Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [756,2,Mod(17,756)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(756, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("756.17");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 756.bm (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: | \(6.03669039281\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} + 5 x^{14} - 17 x^{13} + 22 x^{12} - 31 x^{11} + 62 x^{10} - 52 x^{9} + 52 x^{8} + \cdots + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 3^{6} \) |
Twist minimal: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 89.6 | ||
Root | \(-0.268067 - 1.71118i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 756.89 |
Dual form | 756.2.bm.a.17.6 |
$q$-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 \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) | \(379\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.68574 | 0.753885 | 0.376942 | − | 0.926237i | \(-0.376975\pi\) | ||||
0.376942 | + | 0.926237i | \(0.376975\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.0236360 | + | 2.64565i | −0.00893357 | + | 0.999960i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 3.90538i | − | 1.17752i | −0.808309 | − | 0.588758i | \(-0.799617\pi\) | ||
0.808309 | − | 0.588758i | \(-0.200383\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.24391 | − | 3.02757i | 1.45440 | − | 0.839698i | 0.455673 | − | 0.890147i | \(-0.349399\pi\) |
0.998727 | + | 0.0504496i | \(0.0160654\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.201244 | − | 0.348565i | −0.0488088 | − | 0.0845393i | 0.840589 | − | 0.541674i | \(-0.182209\pi\) |
−0.889398 | + | 0.457134i | \(0.848876\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.145617 | − | 0.0840718i | −0.0334067 | − | 0.0192874i | 0.483204 | − | 0.875508i | \(-0.339473\pi\) |
−0.516610 | + | 0.856221i | \(0.672806\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.88395i | 1.85243i | 0.376993 | + | 0.926216i | \(0.376958\pi\) | ||||
−0.376993 | + | 0.926216i | \(0.623042\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.15829 | −0.431658 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.15380 | + | 3.55290i | 1.14273 | + | 0.659757i | 0.947106 | − | 0.320921i | \(-0.103993\pi\) |
0.195627 | + | 0.980678i | \(0.437326\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.44527 | + | 3.14383i | 0.978000 | + | 0.564649i | 0.901666 | − | 0.432434i | \(-0.142345\pi\) |
0.0763342 | + | 0.997082i | \(0.475678\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.0398441 | + | 4.45986i | −0.00673488 | + | 0.753855i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.13257 | − | 5.42578i | 0.514992 | − | 0.891992i | −0.484857 | − | 0.874594i | \(-0.661128\pi\) |
0.999849 | − | 0.0173987i | \(-0.00553846\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.64707 | + | 2.85281i | 0.257229 | + | 0.445534i | 0.965499 | − | 0.260408i | \(-0.0838571\pi\) |
−0.708269 | + | 0.705942i | \(0.750524\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.80474 | − | 3.12590i | 0.275220 | − | 0.476695i | −0.694971 | − | 0.719038i | \(-0.744583\pi\) |
0.970191 | + | 0.242343i | \(0.0779161\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.38482 | − | 7.59474i | −0.639592 | − | 1.10781i | −0.985522 | − | 0.169546i | \(-0.945770\pi\) |
0.345930 | − | 0.938260i | \(-0.387563\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.99888 | − | 0.125065i | −0.999840 | − | 0.0178664i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.94628 | − | 2.85574i | 0.679424 | − | 0.392266i | −0.120214 | − | 0.992748i | \(-0.538358\pi\) |
0.799638 | + | 0.600482i | \(0.205025\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 6.58345i | − | 0.887712i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.25163 | + | 3.89994i | −0.293138 | + | 0.507729i | −0.974550 | − | 0.224171i | \(-0.928033\pi\) |
0.681412 | + | 0.731900i | \(0.261366\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.43678 | − | 2.56157i | 0.568071 | − | 0.327976i | −0.188308 | − | 0.982110i | \(-0.560300\pi\) |
0.756379 | + | 0.654134i | \(0.226967\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 8.83986 | − | 5.10369i | 1.09645 | − | 0.633035i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.95521 | − | 5.11857i | 0.361036 | − | 0.625332i | −0.627096 | − | 0.778942i | \(-0.715757\pi\) |
0.988132 | + | 0.153610i | \(0.0490899\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.4308i | 1.35658i | 0.734792 | + | 0.678292i | \(0.237280\pi\) | ||||
−0.734792 | + | 0.678292i | \(0.762720\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.05559 | + | 3.49620i | −0.708753 | + | 0.409199i | −0.810599 | − | 0.585601i | \(-0.800858\pi\) |
0.101846 | + | 0.994800i | \(0.467525\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 10.3323 | + | 0.0923076i | 1.17747 | + | 0.0105194i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.603968 | − | 1.04610i | −0.0679517 | − | 0.117696i | 0.830048 | − | 0.557692i | \(-0.188313\pi\) |
−0.898000 | + | 0.439996i | \(0.854980\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.181350 | − | 0.314108i | 0.0199058 | − | 0.0344779i | −0.855901 | − | 0.517140i | \(-0.826997\pi\) |
0.875807 | + | 0.482662i | \(0.160330\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.339244 | − | 0.587588i | −0.0367962 | − | 0.0637329i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.38526 | + | 2.39934i | −0.146837 | + | 0.254329i | −0.930057 | − | 0.367416i | \(-0.880243\pi\) |
0.783220 | + | 0.621745i | \(0.213576\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.88594 | + | 13.9451i | 0.826671 | + | 1.46184i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.245471 | − | 0.141723i | −0.0251848 | − | 0.0145405i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.508914 | + | 0.293821i | 0.0516723 | + | 0.0298330i | 0.525614 | − | 0.850723i | \(-0.323836\pi\) |
−0.473941 | + | 0.880556i | \(0.657169\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.8466 | −1.37779 | −0.688893 | − | 0.724863i | \(-0.741903\pi\) | ||||
−0.688893 | + | 0.724863i | \(0.741903\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.0793i | 1.19021i | 0.803647 | + | 0.595106i | \(0.202890\pi\) | ||||
−0.803647 | + | 0.595106i | \(0.797110\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −15.9299 | − | 9.19711i | −1.54000 | − | 0.889118i | −0.998838 | − | 0.0481978i | \(-0.984652\pi\) |
−0.541159 | − | 0.840920i | \(-0.682014\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.51036 | − | 9.54422i | −0.527796 | − | 0.914170i | −0.999475 | − | 0.0323997i | \(-0.989685\pi\) |
0.471679 | − | 0.881771i | \(-0.343648\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.36811 | − | 4.25398i | 0.693133 | − | 0.400181i | −0.111652 | − | 0.993747i | \(-0.535614\pi\) |
0.804785 | + | 0.593567i | \(0.202281\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 14.9760i | 1.39652i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.926935 | − | 0.524181i | 0.0849720 | − | 0.0480516i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.25200 | −0.386545 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.0670 | −1.07930 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.6312 | −0.943365 | −0.471682 | − | 0.881769i | \(-0.656353\pi\) | ||||
−0.471682 | + | 0.881769i | \(0.656353\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.33480 | −0.553474 | −0.276737 | − | 0.960946i | \(-0.589253\pi\) | ||||
−0.276737 | + | 0.960946i | \(0.589253\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.225866 | − | 0.383263i | 0.0195851 | − | 0.0332331i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 16.6459i | − | 1.42216i | −0.703113 | − | 0.711078i | \(-0.748207\pi\) | ||
0.703113 | − | 0.711078i | \(-0.251793\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.24007 | + | 2.44800i | −0.359638 | + | 0.207637i | −0.668922 | − | 0.743333i | \(-0.733244\pi\) |
0.309284 | + | 0.950970i | \(0.399911\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −11.8238 | − | 20.4795i | −0.988758 | − | 1.71258i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 10.3737 | + | 5.98926i | 0.861489 | + | 0.497381i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 5.28696i | − | 0.433125i | −0.976269 | − | 0.216562i | \(-0.930516\pi\) | ||
0.976269 | − | 0.216562i | \(-0.0694845\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.5833 | −1.18677 | −0.593385 | − | 0.804919i | \(-0.702209\pi\) | ||||
−0.593385 | + | 0.804919i | \(0.702209\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.17930 | + | 5.29967i | 0.737299 | + | 0.425680i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.4160 | − | 8.90044i | −1.23033 | − | 0.710332i | −0.263232 | − | 0.964732i | \(-0.584789\pi\) |
−0.967099 | + | 0.254400i | \(0.918122\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −23.5038 | − | 0.209981i | −1.85236 | − | 0.0165488i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.0482228 | − | 0.0835243i | 0.00377710 | − | 0.00654213i | −0.864131 | − | 0.503267i | \(-0.832131\pi\) |
0.867908 | + | 0.496725i | \(0.165464\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.47872 | + | 4.29327i | 0.191809 | + | 0.332224i | 0.945850 | − | 0.324604i | \(-0.105231\pi\) |
−0.754041 | + | 0.656828i | \(0.771898\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.8324 | − | 20.4943i | 0.910185 | − | 1.57649i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.40033 | + | 12.8177i | 0.562637 | + | 0.974515i | 0.997265 | + | 0.0739055i | \(0.0235463\pi\) |
−0.434629 | + | 0.900610i | \(0.643120\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.0510133 | − | 5.71007i | 0.00385625 | − | 0.431641i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.592751 | + | 0.342225i | −0.0443043 | + | 0.0255791i | −0.521989 | − | 0.852952i | \(-0.674810\pi\) |
0.477684 | + | 0.878532i | \(0.341476\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.84745i | 0.583297i | 0.956526 | + | 0.291648i | \(0.0942037\pi\) | ||||
−0.956526 | + | 0.291648i | \(0.905796\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.28070 | − | 9.14644i | 0.388245 | − | 0.672459i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.36128 | + | 0.785934i | −0.0995464 | + | 0.0574732i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.9694 | − | 9.79729i | 1.22786 | − | 0.708907i | 0.261281 | − | 0.965263i | \(-0.415855\pi\) |
0.966582 | + | 0.256356i | \(0.0825219\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.18116 | + | 15.9022i | −0.660875 | + | 1.14467i | 0.319512 | + | 0.947582i | \(0.396481\pi\) |
−0.980386 | + | 0.197086i | \(0.936852\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.92313i | 0.422006i | 0.977485 | + | 0.211003i | \(0.0676730\pi\) | ||||
−0.977485 | + | 0.211003i | \(0.932327\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.6268 | + | 7.86741i | −0.965975 | + | 0.557706i | −0.898007 | − | 0.439982i | \(-0.854985\pi\) |
−0.0679681 | + | 0.997687i | \(0.521652\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −9.54517 | + | 16.1968i | −0.669939 | + | 1.13679i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.77653 | + | 4.80909i | 0.193921 | + | 0.335881i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.328332 | + | 0.568688i | −0.0227112 | + | 0.0393370i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.06619 | + | 8.77489i | 0.348771 | + | 0.604088i | 0.986031 | − | 0.166560i | \(-0.0532659\pi\) |
−0.637261 | + | 0.770648i | \(0.719933\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.04231 | − | 5.26944i | 0.207484 | − | 0.359373i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.44616 | + | 14.3320i | −0.573363 | + | 0.972917i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.11061 | − | 1.21856i | −0.141975 | − | 0.0819693i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.3944 | − | 7.73325i | −0.896955 | − | 0.517857i | −0.0207437 | − | 0.999785i | \(-0.506603\pi\) |
−0.876211 | + | 0.481928i | \(0.839937\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −28.0719 | −1.86320 | −0.931600 | − | 0.363486i | \(-0.881586\pi\) | ||||
−0.931600 | + | 0.363486i | \(0.881586\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 17.0264i | − | 1.12514i | −0.826751 | − | 0.562568i | \(-0.809814\pi\) | ||
0.826751 | − | 0.562568i | \(-0.190186\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.0015 | + | 9.23847i | 1.04829 | + | 0.605233i | 0.922171 | − | 0.386782i | \(-0.126413\pi\) |
0.126122 | + | 0.992015i | \(0.459747\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.39166 | − | 12.8027i | −0.482179 | − | 0.835158i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.06656 | − | 3.50253i | 0.392413 | − | 0.226560i | −0.290792 | − | 0.956786i | \(-0.593919\pi\) |
0.683205 | + | 0.730226i | \(0.260585\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 6.21759i | − | 0.400510i | −0.979744 | − | 0.200255i | \(-0.935823\pi\) | ||
0.979744 | − | 0.200255i | \(-0.0641771\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −11.7983 | − | 0.210827i | −0.753764 | − | 0.0134692i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.01813 | −0.0647823 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.81844 | 0.619734 | 0.309867 | − | 0.950780i | \(-0.399715\pi\) | ||||
0.309867 | + | 0.950780i | \(0.399715\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 34.6952 | 2.18127 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.33581 | 0.0833254 | 0.0416627 | − | 0.999132i | \(-0.486735\pi\) | ||||
0.0416627 | + | 0.999132i | \(0.486735\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 14.2806 | + | 8.41593i | 0.887356 | + | 0.522940i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 20.3502i | − | 1.25485i | −0.778678 | − | 0.627424i | \(-0.784109\pi\) | ||
0.778678 | − | 0.627424i | \(-0.215891\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.33814 | − | 4.81402i | 0.512208 | − | 0.295723i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.3614 | + | 23.1426i | 0.814659 | + | 1.41103i | 0.909572 | + | 0.415546i | \(0.136409\pi\) |
−0.0949131 | + | 0.995486i | \(0.530257\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.76517 | + | 2.17382i | 0.228718 | + | 0.132050i | 0.609980 | − | 0.792417i | \(-0.291177\pi\) |
−0.381263 | + | 0.924467i | \(0.624511\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 8.42894i | 0.508284i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.39803 | −0.264252 | −0.132126 | − | 0.991233i | \(-0.542180\pi\) | ||||
−0.132126 | + | 0.991233i | \(0.542180\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.62273 | − | 2.66893i | −0.275769 | − | 0.159215i | 0.355738 | − | 0.934586i | \(-0.384230\pi\) |
−0.631506 | + | 0.775371i | \(0.717563\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.5431 | − | 8.97381i | −0.923941 | − | 0.533437i | −0.0390505 | − | 0.999237i | \(-0.512433\pi\) |
−0.884890 | + | 0.465800i | \(0.845767\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.58645 | + | 4.29014i | −0.447814 | + | 0.253239i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.41900 | − | 14.5821i | 0.495235 | − | 0.857773i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −13.1126 | − | 22.7117i | −0.766048 | − | 1.32683i | −0.939691 | − | 0.342026i | \(-0.888887\pi\) |
0.173642 | − | 0.984809i | \(-0.444446\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.79566 | + | 6.57428i | −0.220992 | + | 0.382769i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 26.8968 | + | 46.5867i | 1.55548 | + | 2.69418i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.22735 | + | 4.84858i | 0.474217 | + | 0.279467i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7.47924 | − | 4.31814i | 0.428260 | − | 0.247256i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.19520i | 0.410652i | 0.978694 | + | 0.205326i | \(0.0658254\pi\) | ||||
−0.978694 | + | 0.205326i | \(0.934175\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.08721 | + | 1.88311i | −0.0616503 | + | 0.106781i | −0.895203 | − | 0.445658i | \(-0.852970\pi\) |
0.833553 | + | 0.552440i | \(0.186303\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.2870 | + | 5.93922i | −0.581457 | + | 0.335704i | −0.761712 | − | 0.647916i | \(-0.775641\pi\) |
0.180255 | + | 0.983620i | \(0.442308\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7.09969 | + | 4.09901i | −0.398758 | + | 0.230223i | −0.685948 | − | 0.727651i | \(-0.740612\pi\) |
0.287190 | + | 0.957874i | \(0.407279\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 13.8754 | − | 24.0329i | 0.776875 | − | 1.34559i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.0676757i | 0.00376558i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −11.3179 | + | 6.53438i | −0.627803 | + | 0.362462i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 20.1966 | − | 11.4212i | 1.11348 | − | 0.629670i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.58540 | − | 14.8704i | −0.471897 | − | 0.817349i | 0.527586 | − | 0.849501i | \(-0.323097\pi\) |
−0.999483 | + | 0.0321526i | \(0.989764\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.98170 | − | 8.62856i | 0.272179 | − | 0.471428i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.95399 | + | 6.84850i | 0.215387 | + | 0.373062i | 0.953392 | − | 0.301733i | \(-0.0975653\pi\) |
−0.738005 | + | 0.674795i | \(0.764232\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12.2779 | − | 21.2659i | 0.664883 | − | 1.15161i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.496303 | − | 18.5136i | 0.0267979 | − | 0.999641i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.443850 | + | 0.256257i | 0.0238271 | + | 0.0137566i | 0.511866 | − | 0.859065i | \(-0.328954\pi\) |
−0.488039 | + | 0.872822i | \(0.662288\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.74612 | − | 3.31752i | −0.307583 | − | 0.177583i | 0.338262 | − | 0.941052i | \(-0.390161\pi\) |
−0.645844 | + | 0.763469i | \(0.723494\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −18.0687 | −0.961702 | −0.480851 | − | 0.876802i | \(-0.659672\pi\) | ||||
−0.480851 | + | 0.876802i | \(0.659672\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 19.2693i | 1.02271i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.52677 | + | 0.881479i | 0.0805796 | + | 0.0465227i | 0.539748 | − | 0.841826i | \(-0.318519\pi\) |
−0.459169 | + | 0.888349i | \(0.651853\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.48586 | − | 16.4300i | −0.499256 | − | 0.864737i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −10.2081 | + | 5.89367i | −0.534318 | + | 0.308489i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 33.4417i | 1.74564i | 0.488038 | + | 0.872822i | \(0.337713\pi\) | ||||
−0.488038 | + | 0.872822i | \(0.662287\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.43836 | + | 13.1536i | 0.386180 | + | 0.682902i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 25.5688 | 1.32390 | 0.661952 | − | 0.749546i | \(-0.269728\pi\) | ||||
0.661952 | + | 0.749546i | \(0.269728\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 43.0267 | 2.21599 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 25.7920 | 1.32485 | 0.662423 | − | 0.749130i | \(-0.269528\pi\) | ||||
0.662423 | + | 0.749130i | \(0.269528\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −32.8316 | −1.67762 | −0.838808 | − | 0.544427i | \(-0.816747\pi\) | ||||
−0.838808 | + | 0.544427i | \(0.816747\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 17.4175 | + | 0.155606i | 0.887676 | + | 0.00793044i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 20.1544i | 1.02187i | 0.859619 | + | 0.510935i | \(0.170701\pi\) | ||||
−0.859619 | + | 0.510935i | \(0.829299\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.09663 | − | 1.78784i | 0.156603 | − | 0.0904150i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.01813 | − | 1.76346i | −0.0512278 | − | 0.0887291i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −30.2125 | − | 17.4432i | −1.51632 | − | 0.875449i | −0.999816 | − | 0.0191652i | \(-0.993899\pi\) |
−0.516506 | − | 0.856284i | \(-0.672768\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.66245i | 0.482520i | 0.970461 | + | 0.241260i | \(0.0775606\pi\) | ||||
−0.970461 | + | 0.241260i | \(0.922439\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 38.0727 | 1.89654 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −21.1897 | − | 12.2339i | −1.05034 | − | 0.606412i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 32.1202 | + | 18.5446i | 1.58824 | + | 0.916973i | 0.993597 | + | 0.112986i | \(0.0360416\pi\) |
0.594647 | + | 0.803987i | \(0.297292\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −10.2646 | − | 6.04920i | −0.505090 | − | 0.297662i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.305709 | − | 0.529504i | 0.0150067 | − | 0.0259923i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.84193 | + | 3.19031i | 0.0899841 | + | 0.155857i | 0.907504 | − | 0.420043i | \(-0.137985\pi\) |
−0.817520 | + | 0.575900i | \(0.804652\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.55139 | + | 14.8114i | −0.416769 | + | 0.721866i | −0.995612 | − | 0.0935732i | \(-0.970171\pi\) |
0.578843 | + | 0.815439i | \(0.303504\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.434342 | + | 0.752303i | 0.0210687 | + | 0.0364921i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.67215 | + | 11.7987i | 0.322888 | + | 0.570978i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 27.3242 | − | 15.7756i | 1.31616 | − | 0.759885i | 0.333051 | − | 0.942909i | \(-0.391922\pi\) |
0.983108 | + | 0.183024i | \(0.0585887\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10.0692i | 0.483893i | 0.970290 | + | 0.241947i | \(0.0777859\pi\) | ||||
−0.970290 | + | 0.241947i | \(0.922214\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.746890 | − | 1.29365i | 0.0357286 | − | 0.0618837i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 24.1966 | − | 13.9699i | 1.15484 | − | 0.666748i | 0.204779 | − | 0.978808i | \(-0.434352\pi\) |
0.950062 | + | 0.312060i | \(0.101019\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 30.1930 | − | 17.4319i | 1.43451 | − | 0.828215i | 0.437050 | − | 0.899437i | \(-0.356023\pi\) |
0.997460 | + | 0.0712223i | \(0.0226900\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.33518 | + | 4.04466i | −0.110698 | + | 0.191735i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 23.2411i | 1.09682i | 0.836211 | + | 0.548408i | \(0.184766\pi\) | ||||
−0.836211 | + | 0.548408i | \(0.815234\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.1413 | − | 6.43244i | 0.524624 | − | 0.302892i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 13.2936 | + | 23.5078i | 0.623215 | + | 1.10206i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.10938 | + | 5.38560i | 0.145451 | + | 0.251928i | 0.929541 | − | 0.368719i | \(-0.120203\pi\) |
−0.784090 | + | 0.620647i | \(0.786870\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.17165 | + | 3.76140i | −0.101144 | + | 0.175186i | −0.912156 | − | 0.409843i | \(-0.865584\pi\) |
0.811012 | + | 0.585029i | \(0.198917\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.57451 | + | 6.19124i | 0.166122 | + | 0.287731i | 0.937053 | − | 0.349187i | \(-0.113542\pi\) |
−0.770931 | + | 0.636918i | \(0.780209\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0.944451 | − | 1.63584i | 0.0437040 | − | 0.0756975i | −0.843346 | − | 0.537371i | \(-0.819417\pi\) |
0.887050 | + | 0.461673i | \(0.152751\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.4721 | + | 7.93941i | 0.622082 | + | 0.366608i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −12.2078 | − | 7.04818i | −0.561316 | − | 0.324076i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.314283 | + | 0.181451i | 0.0144203 | + | 0.00832555i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10.4498 | 0.477465 | 0.238732 | − | 0.971085i | \(-0.423268\pi\) | ||||
0.238732 | + | 0.971085i | \(0.423268\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 37.9364i | − | 1.72975i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.857895 | + | 0.495306i | 0.0389550 | + | 0.0224907i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.8298 | − | 20.4898i | −0.536060 | − | 0.928483i | −0.999111 | − | 0.0421513i | \(-0.986579\pi\) |
0.463052 | − | 0.886331i | \(-0.346754\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11.6767 | − | 6.74152i | 0.526960 | − | 0.304241i | −0.212817 | − | 0.977092i | \(-0.568264\pi\) |
0.739778 | + | 0.672851i | \(0.234931\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 2.86000i | − | 0.128808i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −30.2418 | − | 0.270178i | −1.35653 | − | 0.0121191i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.0807 | −0.540807 | −0.270403 | − | 0.962747i | \(-0.587157\pi\) | ||||
−0.270403 | + | 0.962747i | \(0.587157\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 20.5283 | 0.915310 | 0.457655 | − | 0.889130i | \(-0.348690\pi\) | ||||
0.457655 | + | 0.889130i | \(0.348690\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −23.3417 | −1.03869 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −8.18085 | −0.362610 | −0.181305 | − | 0.983427i | \(-0.558032\pi\) | ||||
−0.181305 | + | 0.983427i | \(0.558032\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.10656 | − | 16.1036i | −0.402851 | − | 0.712380i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 20.3626i | 0.897283i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −29.6603 | + | 17.1244i | −1.30446 | + | 0.753131i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.8746 | + | 24.0314i | 0.607856 | + | 1.05284i | 0.991593 | + | 0.129395i | \(0.0413034\pi\) |
−0.383738 | + | 0.923442i | \(0.625363\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 19.8843 | + | 11.4802i | 0.869478 | + | 0.501993i | 0.867175 | − | 0.498004i | \(-0.165934\pi\) |
0.00230311 | + | 0.999997i | \(0.499267\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 2.53071i | − | 0.110239i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −55.9246 | −2.43151 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 17.2742 | + | 9.97325i | 0.748228 | + | 0.431990i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −26.8536 | − | 15.5039i | −1.16098 | − | 0.670292i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.488426 | + | 27.3333i | −0.0210380 | + | 1.17733i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.60405 | + | 4.51035i | −0.111957 | + | 0.193915i | −0.916559 | − | 0.399899i | \(-0.869045\pi\) |
0.804602 | + | 0.593814i | \(0.202379\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −9.28902 | − | 16.0890i | −0.397898 | − | 0.689179i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.6224 | − | 18.3985i | 0.454181 | − | 0.786664i | −0.544460 | − | 0.838787i | \(-0.683265\pi\) |
0.998641 | + | 0.0521229i | \(0.0165988\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.597397 | − | 1.03472i | −0.0254500 | − | 0.0440807i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.78189 | − | 1.57316i | 0.118298 | − | 0.0668976i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 11.0945 | − | 6.40543i | 0.470090 | − | 0.271407i | −0.246187 | − | 0.969222i | \(-0.579178\pi\) |
0.716277 | + | 0.697816i | \(0.245844\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 21.8559i | − | 0.924406i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 18.7396 | − | 32.4580i | 0.789781 | − | 1.36794i | −0.136319 | − | 0.990665i | \(-0.543527\pi\) |
0.926101 | − | 0.377277i | \(-0.123139\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 12.4207 | − | 7.17109i | 0.522542 | − | 0.301690i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.94906 | + | 3.43469i | −0.249397 | + | 0.143990i | −0.619488 | − | 0.785006i | \(-0.712660\pi\) |
0.370091 | + | 0.928996i | \(0.379327\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.0847909 | + | 0.146862i | −0.00354839 | + | 0.00614599i | −0.867794 | − | 0.496924i | \(-0.834463\pi\) |
0.864246 | + | 0.503070i | \(0.167796\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 19.1741i | − | 0.799617i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.41193 | + | 3.12458i | −0.225302 | + | 0.130078i | −0.608403 | − | 0.793628i | \(-0.708189\pi\) |
0.383101 | + | 0.923706i | \(0.374856\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.826733 | + | 0.487213i | 0.0342987 | + | 0.0202130i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11.1527 | − | 19.3171i | −0.461900 | − | 0.800033i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −10.7881 | + | 18.6855i | −0.445273 | + | 0.771235i | −0.998071 | − | 0.0620801i | \(-0.980227\pi\) |
0.552799 | + | 0.833315i | \(0.313560\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.528615 | − | 0.915588i | −0.0217812 | − | 0.0377261i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −4.13036 | + | 7.15399i | −0.169613 | + | 0.293779i | −0.938284 | − | 0.345866i | \(-0.887585\pi\) |
0.768671 | + | 0.639645i | \(0.220919\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.56257 | − | 0.883632i | 0.0640591 | − | 0.0362254i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −30.7618 | − | 17.7603i | −1.25689 | − | 0.725667i | −0.284422 | − | 0.958699i | \(-0.591802\pi\) |
−0.972469 | + | 0.233033i | \(0.925135\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 35.8981 | + | 20.7258i | 1.46432 | + | 0.845423i | 0.999206 | − | 0.0398308i | \(-0.0126819\pi\) |
0.465109 | + | 0.885254i | \(0.346015\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7.16776 | −0.291411 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 2.41990i | − | 0.0982206i | −0.998793 | − | 0.0491103i | \(-0.984361\pi\) | ||
0.998793 | − | 0.0491103i | \(-0.0156386\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −45.9873 | − | 26.5508i | −1.86045 | − | 1.07413i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 21.3228 | + | 36.9321i | 0.861219 | + | 1.49168i | 0.870753 | + | 0.491720i | \(0.163632\pi\) |
−0.00953416 | + | 0.999955i | \(0.503035\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13.2535 | + | 7.65193i | −0.533567 | + | 0.308055i | −0.742468 | − | 0.669882i | \(-0.766345\pi\) |
0.208901 | + | 0.977937i | \(0.433011\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 27.6178i | − | 1.11005i | −0.831833 | − | 0.555026i | \(-0.812708\pi\) | ||
0.831833 | − | 0.555026i | \(-0.187292\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.31506 | − | 3.72162i | −0.253008 | − | 0.149103i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.55034 | −0.382014 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.52164 | −0.100545 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.28775 | 0.329930 | 0.164965 | − | 0.986299i | \(-0.447249\pi\) | ||||
0.164965 | + | 0.986299i | \(0.447249\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −17.9214 | −0.711188 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −37.0802 | + | 20.5338i | −1.46917 | + | 0.813579i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.91088i | 0.391456i | 0.980658 | + | 0.195728i | \(0.0627070\pi\) | ||||
−0.980658 | + | 0.195728i | \(0.937293\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.83668 | − | 3.94716i | 0.269612 | − | 0.155661i | −0.359099 | − | 0.933299i | \(-0.616916\pi\) |
0.628711 | + | 0.777639i | \(0.283583\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.15966 | − | 3.74063i | −0.0849049 | − | 0.147060i | 0.820446 | − | 0.571724i | \(-0.193725\pi\) |
−0.905351 | + | 0.424665i | \(0.860392\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 15.2308 | + | 8.79348i | 0.597859 | + | 0.345174i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 43.3997i | 1.69836i | 0.528102 | + | 0.849181i | \(0.322904\pi\) | ||||
−0.528102 | + | 0.849181i | \(0.677096\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.6788 | −0.417256 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.34894 | + | 5.39761i | 0.364183 | + | 0.210261i | 0.670914 | − | 0.741535i | \(-0.265902\pi\) |
−0.306731 | + | 0.951796i | \(0.599235\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.39495 | + | 1.96008i | 0.132048 | + | 0.0762381i | 0.564569 | − | 0.825386i | \(-0.309042\pi\) |
−0.432521 | + | 0.901624i | \(0.642376\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.380751 | − | 0.646081i | 0.0147649 | − | 0.0250539i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −31.5638 | + | 54.6701i | −1.22216 | + | 2.11683i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −10.0039 | − | 17.3273i | −0.386197 | − | 0.668913i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12.3404 | + | 21.3742i | −0.475687 | + | 0.823915i | −0.999612 | − | 0.0278497i | \(-0.991134\pi\) |
0.523925 | + | 0.851765i | \(0.324467\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −7.36327 | − | 12.7536i | −0.282994 | − | 0.490159i | 0.689127 | − | 0.724641i | \(-0.257994\pi\) |
−0.972121 | + | 0.234481i | \(0.924661\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.789376 | + | 1.33946i | −0.0302935 | + | 0.0514038i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.60128 | − | 0.924499i | 0.0612712 | − | 0.0353750i | −0.469051 | − | 0.883171i | \(-0.655404\pi\) |
0.530323 | + | 0.847796i | \(0.322071\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 28.0606i | − | 1.07214i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 17.2919 | − | 29.9505i | 0.658769 | − | 1.14102i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −33.7613 | + | 19.4921i | −1.28434 | + | 0.741514i | −0.977639 | − | 0.210292i | \(-0.932559\pi\) |
−0.306701 | + | 0.951806i | \(0.599225\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7.14764 | + | 4.12669i | −0.271126 | + | 0.156534i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.662926 | − | 1.14822i | 0.0251101 | − | 0.0434920i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 25.4389i | − | 0.960813i | −0.877046 | − | 0.480406i | \(-0.840489\pi\) | ||
0.877046 | − | 0.480406i | \(-0.159511\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.912310 | + | 0.526722i | −0.0344084 | + | 0.0198657i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.327278 | − | 36.6331i | 0.0123086 | − | 1.37773i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.14517 | + | 12.3758i | 0.268342 | + | 0.464783i | 0.968434 | − | 0.249270i | \(-0.0801908\pi\) |
−0.700092 | + | 0.714053i | \(0.746857\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −27.9296 | + | 48.3756i | −1.04597 | + | 1.81168i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −19.9319 | − | 34.5230i | −0.745410 | − | 1.29109i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 16.7344 | − | 28.9848i | 0.624088 | − | 1.08095i | −0.364629 | − | 0.931153i | \(-0.618804\pi\) |
0.988716 | − | 0.149799i | \(-0.0478626\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −31.9577 | − | 0.285507i | −1.19017 | − | 0.0106329i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −13.2817 | − | 7.66819i | −0.493269 | − | 0.284789i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12.1354 | + | 7.00636i | 0.450076 | + | 0.259851i | 0.707862 | − | 0.706350i | \(-0.249660\pi\) |
−0.257786 | + | 0.966202i | \(0.582993\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.45277 | −0.0537326 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 27.3077i | 1.00863i | 0.863519 | + | 0.504316i | \(0.168255\pi\) | ||||
−0.863519 | + | 0.504316i | \(0.831745\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −19.9899 | − | 11.5412i | −0.736339 | − | 0.425126i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 26.3157 | + | 45.5801i | 0.968039 | + | 1.67669i | 0.701220 | + | 0.712945i | \(0.252639\pi\) |
0.266819 | + | 0.963747i | \(0.414027\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 30.9523 | − | 17.8703i | 1.13553 | − | 0.655599i | 0.190211 | − | 0.981743i | \(-0.439083\pi\) |
0.945320 | + | 0.326144i | \(0.105750\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 8.91243i | − | 0.326526i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 24.7088 | − | 41.9274i | 0.902840 | − | 1.53199i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −33.1282 | −1.20887 | −0.604433 | − | 0.796656i | \(-0.706600\pi\) | ||||
−0.604433 | + | 0.796656i | \(0.706600\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −24.5836 | −0.894687 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13.6903 | −0.497584 | −0.248792 | − | 0.968557i | \(-0.580034\pi\) | ||||
−0.248792 | + | 0.968557i | \(0.580034\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13.0347 | 0.472509 | 0.236255 | − | 0.971691i | \(-0.424080\pi\) | ||||
0.236255 | + | 0.971691i | \(0.424080\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 25.3809 | − | 14.3529i | 0.918849 | − | 0.519609i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 27.2679i | 0.984588i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −18.4866 | + | 10.6732i | −0.666642 | + | 0.384886i | −0.794803 | − | 0.606867i | \(-0.792426\pi\) |
0.128161 | + | 0.991753i | \(0.459093\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5.73940 | + | 9.94093i | 0.206432 | + | 0.357550i | 0.950588 | − | 0.310455i | \(-0.100482\pi\) |
−0.744156 | + | 0.668006i | \(0.767148\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −11.7525 | − | 6.78529i | −0.422161 | − | 0.243735i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 0.553889i | − | 0.0198451i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 44.6416 | 1.59740 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −25.9873 | − | 15.0038i | −0.927528 | − | 0.535509i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 35.6808 | + | 20.6003i | 1.27188 | + | 0.734322i | 0.975342 | − | 0.220698i | \(-0.0708337\pi\) |
0.296541 | + | 0.955020i | \(0.404167\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11.0804 | + | 19.5939i | 0.393972 | + | 0.696681i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15.5107 | − | 26.8653i | 0.550801 | − | 0.954016i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −25.0066 | − | 43.3127i | −0.885779 | − | 1.53421i | −0.844819 | − | 0.535053i | \(-0.820292\pi\) |
−0.0409600 | − | 0.999161i | \(-0.513042\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.76484 | + | 3.05679i | −0.0624355 | + | 0.108141i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 13.6540 | + | 23.6494i | 0.481838 | + | 0.834568i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −39.6212 | − | 0.353973i | −1.39646 | − | 0.0124759i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −43.8995 | + | 25.3454i | −1.54343 | + | 0.891097i | −0.544807 | + | 0.838562i | \(0.683397\pi\) |
−0.998619 | + | 0.0525356i | \(0.983270\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.96566i | 0.314827i | 0.987533 | + | 0.157413i | \(0.0503155\pi\) | ||||
−0.987533 | + | 0.157413i | \(0.949684\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.0812910 | − | 0.140800i | 0.00284750 | − | 0.00493201i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.525599 | + | 0.303455i | −0.0183884 | + | 0.0106165i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 28.2190 | − | 16.2922i | 0.984849 | − | 0.568603i | 0.0811184 | − | 0.996704i | \(-0.474151\pi\) |
0.903731 | + | 0.428102i | \(0.140817\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10.0877 | − | 17.4724i | 0.351636 | − | 0.609051i | −0.634901 | − | 0.772594i | \(-0.718959\pi\) |
0.986536 | + | 0.163543i | \(0.0522923\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 0.253288i | − | 0.00880770i | −0.999990 | − | 0.00440385i | \(-0.998598\pi\) | ||
0.999990 | − | 0.00440385i | \(-0.00140179\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.10909 | + | 3.52708i | −0.212177 | + | 0.122501i | −0.602323 | − | 0.798253i | \(-0.705758\pi\) |
0.390146 | + | 0.920753i | \(0.372425\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.36489 | + | 2.46473i | 0.0472906 | + | 0.0853979i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.17848 | + | 7.23733i | 0.144602 | + | 0.250458i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 17.0936 | − | 29.6069i | 0.590136 | − | 1.02215i | −0.404078 | − | 0.914725i | \(-0.632408\pi\) |
0.994214 | − | 0.107420i | \(-0.0342591\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.7462 | + | 18.6130i | 0.370558 | + | 0.641826i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 19.9463 | − | 34.5480i | 0.686174 | − | 1.18849i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.100500 | − | 11.2493i | 0.00345323 | − | 0.386530i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 48.2024 | + | 27.8296i | 1.65236 | + | 0.953988i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −21.7586 | − | 12.5623i | −0.745000 | − | 0.430126i | 0.0788844 | − | 0.996884i | \(-0.474864\pi\) |
−0.823884 | + | 0.566758i | \(0.808198\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −42.1907 | −1.44121 | −0.720604 | − | 0.693347i | \(-0.756135\pi\) | ||||
−0.720604 | + | 0.693347i | \(0.756135\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.71278i | 0.160798i | 0.996763 | + | 0.0803990i | \(0.0256195\pi\) | ||||
−0.996763 | + | 0.0803990i | \(0.974381\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −30.8409 | − | 17.8060i | −1.04984 | − | 0.606123i | −0.127232 | − | 0.991873i | \(-0.540609\pi\) |
−0.922603 | + | 0.385750i | \(0.873943\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.4750 | + | 21.6074i | 0.424163 | + | 0.734672i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.08543 | + | 2.35873i | −0.138589 | + | 0.0800143i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 35.7884i | − | 1.21264i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.285216 | − | 31.9250i | 0.00964205 | − | 1.07926i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 40.9064 | 1.38131 | 0.690655 | − | 0.723184i | \(-0.257322\pi\) | ||||
0.690655 | + | 0.723184i | \(0.257322\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −37.4443 | −1.26153 | −0.630765 | − | 0.775974i | \(-0.717259\pi\) | ||||
−0.630765 | + | 0.775974i | \(0.717259\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −49.8357 | −1.67711 | −0.838553 | − | 0.544821i | \(-0.816598\pi\) | ||||
−0.838553 | + | 0.544821i | \(0.816598\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −28.8965 | −0.970248 | −0.485124 | − | 0.874445i | \(-0.661226\pi\) | ||||
−0.485124 | + | 0.874445i | \(0.661226\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.251279 | − | 28.1263i | 0.00842761 | − | 0.943327i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.47456i | 0.0493443i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.999223 | + | 0.576902i | −0.0334003 | + | 0.0192837i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 22.3394 | + | 38.6930i | 0.745062 | + | 1.29048i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.99082 | − | 1.14940i | −0.0663238 | − | 0.0382920i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 13.2287i | 0.439738i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −14.8700 | −0.493749 | −0.246874 | − | 0.969048i | \(-0.579403\pi\) | ||||
−0.246874 | + | 0.969048i | \(0.579403\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.81616 | − | 4.51266i | −0.258961 | − | 0.149511i | 0.364899 | − | 0.931047i | \(-0.381103\pi\) |
−0.623861 | + | 0.781536i | \(0.714437\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.22671 | − | 0.708243i | −0.0405982 | − | 0.0234394i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.149729 | − | 16.7596i | 0.00494450 | − | 0.553452i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 13.2083 | − | 22.8774i | 0.435702 | − | 0.754657i | −0.561651 | − | 0.827374i | \(-0.689834\pi\) |
0.997353 | + | 0.0727170i | \(0.0231670\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 34.6075 | + | 59.9420i | 1.13912 | + | 1.97302i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.76100 | + | 11.7104i | −0.222300 | + | 0.385036i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −11.1259 | − | 19.2706i | −0.365029 | − | 0.632249i | 0.623752 | − | 0.781623i | \(-0.285608\pi\) |
−0.988781 | + | 0.149373i | \(0.952274\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.00864 | + | 0.606620i | 0.0330568 | + | 0.0198812i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.29476 | + | 1.32488i | −0.0750465 | + | 0.0433281i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 14.6822i | − | 0.479647i | −0.970817 | − | 0.239823i | \(-0.922910\pi\) | ||
0.970817 | − | 0.239823i | \(-0.0770896\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −23.0396 | + | 39.9058i | −0.751070 | + | 1.30089i | 0.196235 | + | 0.980557i | \(0.437129\pi\) |
−0.947305 | + | 0.320334i | \(0.896205\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −25.3442 | + | 14.6325i | −0.825322 | + | 0.476500i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −6.96116 | + | 4.01903i | −0.226207 | + | 0.130601i | −0.608821 | − | 0.793308i | \(-0.708357\pi\) |
0.382614 | + | 0.923908i | \(0.375024\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −21.1700 | + | 36.6675i | −0.687206 | + | 1.19028i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 54.9348i | 1.77951i | 0.456437 | + | 0.889756i | \(0.349125\pi\) | ||||
−0.456437 | + | 0.889756i | \(0.650875\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 28.6060 | − | 16.5157i | 0.925667 | − | 0.534434i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 44.0392 | + | 0.393443i | 1.42210 | + | 0.0127049i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.26733 | + | 7.39124i | 0.137656 | + | 0.238427i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −15.4770 | + | 26.8070i | −0.498223 | + | 0.862948i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −26.5917 | − | 46.0582i | −0.855132 | − | 1.48113i | −0.876522 | − | 0.481361i | \(-0.840143\pi\) |
0.0213900 | − | 0.999771i | \(-0.493191\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7.61403 | + | 13.1879i | −0.244346 | + | 0.423219i | −0.961947 | − | 0.273234i | \(-0.911907\pi\) |
0.717602 | + | 0.696454i | \(0.245240\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.37634 | − | 11.2756i | −0.204416 | − | 0.361479i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.49418 | − | 0.862667i | −0.0478031 | − | 0.0275992i | 0.475908 | − | 0.879495i | \(-0.342120\pi\) |
−0.523711 | + | 0.851896i | \(0.675453\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.37033 | + | 5.40997i | 0.299477 | + | 0.172903i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 60.2383 | 1.92130 | 0.960651 | − | 0.277758i | \(-0.0895912\pi\) | ||||
0.960651 | + | 0.277758i | \(0.0895912\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.98485i | 0.318144i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 27.7703 | + | 16.0332i | 0.883044 | + | 0.509826i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.87312 | − | 4.97639i | −0.0912676 | − | 0.158080i | 0.816777 | − | 0.576953i | \(-0.195759\pi\) |
−0.908045 | + | 0.418873i | \(0.862425\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −22.9711 | + | 13.2624i | −0.728234 | + | 0.420446i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 0.0259240i | − | 0.000821020i | −1.00000 | 0.000410510i | \(-0.999869\pi\) | |||
1.00000 | 0.000410510i | \(-0.000130669\pi\) | ||||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))