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.09808 | + | 4.09808i | 0.0370794 | + | 0.138382i | 0.981984 | − | 0.188963i | \(-0.0605126\pi\) |
−0.944905 | + | 0.327345i | \(0.893846\pi\) | |||||||
\(878\) | −5.85641 | + | 21.8564i | −0.197644 | + | 0.737618i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 13.8564 | + | 8.00000i | 0.467099 | + | 0.269680i | ||||
\(881\) | −18.0000 | −0.606435 | −0.303218 | − | 0.952921i | \(-0.598061\pi\) | ||||
−0.303218 | + | 0.952921i | \(0.598061\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −25.0000 | + | 25.0000i | −0.841317 | + | 0.841317i | −0.989030 | − | 0.147713i | \(-0.952809\pi\) |
0.147713 | + | 0.989030i | \(0.452809\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.00000 | − | 1.73205i | −0.0335957 | − | 0.0581894i | ||||
\(887\) | −10.3923 | − | 6.00000i | −0.348939 | − | 0.201460i | 0.315279 | − | 0.948999i | \(-0.397902\pi\) |
−0.664218 | + | 0.747539i | \(0.731235\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 56.0000i | 1.87712i | ||||||||
\(891\) | 12.2942 | − | 3.29423i | 0.411872 | − | 0.110361i | ||||
\(892\) | −6.92820 | + | 4.00000i | −0.231973 | + | 0.133930i | ||||
\(893\) | 32.7846 | + | 8.78461i | 1.09710 | + | 0.293966i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −12.0000 | −0.401116 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 10.9808 | + | 40.9808i | 0.366433 | + | 1.36755i | ||||
\(899\) | 76.4974 | + | 20.4974i | 2.55133 | + | 0.683627i | ||||
\(900\) | 15.5885 | − | 9.00000i | 0.519615 | − | 0.300000i | ||||
\(901\) | −2.73205 | + | 0.732051i | −0.0910178 | + | 0.0243881i | ||||
\(902\) | − | 20.0000i | − | 0.665927i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 8.00000 | + | 8.00000i | 0.266076 | + | 0.266076i | ||||
\(905\) | 13.8564 | + | 8.00000i | 0.460603 | + | 0.265929i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.49038 | − | 20.4904i | 0.182305 | − | 0.680372i | −0.812886 | − | 0.582422i | \(-0.802105\pi\) |
0.995191 | − | 0.0979495i | \(-0.0312284\pi\) | |||||||
\(908\) | −5.46410 | + | 1.46410i | −0.181333 | + | 0.0485879i | ||||
\(909\) | −18.0000 | + | 18.0000i | −0.597022 | + | 0.597022i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −48.0000 | −1.59031 | −0.795155 | − | 0.606406i | \(-0.792611\pi\) | ||||
−0.795155 | + | 0.606406i | \(0.792611\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 10.0000 | + | 17.3205i | 0.330952 | + | 0.573225i | ||||
\(914\) | −8.05256 | + | 30.0526i | −0.266355 | + | 0.994050i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 16.0000 | − | 16.0000i | 0.528655 | − | 0.528655i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20.7846 | + | 12.0000i | 0.685621 | + | 0.395843i | 0.801970 | − | 0.597365i | \(-0.203786\pi\) |
−0.116348 | + | 0.993208i | \(0.537119\pi\) | |||||||
\(920\) | −24.0000 | − | 41.5692i | −0.791257 | − | 1.37050i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −27.7128 | − | 16.0000i | −0.912673 | − | 0.526932i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 15.0000 | − | 15.0000i | 0.493197 | − | 0.493197i | ||||
\(926\) | −5.12436 | − | 19.1244i | −0.168397 | − | 0.628465i | ||||
\(927\) | 6.00000 | + | 10.3923i | 0.197066 | + | 0.341328i | ||||
\(928\) | −48.4974 | + | 28.0000i | −1.59201 | + | 0.919145i | ||||
\(929\) | 25.0000 | − | 43.3013i | 0.820223 | − | 1.42067i | −0.0852924 | − | 0.996356i | \(-0.527182\pi\) |
0.905516 | − | 0.424313i | \(-0.139484\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −32.0000 | −1.04819 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 31.1769 | − | 18.0000i | 1.02014 | − | 0.588978i | ||||
\(935\) | −6.92820 | + | 4.00000i | −0.226576 | + | 0.130814i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 58.0000i | − | 1.89478i | −0.320085 | − | 0.947389i | \(-0.603712\pi\) | ||
0.320085 | − | 0.947389i | \(-0.396288\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −17.5692 | − | 65.5692i | −0.573045 | − | 2.13863i | ||||
\(941\) | −35.5167 | − | 9.51666i | −1.15781 | − | 0.310234i | −0.371719 | − | 0.928345i | \(-0.621232\pi\) |
−0.786091 | + | 0.618111i | \(0.787898\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −30.0000 | + | 51.9615i | −0.976934 | + | 1.69210i | ||||
\(944\) | −32.0000 | − | 32.0000i | −1.04151 | − | 1.04151i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.00000 | + | 2.00000i | 0.0650256 | + | 0.0650256i | ||||
\(947\) | 12.0788 | + | 45.0788i | 0.392510 | + | 1.46487i | 0.825981 | + | 0.563698i | \(0.190622\pi\) |
−0.433471 | + | 0.901167i | \(0.642711\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 6.00000 | − | 10.3923i | 0.194666 | − | 0.337171i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 16.0000i | − | 0.518291i | −0.965838 | − | 0.259145i | \(-0.916559\pi\) | ||
0.965838 | − | 0.259145i | \(-0.0834409\pi\) | |||||||
\(954\) | −5.19615 | − | 3.00000i | −0.168232 | − | 0.0971286i | ||||
\(955\) | −13.1769 | + | 49.1769i | −0.426395 | + | 1.59133i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 20.0000 | − | 20.0000i | 0.646171 | − | 0.646171i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16.5000 | + | 28.5788i | −0.532258 | + | 0.921898i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 20.4904 | + | 5.49038i | 0.660293 | + | 0.176925i | ||||
\(964\) | 38.1051 | + | 22.0000i | 1.22728 | + | 0.708572i | ||||
\(965\) | −32.0000 | − | 32.0000i | −1.03012 | − | 1.03012i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.00000i | 0.0643157i | 0.999483 | + | 0.0321578i | \(0.0102379\pi\) | ||||
−0.999483 | + | 0.0321578i | \(0.989762\pi\) | |||||||
\(968\) | 6.58846 | + | 24.5885i | 0.211761 | + | 0.790303i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −4.00000 | − | 6.92820i | −0.128432 | − | 0.222451i | ||||
\(971\) | 5.46410 | − | 1.46410i | 0.175351 | − | 0.0469853i | −0.170075 | − | 0.985431i | \(-0.554401\pi\) |
0.345426 | + | 0.938446i | \(0.387734\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −22.0000 | − | 22.0000i | −0.704925 | − | 0.704925i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 32.7846 | + | 8.78461i | 1.04941 | + | 0.281189i | ||||
\(977\) | −19.0000 | − | 32.9090i | −0.607864 | − | 1.05285i | −0.991592 | − | 0.129405i | \(-0.958693\pi\) |
0.383728 | − | 0.923446i | \(-0.374640\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 14.0000 | − | 14.0000i | 0.447442 | − | 0.447442i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.00000 | − | 9.00000i | −0.287348 | − | 0.287348i | ||||
\(982\) | −19.0000 | + | 32.9090i | −0.606314 | + | 1.05017i | ||||
\(983\) | 38.1051 | − | 22.0000i | 1.21536 | − | 0.701691i | 0.251442 | − | 0.967872i | \(-0.419095\pi\) |
0.963923 | + | 0.266181i | \(0.0857620\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −17.3205 | − | 10.0000i | −0.551877 | − | 0.318626i | ||||
\(986\) | − | 28.0000i | − | 0.891702i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.19615 | − | 8.19615i | −0.0698336 | − | 0.260622i | ||||
\(990\) | −16.3923 | − | 4.39230i | −0.520982 | − | 0.139597i | ||||
\(991\) | −11.0000 | − | 19.0526i | −0.349427 | − | 0.605224i | 0.636721 | − | 0.771094i | \(-0.280290\pi\) |
−0.986148 | + | 0.165870i | \(0.946957\pi\) | |||||||
\(992\) | −11.7128 | − | 43.7128i | −0.371882 | − | 1.38788i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 48.0000 | − | 48.0000i | 1.52170 | − | 1.52170i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −10.9808 | + | 40.9808i | −0.347764 | + | 1.29787i | 0.541585 | + | 0.840646i | \(0.317824\pi\) |
−0.889350 | + | 0.457228i | \(0.848842\pi\) | |||||||
\(998\) | −39.8372 | + | 23.0000i | −1.26102 | + | 0.728052i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 784.2.x.d.373.1 | 4 | ||
7.2 | even | 3 | 112.2.m.b.85.1 | yes | 2 | ||
7.3 | odd | 6 | 784.2.x.e.165.1 | 4 | |||
7.4 | even | 3 | inner | 784.2.x.d.165.1 | 4 | ||
7.5 | odd | 6 | 784.2.m.a.197.1 | 2 | |||
7.6 | odd | 2 | 784.2.x.e.373.1 | 4 | |||
16.13 | even | 4 | inner | 784.2.x.d.765.1 | 4 | ||
28.23 | odd | 6 | 448.2.m.a.113.1 | 2 | |||
56.37 | even | 6 | 896.2.m.b.225.1 | 2 | |||
56.51 | odd | 6 | 896.2.m.c.225.1 | 2 | |||
112.13 | odd | 4 | 784.2.x.e.765.1 | 4 | |||
112.37 | even | 12 | 896.2.m.b.673.1 | 2 | |||
112.45 | odd | 12 | 784.2.x.e.557.1 | 4 | |||
112.51 | odd | 12 | 448.2.m.a.337.1 | 2 | |||
112.61 | odd | 12 | 784.2.m.a.589.1 | 2 | |||
112.93 | even | 12 | 112.2.m.b.29.1 | ✓ | 2 | ||
112.107 | odd | 12 | 896.2.m.c.673.1 | 2 | |||
112.109 | even | 12 | inner | 784.2.x.d.557.1 | 4 | ||
224.51 | odd | 24 | 7168.2.a.k.1.2 | 2 | |||
224.93 | even | 24 | 7168.2.a.b.1.1 | 2 | |||
224.163 | odd | 24 | 7168.2.a.k.1.1 | 2 | |||
224.205 | even | 24 | 7168.2.a.b.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
112.2.m.b.29.1 | ✓ | 2 | 112.93 | even | 12 | ||
112.2.m.b.85.1 | yes | 2 | 7.2 | even | 3 | ||
448.2.m.a.113.1 | 2 | 28.23 | odd | 6 | |||
448.2.m.a.337.1 | 2 | 112.51 | odd | 12 | |||
784.2.m.a.197.1 | 2 | 7.5 | odd | 6 | |||
784.2.m.a.589.1 | 2 | 112.61 | odd | 12 | |||
784.2.x.d.165.1 | 4 | 7.4 | even | 3 | inner | ||
784.2.x.d.373.1 | 4 | 1.1 | even | 1 | trivial | ||
784.2.x.d.557.1 | 4 | 112.109 | even | 12 | inner | ||
784.2.x.d.765.1 | 4 | 16.13 | even | 4 | inner | ||
784.2.x.e.165.1 | 4 | 7.3 | odd | 6 | |||
784.2.x.e.373.1 | 4 | 7.6 | odd | 2 | |||
784.2.x.e.557.1 | 4 | 112.45 | odd | 12 | |||
784.2.x.e.765.1 | 4 | 112.13 | odd | 4 | |||
896.2.m.b.225.1 | 2 | 56.37 | even | 6 | |||
896.2.m.b.673.1 | 2 | 112.37 | even | 12 | |||
896.2.m.c.225.1 | 2 | 56.51 | odd | 6 | |||
896.2.m.c.673.1 | 2 | 112.107 | odd | 12 | |||
7168.2.a.b.1.1 | 2 | 224.93 | even | 24 | |||
7168.2.a.b.1.2 | 2 | 224.205 | even | 24 | |||
7168.2.a.k.1.1 | 2 | 224.163 | odd | 24 | |||
7168.2.a.k.1.2 | 2 | 224.51 | odd | 24 |