Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [966,2,Mod(229,966)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(966, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("966.229");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 966.k (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.71354883526\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 229.12 | ||
Character | \(\chi\) | \(=\) | 966.229 |
Dual form | 966.2.k.a.367.12 |
$q$-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 \(\left(\mathbb{Z}/966\mathbb{Z}\right)^\times\).
\(n\) | \(323\) | \(829\) | \(925\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.353553 | + | 0.612372i | ||||
\(3\) | 0.866025 | − | 0.500000i | 0.500000 | − | 0.288675i | ||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | −0.242904 | + | 0.420722i | −0.108630 | + | 0.188153i | −0.915215 | − | 0.402965i | \(-0.867980\pi\) |
0.806586 | + | 0.591117i | \(0.201313\pi\) | |||||||
\(6\) | 1.00000i | 0.408248i | ||||||||
\(7\) | −2.51079 | − | 0.834227i | −0.948989 | − | 0.315308i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | −0.242904 | − | 0.420722i | −0.0768130 | − | 0.133044i | ||||
\(11\) | 2.65306 | − | 1.53174i | 0.799927 | − | 0.461838i | −0.0435188 | − | 0.999053i | \(-0.513857\pi\) |
0.843446 | + | 0.537215i | \(0.180524\pi\) | |||||||
\(12\) | −0.866025 | − | 0.500000i | −0.250000 | − | 0.144338i | ||||
\(13\) | 5.07423i | 1.40734i | 0.710528 | + | 0.703668i | \(0.248456\pi\) | ||||
−0.710528 | + | 0.703668i | \(0.751544\pi\) | |||||||
\(14\) | 1.97786 | − | 1.75729i | 0.528604 | − | 0.469657i | ||||
\(15\) | 0.485808i | 0.125435i | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 0.418779 | + | 0.725347i | 0.101569 | + | 0.175922i | 0.912331 | − | 0.409453i | \(-0.134280\pi\) |
−0.810762 | + | 0.585375i | \(0.800947\pi\) | |||||||
\(18\) | 0.500000 | + | 0.866025i | 0.117851 | + | 0.204124i | ||||
\(19\) | 3.41446 | − | 5.91401i | 0.783330 | − | 1.35677i | −0.146662 | − | 0.989187i | \(-0.546853\pi\) |
0.929992 | − | 0.367580i | \(-0.119814\pi\) | |||||||
\(20\) | 0.485808 | 0.108630 | ||||||||
\(21\) | −2.59152 | + | 0.532933i | −0.565516 | + | 0.116296i | ||||
\(22\) | 3.06349i | 0.653137i | ||||||||
\(23\) | −2.14246 | − | 4.29067i | −0.446734 | − | 0.894667i | ||||
\(24\) | 0.866025 | − | 0.500000i | 0.176777 | − | 0.102062i | ||||
\(25\) | 2.38200 | + | 4.12574i | 0.476399 | + | 0.825147i | ||||
\(26\) | −4.39441 | − | 2.53711i | −0.861814 | − | 0.497569i | ||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 0.532933 | + | 2.59152i | 0.100715 | + | 0.489751i | ||||
\(29\) | 4.62895 | 0.859574 | 0.429787 | − | 0.902930i | \(-0.358589\pi\) | ||||
0.429787 | + | 0.902930i | \(0.358589\pi\) | |||||||
\(30\) | −0.420722 | − | 0.242904i | −0.0768130 | − | 0.0443480i | ||||
\(31\) | 7.97469 | − | 4.60419i | 1.43230 | − | 0.826937i | 0.435002 | − | 0.900430i | \(-0.356748\pi\) |
0.997296 | + | 0.0734924i | \(0.0234145\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | 1.53174 | − | 2.65306i | 0.266642 | − | 0.461838i | ||||
\(34\) | −0.837558 | −0.143640 | ||||||||
\(35\) | 0.960858 | − | 0.853707i | 0.162415 | − | 0.144303i | ||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | 4.82160 | + | 2.78375i | 0.792665 | + | 0.457646i | 0.840900 | − | 0.541190i | \(-0.182026\pi\) |
−0.0482347 | + | 0.998836i | \(0.515360\pi\) | |||||||
\(38\) | 3.41446 | + | 5.91401i | 0.553898 | + | 0.959379i | ||||
\(39\) | 2.53711 | + | 4.39441i | 0.406263 | + | 0.703668i | ||||
\(40\) | −0.242904 | + | 0.420722i | −0.0384065 | + | 0.0665220i | ||||
\(41\) | − | 8.68814i | − | 1.35686i | −0.734665 | − | 0.678430i | \(-0.762661\pi\) | ||
0.734665 | − | 0.678430i | \(-0.237339\pi\) | |||||||
\(42\) | 0.834227 | − | 2.51079i | 0.128724 | − | 0.387423i | ||||
\(43\) | − | 5.27242i | − | 0.804036i | −0.915632 | − | 0.402018i | \(-0.868309\pi\) | ||
0.915632 | − | 0.402018i | \(-0.131691\pi\) | |||||||
\(44\) | −2.65306 | − | 1.53174i | −0.399963 | − | 0.230919i | ||||
\(45\) | 0.242904 | + | 0.420722i | 0.0362100 | + | 0.0627175i | ||||
\(46\) | 4.78706 | + | 0.289912i | 0.705814 | + | 0.0427452i | ||||
\(47\) | 3.68699 | + | 2.12869i | 0.537803 | + | 0.310501i | 0.744188 | − | 0.667970i | \(-0.232837\pi\) |
−0.206385 | + | 0.978471i | \(0.566170\pi\) | |||||||
\(48\) | 1.00000i | 0.144338i | ||||||||
\(49\) | 5.60813 | + | 4.18914i | 0.801162 | + | 0.598448i | ||||
\(50\) | −4.76399 | −0.673730 | ||||||||
\(51\) | 0.725347 | + | 0.418779i | 0.101569 | + | 0.0586408i | ||||
\(52\) | 4.39441 | − | 2.53711i | 0.609395 | − | 0.351834i | ||||
\(53\) | −7.31519 | + | 4.22343i | −1.00482 | + | 0.580132i | −0.909670 | − | 0.415331i | \(-0.863666\pi\) |
−0.0951481 | + | 0.995463i | \(0.530332\pi\) | |||||||
\(54\) | 0.866025 | + | 0.500000i | 0.117851 | + | 0.0680414i | ||||
\(55\) | 1.48827i | 0.200678i | ||||||||
\(56\) | −2.51079 | − | 0.834227i | −0.335518 | − | 0.111478i | ||||
\(57\) | − | 6.82891i | − | 0.904511i | ||||||
\(58\) | −2.31447 | + | 4.00878i | −0.303905 | + | 0.526379i | ||||
\(59\) | −3.15927 | + | 1.82401i | −0.411302 | + | 0.237465i | −0.691349 | − | 0.722521i | \(-0.742983\pi\) |
0.280047 | + | 0.959986i | \(0.409650\pi\) | |||||||
\(60\) | 0.420722 | − | 0.242904i | 0.0543150 | − | 0.0313588i | ||||
\(61\) | 4.90732 | − | 8.49972i | 0.628318 | − | 1.08828i | −0.359571 | − | 0.933118i | \(-0.617077\pi\) |
0.987889 | − | 0.155161i | \(-0.0495895\pi\) | |||||||
\(62\) | 9.20838i | 1.16947i | ||||||||
\(63\) | −1.97786 | + | 1.75729i | −0.249186 | + | 0.221398i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.13484 | − | 1.23255i | −0.264794 | − | 0.152879i | ||||
\(66\) | 1.53174 | + | 2.65306i | 0.188545 | + | 0.326569i | ||||
\(67\) | 3.54252 | − | 2.04527i | 0.432788 | − | 0.249870i | −0.267746 | − | 0.963490i | \(-0.586279\pi\) |
0.700533 | + | 0.713620i | \(0.252945\pi\) | |||||||
\(68\) | 0.418779 | − | 0.725347i | 0.0507844 | − | 0.0879612i | ||||
\(69\) | −4.00076 | − | 2.64460i | −0.481635 | − | 0.318373i | ||||
\(70\) | 0.258903 | + | 1.25898i | 0.0309449 | + | 0.150477i | ||||
\(71\) | −1.32082 | −0.156752 | −0.0783760 | − | 0.996924i | \(-0.524973\pi\) | ||||
−0.0783760 | + | 0.996924i | \(0.524973\pi\) | |||||||
\(72\) | 0.500000 | − | 0.866025i | 0.0589256 | − | 0.102062i | ||||
\(73\) | 3.26928 | − | 1.88752i | 0.382640 | − | 0.220917i | −0.296326 | − | 0.955087i | \(-0.595762\pi\) |
0.678966 | + | 0.734169i | \(0.262428\pi\) | |||||||
\(74\) | −4.82160 | + | 2.78375i | −0.560499 | + | 0.323604i | ||||
\(75\) | 4.12574 | + | 2.38200i | 0.476399 | + | 0.275049i | ||||
\(76\) | −6.82891 | −0.783330 | ||||||||
\(77\) | −7.93909 | + | 1.63263i | −0.904743 | + | 0.186056i | ||||
\(78\) | −5.07423 | −0.574543 | ||||||||
\(79\) | 9.12312 | + | 5.26723i | 1.02643 | + | 0.592610i | 0.915960 | − | 0.401269i | \(-0.131431\pi\) |
0.110471 | + | 0.993879i | \(0.464764\pi\) | |||||||
\(80\) | −0.242904 | − | 0.420722i | −0.0271575 | − | 0.0470381i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 7.52415 | + | 4.34407i | 0.830904 | + | 0.479723i | ||||
\(83\) | −6.95787 | −0.763725 | −0.381863 | − | 0.924219i | \(-0.624717\pi\) | ||||
−0.381863 | + | 0.924219i | \(0.624717\pi\) | |||||||
\(84\) | 1.75729 | + | 1.97786i | 0.191737 | + | 0.215802i | ||||
\(85\) | −0.406892 | −0.0441337 | ||||||||
\(86\) | 4.56605 | + | 2.63621i | 0.492369 | + | 0.284270i | ||||
\(87\) | 4.00878 | − | 2.31447i | 0.429787 | − | 0.248138i | ||||
\(88\) | 2.65306 | − | 1.53174i | 0.282817 | − | 0.163284i | ||||
\(89\) | 5.22221 | − | 9.04513i | 0.553553 | − | 0.958782i | −0.444462 | − | 0.895798i | \(-0.646605\pi\) |
0.998015 | − | 0.0629838i | \(-0.0200617\pi\) | |||||||
\(90\) | −0.485808 | −0.0512086 | ||||||||
\(91\) | 4.23305 | − | 12.7403i | 0.443745 | − | 1.33555i | ||||
\(92\) | −2.64460 | + | 4.00076i | −0.275719 | + | 0.417108i | ||||
\(93\) | 4.60419 | − | 7.97469i | 0.477432 | − | 0.826937i | ||||
\(94\) | −3.68699 | + | 2.12869i | −0.380284 | + | 0.219557i | ||||
\(95\) | 1.65877 | + | 2.87307i | 0.170186 | + | 0.294771i | ||||
\(96\) | −0.866025 | − | 0.500000i | −0.0883883 | − | 0.0510310i | ||||
\(97\) | −9.53965 | −0.968604 | −0.484302 | − | 0.874901i | \(-0.660926\pi\) | ||||
−0.484302 | + | 0.874901i | \(0.660926\pi\) | |||||||
\(98\) | −6.43196 | + | 2.76222i | −0.649726 | + | 0.279026i | ||||
\(99\) | − | 3.06349i | − | 0.307892i | ||||||
\(100\) | 2.38200 | − | 4.12574i | 0.238200 | − | 0.412574i | ||||
\(101\) | −2.59731 | + | 1.49955i | −0.258442 | + | 0.149211i | −0.623623 | − | 0.781725i | \(-0.714340\pi\) |
0.365182 | + | 0.930936i | \(0.381007\pi\) | |||||||
\(102\) | −0.725347 | + | 0.418779i | −0.0718200 | + | 0.0414653i | ||||
\(103\) | −7.49493 | + | 12.9816i | −0.738497 | + | 1.27911i | 0.214675 | + | 0.976686i | \(0.431131\pi\) |
−0.953172 | + | 0.302429i | \(0.902203\pi\) | |||||||
\(104\) | 5.07423i | 0.497569i | ||||||||
\(105\) | 0.405274 | − | 1.21976i | 0.0395507 | − | 0.119037i | ||||
\(106\) | − | 8.44685i | − | 0.820431i | ||||||
\(107\) | 6.39367 | + | 3.69139i | 0.618099 | + | 0.356860i | 0.776129 | − | 0.630575i | \(-0.217181\pi\) |
−0.158029 | + | 0.987434i | \(0.550514\pi\) | |||||||
\(108\) | −0.866025 | + | 0.500000i | −0.0833333 | + | 0.0481125i | ||||
\(109\) | −1.05921 | + | 0.611537i | −0.101454 | + | 0.0585746i | −0.549869 | − | 0.835251i | \(-0.685322\pi\) |
0.448414 | + | 0.893826i | \(0.351989\pi\) | |||||||
\(110\) | −1.28888 | − | 0.744133i | −0.122889 | − | 0.0709503i | ||||
\(111\) | 5.56750 | 0.528444 | ||||||||
\(112\) | 1.97786 | − | 1.75729i | 0.186890 | − | 0.166049i | ||||
\(113\) | 8.65289i | 0.813995i | 0.913429 | + | 0.406998i | \(0.133424\pi\) | ||||
−0.913429 | + | 0.406998i | \(0.866576\pi\) | |||||||
\(114\) | 5.91401 | + | 3.41446i | 0.553898 | + | 0.319793i | ||||
\(115\) | 2.32559 | + | 0.140842i | 0.216863 | + | 0.0131336i | ||||
\(116\) | −2.31447 | − | 4.00878i | −0.214893 | − | 0.372206i | ||||
\(117\) | 4.39441 | + | 2.53711i | 0.406263 | + | 0.234556i | ||||
\(118\) | − | 3.64801i | − | 0.335827i | ||||||
\(119\) | −0.446363 | − | 2.17055i | −0.0409180 | − | 0.198974i | ||||
\(120\) | 0.485808i | 0.0443480i | ||||||||
\(121\) | −0.807526 | + | 1.39868i | −0.0734115 | + | 0.127152i | ||||
\(122\) | 4.90732 | + | 8.49972i | 0.444288 | + | 0.769529i | ||||
\(123\) | −4.34407 | − | 7.52415i | −0.391692 | − | 0.678430i | ||||
\(124\) | −7.97469 | − | 4.60419i | −0.716149 | − | 0.413469i | ||||
\(125\) | −4.74342 | −0.424265 | ||||||||
\(126\) | −0.532933 | − | 2.59152i | −0.0474775 | − | 0.230871i | ||||
\(127\) | 7.27976 | 0.645974 | 0.322987 | − | 0.946403i | \(-0.395313\pi\) | ||||
0.322987 | + | 0.946403i | \(0.395313\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | −2.63621 | − | 4.56605i | −0.232105 | − | 0.402018i | ||||
\(130\) | 2.13484 | − | 1.23255i | 0.187238 | − | 0.108102i | ||||
\(131\) | −15.3287 | − | 8.85000i | −1.33927 | − | 0.773228i | −0.352571 | − | 0.935785i | \(-0.614693\pi\) |
−0.986699 | + | 0.162557i | \(0.948026\pi\) | |||||||
\(132\) | −3.06349 | −0.266642 | ||||||||
\(133\) | −13.5066 | + | 12.0004i | −1.17117 | + | 1.04057i | ||||
\(134\) | 4.09055i | 0.353370i | ||||||||
\(135\) | 0.420722 | + | 0.242904i | 0.0362100 | + | 0.0209058i | ||||
\(136\) | 0.418779 | + | 0.725347i | 0.0359100 | + | 0.0621980i | ||||
\(137\) | 3.86939 | − | 2.23400i | 0.330585 | − | 0.190863i | −0.325516 | − | 0.945537i | \(-0.605538\pi\) |
0.656101 | + | 0.754673i | \(0.272205\pi\) | |||||||
\(138\) | 4.29067 | − | 2.14246i | 0.365246 | − | 0.182378i | ||||
\(139\) | 19.9740i | 1.69417i | 0.531454 | + | 0.847087i | \(0.321646\pi\) | ||||
−0.531454 | + | 0.847087i | \(0.678354\pi\) | |||||||
\(140\) | −1.21976 | − | 0.405274i | −0.103089 | − | 0.0342519i | ||||
\(141\) | 4.25737 | 0.358536 | ||||||||
\(142\) | 0.660408 | − | 1.14386i | 0.0554202 | − | 0.0959906i | ||||
\(143\) | 7.77241 | + | 13.4622i | 0.649962 | + | 1.12577i | ||||
\(144\) | 0.500000 | + | 0.866025i | 0.0416667 | + | 0.0721688i | ||||
\(145\) | −1.12439 | + | 1.94750i | −0.0933754 | + | 0.161731i | ||||
\(146\) | 3.77504i | 0.312424i | ||||||||
\(147\) | 6.95135 | + | 0.823832i | 0.573338 | + | 0.0679485i | ||||
\(148\) | − | 5.56750i | − | 0.457646i | ||||||
\(149\) | 16.9732 | + | 9.79947i | 1.39050 | + | 0.802804i | 0.993370 | − | 0.114960i | \(-0.0366741\pi\) |
0.397127 | + | 0.917764i | \(0.370007\pi\) | |||||||
\(150\) | −4.12574 | + | 2.38200i | −0.336865 | + | 0.194489i | ||||
\(151\) | 4.34232 | + | 7.52112i | 0.353373 | + | 0.612060i | 0.986838 | − | 0.161711i | \(-0.0517014\pi\) |
−0.633465 | + | 0.773771i | \(0.718368\pi\) | |||||||
\(152\) | 3.41446 | − | 5.91401i | 0.276949 | − | 0.479690i | ||||
\(153\) | 0.837558 | 0.0677126 | ||||||||
\(154\) | 2.55564 | − | 7.69177i | 0.205939 | − | 0.619820i | ||||
\(155\) | 4.47351i | 0.359321i | ||||||||
\(156\) | 2.53711 | − | 4.39441i | 0.203132 | − | 0.351834i | ||||
\(157\) | 3.73996 | + | 6.47780i | 0.298481 | + | 0.516984i | 0.975789 | − | 0.218716i | \(-0.0701867\pi\) |
−0.677308 | + | 0.735700i | \(0.736853\pi\) | |||||||
\(158\) | −9.12312 | + | 5.26723i | −0.725796 | + | 0.419039i | ||||
\(159\) | −4.22343 | + | 7.31519i | −0.334939 | + | 0.580132i | ||||
\(160\) | 0.485808 | 0.0384065 | ||||||||
\(161\) | 1.79987 | + | 12.5603i | 0.141850 | + | 0.989888i | ||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 8.60562 | − | 14.9054i | 0.674044 | − | 1.16748i | −0.302704 | − | 0.953085i | \(-0.597889\pi\) |
0.976747 | − | 0.214393i | \(-0.0687775\pi\) | |||||||
\(164\) | −7.52415 | + | 4.34407i | −0.587538 | + | 0.339215i | ||||
\(165\) | 0.744133 | + | 1.28888i | 0.0579307 | + | 0.100339i | ||||
\(166\) | 3.47893 | − | 6.02569i | 0.270018 | − | 0.467684i | ||||
\(167\) | 19.5560i | 1.51329i | 0.653826 | + | 0.756645i | \(0.273163\pi\) | ||||
−0.653826 | + | 0.756645i | \(0.726837\pi\) | |||||||
\(168\) | −2.59152 | + | 0.532933i | −0.199940 | + | 0.0411167i | ||||
\(169\) | −12.7478 | −0.980597 | ||||||||
\(170\) | 0.203446 | − | 0.352379i | 0.0156036 | − | 0.0270262i | ||||
\(171\) | −3.41446 | − | 5.91401i | −0.261110 | − | 0.452256i | ||||
\(172\) | −4.56605 | + | 2.63621i | −0.348158 | + | 0.201009i | ||||
\(173\) | −18.2657 | − | 10.5457i | −1.38871 | − | 0.801775i | −0.395544 | − | 0.918447i | \(-0.629444\pi\) |
−0.993170 | + | 0.116673i | \(0.962777\pi\) | |||||||
\(174\) | 4.62895i | 0.350919i | ||||||||
\(175\) | −2.53889 | − | 12.3460i | −0.191922 | − | 0.933269i | ||||
\(176\) | 3.06349i | 0.230919i | ||||||||
\(177\) | −1.82401 | + | 3.15927i | −0.137101 | + | 0.237465i | ||||
\(178\) | 5.22221 | + | 9.04513i | 0.391421 | + | 0.677961i | ||||
\(179\) | −8.98104 | − | 15.5556i | −0.671275 | − | 1.16268i | −0.977543 | − | 0.210737i | \(-0.932414\pi\) |
0.306268 | − | 0.951945i | \(-0.400920\pi\) | |||||||
\(180\) | 0.242904 | − | 0.420722i | 0.0181050 | − | 0.0313588i | ||||
\(181\) | −6.32867 | −0.470406 | −0.235203 | − | 0.971946i | \(-0.575576\pi\) | ||||
−0.235203 | + | 0.971946i | \(0.575576\pi\) | |||||||
\(182\) | 8.91691 | + | 10.0361i | 0.660965 | + | 0.743924i | ||||
\(183\) | − | 9.81464i | − | 0.725519i | ||||||
\(184\) | −2.14246 | − | 4.29067i | −0.157944 | − | 0.316313i | ||||
\(185\) | −2.34237 | + | 1.35237i | −0.172214 | + | 0.0994280i | ||||
\(186\) | 4.60419 | + | 7.97469i | 0.337596 | + | 0.584733i | ||||
\(187\) | 2.22209 | + | 1.28292i | 0.162495 | + | 0.0938167i | ||||
\(188\) | − | 4.25737i | − | 0.310501i | ||||||
\(189\) | −0.834227 | + | 2.51079i | −0.0606811 | + | 0.182633i | ||||
\(190\) | −3.31754 | −0.240680 | ||||||||
\(191\) | −15.6759 | − | 9.05046i | −1.13426 | − | 0.654868i | −0.189261 | − | 0.981927i | \(-0.560609\pi\) |
−0.945004 | + | 0.327059i | \(0.893942\pi\) | |||||||
\(192\) | 0.866025 | − | 0.500000i | 0.0625000 | − | 0.0360844i | ||||
\(193\) | −7.59857 | − | 13.1611i | −0.546957 | − | 0.947357i | −0.998481 | − | 0.0550982i | \(-0.982453\pi\) |
0.451524 | − | 0.892259i | \(-0.350881\pi\) | |||||||
\(194\) | 4.76982 | − | 8.26158i | 0.342453 | − | 0.593147i | ||||
\(195\) | −2.46510 | −0.176529 | ||||||||
\(196\) | 0.823832 | − | 6.95135i | 0.0588451 | − | 0.496525i | ||||
\(197\) | −4.52116 | −0.322119 | −0.161060 | − | 0.986945i | \(-0.551491\pi\) | ||||
−0.161060 | + | 0.986945i | \(0.551491\pi\) | |||||||
\(198\) | 2.65306 | + | 1.53174i | 0.188545 | + | 0.108856i | ||||
\(199\) | −1.40852 | − | 2.43964i | −0.0998476 | − | 0.172941i | 0.811774 | − | 0.583972i | \(-0.198502\pi\) |
−0.911621 | + | 0.411031i | \(0.865169\pi\) | |||||||
\(200\) | 2.38200 | + | 4.12574i | 0.168433 | + | 0.291734i | ||||
\(201\) | 2.04527 | − | 3.54252i | 0.144263 | − | 0.249870i | ||||
\(202\) | − | 2.99911i | − | 0.211017i | ||||||
\(203\) | −11.6223 | − | 3.86159i | −0.815726 | − | 0.271030i | ||||
\(204\) | − | 0.837558i | − | 0.0586408i | ||||||
\(205\) | 3.65529 | + | 2.11038i | 0.255297 | + | 0.147396i | ||||
\(206\) | −7.49493 | − | 12.9816i | −0.522196 | − | 0.904470i | ||||
\(207\) | −4.78706 | − | 0.289912i | −0.332724 | − | 0.0201503i | ||||
\(208\) | −4.39441 | − | 2.53711i | −0.304697 | − | 0.175917i | ||||
\(209\) | − | 20.9203i | − | 1.44709i | ||||||
\(210\) | 0.853707 | + | 0.960858i | 0.0589114 | + | 0.0663055i | ||||
\(211\) | 7.17107 | 0.493677 | 0.246838 | − | 0.969057i | \(-0.420608\pi\) | ||||
0.246838 | + | 0.969057i | \(0.420608\pi\) | |||||||
\(212\) | 7.31519 | + | 4.22343i | 0.502409 | + | 0.290066i | ||||
\(213\) | −1.14386 | + | 0.660408i | −0.0783760 | + | 0.0452504i | ||||
\(214\) | −6.39367 | + | 3.69139i | −0.437062 | + | 0.252338i | ||||
\(215\) | 2.21822 | + | 1.28069i | 0.151281 | + | 0.0873424i | ||||
\(216\) | − | 1.00000i | − | 0.0680414i | ||||||
\(217\) | −23.8637 | + | 4.90746i | −1.61997 | + | 0.333140i | ||||
\(218\) | − | 1.22307i | − | 0.0828370i | ||||||
\(219\) | 1.88752 | − | 3.26928i | 0.127547 | − | 0.220917i | ||||
\(220\) | 1.28888 | − | 0.744133i | 0.0868960 | − | 0.0501694i | ||||
\(221\) | −3.68057 | + | 2.12498i | −0.247582 | + | 0.142942i | ||||
\(222\) | −2.78375 | + | 4.82160i | −0.186833 | + | 0.323604i | ||||
\(223\) | − | 7.50608i | − | 0.502645i | −0.967903 | − | 0.251322i | \(-0.919135\pi\) | ||
0.967903 | − | 0.251322i | \(-0.0808654\pi\) | |||||||
\(224\) | 0.532933 | + | 2.59152i | 0.0356081 | + | 0.173153i | ||||
\(225\) | 4.76399 | 0.317599 | ||||||||
\(226\) | −7.49362 | − | 4.32644i | −0.498468 | − | 0.287791i | ||||
\(227\) | −8.87766 | − | 15.3766i | −0.589231 | − | 1.02058i | −0.994333 | − | 0.106306i | \(-0.966098\pi\) |
0.405103 | − | 0.914271i | \(-0.367236\pi\) | |||||||
\(228\) | −5.91401 | + | 3.41446i | −0.391665 | + | 0.226128i | ||||
\(229\) | −10.2713 | + | 17.7904i | −0.678747 | + | 1.17562i | 0.296612 | + | 0.954998i | \(0.404143\pi\) |
−0.975359 | + | 0.220626i | \(0.929190\pi\) | |||||||
\(230\) | −1.28477 | + | 1.94360i | −0.0847151 | + | 0.128157i | ||||
\(231\) | −6.05914 | + | 5.38345i | −0.398662 | + | 0.354205i | ||||
\(232\) | 4.62895 | 0.303905 | ||||||||
\(233\) | 7.83721 | − | 13.5744i | 0.513433 | − | 0.889291i | −0.486446 | − | 0.873711i | \(-0.661707\pi\) |
0.999879 | − | 0.0155807i | \(-0.00495969\pi\) | |||||||
\(234\) | −4.39441 | + | 2.53711i | −0.287271 | + | 0.165856i | ||||
\(235\) | −1.79117 | + | 1.03413i | −0.116843 | + | 0.0674594i | ||||
\(236\) | 3.15927 | + | 1.82401i | 0.205651 | + | 0.118733i | ||||
\(237\) | 10.5345 | 0.684287 | ||||||||
\(238\) | 2.10293 | + | 0.698713i | 0.136313 | + | 0.0452909i | ||||
\(239\) | −11.4132 | −0.738255 | −0.369128 | − | 0.929379i | \(-0.620343\pi\) | ||||
−0.369128 | + | 0.929379i | \(0.620343\pi\) | |||||||
\(240\) | −0.420722 | − | 0.242904i | −0.0271575 | − | 0.0156794i | ||||
\(241\) | 8.55783 | + | 14.8226i | 0.551258 | + | 0.954808i | 0.998184 | + | 0.0602365i | \(0.0191855\pi\) |
−0.446926 | + | 0.894571i | \(0.647481\pi\) | |||||||
\(242\) | −0.807526 | − | 1.39868i | −0.0519098 | − | 0.0899103i | ||||
\(243\) | −0.866025 | − | 0.500000i | −0.0555556 | − | 0.0320750i | ||||
\(244\) | −9.81464 | −0.628318 | ||||||||
\(245\) | −3.12470 | + | 1.34191i | −0.199630 | + | 0.0857313i | ||||
\(246\) | 8.68814 | 0.553936 | ||||||||
\(247\) | 30.0090 | + | 17.3257i | 1.90943 | + | 1.10241i | ||||
\(248\) | 7.97469 | − | 4.60419i | 0.506394 | − | 0.292366i | ||||
\(249\) | −6.02569 | + | 3.47893i | −0.381863 | + | 0.220468i | ||||
\(250\) | 2.37171 | − | 4.10793i | 0.150000 | − | 0.259808i | ||||
\(251\) | −26.4084 | −1.66688 | −0.833441 | − | 0.552608i | \(-0.813632\pi\) | ||||
−0.833441 | + | 0.552608i | \(0.813632\pi\) | |||||||
\(252\) | 2.51079 | + | 0.834227i | 0.158165 | + | 0.0525513i | ||||
\(253\) | −12.2563 | − | 8.10170i | −0.770545 | − | 0.509350i | ||||
\(254\) | −3.63988 | + | 6.30446i | −0.228386 | + | 0.395577i | ||||
\(255\) | −0.352379 | + | 0.203446i | −0.0220668 | + | 0.0127403i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −21.6943 | − | 12.5252i | −1.35325 | − | 0.781300i | −0.364548 | − | 0.931184i | \(-0.618777\pi\) |
−0.988704 | + | 0.149884i | \(0.952110\pi\) | |||||||
\(258\) | 5.27242 | 0.328246 | ||||||||
\(259\) | −9.78373 | − | 11.0117i | −0.607932 | − | 0.684235i | ||||
\(260\) | 2.46510i | 0.152879i | ||||||||
\(261\) | 2.31447 | − | 4.00878i | 0.143262 | − | 0.248138i | ||||
\(262\) | 15.3287 | − | 8.85000i | 0.947007 | − | 0.546755i | ||||
\(263\) | 13.7220 | − | 7.92239i | 0.846134 | − | 0.488515i | −0.0132108 | − | 0.999913i | \(-0.504205\pi\) |
0.859344 | + | 0.511397i | \(0.170872\pi\) | |||||||
\(264\) | 1.53174 | − | 2.65306i | 0.0942723 | − | 0.163284i | ||||
\(265\) | − | 4.10355i | − | 0.252079i | ||||||
\(266\) | −3.63936 | − | 17.6973i | −0.223143 | − | 1.08509i | ||||
\(267\) | − | 10.4444i | − | 0.639188i | ||||||
\(268\) | −3.54252 | − | 2.04527i | −0.216394 | − | 0.124935i | ||||
\(269\) | 15.9218 | − | 9.19246i | 0.970770 | − | 0.560474i | 0.0712992 | − | 0.997455i | \(-0.477285\pi\) |
0.899471 | + | 0.436981i | \(0.143952\pi\) | |||||||
\(270\) | −0.420722 | + | 0.242904i | −0.0256043 | + | 0.0147827i | ||||
\(271\) | −1.82200 | − | 1.05194i | −0.110679 | − | 0.0639005i | 0.443639 | − | 0.896206i | \(-0.353687\pi\) |
−0.554318 | + | 0.832305i | \(0.687021\pi\) | |||||||
\(272\) | −0.837558 | −0.0507844 | ||||||||
\(273\) | −2.70422 | − | 13.1500i | −0.163667 | − | 0.795872i | ||||
\(274\) | 4.46799i | 0.269921i | ||||||||
\(275\) | 12.6391 | + | 7.29721i | 0.762169 | + | 0.440038i | ||||
\(276\) | −0.289912 | + | 4.78706i | −0.0174507 | + | 0.288147i | ||||
\(277\) | −6.61062 | − | 11.4499i | −0.397194 | − | 0.687960i | 0.596185 | − | 0.802847i | \(-0.296683\pi\) |
−0.993378 | + | 0.114888i | \(0.963349\pi\) | |||||||
\(278\) | −17.2980 | − | 9.98701i | −1.03747 | − | 0.598981i | ||||
\(279\) | − | 9.20838i | − | 0.551292i | ||||||
\(280\) | 0.960858 | − | 0.853707i | 0.0574223 | − | 0.0510188i | ||||
\(281\) | 23.3817i | 1.39483i | 0.716665 | + | 0.697417i | \(0.245668\pi\) | ||||
−0.716665 | + | 0.697417i | \(0.754332\pi\) | |||||||
\(282\) | −2.12869 | + | 3.68699i | −0.126761 | + | 0.219557i | ||||
\(283\) | 0.520276 | + | 0.901145i | 0.0309272 | + | 0.0535675i | 0.881075 | − | 0.472977i | \(-0.156821\pi\) |
−0.850148 | + | 0.526545i | \(0.823487\pi\) | |||||||
\(284\) | 0.660408 | + | 1.14386i | 0.0391880 | + | 0.0678756i | ||||
\(285\) | 2.87307 | + | 1.65877i | 0.170186 | + | 0.0982570i | ||||
\(286\) | −15.5448 | −0.919184 | ||||||||
\(287\) | −7.24788 | + | 21.8141i | −0.427829 | + | 1.28765i | ||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 8.14925 | − | 14.1149i | 0.479368 | − | 0.830289i | ||||
\(290\) | −1.12439 | − | 1.94750i | −0.0660264 | − | 0.114361i | ||||
\(291\) | −8.26158 | + | 4.76982i | −0.484302 | + | 0.279612i | ||||
\(292\) | −3.26928 | − | 1.88752i | −0.191320 | − | 0.110459i | ||||
\(293\) | 9.81859 | 0.573608 | 0.286804 | − | 0.957989i | \(-0.407407\pi\) | ||||
0.286804 | + | 0.957989i | \(0.407407\pi\) | |||||||
\(294\) | −4.18914 | + | 5.60813i | −0.244315 | + | 0.327073i | ||||
\(295\) | − | 1.77223i | − | 0.103183i | ||||||
\(296\) | 4.82160 | + | 2.78375i | 0.280250 | + | 0.161802i | ||||
\(297\) | −1.53174 | − | 2.65306i | −0.0888807 | − | 0.153946i | ||||
\(298\) | −16.9732 | + | 9.79947i | −0.983230 | + | 0.567668i | ||||
\(299\) | 21.7718 | − | 10.8713i | 1.25910 | − | 0.628705i | ||||
\(300\) | − | 4.76399i | − | 0.275049i | ||||||
\(301\) | −4.39839 | + | 13.2379i | −0.253519 | + | 0.763021i | ||||
\(302\) | −8.68464 | −0.499745 | ||||||||
\(303\) | −1.49955 | + | 2.59731i | −0.0861472 | + | 0.149211i | ||||
\(304\) | 3.41446 | + | 5.91401i | 0.195832 | + | 0.339192i | ||||
\(305\) | 2.38401 | + | 4.12923i | 0.136508 | + | 0.236439i | ||||
\(306\) | −0.418779 | + | 0.725347i | −0.0239400 | + | 0.0414653i | ||||
\(307\) | 8.35548i | 0.476872i | 0.971158 | + | 0.238436i | \(0.0766348\pi\) | ||||
−0.971158 | + | 0.238436i | \(0.923365\pi\) | |||||||
\(308\) | 5.38345 | + | 6.05914i | 0.306750 | + | 0.345251i | ||||
\(309\) | 14.9899i | 0.852743i | ||||||||
\(310\) | −3.87417 | − | 2.23675i | −0.220038 | − | 0.127039i | ||||
\(311\) | −10.6677 | + | 6.15900i | −0.604910 | + | 0.349245i | −0.770971 | − | 0.636871i | \(-0.780229\pi\) |
0.166061 | + | 0.986116i | \(0.446895\pi\) | |||||||
\(312\) | 2.53711 | + | 4.39441i | 0.143636 | + | 0.248784i | ||||
\(313\) | 13.3301 | − | 23.0884i | 0.753461 | − | 1.30503i | −0.192674 | − | 0.981263i | \(-0.561716\pi\) |
0.946136 | − | 0.323770i | \(-0.104951\pi\) | |||||||
\(314\) | −7.47992 | −0.422116 | ||||||||
\(315\) | −0.258903 | − | 1.25898i | −0.0145875 | − | 0.0709356i | ||||
\(316\) | − | 10.5345i | − | 0.592610i | ||||||
\(317\) | −9.18736 | + | 15.9130i | −0.516014 | + | 0.893762i | 0.483814 | + | 0.875171i | \(0.339251\pi\) |
−0.999827 | + | 0.0185906i | \(0.994082\pi\) | |||||||
\(318\) | −4.22343 | − | 7.31519i | −0.236838 | − | 0.410215i | ||||
\(319\) | 12.2809 | − | 7.09036i | 0.687596 | − | 0.396984i | ||||
\(320\) | −0.242904 | + | 0.420722i | −0.0135787 | + | 0.0235191i | ||||
\(321\) | 7.38277 | 0.412066 | ||||||||
\(322\) | −11.7775 | − | 4.72140i | −0.656332 | − | 0.263113i | ||||
\(323\) | 5.71961 | 0.318248 | ||||||||
\(324\) | −0.500000 | + | 0.866025i | −0.0277778 | + | 0.0481125i | ||||
\(325\) | −20.9349 | + | 12.0868i | −1.16126 | + | 0.670454i | ||||
\(326\) | 8.60562 | + | 14.9054i | 0.476621 | + | 0.825532i | ||||
\(327\) | −0.611537 | + | 1.05921i | −0.0338181 | + | 0.0585746i | ||||
\(328\) | − | 8.68814i | − | 0.479723i | ||||||
\(329\) | −7.48146 | − | 8.42048i | −0.412466 | − | 0.464236i | ||||
\(330\) | −1.48827 | −0.0819263 | ||||||||
\(331\) | −0.155874 | + | 0.269982i | −0.00856763 | + | 0.0148396i | −0.870277 | − | 0.492562i | \(-0.836061\pi\) |
0.861710 | + | 0.507401i | \(0.169394\pi\) | |||||||
\(332\) | 3.47893 | + | 6.02569i | 0.190931 | + | 0.330703i | ||||
\(333\) | 4.82160 | − | 2.78375i | 0.264222 | − | 0.152549i | ||||
\(334\) | −16.9360 | − | 9.77800i | −0.926696 | − | 0.535028i | ||||
\(335\) | 1.98722i | 0.108573i | ||||||||
\(336\) | 0.834227 | − | 2.51079i | 0.0455108 | − | 0.136975i | ||||
\(337\) | 32.9634i | 1.79563i | 0.440373 | + | 0.897815i | \(0.354846\pi\) | ||||
−0.440373 | + | 0.897815i | \(0.645154\pi\) | |||||||
\(338\) | 6.37388 | − | 11.0399i | 0.346693 | − | 0.600491i | ||||
\(339\) | 4.32644 | + | 7.49362i | 0.234980 | + | 0.406998i | ||||
\(340\) | 0.203446 | + | 0.352379i | 0.0110334 | + | 0.0191104i | ||||
\(341\) | 14.1049 | − | 24.4304i | 0.763822 | − | 1.32298i | ||||
\(342\) | 6.82891 | 0.369265 | ||||||||
\(343\) | −10.5862 | − | 15.1965i | −0.571598 | − | 0.820533i | ||||
\(344\) | − | 5.27242i | − | 0.284270i | ||||||
\(345\) | 2.08444 | − | 1.04082i | 0.112223 | − | 0.0560360i | ||||
\(346\) | 18.2657 | − | 10.5457i | 0.981969 | − | 0.566940i | ||||
\(347\) | 13.0936 | + | 22.6787i | 0.702900 | + | 1.21746i | 0.967444 | + | 0.253085i | \(0.0814452\pi\) |
−0.264544 | + | 0.964374i | \(0.585221\pi\) | |||||||
\(348\) | −4.00878 | − | 2.31447i | −0.214893 | − | 0.124069i | ||||
\(349\) | 2.84126i | 0.152089i | 0.997104 | + | 0.0760446i | \(0.0242291\pi\) | ||||
−0.997104 | + | 0.0760446i | \(0.975771\pi\) | |||||||
\(350\) | 11.9614 | + | 3.97425i | 0.639363 | + | 0.212432i | ||||
\(351\) | 5.07423 | 0.270842 | ||||||||
\(352\) | −2.65306 | − | 1.53174i | −0.141408 | − | 0.0816422i | ||||
\(353\) | 3.92196 | − | 2.26435i | 0.208745 | − | 0.120519i | −0.391983 | − | 0.919972i | \(-0.628211\pi\) |
0.600728 | + | 0.799453i | \(0.294877\pi\) | |||||||
\(354\) | −1.82401 | − | 3.15927i | −0.0969448 | − | 0.167913i | ||||
\(355\) | 0.320831 | − | 0.555696i | 0.0170280 | − | 0.0294933i | ||||
\(356\) | −10.4444 | −0.553553 | ||||||||
\(357\) | −1.47184 | − | 1.65657i | −0.0778979 | − | 0.0876750i | ||||
\(358\) | 17.9621 | 0.949326 | ||||||||
\(359\) | 15.4334 | + | 8.91049i | 0.814545 | + | 0.470278i | 0.848532 | − | 0.529145i | \(-0.177487\pi\) |
−0.0339868 | + | 0.999422i | \(0.510820\pi\) | |||||||
\(360\) | 0.242904 | + | 0.420722i | 0.0128022 | + | 0.0221740i | ||||
\(361\) | −13.8170 | − | 23.9318i | −0.727211 | − | 1.25957i | ||||
\(362\) | 3.16433 | − | 5.48079i | 0.166314 | − | 0.288064i | ||||
\(363\) | 1.61505i | 0.0847683i | ||||||||
\(364\) | −13.1500 | + | 2.70422i | −0.689245 | + | 0.141740i | ||||
\(365\) | 1.83394i | 0.0959929i | ||||||||
\(366\) | 8.49972 | + | 4.90732i | 0.444288 | + | 0.256510i | ||||
\(367\) | −11.7504 | − | 20.3523i | −0.613365 | − | 1.06238i | −0.990669 | − | 0.136290i | \(-0.956482\pi\) |
0.377304 | − | 0.926090i | \(-0.376851\pi\) | |||||||
\(368\) | 4.78706 | + | 0.289912i | 0.249543 | + | 0.0151127i | ||||
\(369\) | −7.52415 | − | 4.34407i | −0.391692 | − | 0.226143i | ||||
\(370\) | − | 2.70473i | − | 0.140612i | ||||||
\(371\) | 21.8902 | − | 4.50161i | 1.13648 | − | 0.233712i | ||||
\(372\) | −9.20838 | −0.477432 | ||||||||
\(373\) | −4.55066 | − | 2.62732i | −0.235624 | − | 0.136038i | 0.377540 | − | 0.925993i | \(-0.376770\pi\) |
−0.613164 | + | 0.789956i | \(0.710103\pi\) | |||||||
\(374\) | −2.22209 | + | 1.28292i | −0.114902 | + | 0.0663384i | ||||
\(375\) | −4.10793 | + | 2.37171i | −0.212132 | + | 0.122475i | ||||
\(376\) | 3.68699 | + | 2.12869i | 0.190142 | + | 0.109779i | ||||
\(377\) | 23.4883i | 1.20971i | ||||||||
\(378\) | −1.75729 | − | 1.97786i | −0.0903855 | − | 0.101730i | ||||
\(379\) | 32.0689i | 1.64727i | 0.567121 | + | 0.823635i | \(0.308057\pi\) | ||||
−0.567121 | + | 0.823635i | \(0.691943\pi\) | |||||||
\(380\) | 1.65877 | − | 2.87307i | 0.0850931 | − | 0.147386i | ||||
\(381\) | 6.30446 | − | 3.63988i | 0.322987 | − | 0.186477i | ||||
\(382\) | 15.6759 | − | 9.05046i | 0.802046 | − | 0.463062i | ||||
\(383\) | −9.14917 | + | 15.8468i | −0.467501 | + | 0.809735i | −0.999310 | − | 0.0371291i | \(-0.988179\pi\) |
0.531810 | + | 0.846864i | \(0.321512\pi\) | |||||||
\(384\) | 1.00000i | 0.0510310i | ||||||||
\(385\) | 1.24155 | − | 3.73672i | 0.0632753 | − | 0.190441i | ||||
\(386\) | 15.1971 | 0.773514 | ||||||||
\(387\) | −4.56605 | − | 2.63621i | −0.232105 | − | 0.134006i | ||||
\(388\) | 4.76982 | + | 8.26158i | 0.242151 | + | 0.419418i | ||||
\(389\) | −27.2229 | + | 15.7172i | −1.38026 | + | 0.796892i | −0.992190 | − | 0.124738i | \(-0.960191\pi\) |
−0.388068 | + | 0.921631i | \(0.626858\pi\) | |||||||
\(390\) | 1.23255 | − | 2.13484i | 0.0624126 | − | 0.108102i | ||||
\(391\) | 2.21501 | − | 3.35087i | 0.112018 | − | 0.169461i | ||||
\(392\) | 5.60813 | + | 4.18914i | 0.283253 | + | 0.211583i | ||||
\(393\) | −17.7000 | −0.892847 | ||||||||
\(394\) | 2.26058 | − | 3.91544i | 0.113886 | − | 0.197257i | ||||
\(395\) | −4.43208 | + | 2.55886i | −0.223002 | + | 0.128750i | ||||
\(396\) | −2.65306 | + | 1.53174i | −0.133321 | + | 0.0769730i | ||||
\(397\) | −9.69103 | − | 5.59512i | −0.486379 | − | 0.280811i | 0.236692 | − | 0.971585i | \(-0.423937\pi\) |
−0.723071 | + | 0.690774i | \(0.757270\pi\) | |||||||
\(398\) | 2.81705 | 0.141206 | ||||||||
\(399\) | −5.69686 | + | 17.1460i | −0.285200 | + | 0.858372i | ||||
\(400\) | −4.76399 | −0.238200 | ||||||||
\(401\) | −11.5257 | − | 6.65435i | −0.575565 | − | 0.332303i | 0.183804 | − | 0.982963i | \(-0.441159\pi\) |
−0.759369 | + | 0.650660i | \(0.774492\pi\) | |||||||
\(402\) | 2.04527 | + | 3.54252i | 0.102009 | + | 0.176685i | ||||
\(403\) | 23.3627 | + | 40.4654i | 1.16378 | + | 2.01572i | ||||
\(404\) | 2.59731 | + | 1.49955i | 0.129221 | + | 0.0746056i | ||||
\(405\) | 0.485808 | 0.0241400 | ||||||||
\(406\) | 9.15539 | − | 8.13442i | 0.454374 | − | 0.403705i | ||||
\(407\) | 17.0560 | 0.845432 | ||||||||
\(408\) | 0.725347 | + | 0.418779i | 0.0359100 | + | 0.0207327i | ||||
\(409\) | −22.0680 | + | 12.7409i | −1.09119 | + | 0.629999i | −0.933893 | − | 0.357552i | \(-0.883611\pi\) |
−0.157297 | + | 0.987551i | \(0.550278\pi\) | |||||||
\(410\) | −3.65529 | + | 2.11038i | −0.180522 | + | 0.104224i | ||||
\(411\) | 2.23400 | − | 3.86939i | 0.110195 | − | 0.190863i | ||||
\(412\) | 14.9899 | 0.738497 | ||||||||
\(413\) | 9.45390 | − | 1.94415i | 0.465196 | − | 0.0956652i | ||||
\(414\) | 2.64460 | − | 4.00076i | 0.129975 | − | 0.196627i | ||||
\(415\) | 1.69009 | − | 2.92733i | 0.0829634 | − | 0.143697i | ||||
\(416\) | 4.39441 | − | 2.53711i | 0.215454 | − | 0.124392i | ||||
\(417\) | 9.98701 | + | 17.2980i | 0.489066 | + | 0.847087i | ||||
\(418\) | 18.1175 | + | 10.4601i | 0.886155 | + | 0.511622i | ||||
\(419\) | −13.3786 | −0.653589 | −0.326794 | − | 0.945095i | \(-0.605968\pi\) | ||||
−0.326794 | + | 0.945095i | \(0.605968\pi\) | |||||||
\(420\) | −1.25898 | + | 0.258903i | −0.0614320 | + | 0.0126332i | ||||
\(421\) | 5.07456i | 0.247319i | 0.992325 | + | 0.123659i | \(0.0394630\pi\) | ||||
−0.992325 | + | 0.123659i | \(0.960537\pi\) | |||||||
\(422\) | −3.58553 | + | 6.21033i | −0.174541 | + | 0.302314i | ||||
\(423\) | 3.68699 | − | 2.12869i | 0.179268 | − | 0.103500i | ||||
\(424\) | −7.31519 | + | 4.22343i | −0.355257 | + | 0.205108i | ||||
\(425\) | −1.99506 | + | 3.45555i | −0.0967746 | + | 0.167619i | ||||
\(426\) | − | 1.32082i | − | 0.0639937i | ||||||
\(427\) | −19.4119 | + | 17.2472i | −0.939410 | + | 0.834651i | ||||
\(428\) | − | 7.38277i | − | 0.356860i | ||||||
\(429\) | 13.4622 | + | 7.77241i | 0.649962 | + | 0.375255i | ||||
\(430\) | −2.21822 | + | 1.28069i | −0.106972 | + | 0.0617604i | ||||
\(431\) | 18.8706 | − | 10.8949i | 0.908965 | − | 0.524791i | 0.0288669 | − | 0.999583i | \(-0.490810\pi\) |
0.880098 | + | 0.474792i | \(0.157477\pi\) | |||||||
\(432\) | 0.866025 | + | 0.500000i | 0.0416667 | + | 0.0240563i | ||||
\(433\) | 0.143761 | 0.00690873 | 0.00345437 | − | 0.999994i | \(-0.498900\pi\) | ||||
0.00345437 | + | 0.999994i | \(0.498900\pi\) | |||||||
\(434\) | 7.68188 | − | 23.1203i | 0.368742 | − | 1.10981i | ||||
\(435\) | 2.24878i | 0.107821i | ||||||||
\(436\) | 1.05921 | + | 0.611537i | 0.0507271 | + | 0.0292873i | ||||
\(437\) | −32.6904 | − | 1.97979i | −1.56379 | − | 0.0947060i | ||||
\(438\) | 1.88752 | + | 3.26928i | 0.0901891 | + | 0.156212i | ||||
\(439\) | 24.8389 | + | 14.3408i | 1.18550 | + | 0.684448i | 0.957280 | − | 0.289162i | \(-0.0933767\pi\) |
0.228218 | + | 0.973610i | \(0.426710\pi\) | |||||||
\(440\) | 1.48827i | 0.0709503i | ||||||||
\(441\) | 6.43196 | − | 2.76222i | 0.306284 | − | 0.131534i | ||||
\(442\) | − | 4.24996i | − | 0.202150i | ||||||
\(443\) | 13.9610 | − | 24.1811i | 0.663305 | − | 1.14888i | −0.316437 | − | 0.948613i | \(-0.602487\pi\) |
0.979742 | − | 0.200264i | \(-0.0641800\pi\) | |||||||
\(444\) | −2.78375 | − | 4.82160i | −0.132111 | − | 0.228823i | ||||
\(445\) | 2.53699 | + | 4.39419i | 0.120265 | + | 0.208305i | ||||
\(446\) | 6.50046 | + | 3.75304i | 0.307806 | + | 0.177712i | ||||
\(447\) | 19.5989 | 0.926998 | ||||||||
\(448\) | −2.51079 | − | 0.834227i | −0.118624 | − | 0.0394135i | ||||
\(449\) | 19.7589 | 0.932482 | 0.466241 | − | 0.884658i | \(-0.345608\pi\) | ||||
0.466241 | + | 0.884658i | \(0.345608\pi\) | |||||||
\(450\) | −2.38200 | + | 4.12574i | −0.112288 | + | 0.194489i | ||||
\(451\) | −13.3080 | − | 23.0501i | −0.626650 | − | 1.08539i | ||||
\(452\) | 7.49362 | − | 4.32644i | 0.352470 | − | 0.203499i | ||||
\(453\) | 7.52112 | + | 4.34232i | 0.353373 | + | 0.204020i | ||||
\(454\) | 17.7553 | 0.833298 | ||||||||
\(455\) | 4.33190 | + | 4.87561i | 0.203083 | + | 0.228572i | ||||
\(456\) | − | 6.82891i | − | 0.319793i | ||||||
\(457\) | 28.7619 | + | 16.6057i | 1.34542 | + | 0.776781i | 0.987597 | − | 0.157007i | \(-0.0501847\pi\) |
0.357826 | + | 0.933788i | \(0.383518\pi\) | |||||||
\(458\) | −10.2713 | − | 17.7904i | −0.479947 | − | 0.831292i | ||||
\(459\) | 0.725347 | − | 0.418779i | 0.0338563 | − | 0.0195469i | ||||
\(460\) | −1.04082 | − | 2.08444i | −0.0485286 | − | 0.0971876i | ||||
\(461\) | 18.0808i | 0.842105i | 0.907036 | + | 0.421053i | \(0.138339\pi\) | ||||
−0.907036 | + | 0.421053i | \(0.861661\pi\) | |||||||
\(462\) | −1.63263 | − | 7.93909i | −0.0759570 | − | 0.369360i | ||||
\(463\) | −14.4807 | −0.672975 | −0.336488 | − | 0.941688i | \(-0.609239\pi\) | ||||
−0.336488 | + | 0.941688i | \(0.609239\pi\) | |||||||
\(464\) | −2.31447 | + | 4.00878i | −0.107447 | + | 0.186103i | ||||
\(465\) | 2.23675 | + | 3.87417i | 0.103727 | + | 0.179660i | ||||
\(466\) | 7.83721 | + | 13.5744i | 0.363052 | + | 0.628824i | ||||
\(467\) | 15.4907 | − | 26.8307i | 0.716825 | − | 1.24158i | −0.245427 | − | 0.969415i | \(-0.578928\pi\) |
0.962252 | − | 0.272161i | \(-0.0877385\pi\) | |||||||
\(468\) | − | 5.07423i | − | 0.234556i | ||||||
\(469\) | −10.6007 | + | 2.17999i | −0.489497 | + | 0.100663i | ||||
\(470\) | − | 2.06827i | − | 0.0954020i | ||||||
\(471\) | 6.47780 | + | 3.73996i | 0.298481 | + | 0.172328i | ||||
\(472\) | −3.15927 | + | 1.82401i | −0.145417 | + | 0.0839567i | ||||
\(473\) | −8.07599 | − | 13.9880i | −0.371334 | − | 0.643170i | ||||
\(474\) | −5.26723 | + | 9.12312i | −0.241932 | + | 0.419039i | ||||
\(475\) | 32.5329 | 1.49271 | ||||||||
\(476\) | −1.65657 | + | 1.47184i | −0.0759288 | + | 0.0674615i | ||||
\(477\) | 8.44685i | 0.386755i | ||||||||
\(478\) | 5.70658 | − | 9.88408i | 0.261013 | − | 0.452087i | ||||
\(479\) | −8.04393 | − | 13.9325i | −0.367537 | − | 0.636592i | 0.621643 | − | 0.783301i | \(-0.286465\pi\) |
−0.989180 | + | 0.146709i | \(0.953132\pi\) | |||||||
\(480\) | 0.420722 | − | 0.242904i | 0.0192032 | − | 0.0110870i | ||||
\(481\) | −14.1254 | + | 24.4659i | −0.644061 | + | 1.11555i | ||||
\(482\) | −17.1157 | −0.779597 | ||||||||
\(483\) | 7.83887 | + | 9.97758i | 0.356681 | + | 0.453996i | ||||
\(484\) | 1.61505 | 0.0734115 | ||||||||
\(485\) | 2.31722 | − | 4.01354i | 0.105219 | − | 0.182245i | ||||
\(486\) | 0.866025 | − | 0.500000i | 0.0392837 | − | 0.0226805i | ||||
\(487\) | 4.71230 | + | 8.16194i | 0.213535 | + | 0.369853i | 0.952818 | − | 0.303541i | \(-0.0981690\pi\) |
−0.739284 | + | 0.673394i | \(0.764836\pi\) | |||||||
\(488\) | 4.90732 | − | 8.49972i | 0.222144 | − | 0.384764i | ||||
\(489\) | − | 17.2112i | − | 0.778319i | ||||||
\(490\) | 0.400224 | − | 3.37702i | 0.0180803 | − | 0.152558i | ||||
\(491\) | 26.3527 | 1.18928 | 0.594641 | − | 0.803991i | \(-0.297294\pi\) | ||||
0.594641 | + | 0.803991i | \(0.297294\pi\) | |||||||
\(492\) | −4.34407 | + | 7.52415i | −0.195846 | + | 0.339215i | ||||
\(493\) | 1.93851 | + | 3.35759i | 0.0873059 | + | 0.151218i | ||||
\(494\) | −30.0090 | + | 17.3257i | −1.35017 | + | 0.779521i | ||||
\(495\) | 1.28888 | + | 0.744133i | 0.0579307 | + | 0.0334463i | ||||
\(496\) | 9.20838i | 0.413469i | ||||||||
\(497\) | 3.31629 | + | 1.10186i | 0.148756 | + | 0.0494252i | ||||
\(498\) | − | 6.95787i | − | 0.311789i | ||||||
\(499\) | −14.3554 | + | 24.8642i | −0.642634 | + | 1.11307i | 0.342209 | + | 0.939624i | \(0.388825\pi\) |
−0.984843 | + | 0.173451i | \(0.944508\pi\) | |||||||
\(500\) | 2.37171 | + | 4.10793i | 0.106066 | + | 0.183712i | ||||
\(501\) | 9.77800 | + | 16.9360i | 0.436849 | + | 0.756645i | ||||
\(502\) | 13.2042 | − | 22.8703i | 0.589332 | − | 1.02075i | ||||
\(503\) | 35.8498 | 1.59846 | 0.799232 | − | 0.601023i | \(-0.205240\pi\) | ||||
0.799232 | + | 0.601023i | \(0.205240\pi\) | |||||||
\(504\) | −1.97786 | + | 1.75729i | −0.0881007 | + | 0.0782761i | ||||
\(505\) | − | 1.45699i | − | 0.0648353i | ||||||
\(506\) | 13.1444 | − | 6.56339i | 0.584341 | − | 0.291778i | ||||
\(507\) | −11.0399 | + | 6.37388i | −0.490299 | + | 0.283074i | ||||
\(508\) | −3.63988 | − | 6.30446i | −0.161494 | − | 0.279715i | ||||
\(509\) | 7.57359 | + | 4.37262i | 0.335694 | + | 0.193813i | 0.658366 | − | 0.752698i | \(-0.271248\pi\) |
−0.322672 | + | 0.946511i | \(0.604581\pi\) | |||||||
\(510\) | − | 0.406892i | − | 0.0180175i | ||||||
\(511\) | −9.78309 | + | 2.01184i | −0.432778 | + | 0.0889987i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −5.91401 | − | 3.41446i | −0.261110 | − | 0.150752i | ||||
\(514\) | 21.6943 | − | 12.5252i | 0.956894 | − | 0.552463i | ||||
\(515\) | −3.64109 | − | 6.30656i | −0.160446 | − | 0.277900i | ||||
\(516\) | −2.63621 | + | 4.56605i | −0.116053 | + | 0.201009i | ||||
\(517\) | 13.0424 | 0.573604 | ||||||||
\(518\) | 14.4283 | − | 2.96711i | 0.633943 | − | 0.130367i | ||||
\(519\) | −21.0914 | −0.925810 | ||||||||
\(520\) | −2.13484 | − | 1.23255i | −0.0936188 | − | 0.0540509i | ||||
\(521\) | −9.90828 | − | 17.1616i | −0.434090 | − | 0.751865i | 0.563131 | − | 0.826367i | \(-0.309597\pi\) |
−0.997221 | + | 0.0745023i | \(0.976263\pi\) | |||||||
\(522\) | 2.31447 | + | 4.00878i | 0.101302 | + | 0.175460i | ||||
\(523\) | −4.75142 | + | 8.22970i | −0.207765 | + | 0.359860i | −0.951010 | − | 0.309159i | \(-0.899952\pi\) |
0.743245 | + | 0.669019i | \(0.233286\pi\) | |||||||
\(524\) | 17.7000i | 0.773228i | ||||||||
\(525\) | −8.37173 | − | 9.42249i | −0.365372 | − | 0.411231i | ||||
\(526\) | 15.8448i | 0.690865i | ||||||||
\(527\) | 6.67927 | + | 3.85628i | 0.290954 | + | 0.167982i | ||||
\(528\) | 1.53174 | + | 2.65306i | 0.0666606 | + | 0.115459i | ||||
\(529\) | −13.8197 | + | 18.3852i | −0.600858 | + | 0.799356i | ||||
\(530\) | 3.55378 | + | 2.05177i | 0.154366 | + | 0.0891234i | ||||
\(531\) | 3.64801i | 0.158310i | ||||||||
\(532\) | 17.1460 | + | 5.69686i | 0.743372 | + | 0.246990i | ||||
\(533\) | 44.0856 | 1.90956 | ||||||||
\(534\) | 9.04513 | + | 5.22221i | 0.391421 | + | 0.225987i | ||||
\(535\) | −3.10609 | + | 1.79330i | −0.134288 | + | 0.0775313i | ||||
\(536\) | 3.54252 | − | 2.04527i | 0.153014 | − | 0.0883424i | ||||
\(537\) | −15.5556 | − | 8.98104i | −0.671275 | − | 0.387561i | ||||
\(538\) | 18.3849i | 0.792631i | ||||||||
\(539\) | 21.2954 | + | 2.52380i | 0.917257 | + | 0.108708i | ||||
\(540\) | − | 0.485808i | − | 0.0209058i | ||||||
\(541\) | 18.8075 | − | 32.5755i | 0.808596 | − | 1.40053i | −0.105241 | − | 0.994447i | \(-0.533561\pi\) |
0.913837 | − | 0.406082i | \(-0.133105\pi\) | |||||||
\(542\) | 1.82200 | − | 1.05194i | 0.0782618 | − | 0.0451845i | ||||
\(543\) | −5.48079 | + | 3.16433i | −0.235203 | + | 0.135795i | ||||
\(544\) | 0.418779 | − | 0.725347i | 0.0179550 | − | 0.0310990i | ||||
\(545\) | − | 0.594179i | − | 0.0254518i | ||||||
\(546\) | 12.7403 | + | 4.23305i | 0.545235 | + | 0.181158i | ||||
\(547\) | 30.5698 | 1.30707 | 0.653536 | − | 0.756895i | \(-0.273285\pi\) | ||||
0.653536 | + | 0.756895i | \(0.273285\pi\) | |||||||
\(548\) | −3.86939 | − | 2.23400i | −0.165292 | − | 0.0954316i | ||||
\(549\) | −4.90732 | − | 8.49972i | −0.209439 | − | 0.362759i | ||||
\(550\) | −12.6391 | + | 7.29721i | −0.538935 | + | 0.311154i | ||||
\(551\) | 15.8053 | − | 27.3756i | 0.673330 | − | 1.16624i | ||||
\(552\) | −4.00076 | − | 2.64460i | −0.170284 | − | 0.112562i | ||||
\(553\) | −18.5122 | − | 20.8357i | −0.787217 | − | 0.886023i | ||||
\(554\) | 13.2212 | 0.561717 | ||||||||
\(555\) | −1.35237 | + | 2.34237i | −0.0574048 | + | 0.0994280i | ||||
\(556\) | 17.2980 | − | 9.98701i | 0.733599 | − | 0.423544i | ||||
\(557\) | 5.73818 | − | 3.31294i | 0.243134 | − | 0.140374i | −0.373482 | − | 0.927637i | \(-0.621836\pi\) |
0.616616 | + | 0.787264i | \(0.288503\pi\) | |||||||
\(558\) | 7.97469 | + | 4.60419i | 0.337596 | + | 0.194911i | ||||
\(559\) | 26.7534 | 1.13155 | ||||||||
\(560\) | 0.258903 | + | 1.25898i | 0.0109407 | + | 0.0532017i | ||||
\(561\) | 2.56585 | 0.108330 | ||||||||
\(562\) | −20.2491 | − | 11.6908i | −0.854158 | − | 0.493149i | ||||
\(563\) | 9.16761 | + | 15.8788i | 0.386369 | + | 0.669210i | 0.991958 | − | 0.126567i | \(-0.0403960\pi\) |
−0.605589 | + | 0.795777i | \(0.707063\pi\) | |||||||
\(564\) | −2.12869 | − | 3.68699i | −0.0896339 | − | 0.155250i | ||||
\(565\) | −3.64046 | − | 2.10182i | −0.153155 | − | 0.0884243i | ||||
\(566\) | −1.04055 | −0.0437377 | ||||||||
\(567\) | 0.532933 | + | 2.59152i | 0.0223811 | + | 0.108834i | ||||
\(568\) | −1.32082 | −0.0554202 | ||||||||
\(569\) | 10.7157 | + | 6.18673i | 0.449227 | + | 0.259361i | 0.707504 | − | 0.706710i | \(-0.249821\pi\) |
−0.258277 | + | 0.966071i | \(0.583155\pi\) | |||||||
\(570\) | −2.87307 | + | 1.65877i | −0.120340 | + | 0.0694782i | ||||
\(571\) | 31.4999 | − | 18.1865i | 1.31823 | − | 0.761081i | 0.334787 | − | 0.942294i | \(-0.391336\pi\) |
0.983444 | + | 0.181213i | \(0.0580023\pi\) | |||||||
\(572\) | 7.77241 | − | 13.4622i | 0.324981 | − | 0.562883i | ||||
\(573\) | −18.1009 | −0.756177 | ||||||||
\(574\) | −15.2676 | − | 17.1839i | −0.637259 | − | 0.717242i | ||||
\(575\) | 12.5989 | − | 19.0596i | 0.525409 | − | 0.794840i | ||||
\(576\) | 0.500000 | − | 0.866025i | 0.0208333 | − | 0.0360844i | ||||
\(577\) | −17.6816 | + | 10.2085i | −0.736095 | + | 0.424984i | −0.820648 | − | 0.571435i | \(-0.806387\pi\) |
0.0845530 | + | 0.996419i | \(0.473054\pi\) | |||||||
\(578\) | 8.14925 | + | 14.1149i | 0.338964 | + | 0.587103i | ||||
\(579\) | −13.1611 | − | 7.59857i | −0.546957 | − | 0.315786i | ||||
\(580\) | 2.24878 | 0.0933754 | ||||||||
\(581\) | 17.4697 | + | 5.80444i | 0.724767 | + | 0.240809i | ||||
\(582\) | − | 9.53965i | − | 0.395431i | ||||||
\(583\) | −12.9384 | + | 22.4100i | −0.535854 | + | 0.928127i | ||||
\(584\) | 3.26928 | − | 1.88752i | 0.135284 | − | 0.0781061i | ||||
\(585\) | −2.13484 | + | 1.23255i | −0.0882647 | + | 0.0509596i | ||||
\(586\) | −4.90929 | + | 8.50315i | −0.202801 | + | 0.351262i | ||||
\(587\) | 7.38638i | 0.304869i | 0.988314 | + | 0.152434i | \(0.0487112\pi\) | ||||
−0.988314 | + | 0.152434i | \(0.951289\pi\) | |||||||
\(588\) | −2.76222 | − | 6.43196i | −0.113912 | − | 0.265250i | ||||
\(589\) | − | 62.8832i | − | 2.59106i | ||||||
\(590\) | 1.53480 | + | 0.886116i | 0.0631866 | + | 0.0364808i | ||||
\(591\) | −3.91544 | + | 2.26058i | −0.161060 | + | 0.0929878i | ||||
\(592\) | −4.82160 | + | 2.78375i | −0.198166 | + | 0.114411i | ||||
\(593\) | 4.87777 | + | 2.81618i | 0.200306 | + | 0.115647i | 0.596798 | − | 0.802391i | \(-0.296439\pi\) |
−0.396492 | + | 0.918038i | \(0.629773\pi\) | |||||||
\(594\) | 3.06349 | 0.125696 | ||||||||
\(595\) | 1.02162 | + | 0.339441i | 0.0418824 | + | 0.0139157i | ||||
\(596\) | − | 19.5989i | − | 0.802804i | ||||||
\(597\) | −2.43964 | − | 1.40852i | −0.0998476 | − | 0.0576471i | ||||
\(598\) | −1.47108 | + | 24.2906i | −0.0601570 | + | 0.993318i | ||||
\(599\) | −4.26837 | − | 7.39303i | −0.174401 | − | 0.302071i | 0.765553 | − | 0.643373i | \(-0.222465\pi\) |
−0.939954 | + | 0.341302i | \(0.889132\pi\) | |||||||
\(600\) | 4.12574 | + | 2.38200i | 0.168433 | + | 0.0972446i | ||||
\(601\) | − | 29.9904i | − | 1.22333i | −0.791116 | − | 0.611667i | \(-0.790499\pi\) | ||
0.791116 | − | 0.611667i | \(-0.209501\pi\) | |||||||
\(602\) | −9.26519 | − | 10.4281i | −0.377621 | − | 0.425017i | ||||
\(603\) | − | 4.09055i | − | 0.166580i | ||||||
\(604\) | 4.34232 | − | 7.52112i | 0.176686 | − | 0.306030i | ||||
\(605\) | −0.392303 | − | 0.679488i | −0.0159494 | − | 0.0276251i | ||||
\(606\) | −1.49955 | − | 2.59731i | −0.0609153 | − | 0.105508i | ||||
\(607\) | 11.3972 | + | 6.58018i | 0.462598 | + | 0.267081i | 0.713136 | − | 0.701026i | \(-0.247274\pi\) |
−0.250538 | + | 0.968107i | \(0.580607\pi\) | |||||||
\(608\) | −6.82891 | −0.276949 | ||||||||
\(609\) | −11.9960 | + | 2.46692i | −0.486103 | + | 0.0999647i | ||||
\(610\) | −4.76803 | −0.193052 | ||||||||
\(611\) | −10.8014 | + | 18.7086i | −0.436979 | + | 0.756871i | ||||
\(612\) | −0.418779 | − | 0.725347i | −0.0169281 | − | 0.0293204i | ||||
\(613\) | −22.2084 | + | 12.8220i | −0.896989 | + | 0.517877i | −0.876222 | − | 0.481908i | \(-0.839944\pi\) |
−0.0207667 | + | 0.999784i | \(0.506611\pi\) | |||||||
\(614\) | −7.23605 | − | 4.17774i | −0.292023 | − | 0.168600i | ||||
\(615\) | 4.22077 | 0.170198 | ||||||||
\(616\) | −7.93909 | + | 1.63263i | −0.319875 | + | 0.0657807i | ||||
\(617\) | 8.14544i | 0.327923i | 0.986467 | + | 0.163962i | \(0.0524273\pi\) | ||||
−0.986467 | + | 0.163962i | \(0.947573\pi\) | |||||||
\(618\) | −12.9816 | − | 7.49493i | −0.522196 | − | 0.301490i | ||||
\(619\) | 11.4902 | + | 19.9016i | 0.461830 | + | 0.799914i | 0.999052 | − | 0.0435272i | \(-0.0138595\pi\) |
−0.537222 | + | 0.843441i | \(0.680526\pi\) | |||||||
\(620\) | 3.87417 | − | 2.23675i | 0.155590 | − | 0.0898301i | ||||
\(621\) | −4.29067 | + | 2.14246i | −0.172179 | + | 0.0859739i | ||||
\(622\) | − | 12.3180i | − | 0.493907i | ||||||
\(623\) | −20.6576 | + | 18.3539i | −0.827627 | + | 0.735334i | ||||
\(624\) | −5.07423 | −0.203132 | ||||||||
\(625\) | −10.7578 | + | 18.6330i | −0.430311 | + | 0.745321i | ||||
\(626\) | 13.3301 | + | 23.0884i | 0.532778 | + | 0.922798i | ||||
\(627\) | −10.4601 | − | 18.1175i | −0.417738 | − | 0.723543i | ||||
\(628\) | 3.73996 | − | 6.47780i | 0.149241 | − | 0.258492i | ||||
\(629\) | 4.66310i | 0.185930i | ||||||||
\(630\) | 1.21976 | + | 0.405274i | 0.0485965 | + | 0.0161465i | ||||
\(631\) | − | 30.8839i | − | 1.22947i | −0.788735 | − | 0.614734i | \(-0.789264\pi\) | ||
0.788735 | − | 0.614734i | \(-0.210736\pi\) | |||||||
\(632\) | 9.12312 | + | 5.26723i | 0.362898 | + | 0.209519i | ||||
\(633\) | 6.21033 | − | 3.58553i | 0.246838 | − | 0.142512i | ||||
\(634\) | −9.18736 | − | 15.9130i | −0.364877 | − | 0.631985i | ||||
\(635\) | −1.76828 | + | 3.06276i | −0.0701722 | + | 0.121542i | ||||
\(636\) | 8.44685 | 0.334939 | ||||||||
\(637\) | −21.2566 | + | 28.4569i | −0.842218 | + | 1.12750i | ||||
\(638\) | 14.1807i | 0.561420i | ||||||||
\(639\) | −0.660408 | + | 1.14386i | −0.0261253 | + | 0.0452504i | ||||
\(640\) | −0.242904 | − | 0.420722i | −0.00960162 | − | 0.0166305i | ||||
\(641\) | −19.6895 | + | 11.3677i | −0.777687 | + | 0.448998i | −0.835610 | − | 0.549323i | \(-0.814886\pi\) |
0.0579231 | + | 0.998321i | \(0.481552\pi\) | |||||||
\(642\) | −3.69139 | + | 6.39367i | −0.145687 | + | 0.252338i | ||||
\(643\) | −30.1236 | −1.18796 | −0.593979 | − | 0.804480i | \(-0.702444\pi\) | ||||
−0.593979 | + | 0.804480i | \(0.702444\pi\) | |||||||
\(644\) | 9.97758 | − | 7.83887i | 0.393172 | − | 0.308895i | ||||
\(645\) | 2.56138 | 0.100854 | ||||||||
\(646\) | −2.85981 | + | 4.95333i | −0.112518 | + | 0.194886i | ||||
\(647\) | −9.96335 | + | 5.75234i | −0.391700 | + | 0.226148i | −0.682896 | − | 0.730515i | \(-0.739280\pi\) |
0.291197 | + | 0.956663i | \(0.405947\pi\) | |||||||
\(648\) | −0.500000 | − | 0.866025i | −0.0196419 | − | 0.0340207i | ||||
\(649\) | −5.58782 | + | 9.67838i | −0.219341 | + | 0.379910i | ||||
\(650\) | − | 24.1736i | − | 0.948165i | ||||||
\(651\) | −18.2129 | + | 16.1818i | −0.713818 | + | 0.634216i | ||||
\(652\) | −17.2112 | −0.674044 | ||||||||
\(653\) | 4.31398 | − | 7.47204i | 0.168819 | − | 0.292404i | −0.769186 | − | 0.639025i | \(-0.779338\pi\) |
0.938005 | + | 0.346622i | \(0.112671\pi\) | |||||||
\(654\) | −0.611537 | − | 1.05921i | −0.0239130 | − | 0.0414185i | ||||
\(655\) | 7.44678 | − | 4.29940i | 0.290970 | − | 0.167991i | ||||
\(656\) | 7.52415 | + | 4.34407i | 0.293769 | + | 0.169608i | ||||
\(657\) | − | 3.77504i | − | 0.147278i | ||||||
\(658\) | 11.0331 | − | 2.26890i | 0.430114 | − | 0.0884508i | ||||
\(659\) | 45.4300i | 1.76970i | 0.465875 | + | 0.884851i | \(0.345740\pi\) | ||||
−0.465875 | + | 0.884851i | \(0.654260\pi\) | |||||||
\(660\) | 0.744133 | − | 1.28888i | 0.0289653 | − | 0.0501694i | ||||
\(661\) | 16.4006 | + | 28.4066i | 0.637909 | + | 1.10489i | 0.985891 | + | 0.167389i | \(0.0535336\pi\) |
−0.347982 | + | 0.937501i | \(0.613133\pi\) | |||||||
\(662\) | −0.155874 | − | 0.269982i | −0.00605823 | − | 0.0104932i | ||||
\(663\) | −2.12498 | + | 3.68057i | −0.0825274 | + | 0.142942i | ||||
\(664\) | −6.95787 | −0.270018 | ||||||||
\(665\) | −1.76803 | − | 8.59747i | −0.0685612 | − | 0.333396i | ||||
\(666\) | 5.56750i | 0.215736i | ||||||||
\(667\) | −9.91733 | − | 19.8613i | −0.384000 | − | 0.769032i | ||||
\(668\) | 16.9360 | − | 9.77800i | 0.655273 | − | 0.378322i | ||||
\(669\) | −3.75304 | − | 6.50046i | −0.145101 | − | 0.251322i | ||||
\(670\) | −1.72098 | − | 0.993610i | −0.0664874 | − | 0.0383865i | ||||
\(671\) | − | 30.0670i | − | 1.16072i | ||||||
\(672\) | 1.75729 | + | 1.97786i | 0.0677891 | + | 0.0762975i | ||||
\(673\) | −23.7788 | −0.916606 | −0.458303 | − | 0.888796i | \(-0.651543\pi\) | ||||
−0.458303 | + | 0.888796i | \(0.651543\pi\) | |||||||
\(674\) | −28.5471 | − | 16.4817i | −1.09959 | − | 0.634851i | ||||
\(675\) | 4.12574 | − | 2.38200i | 0.158800 | − | 0.0916830i | ||||
\(676\) | 6.37388 | + | 11.0399i | 0.245149 | + | 0.424611i | ||||
\(677\) | 21.7479 | − | 37.6685i | 0.835841 | − | 1.44772i | −0.0575029 | − | 0.998345i | \(-0.518314\pi\) |
0.893344 | − | 0.449374i | \(-0.148353\pi\) | |||||||
\(678\) | −8.65289 | −0.332312 | ||||||||
\(679\) | 23.9520 | + | 7.95823i | 0.919195 | + | 0.305409i | ||||
\(680\) | −0.406892 | −0.0156036 | ||||||||
\(681\) | −15.3766 | − | 8.87766i | −0.589231 | − | 0.340192i | ||||
\(682\) | 14.1049 | + | 24.4304i | 0.540104 | + | 0.935487i | ||||
\(683\) | 2.58058 | + | 4.46970i | 0.0987431 | + | 0.171028i | 0.911165 | − | 0.412042i | \(-0.135184\pi\) |
−0.812422 | + | 0.583071i | \(0.801851\pi\) | |||||||
\(684\) | −3.41446 | + | 5.91401i | −0.130555 | + | 0.226128i | ||||
\(685\) | 2.17059i | 0.0829338i | ||||||||
\(686\) | 18.4536 | − | 1.56963i | 0.704563 | − | 0.0599288i | ||||
\(687\) | 20.5426i | 0.783749i | ||||||||
\(688\) | 4.56605 | + | 2.63621i | 0.174079 | + | 0.100504i | ||||
\(689\) | −21.4306 | − | 37.1189i | −0.816441 | − | 1.41412i | ||||
\(690\) | −0.140842 | + | 2.32559i | −0.00536175 | + | 0.0885338i | ||||
\(691\) | 5.29687 | + | 3.05815i | 0.201502 | + | 0.116337i | 0.597356 | − | 0.801976i | \(-0.296218\pi\) |
−0.395854 | + | 0.918314i | \(0.629551\pi\) | |||||||
\(692\) | 21.0914i | 0.801775i | ||||||||
\(693\) | −2.55564 | + | 7.69177i | −0.0970808 | + | 0.292186i | ||||
\(694\) | −26.1871 | −0.994051 | ||||||||
\(695\) | −8.40351 | − | 4.85177i | −0.318763 | − | 0.184038i | ||||
\(696\) | 4.00878 | − | 2.31447i | 0.151953 | − | 0.0877299i | ||||
\(697\) | 6.30192 | − | 3.63841i | 0.238702 | − | 0.137815i | ||||
\(698\) | −2.46060 | − | 1.42063i | −0.0931352 | − | 0.0537716i | ||||
\(699\) | − | 15.6744i | − | 0.592861i | ||||||
\(700\) | −9.42249 | + | 8.37173i | −0.356137 | + | 0.316422i | ||||
\(701\) | 40.5366i | 1.53104i | 0.643409 | + | 0.765522i | \(0.277519\pi\) | ||||
−0.643409 | + | 0.765522i | \(0.722481\pi\) | |||||||
\(702\) | −2.53711 | + | 4.39441i | −0.0957571 | + | 0.165856i | ||||
\(703\) | 32.9262 | − | 19.0100i | 1.24184 | − | 0.716975i | ||||
\(704\) | 2.65306 | − | 1.53174i | 0.0999908 | − | 0.0577297i | ||||
\(705\) | −1.03413 | + | 1.79117i | −0.0389477 | + | 0.0674594i | ||||
\(706\) | 4.52869i | 0.170440i | ||||||||
\(707\) | 7.77226 | − | 1.59833i | 0.292306 | − | 0.0601112i | ||||
\(708\) | 3.64801 | 0.137101 | ||||||||
\(709\) | 3.22290 | + | 1.86074i | 0.121038 | + | 0.0698816i | 0.559297 | − | 0.828967i | \(-0.311071\pi\) |
−0.438258 | + | 0.898849i | \(0.644405\pi\) | |||||||
\(710\) | 0.320831 | + | 0.555696i | 0.0120406 | + | 0.0208549i | ||||
\(711\) | 9.12312 | − | 5.26723i | 0.342144 | − | 0.197537i | ||||
\(712\) | 5.22221 | − | 9.04513i | 0.195710 | − | 0.338981i | ||||
\(713\) | −36.8405 | − | 24.3525i | −1.37969 | − | 0.912009i | ||||
\(714\) | 2.17055 | − | 0.446363i | 0.0812308 | − | 0.0167047i | ||||
\(715\) | −7.55180 | −0.282421 | ||||||||
\(716\) | −8.98104 | + | 15.5556i | −0.335637 | + | 0.581341i | ||||
\(717\) | −9.88408 | + | 5.70658i | −0.369128 | + | 0.213116i | ||||
\(718\) | −15.4334 | + | 8.91049i | −0.575970 | + | 0.332537i | ||||
\(719\) | −16.9903 | − | 9.80936i | −0.633632 | − | 0.365827i | 0.148525 | − | 0.988909i | \(-0.452547\pi\) |
−0.782157 | + | 0.623081i | \(0.785881\pi\) | |||||||
\(720\) | −0.485808 | −0.0181050 | ||||||||
\(721\) | 29.6478 | − | 26.3416i | 1.10414 | − | 0.981012i | ||||
\(722\) | 27.6340 | 1.02843 | ||||||||
\(723\) | 14.8226 | + | 8.55783i | 0.551258 | + | 0.318269i | ||||
\(724\) | 3.16433 | + | 5.48079i | 0.117602 | + | 0.203692i | ||||
\(725\) | 11.0261 | + | 19.0978i | 0.409500 | + | 0.709275i | ||||
\(726\) | −1.39868 | − | 0.807526i | −0.0519098 | − | 0.0299701i | ||||
\(727\) | −43.3463 | −1.60762 | −0.803812 | − | 0.594883i | \(-0.797198\pi\) | ||||
−0.803812 | + | 0.594883i | \(0.797198\pi\) | |||||||
\(728\) | 4.23305 | − | 12.7403i | 0.156887 | − | 0.472187i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −1.58824 | − | 0.916971i | −0.0587834 | − | 0.0339386i | ||||
\(731\) | 3.82433 | − | 2.20798i | 0.141448 | − | 0.0816650i | ||||
\(732\) | −8.49972 | + | 4.90732i | −0.314159 | + | 0.181380i | ||||
\(733\) | −18.1992 | + | 31.5219i | −0.672203 | + | 1.16429i | 0.305075 | + | 0.952328i | \(0.401318\pi\) |
−0.977278 | + | 0.211961i | \(0.932015\pi\) | |||||||
\(734\) | 23.5008 | 0.867429 | ||||||||
\(735\) | −2.03512 | + | 2.72447i | −0.0750663 | + | 0.100494i | ||||
\(736\) | −2.64460 | + | 4.00076i | −0.0974813 | + | 0.147470i | ||||
\(737\) | 6.26567 | − | 10.8525i | 0.230799 | − | 0.399755i | ||||
\(738\) | 7.52415 | − | 4.34407i | 0.276968 | − | 0.159908i | ||||
\(739\) | −17.7137 | − | 30.6811i | −0.651610 | − | 1.12862i | −0.982732 | − | 0.185033i | \(-0.940761\pi\) |
0.331122 | − | 0.943588i | \(-0.392573\pi\) | |||||||
\(740\) | 2.34237 | + | 1.35237i | 0.0861072 | + | 0.0497140i | ||||
\(741\) | 34.6514 | 1.27295 | ||||||||
\(742\) | −7.04659 | + | 21.2083i | −0.258688 | + | 0.778580i | ||||
\(743\) | 39.9225i | 1.46461i | 0.680975 | + | 0.732307i | \(0.261556\pi\) | ||||
−0.680975 | + | 0.732307i | \(0.738444\pi\) | |||||||
\(744\) | 4.60419 | − | 7.97469i | 0.168798 | − | 0.292366i | ||||
\(745\) | −8.24570 | + | 4.76066i | −0.302099 | + | 0.174417i | ||||
\(746\) | 4.55066 | − | 2.62732i | 0.166611 | − | 0.0961931i | ||||
\(747\) | −3.47893 | + | 6.02569i | −0.127288 | + | 0.220468i | ||||
\(748\) | − | 2.56585i | − | 0.0938167i | ||||||
\(749\) | −12.9737 | − | 14.6021i | −0.474049 | − | 0.533548i | ||||
\(750\) | − | 4.74342i | − | 0.173205i | ||||||
\(751\) | −17.1730 | − | 9.91482i | −0.626651 | − | 0.361797i | 0.152803 | − | 0.988257i | \(-0.451170\pi\) |
−0.779454 | + | 0.626460i | \(0.784503\pi\) | |||||||
\(752\) | −3.68699 | + | 2.12869i | −0.134451 | + | 0.0776252i | ||||
\(753\) | −22.8703 | + | 13.2042i | −0.833441 | + | 0.481187i | ||||
\(754\) | −20.3415 | − | 11.7442i | −0.740793 | − | 0.427697i | ||||
\(755\) | −4.21906 | −0.153547 | ||||||||
\(756\) | 2.59152 | − | 0.532933i | 0.0942527 | − | 0.0193826i | ||||
\(757\) | 29.3384i | 1.06632i | 0.846013 | + | 0.533162i | \(0.178996\pi\) | ||||
−0.846013 | + | 0.533162i | \(0.821004\pi\) | |||||||
\(758\) | −27.7725 | − | 16.0345i | −1.00874 | − | 0.582398i | ||||
\(759\) | −14.6651 | − | 0.888142i | −0.532309 | − | 0.0322375i | ||||
\(760\) | 1.65877 | + | 2.87307i | 0.0601699 | + | 0.104217i | ||||
\(761\) | −40.7579 | − | 23.5316i | −1.47747 | − | 0.853020i | −0.477798 | − | 0.878470i | \(-0.658565\pi\) |
−0.999676 | + | 0.0254494i | \(0.991898\pi\) | |||||||
\(762\) | 7.27976i | 0.263718i | ||||||||
\(763\) | 3.16962 | − | 0.651817i | 0.114748 | − | 0.0235974i | ||||
\(764\) | 18.1009i | 0.654868i | ||||||||
\(765\) | −0.203446 | + | 0.352379i | −0.00735561 | + | 0.0127403i | ||||
\(766\) | −9.14917 | − | 15.8468i | −0.330573 | − | 0.572569i | ||||
\(767\) | −9.25541 | − | 16.0308i | −0.334194 | − | 0.578840i | ||||
\(768\) | −0.866025 | − | 0.500000i | −0.0312500 | − | 0.0180422i | ||||
\(769\) | 17.8827 | 0.644867 | 0.322433 | − | 0.946592i | \(-0.395499\pi\) | ||||
0.322433 | + | 0.946592i | \(0.395499\pi\) | |||||||
\(770\) | 2.61532 | + | 2.94358i | 0.0942496 | + | 0.106079i | ||||
\(771\) | −25.0504 | −0.902168 | ||||||||
\(772\) | −7.59857 | + | 13.1611i | −0.273478 | + | 0.473679i | ||||
\(773\) | −23.0130 | − | 39.8596i | −0.827719 | − | 1.43365i | −0.899824 | − | 0.436254i | \(-0.856305\pi\) |
0.0721051 | − | 0.997397i | \(-0.477028\pi\) | |||||||
\(774\) | 4.56605 | − | 2.63621i | 0.164123 | − | 0.0947565i | ||||
\(775\) | 37.9914 | + | 21.9343i | 1.36469 | + | 0.787904i | ||||
\(776\) | −9.53965 | −0.342453 | ||||||||
\(777\) | −13.9788 | − | 4.64456i | −0.501487 | − | 0.166623i | ||||
\(778\) | − | 31.4343i | − | 1.12698i | ||||||
\(779\) | −51.3818 | − | 29.6653i | −1.84094 | − | 1.06287i | ||||
\(780\) | 1.23255 | + | 2.13484i | 0.0441323 | + | 0.0764395i | ||||
\(781\) | −3.50420 | + | 2.02315i | −0.125390 | + | 0.0723940i | ||||
\(782\) | 1.79443 | + | 3.59369i | 0.0641688 | + | 0.128510i | ||||
\(783\) | − | 4.62895i | − | 0.165425i | ||||||
\(784\) | −6.43196 | + | 2.76222i | −0.229713 | + | 0.0986506i | ||||
\(785\) | −3.63380 | −0.129696 | ||||||||
\(786\) | 8.85000 | − | 15.3287i | 0.315669 | − | 0.546755i | ||||
\(787\) | −12.0189 | − | 20.8173i | −0.428427 | − | 0.742057i | 0.568307 | − | 0.822817i | \(-0.307599\pi\) |
−0.996734 | + | 0.0807596i | \(0.974265\pi\) | |||||||
\(788\) | 2.26058 | + | 3.91544i | 0.0805298 | + | 0.139482i | ||||
\(789\) | 7.92239 | − | 13.7220i | 0.282045 | − | 0.488515i | ||||
\(790\) | − | 5.11773i | − | 0.182081i | ||||||
\(791\) | 7.21847 | − | 21.7256i | 0.256659 | − | 0.772473i | ||||
\(792\) | − | 3.06349i | − | 0.108856i | ||||||
\(793\) | 43.1295 | + | 24.9008i | 1.53157 | + | 0.884255i | ||||
\(794\) | 9.69103 | − | 5.59512i | 0.343922 | − | 0.198563i | ||||
\(795\) | −2.05177 | − | 3.55378i | −0.0727689 | − | 0.126039i | ||||
\(796\) | −1.40852 | + | 2.43964i | −0.0499238 | + | 0.0864706i | ||||
\(797\) | 25.2324 | 0.893777 | 0.446888 | − | 0.894590i | \(-0.352532\pi\) | ||||
0.446888 | + | 0.894590i | \(0.352532\pi\) | |||||||
\(798\) | −12.0004 | − | 13.5066i | −0.424810 | − | 0.478129i | ||||
\(799\) | 3.56580i | 0.126149i | ||||||||
\(800\) | 2.38200 | − | 4.12574i | 0.0842163 | − | 0.145867i | ||||
\(801\) | −5.22221 | − | 9.04513i | −0.184518 | − | 0.319594i | ||||
\(802\) | 11.5257 | − | 6.65435i | 0.406986 | − | 0.234973i | ||||
\(803\) | 5.78239 | − | 10.0154i | 0.204056 | − | 0.353435i | ||||
\(804\) | −4.09055 | −0.144263 | ||||||||
\(805\) | −5.72158 | − | 2.29369i | −0.201659 | − | 0.0808421i | ||||
\(806\) | −46.7254 | −1.64583 | ||||||||
\(807\) | 9.19246 | − | 15.9218i | 0.323590 | − | 0.560474i | ||||
\(808\) | −2.59731 | + | 1.49955i | −0.0913729 | + | 0.0527542i | ||||
\(809\) | 14.9227 | + | 25.8468i | 0.524653 | + | 0.908725i | 0.999588 | + | 0.0287045i | \(0.00913818\pi\) |
−0.474935 | + | 0.880021i | \(0.657528\pi\) | |||||||
\(810\) | −0.242904 | + | 0.420722i | −0.00853477 | + | 0.0147827i | ||||
\(811\) | − | 9.88754i | − | 0.347198i | −0.984816 | − | 0.173599i | \(-0.944460\pi\) | ||
0.984816 | − | 0.173599i | \(-0.0555397\pi\) | |||||||
\(812\) | 2.46692 | + | 11.9960i | 0.0865719 | + | 0.420977i | ||||
\(813\) | −2.10387 | −0.0737859 | ||||||||
\(814\) | −8.52798 | + | 14.7709i | −0.298905 | + | 0.517719i | ||||
\(815\) | 4.18068 | + | 7.24114i | 0.146443 | + | 0.253646i | ||||
\(816\) | −0.725347 | + | 0.418779i | −0.0253922 | + | 0.0146602i | ||||
\(817\) | −31.1811 | − | 18.0024i | −1.09089 | − | 0.629825i | ||||
\(818\) | − | 25.4819i | − | 0.890953i | ||||||
\(819\) | −8.91691 | − | 10.0361i | −0.311582 | − | 0.350689i | ||||
\(820\) | − | 4.22077i | − | 0.147396i | ||||||
\(821\) | 4.91451 | − | 8.51218i | 0.171518 | − | 0.297077i | −0.767433 | − | 0.641129i | \(-0.778466\pi\) |
0.938951 | + | 0.344052i | \(0.111800\pi\) | |||||||
\(822\) | 2.23400 | + | 3.86939i | 0.0779195 | + | 0.134961i | ||||
\(823\) | −14.2192 | − | 24.6284i | −0.495651 | − | 0.858492i | 0.504337 | − | 0.863507i | \(-0.331737\pi\) |
−0.999987 | + | 0.00501499i | \(0.998404\pi\) | |||||||
\(824\) | −7.49493 | + | 12.9816i | −0.261098 | + | 0.452235i | ||||
\(825\) | 14.5944 | 0.508112 | ||||||||
\(826\) | −3.04327 | + | 9.15939i | −0.105889 | + | 0.318696i | ||||
\(827\) | 11.0980i | 0.385914i | 0.981207 | + | 0.192957i | \(0.0618077\pi\) | ||||
−0.981207 | + | 0.192957i | \(0.938192\pi\) | |||||||
\(828\) | 2.14246 | + | 4.29067i | 0.0744556 | + | 0.149111i | ||||
\(829\) | 41.0940 | − | 23.7257i | 1.42726 | − | 0.824026i | 0.430352 | − | 0.902661i | \(-0.358390\pi\) |
0.996903 | + | 0.0786350i | \(0.0250562\pi\) | |||||||
\(830\) | 1.69009 | + | 2.92733i | 0.0586640 | + | 0.101609i | ||||
\(831\) | −11.4499 | − | 6.61062i | −0.397194 | − | 0.229320i | ||||
\(832\) | 5.07423i | 0.175917i | ||||||||
\(833\) | −0.690007 | + | 5.82216i | −0.0239073 | + | 0.201726i | ||||
\(834\) | −19.9740 | −0.691644 | ||||||||
\(835\) | −8.22764 | − | 4.75023i | −0.284729 | − | 0.164388i | ||||
\(836\) | −18.1175 | + | 10.4601i | −0.626606 | + | 0.361771i | ||||
\(837\) | −4.60419 | − | 7.97469i | −0.159144 | − | 0.275646i | ||||
\(838\) | 6.68932 | − | 11.5862i | 0.231079 | − | 0.400240i | ||||
\(839\) | −2.13043 | −0.0735506 | −0.0367753 | − | 0.999324i | \(-0.511709\pi\) | ||||
−0.0367753 | + | 0.999324i | \(0.511709\pi\) | |||||||
\(840\) | 0.405274 | − | 1.21976i | 0.0139833 | − | 0.0420858i | ||||
\(841\) | −7.57286 | −0.261133 | ||||||||
\(842\) | −4.39470 | − | 2.53728i | −0.151451 | − | 0.0874404i | ||||
\(843\) | 11.6908 | + | 20.2491i | 0.402654 | + | 0.697417i | ||||
\(844\) | −3.58553 | − | 6.21033i | −0.123419 | − | 0.213768i | ||||
\(845\) | 3.09648 | − | 5.36326i | 0.106522 | − | 0.184502i | ||||
\(846\) | 4.25737i | 0.146372i | ||||||||
\(847\) | 3.19434 | − | 2.83812i | 0.109759 | − | 0.0975191i | ||||
\(848\) | − | 8.44685i | − | 0.290066i | ||||||
\(849\) | 0.901145 | + | 0.520276i | 0.0309272 | + | 0.0178558i | ||||
\(850\) | −1.99506 | − | 3.45555i | −0.0684300 | − | 0.118524i | ||||
\(851\) | 1.61409 | − | 26.6520i | 0.0553302 | − | 0.913617i | ||||
\(852\) | 1.14386 | + | 0.660408i | 0.0391880 | + | 0.0226252i | ||||
\(853\) | 6.39947i | 0.219114i | 0.993981 | + | 0.109557i | \(0.0349432\pi\) | ||||
−0.993981 | + | 0.109557i | \(0.965057\pi\) | |||||||
\(854\) | −5.23055 | − | 25.4348i | −0.178986 | − | 0.870362i | ||||
\(855\) | 3.31754 | 0.113457 | ||||||||
\(856\) | 6.39367 | + | 3.69139i | 0.218531 | + | 0.126169i | ||||
\(857\) | −12.9055 | + | 7.45097i | −0.440842 | + | 0.254520i | −0.703955 | − | 0.710245i | \(-0.748584\pi\) |
0.263113 | + | 0.964765i | \(0.415251\pi\) | |||||||
\(858\) | −13.4622 | + | 7.77241i | −0.459592 | + | 0.265346i | ||||
\(859\) | 24.1115 | + | 13.9208i | 0.822674 | + | 0.474971i | 0.851338 | − | 0.524618i | \(-0.175792\pi\) |
−0.0286636 | + | 0.999589i | \(0.509125\pi\) | |||||||
\(860\) | − | 2.56138i | − | 0.0873424i | ||||||
\(861\) | 4.63020 | + | 22.5155i | 0.157797 | + | 0.767327i | ||||
\(862\) | 21.7899i | 0.742167i | ||||||||
\(863\) | −15.0719 | + | 26.1053i | −0.513053 | + | 0.888635i | 0.486832 | + | 0.873496i | \(0.338152\pi\) |
−0.999885 | + | 0.0151390i | \(0.995181\pi\) | |||||||
\(864\) | −0.866025 | + | 0.500000i | −0.0294628 | + | 0.0170103i | ||||
\(865\) | 8.87361 | − | 5.12318i | 0.301712 | − | 0.174193i | ||||
\(866\) | −0.0718807 | + | 0.124501i | −0.00244261 | + | 0.00423072i | ||||
\(867\) | − | 16.2985i | − | 0.553526i | ||||||
\(868\) | 16.1818 | + | 18.2129i | 0.549248 | + | 0.618185i | ||||
\(869\) | 32.2722 | 1.09476 | ||||||||
\(870\) | −1.94750 | − | 1.12439i | −0.0660264 | − | 0.0381204i | ||||
\(871\) | 10.3782 | + | 17.9755i | 0.351651 | + | 0.609078i | ||||
\(872\) | −1.05921 | + | 0.611537i | −0.0358695 | + | 0.0207092i | ||||
\(873\) | −4.76982 | + | 8.26158i | −0.161434 | + | 0.279612i | ||||
\(874\) | 18.0598 | − | 27.3208i | 0.610880 | − | 0.924141i | ||||
\(875\) | 11.9097 | + | 3.95709i | 0.402623 | + | 0.133774i | ||||
\(876\) | −3.77504 | −0.127547 | ||||||||
\(877\) | −18.2441 | + | 31.5997i | −0.616059 | + | 1.06705i | 0.374139 | + | 0.927373i | \(0.377938\pi\) |
−0.990198 | + | 0.139672i | \(0.955395\pi\) | |||||||
\(878\) | −24.8389 | + | 14.3408i | −0.838274 | + | 0.483978i | ||||
\(879\) | 8.50315 | − | 4.90929i | 0.286804 | − | 0.165586i | ||||
\(880\) | −1.28888 | − | 0.744133i | −0.0434480 | − | 0.0250847i | ||||
\(881\) | −52.0502 | −1.75362 | −0.876808 | − | 0.480840i | \(-0.840332\pi\) | ||||
−0.876808 | + | 0.480840i | \(0.840332\pi\) | |||||||
\(882\) | −0.823832 | + | 6.95135i | −0.0277399 | + | 0.234064i | ||||
\(883\) | 31.9734 | 1.07599 | 0.537995 | − | 0.842948i | \(-0.319182\pi\) | ||||
0.537995 | + | 0.842948i | \(0.319182\pi\) | |||||||
\(884\) | 3.68057 | + | 2.12498i | 0.123791 | + | 0.0714708i | ||||
\(885\) | −0.886116 | − | 1.53480i | −0.0297865 | − | 0.0515917i | ||||
\(886\) | 13.9610 | + | 24.1811i | 0.469027 | + | 0.812379i | ||||
\(887\) | 32.0287 | + | 18.4918i | 1.07542 | + | 0.620893i | 0.929657 | − | 0.368427i | \(-0.120104\pi\) |
0.145761 | + | 0.989320i | \(0.453437\pi\) | |||||||
\(888\) | 5.56750 | 0.186833 | ||||||||
\(889\) | −18.2780 | − | 6.07297i | −0.613023 | − | 0.203681i | ||||
\(890\) | −5.07398 | −0.170080 | ||||||||
\(891\) | −2.65306 | − | 1.53174i | −0.0888807 | − | 0.0513153i | ||||
\(892\) | −6.50046 | + | 3.75304i | −0.217651 | + | 0.125661i | ||||
\(893\) | 25.1782 | − | 14.5366i | 0.842555 | − | 0.486449i | ||||
\(894\) | −9.79947 | + | 16.9732i | −0.327743 | + | 0.567668i | ||||
\(895\) | 8.72612 | 0.291682 | ||||||||
\(896\) | 1.97786 | − | 1.75729i | 0.0660755 | − | 0.0587071i | ||||
\(897\) | 13.4193 | − | 20.3008i | 0.448058 | − | 0.677823i | ||||
\(898\) | −9.87947 | + | 17.1117i | −0.329682 | + | 0.571026i | ||||
\(899\) | 36.9144 | − | 21.3126i | 1.23117 | − | 0.710814i | ||||
\(900\) | −2.38200 | − | 4.12574i | −0.0793998 | − | 0.137525i | ||||
\(901\) | −6.12690 | − | 3.53737i | −0.204117 | − | 0.117847i | ||||
\(902\) | 26.6160 | 0.886216 | ||||||||
\(903\) | 2.80985 | + | 13.6636i | 0.0935058 | + | 0.454695i | ||||
\(904\) | 8.65289i | 0.287791i | ||||||||
\(905\) | 1.53726 | − | 2.66261i | 0.0511002 | − | 0.0885081i | ||||
\(906\) | −7.52112 | + | 4.34232i | −0.249872 | + | 0.144264i | ||||
\(907\) | 10.2414 | − | 5.91288i | 0.340061 | − | 0.196334i | −0.320238 | − | 0.947337i | \(-0.603763\pi\) |
0.660299 | + | 0.751003i | \(0.270430\pi\) | |||||||
\(908\) | −8.87766 | + | 15.3766i | −0.294615 | + | 0.510289i | ||||
\(909\) | 2.99911i | 0.0994742i | ||||||||
\(910\) | −6.38835 | + | 1.31373i | −0.211772 | + | 0.0435498i | ||||
\(911\) | 16.1989i | 0.536694i | 0.963322 | + | 0.268347i | \(0.0864774\pi\) | ||||
−0.963322 | + | 0.268347i | \(0.913523\pi\) | |||||||
\(912\) | 5.91401 | + | 3.41446i | 0.195832 | + | 0.113064i | ||||
\(913\) | −18.4596 | + | 10.6577i | −0.610924 | + | 0.352717i | ||||
\(914\) | −28.7619 | + | 16.6057i | −0.951358 | + | 0.549267i | ||||
\(915\) | 4.12923 | + | 2.38401i | 0.136508 | + | 0.0788131i | ||||
\(916\) | 20.5426 | 0.678747 | ||||||||
\(917\) | 31.1041 | + | 35.0081i | 1.02715 | + | 1.15607i | ||||
\(918\) | 0.837558i | 0.0276435i | ||||||||
\(919\) | −51.1444 | − | 29.5282i | −1.68710 | − | 0.974046i | −0.956723 | − | 0.291000i | \(-0.906012\pi\) |
−0.730375 | − | 0.683047i | \(-0.760655\pi\) | |||||||
\(920\) | 2.32559 | + | 0.140842i | 0.0766725 | + | 0.00464341i | ||||
\(921\) | 4.17774 | + | 7.23605i | 0.137661 | + | 0.238436i | ||||
\(922\) | −15.6584 | − | 9.04038i | −0.515682 | − | 0.297729i | ||||
\(923\) | − | 6.70212i | − | 0.220603i | ||||||
\(924\) | 7.69177 | + | 2.55564i | 0.253041 | + | 0.0840744i | ||||
\(925\) | 26.5235i | 0.872088i | ||||||||
\(926\) | 7.24035 | − | 12.5407i | 0.237933 | − | 0.412111i | ||||
\(927\) | 7.49493 | + | 12.9816i | 0.246166 | + | 0.426371i | ||||
\(928\) | −2.31447 | − | 4.00878i | −0.0759763 | − | 0.131595i | ||||
\(929\) | 28.8442 | + | 16.6532i | 0.946349 | + | 0.546375i | 0.891945 | − | 0.452144i | \(-0.149341\pi\) |
0.0544041 | + | 0.998519i | \(0.482674\pi\) | |||||||
\(930\) | −4.47351 | −0.146692 | ||||||||
\(931\) | 43.9233 | − | 18.8629i | 1.43953 | − | 0.618208i | ||||
\(932\) | −15.6744 | −0.513433 | ||||||||
\(933\) | −6.15900 | + | 10.6677i | −0.201637 | + | 0.349245i | ||||
\(934\) | 15.4907 | + | 26.8307i | 0.506871 | + | 0.877927i | ||||
\(935\) | −1.07951 | + | 0.623255i | −0.0353037 | + | 0.0203826i | ||||
\(936\) | 4.39441 | + | 2.53711i | 0.143636 | + | 0.0829281i | ||||
\(937\) | −11.8010 | −0.385520 | −0.192760 | − | 0.981246i | \(-0.561744\pi\) | ||||
−0.192760 | + | 0.981246i | \(0.561744\pi\) | |||||||
\(938\) | 3.41244 | − | 10.2705i | 0.111420 | − | 0.335344i | ||||
\(939\) | − | 26.6602i | − | 0.870022i | ||||||
\(940\) | 1.79117 | + | 1.03413i | 0.0584216 | + | 0.0337297i | ||||
\(941\) | −4.11457 | − | 7.12665i | −0.134131 | − | 0.232322i | 0.791134 | − | 0.611643i | \(-0.209491\pi\) |
−0.925265 | + | 0.379321i | \(0.876158\pi\) | |||||||
\(942\) | −6.47780 | + | 3.73996i | −0.211058 | + | 0.121854i | ||||
\(943\) | −37.2780 | + | 18.6140i | −1.21394 | + | 0.606155i | ||||
\(944\) | − | 3.64801i | − | 0.118733i | ||||||
\(945\) | −0.853707 | − | 0.960858i | −0.0277711 | − | 0.0312567i | ||||
\(946\) | 16.1520 | 0.525146 | ||||||||
\(947\) | −9.99078 | + | 17.3045i | −0.324657 | + | 0.562322i | −0.981443 | − | 0.191755i | \(-0.938582\pi\) |
0.656786 | + | 0.754077i | \(0.271915\pi\) | |||||||
\(948\) | −5.26723 | − | 9.12312i | −0.171072 | − | 0.296305i | ||||
\(949\) | 9.57769 | + | 16.5891i | 0.310905 | + | 0.538503i | ||||
\(950\) | −16.2664 | + | 28.1743i | −0.527753 | + | 0.914095i | ||||
\(951\) | 18.3747i | 0.595841i | ||||||||
\(952\) | −0.446363 | − | 2.17055i | −0.0144667 | − | 0.0703479i | ||||
\(953\) | 11.3231i | 0.366791i | 0.983039 | + | 0.183395i | \(0.0587088\pi\) | ||||
−0.983039 | + | 0.183395i | \(0.941291\pi\) | |||||||
\(954\) | −7.31519 | − | 4.22343i | −0.236838 | − | 0.136738i | ||||
\(955\) | 7.61545 | − | 4.39678i | 0.246430 | − | 0.142277i | ||||
\(956\) | 5.70658 | + | 9.88408i | 0.184564 | + | 0.319674i | ||||
\(957\) | 7.09036 | − | 12.2809i | 0.229199 | − | 0.396984i | ||||
\(958\) | 16.0879 | 0.519775 | ||||||||
\(959\) | −11.5789 | + | 2.38114i | −0.373902 | + | 0.0768911i | ||||
\(960\) | 0.485808i | 0.0156794i | ||||||||
\(961\) | 26.8972 | − | 46.5873i | 0.867651 | − | 1.50281i | ||||
\(962\) | −14.1254 | − | 24.4659i | −0.455420 | − | 0.788811i | ||||
\(963\) | 6.39367 | − | 3.69139i | 0.206033 | − | 0.118953i | ||||
\(964\) | 8.55783 | − | 14.8226i | 0.275629 | − | 0.477404i | ||||
\(965\) | 7.38289 | 0.237664 | ||||||||
\(966\) | −12.5603 | + | 1.79987i | −0.404120 | + | 0.0579099i | ||||
\(967\) | −38.2537 | −1.23016 | −0.615078 | − | 0.788466i | \(-0.710876\pi\) | ||||
−0.615078 | + | 0.788466i | \(0.710876\pi\) | |||||||
\(968\) | −0.807526 | + | 1.39868i | −0.0259549 | + | 0.0449552i | ||||
\(969\) | 4.95333 | − | 2.85981i | 0.159124 | − | 0.0918702i | ||||
\(970\) | 2.31722 | + | 4.01354i | 0.0744014 | + | 0.128867i | ||||
\(971\) | −18.3139 | + | 31.7205i | −0.587720 | + | 1.01796i | 0.406811 | + | 0.913512i | \(0.366641\pi\) |
−0.994530 | + | 0.104448i | \(0.966692\pi\) | |||||||
\(972\) | 1.00000i | 0.0320750i | ||||||||
\(973\) | 16.6629 | − | 50.1506i | 0.534187 | − | 1.60775i | ||||
\(974\) | −9.42460 | −0.301984 | ||||||||
\(975\) | −12.0868 | + | 20.9349i | −0.387087 | + | 0.670454i | ||||
\(976\) | 4.90732 | + | 8.49972i | 0.157079 | + | 0.272070i | ||||
\(977\) | 18.6175 | − | 10.7488i | 0.595625 | − | 0.343884i | −0.171693 | − | 0.985150i | \(-0.554924\pi\) |
0.767319 | + | 0.641266i | \(0.221591\pi\) | |||||||
\(978\) | 14.9054 | + | 8.60562i | 0.476621 | + | 0.275177i | ||||
\(979\) | − | 31.9963i | − | 1.02261i | ||||||
\(980\) | 2.72447 | + | 2.03512i | 0.0870301 | + | 0.0650094i | ||||
\(981\) | 1.22307i | 0.0390497i | ||||||||
\(982\) | −13.1764 | + | 22.8221i | −0.420475 | + | 0.728283i | ||||
\(983\) | −9.84579 | − | 17.0534i | −0.314032 | − | 0.543919i | 0.665199 | − | 0.746666i | \(-0.268347\pi\) |
−0.979231 | + | 0.202747i | \(0.935013\pi\) | |||||||
\(984\) | −4.34407 | − | 7.52415i | −0.138484 | − | 0.239861i | ||||
\(985\) | 1.09821 | − | 1.90215i | 0.0349918 | − | 0.0606075i | ||||
\(986\) | −3.87701 | −0.123469 | ||||||||
\(987\) | −10.6894 | − | 3.55162i | −0.340247 | − | 0.113049i | ||||
\(988\) | − | 34.6514i | − | 1.10241i | ||||||
\(989\) | −22.6222 | + | 11.2959i | −0.719344 | + | 0.359190i | ||||
\(990\) | −1.28888 | + | 0.744133i | −0.0409632 | + | 0.0236501i | ||||
\(991\) | −16.1075 | − | 27.8991i | −0.511673 | − | 0.886243i | −0.999908 | − | 0.0135315i | \(-0.995693\pi\) |
0.488236 | − | 0.872712i | \(-0.337641\pi\) | |||||||
\(992\) | −7.97469 | − | 4.60419i | −0.253197 | − | 0.146183i | ||||
\(993\) | 0.311749i | 0.00989305i | ||||||||
\(994\) | −2.61238 | + | 2.32106i | −0.0828598 | + | 0.0736196i | ||||
\(995\) | 1.36854 | 0.0433858 | ||||||||
\(996\) | 6.02569 | + | 3.47893i | 0.190931 | + | 0.110234i | ||||
\(997\) | −27.9939 | + | 16.1623i | −0.886574 | + | 0.511864i | −0.872820 | − | 0.488042i | \(-0.837711\pi\) |
−0.0137538 | + | 0.999905i | \(0.504378\pi\) | |||||||
\(998\) | −14.3554 | − | 24.8642i | −0.454411 | − | 0.787063i | ||||
\(999\) | 2.78375 | − | 4.82160i | 0.0880739 | − | 0.152549i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 966.2.k.a.229.12 | ✓ | 32 | |
7.3 | odd | 6 | inner | 966.2.k.a.367.13 | yes | 32 | |
23.22 | odd | 2 | inner | 966.2.k.a.229.13 | yes | 32 | |
161.45 | even | 6 | inner | 966.2.k.a.367.12 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
966.2.k.a.229.12 | ✓ | 32 | 1.1 | even | 1 | trivial | |
966.2.k.a.229.13 | yes | 32 | 23.22 | odd | 2 | inner | |
966.2.k.a.367.12 | yes | 32 | 161.45 | even | 6 | inner | |
966.2.k.a.367.13 | yes | 32 | 7.3 | odd | 6 | inner |