Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [360,2,Mod(121,360)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(360, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("360.121");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 360.q (of order \(3\), degree \(2\), 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: | \(2.87461447277\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 121.1 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 360.121 |
Dual form | 360.2.q.b.241.1 |
$q$-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 \(\left(\mathbb{Z}/360\mathbb{Z}\right)^\times\).
\(n\) | \(181\) | \(217\) | \(271\) | \(281\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | 0 | ||||||||
\(3\) | −0.866025 | + | 1.50000i | −0.500000 | + | 0.866025i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.500000 | − | 0.866025i | 0.223607 | − | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.86603 | − | 3.23205i | −0.705291 | − | 1.22160i | −0.966586 | − | 0.256341i | \(-0.917483\pi\) |
0.261295 | − | 0.965259i | \(-0.415850\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.50000 | − | 2.59808i | −0.500000 | − | 0.866025i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.73205 | − | 4.73205i | −0.823744 | − | 1.42677i | −0.902875 | − | 0.429903i | \(-0.858548\pi\) |
0.0791309 | − | 0.996864i | \(-0.474785\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.732051 | + | 1.26795i | −0.203034 | + | 0.351666i | −0.949505 | − | 0.313753i | \(-0.898414\pi\) |
0.746470 | + | 0.665419i | \(0.231747\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.866025 | + | 1.50000i | 0.223607 | + | 0.387298i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.46410 | 1.81031 | 0.905155 | − | 0.425081i | \(-0.139754\pi\) | ||||
0.905155 | + | 0.425081i | \(0.139754\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.00000 | −0.458831 | −0.229416 | − | 0.973329i | \(-0.573682\pi\) | ||||
−0.229416 | + | 0.973329i | \(0.573682\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 6.46410 | 1.41058 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.133975 | + | 0.232051i | −0.0279356 | + | 0.0483859i | −0.879655 | − | 0.475612i | \(-0.842227\pi\) |
0.851720 | + | 0.523998i | \(0.175560\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.19615 | 1.00000 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.23205 | − | 7.33013i | −0.785872 | − | 1.36117i | −0.928477 | − | 0.371391i | \(-0.878881\pi\) |
0.142605 | − | 0.989780i | \(-0.454452\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.00000 | − | 1.73205i | 0.179605 | − | 0.311086i | −0.762140 | − | 0.647412i | \(-0.775851\pi\) |
0.941745 | + | 0.336327i | \(0.109185\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 9.46410 | 1.64749 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.73205 | −0.630832 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.3923 | −1.70848 | −0.854242 | − | 0.519875i | \(-0.825978\pi\) | ||||
−0.854242 | + | 0.519875i | \(0.825978\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.26795 | − | 2.19615i | −0.203034 | − | 0.351666i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.96410 | − | 3.40192i | 0.306741 | − | 0.531291i | −0.670906 | − | 0.741542i | \(-0.734095\pi\) |
0.977647 | + | 0.210251i | \(0.0674281\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.73205 | + | 9.92820i | 0.874130 | + | 1.51404i | 0.857687 | + | 0.514172i | \(0.171901\pi\) |
0.0164424 | + | 0.999865i | \(0.494766\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.00000 | −0.447214 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.86603 | − | 3.23205i | −0.272188 | − | 0.471443i | 0.697234 | − | 0.716844i | \(-0.254414\pi\) |
−0.969422 | + | 0.245401i | \(0.921081\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.46410 | + | 6.00000i | −0.494872 | + | 0.857143i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.46410 | + | 11.1962i | −0.905155 | + | 1.56777i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.00000 | 0.824163 | 0.412082 | − | 0.911147i | \(-0.364802\pi\) | ||||
0.412082 | + | 0.911147i | \(0.364802\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.46410 | −0.736779 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.73205 | − | 3.00000i | 0.229416 | − | 0.397360i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.19615 | − | 5.53590i | 0.416104 | − | 0.720713i | −0.579440 | − | 0.815015i | \(-0.696729\pi\) |
0.995544 | + | 0.0943023i | \(0.0300620\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.767949 | + | 1.33013i | 0.0983258 | + | 0.170305i | 0.910992 | − | 0.412424i | \(-0.135318\pi\) |
−0.812666 | + | 0.582730i | \(0.801985\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −5.59808 | + | 9.69615i | −0.705291 | + | 1.22160i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.732051 | + | 1.26795i | 0.0907997 | + | 0.157270i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.86603 | + | 8.42820i | −0.594480 | + | 1.02967i | 0.399140 | + | 0.916890i | \(0.369309\pi\) |
−0.993620 | + | 0.112779i | \(0.964025\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.232051 | − | 0.401924i | −0.0279356 | − | 0.0483859i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.53590 | 0.300956 | 0.150478 | − | 0.988613i | \(-0.451919\pi\) | ||||
0.150478 | + | 0.988613i | \(0.451919\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.92820 | −0.810885 | −0.405442 | − | 0.914121i | \(-0.632883\pi\) | ||||
−0.405442 | + | 0.914121i | \(0.632883\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.73205 | 0.200000 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −10.1962 | + | 17.6603i | −1.16196 | + | 2.01257i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.26795 | − | 7.39230i | −0.480182 | − | 0.831699i | 0.519560 | − | 0.854434i | \(-0.326096\pi\) |
−0.999742 | + | 0.0227349i | \(0.992763\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | + | 7.79423i | −0.500000 | + | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.40192 | + | 2.42820i | 0.153881 | + | 0.266530i | 0.932651 | − | 0.360780i | \(-0.117489\pi\) |
−0.778770 | + | 0.627310i | \(0.784156\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.73205 | − | 6.46410i | 0.404798 | − | 0.701130i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 14.6603 | 1.57174 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.92820 | 0.416389 | 0.208194 | − | 0.978087i | \(-0.433241\pi\) | ||||
0.208194 | + | 0.978087i | \(0.433241\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.46410 | 0.572793 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.73205 | + | 3.00000i | 0.179605 | + | 0.311086i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.00000 | + | 1.73205i | −0.102598 | + | 0.177705i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.46410 | − | 4.26795i | −0.250192 | − | 0.433345i | 0.713387 | − | 0.700770i | \(-0.247160\pi\) |
−0.963578 | + | 0.267426i | \(0.913827\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −8.19615 | + | 14.1962i | −0.823744 | + | 1.42677i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.46410 | + | 11.1962i | 0.643202 | + | 1.11406i | 0.984714 | + | 0.174181i | \(0.0557278\pi\) |
−0.341511 | + | 0.939878i | \(0.610939\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.19615 | − | 5.53590i | 0.314926 | − | 0.545468i | −0.664496 | − | 0.747292i | \(-0.731354\pi\) |
0.979422 | + | 0.201824i | \(0.0646869\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.23205 | − | 5.59808i | 0.315416 | − | 0.546316i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.19615 | −0.502331 | −0.251166 | − | 0.967944i | \(-0.580814\pi\) | ||||
−0.251166 | + | 0.967944i | \(0.580814\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.39230 | 0.324924 | 0.162462 | − | 0.986715i | \(-0.448057\pi\) | ||||
0.162462 | + | 0.986715i | \(0.448057\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.00000 | − | 15.5885i | 0.854242 | − | 1.47959i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.92820 | − | 12.0000i | 0.651751 | − | 1.12887i | −0.330947 | − | 0.943649i | \(-0.607368\pi\) |
0.982698 | − | 0.185216i | \(-0.0592984\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.133975 | + | 0.232051i | 0.0124932 | + | 0.0216388i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.39230 | 0.406069 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −13.9282 | − | 24.1244i | −1.27680 | − | 2.21148i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.42820 | + | 16.3301i | −0.857109 | + | 1.48456i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.40192 | + | 5.89230i | 0.306741 | + | 0.531291i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.7321 | 1.75094 | 0.875468 | − | 0.483276i | \(-0.160553\pi\) | ||||
0.875468 | + | 0.483276i | \(0.160553\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −19.8564 | −1.74826 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.73205 | + | 3.00000i | −0.151330 | + | 0.262111i | −0.931717 | − | 0.363186i | \(-0.881689\pi\) |
0.780387 | + | 0.625297i | \(0.215022\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.73205 | + | 6.46410i | 0.323610 | + | 0.560509i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.59808 | − | 4.50000i | 0.223607 | − | 0.387298i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.92820 | + | 5.07180i | 0.250173 | + | 0.433313i | 0.963573 | − | 0.267444i | \(-0.0861791\pi\) |
−0.713400 | + | 0.700757i | \(0.752846\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.46410 | 0.544376 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.00000 | 0.668994 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.46410 | −0.702905 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.00000 | − | 10.3923i | −0.494872 | − | 0.857143i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.23205 | + | 3.86603i | −0.182857 | + | 0.316717i | −0.942852 | − | 0.333211i | \(-0.891868\pi\) |
0.759995 | + | 0.649928i | \(0.225201\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.732051 | + | 1.26795i | 0.0595734 | + | 0.103184i | 0.894274 | − | 0.447520i | \(-0.147693\pi\) |
−0.834701 | + | 0.550704i | \(0.814359\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −11.1962 | − | 19.3923i | −0.905155 | − | 1.56777i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.00000 | − | 1.73205i | −0.0803219 | − | 0.139122i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.46410 | − | 7.73205i | 0.356274 | − | 0.617085i | −0.631061 | − | 0.775733i | \(-0.717380\pi\) |
0.987335 | + | 0.158648i | \(0.0507136\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.19615 | + | 9.00000i | −0.412082 | + | 0.713746i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.00000 | 0.0788110 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 21.3205 | 1.66995 | 0.834976 | − | 0.550287i | \(-0.185482\pi\) | ||||
0.834976 | + | 0.550287i | \(0.185482\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.73205 | − | 8.19615i | 0.368390 | − | 0.638070i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.79423 | + | 8.30385i | −0.370989 | + | 0.642571i | −0.989718 | − | 0.143033i | \(-0.954314\pi\) |
0.618729 | + | 0.785604i | \(0.287648\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.42820 | + | 9.40192i | 0.417554 | + | 0.723225i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.00000 | + | 5.19615i | 0.229416 | + | 0.397360i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −11.4641 | − | 19.8564i | −0.871600 | − | 1.50965i | −0.860342 | − | 0.509718i | \(-0.829750\pi\) |
−0.0112580 | − | 0.999937i | \(-0.503584\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.86603 | + | 3.23205i | −0.141058 | + | 0.244320i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.53590 | + | 9.58846i | 0.416104 | + | 0.720713i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.53590 | 0.488516 | 0.244258 | − | 0.969710i | \(-0.421456\pi\) | ||||
0.244258 | + | 0.969710i | \(0.421456\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.4641 | −1.22377 | −0.611884 | − | 0.790948i | \(-0.709588\pi\) | ||||
−0.611884 | + | 0.790948i | \(0.709588\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.66025 | −0.196652 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.19615 | + | 9.00000i | −0.382029 | + | 0.661693i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −20.3923 | − | 35.3205i | −1.49123 | − | 2.58289i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −9.69615 | − | 16.7942i | −0.705291 | − | 1.22160i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.53590 | − | 2.66025i | −0.111134 | − | 0.192489i | 0.805094 | − | 0.593147i | \(-0.202115\pi\) |
−0.916228 | + | 0.400658i | \(0.868782\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.26795 | − | 9.12436i | 0.379195 | − | 0.656785i | −0.611750 | − | 0.791051i | \(-0.709534\pi\) |
0.990945 | + | 0.134266i | \(0.0428675\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.53590 | −0.181599 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.07180 | 0.0763624 | 0.0381812 | − | 0.999271i | \(-0.487844\pi\) | ||||
0.0381812 | + | 0.999271i | \(0.487844\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.9282 | 1.48356 | 0.741780 | − | 0.670643i | \(-0.233982\pi\) | ||||
0.741780 | + | 0.670643i | \(0.233982\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.42820 | − | 14.5981i | −0.594480 | − | 1.02967i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −15.7942 | + | 27.3564i | −1.10854 | + | 1.92004i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.96410 | − | 3.40192i | −0.137179 | − | 0.237601i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.803848 | 0.0558713 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.46410 | + | 9.46410i | 0.377960 | + | 0.654646i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.1962 | − | 17.6603i | 0.701932 | − | 1.21578i | −0.265855 | − | 0.964013i | \(-0.585654\pi\) |
0.967787 | − | 0.251769i | \(-0.0810123\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.19615 | + | 3.80385i | −0.150478 | + | 0.260635i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 11.4641 | 0.781845 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.46410 | −0.506696 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.00000 | − | 10.3923i | 0.405442 | − | 0.702247i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.46410 | + | 9.46410i | −0.367555 | + | 0.636624i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.66987 | − | 4.62436i | −0.178788 | − | 0.309670i | 0.762678 | − | 0.646779i | \(-0.223884\pi\) |
−0.941466 | + | 0.337109i | \(0.890551\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.50000 | + | 2.59808i | −0.100000 | + | 0.173205i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.1244 | + | 21.0000i | 0.804722 | + | 1.39382i | 0.916479 | + | 0.400083i | \(0.131019\pi\) |
−0.111757 | + | 0.993736i | \(0.535648\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.6244 | − | 20.1340i | 0.768159 | − | 1.33049i | −0.170401 | − | 0.985375i | \(-0.554506\pi\) |
0.938560 | − | 0.345116i | \(-0.112160\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −17.6603 | − | 30.5885i | −1.16196 | − | 2.01257i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.3923 | 0.680823 | 0.340411 | − | 0.940277i | \(-0.389434\pi\) | ||||
0.340411 | + | 0.940277i | \(0.389434\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.73205 | −0.243452 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 14.7846 | 0.960364 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.3923 | − | 18.0000i | 0.672222 | − | 1.16432i | −0.305050 | − | 0.952336i | \(-0.598673\pi\) |
0.977273 | − | 0.211987i | \(-0.0679934\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.96410 | + | 17.2583i | 0.641844 | + | 1.11171i | 0.985021 | + | 0.172436i | \(0.0551638\pi\) |
−0.343177 | + | 0.939271i | \(0.611503\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −7.79423 | − | 13.5000i | −0.500000 | − | 0.866025i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.46410 | + | 6.00000i | 0.221313 | + | 0.383326i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.46410 | − | 2.53590i | 0.0931586 | − | 0.161355i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.85641 | −0.307762 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 19.8564 | 1.25333 | 0.626663 | − | 0.779291i | \(-0.284420\pi\) | ||||
0.626663 | + | 0.779291i | \(0.284420\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.46410 | 0.0920473 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.46410 | + | 11.1962i | 0.404798 | + | 0.701130i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.46410 | + | 11.1962i | −0.403220 | + | 0.698397i | −0.994112 | − | 0.108353i | \(-0.965442\pi\) |
0.590893 | + | 0.806750i | \(0.298776\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 19.3923 | + | 33.5885i | 1.20498 | + | 2.08709i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −12.6962 | + | 21.9904i | −0.785872 | + | 1.36117i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.803848 | − | 1.39230i | −0.0495674 | − | 0.0858532i | 0.840177 | − | 0.542312i | \(-0.182451\pi\) |
−0.889745 | + | 0.456459i | \(0.849118\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.00000 | − | 5.19615i | 0.184289 | − | 0.319197i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.40192 | + | 5.89230i | −0.208194 | + | 0.360603i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −9.39230 | −0.572659 | −0.286329 | − | 0.958131i | \(-0.592435\pi\) | ||||
−0.286329 | + | 0.958131i | \(0.592435\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.85641 | 0.477243 | 0.238621 | − | 0.971113i | \(-0.423305\pi\) | ||||
0.238621 | + | 0.971113i | \(0.423305\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.73205 | + | 8.19615i | −0.286397 | + | 0.496054i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.73205 | + | 4.73205i | −0.164749 | + | 0.285353i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.19615 | − | 5.53590i | −0.192038 | − | 0.332620i | 0.753887 | − | 0.657004i | \(-0.228176\pi\) |
−0.945926 | + | 0.324384i | \(0.894843\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.00000 | −0.359211 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.42820 | − | 11.1340i | −0.383474 | − | 0.664197i | 0.608082 | − | 0.793874i | \(-0.291939\pi\) |
−0.991556 | + | 0.129677i | \(0.958606\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.13397 | + | 15.8205i | −0.542958 | + | 0.940432i | 0.455774 | + | 0.890096i | \(0.349363\pi\) |
−0.998732 | + | 0.0503360i | \(0.983971\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.73205 | − | 3.00000i | −0.102598 | − | 0.177705i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −14.6603 | −0.865367 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 38.7128 | 2.27722 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.53590 | 0.500383 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.267949 | − | 0.464102i | 0.0156538 | − | 0.0271131i | −0.858092 | − | 0.513495i | \(-0.828350\pi\) |
0.873746 | + | 0.486382i | \(0.161684\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.19615 | − | 5.53590i | −0.186087 | − | 0.322312i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −14.1962 | − | 24.5885i | −0.823744 | − | 1.42677i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.196152 | − | 0.339746i | −0.0113438 | − | 0.0196480i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 21.3923 | − | 37.0526i | 1.23303 | − | 2.13567i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −22.3923 | −1.28640 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.53590 | 0.0879453 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −20.1244 | −1.14856 | −0.574279 | − | 0.818660i | \(-0.694717\pi\) | ||||
−0.574279 | + | 0.818660i | \(0.694717\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.53590 | + | 9.58846i | 0.314926 | + | 0.545468i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.46410 | + | 14.6603i | −0.479955 | + | 0.831307i | −0.999736 | − | 0.0229931i | \(-0.992680\pi\) |
0.519780 | + | 0.854300i | \(0.326014\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.19615 | + | 7.26795i | 0.237181 | + | 0.410809i | 0.959904 | − | 0.280328i | \(-0.0904434\pi\) |
−0.722724 | + | 0.691137i | \(0.757110\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5.59808 | + | 9.69615i | 0.315416 | + | 0.546316i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.73205 | − | 8.19615i | −0.265778 | − | 0.460342i | 0.701989 | − | 0.712188i | \(-0.252296\pi\) |
−0.967767 | + | 0.251846i | \(0.918962\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −23.1244 | + | 40.0526i | −1.29472 | + | 2.24251i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.50000 | − | 7.79423i | 0.251166 | − | 0.435031i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −14.9282 | −0.830627 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.46410 | 0.0812137 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.93782 | + | 5.08846i | −0.162462 | + | 0.281392i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.96410 | + | 12.0622i | −0.383943 | + | 0.665009i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.73205 | − | 3.00000i | −0.0952021 | − | 0.164895i | 0.814491 | − | 0.580176i | \(-0.197016\pi\) |
−0.909693 | + | 0.415282i | \(0.863683\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 15.5885 | + | 27.0000i | 0.854242 | + | 1.47959i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.86603 | + | 8.42820i | 0.265859 | + | 0.460482i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.4641 | + | 19.8564i | −0.624489 | + | 1.08165i | 0.364150 | + | 0.931340i | \(0.381360\pi\) |
−0.988639 | + | 0.150307i | \(0.951974\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 12.0000 | + | 20.7846i | 0.651751 | + | 1.12887i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10.9282 | −0.591795 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.267949 | −0.0144679 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.464102 | −0.0249864 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.19615 | + | 2.07180i | −0.0642128 | + | 0.111220i | −0.896345 | − | 0.443358i | \(-0.853787\pi\) |
0.832132 | + | 0.554578i | \(0.187120\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.23205 | + | 5.59808i | 0.173008 | + | 0.299658i | 0.939470 | − | 0.342631i | \(-0.111318\pi\) |
−0.766462 | + | 0.642289i | \(0.777985\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.80385 | + | 6.58846i | −0.203034 | + | 0.351666i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.92820 | − | 5.07180i | −0.155853 | − | 0.269945i | 0.777517 | − | 0.628862i | \(-0.216479\pi\) |
−0.933369 | + | 0.358918i | \(0.883146\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.26795 | − | 2.19615i | 0.0672958 | − | 0.116560i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 48.2487 | 2.55359 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0.928203 | 0.0489887 | 0.0244943 | − | 0.999700i | \(-0.492202\pi\) | ||||
0.0244943 | + | 0.999700i | \(0.492202\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | −0.789474 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −16.3301 | − | 28.2846i | −0.857109 | − | 1.48456i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.46410 | + | 6.00000i | −0.181319 | + | 0.314054i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.19615 | − | 5.53590i | −0.166838 | − | 0.288972i | 0.770469 | − | 0.637478i | \(-0.220022\pi\) |
−0.937306 | + | 0.348506i | \(0.886689\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −11.7846 | −0.613482 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −11.1962 | − | 19.3923i | −0.581275 | − | 1.00680i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.46410 | + | 4.26795i | −0.127586 | + | 0.220986i | −0.922741 | − | 0.385421i | \(-0.874056\pi\) |
0.795155 | + | 0.606407i | \(0.207390\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.866025 | − | 1.50000i | 0.0447214 | − | 0.0774597i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 12.3923 | 0.638236 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −27.1769 | −1.39598 | −0.697992 | − | 0.716105i | \(-0.745923\pi\) | ||||
−0.697992 | + | 0.716105i | \(0.745923\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −17.0885 | + | 29.5981i | −0.875468 | + | 1.51636i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.73205 | − | 3.00000i | 0.0885037 | − | 0.153293i | −0.818375 | − | 0.574684i | \(-0.805125\pi\) |
0.906879 | + | 0.421392i | \(0.138458\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 10.1962 | + | 17.6603i | 0.519644 | + | 0.900050i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 17.1962 | − | 29.7846i | 0.874130 | − | 1.51404i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 15.2321 | + | 26.3827i | 0.772296 | + | 1.33766i | 0.936302 | + | 0.351196i | \(0.114225\pi\) |
−0.164006 | + | 0.986459i | \(0.552442\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.00000 | + | 1.73205i | −0.0505722 | + | 0.0875936i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.00000 | − | 5.19615i | −0.151330 | − | 0.262111i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −8.53590 | −0.429488 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.0000 | 0.501886 | 0.250943 | − | 0.968002i | \(-0.419259\pi\) | ||||
0.250943 | + | 0.968002i | \(0.419259\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −12.9282 | −0.647220 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.3923 | − | 23.1962i | 0.668780 | − | 1.15836i | −0.309466 | − | 0.950911i | \(-0.600150\pi\) |
0.978246 | − | 0.207450i | \(-0.0665164\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.46410 | + | 2.53590i | 0.0729321 | + | 0.126322i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4.50000 | + | 7.79423i | 0.223607 | + | 0.387298i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 28.3923 | + | 49.1769i | 1.40735 | + | 2.43761i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.46410 | − | 7.73205i | 0.220736 | − | 0.382325i | −0.734296 | − | 0.678829i | \(-0.762488\pi\) |
0.955032 | + | 0.296504i | \(0.0958209\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −10.1436 | −0.500347 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −23.8564 | −1.17390 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.80385 | 0.137635 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9.12436 | − | 15.8038i | 0.445754 | − | 0.772068i | −0.552350 | − | 0.833612i | \(-0.686269\pi\) |
0.998104 | + | 0.0615435i | \(0.0196023\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.5359 | + | 19.9808i | 0.562225 | + | 0.973803i | 0.997302 | + | 0.0734093i | \(0.0233880\pi\) |
−0.435077 | + | 0.900393i | \(0.643279\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.59808 | + | 9.69615i | −0.272188 | + | 0.471443i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.73205 | − | 6.46410i | −0.181031 | − | 0.313555i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.86603 | − | 4.96410i | 0.138697 | − | 0.240230i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.92820 | + | 12.0000i | −0.334497 | + | 0.579365i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11.4641 | −0.552206 | −0.276103 | − | 0.961128i | \(-0.589043\pi\) | ||||
−0.276103 | + | 0.961128i | \(0.589043\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −19.4641 | −0.935385 | −0.467693 | − | 0.883891i | \(-0.654915\pi\) | ||||
−0.467693 | + | 0.883891i | \(0.654915\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7.33013 | − | 12.6962i | 0.351453 | − | 0.608734i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.267949 | − | 0.464102i | 0.0128177 | − | 0.0222010i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −17.4641 | − | 30.2487i | −0.833516 | − | 1.44369i | −0.895233 | − | 0.445599i | \(-0.852991\pi\) |
0.0617168 | − | 0.998094i | \(-0.480342\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 20.7846 | 0.989743 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.25833 | + | 9.10770i | 0.249831 | + | 0.432720i | 0.963479 | − | 0.267785i | \(-0.0862917\pi\) |
−0.713648 | + | 0.700505i | \(0.752958\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.96410 | − | 3.40192i | 0.0931073 | − | 0.161267i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.86603 | − | 6.69615i | −0.182857 | − | 0.316717i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 31.8564 | 1.50340 | 0.751698 | − | 0.659507i | \(-0.229235\pi\) | ||||
0.751698 | + | 0.659507i | \(0.229235\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −21.4641 | −1.01071 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.53590 | −0.119147 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.73205 | − | 4.73205i | 0.128081 | − | 0.221842i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13.1962 | − | 22.8564i | −0.617290 | − | 1.06918i | −0.989978 | − | 0.141221i | \(-0.954897\pi\) |
0.372688 | − | 0.927957i | \(-0.378436\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 38.7846 | 1.81031 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.6962 | − | 21.9904i | −0.591319 | − | 1.02419i | −0.994055 | − | 0.108878i | \(-0.965274\pi\) |
0.402736 | − | 0.915316i | \(-0.368059\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.73205 | + | 3.00000i | −0.0804952 | + | 0.139422i | −0.903463 | − | 0.428667i | \(-0.858984\pi\) |
0.822968 | + | 0.568088i | \(0.192317\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.46410 | 0.160644 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −9.60770 | −0.444591 | −0.222296 | − | 0.974979i | \(-0.571355\pi\) | ||||
−0.222296 | + | 0.974979i | \(0.571355\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 36.3205 | 1.67713 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.73205 | + | 13.3923i | 0.356274 | + | 0.617085i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 31.3205 | − | 54.2487i | 1.44012 | − | 2.49436i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.00000 | + | 1.73205i | 0.0458831 | + | 0.0794719i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −9.00000 | − | 15.5885i | −0.412082 | − | 0.713746i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.19615 | − | 5.53590i | −0.146036 | − | 0.252942i | 0.783723 | − | 0.621110i | \(-0.213318\pi\) |
−0.929759 | + | 0.368169i | \(0.879985\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.60770 | − | 13.1769i | 0.346881 | − | 0.600816i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.866025 | + | 1.50000i | −0.0394055 | + | 0.0682524i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.92820 | −0.223778 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.24871 | −0.373785 | −0.186892 | − | 0.982380i | \(-0.559842\pi\) | ||||
−0.186892 | + | 0.982380i | \(0.559842\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −18.4641 | + | 31.9808i | −0.834976 | + | 1.44622i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.928203 | + | 1.60770i | −0.0418892 | + | 0.0725543i | −0.886210 | − | 0.463284i | \(-0.846671\pi\) |
0.844321 | + | 0.535838i | \(0.180004\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −31.5885 | − | 54.7128i | −1.42267 | − | 2.46414i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 8.19615 | + | 14.1962i | 0.368390 | + | 0.638070i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.73205 | − | 8.19615i | −0.212261 | − | 0.367648i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.92820 | + | 8.53590i | −0.220617 | + | 0.382119i | −0.954995 | − | 0.296621i | \(-0.904140\pi\) |
0.734379 | + | 0.678740i | \(0.237474\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.30385 | − | 14.3827i | −0.370989 | − | 0.642571i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6.12436 | 0.273072 | 0.136536 | − | 0.990635i | \(-0.456403\pi\) | ||||
0.136536 | + | 0.990635i | \(0.456403\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.9282 | 0.575297 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −18.8038 | −0.835108 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 20.6962 | − | 35.8468i | 0.917341 | − | 1.58888i | 0.113903 | − | 0.993492i | \(-0.463665\pi\) |
0.803438 | − | 0.595389i | \(-0.203002\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.9282 | + | 22.3923i | 0.571910 | + | 0.990577i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −10.3923 | −0.458831 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.19615 | − | 5.53590i | −0.140839 | − | 0.243941i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.1962 | + | 17.6603i | −0.448426 | + | 0.776697i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 39.7128 | 1.74320 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13.0000 | −0.569540 | −0.284770 | − | 0.958596i | \(-0.591917\pi\) | ||||
−0.284770 | + | 0.958596i | \(0.591917\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 21.1962 | 0.926843 | 0.463422 | − | 0.886138i | \(-0.346622\pi\) | ||||
0.463422 | + | 0.886138i | \(0.346622\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.23205 | − | 5.59808i | −0.141058 | − | 0.244320i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 7.46410 | − | 12.9282i | 0.325141 | − | 0.563161i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.4641 | + | 19.8564i | 0.498439 | + | 0.863322i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −19.1769 | −0.832207 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.87564 | + | 4.98076i | 0.124558 | + | 0.215741i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.59808 | + | 4.50000i | −0.112325 | + | 0.194552i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5.66025 | + | 9.80385i | −0.244258 | + | 0.423067i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 37.8564 | 1.63059 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −39.3923 | −1.69361 | −0.846804 | − | 0.531905i | \(-0.821476\pi\) | ||||
−0.846804 | + | 0.531905i | \(0.821476\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 14.2583 | − | 24.6962i | 0.611884 | − | 1.05981i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.69615 | − | 2.93782i | 0.0726552 | − | 0.125842i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.99038 | + | 5.17949i | 0.127859 | + | 0.221459i | 0.922847 | − | 0.385167i | \(-0.125856\pi\) |
−0.794988 | + | 0.606626i | \(0.792523\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.30385 | − | 3.99038i | 0.0983258 | − | 0.170305i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.46410 | + | 14.6603i | 0.360583 | + | 0.624548i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −15.9282 | + | 27.5885i | −0.677336 | + | 1.17318i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −9.00000 | − | 15.5885i | −0.382029 | − | 0.661693i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −36.6410 | −1.55253 | −0.776265 | − | 0.630407i | \(-0.782888\pi\) | ||||
−0.776265 | + | 0.630407i | \(0.782888\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −16.7846 | −0.709913 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 70.6410 | 2.98247 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 21.7942 | − | 37.7487i | 0.918517 | − | 1.59092i | 0.116849 | − | 0.993150i | \(-0.462721\pi\) |
0.801669 | − | 0.597769i | \(-0.203946\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.92820 | − | 12.0000i | −0.291472 | − | 0.504844i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 33.5885 | 1.41058 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.00000 | − | 8.66025i | −0.209611 | − | 0.363057i | 0.741981 | − | 0.670421i | \(-0.233886\pi\) |
−0.951592 | + | 0.307364i | \(0.900553\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.392305 | + | 0.679492i | −0.0164174 | + | 0.0284359i | −0.874117 | − | 0.485715i | \(-0.838559\pi\) |
0.857700 | + | 0.514151i | \(0.171893\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5.32051 | 0.222267 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.267949 | 0.0111743 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 19.0718 | 0.793969 | 0.396985 | − | 0.917825i | \(-0.370057\pi\) | ||||
0.396985 | + | 0.917825i | \(0.370057\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 9.12436 | + | 15.8038i | 0.379195 | + | 0.656785i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.23205 | − | 9.06218i | 0.217062 | − | 0.375962i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −16.3923 | − | 28.3923i | −0.678900 | − | 1.17589i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.19615 | − | 3.80385i | 0.0907997 | − | 0.157270i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −19.7942 | − | 34.2846i | −0.816995 | − | 1.41508i | −0.907886 | − | 0.419216i | \(-0.862305\pi\) |
0.0908911 | − | 0.995861i | \(-0.471028\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.00000 | + | 3.46410i | −0.0824086 | + | 0.142736i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.928203 | + | 1.60770i | −0.0381812 | + | 0.0661317i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −32.5359 | −1.33609 | −0.668045 | − | 0.744121i | \(-0.732868\pi\) | ||||
−0.668045 | + | 0.744121i | \(0.732868\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −27.8564 | −1.14200 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −18.1244 | + | 31.3923i | −0.741780 | + | 1.28480i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −11.1962 | + | 19.3923i | −0.457462 | + | 0.792348i | −0.998826 | − | 0.0484404i | \(-0.984575\pi\) |
0.541364 | + | 0.840789i | \(0.317908\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.39230 | + | 9.33975i | 0.219957 | + | 0.380976i | 0.954794 | − | 0.297267i | \(-0.0960751\pi\) |
−0.734838 | + | 0.678243i | \(0.762742\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 29.1962 | 1.18896 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9.42820 | + | 16.3301i | 0.383311 | + | 0.663914i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −21.8660 | + | 37.8731i | −0.887515 | + | 1.53722i | −0.0447105 | + | 0.999000i | \(0.514237\pi\) |
−0.842804 | + | 0.538220i | \(0.819097\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −27.3564 | − | 47.3827i | −1.10854 | − | 1.92004i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.46410 | 0.221054 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.60770 | 0.0649342 | 0.0324671 | − | 0.999473i | \(-0.489664\pi\) | ||||
0.0324671 | + | 0.999473i | \(0.489664\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 6.80385 | 0.274358 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8.53590 | + | 14.7846i | −0.343642 | + | 0.595206i | −0.985106 | − | 0.171947i | \(-0.944994\pi\) |
0.641464 | + | 0.767153i | \(0.278327\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.85641 | − | 15.3397i | −0.355969 | − | 0.616556i | 0.631314 | − | 0.775527i | \(-0.282516\pi\) |
−0.987283 | + | 0.158971i | \(0.949182\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.696152 | + | 1.20577i | −0.0279356 | + | 0.0483859i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −7.33013 | − | 12.6962i | −0.293675 | − | 0.508661i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −18.9282 | −0.755920 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −77.5692 | −3.09289 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.7128 | −0.943992 | −0.471996 | − | 0.881601i | \(-0.656466\pi\) | ||||
−0.471996 | + | 0.881601i | \(0.656466\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 17.6603 | + | 30.5885i | 0.701932 | + | 1.21578i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 9.86603 | − | 17.0885i | 0.391521 | − | 0.678135i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.07180 | − | 8.78461i | −0.200952 | − | 0.348059i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.80385 | − | 6.58846i | −0.150478 | − | 0.260635i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.57180 | + | 6.18653i | 0.141077 | + | 0.244353i | 0.927903 | − | 0.372823i | \(-0.121610\pi\) |
−0.786825 | + | 0.617176i | \(0.788277\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18.8660 | − | 32.6769i | 0.744003 | − | 1.28865i | −0.206656 | − | 0.978414i | \(-0.566258\pi\) |
0.950659 | − | 0.310238i | \(-0.100409\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −9.92820 | + | 17.1962i | −0.390923 | + | 0.677098i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 28.5167 | 1.12111 | 0.560553 | − | 0.828119i | \(-0.310589\pi\) | ||||
0.560553 | + | 0.828119i | \(0.310589\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −34.9282 | −1.37105 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.46410 | − | 11.1962i | 0.253348 | − | 0.438812i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −12.2679 | + | 21.2487i | −0.480082 | + | 0.831526i | −0.999739 | − | 0.0228487i | \(-0.992726\pi\) |
0.519657 | + | 0.854375i | \(0.326060\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.73205 | + | 3.00000i | 0.0676768 | + | 0.117220i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 10.3923 | + | 18.0000i | 0.405442 | + | 0.702247i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −10.3923 | − | 18.0000i | −0.404827 | − | 0.701180i | 0.589475 | − | 0.807787i | \(-0.299335\pi\) |
−0.994301 | + | 0.106606i | \(0.966001\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16.8564 | − | 29.1962i | 0.655638 | − | 1.13560i | −0.326095 | − | 0.945337i | \(-0.605733\pi\) |
0.981733 | − | 0.190262i | \(-0.0609337\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −9.46410 | − | 16.3923i | −0.367555 | − | 0.636624i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 7.46410 | 0.289445 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.26795 | 0.0878153 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 9.24871 | 0.357576 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.19615 | − | 7.26795i | 0.161991 | − | 0.280576i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23.6603 | + | 40.9808i | 0.912036 | + | 1.57969i | 0.811184 | + | 0.584791i | \(0.198823\pi\) |
0.100852 | + | 0.994901i | \(0.467843\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.59808 | − | 4.50000i | −0.100000 | − | 0.173205i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −22.5885 | − | 39.1244i | −0.868145 | − | 1.50367i | −0.863890 | − | 0.503680i | \(-0.831979\pi\) |
−0.00425474 | − | 0.999991i | \(-0.501354\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.19615 | + | 15.9282i | −0.352916 | + | 0.611268i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −42.0000 | −1.60944 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.60770 | 0.0615167 | 0.0307584 | − | 0.999527i | \(-0.490208\pi\) | ||||
0.0307584 | + | 0.999527i | \(0.490208\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.85641 | 0.223762 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 20.1340 | + | 34.8731i | 0.768159 | + | 1.33049i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.39230 | + | 7.60770i | −0.167333 | + | 0.289830i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14.8038 | + | 25.6410i | 0.563165 | + | 0.975430i | 0.997218 | + | 0.0745428i | \(0.0237498\pi\) |
−0.434053 | + | 0.900887i | \(0.642917\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 61.1769 | 2.32392 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14.6603 | − | 25.3923i | 0.555297 | − | 0.961802i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9.00000 | + | 15.5885i | −0.340411 | + | 0.589610i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 38.1769 | 1.44192 | 0.720961 | − | 0.692976i | \(-0.243701\pi\) | ||||
0.720961 | + | 0.692976i | \(0.243701\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 20.7846 | 0.783906 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.23205 | − | 5.59808i | 0.121726 | − | 0.210836i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 24.1244 | − | 41.7846i | 0.907290 | − | 1.57147i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.69615 | + | 4.66987i | 0.101256 | + | 0.175381i | 0.912202 | − | 0.409740i | \(-0.134381\pi\) |
−0.810946 | + | 0.585121i | \(0.801047\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −12.8038 | + | 22.1769i | −0.480182 | + | 0.831699i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.267949 | + | 0.464102i | 0.0100348 | + | 0.0173807i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.00000 | − | 6.92820i | 0.149592 | − | 0.259100i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 18.0000 | + | 31.1769i | 0.672222 | + | 1.16432i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.32051 | 0.0492466 | 0.0246233 | − | 0.999697i | \(-0.492161\pi\) | ||||
0.0246233 | + | 0.999697i | \(0.492161\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −23.8564 | −0.888459 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −34.5167 | −1.28369 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.23205 | + | 7.33013i | −0.157174 | + | 0.272234i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17.9904 | + | 31.1603i | 0.667226 | + | 1.15567i | 0.978677 | + | 0.205407i | \(0.0658519\pi\) |
−0.311450 | + | 0.950262i | \(0.600815\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 42.7846 | + | 74.1051i | 1.58245 | + | 2.74088i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −21.9282 | + | 37.9808i | −0.809937 | + | 1.40285i | 0.102971 | + | 0.994684i | \(0.467165\pi\) |
−0.912907 | + | 0.408167i | \(0.866168\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −12.0000 | −0.442627 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 53.1769 | 1.95880 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 48.2487 | 1.77486 | 0.887429 | − | 0.460945i | \(-0.152489\pi\) | ||||
0.887429 | + | 0.460945i | \(0.152489\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.53590 | + | 4.39230i | 0.0931586 | + | 0.161355i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −22.9186 | + | 39.6962i | −0.840801 | + | 1.45631i | 0.0484169 | + | 0.998827i | \(0.484582\pi\) |
−0.889218 | + | 0.457483i | \(0.848751\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.23205 | + | 3.86603i | 0.0817760 | + | 0.141640i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.20577 | − | 7.28461i | 0.153881 | − | 0.266530i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.69615 | + | 16.7942i | 0.354290 | + | 0.613648i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.19615 | − | 3.80385i | 0.0801387 | − | 0.138804i | −0.823171 | − | 0.567794i | \(-0.807797\pi\) |
0.903309 | + | 0.428990i | \(0.141130\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −17.1962 | + | 29.7846i | −0.626663 | + | 1.08541i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.46410 | 0.0532841 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0.392305 | 0.0142586 | 0.00712928 | − | 0.999975i | \(-0.497731\pi\) | ||||
0.00712928 | + | 0.999975i | \(0.497731\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.26795 | + | 2.19615i | −0.0460236 | + | 0.0797153i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10.5000 | − | 18.1865i | 0.380625 | − | 0.659261i | −0.610527 | − | 0.791995i | \(-0.709042\pi\) |
0.991152 | + | 0.132734i | \(0.0423756\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.33013 | − | 10.9641i | −0.229166 | − | 0.396927i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −22.3923 | −0.809595 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.67949 | + | 8.10512i | 0.168967 | + | 0.292659i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.89230 | − | 6.74167i | 0.140360 | − | 0.243111i | −0.787272 | − | 0.616606i | \(-0.788507\pi\) |
0.927632 | + | 0.373495i | \(0.121841\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −11.1962 | − | 19.3923i | −0.403220 | − | 0.698397i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 32.7846 | 1.17918 | 0.589590 | − | 0.807703i | \(-0.299289\pi\) | ||||
0.589590 | + | 0.807703i | \(0.299289\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.00000 | −0.0718421 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −67.1769 | −2.40996 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.92820 | + | 6.80385i | −0.140742 | + | 0.243773i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.92820 | − | 12.0000i | −0.247911 | − | 0.429394i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −21.9904 | − | 38.0885i | −0.785872 | − | 1.36117i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.46410 | − | 7.73205i | −0.159331 | − | 0.275969i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16.6603 | − | 28.8564i | 0.593874 | − | 1.02862i | −0.399831 | − | 0.916589i | \(-0.630931\pi\) |
0.993705 | − | 0.112031i | \(-0.0357355\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.78461 | 0.0991347 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −51.7128 | −1.83870 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.24871 | −0.0798541 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 5.19615 | + | 9.00000i | 0.184289 | + | 0.319197i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 14.1962 | − | 24.5885i | 0.502854 | − | 0.870968i | −0.497141 | − | 0.867670i | \(-0.665617\pi\) |
0.999995 | − | 0.00329810i | \(-0.00104982\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −13.9282 | − | 24.1244i | −0.492744 | − | 0.853458i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.89230 | − | 10.2058i | −0.208194 | − | 0.360603i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 18.9282 | + | 32.7846i | 0.667962 | + | 1.15694i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.500000 | − | 0.866025i | 0.0176227 | − | 0.0305234i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8.13397 | − | 14.0885i | 0.286329 | − | 0.495937i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −35.0718 | −1.23306 | −0.616529 | − | 0.787332i | \(-0.711462\pi\) | ||||
−0.616529 | + | 0.787332i | \(0.711462\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −29.6077 | −1.03967 | −0.519833 | − | 0.854268i | \(-0.674006\pi\) | ||||
−0.519833 | + | 0.854268i | \(0.674006\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6.80385 | + | 11.7846i | −0.238621 | + | 0.413304i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 10.6603 | − | 18.4641i | 0.373412 | − | 0.646769i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −11.4641 | − | 19.8564i | −0.401078 | − | 0.694688i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −8.19615 | − | 14.1962i | −0.286397 | − | 0.496054i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12.6244 | + | 21.8660i | 0.440593 | + | 0.763130i | 0.997734 | − | 0.0672887i | \(-0.0214349\pi\) |
−0.557140 | + | 0.830418i | \(0.688102\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10.1340 | + | 17.5526i | −0.353248 | + | 0.611844i | −0.986817 | − | 0.161843i | \(-0.948256\pi\) |
0.633568 | + | 0.773687i | \(0.281590\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.73205 | − | 8.19615i | −0.164749 | − | 0.285353i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −55.0526 | −1.91437 | −0.957183 | − | 0.289485i | \(-0.906516\pi\) | ||||
−0.957183 | + | 0.289485i | \(0.906516\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9.39230 | −0.326208 | −0.163104 | − | 0.986609i | \(-0.552151\pi\) | ||||
−0.163104 | + | 0.986609i | \(0.552151\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 11.0718 | 0.384076 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −25.8564 | + | 44.7846i | −0.895871 | + | 1.55169i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.79423 | + | 8.30385i | 0.165911 | + | 0.287366i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.19615 | − | 9.00000i | 0.179605 | − | 0.311086i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −4.07180 | − | 7.05256i | −0.140574 | − | 0.243481i | 0.787139 | − | 0.616776i | \(-0.211561\pi\) |
−0.927713 | + | 0.373294i | \(0.878228\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.3205 | + | 36.9282i | −0.735190 | + | 1.27339i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 22.2679 | 0.766949 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 10.8564 | 0.373472 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 70.3731 | 2.41805 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −15.8205 | − | 27.4019i | −0.542958 | − | 0.940432i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.39230 | − | 2.41154i | 0.0477276 | − | 0.0826666i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21.2679 | + | 36.8372i | 0.728201 | + | 1.26128i | 0.957643 | + | 0.287958i | \(0.0929765\pi\) |
−0.229442 | + | 0.973322i | \(0.573690\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.00000 | 0.205196 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 15.1244 | + | 26.1962i | 0.516638 | + | 0.894844i | 0.999813 | + | 0.0193198i | \(0.00615008\pi\) |
−0.483175 | + | 0.875524i | \(0.660517\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.196152 | + | 0.339746i | −0.00669263 | + | 0.0115920i | −0.869352 | − | 0.494193i | \(-0.835464\pi\) |
0.862660 | + | 0.505785i | \(0.168797\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 12.6962 | − | 21.9904i | 0.432684 | − | 0.749430i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9.33975 | 0.317929 | 0.158964 | − | 0.987284i | \(-0.449185\pi\) | ||||
0.158964 | + | 0.987284i | \(0.449185\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −22.9282 | −0.779582 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −33.5263 | + | 58.0692i | −1.13861 | + | 1.97213i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −23.3205 | + | 40.3923i | −0.791094 | + | 1.37022i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.12436 | − | 12.3397i | −0.241400 | − | 0.418116i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −7.39230 | + | 12.8038i | −0.250192 | + | 0.433345i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.86603 | + | 3.23205i | 0.0630832 | + | 0.109263i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −16.1962 | + | 28.0526i | −0.546905 | + | 0.947268i | 0.451579 | + | 0.892231i | \(0.350861\pi\) |
−0.998484 | + | 0.0550365i | \(0.982472\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0.464102 | + | 0.803848i | 0.0156538 | + | 0.0271131i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −31.6410 | −1.06601 | −0.533006 | − | 0.846111i | \(-0.678938\pi\) | ||||
−0.533006 | + | 0.846111i | \(0.678938\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.19615 | 0.0402537 | 0.0201269 | − | 0.999797i | \(-0.493593\pi\) | ||||
0.0201269 | + | 0.999797i | \(0.493593\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 11.0718 | 0.372174 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −12.6603 | + | 21.9282i | −0.425090 | + | 0.736277i | −0.996429 | − | 0.0844371i | \(-0.973091\pi\) |
0.571339 | + | 0.820714i | \(0.306424\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −36.8205 | − | 63.7750i | −1.23492 | − | 2.13894i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 49.1769 | 1.64749 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.73205 | + | 6.46410i | 0.124888 | + | 0.216313i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.26795 | − | 5.66025i | 0.109235 | − | 0.189201i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.679492 | 0.0226876 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −16.9282 | −0.564587 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 44.7846 | 1.49199 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 37.0526 | + | 64.1769i | 1.23303 | + | 2.13567i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −8.23205 | + | 14.2583i | −0.273643 | + | 0.473963i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.13397 | + | 8.89230i | 0.170471 | + | 0.295264i | 0.938585 | − | 0.345049i | \(-0.112138\pi\) |
−0.768114 | + | 0.640313i | \(0.778804\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 19.3923 | − | 33.5885i | 0.643202 | − | 1.11406i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.73205 | + | 16.8564i | 0.322437 | + | 0.558478i | 0.980990 | − | 0.194057i | \(-0.0621645\pi\) |
−0.658553 | + | 0.752534i | \(0.728831\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.66025 | − | 13.2679i | 0.253517 | − | 0.439105i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.33013 | + | 2.30385i | −0.0439726 | + | 0.0761629i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 12.9282 | 0.426927 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −38.3923 | −1.26645 | −0.633223 | − | 0.773970i | \(-0.718268\pi\) | ||||
−0.633223 | + | 0.773970i | \(0.718268\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 17.4282 | − | 30.1865i | 0.574279 | − | 0.994680i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.85641 | + | 3.21539i | −0.0611044 | + | 0.105836i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.19615 | + | 9.00000i | 0.170848 | + | 0.295918i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −19.1769 | −0.629853 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 22.3205 | + | 38.6603i | 0.732312 | + | 1.26840i | 0.955893 | + | 0.293716i | \(0.0948921\pi\) |
−0.223581 | + | 0.974685i | \(0.571775\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.92820 | − | 12.0000i | 0.227063 | − | 0.393284i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −14.6603 | − | 25.3923i | −0.479955 | − | 0.831307i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −40.7846 | −1.33380 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 43.7128 | 1.42804 | 0.714018 | − | 0.700128i | \(-0.246874\pi\) | ||||
0.714018 | + | 0.700128i | \(0.246874\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −14.5359 | −0.474361 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.30385 | − | 2.25833i | 0.0425042 | − | 0.0736195i | −0.843991 | − | 0.536358i | \(-0.819800\pi\) |
0.886495 | + | 0.462738i | \(0.153133\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.526279 | + | 0.911543i | 0.0171380 | + | 0.0296839i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −19.3923 | −0.630832 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −15.2583 | − | 26.4282i | −0.495829 | − | 0.858801i | 0.504159 | − | 0.863611i | \(-0.331802\pi\) |
−0.999988 | + | 0.00480945i | \(0.998469\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.07180 | − | 8.78461i | 0.164637 | − | 0.285160i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 16.3923 | 0.531557 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 19.6077 | 0.635156 | 0.317578 | − | 0.948232i | \(-0.397131\pi\) | ||||
0.317578 | + | 0.948232i | \(0.397131\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.07180 | −0.0994010 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −40.0526 | − | 69.3731i | −1.29472 | − | 2.24251i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 10.9282 | − | 18.9282i | 0.352890 | − | 0.611224i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.5000 | + | 23.3827i | 0.435484 | + | 0.754280i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7.79423 | + | 13.5000i | 0.251166 | + | 0.435031i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −5.26795 | − | 9.12436i | −0.169581 | − | 0.293723i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −19.3301 | + | 33.4808i | −0.621615 | + | 1.07667i | 0.367570 | + | 0.929996i | \(0.380190\pi\) |
−0.989185 | + | 0.146673i | \(0.953144\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 12.9282 | − | 22.3923i | 0.415314 | − | 0.719344i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −29.7128 | −0.953530 | −0.476765 | − | 0.879031i | \(-0.658191\pi\) | ||||
−0.476765 | + | 0.879031i | \(0.658191\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.26795 | + | 2.19615i | −0.0406069 | + | 0.0703332i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 22.5885 | − | 39.1244i | 0.722669 | − | 1.25170i | −0.237258 | − | 0.971447i | \(-0.576249\pi\) |
0.959926 | − | 0.280252i | \(-0.0904181\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −10.7321 | − | 18.5885i | −0.342998 | − | 0.594090i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.08846 | − | 8.81347i | −0.162462 | − | 0.281392i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.25833 | + | 3.91154i | 0.0720295 | + | 0.124759i | 0.899791 | − | 0.436322i | \(-0.143719\pi\) |
−0.827761 | + | 0.561081i | \(0.810386\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.535898 | − | 0.928203i | 0.0170751 | − | 0.0295750i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −12.0622 | − | 20.8923i | −0.383943 | − | 0.665009i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.07180 | −0.0976775 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 53.0333 | 1.68466 | 0.842329 | − | 0.538963i | \(-0.181184\pi\) | ||||
0.842329 | + | 0.538963i | \(0.181184\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 6.00000 | 0.190404 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 10.4641 | − | 18.1244i | 0.331734 | − | 0.574581i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17.7846 | + | 30.8038i | 0.563244 | + | 0.975568i | 0.997211 | + | 0.0746386i | \(0.0237803\pi\) |
−0.433966 | + | 0.900929i | \(0.642886\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −54.0000 | −1.70848 |
(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 | 360.2.q.b.121.1 | ✓ | 4 | |
3.2 | odd | 2 | 1080.2.q.b.361.1 | 4 | |||
4.3 | odd | 2 | 720.2.q.h.481.2 | 4 | |||
9.2 | odd | 6 | 1080.2.q.b.721.1 | 4 | |||
9.4 | even | 3 | 3240.2.a.k.1.2 | 2 | |||
9.5 | odd | 6 | 3240.2.a.p.1.2 | 2 | |||
9.7 | even | 3 | inner | 360.2.q.b.241.1 | yes | 4 | |
12.11 | even | 2 | 2160.2.q.h.1441.2 | 4 | |||
36.7 | odd | 6 | 720.2.q.h.241.2 | 4 | |||
36.11 | even | 6 | 2160.2.q.h.721.2 | 4 | |||
36.23 | even | 6 | 6480.2.a.bk.1.1 | 2 | |||
36.31 | odd | 6 | 6480.2.a.ba.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
360.2.q.b.121.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
360.2.q.b.241.1 | yes | 4 | 9.7 | even | 3 | inner | |
720.2.q.h.241.2 | 4 | 36.7 | odd | 6 | |||
720.2.q.h.481.2 | 4 | 4.3 | odd | 2 | |||
1080.2.q.b.361.1 | 4 | 3.2 | odd | 2 | |||
1080.2.q.b.721.1 | 4 | 9.2 | odd | 6 | |||
2160.2.q.h.721.2 | 4 | 36.11 | even | 6 | |||
2160.2.q.h.1441.2 | 4 | 12.11 | even | 2 | |||
3240.2.a.k.1.2 | 2 | 9.4 | even | 3 | |||
3240.2.a.p.1.2 | 2 | 9.5 | odd | 6 | |||
6480.2.a.ba.1.1 | 2 | 36.31 | odd | 6 | |||
6480.2.a.bk.1.1 | 2 | 36.23 | even | 6 |