Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,2,Mod(337,1008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.337");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.r (of order \(3\), 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: | \(8.04892052375\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.309123.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 673.2 | ||
Root | \(0.500000 - 2.05195i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1008.673 |
Dual form | 1008.2.r.g.337.2 |
$q$-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 \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.796790 | + | 1.53790i | −0.460027 | + | 0.887905i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.02704 | − | 1.77889i | −0.459307 | − | 0.795543i | 0.539617 | − | 0.841910i | \(-0.318569\pi\) |
−0.998924 | + | 0.0463670i | \(0.985236\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.500000 | − | 0.866025i | 0.188982 | − | 0.327327i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.73025 | − | 2.45076i | −0.576751 | − | 0.816920i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.52704 | + | 4.37697i | −0.761932 | + | 1.31970i | 0.179922 | + | 0.983681i | \(0.442416\pi\) |
−0.941854 | + | 0.336024i | \(0.890918\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.500000 | + | 0.866025i | 0.138675 | + | 0.240192i | 0.926995 | − | 0.375073i | \(-0.122382\pi\) |
−0.788320 | + | 0.615265i | \(0.789049\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.55408 | − | 0.162084i | 0.917661 | − | 0.0418500i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.273346 | 0.0662962 | 0.0331481 | − | 0.999450i | \(-0.489447\pi\) | ||||
0.0331481 | + | 0.999450i | \(0.489447\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.38151 | 1.23460 | 0.617302 | − | 0.786726i | \(-0.288226\pi\) | ||||
0.617302 | + | 0.786726i | \(0.288226\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.933463 | + | 1.45899i | 0.203698 | + | 0.318377i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.66372 | − | 4.61369i | −0.555423 | − | 0.962021i | −0.997870 | − | 0.0652265i | \(-0.979223\pi\) |
0.442447 | − | 0.896794i | \(-0.354110\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.390369 | − | 0.676139i | 0.0780738 | − | 0.135228i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.14766 | − | 0.708209i | 0.990668 | − | 0.136295i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.16372 | − | 7.21177i | 0.773183 | − | 1.33919i | −0.162628 | − | 0.986687i | \(-0.551997\pi\) |
0.935810 | − | 0.352504i | \(-0.114670\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.08113 | − | 8.80077i | −0.912597 | − | 1.58066i | −0.810382 | − | 0.585903i | \(-0.800740\pi\) |
−0.102216 | − | 0.994762i | \(-0.532593\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.71780 | − | 7.37385i | −0.821263 | − | 1.28362i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.05408 | −0.347204 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.16225 | 1.34187 | 0.670933 | − | 0.741518i | \(-0.265894\pi\) | ||||
0.670933 | + | 0.741518i | \(0.265894\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.73025 | + | 0.0789082i | −0.277062 | + | 0.0126354i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.52704 | + | 4.37697i | 0.394658 | + | 0.683567i | 0.993057 | − | 0.117631i | \(-0.0375299\pi\) |
−0.598400 | + | 0.801198i | \(0.704197\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.30039 | − | 3.98439i | 0.350806 | − | 0.607614i | −0.635585 | − | 0.772031i | \(-0.719241\pi\) |
0.986391 | + | 0.164417i | \(0.0525743\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.58259 | + | 5.59496i | −0.384990 | + | 0.834048i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.690757 | − | 1.19643i | 0.100757 | − | 0.174517i | −0.811240 | − | 0.584714i | \(-0.801207\pi\) |
0.911997 | + | 0.410197i | \(0.134540\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.500000 | − | 0.866025i | −0.0714286 | − | 0.123718i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.217799 | + | 0.420378i | −0.0304980 | + | 0.0588647i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.43560 | 0.471916 | 0.235958 | − | 0.971763i | \(-0.424177\pi\) | ||||
0.235958 | + | 0.971763i | \(0.424177\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.3815 | 1.39984 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.28794 | + | 8.27621i | −0.567951 | + | 1.09621i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.890369 | + | 1.54216i | 0.115916 | + | 0.200773i | 0.918146 | − | 0.396243i | \(-0.129686\pi\) |
−0.802229 | + | 0.597016i | \(0.796353\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.390369 | + | 0.676139i | −0.0499816 | + | 0.0865707i | −0.889934 | − | 0.456090i | \(-0.849250\pi\) |
0.839952 | + | 0.542660i | \(0.182583\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.98755 | + | 0.273062i | −0.376396 | + | 0.0344026i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.02704 | − | 1.77889i | 0.127389 | − | 0.220644i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.19076 | − | 7.25860i | −0.511982 | − | 0.886780i | −0.999904 | − | 0.0138919i | \(-0.995578\pi\) |
0.487921 | − | 0.872888i | \(-0.337755\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 9.21780 | − | 0.420378i | 1.10969 | − | 0.0506076i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.78074 | 0.923404 | 0.461702 | − | 0.887035i | \(-0.347239\pi\) | ||||
0.461702 | + | 0.887035i | \(0.347239\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.38151 | 1.09802 | 0.549012 | − | 0.835815i | \(-0.315004\pi\) | ||||
0.549012 | + | 0.835815i | \(0.315004\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.728790 | + | 1.13909i | 0.0841534 | + | 0.131531i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.52704 | + | 4.37697i | 0.287983 | + | 0.498801i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.47150 | − | 11.2090i | 0.728100 | − | 1.26111i | −0.229585 | − | 0.973289i | \(-0.573737\pi\) |
0.957685 | − | 0.287818i | \(-0.0929298\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.01245 | + | 8.48087i | −0.334717 | + | 0.942319i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.86333 | + | 4.95943i | −0.314291 | + | 0.544368i | −0.979287 | − | 0.202479i | \(-0.935100\pi\) |
0.664996 | + | 0.746847i | \(0.268433\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.280738 | − | 0.486253i | −0.0304503 | − | 0.0527415i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.77335 | + | 12.1496i | 0.833390 | + | 1.30258i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −13.8171 | −1.46461 | −0.732306 | − | 0.680976i | \(-0.761556\pi\) | ||||
−0.732306 | + | 0.680976i | \(0.761556\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.00000 | 0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 17.5833 | − | 0.801886i | 1.82330 | − | 0.0831517i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.52704 | − | 9.57312i | −0.567063 | − | 0.982181i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.10963 | − | 1.92194i | 0.112666 | − | 0.195143i | −0.804178 | − | 0.594388i | \(-0.797394\pi\) |
0.916844 | + | 0.399245i | \(0.130728\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 15.0993 | − | 1.38008i | 1.51754 | − | 0.138703i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.36333 | + | 2.36135i | −0.135656 | + | 0.234963i | −0.925848 | − | 0.377896i | \(-0.876648\pi\) |
0.790192 | + | 0.612860i | \(0.209981\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.99115 | + | 15.5731i | 0.885924 | + | 1.53447i | 0.844651 | + | 0.535317i | \(0.179808\pi\) |
0.0412728 | + | 0.999148i | \(0.486859\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.63667 | − | 3.15897i | 0.159723 | − | 0.308284i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.10817 | −0.107131 | −0.0535653 | − | 0.998564i | \(-0.517059\pi\) | ||||
−0.0535653 | + | 0.998564i | \(0.517059\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.38151 | 0.323890 | 0.161945 | − | 0.986800i | \(-0.448223\pi\) | ||||
0.161945 | + | 0.986800i | \(0.448223\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.50360 | + | 12.5527i | −0.617294 | + | 1.19145i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.43560 | − | 16.3429i | −0.887626 | − | 1.53741i | −0.842673 | − | 0.538425i | \(-0.819020\pi\) |
−0.0449531 | − | 0.998989i | \(-0.514314\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.47150 | + | 9.47691i | −0.510220 | + | 0.883726i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.25729 | − | 2.72382i | 0.116237 | − | 0.251818i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.136673 | − | 0.236725i | 0.0125288 | − | 0.0217005i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.27188 | − | 12.5953i | −0.661080 | − | 1.14502i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −8.74484 | + | 0.398809i | −0.788496 | + | 0.0359594i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.8741 | −1.06205 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17.1623 | −1.52290 | −0.761452 | − | 0.648221i | \(-0.775513\pi\) | ||||
−0.761452 | + | 0.648221i | \(0.775513\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.29465 | + | 6.71248i | 0.378123 | + | 0.591001i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.94445 | − | 15.4922i | −0.781481 | − | 1.35356i | −0.931079 | − | 0.364817i | \(-0.881132\pi\) |
0.149599 | − | 0.988747i | \(-0.452202\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.69076 | − | 4.66053i | 0.233318 | − | 0.404119i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −6.54669 | − | 8.42976i | −0.563450 | − | 0.725518i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.24630 | − | 3.89071i | 0.191915 | − | 0.332406i | −0.753970 | − | 0.656909i | \(-0.771864\pi\) |
0.945885 | + | 0.324503i | \(0.105197\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.07227 | + | 15.7136i | 0.769500 | + | 1.33281i | 0.937834 | + | 0.347083i | \(0.112828\pi\) |
−0.168334 | + | 0.985730i | \(0.553839\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.28959 | + | 2.01561i | 0.108603 | + | 0.169745i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.05408 | −0.422644 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −17.1052 | −1.42051 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.73025 | − | 0.0789082i | 0.142709 | − | 0.00650824i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.25370 | + | 3.90352i | 0.184630 | + | 0.319788i | 0.943452 | − | 0.331510i | \(-0.107558\pi\) |
−0.758822 | + | 0.651298i | \(0.774225\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.49115 | + | 9.51094i | −0.446863 | + | 0.773990i | −0.998180 | − | 0.0603064i | \(-0.980792\pi\) |
0.551317 | + | 0.834296i | \(0.314126\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.472958 | − | 0.669906i | −0.0382364 | − | 0.0541587i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −10.4371 | + | 18.0775i | −0.838325 | + | 1.45202i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.08998 | − | 3.61995i | −0.166799 | − | 0.288904i | 0.770494 | − | 0.637447i | \(-0.220010\pi\) |
−0.937293 | + | 0.348544i | \(0.886676\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.73745 | + | 5.28360i | −0.217094 | + | 0.419016i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.32743 | −0.419860 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.61849 | 0.440074 | 0.220037 | − | 0.975492i | \(-0.429382\pi\) | ||||
0.220037 | + | 0.975492i | \(0.429382\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −8.27188 | + | 15.9657i | −0.643965 | + | 1.24293i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.44592 | − | 9.43260i | −0.421418 | − | 0.729917i | 0.574661 | − | 0.818392i | \(-0.305134\pi\) |
−0.996078 | + | 0.0884750i | \(0.971801\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.00000 | − | 10.3923i | 0.461538 | − | 0.799408i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −9.31138 | − | 13.1888i | −0.712059 | − | 1.00857i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.30039 | + | 12.6446i | −0.555038 | + | 0.961354i | 0.442862 | + | 0.896590i | \(0.353963\pi\) |
−0.997901 | + | 0.0647648i | \(0.979370\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.390369 | − | 0.676139i | −0.0295091 | − | 0.0511113i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.08113 | + | 0.140515i | −0.231592 | + | 0.0105617i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 23.4897 | 1.75570 | 0.877851 | − | 0.478934i | \(-0.158977\pi\) | ||||
0.877851 | + | 0.478934i | \(0.158977\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.39922 | −0.104003 | −0.0520017 | − | 0.998647i | \(-0.516560\pi\) | ||||
−0.0520017 | + | 0.998647i | \(0.516560\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.728790 | − | 1.13909i | −0.0538737 | − | 0.0842038i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8.38298 | − | 14.5197i | −0.616329 | − | 1.06751i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.690757 | + | 1.19643i | −0.0505132 | + | 0.0874914i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.96050 | − | 4.81211i | 0.142606 | − | 0.350030i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.6819 | − | 20.2336i | 0.845273 | − | 1.46406i | −0.0401112 | − | 0.999195i | \(-0.512771\pi\) |
0.885384 | − | 0.464860i | \(-0.153895\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.27188 | + | 12.5953i | 0.523442 | + | 0.906628i | 0.999628 | + | 0.0272830i | \(0.00868552\pi\) |
−0.476186 | + | 0.879345i | \(0.657981\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.91741 | + | 2.99689i | 0.137309 | + | 0.214611i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −17.3422 | −1.23558 | −0.617791 | − | 0.786343i | \(-0.711972\pi\) | ||||
−0.617791 | + | 0.786343i | \(0.711972\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.5438 | 0.818316 | 0.409158 | − | 0.912464i | \(-0.365822\pi\) | ||||
0.409158 | + | 0.912464i | \(0.365822\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 14.5021 | − | 0.661371i | 1.02290 | − | 0.0466495i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.16372 | − | 7.21177i | −0.292236 | − | 0.506167i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.19076 | − | 8.99066i | 0.362538 | − | 0.627935i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.69815 | + | 14.5110i | −0.465554 | + | 1.00858i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −13.5993 | + | 23.5547i | −0.940684 | + | 1.62931i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.2630 | − | 21.2402i | −0.844222 | − | 1.46223i | −0.886295 | − | 0.463120i | \(-0.846730\pi\) |
0.0420736 | − | 0.999115i | \(-0.486604\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.19961 | + | 11.9660i | −0.424790 | + | 0.819895i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −9.45038 | −0.644511 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.1623 | −0.689859 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7.47509 | + | 14.4278i | −0.505120 | + | 0.974940i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.136673 | + | 0.236725i | 0.00919363 | + | 0.0159238i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.28074 | − | 7.41446i | 0.286659 | − | 0.496509i | −0.686351 | − | 0.727271i | \(-0.740789\pi\) |
0.973010 | + | 0.230762i | \(0.0741219\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.33249 | + | 0.213190i | −0.155499 | + | 0.0142127i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −10.5993 | + | 18.3586i | −0.703501 | + | 1.21850i | 0.263729 | + | 0.964597i | \(0.415048\pi\) |
−0.967230 | + | 0.253903i | \(0.918286\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.28074 | + | 3.95035i | 0.150715 | + | 0.261047i | 0.931491 | − | 0.363765i | \(-0.118509\pi\) |
−0.780775 | + | 0.624812i | \(0.785176\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.74484 | + | 0.398809i | −0.575368 | + | 0.0262397i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 13.5074 | 0.884899 | 0.442449 | − | 0.896794i | \(-0.354110\pi\) | ||||
0.442449 | + | 0.896794i | \(0.354110\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.83775 | −0.185114 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 12.0818 | + | 18.8837i | 0.784797 | + | 1.22663i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.82743 | − | 11.8255i | −0.441630 | − | 0.764925i | 0.556181 | − | 0.831061i | \(-0.312266\pi\) |
−0.997811 | + | 0.0661361i | \(0.978933\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.60963 | + | 2.78796i | −0.103685 | + | 0.179588i | −0.913200 | − | 0.407511i | \(-0.866397\pi\) |
0.809515 | + | 0.587099i | \(0.199730\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −10.6424 | − | 11.3903i | −0.682711 | − | 0.730689i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.02704 | + | 1.77889i | −0.0656153 | + | 0.113649i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.69076 | + | 4.66053i | 0.171209 | + | 0.296542i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.34562 | − | 8.35512i | −0.338765 | − | 0.529484i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.38151 | −0.276559 | −0.138279 | − | 0.990393i | \(-0.544157\pi\) | ||||
−0.138279 | + | 0.990393i | \(0.544157\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 26.9253 | 1.69278 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.971495 | − | 0.0443051i | 0.0608374 | − | 0.00277449i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.72665 | − | 9.91886i | −0.357219 | − | 0.618721i | 0.630276 | − | 0.776371i | \(-0.282942\pi\) |
−0.987495 | + | 0.157650i | \(0.949608\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.08113 | − | 7.06872i | 0.253589 | − | 0.439229i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −24.8786 | + | 2.27391i | −1.53995 | + | 0.140751i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.41741 | + | 5.91913i | −0.210727 | + | 0.364989i | −0.951942 | − | 0.306278i | \(-0.900916\pi\) |
0.741216 | + | 0.671267i | \(0.234250\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.52850 | − | 6.11155i | −0.216754 | − | 0.375429i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 11.0093 | − | 21.2493i | 0.673760 | − | 1.30044i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.67257 | 0.589747 | 0.294873 | − | 0.955536i | \(-0.404722\pi\) | ||||
0.294873 | + | 0.955536i | \(0.404722\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.8377 | 0.779838 | 0.389919 | − | 0.920849i | \(-0.372503\pi\) | ||||
0.389919 | + | 0.920849i | \(0.372503\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.796790 | + | 1.53790i | −0.0482239 | + | 0.0930777i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.97296 | + | 3.41726i | 0.118974 | + | 0.206069i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.79153 | + | 10.0312i | −0.347980 | + | 0.602718i | −0.985890 | − | 0.167392i | \(-0.946465\pi\) |
0.637911 | + | 0.770110i | \(0.279799\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −12.7769 | + | 27.6802i | −0.764936 | + | 1.65717i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.46410 | − | 4.26795i | 0.146996 | − | 0.254605i | −0.783120 | − | 0.621871i | \(-0.786373\pi\) |
0.930116 | + | 0.367266i | \(0.119706\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.30039 | − | 16.1087i | −0.552851 | − | 0.957565i | −0.998067 | − | 0.0621426i | \(-0.980207\pi\) |
0.445217 | − | 0.895423i | \(-0.353127\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 19.1264 | − | 0.872258i | 1.13295 | − | 0.0516681i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.05408 | 0.298333 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9253 | −0.995605 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.07160 | + | 3.23788i | 0.121439 | + | 0.189808i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12.3801 | + | 21.4429i | 0.723250 | + | 1.25271i | 0.959690 | + | 0.281060i | \(0.0906861\pi\) |
−0.236440 | + | 0.971646i | \(0.575981\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.82889 | − | 3.16774i | 0.106482 | − | 0.184433i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −9.90856 | + | 24.3208i | −0.574953 | + | 1.41124i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.66372 | − | 4.61369i | 0.154047 | − | 0.266817i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.30039 | − | 3.98439i | −0.132592 | − | 0.229656i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.54523 | − | 3.97816i | −0.146220 | − | 0.228539i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.60370 | 0.0918277 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −21.9430 | −1.25235 | −0.626176 | − | 0.779681i | \(-0.715381\pi\) | ||||
−0.626176 | + | 0.779681i | \(0.715381\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −31.1139 | + | 1.41895i | −1.77001 | + | 0.0807213i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.5811 | + | 23.5232i | 0.770115 | + | 1.33388i | 0.937499 | + | 0.347987i | \(0.113135\pi\) |
−0.167384 | + | 0.985892i | \(0.553532\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.27188 | − | 7.39912i | 0.241461 | − | 0.418223i | −0.719670 | − | 0.694317i | \(-0.755707\pi\) |
0.961131 | + | 0.276094i | \(0.0890400\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.55408 | + | 5.03407i | 0.200250 | + | 0.283638i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −0.199612 | + | 0.345738i | −0.0112113 | + | 0.0194186i | −0.871577 | − | 0.490259i | \(-0.836902\pi\) |
0.860365 | + | 0.509678i | \(0.170235\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 21.0438 | + | 36.4489i | 1.17822 | + | 2.04075i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.882977 | − | 1.70425i | 0.0492830 | − | 0.0951219i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.47102 | 0.0818495 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.780738 | 0.0433076 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.69436 | + | 5.20042i | −0.148998 | + | 0.287584i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.690757 | − | 1.19643i | −0.0380827 | − | 0.0659611i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.80924 | + | 4.86575i | −0.154410 | + | 0.267446i | −0.932844 | − | 0.360281i | \(-0.882681\pi\) |
0.778434 | + | 0.627726i | \(0.216014\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −14.1228 | − | 20.0037i | −0.773922 | − | 1.09620i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.60817 | + | 14.9098i | −0.470314 | + | 0.814609i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.4911 | + | 25.0994i | 0.789383 | + | 1.36725i | 0.926345 | + | 0.376675i | \(0.122933\pi\) |
−0.136962 | + | 0.990576i | \(0.543734\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 32.6519 | − | 1.48909i | 1.77341 | − | 0.0808764i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 51.3609 | 2.78135 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −10.2149 | − | 15.9657i | −0.549950 | − | 0.859564i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 17.2345 | + | 29.8511i | 0.925198 | + | 1.60249i | 0.791243 | + | 0.611502i | \(0.209434\pi\) |
0.133955 | + | 0.990987i | \(0.457232\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.78074 | + | 15.2087i | −0.470022 | + | 0.814102i | −0.999412 | − | 0.0342762i | \(-0.989087\pi\) |
0.529390 | + | 0.848378i | \(0.322421\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.18716 | + | 4.10390i | 0.170118 | + | 0.219050i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −16.4445 | + | 28.4826i | −0.875250 | + | 1.51598i | −0.0187537 | + | 0.999824i | \(0.505970\pi\) |
−0.856496 | + | 0.516153i | \(0.827364\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.99115 | − | 13.8411i | −0.424126 | − | 0.734608i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.255158 | + | 0.398809i | 0.0135044 | + | 0.0211072i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.96362 | −0.156414 | −0.0782071 | − | 0.996937i | \(-0.524920\pi\) | ||||
−0.0782071 | + | 0.996937i | \(0.524920\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.96070 | 0.524247 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 25.1644 | − | 1.14762i | 1.32079 | − | 0.0602346i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9.63521 | − | 16.6887i | −0.504330 | − | 0.873525i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.68190 | − | 11.5734i | 0.348792 | − | 0.604126i | −0.637243 | − | 0.770663i | \(-0.719925\pi\) |
0.986035 | + | 0.166537i | \(0.0532585\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.35447 | − | 13.7664i | 0.330801 | − | 0.716652i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.71780 | − | 2.97532i | 0.0891837 | − | 0.154471i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.30039 | − | 3.98439i | −0.119110 | − | 0.206304i | 0.800305 | − | 0.599592i | \(-0.204671\pi\) |
−0.919415 | + | 0.393289i | \(0.871337\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 9.46118 | − | 18.2612i | 0.488573 | − | 0.943003i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.32743 | 0.428884 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.21926 | 0.113996 | 0.0569979 | − | 0.998374i | \(-0.481847\pi\) | ||||
0.0569979 | + | 0.998374i | \(0.481847\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 13.6747 | − | 26.3938i | 0.700576 | − | 1.35219i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −15.5167 | − | 26.8758i | −0.792868 | − | 1.37329i | −0.924184 | − | 0.381947i | \(-0.875254\pi\) |
0.131317 | − | 0.991340i | \(-0.458079\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.19076 | − | 8.99066i | 0.264545 | − | 0.458206i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −13.7450 | + | 1.25630i | −0.698699 | + | 0.0638613i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 12.4174 | − | 21.5076i | 0.629588 | − | 1.09048i | −0.358047 | − | 0.933704i | \(-0.616557\pi\) |
0.987634 | − | 0.156774i | \(-0.0501095\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.728116 | − | 1.26113i | −0.0368224 | − | 0.0637783i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 30.9523 | − | 1.41158i | 1.56134 | − | 0.0712049i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −26.5860 | −1.33769 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 17.7237 | 0.889528 | 0.444764 | − | 0.895648i | \(-0.353287\pi\) | ||||
0.444764 | + | 0.895648i | \(0.353287\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.02344 | + | 7.85157i | 0.251487 | + | 0.393070i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.0885 | − | 26.1341i | −0.753485 | − | 1.30507i | −0.946124 | − | 0.323804i | \(-0.895038\pi\) |
0.192640 | − | 0.981270i | \(-0.438295\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.08113 | − | 8.80077i | 0.253109 | − | 0.438398i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 18.1804 | − | 3.35139i | 0.903393 | − | 0.166532i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −20.6264 | + | 35.7259i | −1.02241 | + | 1.77087i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.38151 | − | 14.5172i | −0.414439 | − | 0.717830i | 0.580930 | − | 0.813953i | \(-0.302689\pi\) |
−0.995369 | + | 0.0961236i | \(0.969356\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.19368 | + | 6.55466i | 0.206859 | + | 0.323318i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.78074 | 0.0876244 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11.7630 | 0.577424 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −31.3946 | + | 1.43175i | −1.53740 | + | 0.0701133i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.44445 | + | 2.50187i | 0.0705662 | + | 0.122224i | 0.899150 | − | 0.437641i | \(-0.144186\pi\) |
−0.828583 | + | 0.559866i | \(0.810853\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.0899807 | − | 0.155851i | 0.00438539 | − | 0.00759572i | −0.863824 | − | 0.503793i | \(-0.831937\pi\) |
0.868210 | + | 0.496197i | \(0.165271\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.12734 | + | 0.377240i | −0.200678 | + | 0.0183420i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.106706 | − | 0.184820i | 0.00517600 | − | 0.00896509i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.390369 | + | 0.676139i | 0.0188913 | + | 0.0327207i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.02704 | − | 7.77266i | 0.194427 | − | 0.375268i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.76595 | 0.229568 | 0.114784 | − | 0.993390i | \(-0.463382\pi\) | ||||
0.114784 | + | 0.993390i | \(0.463382\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −27.7630 | −1.33421 | −0.667103 | − | 0.744965i | \(-0.732466\pi\) | ||||
−0.667103 | + | 0.744965i | \(0.732466\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 13.6293 | − | 26.3061i | 0.653474 | − | 1.26128i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −14.3348 | − | 24.8286i | −0.685728 | − | 1.18771i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.32889 | + | 4.03376i | −0.111152 | + | 0.192521i | −0.916235 | − | 0.400641i | \(-0.868787\pi\) |
0.805083 | + | 0.593162i | \(0.202121\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.25729 | + | 2.72382i | −0.0598712 | + | 0.129706i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.38151 | + | 2.39285i | −0.0656377 | + | 0.113688i | −0.896977 | − | 0.442078i | \(-0.854242\pi\) |
0.831339 | + | 0.555766i | \(0.187575\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 14.1908 | + | 24.5791i | 0.672706 | + | 1.16516i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −7.79893 | + | 0.355670i | −0.368877 | + | 0.0168226i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 19.9430 | 0.941168 | 0.470584 | − | 0.882355i | \(-0.344043\pi\) | ||||
0.470584 | + | 0.882355i | \(0.344043\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −25.5438 | −1.20281 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −10.2516 | − | 16.0230i | −0.481660 | − | 0.752828i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.02704 | − | 1.77889i | −0.0481485 | − | 0.0833956i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13.6908 | + | 23.7131i | −0.640427 | + | 1.10925i | 0.344911 | + | 0.938635i | \(0.387909\pi\) |
−0.985338 | + | 0.170616i | \(0.945424\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.40709 | − | 0.193586i | 0.0656775 | − | 0.00903583i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.02558 | − | 5.24046i | 0.140915 | − | 0.244072i | −0.786926 | − | 0.617047i | \(-0.788329\pi\) |
0.927842 | + | 0.372975i | \(0.121662\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.77188 | − | 15.1933i | −0.407664 | − | 0.706095i | 0.586964 | − | 0.809613i | \(-0.300323\pi\) |
−0.994628 | + | 0.103519i | \(0.966990\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −19.4852 | − | 30.4551i | −0.903605 | − | 1.41232i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 23.6156 | 1.09280 | 0.546399 | − | 0.837525i | \(-0.315998\pi\) | ||||
0.546399 | + | 0.837525i | \(0.315998\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.38151 | −0.387022 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.23239 | − | 0.329833i | 0.333251 | − | 0.0151979i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 11.6264 | + | 20.1374i | 0.534580 | + | 0.925920i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.10078 | − | 3.63865i | 0.0963902 | − | 0.166953i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.94445 | − | 8.41983i | −0.272178 | − | 0.385518i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 19.1264 | − | 33.1278i | 0.873906 | − | 1.51365i | 0.0159814 | − | 0.999872i | \(-0.494913\pi\) |
0.857924 | − | 0.513776i | \(-0.171754\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.08113 | + | 7.06872i | 0.186083 | + | 0.322306i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.24484 | − | 8.19304i | 0.193147 | − | 0.372796i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.55855 | −0.206993 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.57918 | 0.298131 | 0.149066 | − | 0.988827i | \(-0.452373\pi\) | ||||
0.149066 | + | 0.988827i | \(0.452373\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.47675 | + | 8.64065i | −0.202446 | + | 0.390744i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.02704 | − | 1.77889i | −0.0463498 | − | 0.0802801i | 0.841920 | − | 0.539603i | \(-0.181426\pi\) |
−0.888270 | + | 0.459323i | \(0.848092\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.13814 | − | 1.97131i | 0.0512591 | − | 0.0887833i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −17.9626 | − | 25.4426i | −0.807361 | − | 1.14356i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.89037 | − | 6.73832i | 0.174507 | − | 0.302255i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.16225 | − | 14.1374i | −0.365393 | − | 0.632879i | 0.623446 | − | 0.781866i | \(-0.285732\pi\) |
−0.988839 | + | 0.148987i | \(0.952399\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 18.8456 | − | 0.859455i | 0.841960 | − | 0.0383976i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.60078 | 0.249726 | 0.124863 | − | 0.992174i | \(-0.460151\pi\) | ||||
0.124863 | + | 0.992174i | \(0.460151\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.60078 | 0.249231 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 11.2016 | + | 17.5079i | 0.497478 | + | 0.777551i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.336285 | − | 0.582462i | −0.0149056 | − | 0.0258172i | 0.858476 | − | 0.512853i | \(-0.171411\pi\) |
−0.873382 | + | 0.487036i | \(0.838078\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.69076 | − | 8.12463i | 0.207507 | − | 0.359412i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 27.7022 | − | 3.81124i | 1.22308 | − | 0.168270i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 18.4686 | − | 31.9885i | 0.813822 | − | 1.40958i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.49115 | + | 6.04684i | 0.153540 | + | 0.265940i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −13.6293 | − | 21.3024i | −0.598259 | − | 0.935070i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 26.4533 | 1.15894 | 0.579470 | − | 0.814993i | \(-0.303260\pi\) | ||||
0.579470 | + | 0.814993i | \(0.303260\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −27.3068 | −1.19404 | −0.597021 | − | 0.802225i | \(-0.703649\pi\) | ||||
−0.597021 | + | 0.802225i | \(0.703649\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.35087 | − | 0.0616067i | 0.0589570 | − | 0.00268874i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.38891 | − | 2.40566i | −0.0605017 | − | 0.104792i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.69076 | + | 4.66053i | −0.116989 | + | 0.202632i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.23891 | − | 4.85041i | 0.0971605 | − | 0.210490i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.52704 | + | 4.37697i | −0.109458 | + | 0.189587i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.13814 | + | 1.97131i | 0.0492059 | + | 0.0852271i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −18.7163 | + | 36.1247i | −0.807670 | + | 1.55890i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.05408 | 0.217695 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −19.3245 | −0.830825 | −0.415413 | − | 0.909633i | \(-0.636363\pi\) | ||||
−0.415413 | + | 0.909633i | \(0.636363\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.11489 | − | 2.15186i | 0.0478444 | − | 0.0923452i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.47296 | − | 6.01534i | −0.148765 | − | 0.257669i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.17111 | + | 15.8848i | −0.392128 | + | 0.679186i | −0.992730 | − | 0.120362i | \(-0.961594\pi\) |
0.600602 | + | 0.799548i | \(0.294928\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.33249 | − | 0.213190i | 0.0995483 | − | 0.00909873i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 22.4071 | − | 38.8102i | 0.954574 | − | 1.65337i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.47150 | − | 11.2090i | −0.275196 | − | 0.476653i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 29.0093 | − | 1.32297i | 1.23138 | − | 0.0561570i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9.19863 | 0.389758 | 0.194879 | − | 0.980827i | \(-0.437569\pi\) | ||||
0.194879 | + | 0.980827i | \(0.437569\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.60078 | 0.194592 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.28959 | − | 2.01561i | −0.0544466 | − | 0.0850993i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 16.5811 | + | 28.7194i | 0.698811 | + | 1.21038i | 0.968879 | + | 0.247535i | \(0.0796206\pi\) |
−0.270068 | + | 0.962841i | \(0.587046\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −19.3815 | + | 33.5698i | −0.815386 | + | 1.41229i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 5.83842 | + | 6.84929i | 0.245191 | + | 0.287643i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −13.1008 | + | 22.6912i | −0.549213 | + | 0.951265i | 0.449116 | + | 0.893474i | \(0.351739\pi\) |
−0.998329 | + | 0.0577914i | \(0.981594\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.89037 | + | 8.47037i | 0.204656 | + | 0.354474i | 0.950023 | − | 0.312180i | \(-0.101059\pi\) |
−0.745367 | + | 0.666654i | \(0.767726\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 21.8092 | + | 34.0875i | 0.911094 | + | 1.42403i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.15933 | −0.173456 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 36.3068 | 1.51147 | 0.755736 | − | 0.654877i | \(-0.227279\pi\) | ||||
0.755736 | + | 0.654877i | \(0.227279\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −25.1644 | + | 1.14762i | −1.04580 | + | 0.0476936i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.86333 | + | 4.95943i | 0.118791 | + | 0.205752i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.68190 | + | 15.0375i | −0.359568 | + | 0.622789i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −6.13667 | + | 0.560893i | −0.253720 | + | 0.0231901i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −12.0737 | + | 20.9123i | −0.498336 | + | 0.863144i | −0.999998 | − | 0.00191995i | \(-0.999389\pi\) |
0.501662 | + | 0.865064i | \(0.332722\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −27.3442 | − | 47.3615i | −1.12670 | − | 1.95150i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 13.8181 | − | 26.6705i | 0.568401 | − | 1.09708i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 41.4897 | 1.70378 | 0.851889 | − | 0.523723i | \(-0.175457\pi\) | ||||
0.851889 | + | 0.523723i | \(0.175457\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.561476 | −0.0230183 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −9.19795 | + | 17.7531i | −0.376447 | + | 0.726587i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −11.3422 | − | 19.6453i | −0.463430 | − | 0.802685i | 0.535699 | − | 0.844409i | \(-0.320048\pi\) |
−0.999129 | + | 0.0417243i | \(0.986715\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.1249 | − | 34.8573i | 0.820912 | − | 1.42186i | −0.0840927 | − | 0.996458i | \(-0.526799\pi\) |
0.905004 | − | 0.425403i | \(-0.139867\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −10.5380 | + | 22.8298i | −0.429142 | + | 0.929700i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −14.9371 | + | 25.8717i | −0.607278 | + | 1.05184i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.66225 | + | 15.0035i | 0.351590 | + | 0.608972i | 0.986528 | − | 0.163591i | \(-0.0523078\pi\) |
−0.634938 | + | 0.772563i | \(0.718974\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 14.4086 | − | 0.657103i | 0.583864 | − | 0.0266272i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.38151 | 0.0558901 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −32.9646 | −1.33143 | −0.665713 | − | 0.746207i | \(-0.731873\pi\) | ||||
−0.665713 | + | 0.746207i | \(0.731873\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 9.69076 | + | 15.1465i | 0.390769 | + | 0.610766i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13.4700 | + | 23.3308i | 0.542283 | + | 0.939262i | 0.998772 | + | 0.0495330i | \(0.0157733\pi\) |
−0.456489 | + | 0.889729i | \(0.650893\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.991146 | + | 1.71671i | −0.0398375 | + | 0.0690006i | −0.885257 | − | 0.465103i | \(-0.846017\pi\) |
0.845419 | + | 0.534103i | \(0.179351\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −16.9794 | − | 21.8633i | −0.681358 | − | 0.877342i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.90856 | + | 11.9660i | −0.276785 | + | 0.479407i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 10.2434 | + | 17.7421i | 0.409735 | + | 0.709682i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −25.3889 | − | 39.6825i | −1.01394 | − | 1.58477i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.23112 | 0.0889606 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25.4868 | 1.01461 | 0.507306 | − | 0.861766i | \(-0.330641\pi\) | ||||
0.507306 | + | 0.861766i | \(0.330641\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 42.4363 | − | 1.93531i | 1.68669 | − | 0.0769216i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 17.6264 | + | 30.5297i | 0.699481 | + | 1.21154i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.500000 | − | 0.866025i | 0.0198107 | − | 0.0343132i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −13.4626 | − | 19.0687i | −0.532574 | − | 0.754347i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 20.0423 | − | 34.7143i | 0.791623 | − | 1.37113i | −0.133338 | − | 0.991071i | \(-0.542570\pi\) |
0.924961 | − | 0.380061i | \(-0.124097\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.50885 | + | 6.07751i | 0.138376 | + | 0.239674i | 0.926882 | − | 0.375353i | \(-0.122479\pi\) |
−0.788506 | + | 0.615027i | \(0.789145\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7.52997 | − | 14.5337i | 0.296492 | − | 0.572264i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 11.8142 | 0.464464 | 0.232232 | − | 0.972660i | \(-0.425397\pi\) | ||||
0.232232 | + | 0.972660i | \(0.425397\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.00000 | −0.353281 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.09718 | − | 15.6285i | 0.317353 | − | 0.612529i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −0.136673 | − | 0.236725i | −0.00534843 | − | 0.00926375i | 0.863339 | − | 0.504625i | \(-0.168369\pi\) |
−0.868687 | + | 0.495361i | \(0.835036\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −18.3727 | + | 31.8224i | −0.717879 | + | 1.24340i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −16.2324 | − | 22.9918i | −0.633286 | − | 0.896997i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.39970 | − | 12.8167i | 0.288251 | − | 0.499266i | −0.685141 | − | 0.728410i | \(-0.740259\pi\) |
0.973392 | + | 0.229144i | \(0.0735928\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.50885 | + | 7.80956i | 0.175374 | + | 0.303757i | 0.940291 | − | 0.340372i | \(-0.110553\pi\) |
−0.764917 | + | 0.644129i | \(0.777220\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.472958 | + | 0.0215693i | −0.0183682 | + | 0.000837681i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −11.0541 | −0.428659 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −44.3638 | −1.71777 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 7.99182 | + | 12.4911i | 0.308982 | + | 0.482934i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.97296 | − | 3.41726i | −0.0761652 | − | 0.131922i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.9803 | + | 20.7506i | −0.461809 | + | 0.799876i | −0.999051 | − | 0.0435519i | \(-0.986133\pi\) |
0.537243 | + | 0.843428i | \(0.319466\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.53064 | − | 3.75700i | 0.0589144 | − | 0.144607i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.32889 | − | 5.76581i | 0.127940 | − | 0.221598i | −0.794938 | − | 0.606690i | \(-0.792497\pi\) |
0.922878 | + | 0.385092i | \(0.125830\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.10963 | − | 1.92194i | −0.0425837 | − | 0.0737572i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −19.7881 | − | 30.9286i | −0.758283 | − | 1.18518i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 30.0728 | 1.15070 | 0.575351 | − | 0.817907i | \(-0.304865\pi\) | ||||
0.575351 | + | 0.817907i | \(0.304865\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.22820 | −0.352591 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.89251 | + | 0.359938i | −0.301118 | + | 0.0137325i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.71780 | + | 2.97532i | 0.0654429 | + | 0.113351i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.63814 | + | 2.83733i | −0.0623176 | + | 0.107937i | −0.895501 | − | 0.445060i | \(-0.853183\pi\) |
0.833183 | + | 0.552997i | \(0.186516\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.35447 | − | 13.7664i | 0.241386 | − | 0.522943i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 18.6352 | − | 32.2771i | 0.706874 | − | 1.22434i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.690757 | + | 1.19643i | 0.0261643 | + | 0.0453179i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −10.7626 | + | 20.7730i | −0.407077 | + | 0.785706i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −32.2891 | −1.21954 | −0.609771 | − | 0.792578i | \(-0.708739\pi\) | ||||
−0.609771 | + | 0.792578i | \(0.708739\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 43.9253 | 1.65667 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.26109 | − | 4.36416i | 0.0851575 | − | 0.164364i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.36333 | + | 2.36135i | 0.0512732 | + | 0.0888078i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 24.5438 | − | 42.5111i | 0.921761 | − | 1.59654i | 0.125071 | − | 0.992148i | \(-0.460084\pi\) |
0.796690 | − | 0.604388i | \(-0.206582\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −38.6678 | + | 3.53424i | −1.45016 | + | 0.132544i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −27.0693 | + | 46.8855i | −1.01376 | + | 1.75588i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.19076 | + | 8.99066i | 0.194123 | + | 0.336231i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 23.6264 | − | 1.07748i | 0.882342 | − | 0.0402393i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 41.9617 | 1.56491 | 0.782453 | − | 0.622710i | \(-0.213968\pi\) | ||||
0.782453 | + | 0.622710i | \(0.213968\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 17.9823 | 0.669696 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3.00506 | − | 4.69687i | −0.111759 | − | 0.174678i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.25077 | − | 5.63050i | −0.120731 | − | 0.209112i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −14.2434 | + | 24.6703i | −0.528258 | + | 0.914969i | 0.471200 | + | 0.882027i | \(0.343821\pi\) |
−0.999457 | + | 0.0329425i | \(0.989512\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 25.9969 | − | 7.29124i | 0.962847 | − | 0.270046i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.628802 | − | 1.08912i | 0.0232571 | − | 0.0402825i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14.2630 | − | 24.7043i | −0.526817 | − | 0.912474i | −0.999512 | − | 0.0312475i | \(-0.990052\pi\) |
0.472695 | − | 0.881226i | \(-0.343281\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.91741 | − | 2.99689i | −0.0707248 | − | 0.110542i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 42.3609 | 1.56038 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.85934 | −0.289110 | −0.144555 | − | 0.989497i | \(-0.546175\pi\) | ||||
−0.144555 | + | 0.989497i | \(0.546175\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −9.31138 | + | 0.424646i | −0.342062 | + | 0.0155998i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3.37364 | − | 5.84332i | −0.123767 | − | 0.214371i | 0.797483 | − | 0.603341i | \(-0.206164\pi\) |
−0.921250 | + | 0.388970i | \(0.872831\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.62928 | − | 8.01815i | 0.169604 | − | 0.293762i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 17.1086 | − | 1.56373i | 0.625973 | − | 0.0572140i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.554084 | + | 0.959702i | −0.0202458 | + | 0.0350667i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.0900 | + | 19.2084i | 0.404679 | + | 0.700925i | 0.994284 | − | 0.106767i | \(-0.0340499\pi\) |
−0.589605 | + | 0.807692i | \(0.700717\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.49115 | − | 6.73832i | 0.127224 | − | 0.245558i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 22.5586 | 0.820990 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20.3815 | −0.740779 | −0.370389 | − | 0.928877i | \(-0.620776\pi\) | ||||
−0.370389 | + | 0.928877i | \(0.620776\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −21.4538 | + | 41.4083i | −0.778723 | + | 1.50303i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −20.3274 | − | 35.2081i | −0.736869 | − | 1.27629i | −0.953899 | − | 0.300129i | \(-0.902970\pi\) |
0.217030 | − | 0.976165i | \(-0.430363\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.69076 | − | 2.92848i | 0.0612095 | − | 0.106018i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.705941 | + | 1.52936i | −0.0255233 | + | 0.0552942i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.890369 | + | 1.54216i | −0.0321494 | + | 0.0556843i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16.9518 | + | 29.3615i | 0.611299 | + | 1.05880i | 0.991022 | + | 0.133701i | \(0.0426861\pi\) |
−0.379723 | + | 0.925100i | \(0.623981\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 19.8171 | − | 0.903760i | 0.713696 | − | 0.0325481i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −8.74825 | −0.314653 | −0.157326 | − | 0.987547i | \(-0.550287\pi\) | ||||
−0.157326 | + | 0.987547i | \(0.550287\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.93406 | −0.285000 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7.61916 | + | 11.9086i | 0.273336 | + | 0.427220i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 13.5993 | + | 23.5547i | 0.487246 | + | 0.843935i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −19.6623 | + | 34.0560i | −0.703571 | + | 1.21862i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 16.3260 | − | 40.0725i | 0.583442 | − | 1.43208i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.29300 | + | 7.43569i | −0.153224 | + | 0.265391i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.64260 | + | 8.04122i | 0.165491 | + | 0.286639i | 0.936830 | − | 0.349786i | \(-0.113746\pi\) |
−0.771339 | + | 0.636425i | \(0.780412\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −6.38005 | − | 9.97193i | −0.227136 | − | 0.355010i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −18.8712 | −0.670983 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.780738 | −0.0277248 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 12.2104 | − | 0.556856i | 0.433059 | − | 0.0197497i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −11.2271 | − | 19.4460i | −0.397685 | − | 0.688811i | 0.595754 | − | 0.803167i | \(-0.296853\pi\) |
−0.993440 | + | 0.114355i | \(0.963520\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.188816 | − | 0.327039i | 0.00667983 | − | 0.0115698i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 23.9071 | + | 33.8624i | 0.844716 | + | 1.19647i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −23.7075 | + | 41.0626i | −0.836619 | + | 1.44907i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.47150 | + | 9.47691i | 0.192845 | + | 0.334017i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −7.70700 | + | 14.8754i | −0.271299 | + | 0.523639i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −5.40215 | −0.189929 | −0.0949647 | − | 0.995481i | \(-0.530274\pi\) | ||||
−0.0949647 | + | 0.995481i | \(0.530274\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0.0177088 | 0.000621841 | 0.000310920 | − | 1.00000i | \(-0.499901\pi\) | ||||
0.000310920 | 1.00000i | \(0.499901\pi\) | ||||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −10.2290 | + | 19.7431i | −0.358746 | + | 0.692422i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.77042 | − | 9.99466i | −0.202129 | − | 0.350098i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12.3796 | − | 21.4420i | 0.433106 | − | 0.750162i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.73025 | − | 2.45076i | −0.0604599 | − | 0.0856365i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0.528505 | − | 0.915397i | 0.0184449 | − | 0.0319476i | −0.856656 | − | 0.515889i | \(-0.827462\pi\) |
0.875101 | + | 0.483941i | \(0.160795\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.76303 | + | 11.7139i | 0.235744 | + | 0.408321i | 0.959489 | − | 0.281747i | \(-0.0909139\pi\) |
−0.723744 | + | 0.690068i | \(0.757581\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −6.82743 | + | 0.311365i | −0.237701 | + | 0.0108403i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 49.3068 | 1.71457 | 0.857283 | − | 0.514846i | \(-0.172151\pi\) | ||||
0.857283 | + | 0.514846i | \(0.172151\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −53.7060 | −1.86529 | −0.932644 | − | 0.360799i | \(-0.882504\pi\) | ||||
−0.932644 | + | 0.360799i | \(0.882504\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −10.8124 | − | 16.8996i | −0.375077 | − | 0.586239i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.136673 | − | 0.236725i | −0.00473544 | − | 0.00820203i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −11.1864 | + | 19.3754i | −0.387120 | + | 0.670512i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −32.3887 | − | 41.7049i | −1.11952 | − | 1.44153i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −18.7163 | + | 32.4176i | −0.646160 | + | 1.11918i | 0.337873 | + | 0.941192i | \(0.390293\pi\) |
−0.984032 | + | 0.177990i | \(0.943041\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.1730 | − | 34.9407i | −0.695622 | − | 1.20485i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.60030 | + | 7.19020i | 0.158443 | + | 0.247644i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −24.6490 | −0.847952 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −14.5438 | −0.499730 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 32.1840 | − | 1.46775i | 1.10455 | − | 0.0503732i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −21.7419 | − | 37.6581i | −0.745303 | − | 1.29090i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10.3092 | − | 17.8561i | 0.352982 | − | 0.611382i | −0.633789 | − | 0.773506i | \(-0.718501\pi\) |
0.986770 | + | 0.162124i | \(0.0518344\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −13.8982 | + | 30.1094i | −0.475310 | + | 1.02972i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −10.4445 | + | 18.0903i | −0.356776 | + | 0.617954i | −0.987420 | − | 0.158118i | \(-0.949457\pi\) |
0.630644 | + | 0.776072i | \(0.282791\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13.4430 | + | 23.2839i | 0.458669 | + | 0.794438i | 0.998891 | − | 0.0470847i | \(-0.0149931\pi\) |
−0.540222 | + | 0.841523i | \(0.681660\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.02704 | + | 7.77266i | −0.137241 | + | 0.264892i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −26.8142 | −0.912766 | −0.456383 | − | 0.889784i | \(-0.650855\pi\) | ||||
−0.456383 | + | 0.889784i | \(0.650855\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 29.9912 | 1.01973 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 13.4859 | − | 26.0293i | 0.458005 | − | 0.884003i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 32.7075 | + | 56.6510i | 1.10953 | + | 1.92175i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.19076 | − | 7.25860i | 0.141998 | − | 0.245948i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −6.63015 | + | 0.605997i | −0.224397 | + | 0.0205099i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5.93706 | + | 10.2833i | −0.200709 | + | 0.347639i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18.9538 | + | 32.8289i | 0.640024 | + | 1.10855i | 0.985427 | + | 0.170099i | \(0.0544089\pi\) |
−0.345403 | + | 0.938454i | \(0.612258\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −42.8412 | + | 1.95378i | −1.44500 | + | 0.0658992i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.47782 | 0.251934 | 0.125967 | − | 0.992034i | \(-0.459797\pi\) | ||||
0.125967 | + | 0.992034i | \(0.459797\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.07472 | −0.170778 | −0.0853889 | − | 0.996348i | \(-0.527213\pi\) | ||||
−0.0853889 | + | 0.996348i | \(0.527213\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.41441 | + | 5.33667i | 0.114774 | + | 0.179390i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 9.26157 | + | 16.0415i | 0.310973 | + | 0.538621i | 0.978573 | − | 0.205899i | \(-0.0660118\pi\) |
−0.667600 | + | 0.744520i | \(0.732678\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.58113 | + | 14.8629i | −0.287802 | + | 0.498487i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −29.5079 | − | 34.6169i | −0.988551 | − | 1.15971i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.71732 | − | 6.43859i | 0.124395 | − | 0.215459i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −24.1249 | − | 41.7855i | −0.806406 | − | 1.39674i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.97296 | + | 7.77266i | 0.166042 | + | 0.259522i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −84.6255 | −2.82242 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.939108 | 0.0312862 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 7.96050 | − | 0.363039i | 0.264909 | − | 0.0120812i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.43706 | + | 2.48906i | 0.0477695 | + | 0.0827393i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −24.8245 | + | 42.9973i | −0.824284 | + | 1.42770i | 0.0781810 | + | 0.996939i | \(0.475089\pi\) |
−0.902465 | + | 0.430763i | \(0.858245\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 8.14601 | − | 0.744547i | 0.270186 | − | 0.0246951i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11.9808 | − | 20.7514i | 0.396943 | − | 0.687525i | −0.596404 | − | 0.802684i | \(-0.703405\pi\) |
0.993347 | + | 0.115159i | \(0.0367379\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −14.4715 | − | 25.0654i | −0.478937 | − | 0.829543i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.27781 | + | 2.46633i | −0.0422432 | + | 0.0815343i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −17.8889 | −0.590744 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18.8377 | 0.621400 | 0.310700 | − | 0.950508i | \(-0.399437\pi\) | ||||
0.310700 | + | 0.950508i | \(0.399437\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 17.4839 | − | 33.7461i | 0.576116 | − | 1.11197i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.89037 | + | 6.73832i | 0.128053 | + | 0.221794i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.18629 | − | 5.51882i | 0.104765 | − | 0.181458i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 22.6090 | − | 48.9806i | 0.742578 | − | 1.60873i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −7.45185 | + | 12.9070i | −0.244487 | + | 0.423464i | −0.961987 | − | 0.273094i | \(-0.911953\pi\) |
0.717500 | + | 0.696558i | \(0.245286\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.69076 | − | 4.66053i | −0.0881860 | − | 0.152743i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −46.9976 | + | 2.14333i | −1.53863 | + | 0.0701693i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.83775 | 0.0928043 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.94299 | 0.128812 | 0.0644059 | − | 0.997924i | \(-0.479485\pi\) | ||||
0.0644059 | + | 0.997924i | \(0.479485\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7.97529 | + | 12.4653i | 0.260264 | + | 0.406788i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 21.4056 | + | 37.0756i | 0.697804 | + | 1.20863i | 0.969226 | + | 0.246171i | \(0.0791725\pi\) |
−0.271423 | + | 0.962460i | \(0.587494\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13.4626 | − | 23.3180i | 0.438404 | − | 0.759338i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −10.5737 | + | 1.45472i | −0.343964 | + | 0.0473221i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −13.5919 | + | 23.5419i | −0.441678 | + | 0.765009i | −0.997814 | − | 0.0660823i | \(-0.978950\pi\) |
0.556136 | + | 0.831091i | \(0.312283\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.69076 | + | 8.12463i | 0.152268 | + | 0.263737i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.372660 | − | 0.582462i | −0.0120843 | − | 0.0188876i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.12295 | 0.0363760 | 0.0181880 | − | 0.999835i | \(-0.494210\pi\) | ||||
0.0181880 | + | 0.999835i | \(0.494210\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −47.9912 | −1.55296 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −72.8221 | + | 3.32105i | −2.35400 | + | 0.107354i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.24630 | − | 3.89071i | −0.0725369 | − | 0.125638i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −36.1357 | + | 62.5889i | −1.16567 | + | 2.01900i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.91741 | + | 2.71586i | 0.0617877 | + | 0.0875172i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 14.9371 | − | 25.8717i | 0.480841 | − | 0.832841i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.75223 | − | 8.23111i | −0.152822 | − | 0.264695i | 0.779442 | − | 0.626474i | \(-0.215503\pi\) |
−0.932264 | + | 0.361780i | \(0.882169\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.17209 | + | 2.26227i | −0.0376530 | + | 0.0726746i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 24.5979 | 0.789383 | 0.394691 | − | 0.918814i | \(-0.370852\pi\) | ||||
0.394691 | + | 0.918814i | \(0.370852\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 18.1445 | 0.581687 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.622084 | + | 1.20069i | −0.0199226 | + | 0.0384530i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 12.7016 | + | 21.9997i | 0.406359 | + | 0.703834i | 0.994479 | − | 0.104940i | \(-0.0334650\pi\) |
−0.588120 | + | 0.808774i | \(0.700132\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 34.9164 | − | 60.4770i | 1.11593 | − | 1.93285i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.85087 | − | 8.28728i | −0.186804 | − | 0.264593i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 11.4267 | − | 19.7917i | 0.364457 | − | 0.631257i | −0.624232 | − | 0.781239i | \(-0.714588\pi\) |
0.988689 | + | 0.149982i | \(0.0479214\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 17.8112 | + | 30.8499i | 0.567512 | + | 0.982959i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.39037 | − | 0.109013i | 0.0760863 | − | 0.00346992i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −24.5103 | −0.779383 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −24.4690 | −0.777285 | −0.388642 | − | 0.921389i | \(-0.627056\pi\) | ||||
−0.388642 | + | 0.921389i | \(0.627056\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −5.24465 | − | 8.19731i | −0.166434 | − | 0.260134i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −11.8559 | − | 20.5351i | −0.375858 | − | 0.651006i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −13.0000 | + | 22.5167i | −0.411714 | + | 0.713110i | −0.995077 | − | 0.0991016i | \(-0.968403\pi\) |
0.583363 | + | 0.812211i | \(0.301736\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 42.0165 | − | 5.78058i | 1.32934 | − | 0.182889i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))