Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [324,2,Mod(107,324)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(324, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("324.107");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 324 = 2^{2} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 324.h (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.58715302549\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.12960000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{6} + 8x^{4} - 3x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | no (minimal twist has level 108) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 215.1 | ||
Root | \(1.40126 - 0.809017i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 324.215 |
Dual form | 324.2.h.d.107.1 |
$q$-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 \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).
\(n\) | \(163\) | \(245\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.40126 | − | 0.190983i | −0.990839 | − | 0.135045i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.92705 | + | 0.535233i | 0.963525 | + | 0.267617i | ||||
\(5\) | 1.93649 | + | 1.11803i | 0.866025 | + | 0.500000i | 0.866025 | − | 0.500000i | \(-0.166667\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.35410 | − | 1.93649i | 1.26773 | − | 0.731925i | 0.293173 | − | 0.956059i | \(-0.405289\pi\) |
0.974558 | + | 0.224134i | \(0.0719554\pi\) | |||||||
\(8\) | −2.59808 | − | 1.11803i | −0.918559 | − | 0.395285i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.50000 | − | 1.93649i | −0.790569 | − | 0.612372i | ||||
\(11\) | −0.866025 | − | 1.50000i | −0.261116 | − | 0.452267i | 0.705422 | − | 0.708787i | \(-0.250757\pi\) |
−0.966539 | + | 0.256520i | \(0.917424\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | + | 1.73205i | −0.277350 | + | 0.480384i | −0.970725 | − | 0.240192i | \(-0.922790\pi\) |
0.693375 | + | 0.720577i | \(0.256123\pi\) | |||||||
\(14\) | −5.06980 | + | 2.07295i | −1.35496 | + | 0.554019i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.42705 | + | 2.06284i | 0.856763 | + | 0.515711i | ||||
\(17\) | 4.47214i | 1.08465i | 0.840168 | + | 0.542326i | \(0.182456\pi\) | ||||
−0.840168 | + | 0.542326i | \(0.817544\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(20\) | 3.13331 | + | 3.19098i | 0.700629 | + | 0.713525i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.927051 | + | 2.26728i | 0.197648 | + | 0.483387i | ||||
\(23\) | 3.46410 | − | 6.00000i | 0.722315 | − | 1.25109i | −0.237754 | − | 0.971325i | \(-0.576411\pi\) |
0.960070 | − | 0.279761i | \(-0.0902553\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.73205 | − | 2.23607i | 0.339683 | − | 0.438529i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 7.50000 | − | 1.93649i | 1.41737 | − | 0.365963i | ||||
\(29\) | 3.87298 | − | 2.23607i | 0.719195 | − | 0.415227i | −0.0952614 | − | 0.995452i | \(-0.530369\pi\) |
0.814456 | + | 0.580225i | \(0.197035\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.35410 | + | 1.93649i | 0.602414 | + | 0.347804i | 0.769991 | − | 0.638055i | \(-0.220261\pi\) |
−0.167576 | + | 0.985859i | \(0.553594\pi\) | |||||||
\(32\) | −4.40822 | − | 3.54508i | −0.779270 | − | 0.626688i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.854102 | − | 6.26662i | 0.146477 | − | 1.07472i | ||||
\(35\) | 8.66025 | 1.46385 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.00000 | −0.657596 | −0.328798 | − | 0.944400i | \(-0.606644\pi\) | ||||
−0.328798 | + | 0.944400i | \(0.606644\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.78115 | − | 5.06980i | −0.597853 | − | 0.801606i | ||||
\(41\) | 7.74597 | + | 4.47214i | 1.20972 | + | 0.698430i | 0.962697 | − | 0.270580i | \(-0.0872155\pi\) |
0.247019 | + | 0.969011i | \(0.420549\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.70820 | + | 3.87298i | −1.02299 | + | 0.590624i | −0.914969 | − | 0.403524i | \(-0.867785\pi\) |
−0.108022 | + | 0.994148i | \(0.534452\pi\) | |||||||
\(44\) | −0.866025 | − | 3.35410i | −0.130558 | − | 0.505650i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.00000 | + | 7.74597i | −0.884652 | + | 1.14208i | ||||
\(47\) | 1.73205 | + | 3.00000i | 0.252646 | + | 0.437595i | 0.964253 | − | 0.264982i | \(-0.0853660\pi\) |
−0.711608 | + | 0.702577i | \(0.752033\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.00000 | − | 6.92820i | 0.571429 | − | 0.989743i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.85410 | + | 2.80252i | −0.395793 | + | 0.388639i | ||||
\(53\) | − | 2.23607i | − | 0.307148i | −0.988137 | − | 0.153574i | \(-0.950922\pi\) | ||
0.988137 | − | 0.153574i | \(-0.0490783\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 3.87298i | − | 0.522233i | ||||||
\(56\) | −10.8793 | + | 1.28115i | −1.45380 | + | 0.171201i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.85410 | + | 2.39364i | −0.768681 | + | 0.314300i | ||||
\(59\) | −1.73205 | + | 3.00000i | −0.225494 | + | 0.390567i | −0.956467 | − | 0.291839i | \(-0.905733\pi\) |
0.730974 | + | 0.682406i | \(0.239066\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.00000 | + | 3.46410i | 0.256074 | + | 0.443533i | 0.965187 | − | 0.261562i | \(-0.0842377\pi\) |
−0.709113 | + | 0.705095i | \(0.750904\pi\) | |||||||
\(62\) | −4.33013 | − | 3.35410i | −0.549927 | − | 0.425971i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 5.50000 | + | 5.80948i | 0.687500 | + | 0.726184i | ||||
\(65\) | −3.87298 | + | 2.23607i | −0.480384 | + | 0.277350i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.70820 | − | 3.87298i | −0.819538 | − | 0.473160i | 0.0307194 | − | 0.999528i | \(-0.490220\pi\) |
−0.850257 | + | 0.526368i | \(0.823553\pi\) | |||||||
\(68\) | −2.39364 | + | 8.61803i | −0.290271 | + | 1.04509i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −12.1353 | − | 1.65396i | −1.45044 | − | 0.197686i | ||||
\(71\) | −10.3923 | −1.23334 | −0.616670 | − | 0.787222i | \(-0.711519\pi\) | ||||
−0.616670 | + | 0.787222i | \(0.711519\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.00000 | 0.585206 | 0.292603 | − | 0.956234i | \(-0.405479\pi\) | ||||
0.292603 | + | 0.956234i | \(0.405479\pi\) | |||||||
\(74\) | 5.60503 | + | 0.763932i | 0.651572 | + | 0.0888053i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.80948 | − | 3.35410i | −0.662051 | − | 0.382235i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.70820 | + | 3.87298i | −0.754732 | + | 0.435745i | −0.827401 | − | 0.561611i | \(-0.810182\pi\) |
0.0726692 | + | 0.997356i | \(0.476848\pi\) | |||||||
\(80\) | 4.33013 | + | 7.82624i | 0.484123 | + | 0.875000i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −10.0000 | − | 7.74597i | −1.10432 | − | 0.855399i | ||||
\(83\) | −6.06218 | − | 10.5000i | −0.665410 | − | 1.15252i | −0.979174 | − | 0.203024i | \(-0.934923\pi\) |
0.313763 | − | 0.949501i | \(-0.398410\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.00000 | + | 8.66025i | −0.542326 | + | 0.939336i | ||||
\(86\) | 10.1396 | − | 4.14590i | 1.09338 | − | 0.447064i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.572949 | + | 4.86536i | 0.0610766 | + | 0.518649i | ||||
\(89\) | 4.47214i | 0.474045i | 0.971504 | + | 0.237023i | \(0.0761716\pi\) | ||||
−0.971504 | + | 0.237023i | \(0.923828\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.74597i | 0.811998i | ||||||||
\(92\) | 9.88690 | − | 9.70820i | 1.03078 | − | 1.01215i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.85410 | − | 4.53457i | −0.191236 | − | 0.467705i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.50000 | − | 9.52628i | −0.558440 | − | 0.967247i | −0.997627 | − | 0.0688512i | \(-0.978067\pi\) |
0.439187 | − | 0.898396i | \(-0.355267\pi\) | |||||||
\(98\) | −6.92820 | + | 8.94427i | −0.699854 | + | 0.903508i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.93649 | + | 1.11803i | −0.192688 | + | 0.111249i | −0.593240 | − | 0.805025i | \(-0.702152\pi\) |
0.400552 | + | 0.916274i | \(0.368818\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.70820 | − | 3.87298i | −0.660979 | − | 0.381616i | 0.131671 | − | 0.991293i | \(-0.457966\pi\) |
−0.792650 | + | 0.609677i | \(0.791299\pi\) | |||||||
\(104\) | 4.53457 | − | 3.38197i | 0.444651 | − | 0.331629i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.427051 | + | 3.13331i | −0.0414789 | + | 0.304334i | ||||
\(107\) | −5.19615 | −0.502331 | −0.251166 | − | 0.967944i | \(-0.580814\pi\) | ||||
−0.251166 | + | 0.967944i | \(0.580814\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.00000 | −0.383131 | −0.191565 | − | 0.981480i | \(-0.561356\pi\) | ||||
−0.191565 | + | 0.981480i | \(0.561356\pi\) | |||||||
\(110\) | −0.739674 | + | 5.42705i | −0.0705251 | + | 0.517449i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 15.4894 | + | 0.282530i | 1.46361 | + | 0.0266966i | ||||
\(113\) | −15.4919 | − | 8.94427i | −1.45736 | − | 0.841406i | −0.458478 | − | 0.888706i | \(-0.651605\pi\) |
−0.998881 | + | 0.0472996i | \(0.984938\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 13.4164 | − | 7.74597i | 1.25109 | − | 0.722315i | ||||
\(116\) | 8.66025 | − | 2.23607i | 0.804084 | − | 0.207614i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.00000 | − | 3.87298i | 0.276172 | − | 0.356537i | ||||
\(119\) | 8.66025 | + | 15.0000i | 0.793884 | + | 1.37505i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.00000 | − | 6.92820i | 0.363636 | − | 0.629837i | ||||
\(122\) | −2.14093 | − | 5.23607i | −0.193831 | − | 0.474051i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 5.42705 | + | 5.52694i | 0.487364 | + | 0.496334i | ||||
\(125\) | − | 11.1803i | − | 1.00000i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.6190i | 1.03102i | 0.856885 | + | 0.515508i | \(0.172397\pi\) | ||||
−0.856885 | + | 0.515508i | \(0.827603\pi\) | |||||||
\(128\) | −6.59741 | − | 9.19098i | −0.583134 | − | 0.812376i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 5.85410 | − | 2.39364i | 0.513439 | − | 0.209936i | ||||
\(131\) | −9.52628 | + | 16.5000i | −0.832315 | + | 1.44161i | 0.0638831 | + | 0.997957i | \(0.479652\pi\) |
−0.896198 | + | 0.443654i | \(0.853682\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 8.66025 | + | 6.70820i | 0.748132 | + | 0.579501i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.00000 | − | 11.6190i | 0.428746 | − | 0.996317i | ||||
\(137\) | 3.87298 | − | 2.23607i | 0.330891 | − | 0.191040i | −0.325345 | − | 0.945595i | \(-0.605481\pi\) |
0.656237 | + | 0.754555i | \(0.272147\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.4164 | + | 7.74597i | 1.13796 | + | 0.657004i | 0.945926 | − | 0.324383i | \(-0.105157\pi\) |
0.192039 | + | 0.981387i | \(0.438490\pi\) | |||||||
\(140\) | 16.6888 | + | 4.63525i | 1.41046 | + | 0.391751i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 14.5623 | + | 1.98475i | 1.22204 | + | 0.166557i | ||||
\(143\) | 3.46410 | 0.289683 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 10.0000 | 0.830455 | ||||||||
\(146\) | −7.00629 | − | 0.954915i | −0.579845 | − | 0.0790293i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −7.70820 | − | 2.14093i | −0.633610 | − | 0.175984i | ||||
\(149\) | 1.93649 | + | 1.11803i | 0.158644 | + | 0.0915929i | 0.577220 | − | 0.816589i | \(-0.304137\pi\) |
−0.418576 | + | 0.908182i | \(0.637471\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.35410 | − | 1.93649i | 0.272953 | − | 0.157589i | −0.357276 | − | 0.933999i | \(-0.616294\pi\) |
0.630229 | + | 0.776409i | \(0.282961\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 7.50000 | + | 5.80948i | 0.604367 | + | 0.468141i | ||||
\(155\) | 4.33013 | + | 7.50000i | 0.347804 | + | 0.602414i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.0000 | + | 17.3205i | −0.798087 | + | 1.38233i | 0.122774 | + | 0.992435i | \(0.460821\pi\) |
−0.920860 | + | 0.389892i | \(0.872512\pi\) | |||||||
\(158\) | 10.1396 | − | 4.14590i | 0.806663 | − | 0.329830i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −4.57295 | − | 11.7936i | −0.361523 | − | 0.932363i | ||||
\(161\) | − | 26.8328i | − | 2.11472i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 23.2379i | − | 1.82013i | −0.414462 | − | 0.910066i | \(-0.636030\pi\) | ||
0.414462 | − | 0.910066i | \(-0.363970\pi\) | |||||||
\(164\) | 12.5332 | + | 12.7639i | 0.978681 | + | 0.996696i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.48936 | + | 15.8710i | 0.503672 | + | 1.23183i | ||||
\(167\) | −1.73205 | + | 3.00000i | −0.134030 | + | 0.232147i | −0.925227 | − | 0.379415i | \(-0.876125\pi\) |
0.791196 | + | 0.611562i | \(0.209459\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.50000 | + | 7.79423i | 0.346154 | + | 0.599556i | ||||
\(170\) | 8.66025 | − | 11.1803i | 0.664211 | − | 0.857493i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −15.0000 | + | 3.87298i | −1.14374 | + | 0.295312i | ||||
\(173\) | −13.5554 | + | 7.82624i | −1.03060 | + | 0.595018i | −0.917157 | − | 0.398527i | \(-0.869522\pi\) |
−0.113444 | + | 0.993544i | \(0.536188\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.126351 | − | 6.92705i | 0.00952410 | − | 0.522146i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.854102 | − | 6.26662i | 0.0640176 | − | 0.469703i | ||||
\(179\) | 5.19615 | 0.388379 | 0.194189 | − | 0.980964i | \(-0.437792\pi\) | ||||
0.194189 | + | 0.980964i | \(0.437792\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.0000 | −1.18927 | −0.594635 | − | 0.803996i | \(-0.702704\pi\) | ||||
−0.594635 | + | 0.803996i | \(0.702704\pi\) | |||||||
\(182\) | 1.47935 | − | 10.8541i | 0.109657 | − | 0.804560i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −15.7082 | + | 11.7155i | −1.15802 | + | 0.863676i | ||||
\(185\) | −7.74597 | − | 4.47214i | −0.569495 | − | 0.328798i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.70820 | − | 3.87298i | 0.490552 | − | 0.283221i | ||||
\(188\) | 1.73205 | + | 6.70820i | 0.126323 | + | 0.489246i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.66025 | − | 15.0000i | −0.626634 | − | 1.08536i | −0.988222 | − | 0.153024i | \(-0.951099\pi\) |
0.361588 | − | 0.932338i | \(-0.382235\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.5000 | − | 21.6506i | 0.899770 | − | 1.55845i | 0.0719816 | − | 0.997406i | \(-0.477068\pi\) |
0.827788 | − | 0.561041i | \(-0.189599\pi\) | |||||||
\(194\) | 5.88756 | + | 14.3992i | 0.422702 | + | 1.03380i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 11.4164 | − | 11.2101i | 0.815458 | − | 0.800719i | ||||
\(197\) | 24.5967i | 1.75245i | 0.481906 | + | 0.876223i | \(0.339945\pi\) | ||||
−0.481906 | + | 0.876223i | \(0.660055\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 11.6190i | − | 0.823646i | −0.911264 | − | 0.411823i | \(-0.864892\pi\) | ||
0.911264 | − | 0.411823i | \(-0.135108\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.92705 | − | 1.19682i | 0.205947 | − | 0.0842078i | ||||
\(203\) | 8.66025 | − | 15.0000i | 0.607831 | − | 1.05279i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 10.0000 | + | 17.3205i | 0.698430 | + | 1.20972i | ||||
\(206\) | 8.66025 | + | 6.70820i | 0.603388 | + | 0.467383i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −7.00000 | + | 3.87298i | −0.485363 | + | 0.268543i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.4164 | + | 7.74597i | 0.923624 | + | 0.533254i | 0.884789 | − | 0.465991i | \(-0.154302\pi\) |
0.0388343 | + | 0.999246i | \(0.487636\pi\) | |||||||
\(212\) | 1.19682 | − | 4.30902i | 0.0821978 | − | 0.295945i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 7.28115 | + | 0.992377i | 0.497729 | + | 0.0678375i | ||||
\(215\) | −17.3205 | −1.18125 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 15.0000 | 1.01827 | ||||||||
\(218\) | 5.60503 | + | 0.763932i | 0.379621 | + | 0.0517400i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2.07295 | − | 7.46344i | 0.139758 | − | 0.503185i | ||||
\(221\) | −7.74597 | − | 4.47214i | −0.521050 | − | 0.300828i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.70820 | + | 3.87298i | −0.449215 | + | 0.259354i | −0.707498 | − | 0.706715i | \(-0.750176\pi\) |
0.258284 | + | 0.966069i | \(0.416843\pi\) | |||||||
\(224\) | −21.6506 | − | 3.35410i | −1.44659 | − | 0.224105i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 20.0000 | + | 15.4919i | 1.33038 | + | 1.03051i | ||||
\(227\) | 1.73205 | + | 3.00000i | 0.114960 | + | 0.199117i | 0.917764 | − | 0.397127i | \(-0.129993\pi\) |
−0.802804 | + | 0.596244i | \(0.796659\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.00000 | + | 1.73205i | −0.0660819 | + | 0.114457i | −0.897173 | − | 0.441679i | \(-0.854383\pi\) |
0.831092 | + | 0.556136i | \(0.187717\pi\) | |||||||
\(230\) | −20.2792 | + | 8.29180i | −1.33717 | + | 0.546745i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −12.5623 | + | 1.47935i | −0.824756 | + | 0.0971240i | ||||
\(233\) | 4.47214i | 0.292979i | 0.989212 | + | 0.146490i | \(0.0467975\pi\) | ||||
−0.989212 | + | 0.146490i | \(0.953202\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.74597i | 0.505291i | ||||||||
\(236\) | −4.94345 | + | 4.85410i | −0.321791 | + | 0.315975i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −9.27051 | − | 22.6728i | −0.600918 | − | 1.46966i | ||||
\(239\) | −6.92820 | + | 12.0000i | −0.448148 | + | 0.776215i | −0.998266 | − | 0.0588719i | \(-0.981250\pi\) |
0.550117 | + | 0.835087i | \(0.314583\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.00000 | − | 12.1244i | −0.450910 | − | 0.780998i | 0.547533 | − | 0.836784i | \(-0.315567\pi\) |
−0.998443 | + | 0.0557856i | \(0.982234\pi\) | |||||||
\(242\) | −6.92820 | + | 8.94427i | −0.445362 | + | 0.574960i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.00000 | + | 7.74597i | 0.128037 | + | 0.495885i | ||||
\(245\) | 15.4919 | − | 8.94427i | 0.989743 | − | 0.571429i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −6.54915 | − | 8.78115i | −0.415871 | − | 0.557604i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2.13525 | + | 15.6665i | −0.135045 | + | 0.990839i | ||||
\(251\) | −10.3923 | −0.655956 | −0.327978 | − | 0.944685i | \(-0.606367\pi\) | ||||
−0.327978 | + | 0.944685i | \(0.606367\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.0000 | −0.754434 | ||||||||
\(254\) | 2.21902 | − | 16.2812i | 0.139234 | − | 1.02157i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 7.48936 | + | 14.1389i | 0.468085 | + | 0.883684i | ||||
\(257\) | 19.3649 | + | 11.1803i | 1.20795 | + | 0.697410i | 0.962311 | − | 0.271951i | \(-0.0876688\pi\) |
0.245639 | + | 0.969361i | \(0.421002\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −13.4164 | + | 7.74597i | −0.833655 | + | 0.481311i | ||||
\(260\) | −8.66025 | + | 2.23607i | −0.537086 | + | 0.138675i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 16.5000 | − | 21.3014i | 1.01937 | − | 1.31601i | ||||
\(263\) | −3.46410 | − | 6.00000i | −0.213606 | − | 0.369976i | 0.739235 | − | 0.673448i | \(-0.235187\pi\) |
−0.952840 | + | 0.303472i | \(0.901854\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.50000 | − | 4.33013i | 0.153574 | − | 0.265998i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −10.8541 | − | 11.0539i | −0.663020 | − | 0.675224i | ||||
\(269\) | 4.47214i | 0.272671i | 0.990663 | + | 0.136335i | \(0.0435325\pi\) | ||||
−0.990663 | + | 0.136335i | \(0.956467\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.6190i | 0.705801i | 0.935661 | + | 0.352900i | \(0.114805\pi\) | ||||
−0.935661 | + | 0.352900i | \(0.885195\pi\) | |||||||
\(272\) | −9.22531 | + | 15.3262i | −0.559367 | + | 0.929290i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5.85410 | + | 2.39364i | −0.353659 | + | 0.144605i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.0000 | − | 17.3205i | −0.600842 | − | 1.04069i | −0.992694 | − | 0.120660i | \(-0.961499\pi\) |
0.391852 | − | 0.920028i | \(-0.371834\pi\) | |||||||
\(278\) | −17.3205 | − | 13.4164i | −1.03882 | − | 0.804663i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −22.5000 | − | 9.68246i | −1.34463 | − | 0.578638i | ||||
\(281\) | 3.87298 | − | 2.23607i | 0.231043 | − | 0.133393i | −0.380010 | − | 0.924982i | \(-0.624080\pi\) |
0.611053 | + | 0.791590i | \(0.290746\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −26.8328 | − | 15.4919i | −1.59505 | − | 0.920900i | −0.992422 | − | 0.122874i | \(-0.960789\pi\) |
−0.602623 | − | 0.798026i | \(-0.705878\pi\) | |||||||
\(284\) | −20.0265 | − | 5.56231i | −1.18835 | − | 0.330062i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.85410 | − | 0.661585i | −0.287029 | − | 0.0391203i | ||||
\(287\) | 34.6410 | 2.04479 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.00000 | −0.176471 | ||||||||
\(290\) | −14.0126 | − | 1.90983i | −0.822847 | − | 0.112149i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 9.63525 | + | 2.67617i | 0.563861 | + | 0.156611i | ||||
\(293\) | 19.3649 | + | 11.1803i | 1.13131 | + | 0.653162i | 0.944264 | − | 0.329189i | \(-0.106775\pi\) |
0.187046 | + | 0.982351i | \(0.440109\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.70820 | + | 3.87298i | −0.390567 | + | 0.225494i | ||||
\(296\) | 10.3923 | + | 4.47214i | 0.604040 | + | 0.259938i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2.50000 | − | 1.93649i | −0.144821 | − | 0.112178i | ||||
\(299\) | 6.92820 | + | 12.0000i | 0.400668 | + | 0.693978i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −15.0000 | + | 25.9808i | −0.864586 | + | 1.49751i | ||||
\(302\) | −5.06980 | + | 2.07295i | −0.291734 | + | 0.119285i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.94427i | 0.512148i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.2379i | 1.32626i | 0.748506 | + | 0.663129i | \(0.230772\pi\) | ||||
−0.748506 | + | 0.663129i | \(0.769228\pi\) | |||||||
\(308\) | −9.39993 | − | 9.57295i | −0.535611 | − | 0.545469i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −4.63525 | − | 11.3364i | −0.263265 | − | 0.643865i | ||||
\(311\) | 13.8564 | − | 24.0000i | 0.785725 | − | 1.36092i | −0.142840 | − | 0.989746i | \(-0.545624\pi\) |
0.928565 | − | 0.371169i | \(-0.121043\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.50000 | − | 4.33013i | −0.141308 | − | 0.244753i | 0.786681 | − | 0.617359i | \(-0.211798\pi\) |
−0.927990 | + | 0.372606i | \(0.878464\pi\) | |||||||
\(314\) | 17.3205 | − | 22.3607i | 0.977453 | − | 1.26189i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −15.0000 | + | 3.87298i | −0.843816 | + | 0.217872i | ||||
\(317\) | −13.5554 | + | 7.82624i | −0.761349 | + | 0.439565i | −0.829780 | − | 0.558091i | \(-0.811534\pi\) |
0.0684306 | + | 0.997656i | \(0.478201\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.70820 | − | 3.87298i | −0.375587 | − | 0.216845i | ||||
\(320\) | 4.15551 | + | 17.3992i | 0.232300 | + | 0.972644i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −5.12461 | + | 37.5997i | −0.285583 | + | 2.09535i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −4.43804 | + | 32.5623i | −0.245801 | + | 1.80346i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −15.1246 | − | 20.2792i | −0.835117 | − | 1.11973i | ||||
\(329\) | 11.6190 | + | 6.70820i | 0.640573 | + | 0.369835i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.70820 | + | 3.87298i | −0.368716 | + | 0.212878i | −0.672897 | − | 0.739736i | \(-0.734950\pi\) |
0.304181 | + | 0.952614i | \(0.401617\pi\) | |||||||
\(332\) | −6.06218 | − | 23.4787i | −0.332705 | − | 1.28856i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 3.00000 | − | 3.87298i | 0.164153 | − | 0.211920i | ||||
\(335\) | −8.66025 | − | 15.0000i | −0.473160 | − | 0.819538i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.00000 | − | 8.66025i | 0.272367 | − | 0.471754i | −0.697100 | − | 0.716974i | \(-0.745527\pi\) |
0.969468 | + | 0.245220i | \(0.0788601\pi\) | |||||||
\(338\) | −4.81710 | − | 11.7812i | −0.262016 | − | 0.640810i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −14.2705 | + | 14.0126i | −0.773927 | + | 0.759939i | ||||
\(341\) | − | 6.70820i | − | 0.363270i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 3.87298i | − | 0.209121i | ||||||
\(344\) | 21.7586 | − | 2.56231i | 1.17314 | − | 0.138150i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 20.4894 | − | 8.37772i | 1.10151 | − | 0.450389i | ||||
\(347\) | 16.4545 | − | 28.5000i | 0.883323 | − | 1.52996i | 0.0356990 | − | 0.999363i | \(-0.488634\pi\) |
0.847624 | − | 0.530598i | \(-0.178032\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.00000 | + | 13.8564i | 0.428230 | + | 0.741716i | 0.996716 | − | 0.0809766i | \(-0.0258039\pi\) |
−0.568486 | + | 0.822693i | \(0.692471\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.50000 | + | 9.68246i | −0.0799503 | + | 0.516077i | ||||
\(353\) | 15.4919 | − | 8.94427i | 0.824552 | − | 0.476056i | −0.0274314 | − | 0.999624i | \(-0.508733\pi\) |
0.851984 | + | 0.523568i | \(0.175399\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −20.1246 | − | 11.6190i | −1.06810 | − | 0.616670i | ||||
\(356\) | −2.39364 | + | 8.61803i | −0.126862 | + | 0.456755i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −7.28115 | − | 0.992377i | −0.384821 | − | 0.0524487i | ||||
\(359\) | 31.1769 | 1.64545 | 0.822727 | − | 0.568436i | \(-0.192451\pi\) | ||||
0.822727 | + | 0.568436i | \(0.192451\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 19.0000 | 1.00000 | ||||||||
\(362\) | 22.4201 | + | 3.05573i | 1.17838 | + | 0.160606i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −4.14590 | + | 14.9269i | −0.217304 | + | 0.782381i | ||||
\(365\) | 9.68246 | + | 5.59017i | 0.506803 | + | 0.292603i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 23.4787 | − | 13.5554i | 1.22558 | − | 0.707588i | 0.259477 | − | 0.965749i | \(-0.416450\pi\) |
0.966102 | + | 0.258161i | \(0.0831165\pi\) | |||||||
\(368\) | 24.2487 | − | 13.4164i | 1.26405 | − | 0.699379i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 10.0000 | + | 7.74597i | 0.519875 | + | 0.402694i | ||||
\(371\) | −4.33013 | − | 7.50000i | −0.224809 | − | 0.389381i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.00000 | − | 8.66025i | 0.258890 | − | 0.448411i | −0.707055 | − | 0.707159i | \(-0.749977\pi\) |
0.965945 | + | 0.258748i | \(0.0833099\pi\) | |||||||
\(374\) | −10.1396 | + | 4.14590i | −0.524306 | + | 0.214379i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.14590 | − | 9.73072i | −0.0590952 | − | 0.501824i | ||||
\(377\) | 8.94427i | 0.460653i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 9.27051 | + | 22.6728i | 0.474321 | + | 1.16004i | ||||
\(383\) | −12.1244 | + | 21.0000i | −0.619526 | + | 1.07305i | 0.370047 | + | 0.929013i | \(0.379342\pi\) |
−0.989572 | + | 0.144037i | \(0.953992\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.50000 | − | 12.9904i | −0.382235 | − | 0.662051i | ||||
\(386\) | −21.6506 | + | 27.9508i | −1.10199 | + | 1.42266i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −5.50000 | − | 21.3014i | −0.279220 | − | 1.08142i | ||||
\(389\) | −1.93649 | + | 1.11803i | −0.0981840 | + | 0.0566866i | −0.548288 | − | 0.836290i | \(-0.684720\pi\) |
0.450104 | + | 0.892976i | \(0.351387\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 26.8328 | + | 15.4919i | 1.35699 | + | 0.783461i | ||||
\(392\) | −18.1383 | + | 13.5279i | −0.916121 | + | 0.683260i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 4.69756 | − | 34.4664i | 0.236660 | − | 1.73639i | ||||
\(395\) | −17.3205 | −0.871489 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.0000 | 0.702640 | 0.351320 | − | 0.936255i | \(-0.385733\pi\) | ||||
0.351320 | + | 0.936255i | \(0.385733\pi\) | |||||||
\(398\) | −2.21902 | + | 16.2812i | −0.111230 | + | 0.816100i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.4919 | − | 8.94427i | −0.773630 | − | 0.446656i | 0.0605379 | − | 0.998166i | \(-0.480718\pi\) |
−0.834168 | + | 0.551510i | \(0.814052\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.70820 | + | 3.87298i | −0.334159 | + | 0.192927i | ||||
\(404\) | −4.33013 | + | 1.11803i | −0.215432 | + | 0.0556243i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −15.0000 | + | 19.3649i | −0.744438 | + | 0.961065i | ||||
\(407\) | 3.46410 | + | 6.00000i | 0.171709 | + | 0.297409i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.50000 | − | 6.06218i | 0.173064 | − | 0.299755i | −0.766426 | − | 0.642333i | \(-0.777967\pi\) |
0.939490 | + | 0.342578i | \(0.111300\pi\) | |||||||
\(410\) | −10.7047 | − | 26.1803i | −0.528666 | − | 1.29295i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −10.8541 | − | 11.0539i | −0.534743 | − | 0.544586i | ||||
\(413\) | 13.4164i | 0.660178i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 27.1109i | − | 1.33082i | ||||||
\(416\) | 10.5485 | − | 4.09017i | 0.517182 | − | 0.200537i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8.66025 | − | 15.0000i | 0.423081 | − | 0.732798i | −0.573158 | − | 0.819445i | \(-0.694282\pi\) |
0.996239 | + | 0.0866469i | \(0.0276152\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.00000 | + | 3.46410i | 0.0974740 | + | 0.168830i | 0.910638 | − | 0.413204i | \(-0.135590\pi\) |
−0.813164 | + | 0.582034i | \(0.802257\pi\) | |||||||
\(422\) | −17.3205 | − | 13.4164i | −0.843149 | − | 0.653101i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2.50000 | + | 5.80948i | −0.121411 | + | 0.282133i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 13.4164 | + | 7.74597i | 0.649265 | + | 0.374854i | ||||
\(428\) | −10.0133 | − | 2.78115i | −0.484009 | − | 0.134432i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 24.2705 | + | 3.30792i | 1.17043 | + | 0.159522i | ||||
\(431\) | −10.3923 | −0.500580 | −0.250290 | − | 0.968171i | \(-0.580526\pi\) | ||||
−0.250290 | + | 0.968171i | \(0.580526\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13.0000 | −0.624740 | −0.312370 | − | 0.949960i | \(-0.601123\pi\) | ||||
−0.312370 | + | 0.949960i | \(0.601123\pi\) | |||||||
\(434\) | −21.0189 | − | 2.86475i | −1.00894 | − | 0.137512i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −7.70820 | − | 2.14093i | −0.369156 | − | 0.102532i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.35410 | − | 1.93649i | 0.160083 | − | 0.0924237i | −0.417819 | − | 0.908530i | \(-0.637205\pi\) |
0.577901 | + | 0.816107i | \(0.303872\pi\) | |||||||
\(440\) | −4.33013 | + | 10.0623i | −0.206431 | + | 0.479702i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 10.0000 | + | 7.74597i | 0.475651 | + | 0.368438i | ||||
\(443\) | 12.1244 | + | 21.0000i | 0.576046 | + | 0.997740i | 0.995927 | + | 0.0901612i | \(0.0287382\pi\) |
−0.419882 | + | 0.907579i | \(0.637928\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.00000 | + | 8.66025i | −0.237023 | + | 0.410535i | ||||
\(446\) | 10.1396 | − | 4.14590i | 0.480124 | − | 0.196314i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 29.6976 | + | 8.83487i | 1.40308 | + | 0.417408i | ||||
\(449\) | 17.8885i | 0.844213i | 0.906546 | + | 0.422106i | \(0.138709\pi\) | ||||
−0.906546 | + | 0.422106i | \(0.861291\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 15.4919i | − | 0.729487i | ||||||
\(452\) | −25.0665 | − | 25.5279i | −1.17903 | − | 1.20073i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1.85410 | − | 4.53457i | −0.0870173 | − | 0.212818i | ||||
\(455\) | −8.66025 | + | 15.0000i | −0.405999 | + | 0.703211i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.5000 | + | 26.8468i | 0.725059 | + | 1.25584i | 0.958950 | + | 0.283577i | \(0.0915211\pi\) |
−0.233890 | + | 0.972263i | \(0.575146\pi\) | |||||||
\(458\) | 1.73205 | − | 2.23607i | 0.0809334 | − | 0.104485i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 30.0000 | − | 7.74597i | 1.39876 | − | 0.361158i | ||||
\(461\) | 32.9204 | − | 19.0066i | 1.53325 | − | 0.885225i | 0.534045 | − | 0.845456i | \(-0.320671\pi\) |
0.999209 | − | 0.0397685i | \(-0.0126621\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.35410 | + | 1.93649i | 0.155878 | + | 0.0899964i | 0.575910 | − | 0.817513i | \(-0.304648\pi\) |
−0.420032 | + | 0.907509i | \(0.637981\pi\) | |||||||
\(464\) | 17.8856 | + | 0.326238i | 0.830317 | + | 0.0151452i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.854102 | − | 6.26662i | 0.0395655 | − | 0.290296i | ||||
\(467\) | 5.19615 | 0.240449 | 0.120225 | − | 0.992747i | \(-0.461639\pi\) | ||||
0.120225 | + | 0.992747i | \(0.461639\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −30.0000 | −1.38527 | ||||||||
\(470\) | 1.47935 | − | 10.8541i | 0.0682372 | − | 0.500662i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 7.85410 | − | 5.85774i | 0.361514 | − | 0.269624i | ||||
\(473\) | 11.6190 | + | 6.70820i | 0.534240 | + | 0.308444i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 8.66025 | + | 33.5410i | 0.396942 | + | 1.53735i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 12.0000 | − | 15.4919i | 0.548867 | − | 0.708585i | ||||
\(479\) | −8.66025 | − | 15.0000i | −0.395697 | − | 0.685367i | 0.597493 | − | 0.801874i | \(-0.296164\pi\) |
−0.993190 | + | 0.116507i | \(0.962830\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.00000 | − | 6.92820i | 0.182384 | − | 0.315899i | ||||
\(482\) | 7.49326 | + | 18.3262i | 0.341309 | + | 0.834737i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 11.4164 | − | 11.2101i | 0.518928 | − | 0.509549i | ||||
\(485\) | − | 24.5967i | − | 1.11688i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 23.2379i | 1.05301i | 0.850172 | + | 0.526505i | \(0.176498\pi\) | ||||
−0.850172 | + | 0.526505i | \(0.823502\pi\) | |||||||
\(488\) | −1.32317 | − | 11.2361i | −0.0598970 | − | 0.508633i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −23.4164 | + | 9.57454i | −1.05785 | + | 0.432534i | ||||
\(491\) | −4.33013 | + | 7.50000i | −0.195416 | + | 0.338470i | −0.947037 | − | 0.321125i | \(-0.895939\pi\) |
0.751621 | + | 0.659595i | \(0.229272\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10.0000 | + | 17.3205i | 0.450377 | + | 0.780076i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7.50000 | + | 13.5554i | 0.336760 | + | 0.608657i | ||||
\(497\) | −34.8569 | + | 20.1246i | −1.56354 | + | 0.902712i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 33.5410 | + | 19.3649i | 1.50150 | + | 0.866893i | 0.999998 | + | 0.00173727i | \(0.000552990\pi\) |
0.501504 | + | 0.865155i | \(0.332780\pi\) | |||||||
\(500\) | 5.98409 | − | 21.5451i | 0.267617 | − | 0.963525i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 14.5623 | + | 1.98475i | 0.649948 | + | 0.0885839i | ||||
\(503\) | −20.7846 | −0.926740 | −0.463370 | − | 0.886165i | \(-0.653360\pi\) | ||||
−0.463370 | + | 0.886165i | \(0.653360\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.00000 | −0.222497 | ||||||||
\(506\) | 16.8151 | + | 2.29180i | 0.747522 | + | 0.101883i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −6.21885 | + | 22.3903i | −0.275917 | + | 0.993409i | ||||
\(509\) | −9.68246 | − | 5.59017i | −0.429167 | − | 0.247780i | 0.269824 | − | 0.962910i | \(-0.413034\pi\) |
−0.698992 | + | 0.715130i | \(0.746368\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16.7705 | − | 9.68246i | 0.741884 | − | 0.428327i | ||||
\(512\) | −7.79423 | − | 21.2426i | −0.344459 | − | 0.938801i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −25.0000 | − | 19.3649i | −1.10270 | − | 0.854150i | ||||
\(515\) | −8.66025 | − | 15.0000i | −0.381616 | − | 0.660979i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.00000 | − | 5.19615i | 0.131940 | − | 0.228527i | ||||
\(518\) | 20.2792 | − | 8.29180i | 0.891017 | − | 0.364321i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 12.5623 | − | 1.47935i | 0.550894 | − | 0.0648737i | ||||
\(521\) | − | 22.3607i | − | 0.979639i | −0.871824 | − | 0.489820i | \(-0.837063\pi\) | ||
0.871824 | − | 0.489820i | \(-0.162937\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 23.2379i | − | 1.01612i | −0.861321 | − | 0.508061i | \(-0.830362\pi\) | ||
0.861321 | − | 0.508061i | \(-0.169638\pi\) | |||||||
\(524\) | −27.1890 | + | 26.6976i | −1.18776 | + | 1.16629i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.70820 | + | 9.06914i | 0.161685 | + | 0.395433i | ||||
\(527\) | −8.66025 | + | 15.0000i | −0.377247 | + | 0.653410i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12.5000 | − | 21.6506i | −0.543478 | − | 0.941332i | ||||
\(530\) | −4.33013 | + | 5.59017i | −0.188089 | + | 0.242821i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −15.4919 | + | 8.94427i | −0.671030 | + | 0.387419i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −10.0623 | − | 5.80948i | −0.435031 | − | 0.251166i | ||||
\(536\) | 13.0983 | + | 17.5623i | 0.565760 | + | 0.758576i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0.854102 | − | 6.26662i | 0.0368230 | − | 0.270173i | ||||
\(539\) | −13.8564 | −0.596838 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.00000 | −0.171973 | −0.0859867 | − | 0.996296i | \(-0.527404\pi\) | ||||
−0.0859867 | + | 0.996296i | \(0.527404\pi\) | |||||||
\(542\) | 2.21902 | − | 16.2812i | 0.0953152 | − | 0.699335i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 15.8541 | − | 19.7141i | 0.679739 | − | 0.845237i | ||||
\(545\) | −7.74597 | − | 4.47214i | −0.331801 | − | 0.191565i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.70820 | + | 3.87298i | −0.286822 | + | 0.165597i | −0.636508 | − | 0.771270i | \(-0.719622\pi\) |
0.349686 | + | 0.936867i | \(0.386288\pi\) | |||||||
\(548\) | 8.66025 | − | 2.23607i | 0.369948 | − | 0.0955201i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −15.0000 | + | 25.9808i | −0.637865 | + | 1.10481i | ||||
\(554\) | 10.7047 | + | 26.1803i | 0.454798 | + | 1.11230i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 21.7082 | + | 22.1078i | 0.920633 | + | 0.937579i | ||||
\(557\) | − | 15.6525i | − | 0.663217i | −0.943417 | − | 0.331608i | \(-0.892409\pi\) | ||
0.943417 | − | 0.331608i | \(-0.107591\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 15.4919i | − | 0.655239i | ||||||
\(560\) | 29.6791 | + | 17.8647i | 1.25417 | + | 0.754923i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −5.85410 | + | 2.39364i | −0.246940 | + | 0.100969i | ||||
\(563\) | −9.52628 | + | 16.5000i | −0.401485 | + | 0.695392i | −0.993905 | − | 0.110237i | \(-0.964839\pi\) |
0.592421 | + | 0.805629i | \(0.298172\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −20.0000 | − | 34.6410i | −0.841406 | − | 1.45736i | ||||
\(566\) | 34.6410 | + | 26.8328i | 1.45607 | + | 1.12787i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 27.0000 | + | 11.6190i | 1.13289 | + | 0.487520i | ||||
\(569\) | −30.9839 | + | 17.8885i | −1.29891 | + | 0.749927i | −0.980216 | − | 0.197930i | \(-0.936578\pi\) |
−0.318695 | + | 0.947857i | \(0.603245\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.70820 | − | 3.87298i | −0.280730 | − | 0.162079i | 0.353024 | − | 0.935614i | \(-0.385153\pi\) |
−0.633754 | + | 0.773535i | \(0.718487\pi\) | |||||||
\(572\) | 6.67550 | + | 1.85410i | 0.279117 | + | 0.0775239i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −48.5410 | − | 6.61585i | −2.02606 | − | 0.276140i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.0000 | 0.582828 | 0.291414 | − | 0.956597i | \(-0.405874\pi\) | ||||
0.291414 | + | 0.956597i | \(0.405874\pi\) | |||||||
\(578\) | 4.20378 | + | 0.572949i | 0.174854 | + | 0.0238315i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 19.2705 | + | 5.35233i | 0.800164 | + | 0.222243i | ||||
\(581\) | −40.6663 | − | 23.4787i | −1.68712 | − | 0.974061i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.35410 | + | 1.93649i | −0.138913 | + | 0.0802013i | ||||
\(584\) | −12.9904 | − | 5.59017i | −0.537546 | − | 0.231323i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −25.0000 | − | 19.3649i | −1.03274 | − | 0.799957i | ||||
\(587\) | 9.52628 | + | 16.5000i | 0.393192 | + | 0.681028i | 0.992869 | − | 0.119214i | \(-0.0380376\pi\) |
−0.599677 | + | 0.800242i | \(0.704704\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 10.1396 | − | 4.14590i | 0.417441 | − | 0.170684i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −13.7082 | − | 8.25137i | −0.563404 | − | 0.339129i | ||||
\(593\) | 4.47214i | 0.183649i | 0.995775 | + | 0.0918243i | \(0.0292698\pi\) | ||||
−0.995775 | + | 0.0918243i | \(0.970730\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 38.7298i | 1.58777i | ||||||||
\(596\) | 3.13331 | + | 3.19098i | 0.128345 | + | 0.130708i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −7.41641 | − | 18.1383i | −0.303279 | − | 0.741729i | ||||
\(599\) | 8.66025 | − | 15.0000i | 0.353848 | − | 0.612883i | −0.633072 | − | 0.774093i | \(-0.718206\pi\) |
0.986920 | + | 0.161210i | \(0.0515395\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.5000 | + | 26.8468i | 0.632258 | + | 1.09510i | 0.987089 | + | 0.160173i | \(0.0512051\pi\) |
−0.354831 | + | 0.934931i | \(0.615462\pi\) | |||||||
\(602\) | 25.9808 | − | 33.5410i | 1.05890 | − | 1.36703i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 7.50000 | − | 1.93649i | 0.305171 | − | 0.0787947i | ||||
\(605\) | 15.4919 | − | 8.94427i | 0.629837 | − | 0.363636i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.70820 | − | 3.87298i | −0.272278 | − | 0.157200i | 0.357645 | − | 0.933858i | \(-0.383580\pi\) |
−0.629922 | + | 0.776658i | \(0.716913\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.70820 | − | 12.5332i | 0.0691632 | − | 0.507456i | ||||
\(611\) | −6.92820 | −0.280285 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 38.0000 | 1.53481 | 0.767403 | − | 0.641165i | \(-0.221549\pi\) | ||||
0.767403 | + | 0.641165i | \(0.221549\pi\) | |||||||
\(614\) | 4.43804 | − | 32.5623i | 0.179105 | − | 1.31411i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 11.3435 | + | 15.2094i | 0.457041 | + | 0.612804i | ||||
\(617\) | −15.4919 | − | 8.94427i | −0.623682 | − | 0.360083i | 0.154619 | − | 0.987974i | \(-0.450585\pi\) |
−0.778301 | + | 0.627891i | \(0.783918\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 33.5410 | − | 19.3649i | 1.34813 | − | 0.778342i | 0.360143 | − | 0.932897i | \(-0.382728\pi\) |
0.987984 | + | 0.154555i | \(0.0493945\pi\) | |||||||
\(620\) | 4.33013 | + | 16.7705i | 0.173902 | + | 0.673520i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −24.0000 | + | 30.9839i | −0.962312 | + | 1.24234i | ||||
\(623\) | 8.66025 | + | 15.0000i | 0.346966 | + | 0.600962i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12.5000 | − | 21.6506i | 0.500000 | − | 0.866025i | ||||
\(626\) | 2.67617 | + | 6.54508i | 0.106961 | + | 0.261594i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −28.5410 | + | 28.0252i | −1.13891 | + | 1.11833i | ||||
\(629\) | − | 17.8885i | − | 0.713263i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 34.8569i | 1.38763i | 0.720154 | + | 0.693815i | \(0.244071\pi\) | ||||
−0.720154 | + | 0.693815i | \(0.755929\pi\) | |||||||
\(632\) | 21.7586 | − | 2.56231i | 0.865509 | − | 0.101923i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 20.4894 | − | 8.37772i | 0.813736 | − | 0.332722i | ||||
\(635\) | −12.9904 | + | 22.5000i | −0.515508 | + | 0.892885i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.00000 | + | 13.8564i | 0.316972 | + | 0.549011i | ||||
\(638\) | 8.66025 | + | 6.70820i | 0.342863 | + | 0.265580i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2.50000 | − | 25.1744i | −0.0988212 | − | 0.995105i | ||||
\(641\) | 38.7298 | − | 22.3607i | 1.52974 | − | 0.883194i | 0.530364 | − | 0.847770i | \(-0.322055\pi\) |
0.999372 | − | 0.0354238i | \(-0.0112781\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −26.8328 | − | 15.4919i | −1.05818 | − | 0.610942i | −0.133254 | − | 0.991082i | \(-0.542543\pi\) |
−0.924929 | + | 0.380140i | \(0.875876\pi\) | |||||||
\(644\) | 14.3618 | − | 51.7082i | 0.565935 | − | 2.03759i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 20.7846 | 0.817127 | 0.408564 | − | 0.912730i | \(-0.366030\pi\) | ||||
0.408564 | + | 0.912730i | \(0.366030\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.00000 | 0.235521 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 12.4377 | − | 44.7806i | 0.487098 | − | 1.75374i | ||||
\(653\) | −9.68246 | − | 5.59017i | −0.378904 | − | 0.218760i | 0.298437 | − | 0.954429i | \(-0.403535\pi\) |
−0.677341 | + | 0.735669i | \(0.736868\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −36.8951 | + | 21.3014i | −1.44161 | + | 0.832315i | ||||
\(656\) | 17.3205 | + | 31.3050i | 0.676252 | + | 1.22225i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −15.0000 | − | 11.6190i | −0.584761 | − | 0.452954i | ||||
\(659\) | 4.33013 | + | 7.50000i | 0.168678 | + | 0.292159i | 0.937955 | − | 0.346756i | \(-0.112717\pi\) |
−0.769277 | + | 0.638915i | \(0.779384\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.00000 | − | 13.8564i | 0.311164 | − | 0.538952i | −0.667451 | − | 0.744654i | \(-0.732615\pi\) |
0.978615 | + | 0.205702i | \(0.0659478\pi\) | |||||||
\(662\) | 10.1396 | − | 4.14590i | 0.394087 | − | 0.161135i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4.01064 | + | 34.0575i | 0.155643 | + | 1.32169i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 30.9839i | − | 1.19970i | ||||||
\(668\) | −4.94345 | + | 4.85410i | −0.191268 | + | 0.187811i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 9.27051 | + | 22.6728i | 0.358151 | + | 0.875928i | ||||
\(671\) | 3.46410 | − | 6.00000i | 0.133730 | − | 0.231627i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.5000 | − | 19.9186i | −0.443292 | − | 0.767805i | 0.554639 | − | 0.832091i | \(-0.312856\pi\) |
−0.997932 | + | 0.0642860i | \(0.979523\pi\) | |||||||
\(674\) | −8.66025 | + | 11.1803i | −0.333581 | + | 0.430651i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.50000 | + | 17.4284i | 0.173077 | + | 0.670324i | ||||
\(677\) | −19.3649 | + | 11.1803i | −0.744254 | + | 0.429695i | −0.823614 | − | 0.567151i | \(-0.808046\pi\) |
0.0793599 | + | 0.996846i | \(0.474712\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −36.8951 | − | 21.3014i | −1.41590 | − | 0.817473i | ||||
\(680\) | 22.6728 | − | 16.9098i | 0.869464 | − | 0.648462i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.28115 | + | 9.39993i | −0.0490579 | + | 0.359942i | ||||
\(683\) | 10.3923 | 0.397650 | 0.198825 | − | 0.980035i | \(-0.436287\pi\) | ||||
0.198825 | + | 0.980035i | \(0.436287\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10.0000 | 0.382080 | ||||||||
\(686\) | −0.739674 | + | 5.42705i | −0.0282409 | + | 0.207206i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −30.9787 | − | 0.565061i | −1.18105 | − | 0.0215427i | ||||
\(689\) | 3.87298 | + | 2.23607i | 0.147549 | + | 0.0851874i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.4164 | − | 7.74597i | 0.510384 | − | 0.294670i | −0.222607 | − | 0.974908i | \(-0.571457\pi\) |
0.732992 | + | 0.680238i | \(0.238123\pi\) | |||||||
\(692\) | −30.3109 | + | 7.82624i | −1.15225 | + | 0.297509i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −28.5000 | + | 36.7933i | −1.08185 | + | 1.39666i | ||||
\(695\) | 17.3205 | + | 30.0000i | 0.657004 | + | 1.13796i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −20.0000 | + | 34.6410i | −0.757554 | + | 1.31212i | ||||
\(698\) | −8.56373 | − | 20.9443i | −0.324142 | − | 0.792752i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 15.6525i | − | 0.591186i | −0.955314 | − | 0.295593i | \(-0.904483\pi\) | ||
0.955314 | − | 0.295593i | \(-0.0955172\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 3.95107 | − | 13.2812i | 0.148912 | − | 0.500552i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −23.4164 | + | 9.57454i | −0.881288 | + | 0.360343i | ||||
\(707\) | −4.33013 | + | 7.50000i | −0.162851 | + | 0.282067i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16.0000 | − | 27.7128i | −0.600893 | − | 1.04078i | −0.992686 | − | 0.120723i | \(-0.961479\pi\) |
0.391794 | − | 0.920053i | \(-0.371855\pi\) | |||||||
\(710\) | 25.9808 | + | 20.1246i | 0.975041 | + | 0.755263i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 5.00000 | − | 11.6190i | 0.187383 | − | 0.435439i | ||||
\(713\) | 23.2379 | − | 13.4164i | 0.870266 | − | 0.502448i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.70820 | + | 3.87298i | 0.250873 | + | 0.144841i | ||||
\(716\) | 10.0133 | + | 2.78115i | 0.374213 | + | 0.103937i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −43.6869 | − | 5.95426i | −1.63038 | − | 0.222211i | ||||
\(719\) | −20.7846 | −0.775135 | −0.387568 | − | 0.921841i | \(-0.626685\pi\) | ||||
−0.387568 | + | 0.921841i | \(0.626685\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −30.0000 | −1.11726 | ||||||||
\(722\) | −26.6239 | − | 3.62868i | −0.990839 | − | 0.135045i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −30.8328 | − | 8.56373i | −1.14589 | − | 0.318269i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −36.8951 | + | 21.3014i | −1.36836 | + | 0.790026i | −0.990719 | − | 0.135925i | \(-0.956599\pi\) |
−0.377645 | + | 0.925950i | \(0.623266\pi\) | |||||||
\(728\) | 8.66025 | − | 20.1246i | 0.320970 | − | 0.745868i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −12.5000 | − | 9.68246i | −0.462646 | − | 0.358364i | ||||
\(731\) | −17.3205 | − | 30.0000i | −0.640622 | − | 1.10959i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.00000 | + | 6.92820i | −0.147743 | + | 0.255899i | −0.930393 | − | 0.366563i | \(-0.880534\pi\) |
0.782650 | + | 0.622462i | \(0.213868\pi\) | |||||||
\(734\) | −35.4886 | + | 14.5106i | −1.30991 | + | 0.535598i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −36.5410 | + | 14.1688i | −1.34692 | + | 0.522268i | ||||
\(737\) | 13.4164i | 0.494200i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 23.2379i | 0.854820i | 0.904058 | + | 0.427410i | \(0.140574\pi\) | ||||
−0.904058 | + | 0.427410i | \(0.859426\pi\) | |||||||
\(740\) | −12.5332 | − | 12.7639i | −0.460731 | − | 0.469211i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 4.63525 | + | 11.3364i | 0.170166 | + | 0.416173i | ||||
\(743\) | −12.1244 | + | 21.0000i | −0.444799 | + | 0.770415i | −0.998038 | − | 0.0626075i | \(-0.980058\pi\) |
0.553239 | + | 0.833023i | \(0.313392\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.50000 | + | 4.33013i | 0.0915929 | + | 0.158644i | ||||
\(746\) | −8.66025 | + | 11.1803i | −0.317074 | + | 0.409341i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 15.0000 | − | 3.87298i | 0.548454 | − | 0.141610i | ||||
\(749\) | −17.4284 | + | 10.0623i | −0.636821 | + | 0.367669i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.35410 | + | 1.93649i | 0.122393 | + | 0.0706636i | 0.559947 | − | 0.828529i | \(-0.310822\pi\) |
−0.437554 | + | 0.899192i | \(0.644155\pi\) | |||||||
\(752\) | −0.252703 | + | 13.8541i | −0.00921512 | + | 0.505207i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.70820 | − | 12.5332i | 0.0622091 | − | 0.456434i | ||||
\(755\) | 8.66025 | 0.315179 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −34.0000 | −1.23575 | −0.617876 | − | 0.786276i | \(-0.712006\pi\) | ||||
−0.617876 | + | 0.786276i | \(0.712006\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −15.4919 | − | 8.94427i | −0.561582 | − | 0.324230i | 0.192198 | − | 0.981356i | \(-0.438438\pi\) |
−0.753780 | + | 0.657127i | \(0.771772\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −13.4164 | + | 7.74597i | −0.485707 | + | 0.280423i | ||||
\(764\) | −8.66025 | − | 33.5410i | −0.313317 | − | 1.21347i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 21.0000 | − | 27.1109i | 0.758761 | − | 0.979556i | ||||
\(767\) | −3.46410 | − | 6.00000i | −0.125081 | − | 0.216647i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.50000 | + | 9.52628i | −0.198335 | + | 0.343526i | −0.947989 | − | 0.318304i | \(-0.896887\pi\) |
0.749654 | + | 0.661830i | \(0.230220\pi\) | |||||||
\(770\) | 8.02850 | + | 19.6353i | 0.289327 | + | 0.707605i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 35.6763 | − | 35.0315i | 1.28402 | − | 1.26081i | ||||
\(773\) | 4.47214i | 0.160852i | 0.996761 | + | 0.0804258i | \(0.0256280\pi\) | ||||
−0.996761 | + | 0.0804258i | \(0.974372\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 3.63871 | + | 30.8992i | 0.130622 | + | 1.10922i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2.92705 | − | 1.19682i | 0.104940 | − | 0.0429080i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.00000 | + | 15.5885i | 0.322045 | + | 0.557799i | ||||
\(782\) | −34.6410 | − | 26.8328i | −1.23876 | − | 0.959540i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 28.0000 | − | 15.4919i | 1.00000 | − | 0.553283i | ||||
\(785\) | −38.7298 | + | 22.3607i | −1.38233 | + | 0.798087i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13.4164 | + | 7.74597i | 0.478243 | + | 0.276114i | 0.719684 | − | 0.694302i | \(-0.244287\pi\) |
−0.241441 | + | 0.970416i | \(0.577620\pi\) | |||||||
\(788\) | −13.1650 | + | 47.3992i | −0.468984 | + | 1.68853i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 24.2705 | + | 3.30792i | 0.863506 | + | 0.117691i | ||||
\(791\) | −69.2820 | −2.46339 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.00000 | −0.284088 | ||||||||
\(794\) | −19.6176 | − | 2.67376i | −0.696203 | − | 0.0948883i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 6.21885 | − | 22.3903i | 0.220421 | − | 0.793603i | ||||
\(797\) | 36.7933 | + | 21.2426i | 1.30329 | + | 0.752453i | 0.980966 | − | 0.194177i | \(-0.0622038\pi\) |
0.322321 | + | 0.946631i | \(0.395537\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −13.4164 | + | 7.74597i | −0.474638 | + | 0.274033i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 20.0000 | + | 15.4919i | 0.706225 | + | 0.547039i | ||||
\(803\) | −4.33013 | − | 7.50000i | −0.152807 | − | 0.264669i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 30.0000 | − | 51.9615i | 1.05736 | − | 1.83140i | ||||
\(806\) | 10.1396 | − | 4.14590i | 0.357152 | − | 0.146033i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 6.28115 | − | 0.739674i | 0.220970 | − | 0.0260216i | ||||
\(809\) | 4.47214i | 0.157232i | 0.996905 | + | 0.0786160i | \(0.0250501\pi\) | ||||
−0.996905 | + | 0.0786160i | \(0.974950\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(812\) | 24.7172 | − | 24.2705i | 0.867405 | − | 0.851728i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −3.70820 | − | 9.06914i | −0.129972 | − | 0.317873i | ||||
\(815\) | 25.9808 | − | 45.0000i | 0.910066 | − | 1.57628i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −6.06218 | + | 7.82624i | −0.211959 | + | 0.273638i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 10.0000 | + | 38.7298i | 0.349215 | + | 1.35250i | ||||
\(821\) | 3.87298 | − | 2.23607i | 0.135168 | − | 0.0780393i | −0.430891 | − | 0.902404i | \(-0.641801\pi\) |
0.566059 | + | 0.824365i | \(0.308467\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 23.4787 | + | 13.5554i | 0.818417 | + | 0.472513i | 0.849870 | − | 0.526992i | \(-0.176680\pi\) |
−0.0314536 | + | 0.999505i | \(0.510014\pi\) | |||||||
\(824\) | 13.0983 | + | 17.5623i | 0.456301 | + | 0.611812i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.56231 | − | 18.7999i | 0.0891540 | − | 0.654131i | ||||
\(827\) | 31.1769 | 1.08413 | 0.542064 | − | 0.840337i | \(-0.317643\pi\) | ||||
0.542064 | + | 0.840337i | \(0.317643\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 38.0000 | 1.31979 | 0.659897 | − | 0.751356i | \(-0.270600\pi\) | ||||
0.659897 | + | 0.751356i | \(0.270600\pi\) | |||||||
\(830\) | −5.17772 | + | 37.9894i | −0.179721 | + | 1.31863i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −15.5623 | + | 3.71680i | −0.539526 | + | 0.128857i | ||||
\(833\) | 30.9839 | + | 17.8885i | 1.07353 | + | 0.619801i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.70820 | + | 3.87298i | −0.232147 | + | 0.134030i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −15.0000 | + | 19.3649i | −0.518166 | + | 0.668950i | ||||
\(839\) | −19.0526 | − | 33.0000i | −0.657767 | − | 1.13929i | −0.981192 | − | 0.193033i | \(-0.938168\pi\) |
0.323425 | − | 0.946254i | \(-0.395166\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.50000 | + | 7.79423i | −0.155172 | + | 0.268767i | ||||
\(842\) | −2.14093 | − | 5.23607i | −0.0737814 | − | 0.180447i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 21.7082 | + | 22.1078i | 0.747227 | + | 0.760981i | ||||
\(845\) | 20.1246i | 0.692308i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 30.9839i | − | 1.06462i | ||||||
\(848\) | 4.61266 | − | 7.66312i | 0.158399 | − | 0.263153i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −13.8564 | + | 24.0000i | −0.474991 | + | 0.822709i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.00000 | − | 1.73205i | −0.0342393 | − | 0.0593043i | 0.848398 | − | 0.529359i | \(-0.177568\pi\) |
−0.882637 | + | 0.470055i | \(0.844234\pi\) | |||||||
\(854\) | −17.3205 | − | 13.4164i | −0.592696 | − | 0.459100i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 13.5000 | + | 5.80948i | 0.461421 | + | 0.198564i | ||||
\(857\) | 3.87298 | − | 2.23607i | 0.132299 | − | 0.0763826i | −0.432390 | − | 0.901687i | \(-0.642330\pi\) |
0.564689 | + | 0.825304i | \(0.308996\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13.4164 | + | 7.74597i | 0.457762 | + | 0.264289i | 0.711103 | − | 0.703088i | \(-0.248196\pi\) |
−0.253341 | + | 0.967377i | \(0.581529\pi\) | |||||||
\(860\) | −33.3775 | − | 9.27051i | −1.13816 | − | 0.316122i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 14.5623 | + | 1.98475i | 0.495994 | + | 0.0676010i | ||||
\(863\) | 20.7846 | 0.707516 | 0.353758 | − | 0.935337i | \(-0.384904\pi\) | ||||
0.353758 | + | 0.935337i | \(0.384904\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −35.0000 | −1.19004 | ||||||||
\(866\) | 18.2164 | + | 2.48278i | 0.619017 | + | 0.0843683i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 28.9058 | + | 8.02850i | 0.981126 | + | 0.272505i | ||||
\(869\) | 11.6190 | + | 6.70820i | 0.394146 | + | 0.227560i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 13.4164 | − | 7.74597i | 0.454598 | − | 0.262462i | ||||
\(872\) | 10.3923 | + | 4.47214i | 0.351928 | + | 0.151446i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −21.6506 | − | 37.5000i | −0.731925 | − | 1.26773i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 17.0000 | − | 29.4449i | 0.574049 | − | 0.994282i | −0.422095 | − | 0.906552i | \(-0.638705\pi\) |
0.996144 | − | 0.0877308i | \(-0.0279615\pi\) | |||||||
\(878\) | −5.06980 | + | 2.07295i | −0.171097 | + | 0.0699586i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 7.98936 | − | 13.2729i | 0.269321 | − | 0.447430i | ||||
\(881\) | − | 22.3607i | − | 0.753350i | −0.926345 | − | 0.376675i | \(-0.877067\pi\) | ||
0.926345 | − | 0.376675i | \(-0.122933\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(884\) | −12.5332 | − | 12.7639i | −0.421538 | − | 0.429297i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −12.9787 | − | 31.7420i | −0.436028 | − | 1.06639i | ||||
\(887\) | 19.0526 | − | 33.0000i | 0.639722 | − | 1.10803i | −0.345771 | − | 0.938319i | \(-0.612383\pi\) |
0.985494 | − | 0.169713i | \(-0.0542840\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 22.5000 | + | 38.9711i | 0.754626 | + | 1.30705i | ||||
\(890\) | 8.66025 | − | 11.1803i | 0.290292 | − | 0.374766i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −15.0000 | + | 3.87298i | −0.502237 | + | 0.129677i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 10.0623 | + | 5.80948i | 0.336346 | + | 0.194189i | ||||
\(896\) | −39.9267 | − | 18.0517i | −1.33386 | − | 0.603064i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 3.41641 | − | 25.0665i | 0.114007 | − | 0.836479i | ||||
\(899\) | 17.3205 | 0.577671 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.0000 | 0.333148 | ||||||||
\(902\) | −2.95870 | + | 21.7082i | −0.0985138 | + | 0.722804i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 30.2492 | + | 40.5584i | 1.00607 | + | 1.34895i | ||||
\(905\) | −30.9839 | − | 17.8885i | −1.02994 | − | 0.594635i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 13.4164 | − | 7.74597i | 0.445485 | − | 0.257201i | −0.260437 | − | 0.965491i | \(-0.583867\pi\) |
0.705921 | + | 0.708290i | \(0.250533\pi\) | |||||||
\(908\) | 1.73205 | + | 6.70820i | 0.0574801 | + | 0.222620i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 15.0000 | − | 19.3649i | 0.497245 | − | 0.641941i | ||||
\(911\) | 22.5167 | + | 39.0000i | 0.746010 | + | 1.29213i | 0.949721 | + | 0.313097i | \(0.101366\pi\) |
−0.203711 | + | 0.979031i | \(0.565300\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10.5000 | + | 18.1865i | −0.347499 | + | 0.601886i | ||||
\(914\) | −16.5922 | − | 40.5795i | −0.548822 | − | 1.34225i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.85410 | + | 2.80252i | −0.0943022 | + | 0.0925978i | ||||
\(917\) | 73.7902i | 2.43677i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 11.6190i | − | 0.383274i | −0.981466 | − | 0.191637i | \(-0.938620\pi\) | ||
0.981466 | − | 0.191637i | \(-0.0613796\pi\) | |||||||
\(920\) | −43.5171 | + | 5.12461i | −1.43472 | + | 0.168953i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −49.7599 | + | 20.3459i | −1.63875 | + | 0.670057i | ||||
\(923\) | 10.3923 | − | 18.0000i | 0.342067 | − | 0.592477i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −4.33013 | − | 3.35410i | −0.142297 | − | 0.110223i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −25.0000 | − | 3.87298i | −0.820665 | − | 0.127137i | ||||
\(929\) | 38.7298 | − | 22.3607i | 1.27068 | − | 0.733630i | 0.295568 | − | 0.955322i | \(-0.404491\pi\) |
0.975117 | + | 0.221692i | \(0.0711578\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −2.39364 | + | 8.61803i | −0.0784061 | + | 0.282293i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −7.28115 | − | 0.992377i | −0.238247 | − | 0.0324716i | ||||
\(935\) | 17.3205 | 0.566441 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −31.0000 | −1.01273 | −0.506363 | − | 0.862320i | \(-0.669010\pi\) | ||||
−0.506363 | + | 0.862320i | \(0.669010\pi\) | |||||||
\(938\) | 42.0378 | + | 5.72949i | 1.37258 | + | 0.187074i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −4.14590 | + | 14.9269i | −0.135224 | + | 0.486861i | ||||
\(941\) | 36.7933 | + | 21.2426i | 1.19943 | + | 0.692490i | 0.960428 | − | 0.278529i | \(-0.0898468\pi\) |
0.239001 | + | 0.971019i | \(0.423180\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 53.6656 | − | 30.9839i | 1.74759 | − | 1.00897i | ||||
\(944\) | −12.1244 | + | 6.70820i | −0.394614 | + | 0.218333i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −15.0000 | − | 11.6190i | −0.487692 | − | 0.377765i | ||||
\(947\) | 25.1147 | + | 43.5000i | 0.816119 | + | 1.41356i | 0.908521 | + | 0.417838i | \(0.137212\pi\) |
−0.0924021 | + | 0.995722i | \(0.529455\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.00000 | + | 8.66025i | −0.162307 | + | 0.281124i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −5.72949 | − | 48.6536i | −0.185694 | − | 1.57687i | ||||
\(953\) | − | 35.7771i | − | 1.15893i | −0.814996 | − | 0.579467i | \(-0.803261\pi\) | ||
0.814996 | − | 0.579467i | \(-0.196739\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 38.7298i | − | 1.25327i | ||||||
\(956\) | −19.7738 | + | 19.4164i | −0.639530 | + | 0.627972i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 9.27051 | + | 22.6728i | 0.299517 | + | 0.732526i | ||||
\(959\) | 8.66025 | − | 15.0000i | 0.279654 | − | 0.484375i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.00000 | − | 13.8564i | −0.258065 | − | 0.446981i | ||||
\(962\) | −6.92820 | + | 8.94427i | −0.223374 | + | 0.288375i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −7.00000 | − | 27.1109i | −0.225455 | − | 0.873183i | ||||
\(965\) | 48.4123 | − | 27.9508i | 1.55845 | − | 0.899770i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23.4787 | + | 13.5554i | 0.755025 | + | 0.435914i | 0.827507 | − | 0.561456i | \(-0.189759\pi\) |
−0.0724820 | + | 0.997370i | \(0.523092\pi\) | |||||||
\(968\) | −18.1383 | + | 13.5279i | −0.582986 | + | 0.434802i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −4.69756 | + | 34.4664i | −0.150830 | + | 1.10665i | ||||
\(971\) | 36.3731 | 1.16727 | 0.583634 | − | 0.812017i | \(-0.301630\pi\) | ||||
0.583634 | + | 0.812017i | \(0.301630\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 60.0000 | 1.92351 | ||||||||
\(974\) | 4.43804 | − | 32.5623i | 0.142204 | − | 1.04336i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.291796 | + | 15.9973i | −0.00934016 | + | 0.512062i | ||||
\(977\) | 42.6028 | + | 24.5967i | 1.36298 | + | 0.786920i | 0.990020 | − | 0.140926i | \(-0.0450079\pi\) |
0.372965 | + | 0.927846i | \(0.378341\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.70820 | − | 3.87298i | 0.214395 | − | 0.123781i | ||||
\(980\) | 34.6410 | − | 8.94427i | 1.10657 | − | 0.285714i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 7.50000 | − | 9.68246i | 0.239335 | − | 0.308980i | ||||
\(983\) | 12.1244 | + | 21.0000i | 0.386707 | + | 0.669796i | 0.992004 | − | 0.126203i | \(-0.0402792\pi\) |
−0.605298 | + | 0.795999i | \(0.706946\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −27.5000 | + | 47.6314i | −0.876223 | + | 1.51766i | ||||
\(986\) | −10.7047 | − | 26.1803i | −0.340906 | − | 0.833752i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 53.6656i | 1.70647i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11.6190i | 0.369088i | 0.982824 | + | 0.184544i | \(0.0590808\pi\) | ||||
−0.982824 | + | 0.184544i | \(0.940919\pi\) | |||||||
\(992\) | −7.92058 | − | 20.4271i | −0.251479 | − | 0.648560i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 52.6869 | − | 21.5427i | 1.67113 | − | 0.683294i | ||||
\(995\) | 12.9904 | − | 22.5000i | 0.411823 | − | 0.713298i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7.00000 | − | 12.1244i | −0.221692 | − | 0.383982i | 0.733630 | − | 0.679549i | \(-0.237825\pi\) |
−0.955322 | + | 0.295567i | \(0.904491\pi\) | |||||||
\(998\) | −43.3013 | − | 33.5410i | −1.37068 | − | 1.06172i | ||||
\(999\) | 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 | 324.2.h.d.215.1 | 8 | ||
3.2 | odd | 2 | inner | 324.2.h.d.215.4 | 8 | ||
4.3 | odd | 2 | inner | 324.2.h.d.215.2 | 8 | ||
9.2 | odd | 6 | inner | 324.2.h.d.107.2 | 8 | ||
9.4 | even | 3 | 108.2.b.a.107.3 | yes | 4 | ||
9.5 | odd | 6 | 108.2.b.a.107.2 | yes | 4 | ||
9.7 | even | 3 | inner | 324.2.h.d.107.3 | 8 | ||
12.11 | even | 2 | inner | 324.2.h.d.215.3 | 8 | ||
36.7 | odd | 6 | inner | 324.2.h.d.107.4 | 8 | ||
36.11 | even | 6 | inner | 324.2.h.d.107.1 | 8 | ||
36.23 | even | 6 | 108.2.b.a.107.4 | yes | 4 | ||
36.31 | odd | 6 | 108.2.b.a.107.1 | ✓ | 4 | ||
72.5 | odd | 6 | 1728.2.c.c.1727.2 | 4 | |||
72.13 | even | 6 | 1728.2.c.c.1727.4 | 4 | |||
72.59 | even | 6 | 1728.2.c.c.1727.1 | 4 | |||
72.67 | odd | 6 | 1728.2.c.c.1727.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.2.b.a.107.1 | ✓ | 4 | 36.31 | odd | 6 | ||
108.2.b.a.107.2 | yes | 4 | 9.5 | odd | 6 | ||
108.2.b.a.107.3 | yes | 4 | 9.4 | even | 3 | ||
108.2.b.a.107.4 | yes | 4 | 36.23 | even | 6 | ||
324.2.h.d.107.1 | 8 | 36.11 | even | 6 | inner | ||
324.2.h.d.107.2 | 8 | 9.2 | odd | 6 | inner | ||
324.2.h.d.107.3 | 8 | 9.7 | even | 3 | inner | ||
324.2.h.d.107.4 | 8 | 36.7 | odd | 6 | inner | ||
324.2.h.d.215.1 | 8 | 1.1 | even | 1 | trivial | ||
324.2.h.d.215.2 | 8 | 4.3 | odd | 2 | inner | ||
324.2.h.d.215.3 | 8 | 12.11 | even | 2 | inner | ||
324.2.h.d.215.4 | 8 | 3.2 | odd | 2 | inner | ||
1728.2.c.c.1727.1 | 4 | 72.59 | even | 6 | |||
1728.2.c.c.1727.2 | 4 | 72.5 | odd | 6 | |||
1728.2.c.c.1727.3 | 4 | 72.67 | odd | 6 | |||
1728.2.c.c.1727.4 | 4 | 72.13 | even | 6 |