Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2268,2,Mod(1781,2268)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2268, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 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("2268.1781");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2268.t (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(18.1100711784\) |
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: | \(\Z[a_1, \ldots, a_{13}]\) |
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 | 1781.6 | ||
Root | \(-0.268067 - 1.71118i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2268.1781 |
Dual form | 2268.2.t.a.2105.6 |
$q$-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 \(\left(\mathbb{Z}/2268\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(1135\) | \(1541\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(-1\) |
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 | ||||||||
\(5\) | 0.842869 | + | 1.45989i | 0.376942 | + | 0.652883i | 0.990616 | − | 0.136677i | \(-0.0436422\pi\) |
−0.613673 | + | 0.789560i | \(0.710309\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.30301 | + | 1.30235i | 0.870458 | + | 0.492243i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.38216 | + | 1.95269i | 1.01976 | + | 0.588758i | 0.914034 | − | 0.405637i | \(-0.132950\pi\) |
0.105725 | + | 0.994395i | \(0.466284\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 6.05515i | − | 1.67940i | −0.543054 | − | 0.839698i | \(-0.682732\pi\) | ||
0.543054 | − | 0.839698i | \(-0.317268\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.201244 | − | 0.348565i | 0.0488088 | − | 0.0845393i | −0.840589 | − | 0.541674i | \(-0.817791\pi\) |
0.889398 | + | 0.457134i | \(0.151124\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.145617 | + | 0.0840718i | −0.0334067 | + | 0.0192874i | −0.516610 | − | 0.856221i | \(-0.672806\pi\) |
0.483204 | + | 0.875508i | \(0.339473\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.69373 | − | 4.44198i | 1.60425 | − | 0.926216i | 0.613630 | − | 0.789593i | \(-0.289709\pi\) |
0.990623 | − | 0.136623i | \(-0.0436248\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.07914 | − | 1.86913i | 0.215829 | − | 0.373827i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 7.10580i | − | 1.31951i | −0.751479 | − | 0.659757i | \(-0.770659\pi\) | ||
0.751479 | − | 0.659757i | \(-0.229341\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.44527 | − | 3.14383i | −0.978000 | − | 0.564649i | −0.0763342 | − | 0.997082i | \(-0.524322\pi\) |
−0.901666 | + | 0.432434i | \(0.857655\pi\) | |||||||
\(32\) | 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 | 0.999849 | + | 0.0173987i | \(0.00553846\pi\) |
−0.484857 | + | 0.874594i | \(0.661128\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.29414 | 0.514458 | 0.257229 | − | 0.966350i | \(-0.417190\pi\) | ||||
0.257229 | + | 0.966350i | \(0.417190\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.60947 | −0.550439 | −0.275220 | − | 0.961381i | \(-0.588751\pi\) | ||||
−0.275220 | + | 0.961381i | \(0.588751\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.38482 | + | 7.59474i | 0.639592 | + | 1.10781i | 0.985522 | + | 0.169546i | \(0.0542301\pi\) |
−0.345930 | + | 0.938260i | \(0.612437\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.60775 | + | 5.99868i | 0.515393 | + | 0.856954i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.94628 | − | 2.85574i | −0.679424 | − | 0.392266i | 0.120214 | − | 0.992748i | \(-0.461642\pi\) |
−0.799638 | + | 0.600482i | \(0.794975\pi\) | |||||||
\(54\) | 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 | −0.681412 | − | 0.731900i | \(-0.738634\pi\) |
0.974550 | + | 0.224171i | \(0.0719673\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.43678 | + | 2.56157i | −0.568071 | + | 0.327976i | −0.756379 | − | 0.654134i | \(-0.773033\pi\) |
0.188308 | + | 0.982110i | \(0.439700\pi\) | |||||||
\(62\) | 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 | 0.101846 | − | 0.994800i | \(-0.467525\pi\) |
−0.810599 | + | 0.585601i | \(0.800858\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.24607 | + | 8.90184i | 0.597845 | + | 1.01446i | ||||
\(78\) | 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 | ||||||||
\(83\) | 0.362701 | 0.0398116 | 0.0199058 | − | 0.999802i | \(-0.493663\pi\) | ||||
0.0199058 | + | 0.999802i | \(0.493663\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.678488 | 0.0735924 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.38526 | + | 2.39934i | 0.146837 | + | 0.254329i | 0.930057 | − | 0.367416i | \(-0.119757\pi\) |
−0.783220 | + | 0.621745i | \(0.786424\pi\) | |||||||
\(90\) | 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 | ||||||||
\(97\) | 0.587643i | 0.0596661i | 0.999555 | + | 0.0298330i | \(0.00949756\pi\) | ||||
−0.999555 | + | 0.0298330i | \(0.990502\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.92329 | + | 11.9915i | −0.688893 | + | 1.19320i | 0.283303 | + | 0.959030i | \(0.408570\pi\) |
−0.972196 | + | 0.234167i | \(0.924764\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.4610 | + | 6.03967i | −1.03075 | + | 0.595106i | −0.917201 | − | 0.398425i | \(-0.869557\pi\) |
−0.113554 | + | 0.993532i | \(0.536223\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.9299 | − | 9.19711i | 1.54000 | − | 0.889118i | 0.541159 | − | 0.840920i | \(-0.317986\pi\) |
0.998838 | − | 0.0481978i | \(-0.0153478\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.51036 | + | 9.54422i | −0.527796 | + | 0.914170i | 0.471679 | + | 0.881771i | \(0.343648\pi\) |
−0.999475 | + | 0.0323997i | \(0.989685\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.50796i | 0.800361i | 0.916436 | + | 0.400181i | \(0.131053\pi\) | ||||
−0.916436 | + | 0.400181i | \(0.868947\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 12.9696 | + | 7.48801i | 1.20942 | + | 0.698260i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.917422 | − | 0.540659i | 0.0840999 | − | 0.0495621i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.12600 | + | 3.68234i | 0.193273 | + | 0.334758i | ||||
\(122\) | 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 | ||||||||
\(131\) | −3.16740 | − | 5.48610i | −0.276737 | − | 0.479322i | 0.693835 | − | 0.720134i | \(-0.255920\pi\) |
−0.970572 | + | 0.240812i | \(0.922586\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.444848 | + | 0.00397424i | −0.0385732 | + | 0.000344611i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 14.4158 | + | 8.32296i | 1.23162 | + | 0.711078i | 0.967368 | − | 0.253375i | \(-0.0815406\pi\) |
0.264255 | + | 0.964453i | \(0.414874\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.89601i | 0.415274i | 0.978206 | + | 0.207637i | \(0.0665773\pi\) | ||||
−0.978206 | + | 0.207637i | \(0.933423\pi\) | |||||||
\(140\) | 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 | ||||||||
\(149\) | −4.57864 | + | 2.64348i | −0.375097 | + | 0.216562i | −0.675683 | − | 0.737192i | \(-0.736151\pi\) |
0.300586 | + | 0.953755i | \(0.402818\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.29163 | − | 12.6295i | 0.593385 | − | 1.02777i | −0.400388 | − | 0.916346i | \(-0.631125\pi\) |
0.993773 | − | 0.111427i | \(-0.0355421\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 10.5993i | − | 0.851360i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.4160 | + | 8.90044i | 1.23033 | + | 0.710332i | 0.967099 | − | 0.254400i | \(-0.0818781\pi\) |
0.263232 | + | 0.964732i | \(0.415211\pi\) | |||||||
\(158\) | 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 | 0.867908 | − | 0.496725i | \(-0.165464\pi\) |
−0.864131 | + | 0.503267i | \(0.832131\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.95745 | 0.383619 | 0.191809 | − | 0.981432i | \(-0.438564\pi\) | ||||
0.191809 | + | 0.981432i | \(0.438564\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −23.6648 | −1.82037 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.40033 | − | 12.8177i | −0.562637 | − | 0.974515i | −0.997265 | − | 0.0739055i | \(-0.976454\pi\) |
0.434629 | − | 0.900610i | \(-0.356880\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.91956 | − | 2.89921i | 0.371884 | − | 0.219160i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.592751 | + | 0.342225i | 0.0443043 | + | 0.0255791i | 0.521989 | − | 0.852952i | \(-0.325190\pi\) |
−0.477684 | + | 0.878532i | \(0.658524\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 7.84745i | − | 0.583297i | −0.956526 | − | 0.291648i | \(-0.905796\pi\) | ||
0.956526 | − | 0.291648i | \(-0.0942037\pi\) | |||||||
\(182\) | 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 | −0.0679681 | − | 0.997687i | \(-0.521652\pi\) |
−0.898007 | + | 0.439982i | \(0.854985\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.25426 | − | 16.3648i | 0.649522 | − | 1.14858i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.77653 | + | 4.80909i | 0.193921 | + | 0.335881i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.656665 | −0.0454225 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.1324 | −0.697541 | −0.348771 | − | 0.937208i | \(-0.613401\pi\) | ||||
−0.348771 | + | 0.937208i | \(0.613401\pi\) | |||||||
\(212\) | 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 | ||||||||
\(223\) | − | 15.4665i | − | 1.03571i | −0.855467 | − | 0.517857i | \(-0.826730\pi\) | ||
0.855467 | − | 0.517857i | \(-0.173270\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −14.0360 | + | 24.3110i | −0.931600 | + | 1.61358i | −0.151011 | + | 0.988532i | \(0.548253\pi\) |
−0.780588 | + | 0.625046i | \(0.785080\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.7453 | − | 8.51319i | 0.974396 | − | 0.562568i | 0.0738222 | − | 0.997271i | \(-0.476480\pi\) |
0.900573 | + | 0.434704i | \(0.143147\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −16.0015 | + | 9.23847i | −1.04829 | + | 0.605233i | −0.922171 | − | 0.386782i | \(-0.873587\pi\) |
−0.126122 | + | 0.992015i | \(0.540253\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.39166 | + | 12.8027i | −0.482179 | + | 0.835158i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.00506i | 0.453120i | 0.973997 | + | 0.226560i | \(0.0727479\pi\) | ||||
−0.973997 | + | 0.226560i | \(0.927252\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.38459 | − | 3.10879i | −0.346852 | − | 0.200255i | 0.316446 | − | 0.948611i | \(-0.397510\pi\) |
−0.663298 | + | 0.748355i | \(0.730844\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.71656 | + | 10.3230i | −0.365217 | + | 0.659514i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.509067 | + | 0.881730i | 0.0323912 | + | 0.0561031i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.81844 | −0.619734 | −0.309867 | − | 0.950780i | \(-0.600285\pi\) | ||||
−0.309867 | + | 0.950780i | \(0.600285\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 34.6952 | 2.18127 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.667904 | + | 1.15684i | 0.0416627 | + | 0.0721619i | 0.886105 | − | 0.463485i | \(-0.153401\pi\) |
−0.844442 | + | 0.535647i | \(0.820068\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.148083 | + | 16.5754i | 0.00920144 | + | 1.02994i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 17.6238 | + | 10.1751i | 1.08673 | + | 0.627424i | 0.932704 | − | 0.360643i | \(-0.117443\pi\) |
0.154026 | + | 0.988067i | \(0.450776\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 9.62805i | − | 0.591446i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −13.3614 | + | 23.1426i | −0.814659 | + | 1.41103i | 0.0949131 | + | 0.995486i | \(0.469743\pi\) |
−0.909572 | + | 0.415546i | \(0.863591\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.76517 | − | 2.17382i | 0.228718 | − | 0.132050i | −0.381263 | − | 0.924467i | \(-0.624511\pi\) |
0.609980 | + | 0.792417i | \(0.291177\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 7.29968 | − | 4.21447i | 0.440187 | − | 0.254142i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.19901 | − | 3.80880i | 0.132126 | − | 0.228849i | −0.792370 | − | 0.610041i | \(-0.791153\pi\) |
0.924496 | + | 0.381192i | \(0.124486\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.33787i | 0.318430i | 0.987244 | + | 0.159215i | \(0.0508964\pi\) | ||||
−0.987244 | + | 0.159215i | \(0.949104\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.5431 | + | 8.97381i | 0.923941 | + | 0.533437i | 0.884890 | − | 0.465800i | \(-0.154233\pi\) |
0.0390505 | + | 0.999237i | \(0.487567\pi\) | |||||||
\(284\) | 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 | ||||||||
\(293\) | −26.2253 | −1.53210 | −0.766048 | − | 0.642783i | \(-0.777780\pi\) | ||||
−0.766048 | + | 0.642783i | \(0.777780\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.59132 | 0.441984 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −26.8968 | − | 46.5867i | −1.55548 | − | 2.69418i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.31267 | − | 4.70081i | −0.479134 | − | 0.270950i | ||||
\(302\) | 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 | \(-0.934175\pi\) | ||
0.978694 | − | 0.205326i | \(-0.0658254\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.08721 | − | 1.88311i | 0.0616503 | − | 0.106781i | −0.833553 | − | 0.552440i | \(-0.813697\pi\) |
0.895203 | + | 0.445658i | \(0.147030\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.2870 | − | 5.93922i | 0.581457 | − | 0.335704i | −0.180255 | − | 0.983620i | \(-0.557692\pi\) |
0.761712 | + | 0.647916i | \(0.224359\pi\) | |||||||
\(314\) | 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 | ||||||||
\(329\) | 0.207279 | + | 23.2014i | 0.0114277 | + | 1.27913i | ||||
\(330\) | 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 | ||||||||
\(335\) | 9.96340 | 0.544359 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.90797 | −0.430775 | −0.215387 | − | 0.976529i | \(-0.569101\pi\) | ||||
−0.215387 | + | 0.976529i | \(0.569101\pi\) | |||||||
\(338\) | 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 | ||||||||
\(349\) | − | 6.63505i | − | 0.355166i | −0.984106 | − | 0.177583i | \(-0.943172\pi\) | ||
0.984106 | − | 0.177583i | \(-0.0568278\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9.03437 | + | 15.6480i | −0.480851 | + | 0.832858i | −0.999759 | − | 0.0219721i | \(-0.993006\pi\) |
0.518908 | + | 0.854830i | \(0.326339\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −16.6877 | + | 9.63465i | −0.885691 | + | 0.511354i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.52677 | + | 0.881479i | −0.0805796 | + | 0.0465227i | −0.539748 | − | 0.841826i | \(-0.681481\pi\) |
0.459169 | + | 0.888349i | \(0.348147\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.48586 | + | 16.4300i | −0.499256 | + | 0.864737i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 11.7873i | − | 0.616977i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 28.9614 | + | 16.7209i | 1.51177 | + | 0.872822i | 0.999905 | + | 0.0137576i | \(0.00437931\pi\) |
0.511867 | + | 0.859065i | \(0.328954\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.67218 | − | 13.0186i | −0.398320 | − | 0.675893i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.7844 | − | 22.1433i | −0.661952 | − | 1.14653i | −0.980102 | − | 0.198494i | \(-0.936395\pi\) |
0.318150 | − | 0.948040i | \(-0.396938\pi\) | |||||||
\(374\) | 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 | ||||||||
\(383\) | −16.4158 | − | 28.4330i | −0.838808 | − | 1.45286i | −0.890892 | − | 0.454215i | \(-0.849920\pi\) |
0.0520838 | − | 0.998643i | \(-0.483414\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.57397 | + | 15.1618i | −0.436970 | + | 0.772715i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −17.4542 | − | 10.0772i | −0.884965 | − | 0.510935i | −0.0126730 | − | 0.999920i | \(-0.504034\pi\) |
−0.872292 | + | 0.488985i | \(0.837367\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 3.57568i | − | 0.180830i | ||||||
\(392\) | 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 | −0.516506 | + | 0.856284i | \(0.672768\pi\) |
−0.999816 | + | 0.0191652i | \(0.993899\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.36793 | − | 4.83122i | 0.417874 | − | 0.241260i | −0.276293 | − | 0.961073i | \(-0.589106\pi\) |
0.694167 | + | 0.719814i | \(0.255773\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −19.0364 | + | 32.9719i | −0.948268 | + | 1.64245i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 24.4678i | 1.21282i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −32.1202 | − | 18.5446i | −1.58824 | − | 0.916973i | −0.993597 | − | 0.112986i | \(-0.963958\pi\) |
−0.594647 | − | 0.803987i | \(-0.702708\pi\) | |||||||
\(410\) | 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 | ||||||||
\(419\) | 3.68386 | 0.179968 | 0.0899841 | − | 0.995943i | \(-0.471318\pi\) | ||||
0.0899841 | + | 0.995943i | \(0.471318\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.1028 | 0.833539 | 0.416769 | − | 0.909012i | \(-0.363162\pi\) | ||||
0.416769 | + | 0.909012i | \(0.363162\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.434342 | − | 0.752303i | −0.0210687 | − | 0.0364921i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −13.5540 | + | 0.121091i | −0.655926 | + | 0.00585999i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −27.3242 | − | 15.7756i | −1.31616 | − | 0.759885i | −0.333051 | − | 0.942909i | \(-0.608078\pi\) |
−0.983108 | + | 0.183024i | \(0.941411\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 10.0692i | − | 0.483893i | −0.970290 | − | 0.241947i | \(-0.922214\pi\) | ||
0.970290 | − | 0.241947i | \(-0.0777859\pi\) | |||||||
\(434\) | 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 | −0.950062 | − | 0.312060i | \(-0.898981\pi\) |
−0.204779 | + | 0.978808i | \(0.565648\pi\) | |||||||
\(440\) | 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 | ||||||||
\(455\) | 27.0051 | − | 0.241262i | 1.26602 | − | 0.0113105i | ||||
\(456\) | 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 | ||||||||
\(461\) | −4.34329 | −0.202287 | −0.101144 | − | 0.994872i | \(-0.532250\pi\) | ||||
−0.101144 | + | 0.994872i | \(0.532250\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.14903 | −0.332243 | −0.166122 | − | 0.986105i | \(-0.553124\pi\) | ||||
−0.166122 | + | 0.986105i | \(0.553124\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −0.944451 | − | 1.63584i | −0.0437040 | − | 0.0756975i | 0.843346 | − | 0.537371i | \(-0.180583\pi\) |
−0.887050 | + | 0.461673i | \(0.847249\pi\) | |||||||
\(468\) | 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 | ||||||||
\(475\) | 0.362903i | 0.0166511i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.22491 | − | 9.04981i | 0.238732 | − | 0.413497i | −0.721618 | − | 0.692291i | \(-0.756601\pi\) |
0.960351 | + | 0.278794i | \(0.0899348\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 32.8539 | − | 18.9682i | 1.49801 | − | 0.864875i | ||||
\(482\) | 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 | 0.463052 | + | 0.886331i | \(0.346754\pi\) |
−0.999111 | + | 0.0421513i | \(0.986579\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13.4830i | 0.608481i | 0.952595 | + | 0.304241i | \(0.0984027\pi\) | ||||
−0.952595 | + | 0.304241i | \(0.901597\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.47683 | − | 1.43000i | −0.111551 | − | 0.0644039i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −14.8869 | + | 26.3253i | −0.667770 | + | 1.18085i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.04035 | + | 10.4622i | 0.270403 | + | 0.468352i | 0.968965 | − | 0.247197i | \(-0.0795096\pi\) |
−0.698562 | + | 0.715550i | \(0.746176\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −20.5283 | −0.915310 | −0.457655 | − | 0.889130i | \(-0.651310\pi\) | ||||
−0.457655 | + | 0.889130i | \(0.651310\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −23.3417 | −1.03869 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.09043 | − | 7.08483i | −0.181305 | − | 0.314029i | 0.761020 | − | 0.648728i | \(-0.224699\pi\) |
−0.942325 | + | 0.334699i | \(0.891365\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.39282 | − | 15.9383i | −0.415514 | − | 0.705069i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −17.6345 | − | 10.1813i | −0.777070 | − | 0.448642i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 34.2488i | 1.50626i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13.8746 | + | 24.0314i | −0.607856 | + | 1.05284i | 0.383738 | + | 0.923442i | \(0.374637\pi\) |
−0.991593 | + | 0.129395i | \(0.958697\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 19.8843 | − | 11.4802i | 0.869478 | − | 0.501993i | 0.00230311 | − | 0.999997i | \(-0.499267\pi\) |
0.867175 | + | 0.498004i | \(0.165934\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.19166 | + | 1.26535i | −0.0954700 | + | 0.0551196i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 27.9623 | − | 48.4322i | 1.21575 | − | 2.10575i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 19.9465i | − | 0.863979i | ||||||
\(534\) | 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 | 0.804602 | − | 0.593814i | \(-0.202379\pi\) |
−0.916559 | + | 0.399899i | \(0.869045\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −18.5780 | −0.795795 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −21.2448 | −0.908361 | −0.454181 | − | 0.890910i | \(-0.650068\pi\) | ||||
−0.454181 | + | 0.890910i | \(0.650068\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.597397 | + | 1.03472i | 0.0254500 | + | 0.0440807i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.0285508 | − | 3.19577i | −0.00121410 | − | 0.135898i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −11.0945 | − | 6.40543i | −0.470090 | − | 0.271407i | 0.246187 | − | 0.969222i | \(-0.420822\pi\) |
−0.716277 | + | 0.697816i | \(0.754156\pi\) | |||||||
\(558\) | 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 | \(0.456473\pi\) |
−0.926101 | + | 0.377277i | \(0.876861\pi\) | |||||||
\(564\) | 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 | 0.383101 | − | 0.923706i | \(-0.374856\pi\) |
−0.608403 | + | 0.793628i | \(0.708189\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.835305 | + | 0.472365i | 0.0346543 | + | 0.0195970i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11.1527 | − | 19.3171i | −0.461900 | − | 0.800033i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −21.5762 | −0.890545 | −0.445273 | − | 0.895395i | \(-0.646893\pi\) | ||||
−0.445273 | + | 0.895395i | \(0.646893\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.05723 | 0.0435624 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.13036 | + | 7.15399i | 0.169613 | + | 0.293779i | 0.938284 | − | 0.345866i | \(-0.112415\pi\) |
−0.768671 | + | 0.639645i | \(0.779081\pi\) | |||||||
\(594\) | 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 | ||||||||
\(601\) | 41.4516i | 1.69085i | 0.534098 | + | 0.845423i | \(0.320651\pi\) | ||||
−0.534098 | + | 0.845423i | \(0.679349\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.58388 | + | 6.20746i | −0.145705 | + | 0.252369i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.09569 | − | 1.20995i | 0.0850616 | − | 0.0491103i | −0.456866 | − | 0.889536i | \(-0.651028\pi\) |
0.541927 | + | 0.840425i | \(0.317695\pi\) | |||||||
\(608\) | 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 | −0.00953416 | − | 0.999955i | \(-0.503035\pi\) |
0.870753 | − | 0.491720i | \(-0.163632\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 15.3039i | − | 0.616110i | −0.951369 | − | 0.308055i | \(-0.900322\pi\) | ||
0.951369 | − | 0.308055i | \(-0.0996781\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −23.9177 | − | 13.8089i | −0.961334 | − | 0.555026i | −0.0647505 | − | 0.997901i | \(-0.520625\pi\) |
−0.896583 | + | 0.442875i | \(0.853958\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.0654840 | + | 7.32981i | 0.00262356 | + | 0.293663i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.77517 | + | 8.27084i | 0.191007 | + | 0.330834i | ||||
\(626\) | 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 | ||||||||
\(635\) | −8.96069 | − | 15.5204i | −0.355594 | − | 0.615907i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 36.3229 | − | 21.8455i | 1.43916 | − | 0.865549i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.58307 | − | 4.95544i | −0.339011 | − | 0.195728i | 0.320824 | − | 0.947139i | \(-0.396040\pi\) |
−0.659835 | + | 0.751411i | \(0.729374\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 7.89432i | − | 0.311321i | −0.987811 | − | 0.155661i | \(-0.950249\pi\) | ||
0.987811 | − | 0.155661i | \(-0.0497507\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.15966 | − | 3.74063i | 0.0849049 | − | 0.147060i | −0.820446 | − | 0.571724i | \(-0.806275\pi\) |
0.905351 | + | 0.424665i | \(0.139608\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 15.2308 | − | 8.79348i | 0.597859 | − | 0.345174i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 37.5853 | − | 21.6999i | 1.47082 | − | 0.849181i | 0.471361 | − | 0.881940i | \(-0.343763\pi\) |
0.999463 | + | 0.0327591i | \(0.0104294\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.33940 | − | 9.24812i | 0.208628 | − | 0.361354i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 10.7952i | − | 0.420522i | −0.977645 | − | 0.210261i | \(-0.932569\pi\) | ||
0.977645 | − | 0.210261i | \(-0.0674314\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.39495 | − | 1.96008i | −0.132048 | − | 0.0762381i | 0.432521 | − | 0.901624i | \(-0.357624\pi\) |
−0.564569 | + | 0.825386i | \(0.690958\pi\) | |||||||
\(662\) | 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 | ||||||||
\(671\) | −20.0078 | −0.772394 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24.6808 | 0.951375 | 0.475687 | − | 0.879614i | \(-0.342199\pi\) | ||||
0.475687 | + | 0.879614i | \(0.342199\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.36327 | + | 12.7536i | 0.282994 | + | 0.490159i | 0.972121 | − | 0.234481i | \(-0.0753392\pi\) |
−0.689127 | + | 0.724641i | \(0.742006\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.765319 | + | 1.35335i | −0.0293702 | + | 0.0519368i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.60128 | − | 0.924499i | −0.0612712 | − | 0.0353750i | 0.469051 | − | 0.883171i | \(-0.344596\pi\) |
−0.530323 | + | 0.847796i | \(0.677929\pi\) | |||||||
\(684\) | 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 | 0.306701 | − | 0.951806i | \(-0.400775\pi\) |
0.977639 | + | 0.210292i | \(0.0674415\pi\) | |||||||
\(692\) | 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 | ||||||||
\(707\) | −31.5616 | + | 18.6000i | −1.18700 | + | 0.699525i | ||||
\(708\) | 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 | ||||||||
\(713\) | −55.8593 | −2.09195 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 39.8637 | 1.49082 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −16.7344 | − | 28.9848i | −0.624088 | − | 1.08095i | −0.988716 | − | 0.149799i | \(-0.952137\pi\) |
0.364629 | − | 0.931153i | \(-0.381196\pi\) | |||||||
\(720\) | 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 | ||||||||
\(727\) | 14.0127i | 0.519703i | 0.965649 | + | 0.259851i | \(0.0836736\pi\) | ||||
−0.965649 | + | 0.259851i | \(0.916326\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.726384 | + | 1.25813i | −0.0268663 | + | 0.0465338i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −23.6491 | + | 13.6538i | −0.873501 | + | 0.504316i | −0.868510 | − | 0.495672i | \(-0.834922\pi\) |
−0.00499085 | + | 0.999988i | \(0.501589\pi\) | |||||||
\(734\) | 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 | 0.266819 | − | 0.963747i | \(-0.414027\pi\) |
0.701220 | − | 0.712945i | \(-0.252639\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 35.7407i | 1.31120i | 0.755109 | + | 0.655599i | \(0.227584\pi\) | ||||
−0.755109 | + | 0.655599i | \(0.772416\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.71839 | − | 4.45621i | −0.282780 | − | 0.163263i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 48.6646 | − | 0.434766i | 1.77816 | − | 0.0158860i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16.5641 | + | 28.6899i | 0.604433 | + | 1.04691i | 0.992141 | + | 0.125126i | \(0.0399336\pi\) |
−0.387708 | + | 0.921782i | \(0.626733\pi\) | |||||||
\(752\) | 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 | ||||||||
\(761\) | 6.51737 | + | 11.2884i | 0.236255 | + | 0.409205i | 0.959637 | − | 0.281243i | \(-0.0907467\pi\) |
−0.723382 | + | 0.690448i | \(0.757413\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −25.1204 | + | 14.8040i | −0.909419 | + | 0.535942i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −23.6147 | − | 13.6340i | −0.852678 | − | 0.492294i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 21.3464i | 0.769772i | 0.922964 | + | 0.384886i | \(0.125759\pi\) | ||||
−0.922964 | + | 0.384886i | \(0.874241\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −5.73940 | + | 9.94093i | −0.206432 | + | 0.357550i | −0.950588 | − | 0.310455i | \(-0.899518\pi\) |
0.744156 | + | 0.668006i | \(0.232852\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −11.7525 | + | 6.78529i | −0.422161 | + | 0.243735i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.479682 | + | 0.276944i | −0.0171864 | + | 0.00992256i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −22.3208 | + | 38.6607i | −0.798701 | + | 1.38339i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 30.0076i | 1.07102i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −35.6808 | − | 20.6003i | −1.27188 | − | 0.734322i | −0.296541 | − | 0.955020i | \(-0.595833\pi\) |
−0.975342 | + | 0.220698i | \(0.929166\pi\) | |||||||
\(788\) | 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 | ||||||||
\(797\) | −50.0132 | −1.77156 | −0.885779 | − | 0.464108i | \(-0.846375\pi\) | ||||
−0.885779 | + | 0.464108i | \(0.846375\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.52967 | 0.124871 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −13.6540 | − | 23.6494i | −0.481838 | − | 0.834568i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 20.1172 | + | 34.1360i | 0.709037 | + | 1.20314i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 43.8995 | + | 25.3454i | 1.54343 | + | 0.891097i | 0.998619 | + | 0.0525356i | \(0.0167303\pi\) |
0.544807 | + | 0.838562i | \(0.316603\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 8.96566i | − | 0.314827i | −0.987533 | − | 0.157413i | \(-0.949684\pi\) | ||
0.987533 | − | 0.157413i | \(-0.0503155\pi\) | |||||||
\(812\) | 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 | 0.390146 | − | 0.920753i | \(-0.372425\pi\) |
−0.602323 | + | 0.798253i | \(0.705758\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.81696 | − | 0.0503371i | 0.0976020 | − | 0.00174408i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.17848 | + | 7.23733i | 0.144602 | + | 0.250458i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 34.1871 | 1.18027 | 0.590136 | − | 0.807304i | \(-0.299074\pi\) | ||||
0.590136 | + | 0.807304i | \(0.299074\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.4924 | −0.741117 | ||||||||
\(842\) | 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 | ||||||||
\(853\) | − | 25.1247i | − | 0.860252i | −0.902769 | − | 0.430126i | \(-0.858469\pi\) | ||
0.902769 | − | 0.430126i | \(-0.141531\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −21.0954 | + | 36.5383i | −0.720604 | + | 1.24812i | 0.240154 | + | 0.970735i | \(0.422802\pi\) |
−0.960758 | + | 0.277388i | \(0.910531\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.08139 | + | 2.35639i | −0.139255 | + | 0.0803990i | −0.568009 | − | 0.823022i | \(-0.692286\pi\) |
0.428754 | + | 0.903421i | \(0.358953\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 30.8409 | − | 17.8060i | 1.04984 | − | 0.606123i | 0.127232 | − | 0.991873i | \(-0.459391\pi\) |
0.922603 | + | 0.385750i | \(0.126057\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.4750 | − | 21.6074i | 0.424163 | − | 0.734672i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 4.71745i | − | 0.160029i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −30.9937 | − | 17.8942i | −1.05018 | − | 0.606322i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 27.7905 | + | 15.7155i | 0.939489 | + | 0.531281i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20.4532 | − | 35.4260i | −0.690655 | − | 1.19625i | −0.971624 | − | 0.236532i | \(-0.923989\pi\) |
0.280969 | − | 0.959717i | \(-0.409344\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 37.4443 | 1.26153 | 0.630765 | − | 0.775974i | \(-0.282741\pi\) | ||||
0.630765 | + | 0.775974i | \(0.282741\pi\) | |||||||
\(882\) | 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 | ||||||||
\(887\) | −14.4482 | − | 25.0251i | −0.485124 | − | 0.840260i | 0.514730 | − | 0.857352i | \(-0.327892\pi\) |
−0.999854 | + | 0.0170929i | \(0.994559\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −24.4838 | − | 13.8456i | −0.821159 | − | 0.464365i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.27701 | − | 0.737280i | −0.0427334 | − | 0.0246721i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.15380i | 0.0385674i | ||||||||
\(896\) | 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 | ||||||||
\(905\) | 11.4564 | − | 6.61437i | 0.380825 | − | 0.219869i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.43498 | − | 12.8778i | 0.246874 | − | 0.427599i | −0.715783 | − | 0.698323i | \(-0.753930\pi\) |
0.962657 | + | 0.270724i | \(0.0872632\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.02533i | 0.299022i | 0.988760 | + | 0.149511i | \(0.0477700\pi\) | ||||
−0.988760 | + | 0.149511i | \(0.952230\pi\) | |||||||
\(912\) | 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 | 0.997353 | − | 0.0727170i | \(-0.0231670\pi\) |
−0.561651 | + | 0.827374i | \(0.689834\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 69.2151 | 2.27824 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 13.5220 | 0.444601 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 11.1259 | + | 19.2706i | 0.365029 | + | 0.632249i | 0.988781 | − | 0.149373i | \(-0.0477257\pi\) |
−0.623752 | + | 0.781623i | \(0.714392\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.02967 | − | 0.570197i | −0.0337460 | − | 0.0186875i | ||||
\(932\) | 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 | \(0.0770896\pi\) | ||||
−0.970817 | + | 0.239823i | \(0.922910\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 23.0396 | − | 39.9058i | 0.751070 | − | 1.30089i | −0.196235 | − | 0.980557i | \(-0.562871\pi\) |
0.947305 | − | 0.320334i | \(-0.103795\pi\) | |||||||
\(942\) | 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 | ||||||||
\(959\) | 22.3603 | + | 37.9423i | 0.722053 | + | 1.22522i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.26733 | + | 7.39124i | 0.137656 | + | 0.238427i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −30.9541 | −0.996446 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 53.1835 | 1.71026 | 0.855132 | − | 0.518410i | \(-0.173476\pi\) | ||||
0.855132 | + | 0.518410i | \(0.173476\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.61403 | + | 13.1879i | 0.244346 | + | 0.423219i | 0.961947 | − | 0.273234i | \(-0.0880935\pi\) |
−0.717602 | + | 0.696454i | \(0.754760\pi\) | |||||||
\(972\) | 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 | ||||||||
\(979\) | 10.8199i | 0.345806i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 30.1191 | − | 52.1679i | 0.960651 | − | 1.66390i | 0.239780 | − | 0.970827i | \(-0.422925\pi\) |
0.720871 | − | 0.693070i | \(-0.243742\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.64713 | + | 4.99242i | −0.275521 | + | 0.159072i | ||||
\(986\) | 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 | −0.908045 | − | 0.418873i | \(-0.862425\pi\) |
0.816777 | + | 0.576953i | \(0.195759\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 26.5248i | − | 0.840892i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.0224508 | − | 0.0129620i | −0.000711024 | − | 0.000410510i | 0.499644 | − | 0.866231i | \(-0.333464\pi\) |
−0.500355 | + | 0.865820i | \(0.666797\pi\) | |||||||
\(998\) | 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 \(a_p\))