Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,2,Mod(85,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([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("252.85");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.j (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.01223013094\) |
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: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 169.2 | ||
Root | \(0.500000 + 2.05195i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 252.169 |
Dual form | 252.2.j.b.85.2 |
$q$-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 \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 0.796790 | − | 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 | \(-0.557584\pi\) |
0.941854 | − | 0.336024i | \(-0.109082\pi\) | |||||||
\(12\) | 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 | \(-0.711774\pi\) | ||||
−0.617302 | + | 0.786726i | \(0.711774\pi\) | |||||||
\(20\) | 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 | \(0.0207770\pi\) |
−0.442447 | + | 0.896794i | \(0.645890\pi\) | |||||||
\(24\) | 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 | \(0.199260\pi\) |
0.102216 | + | 0.994762i | \(0.467407\pi\) | |||||||
\(32\) | 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 | −0.986391 | − | 0.164417i | \(-0.947426\pi\) |
0.635585 | + | 0.772031i | \(0.280759\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.58259 | + | 5.59496i | −0.384990 | + | 0.834048i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.690757 | + | 1.19643i | −0.100757 | + | 0.174517i | −0.911997 | − | 0.410197i | \(-0.865460\pi\) |
0.811240 | + | 0.584714i | \(0.198793\pi\) | |||||||
\(48\) | 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 | 0.802229 | − | 0.597016i | \(-0.203647\pi\) |
−0.918146 | + | 0.396243i | \(0.870314\pi\) | |||||||
\(60\) | 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 | \(0.00442207\pi\) |
−0.487921 | + | 0.872888i | \(0.662245\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 9.21780 | − | 0.420378i | 1.10969 | − | 0.0506076i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.78074 | −0.923404 | −0.461702 | − | 0.887035i | \(-0.652761\pi\) | ||||
−0.461702 | + | 0.887035i | \(0.652761\pi\) | |||||||
\(72\) | 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 | \(0.426263\pi\) |
−0.957685 | + | 0.287818i | \(0.907070\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.01245 | + | 8.48087i | −0.334717 | + | 0.942319i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.86333 | − | 4.95943i | 0.314291 | − | 0.544368i | −0.664996 | − | 0.746847i | \(-0.731567\pi\) |
0.979287 | + | 0.202479i | \(0.0648999\pi\) | |||||||
\(84\) | 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 | \(-0.820192\pi\) |
−0.0412728 | − | 0.999148i | \(-0.513141\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.63667 | − | 3.15897i | 0.159723 | − | 0.308284i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.10817 | 0.107131 | 0.0535653 | − | 0.998564i | \(-0.482941\pi\) | ||||
0.0535653 | + | 0.998564i | \(0.482941\pi\) | |||||||
\(108\) | 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 | \(-0.224487\pi\) | ||||
0.761452 | + | 0.648221i | \(0.224487\pi\) | |||||||
\(128\) | 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 | \(0.118868\pi\) |
−0.149599 | + | 0.988747i | \(0.547798\pi\) | |||||||
\(132\) | 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 | \(-0.887172\pi\) |
0.168334 | − | 0.985730i | \(-0.446161\pi\) | |||||||
\(140\) | 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 | −0.551317 | − | 0.834296i | \(-0.685874\pi\) |
0.998180 | + | 0.0603064i | \(0.0192078\pi\) | |||||||
\(152\) | 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 | \(-0.570618\pi\) | ||||
−0.220037 | + | 0.975492i | \(0.570618\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −8.27188 | + | 15.9657i | −0.643965 | + | 1.24293i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.44592 | + | 9.43260i | 0.421418 | + | 0.729917i | 0.996078 | − | 0.0884750i | \(-0.0281993\pi\) |
−0.574661 | + | 0.818392i | \(0.694866\pi\) | |||||||
\(168\) | 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 | \(-0.841023\pi\) | ||||
−0.877851 | + | 0.478934i | \(0.841023\pi\) | |||||||
\(180\) | 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 | \(0.487229\pi\) |
−0.885384 | + | 0.464860i | \(0.846105\pi\) | |||||||
\(192\) | 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 | \(-0.634178\pi\) | ||||
−0.409158 | + | 0.912464i | \(0.634178\pi\) | |||||||
\(200\) | 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 | \(0.153270\pi\) |
−0.0420736 | + | 0.999115i | \(0.513396\pi\) | |||||||
\(212\) | 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 | −0.973010 | − | 0.230762i | \(-0.925878\pi\) |
0.686351 | + | 0.727271i | \(0.259211\pi\) | |||||||
\(224\) | 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 | \(-0.584952\pi\) |
0.967230 | − | 0.253903i | \(-0.0817144\pi\) | |||||||
\(228\) | 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 | 0.997811 | − | 0.0661361i | \(-0.0210672\pi\) |
−0.556181 | + | 0.831061i | \(0.687734\pi\) | |||||||
\(240\) | 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 | \(-0.455843\pi\) | ||||
0.138279 | + | 0.990393i | \(0.455843\pi\) | |||||||
\(252\) | 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 | −0.741216 | − | 0.671267i | \(-0.765750\pi\) |
0.951942 | + | 0.306278i | \(0.0990837\pi\) | |||||||
\(264\) | 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 | \(-0.627497\pi\) | ||||
−0.389919 | + | 0.920849i | \(0.627497\pi\) | |||||||
\(272\) | 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 | \(0.0197934\pi\) |
−0.445217 | + | 0.895423i | \(0.646873\pi\) | |||||||
\(284\) | 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 | \(-0.284619\pi\) | ||||
0.626176 | + | 0.779681i | \(0.284619\pi\) | |||||||
\(308\) | 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 | \(-0.886865\pi\) |
0.167384 | − | 0.985892i | \(-0.446468\pi\) | |||||||
\(312\) | 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 | −0.778434 | − | 0.627726i | \(-0.783986\pi\) |
0.932844 | + | 0.360281i | \(0.117319\pi\) | |||||||
\(332\) | 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 | \(-0.790566\pi\) |
−0.133955 | − | 0.990987i | \(-0.542768\pi\) | |||||||
\(348\) | 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 | \(-0.475080\pi\) | ||||
0.0782071 | + | 0.996937i | \(0.475080\pi\) | |||||||
\(360\) | 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 | −0.986035 | − | 0.166537i | \(-0.946742\pi\) |
0.637243 | + | 0.770663i | \(0.280075\pi\) | |||||||
\(368\) | 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 | \(-0.518153\pi\) | ||||
−0.0569979 | + | 0.998374i | \(0.518153\pi\) | |||||||
\(380\) | 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 | \(0.124746\pi\) |
−0.131317 | + | 0.991340i | \(0.541921\pi\) | |||||||
\(384\) | 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 | 0.828583 | − | 0.559866i | \(-0.189147\pi\) |
−0.899150 | + | 0.437641i | \(0.855814\pi\) | |||||||
\(420\) | 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 | \(-0.536618\pi\) | ||||
−0.114784 | + | 0.993390i | \(0.536618\pi\) | |||||||
\(432\) | 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 | −0.805083 | − | 0.593162i | \(-0.797879\pi\) |
0.916235 | + | 0.400641i | \(0.131213\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.25729 | + | 2.72382i | −0.0598712 | + | 0.129706i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.38151 | − | 2.39285i | 0.0656377 | − | 0.113688i | −0.831339 | − | 0.555766i | \(-0.812425\pi\) |
0.896977 | + | 0.442078i | \(0.145758\pi\) | |||||||
\(444\) | 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 | 0.994628 | − | 0.103519i | \(-0.0330101\pi\) |
−0.586964 | + | 0.809613i | \(0.699677\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −19.4852 | − | 30.4551i | −0.903605 | − | 1.41232i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −23.6156 | −1.09280 | −0.546399 | − | 0.837525i | \(-0.684002\pi\) | ||||
−0.546399 | + | 0.837525i | \(0.684002\pi\) | |||||||
\(468\) | 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 | \(0.505087\pi\) |
−0.857924 | + | 0.513776i | \(0.828246\pi\) | |||||||
\(480\) | 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 | \(-0.547627\pi\) | ||||
−0.149066 | + | 0.988827i | \(0.547627\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.47675 | + | 8.64065i | −0.202446 | + | 0.390744i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.02704 | + | 1.77889i | 0.0463498 | + | 0.0802801i | 0.888270 | − | 0.459323i | \(-0.151908\pi\) |
−0.841920 | + | 0.539603i | \(0.818574\pi\) | |||||||
\(492\) | 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 | 0.988839 | − | 0.148987i | \(-0.0476014\pi\) |
−0.623446 | + | 0.781866i | \(0.714268\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 18.8456 | − | 0.859455i | 0.841960 | − | 0.0383976i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5.60078 | −0.249726 | −0.124863 | − | 0.992174i | \(-0.539849\pi\) | ||||
−0.124863 | + | 0.992174i | \(0.539849\pi\) | |||||||
\(504\) | 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 | \(-0.296351\pi\) | ||||
0.597021 | + | 0.802225i | \(0.296351\pi\) | |||||||
\(524\) | 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 | −0.600602 | − | 0.799548i | \(-0.705072\pi\) |
0.992730 | + | 0.120362i | \(0.0384056\pi\) | |||||||
\(548\) | 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 | \(-0.920379\pi\) |
0.270068 | − | 0.962841i | \(-0.412954\pi\) | |||||||
\(564\) | 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 | 0.745367 | − | 0.666654i | \(-0.232274\pi\) |
−0.950023 | + | 0.312180i | \(0.898941\pi\) | |||||||
\(572\) | 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 | −0.501662 | − | 0.865064i | \(-0.667278\pi\) |
0.999998 | + | 0.00191995i | \(0.000611139\pi\) | |||||||
\(588\) | 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 | 0.999129 | − | 0.0417243i | \(-0.0132851\pi\) |
−0.535699 | + | 0.844409i | \(0.679952\pi\) | |||||||
\(600\) | 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 | 0.634938 | − | 0.772563i | \(-0.281026\pi\) |
−0.986528 | + | 0.163591i | \(0.947692\pi\) | |||||||
\(608\) | 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 | −0.845419 | − | 0.534103i | \(-0.820649\pi\) |
0.885257 | + | 0.465103i | \(0.153983\pi\) | |||||||
\(620\) | 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 | \(-0.669359\pi\) | ||||
−0.507306 | + | 0.861766i | \(0.669359\pi\) | |||||||
\(632\) | 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 | 0.788506 | − | 0.615027i | \(-0.210855\pi\) |
−0.926882 | + | 0.375353i | \(0.877521\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7.52997 | − | 14.5337i | 0.296492 | − | 0.572264i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −11.8142 | −0.464464 | −0.232232 | − | 0.972660i | \(-0.574603\pi\) | ||||
−0.232232 | + | 0.972660i | \(0.574603\pi\) | |||||||
\(648\) | 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 | −0.973392 | − | 0.229144i | \(-0.926407\pi\) |
0.685141 | + | 0.728410i | \(0.259741\pi\) | |||||||
\(660\) | 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 | \(-0.695135\pi\) | ||||
−0.575351 | + | 0.817907i | \(0.695135\pi\) | |||||||
\(684\) | 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 | −0.833183 | − | 0.552997i | \(-0.813484\pi\) |
0.895501 | + | 0.445060i | \(0.146817\pi\) | |||||||
\(692\) | 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 | \(-0.786032\pi\) | ||||
−0.782453 | + | 0.622710i | \(0.786032\pi\) | |||||||
\(720\) | 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 | \(-0.656179\pi\) |
0.999457 | − | 0.0329425i | \(-0.0104878\pi\) | |||||||
\(728\) | 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 | \(-0.453825\pi\) | ||||
0.144555 | + | 0.989497i | \(0.453825\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −9.31138 | + | 0.424646i | −0.342062 | + | 0.0155998i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.37364 | + | 5.84332i | 0.123767 | + | 0.214371i | 0.921250 | − | 0.388970i | \(-0.127169\pi\) |
−0.797483 | + | 0.603341i | \(0.793836\pi\) | |||||||
\(744\) | 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 | 0.589605 | − | 0.807692i | \(-0.299283\pi\) |
−0.994284 | + | 0.106767i | \(0.965950\pi\) | |||||||
\(752\) | 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 | 0.771339 | − | 0.636425i | \(-0.219588\pi\) |
−0.936830 | + | 0.349786i | \(0.886254\pi\) | |||||||
\(788\) | 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 | \(-0.500099\pi\) | ||||
−0.000310920 | 1.00000i | \(0.500099\pi\) | ||||||||
\(812\) | 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 | 0.723744 | − | 0.690068i | \(-0.242419\pi\) |
−0.959489 | + | 0.281747i | \(0.909086\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −6.82743 | + | 0.311365i | −0.237701 | + | 0.0108403i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −49.3068 | −1.71457 | −0.857283 | − | 0.514846i | \(-0.827849\pi\) | ||||
−0.857283 | + | 0.514846i | \(0.827849\pi\) | |||||||
\(828\) | 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 | \(-0.609707\pi\) |
0.984032 | − | 0.177990i | \(-0.0569593\pi\) | |||||||
\(840\) | 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 | 0.540222 | − | 0.841523i | \(-0.318340\pi\) |
−0.998891 | + | 0.0470847i | \(0.985007\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.02704 | + | 7.77266i | −0.137241 | + | 0.264892i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 26.8142 | 0.912766 | 0.456383 | − | 0.889784i | \(-0.349145\pi\) | ||||
0.456383 | + | 0.889784i | \(0.349145\pi\) | |||||||
\(864\) | 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 | \(-0.472787\pi\) | ||||
0.0853889 | + | 0.996348i | \(0.472787\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.41441 | + | 5.33667i | 0.114774 | + | 0.179390i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −9.26157 | − | 16.0415i | −0.310973 | − | 0.538621i | 0.667600 | − | 0.744520i | \(-0.267322\pi\) |
−0.978573 | + | 0.205899i | \(0.933988\pi\) | |||||||
\(888\) | 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 | \(-0.524911\pi\) |
0.902465 | − | 0.430763i | \(-0.141755\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 8.14601 | − | 0.744547i | 0.270186 | − | 0.0246951i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −11.9808 | + | 20.7514i | −0.396943 | + | 0.687525i | −0.993347 | − | 0.115159i | \(-0.963262\pi\) |
0.596404 | + | 0.802684i | \(0.296595\pi\) | |||||||
\(912\) | 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 | \(-0.600563\pi\) | ||||
−0.310700 | + | 0.950508i | \(0.600563\pi\) | |||||||
\(920\) | 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 | −0.556136 | − | 0.831091i | \(-0.687717\pi\) |
0.997814 | + | 0.0660823i | \(0.0210500\pi\) | |||||||
\(948\) | 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 | 0.932264 | − | 0.361780i | \(-0.117831\pi\) |
−0.779442 | + | 0.626474i | \(0.784497\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.17209 | + | 2.26227i | −0.0376530 | + | 0.0726746i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −24.5979 | −0.789383 | −0.394691 | − | 0.918814i | \(-0.629148\pi\) | ||||
−0.394691 | + | 0.918814i | \(0.629148\pi\) | |||||||
\(972\) | 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 | −0.988689 | − | 0.149982i | \(-0.952079\pi\) |
0.624232 | + | 0.781239i | \(0.285412\pi\) | |||||||
\(984\) | 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 | \(-0.372944\pi\) | ||||
0.388642 | + | 0.921389i | \(0.372944\pi\) | |||||||
\(992\) | 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 \(a_p\))