Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(121,1110)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1110, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1110.121");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.i (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: | \(8.86339462436\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 121.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1110.121 |
Dual form | 1110.2.i.a.211.1 |
$q$-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 \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 | ||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | ||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 0.500000 | + | 0.866025i | 0.223607 | + | 0.387298i | ||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 2.00000 | + | 3.46410i | 0.755929 | + | 1.30931i | 0.944911 | + | 0.327327i | \(0.106148\pi\) |
−0.188982 | + | 0.981981i | \(0.560519\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 3.00000 | 0.904534 | 0.452267 | − | 0.891883i | \(-0.350615\pi\) | ||||
0.452267 | + | 0.891883i | \(0.350615\pi\) | |||||||
\(12\) | −0.500000 | + | 0.866025i | −0.144338 | + | 0.250000i | ||||
\(13\) | 0.500000 | + | 0.866025i | 0.138675 | + | 0.240192i | 0.926995 | − | 0.375073i | \(-0.122382\pi\) |
−0.788320 | + | 0.615265i | \(0.789049\pi\) | |||||||
\(14\) | −4.00000 | −1.06904 | ||||||||
\(15\) | 0.500000 | − | 0.866025i | 0.129099 | − | 0.223607i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −1.50000 | + | 2.59808i | −0.363803 | + | 0.630126i | −0.988583 | − | 0.150675i | \(-0.951855\pi\) |
0.624780 | + | 0.780801i | \(0.285189\pi\) | |||||||
\(18\) | −0.500000 | − | 0.866025i | −0.117851 | − | 0.204124i | ||||
\(19\) | −1.00000 | − | 1.73205i | −0.229416 | − | 0.397360i | 0.728219 | − | 0.685344i | \(-0.240348\pi\) |
−0.957635 | + | 0.287984i | \(0.907015\pi\) | |||||||
\(20\) | 0.500000 | − | 0.866025i | 0.111803 | − | 0.193649i | ||||
\(21\) | 2.00000 | − | 3.46410i | 0.436436 | − | 0.755929i | ||||
\(22\) | −1.50000 | + | 2.59808i | −0.319801 | + | 0.553912i | ||||
\(23\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(24\) | −0.500000 | − | 0.866025i | −0.102062 | − | 0.176777i | ||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 2.00000 | − | 3.46410i | 0.377964 | − | 0.654654i | ||||
\(29\) | −3.00000 | −0.557086 | −0.278543 | − | 0.960424i | \(-0.589851\pi\) | ||||
−0.278543 | + | 0.960424i | \(0.589851\pi\) | |||||||
\(30\) | 0.500000 | + | 0.866025i | 0.0912871 | + | 0.158114i | ||||
\(31\) | −4.00000 | −0.718421 | −0.359211 | − | 0.933257i | \(-0.616954\pi\) | ||||
−0.359211 | + | 0.933257i | \(0.616954\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | −1.50000 | − | 2.59808i | −0.261116 | − | 0.452267i | ||||
\(34\) | −1.50000 | − | 2.59808i | −0.257248 | − | 0.445566i | ||||
\(35\) | −2.00000 | + | 3.46410i | −0.338062 | + | 0.585540i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 5.50000 | + | 2.59808i | 0.904194 | + | 0.427121i | ||||
\(38\) | 2.00000 | 0.324443 | ||||||||
\(39\) | 0.500000 | − | 0.866025i | 0.0800641 | − | 0.138675i | ||||
\(40\) | 0.500000 | + | 0.866025i | 0.0790569 | + | 0.136931i | ||||
\(41\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(42\) | 2.00000 | + | 3.46410i | 0.308607 | + | 0.534522i | ||||
\(43\) | 8.00000 | 1.21999 | 0.609994 | − | 0.792406i | \(-0.291172\pi\) | ||||
0.609994 | + | 0.792406i | \(0.291172\pi\) | |||||||
\(44\) | −1.50000 | − | 2.59808i | −0.226134 | − | 0.391675i | ||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.00000 | −1.31278 | −0.656392 | − | 0.754420i | \(-0.727918\pi\) | ||||
−0.656392 | + | 0.754420i | \(0.727918\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −4.50000 | + | 7.79423i | −0.642857 | + | 1.11346i | ||||
\(50\) | −0.500000 | − | 0.866025i | −0.0707107 | − | 0.122474i | ||||
\(51\) | 3.00000 | 0.420084 | ||||||||
\(52\) | 0.500000 | − | 0.866025i | 0.0693375 | − | 0.120096i | ||||
\(53\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(54\) | −0.500000 | + | 0.866025i | −0.0680414 | + | 0.117851i | ||||
\(55\) | 1.50000 | + | 2.59808i | 0.202260 | + | 0.350325i | ||||
\(56\) | 2.00000 | + | 3.46410i | 0.267261 | + | 0.462910i | ||||
\(57\) | −1.00000 | + | 1.73205i | −0.132453 | + | 0.229416i | ||||
\(58\) | 1.50000 | − | 2.59808i | 0.196960 | − | 0.341144i | ||||
\(59\) | −1.50000 | + | 2.59808i | −0.195283 | + | 0.338241i | −0.946993 | − | 0.321253i | \(-0.895896\pi\) |
0.751710 | + | 0.659494i | \(0.229229\pi\) | |||||||
\(60\) | −1.00000 | −0.129099 | ||||||||
\(61\) | 5.00000 | + | 8.66025i | 0.640184 | + | 1.10883i | 0.985391 | + | 0.170305i | \(0.0544754\pi\) |
−0.345207 | + | 0.938527i | \(0.612191\pi\) | |||||||
\(62\) | 2.00000 | − | 3.46410i | 0.254000 | − | 0.439941i | ||||
\(63\) | −4.00000 | −0.503953 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.500000 | + | 0.866025i | −0.0620174 | + | 0.107417i | ||||
\(66\) | 3.00000 | 0.369274 | ||||||||
\(67\) | 6.50000 | + | 11.2583i | 0.794101 | + | 1.37542i | 0.923408 | + | 0.383819i | \(0.125391\pi\) |
−0.129307 | + | 0.991605i | \(0.541275\pi\) | |||||||
\(68\) | 3.00000 | 0.363803 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.00000 | − | 3.46410i | −0.239046 | − | 0.414039i | ||||
\(71\) | −3.00000 | − | 5.19615i | −0.356034 | − | 0.616670i | 0.631260 | − | 0.775571i | \(-0.282538\pi\) |
−0.987294 | + | 0.158901i | \(0.949205\pi\) | |||||||
\(72\) | −0.500000 | + | 0.866025i | −0.0589256 | + | 0.102062i | ||||
\(73\) | −4.00000 | −0.468165 | −0.234082 | − | 0.972217i | \(-0.575209\pi\) | ||||
−0.234082 | + | 0.972217i | \(0.575209\pi\) | |||||||
\(74\) | −5.00000 | + | 3.46410i | −0.581238 | + | 0.402694i | ||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | −1.00000 | + | 1.73205i | −0.114708 | + | 0.198680i | ||||
\(77\) | 6.00000 | + | 10.3923i | 0.683763 | + | 1.18431i | ||||
\(78\) | 0.500000 | + | 0.866025i | 0.0566139 | + | 0.0980581i | ||||
\(79\) | 8.00000 | + | 13.8564i | 0.900070 | + | 1.55897i | 0.827401 | + | 0.561611i | \(0.189818\pi\) |
0.0726692 | + | 0.997356i | \(0.476848\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.00000 | + | 10.3923i | −0.658586 | + | 1.14070i | 0.322396 | + | 0.946605i | \(0.395512\pi\) |
−0.980982 | + | 0.194099i | \(0.937822\pi\) | |||||||
\(84\) | −4.00000 | −0.436436 | ||||||||
\(85\) | −3.00000 | −0.325396 | ||||||||
\(86\) | −4.00000 | + | 6.92820i | −0.431331 | + | 0.747087i | ||||
\(87\) | 1.50000 | + | 2.59808i | 0.160817 | + | 0.278543i | ||||
\(88\) | 3.00000 | 0.319801 | ||||||||
\(89\) | 3.00000 | − | 5.19615i | 0.317999 | − | 0.550791i | −0.662071 | − | 0.749441i | \(-0.730322\pi\) |
0.980071 | + | 0.198650i | \(0.0636557\pi\) | |||||||
\(90\) | 0.500000 | − | 0.866025i | 0.0527046 | − | 0.0912871i | ||||
\(91\) | −2.00000 | + | 3.46410i | −0.209657 | + | 0.363137i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.00000 | + | 3.46410i | 0.207390 | + | 0.359211i | ||||
\(94\) | 4.50000 | − | 7.79423i | 0.464140 | − | 0.803913i | ||||
\(95\) | 1.00000 | − | 1.73205i | 0.102598 | − | 0.177705i | ||||
\(96\) | −0.500000 | + | 0.866025i | −0.0510310 | + | 0.0883883i | ||||
\(97\) | 2.00000 | 0.203069 | 0.101535 | − | 0.994832i | \(-0.467625\pi\) | ||||
0.101535 | + | 0.994832i | \(0.467625\pi\) | |||||||
\(98\) | −4.50000 | − | 7.79423i | −0.454569 | − | 0.787336i | ||||
\(99\) | −1.50000 | + | 2.59808i | −0.150756 | + | 0.261116i | ||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −9.00000 | −0.895533 | −0.447767 | − | 0.894150i | \(-0.647781\pi\) | ||||
−0.447767 | + | 0.894150i | \(0.647781\pi\) | |||||||
\(102\) | −1.50000 | + | 2.59808i | −0.148522 | + | 0.257248i | ||||
\(103\) | 14.0000 | 1.37946 | 0.689730 | − | 0.724066i | \(-0.257729\pi\) | ||||
0.689730 | + | 0.724066i | \(0.257729\pi\) | |||||||
\(104\) | 0.500000 | + | 0.866025i | 0.0490290 | + | 0.0849208i | ||||
\(105\) | 4.00000 | 0.390360 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(108\) | −0.500000 | − | 0.866025i | −0.0481125 | − | 0.0833333i | ||||
\(109\) | 2.00000 | − | 3.46410i | 0.191565 | − | 0.331801i | −0.754204 | − | 0.656640i | \(-0.771977\pi\) |
0.945769 | + | 0.324840i | \(0.105310\pi\) | |||||||
\(110\) | −3.00000 | −0.286039 | ||||||||
\(111\) | −0.500000 | − | 6.06218i | −0.0474579 | − | 0.575396i | ||||
\(112\) | −4.00000 | −0.377964 | ||||||||
\(113\) | 4.50000 | − | 7.79423i | 0.423324 | − | 0.733219i | −0.572938 | − | 0.819599i | \(-0.694196\pi\) |
0.996262 | + | 0.0863794i | \(0.0275297\pi\) | |||||||
\(114\) | −1.00000 | − | 1.73205i | −0.0936586 | − | 0.162221i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.50000 | + | 2.59808i | 0.139272 | + | 0.241225i | ||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | −1.50000 | − | 2.59808i | −0.138086 | − | 0.239172i | ||||
\(119\) | −12.0000 | −1.10004 | ||||||||
\(120\) | 0.500000 | − | 0.866025i | 0.0456435 | − | 0.0790569i | ||||
\(121\) | −2.00000 | −0.181818 | ||||||||
\(122\) | −10.0000 | −0.905357 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.00000 | + | 3.46410i | 0.179605 | + | 0.311086i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 2.00000 | − | 3.46410i | 0.178174 | − | 0.308607i | ||||
\(127\) | 2.00000 | − | 3.46410i | 0.177471 | − | 0.307389i | −0.763542 | − | 0.645758i | \(-0.776542\pi\) |
0.941014 | + | 0.338368i | \(0.109875\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | −4.00000 | − | 6.92820i | −0.352180 | − | 0.609994i | ||||
\(130\) | −0.500000 | − | 0.866025i | −0.0438529 | − | 0.0759555i | ||||
\(131\) | −1.50000 | + | 2.59808i | −0.131056 | + | 0.226995i | −0.924084 | − | 0.382190i | \(-0.875170\pi\) |
0.793028 | + | 0.609185i | \(0.208503\pi\) | |||||||
\(132\) | −1.50000 | + | 2.59808i | −0.130558 | + | 0.226134i | ||||
\(133\) | 4.00000 | − | 6.92820i | 0.346844 | − | 0.600751i | ||||
\(134\) | −13.0000 | −1.12303 | ||||||||
\(135\) | 0.500000 | + | 0.866025i | 0.0430331 | + | 0.0745356i | ||||
\(136\) | −1.50000 | + | 2.59808i | −0.128624 | + | 0.222783i | ||||
\(137\) | 9.00000 | 0.768922 | 0.384461 | − | 0.923141i | \(-0.374387\pi\) | ||||
0.384461 | + | 0.923141i | \(0.374387\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.0000 | + | 17.3205i | −0.848189 | + | 1.46911i | 0.0346338 | + | 0.999400i | \(0.488974\pi\) |
−0.882823 | + | 0.469706i | \(0.844360\pi\) | |||||||
\(140\) | 4.00000 | 0.338062 | ||||||||
\(141\) | 4.50000 | + | 7.79423i | 0.378968 | + | 0.656392i | ||||
\(142\) | 6.00000 | 0.503509 | ||||||||
\(143\) | 1.50000 | + | 2.59808i | 0.125436 | + | 0.217262i | ||||
\(144\) | −0.500000 | − | 0.866025i | −0.0416667 | − | 0.0721688i | ||||
\(145\) | −1.50000 | − | 2.59808i | −0.124568 | − | 0.215758i | ||||
\(146\) | 2.00000 | − | 3.46410i | 0.165521 | − | 0.286691i | ||||
\(147\) | 9.00000 | 0.742307 | ||||||||
\(148\) | −0.500000 | − | 6.06218i | −0.0410997 | − | 0.498308i | ||||
\(149\) | −15.0000 | −1.22885 | −0.614424 | − | 0.788976i | \(-0.710612\pi\) | ||||
−0.614424 | + | 0.788976i | \(0.710612\pi\) | |||||||
\(150\) | −0.500000 | + | 0.866025i | −0.0408248 | + | 0.0707107i | ||||
\(151\) | −4.00000 | − | 6.92820i | −0.325515 | − | 0.563809i | 0.656101 | − | 0.754673i | \(-0.272204\pi\) |
−0.981617 | + | 0.190864i | \(0.938871\pi\) | |||||||
\(152\) | −1.00000 | − | 1.73205i | −0.0811107 | − | 0.140488i | ||||
\(153\) | −1.50000 | − | 2.59808i | −0.121268 | − | 0.210042i | ||||
\(154\) | −12.0000 | −0.966988 | ||||||||
\(155\) | −2.00000 | − | 3.46410i | −0.160644 | − | 0.278243i | ||||
\(156\) | −1.00000 | −0.0800641 | ||||||||
\(157\) | 9.50000 | − | 16.4545i | 0.758183 | − | 1.31321i | −0.185594 | − | 0.982627i | \(-0.559421\pi\) |
0.943777 | − | 0.330584i | \(-0.107246\pi\) | |||||||
\(158\) | −16.0000 | −1.27289 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.500000 | − | 0.866025i | 0.0395285 | − | 0.0684653i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −5.50000 | + | 9.52628i | −0.430793 | + | 0.746156i | −0.996942 | − | 0.0781474i | \(-0.975100\pi\) |
0.566149 | + | 0.824303i | \(0.308433\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.50000 | − | 2.59808i | 0.116775 | − | 0.202260i | ||||
\(166\) | −6.00000 | − | 10.3923i | −0.465690 | − | 0.806599i | ||||
\(167\) | −4.50000 | − | 7.79423i | −0.348220 | − | 0.603136i | 0.637713 | − | 0.770274i | \(-0.279881\pi\) |
−0.985933 | + | 0.167139i | \(0.946547\pi\) | |||||||
\(168\) | 2.00000 | − | 3.46410i | 0.154303 | − | 0.267261i | ||||
\(169\) | 6.00000 | − | 10.3923i | 0.461538 | − | 0.799408i | ||||
\(170\) | 1.50000 | − | 2.59808i | 0.115045 | − | 0.199263i | ||||
\(171\) | 2.00000 | 0.152944 | ||||||||
\(172\) | −4.00000 | − | 6.92820i | −0.304997 | − | 0.528271i | ||||
\(173\) | 6.00000 | − | 10.3923i | 0.456172 | − | 0.790112i | −0.542583 | − | 0.840002i | \(-0.682554\pi\) |
0.998755 | + | 0.0498898i | \(0.0158870\pi\) | |||||||
\(174\) | −3.00000 | −0.227429 | ||||||||
\(175\) | −4.00000 | −0.302372 | ||||||||
\(176\) | −1.50000 | + | 2.59808i | −0.113067 | + | 0.195837i | ||||
\(177\) | 3.00000 | 0.225494 | ||||||||
\(178\) | 3.00000 | + | 5.19615i | 0.224860 | + | 0.389468i | ||||
\(179\) | −12.0000 | −0.896922 | −0.448461 | − | 0.893802i | \(-0.648028\pi\) | ||||
−0.448461 | + | 0.893802i | \(0.648028\pi\) | |||||||
\(180\) | 0.500000 | + | 0.866025i | 0.0372678 | + | 0.0645497i | ||||
\(181\) | −13.0000 | − | 22.5167i | −0.966282 | − | 1.67365i | −0.706129 | − | 0.708083i | \(-0.749560\pi\) |
−0.260153 | − | 0.965567i | \(-0.583773\pi\) | |||||||
\(182\) | −2.00000 | − | 3.46410i | −0.148250 | − | 0.256776i | ||||
\(183\) | 5.00000 | − | 8.66025i | 0.369611 | − | 0.640184i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.500000 | + | 6.06218i | 0.0367607 | + | 0.445700i | ||||
\(186\) | −4.00000 | −0.293294 | ||||||||
\(187\) | −4.50000 | + | 7.79423i | −0.329073 | + | 0.569970i | ||||
\(188\) | 4.50000 | + | 7.79423i | 0.328196 | + | 0.568453i | ||||
\(189\) | 2.00000 | + | 3.46410i | 0.145479 | + | 0.251976i | ||||
\(190\) | 1.00000 | + | 1.73205i | 0.0725476 | + | 0.125656i | ||||
\(191\) | 24.0000 | 1.73658 | 0.868290 | − | 0.496058i | \(-0.165220\pi\) | ||||
0.868290 | + | 0.496058i | \(0.165220\pi\) | |||||||
\(192\) | −0.500000 | − | 0.866025i | −0.0360844 | − | 0.0625000i | ||||
\(193\) | 8.00000 | 0.575853 | 0.287926 | − | 0.957653i | \(-0.407034\pi\) | ||||
0.287926 | + | 0.957653i | \(0.407034\pi\) | |||||||
\(194\) | −1.00000 | + | 1.73205i | −0.0717958 | + | 0.124354i | ||||
\(195\) | 1.00000 | 0.0716115 | ||||||||
\(196\) | 9.00000 | 0.642857 | ||||||||
\(197\) | 3.00000 | − | 5.19615i | 0.213741 | − | 0.370211i | −0.739141 | − | 0.673550i | \(-0.764768\pi\) |
0.952882 | + | 0.303340i | \(0.0981018\pi\) | |||||||
\(198\) | −1.50000 | − | 2.59808i | −0.106600 | − | 0.184637i | ||||
\(199\) | −7.00000 | −0.496217 | −0.248108 | − | 0.968732i | \(-0.579809\pi\) | ||||
−0.248108 | + | 0.968732i | \(0.579809\pi\) | |||||||
\(200\) | −0.500000 | + | 0.866025i | −0.0353553 | + | 0.0612372i | ||||
\(201\) | 6.50000 | − | 11.2583i | 0.458475 | − | 0.794101i | ||||
\(202\) | 4.50000 | − | 7.79423i | 0.316619 | − | 0.548400i | ||||
\(203\) | −6.00000 | − | 10.3923i | −0.421117 | − | 0.729397i | ||||
\(204\) | −1.50000 | − | 2.59808i | −0.105021 | − | 0.181902i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −7.00000 | + | 12.1244i | −0.487713 | + | 0.844744i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.00000 | −0.0693375 | ||||||||
\(209\) | −3.00000 | − | 5.19615i | −0.207514 | − | 0.359425i | ||||
\(210\) | −2.00000 | + | 3.46410i | −0.138013 | + | 0.239046i | ||||
\(211\) | 8.00000 | 0.550743 | 0.275371 | − | 0.961338i | \(-0.411199\pi\) | ||||
0.275371 | + | 0.961338i | \(0.411199\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.00000 | + | 5.19615i | −0.205557 | + | 0.356034i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.00000 | + | 6.92820i | 0.272798 | + | 0.472500i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −8.00000 | − | 13.8564i | −0.543075 | − | 0.940634i | ||||
\(218\) | 2.00000 | + | 3.46410i | 0.135457 | + | 0.234619i | ||||
\(219\) | 2.00000 | + | 3.46410i | 0.135147 | + | 0.234082i | ||||
\(220\) | 1.50000 | − | 2.59808i | 0.101130 | − | 0.175162i | ||||
\(221\) | −3.00000 | −0.201802 | ||||||||
\(222\) | 5.50000 | + | 2.59808i | 0.369136 | + | 0.174371i | ||||
\(223\) | 20.0000 | 1.33930 | 0.669650 | − | 0.742677i | \(-0.266444\pi\) | ||||
0.669650 | + | 0.742677i | \(0.266444\pi\) | |||||||
\(224\) | 2.00000 | − | 3.46410i | 0.133631 | − | 0.231455i | ||||
\(225\) | −0.500000 | − | 0.866025i | −0.0333333 | − | 0.0577350i | ||||
\(226\) | 4.50000 | + | 7.79423i | 0.299336 | + | 0.518464i | ||||
\(227\) | 12.0000 | + | 20.7846i | 0.796468 | + | 1.37952i | 0.921903 | + | 0.387421i | \(0.126634\pi\) |
−0.125435 | + | 0.992102i | \(0.540033\pi\) | |||||||
\(228\) | 2.00000 | 0.132453 | ||||||||
\(229\) | −7.00000 | − | 12.1244i | −0.462573 | − | 0.801200i | 0.536515 | − | 0.843891i | \(-0.319740\pi\) |
−0.999088 | + | 0.0426906i | \(0.986407\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.00000 | − | 10.3923i | 0.394771 | − | 0.683763i | ||||
\(232\) | −3.00000 | −0.196960 | ||||||||
\(233\) | 6.00000 | 0.393073 | 0.196537 | − | 0.980497i | \(-0.437031\pi\) | ||||
0.196537 | + | 0.980497i | \(0.437031\pi\) | |||||||
\(234\) | 0.500000 | − | 0.866025i | 0.0326860 | − | 0.0566139i | ||||
\(235\) | −4.50000 | − | 7.79423i | −0.293548 | − | 0.508439i | ||||
\(236\) | 3.00000 | 0.195283 | ||||||||
\(237\) | 8.00000 | − | 13.8564i | 0.519656 | − | 0.900070i | ||||
\(238\) | 6.00000 | − | 10.3923i | 0.388922 | − | 0.673633i | ||||
\(239\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(240\) | 0.500000 | + | 0.866025i | 0.0322749 | + | 0.0559017i | ||||
\(241\) | −2.50000 | − | 4.33013i | −0.161039 | − | 0.278928i | 0.774202 | − | 0.632938i | \(-0.218151\pi\) |
−0.935242 | + | 0.354010i | \(0.884818\pi\) | |||||||
\(242\) | 1.00000 | − | 1.73205i | 0.0642824 | − | 0.111340i | ||||
\(243\) | −0.500000 | + | 0.866025i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | 5.00000 | − | 8.66025i | 0.320092 | − | 0.554416i | ||||
\(245\) | −9.00000 | −0.574989 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.00000 | − | 1.73205i | 0.0636285 | − | 0.110208i | ||||
\(248\) | −4.00000 | −0.254000 | ||||||||
\(249\) | 12.0000 | 0.760469 | ||||||||
\(250\) | 0.500000 | − | 0.866025i | 0.0316228 | − | 0.0547723i | ||||
\(251\) | 9.00000 | 0.568075 | 0.284037 | − | 0.958813i | \(-0.408326\pi\) | ||||
0.284037 | + | 0.958813i | \(0.408326\pi\) | |||||||
\(252\) | 2.00000 | + | 3.46410i | 0.125988 | + | 0.218218i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 2.00000 | + | 3.46410i | 0.125491 | + | 0.217357i | ||||
\(255\) | 1.50000 | + | 2.59808i | 0.0939336 | + | 0.162698i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −1.50000 | + | 2.59808i | −0.0935674 | + | 0.162064i | −0.909010 | − | 0.416775i | \(-0.863160\pi\) |
0.815442 | + | 0.578838i | \(0.196494\pi\) | |||||||
\(258\) | 8.00000 | 0.498058 | ||||||||
\(259\) | 2.00000 | + | 24.2487i | 0.124274 | + | 1.50674i | ||||
\(260\) | 1.00000 | 0.0620174 | ||||||||
\(261\) | 1.50000 | − | 2.59808i | 0.0928477 | − | 0.160817i | ||||
\(262\) | −1.50000 | − | 2.59808i | −0.0926703 | − | 0.160510i | ||||
\(263\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(264\) | −1.50000 | − | 2.59808i | −0.0923186 | − | 0.159901i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 4.00000 | + | 6.92820i | 0.245256 | + | 0.424795i | ||||
\(267\) | −6.00000 | −0.367194 | ||||||||
\(268\) | 6.50000 | − | 11.2583i | 0.397051 | − | 0.687712i | ||||
\(269\) | −6.00000 | −0.365826 | −0.182913 | − | 0.983129i | \(-0.558553\pi\) | ||||
−0.182913 | + | 0.983129i | \(0.558553\pi\) | |||||||
\(270\) | −1.00000 | −0.0608581 | ||||||||
\(271\) | 3.50000 | − | 6.06218i | 0.212610 | − | 0.368251i | −0.739921 | − | 0.672694i | \(-0.765137\pi\) |
0.952531 | + | 0.304443i | \(0.0984703\pi\) | |||||||
\(272\) | −1.50000 | − | 2.59808i | −0.0909509 | − | 0.157532i | ||||
\(273\) | 4.00000 | 0.242091 | ||||||||
\(274\) | −4.50000 | + | 7.79423i | −0.271855 | + | 0.470867i | ||||
\(275\) | −1.50000 | + | 2.59808i | −0.0904534 | + | 0.156670i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.50000 | − | 14.7224i | −0.510716 | − | 0.884585i | −0.999923 | − | 0.0124177i | \(-0.996047\pi\) |
0.489207 | − | 0.872167i | \(-0.337286\pi\) | |||||||
\(278\) | −10.0000 | − | 17.3205i | −0.599760 | − | 1.03882i | ||||
\(279\) | 2.00000 | − | 3.46410i | 0.119737 | − | 0.207390i | ||||
\(280\) | −2.00000 | + | 3.46410i | −0.119523 | + | 0.207020i | ||||
\(281\) | −3.00000 | + | 5.19615i | −0.178965 | + | 0.309976i | −0.941526 | − | 0.336939i | \(-0.890608\pi\) |
0.762561 | + | 0.646916i | \(0.223942\pi\) | |||||||
\(282\) | −9.00000 | −0.535942 | ||||||||
\(283\) | 9.50000 | + | 16.4545i | 0.564716 | + | 0.978117i | 0.997076 | + | 0.0764162i | \(0.0243478\pi\) |
−0.432360 | + | 0.901701i | \(0.642319\pi\) | |||||||
\(284\) | −3.00000 | + | 5.19615i | −0.178017 | + | 0.308335i | ||||
\(285\) | −2.00000 | −0.118470 | ||||||||
\(286\) | −3.00000 | −0.177394 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 4.00000 | + | 6.92820i | 0.235294 | + | 0.407541i | ||||
\(290\) | 3.00000 | 0.176166 | ||||||||
\(291\) | −1.00000 | − | 1.73205i | −0.0586210 | − | 0.101535i | ||||
\(292\) | 2.00000 | + | 3.46410i | 0.117041 | + | 0.202721i | ||||
\(293\) | 3.00000 | + | 5.19615i | 0.175262 | + | 0.303562i | 0.940252 | − | 0.340480i | \(-0.110589\pi\) |
−0.764990 | + | 0.644042i | \(0.777256\pi\) | |||||||
\(294\) | −4.50000 | + | 7.79423i | −0.262445 | + | 0.454569i | ||||
\(295\) | −3.00000 | −0.174667 | ||||||||
\(296\) | 5.50000 | + | 2.59808i | 0.319681 | + | 0.151010i | ||||
\(297\) | 3.00000 | 0.174078 | ||||||||
\(298\) | 7.50000 | − | 12.9904i | 0.434463 | − | 0.752513i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −0.500000 | − | 0.866025i | −0.0288675 | − | 0.0500000i | ||||
\(301\) | 16.0000 | + | 27.7128i | 0.922225 | + | 1.59734i | ||||
\(302\) | 8.00000 | 0.460348 | ||||||||
\(303\) | 4.50000 | + | 7.79423i | 0.258518 | + | 0.447767i | ||||
\(304\) | 2.00000 | 0.114708 | ||||||||
\(305\) | −5.00000 | + | 8.66025i | −0.286299 | + | 0.495885i | ||||
\(306\) | 3.00000 | 0.171499 | ||||||||
\(307\) | 8.00000 | 0.456584 | 0.228292 | − | 0.973593i | \(-0.426686\pi\) | ||||
0.228292 | + | 0.973593i | \(0.426686\pi\) | |||||||
\(308\) | 6.00000 | − | 10.3923i | 0.341882 | − | 0.592157i | ||||
\(309\) | −7.00000 | − | 12.1244i | −0.398216 | − | 0.689730i | ||||
\(310\) | 4.00000 | 0.227185 | ||||||||
\(311\) | 3.00000 | − | 5.19615i | 0.170114 | − | 0.294647i | −0.768345 | − | 0.640036i | \(-0.778920\pi\) |
0.938460 | + | 0.345389i | \(0.112253\pi\) | |||||||
\(312\) | 0.500000 | − | 0.866025i | 0.0283069 | − | 0.0490290i | ||||
\(313\) | −7.00000 | + | 12.1244i | −0.395663 | + | 0.685309i | −0.993186 | − | 0.116543i | \(-0.962819\pi\) |
0.597522 | + | 0.801852i | \(0.296152\pi\) | |||||||
\(314\) | 9.50000 | + | 16.4545i | 0.536116 | + | 0.928580i | ||||
\(315\) | −2.00000 | − | 3.46410i | −0.112687 | − | 0.195180i | ||||
\(316\) | 8.00000 | − | 13.8564i | 0.450035 | − | 0.779484i | ||||
\(317\) | 12.0000 | − | 20.7846i | 0.673987 | − | 1.16738i | −0.302777 | − | 0.953062i | \(-0.597914\pi\) |
0.976764 | − | 0.214318i | \(-0.0687530\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.00000 | −0.503903 | ||||||||
\(320\) | 0.500000 | + | 0.866025i | 0.0279508 | + | 0.0484123i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.00000 | 0.333849 | ||||||||
\(324\) | −0.500000 | + | 0.866025i | −0.0277778 | + | 0.0481125i | ||||
\(325\) | −1.00000 | −0.0554700 | ||||||||
\(326\) | −5.50000 | − | 9.52628i | −0.304617 | − | 0.527612i | ||||
\(327\) | −4.00000 | −0.221201 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −18.0000 | − | 31.1769i | −0.992372 | − | 1.71884i | ||||
\(330\) | 1.50000 | + | 2.59808i | 0.0825723 | + | 0.143019i | ||||
\(331\) | 5.00000 | − | 8.66025i | 0.274825 | − | 0.476011i | −0.695266 | − | 0.718752i | \(-0.744713\pi\) |
0.970091 | + | 0.242742i | \(0.0780468\pi\) | |||||||
\(332\) | 12.0000 | 0.658586 | ||||||||
\(333\) | −5.00000 | + | 3.46410i | −0.273998 | + | 0.189832i | ||||
\(334\) | 9.00000 | 0.492458 | ||||||||
\(335\) | −6.50000 | + | 11.2583i | −0.355133 | + | 0.615108i | ||||
\(336\) | 2.00000 | + | 3.46410i | 0.109109 | + | 0.188982i | ||||
\(337\) | −10.0000 | − | 17.3205i | −0.544735 | − | 0.943508i | −0.998624 | − | 0.0524499i | \(-0.983297\pi\) |
0.453889 | − | 0.891058i | \(-0.350036\pi\) | |||||||
\(338\) | 6.00000 | + | 10.3923i | 0.326357 | + | 0.565267i | ||||
\(339\) | −9.00000 | −0.488813 | ||||||||
\(340\) | 1.50000 | + | 2.59808i | 0.0813489 | + | 0.140900i | ||||
\(341\) | −12.0000 | −0.649836 | ||||||||
\(342\) | −1.00000 | + | 1.73205i | −0.0540738 | + | 0.0936586i | ||||
\(343\) | −8.00000 | −0.431959 | ||||||||
\(344\) | 8.00000 | 0.431331 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6.00000 | + | 10.3923i | 0.322562 | + | 0.558694i | ||||
\(347\) | 6.00000 | 0.322097 | 0.161048 | − | 0.986947i | \(-0.448512\pi\) | ||||
0.161048 | + | 0.986947i | \(0.448512\pi\) | |||||||
\(348\) | 1.50000 | − | 2.59808i | 0.0804084 | − | 0.139272i | ||||
\(349\) | 14.0000 | − | 24.2487i | 0.749403 | − | 1.29800i | −0.198706 | − | 0.980059i | \(-0.563674\pi\) |
0.948109 | − | 0.317945i | \(-0.102993\pi\) | |||||||
\(350\) | 2.00000 | − | 3.46410i | 0.106904 | − | 0.185164i | ||||
\(351\) | 0.500000 | + | 0.866025i | 0.0266880 | + | 0.0462250i | ||||
\(352\) | −1.50000 | − | 2.59808i | −0.0799503 | − | 0.138478i | ||||
\(353\) | 3.00000 | − | 5.19615i | 0.159674 | − | 0.276563i | −0.775077 | − | 0.631867i | \(-0.782289\pi\) |
0.934751 | + | 0.355303i | \(0.115622\pi\) | |||||||
\(354\) | −1.50000 | + | 2.59808i | −0.0797241 | + | 0.138086i | ||||
\(355\) | 3.00000 | − | 5.19615i | 0.159223 | − | 0.275783i | ||||
\(356\) | −6.00000 | −0.317999 | ||||||||
\(357\) | 6.00000 | + | 10.3923i | 0.317554 | + | 0.550019i | ||||
\(358\) | 6.00000 | − | 10.3923i | 0.317110 | − | 0.549250i | ||||
\(359\) | −30.0000 | −1.58334 | −0.791670 | − | 0.610949i | \(-0.790788\pi\) | ||||
−0.791670 | + | 0.610949i | \(0.790788\pi\) | |||||||
\(360\) | −1.00000 | −0.0527046 | ||||||||
\(361\) | 7.50000 | − | 12.9904i | 0.394737 | − | 0.683704i | ||||
\(362\) | 26.0000 | 1.36653 | ||||||||
\(363\) | 1.00000 | + | 1.73205i | 0.0524864 | + | 0.0909091i | ||||
\(364\) | 4.00000 | 0.209657 | ||||||||
\(365\) | −2.00000 | − | 3.46410i | −0.104685 | − | 0.181319i | ||||
\(366\) | 5.00000 | + | 8.66025i | 0.261354 | + | 0.452679i | ||||
\(367\) | −10.0000 | − | 17.3205i | −0.521996 | − | 0.904123i | −0.999673 | − | 0.0255875i | \(-0.991854\pi\) |
0.477677 | − | 0.878536i | \(-0.341479\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −5.50000 | − | 2.59808i | −0.285931 | − | 0.135068i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 2.00000 | − | 3.46410i | 0.103695 | − | 0.179605i | ||||
\(373\) | 11.0000 | + | 19.0526i | 0.569558 | + | 0.986504i | 0.996610 | + | 0.0822766i | \(0.0262191\pi\) |
−0.427051 | + | 0.904227i | \(0.640448\pi\) | |||||||
\(374\) | −4.50000 | − | 7.79423i | −0.232689 | − | 0.403030i | ||||
\(375\) | 0.500000 | + | 0.866025i | 0.0258199 | + | 0.0447214i | ||||
\(376\) | −9.00000 | −0.464140 | ||||||||
\(377\) | −1.50000 | − | 2.59808i | −0.0772539 | − | 0.133808i | ||||
\(378\) | −4.00000 | −0.205738 | ||||||||
\(379\) | 8.00000 | − | 13.8564i | 0.410932 | − | 0.711756i | −0.584060 | − | 0.811711i | \(-0.698537\pi\) |
0.994992 | + | 0.0999550i | \(0.0318699\pi\) | |||||||
\(380\) | −2.00000 | −0.102598 | ||||||||
\(381\) | −4.00000 | −0.204926 | ||||||||
\(382\) | −12.0000 | + | 20.7846i | −0.613973 | + | 1.06343i | ||||
\(383\) | 4.50000 | + | 7.79423i | 0.229939 | + | 0.398266i | 0.957790 | − | 0.287469i | \(-0.0928139\pi\) |
−0.727851 | + | 0.685736i | \(0.759481\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −6.00000 | + | 10.3923i | −0.305788 | + | 0.529641i | ||||
\(386\) | −4.00000 | + | 6.92820i | −0.203595 | + | 0.352636i | ||||
\(387\) | −4.00000 | + | 6.92820i | −0.203331 | + | 0.352180i | ||||
\(388\) | −1.00000 | − | 1.73205i | −0.0507673 | − | 0.0879316i | ||||
\(389\) | −15.0000 | − | 25.9808i | −0.760530 | − | 1.31728i | −0.942578 | − | 0.333987i | \(-0.891606\pi\) |
0.182047 | − | 0.983290i | \(-0.441728\pi\) | |||||||
\(390\) | −0.500000 | + | 0.866025i | −0.0253185 | + | 0.0438529i | ||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −4.50000 | + | 7.79423i | −0.227284 | + | 0.393668i | ||||
\(393\) | 3.00000 | 0.151330 | ||||||||
\(394\) | 3.00000 | + | 5.19615i | 0.151138 | + | 0.261778i | ||||
\(395\) | −8.00000 | + | 13.8564i | −0.402524 | + | 0.697191i | ||||
\(396\) | 3.00000 | 0.150756 | ||||||||
\(397\) | −25.0000 | −1.25471 | −0.627357 | − | 0.778732i | \(-0.715863\pi\) | ||||
−0.627357 | + | 0.778732i | \(0.715863\pi\) | |||||||
\(398\) | 3.50000 | − | 6.06218i | 0.175439 | − | 0.303870i | ||||
\(399\) | −8.00000 | −0.400501 | ||||||||
\(400\) | −0.500000 | − | 0.866025i | −0.0250000 | − | 0.0433013i | ||||
\(401\) | 24.0000 | 1.19850 | 0.599251 | − | 0.800561i | \(-0.295465\pi\) | ||||
0.599251 | + | 0.800561i | \(0.295465\pi\) | |||||||
\(402\) | 6.50000 | + | 11.2583i | 0.324191 | + | 0.561514i | ||||
\(403\) | −2.00000 | − | 3.46410i | −0.0996271 | − | 0.172559i | ||||
\(404\) | 4.50000 | + | 7.79423i | 0.223883 | + | 0.387777i | ||||
\(405\) | 0.500000 | − | 0.866025i | 0.0248452 | − | 0.0430331i | ||||
\(406\) | 12.0000 | 0.595550 | ||||||||
\(407\) | 16.5000 | + | 7.79423i | 0.817875 | + | 0.386346i | ||||
\(408\) | 3.00000 | 0.148522 | ||||||||
\(409\) | −5.50000 | + | 9.52628i | −0.271957 | + | 0.471044i | −0.969363 | − | 0.245633i | \(-0.921004\pi\) |
0.697406 | + | 0.716677i | \(0.254338\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.50000 | − | 7.79423i | −0.221969 | − | 0.384461i | ||||
\(412\) | −7.00000 | − | 12.1244i | −0.344865 | − | 0.597324i | ||||
\(413\) | −12.0000 | −0.590481 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.0000 | −0.589057 | ||||||||
\(416\) | 0.500000 | − | 0.866025i | 0.0245145 | − | 0.0424604i | ||||
\(417\) | 20.0000 | 0.979404 | ||||||||
\(418\) | 6.00000 | 0.293470 | ||||||||
\(419\) | 18.0000 | − | 31.1769i | 0.879358 | − | 1.52309i | 0.0273103 | − | 0.999627i | \(-0.491306\pi\) |
0.852047 | − | 0.523465i | \(-0.175361\pi\) | |||||||
\(420\) | −2.00000 | − | 3.46410i | −0.0975900 | − | 0.169031i | ||||
\(421\) | −10.0000 | −0.487370 | −0.243685 | − | 0.969854i | \(-0.578356\pi\) | ||||
−0.243685 | + | 0.969854i | \(0.578356\pi\) | |||||||
\(422\) | −4.00000 | + | 6.92820i | −0.194717 | + | 0.337260i | ||||
\(423\) | 4.50000 | − | 7.79423i | 0.218797 | − | 0.378968i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.50000 | − | 2.59808i | −0.0727607 | − | 0.126025i | ||||
\(426\) | −3.00000 | − | 5.19615i | −0.145350 | − | 0.251754i | ||||
\(427\) | −20.0000 | + | 34.6410i | −0.967868 | + | 1.67640i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.50000 | − | 2.59808i | 0.0724207 | − | 0.125436i | ||||
\(430\) | −8.00000 | −0.385794 | ||||||||
\(431\) | −15.0000 | − | 25.9808i | −0.722525 | − | 1.25145i | −0.959985 | − | 0.280052i | \(-0.909648\pi\) |
0.237460 | − | 0.971397i | \(-0.423685\pi\) | |||||||
\(432\) | −0.500000 | + | 0.866025i | −0.0240563 | + | 0.0416667i | ||||
\(433\) | −16.0000 | −0.768911 | −0.384455 | − | 0.923144i | \(-0.625611\pi\) | ||||
−0.384455 | + | 0.923144i | \(0.625611\pi\) | |||||||
\(434\) | 16.0000 | 0.768025 | ||||||||
\(435\) | −1.50000 | + | 2.59808i | −0.0719195 | + | 0.124568i | ||||
\(436\) | −4.00000 | −0.191565 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −4.00000 | −0.191127 | ||||||||
\(439\) | 6.50000 | + | 11.2583i | 0.310228 | + | 0.537331i | 0.978412 | − | 0.206666i | \(-0.0662612\pi\) |
−0.668184 | + | 0.743996i | \(0.732928\pi\) | |||||||
\(440\) | 1.50000 | + | 2.59808i | 0.0715097 | + | 0.123858i | ||||
\(441\) | −4.50000 | − | 7.79423i | −0.214286 | − | 0.371154i | ||||
\(442\) | 1.50000 | − | 2.59808i | 0.0713477 | − | 0.123578i | ||||
\(443\) | −12.0000 | −0.570137 | −0.285069 | − | 0.958507i | \(-0.592016\pi\) | ||||
−0.285069 | + | 0.958507i | \(0.592016\pi\) | |||||||
\(444\) | −5.00000 | + | 3.46410i | −0.237289 | + | 0.164399i | ||||
\(445\) | 6.00000 | 0.284427 | ||||||||
\(446\) | −10.0000 | + | 17.3205i | −0.473514 | + | 0.820150i | ||||
\(447\) | 7.50000 | + | 12.9904i | 0.354738 | + | 0.614424i | ||||
\(448\) | 2.00000 | + | 3.46410i | 0.0944911 | + | 0.163663i | ||||
\(449\) | 18.0000 | + | 31.1769i | 0.849473 | + | 1.47133i | 0.881680 | + | 0.471848i | \(0.156413\pi\) |
−0.0322072 | + | 0.999481i | \(0.510254\pi\) | |||||||
\(450\) | 1.00000 | 0.0471405 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −9.00000 | −0.423324 | ||||||||
\(453\) | −4.00000 | + | 6.92820i | −0.187936 | + | 0.325515i | ||||
\(454\) | −24.0000 | −1.12638 | ||||||||
\(455\) | −4.00000 | −0.187523 | ||||||||
\(456\) | −1.00000 | + | 1.73205i | −0.0468293 | + | 0.0811107i | ||||
\(457\) | −4.00000 | − | 6.92820i | −0.187112 | − | 0.324088i | 0.757174 | − | 0.653213i | \(-0.226579\pi\) |
−0.944286 | + | 0.329125i | \(0.893246\pi\) | |||||||
\(458\) | 14.0000 | 0.654177 | ||||||||
\(459\) | −1.50000 | + | 2.59808i | −0.0700140 | + | 0.121268i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.50000 | − | 12.9904i | 0.349310 | − | 0.605022i | −0.636817 | − | 0.771015i | \(-0.719749\pi\) |
0.986127 | + | 0.165992i | \(0.0530827\pi\) | |||||||
\(462\) | 6.00000 | + | 10.3923i | 0.279145 | + | 0.483494i | ||||
\(463\) | 11.0000 | + | 19.0526i | 0.511213 | + | 0.885448i | 0.999916 | + | 0.0129968i | \(0.00413714\pi\) |
−0.488702 | + | 0.872451i | \(0.662530\pi\) | |||||||
\(464\) | 1.50000 | − | 2.59808i | 0.0696358 | − | 0.120613i | ||||
\(465\) | −2.00000 | + | 3.46410i | −0.0927478 | + | 0.160644i | ||||
\(466\) | −3.00000 | + | 5.19615i | −0.138972 | + | 0.240707i | ||||
\(467\) | −6.00000 | −0.277647 | −0.138823 | − | 0.990317i | \(-0.544332\pi\) | ||||
−0.138823 | + | 0.990317i | \(0.544332\pi\) | |||||||
\(468\) | 0.500000 | + | 0.866025i | 0.0231125 | + | 0.0400320i | ||||
\(469\) | −26.0000 | + | 45.0333i | −1.20057 | + | 2.07945i | ||||
\(470\) | 9.00000 | 0.415139 | ||||||||
\(471\) | −19.0000 | −0.875474 | ||||||||
\(472\) | −1.50000 | + | 2.59808i | −0.0690431 | + | 0.119586i | ||||
\(473\) | 24.0000 | 1.10352 | ||||||||
\(474\) | 8.00000 | + | 13.8564i | 0.367452 | + | 0.636446i | ||||
\(475\) | 2.00000 | 0.0917663 | ||||||||
\(476\) | 6.00000 | + | 10.3923i | 0.275010 | + | 0.476331i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9.00000 | − | 15.5885i | 0.411220 | − | 0.712255i | −0.583803 | − | 0.811895i | \(-0.698436\pi\) |
0.995023 | + | 0.0996406i | \(0.0317693\pi\) | |||||||
\(480\) | −1.00000 | −0.0456435 | ||||||||
\(481\) | 0.500000 | + | 6.06218i | 0.0227980 | + | 0.276412i | ||||
\(482\) | 5.00000 | 0.227744 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | + | 1.73205i | 0.0454545 | + | 0.0787296i | ||||
\(485\) | 1.00000 | + | 1.73205i | 0.0454077 | + | 0.0786484i | ||||
\(486\) | −0.500000 | − | 0.866025i | −0.0226805 | − | 0.0392837i | ||||
\(487\) | −34.0000 | −1.54069 | −0.770344 | − | 0.637629i | \(-0.779915\pi\) | ||||
−0.770344 | + | 0.637629i | \(0.779915\pi\) | |||||||
\(488\) | 5.00000 | + | 8.66025i | 0.226339 | + | 0.392031i | ||||
\(489\) | 11.0000 | 0.497437 | ||||||||
\(490\) | 4.50000 | − | 7.79423i | 0.203289 | − | 0.352107i | ||||
\(491\) | −12.0000 | −0.541552 | −0.270776 | − | 0.962642i | \(-0.587280\pi\) | ||||
−0.270776 | + | 0.962642i | \(0.587280\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.50000 | − | 7.79423i | 0.202670 | − | 0.351034i | ||||
\(494\) | 1.00000 | + | 1.73205i | 0.0449921 | + | 0.0779287i | ||||
\(495\) | −3.00000 | −0.134840 | ||||||||
\(496\) | 2.00000 | − | 3.46410i | 0.0898027 | − | 0.155543i | ||||
\(497\) | 12.0000 | − | 20.7846i | 0.538274 | − | 0.932317i | ||||
\(498\) | −6.00000 | + | 10.3923i | −0.268866 | + | 0.465690i | ||||
\(499\) | 11.0000 | + | 19.0526i | 0.492428 | + | 0.852910i | 0.999962 | − | 0.00872186i | \(-0.00277629\pi\) |
−0.507534 | + | 0.861632i | \(0.669443\pi\) | |||||||
\(500\) | 0.500000 | + | 0.866025i | 0.0223607 | + | 0.0387298i | ||||
\(501\) | −4.50000 | + | 7.79423i | −0.201045 | + | 0.348220i | ||||
\(502\) | −4.50000 | + | 7.79423i | −0.200845 | + | 0.347873i | ||||
\(503\) | 10.5000 | − | 18.1865i | 0.468172 | − | 0.810897i | −0.531167 | − | 0.847267i | \(-0.678246\pi\) |
0.999338 | + | 0.0363700i | \(0.0115795\pi\) | |||||||
\(504\) | −4.00000 | −0.178174 | ||||||||
\(505\) | −4.50000 | − | 7.79423i | −0.200247 | − | 0.346839i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.0000 | −0.532939 | ||||||||
\(508\) | −4.00000 | −0.177471 | ||||||||
\(509\) | 9.00000 | − | 15.5885i | 0.398918 | − | 0.690946i | −0.594675 | − | 0.803966i | \(-0.702719\pi\) |
0.993593 | + | 0.113020i | \(0.0360525\pi\) | |||||||
\(510\) | −3.00000 | −0.132842 | ||||||||
\(511\) | −8.00000 | − | 13.8564i | −0.353899 | − | 0.612971i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −1.00000 | − | 1.73205i | −0.0441511 | − | 0.0764719i | ||||
\(514\) | −1.50000 | − | 2.59808i | −0.0661622 | − | 0.114596i | ||||
\(515\) | 7.00000 | + | 12.1244i | 0.308457 | + | 0.534263i | ||||
\(516\) | −4.00000 | + | 6.92820i | −0.176090 | + | 0.304997i | ||||
\(517\) | −27.0000 | −1.18746 | ||||||||
\(518\) | −22.0000 | − | 10.3923i | −0.966625 | − | 0.456612i | ||||
\(519\) | −12.0000 | −0.526742 | ||||||||
\(520\) | −0.500000 | + | 0.866025i | −0.0219265 | + | 0.0379777i | ||||
\(521\) | 18.0000 | + | 31.1769i | 0.788594 | + | 1.36589i | 0.926828 | + | 0.375486i | \(0.122524\pi\) |
−0.138234 | + | 0.990400i | \(0.544143\pi\) | |||||||
\(522\) | 1.50000 | + | 2.59808i | 0.0656532 | + | 0.113715i | ||||
\(523\) | 8.00000 | + | 13.8564i | 0.349816 | + | 0.605898i | 0.986216 | − | 0.165460i | \(-0.0529109\pi\) |
−0.636401 | + | 0.771358i | \(0.719578\pi\) | |||||||
\(524\) | 3.00000 | 0.131056 | ||||||||
\(525\) | 2.00000 | + | 3.46410i | 0.0872872 | + | 0.151186i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.00000 | − | 10.3923i | 0.261364 | − | 0.452696i | ||||
\(528\) | 3.00000 | 0.130558 | ||||||||
\(529\) | −23.0000 | −1.00000 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.50000 | − | 2.59808i | −0.0650945 | − | 0.112747i | ||||
\(532\) | −8.00000 | −0.346844 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 3.00000 | − | 5.19615i | 0.129823 | − | 0.224860i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 6.50000 | + | 11.2583i | 0.280757 | + | 0.486286i | ||||
\(537\) | 6.00000 | + | 10.3923i | 0.258919 | + | 0.448461i | ||||
\(538\) | 3.00000 | − | 5.19615i | 0.129339 | − | 0.224022i | ||||
\(539\) | −13.5000 | + | 23.3827i | −0.581486 | + | 1.00716i | ||||
\(540\) | 0.500000 | − | 0.866025i | 0.0215166 | − | 0.0372678i | ||||
\(541\) | 26.0000 | 1.11783 | 0.558914 | − | 0.829226i | \(-0.311218\pi\) | ||||
0.558914 | + | 0.829226i | \(0.311218\pi\) | |||||||
\(542\) | 3.50000 | + | 6.06218i | 0.150338 | + | 0.260393i | ||||
\(543\) | −13.0000 | + | 22.5167i | −0.557883 | + | 0.966282i | ||||
\(544\) | 3.00000 | 0.128624 | ||||||||
\(545\) | 4.00000 | 0.171341 | ||||||||
\(546\) | −2.00000 | + | 3.46410i | −0.0855921 | + | 0.148250i | ||||
\(547\) | −28.0000 | −1.19719 | −0.598597 | − | 0.801050i | \(-0.704275\pi\) | ||||
−0.598597 | + | 0.801050i | \(0.704275\pi\) | |||||||
\(548\) | −4.50000 | − | 7.79423i | −0.192230 | − | 0.332953i | ||||
\(549\) | −10.0000 | −0.426790 | ||||||||
\(550\) | −1.50000 | − | 2.59808i | −0.0639602 | − | 0.110782i | ||||
\(551\) | 3.00000 | + | 5.19615i | 0.127804 | + | 0.221364i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −32.0000 | + | 55.4256i | −1.36078 | + | 2.35694i | ||||
\(554\) | 17.0000 | 0.722261 | ||||||||
\(555\) | 5.00000 | − | 3.46410i | 0.212238 | − | 0.147043i | ||||
\(556\) | 20.0000 | 0.848189 | ||||||||
\(557\) | −3.00000 | + | 5.19615i | −0.127114 | + | 0.220168i | −0.922557 | − | 0.385860i | \(-0.873905\pi\) |
0.795443 | + | 0.606028i | \(0.207238\pi\) | |||||||
\(558\) | 2.00000 | + | 3.46410i | 0.0846668 | + | 0.146647i | ||||
\(559\) | 4.00000 | + | 6.92820i | 0.169182 | + | 0.293032i | ||||
\(560\) | −2.00000 | − | 3.46410i | −0.0845154 | − | 0.146385i | ||||
\(561\) | 9.00000 | 0.379980 | ||||||||
\(562\) | −3.00000 | − | 5.19615i | −0.126547 | − | 0.219186i | ||||
\(563\) | −42.0000 | −1.77009 | −0.885044 | − | 0.465506i | \(-0.845872\pi\) | ||||
−0.885044 | + | 0.465506i | \(0.845872\pi\) | |||||||
\(564\) | 4.50000 | − | 7.79423i | 0.189484 | − | 0.328196i | ||||
\(565\) | 9.00000 | 0.378633 | ||||||||
\(566\) | −19.0000 | −0.798630 | ||||||||
\(567\) | 2.00000 | − | 3.46410i | 0.0839921 | − | 0.145479i | ||||
\(568\) | −3.00000 | − | 5.19615i | −0.125877 | − | 0.218026i | ||||
\(569\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(570\) | 1.00000 | − | 1.73205i | 0.0418854 | − | 0.0725476i | ||||
\(571\) | −1.00000 | + | 1.73205i | −0.0418487 | + | 0.0724841i | −0.886191 | − | 0.463320i | \(-0.846658\pi\) |
0.844342 | + | 0.535804i | \(0.179991\pi\) | |||||||
\(572\) | 1.50000 | − | 2.59808i | 0.0627182 | − | 0.108631i | ||||
\(573\) | −12.0000 | − | 20.7846i | −0.501307 | − | 0.868290i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | −1.00000 | + | 1.73205i | −0.0416305 | + | 0.0721062i | −0.886090 | − | 0.463513i | \(-0.846589\pi\) |
0.844459 | + | 0.535620i | \(0.179922\pi\) | |||||||
\(578\) | −8.00000 | −0.332756 | ||||||||
\(579\) | −4.00000 | − | 6.92820i | −0.166234 | − | 0.287926i | ||||
\(580\) | −1.50000 | + | 2.59808i | −0.0622841 | + | 0.107879i | ||||
\(581\) | −48.0000 | −1.99138 | ||||||||
\(582\) | 2.00000 | 0.0829027 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −4.00000 | −0.165521 | ||||||||
\(585\) | −0.500000 | − | 0.866025i | −0.0206725 | − | 0.0358057i | ||||
\(586\) | −6.00000 | −0.247858 | ||||||||
\(587\) | −12.0000 | − | 20.7846i | −0.495293 | − | 0.857873i | 0.504692 | − | 0.863299i | \(-0.331606\pi\) |
−0.999985 | + | 0.00542667i | \(0.998273\pi\) | |||||||
\(588\) | −4.50000 | − | 7.79423i | −0.185577 | − | 0.321429i | ||||
\(589\) | 4.00000 | + | 6.92820i | 0.164817 | + | 0.285472i | ||||
\(590\) | 1.50000 | − | 2.59808i | 0.0617540 | − | 0.106961i | ||||
\(591\) | −6.00000 | −0.246807 | ||||||||
\(592\) | −5.00000 | + | 3.46410i | −0.205499 | + | 0.142374i | ||||
\(593\) | 39.0000 | 1.60154 | 0.800769 | − | 0.598973i | \(-0.204424\pi\) | ||||
0.800769 | + | 0.598973i | \(0.204424\pi\) | |||||||
\(594\) | −1.50000 | + | 2.59808i | −0.0615457 | + | 0.106600i | ||||
\(595\) | −6.00000 | − | 10.3923i | −0.245976 | − | 0.426043i | ||||
\(596\) | 7.50000 | + | 12.9904i | 0.307212 | + | 0.532107i | ||||
\(597\) | 3.50000 | + | 6.06218i | 0.143245 | + | 0.248108i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(600\) | 1.00000 | 0.0408248 | ||||||||
\(601\) | 21.5000 | − | 37.2391i | 0.877003 | − | 1.51901i | 0.0223900 | − | 0.999749i | \(-0.492872\pi\) |
0.854613 | − | 0.519265i | \(-0.173794\pi\) | |||||||
\(602\) | −32.0000 | −1.30422 | ||||||||
\(603\) | −13.0000 | −0.529401 | ||||||||
\(604\) | −4.00000 | + | 6.92820i | −0.162758 | + | 0.281905i | ||||
\(605\) | −1.00000 | − | 1.73205i | −0.0406558 | − | 0.0704179i | ||||
\(606\) | −9.00000 | −0.365600 | ||||||||
\(607\) | 11.0000 | − | 19.0526i | 0.446476 | − | 0.773320i | −0.551678 | − | 0.834058i | \(-0.686012\pi\) |
0.998154 | + | 0.0607380i | \(0.0193454\pi\) | |||||||
\(608\) | −1.00000 | + | 1.73205i | −0.0405554 | + | 0.0702439i | ||||
\(609\) | −6.00000 | + | 10.3923i | −0.243132 | + | 0.421117i | ||||
\(610\) | −5.00000 | − | 8.66025i | −0.202444 | − | 0.350643i | ||||
\(611\) | −4.50000 | − | 7.79423i | −0.182051 | − | 0.315321i | ||||
\(612\) | −1.50000 | + | 2.59808i | −0.0606339 | + | 0.105021i | ||||
\(613\) | −5.50000 | + | 9.52628i | −0.222143 | + | 0.384763i | −0.955458 | − | 0.295126i | \(-0.904638\pi\) |
0.733316 | + | 0.679888i | \(0.237972\pi\) | |||||||
\(614\) | −4.00000 | + | 6.92820i | −0.161427 | + | 0.279600i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.00000 | + | 10.3923i | 0.241747 | + | 0.418718i | ||||
\(617\) | 13.5000 | − | 23.3827i | 0.543490 | − | 0.941351i | −0.455211 | − | 0.890384i | \(-0.650436\pi\) |
0.998700 | − | 0.0509678i | \(-0.0162306\pi\) | |||||||
\(618\) | 14.0000 | 0.563163 | ||||||||
\(619\) | 20.0000 | 0.803868 | 0.401934 | − | 0.915669i | \(-0.368338\pi\) | ||||
0.401934 | + | 0.915669i | \(0.368338\pi\) | |||||||
\(620\) | −2.00000 | + | 3.46410i | −0.0803219 | + | 0.139122i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 3.00000 | + | 5.19615i | 0.120289 | + | 0.208347i | ||||
\(623\) | 24.0000 | 0.961540 | ||||||||
\(624\) | 0.500000 | + | 0.866025i | 0.0200160 | + | 0.0346688i | ||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | −7.00000 | − | 12.1244i | −0.279776 | − | 0.484587i | ||||
\(627\) | −3.00000 | + | 5.19615i | −0.119808 | + | 0.207514i | ||||
\(628\) | −19.0000 | −0.758183 | ||||||||
\(629\) | −15.0000 | + | 10.3923i | −0.598089 | + | 0.414368i | ||||
\(630\) | 4.00000 | 0.159364 | ||||||||
\(631\) | 18.5000 | − | 32.0429i | 0.736473 | − | 1.27561i | −0.217601 | − | 0.976038i | \(-0.569823\pi\) |
0.954074 | − | 0.299571i | \(-0.0968437\pi\) | |||||||
\(632\) | 8.00000 | + | 13.8564i | 0.318223 | + | 0.551178i | ||||
\(633\) | −4.00000 | − | 6.92820i | −0.158986 | − | 0.275371i | ||||
\(634\) | 12.0000 | + | 20.7846i | 0.476581 | + | 0.825462i | ||||
\(635\) | 4.00000 | 0.158735 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −9.00000 | −0.356593 | ||||||||
\(638\) | 4.50000 | − | 7.79423i | 0.178157 | − | 0.308576i | ||||
\(639\) | 6.00000 | 0.237356 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | 9.00000 | − | 15.5885i | 0.355479 | − | 0.615707i | −0.631721 | − | 0.775196i | \(-0.717651\pi\) |
0.987200 | + | 0.159489i | \(0.0509845\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −25.0000 | −0.985904 | −0.492952 | − | 0.870057i | \(-0.664082\pi\) | ||||
−0.492952 | + | 0.870057i | \(0.664082\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.00000 | − | 6.92820i | 0.157500 | − | 0.272798i | ||||
\(646\) | −3.00000 | + | 5.19615i | −0.118033 | + | 0.204440i | ||||
\(647\) | 1.50000 | + | 2.59808i | 0.0589711 | + | 0.102141i | 0.894004 | − | 0.448059i | \(-0.147885\pi\) |
−0.835033 | + | 0.550200i | \(0.814551\pi\) | |||||||
\(648\) | −0.500000 | − | 0.866025i | −0.0196419 | − | 0.0340207i | ||||
\(649\) | −4.50000 | + | 7.79423i | −0.176640 | + | 0.305950i | ||||
\(650\) | 0.500000 | − | 0.866025i | 0.0196116 | − | 0.0339683i | ||||
\(651\) | −8.00000 | + | 13.8564i | −0.313545 | + | 0.543075i | ||||
\(652\) | 11.0000 | 0.430793 | ||||||||
\(653\) | 24.0000 | + | 41.5692i | 0.939193 | + | 1.62673i | 0.766982 | + | 0.641669i | \(0.221758\pi\) |
0.172211 | + | 0.985060i | \(0.444909\pi\) | |||||||
\(654\) | 2.00000 | − | 3.46410i | 0.0782062 | − | 0.135457i | ||||
\(655\) | −3.00000 | −0.117220 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.00000 | − | 3.46410i | 0.0780274 | − | 0.135147i | ||||
\(658\) | 36.0000 | 1.40343 | ||||||||
\(659\) | 13.5000 | + | 23.3827i | 0.525885 | + | 0.910860i | 0.999545 | + | 0.0301523i | \(0.00959924\pi\) |
−0.473660 | + | 0.880708i | \(0.657067\pi\) | |||||||
\(660\) | −3.00000 | −0.116775 | ||||||||
\(661\) | 2.00000 | + | 3.46410i | 0.0777910 | + | 0.134738i | 0.902297 | − | 0.431116i | \(-0.141880\pi\) |
−0.824506 | + | 0.565854i | \(0.808547\pi\) | |||||||
\(662\) | 5.00000 | + | 8.66025i | 0.194331 | + | 0.336590i | ||||
\(663\) | 1.50000 | + | 2.59808i | 0.0582552 | + | 0.100901i | ||||
\(664\) | −6.00000 | + | 10.3923i | −0.232845 | + | 0.403300i | ||||
\(665\) | 8.00000 | 0.310227 | ||||||||
\(666\) | −0.500000 | − | 6.06218i | −0.0193746 | − | 0.234905i | ||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −4.50000 | + | 7.79423i | −0.174110 | + | 0.301568i | ||||
\(669\) | −10.0000 | − | 17.3205i | −0.386622 | − | 0.669650i | ||||
\(670\) | −6.50000 | − | 11.2583i | −0.251117 | − | 0.434947i | ||||
\(671\) | 15.0000 | + | 25.9808i | 0.579069 | + | 1.00298i | ||||
\(672\) | −4.00000 | −0.154303 | ||||||||
\(673\) | −4.00000 | − | 6.92820i | −0.154189 | − | 0.267063i | 0.778575 | − | 0.627552i | \(-0.215943\pi\) |
−0.932763 | + | 0.360489i | \(0.882610\pi\) | |||||||
\(674\) | 20.0000 | 0.770371 | ||||||||
\(675\) | −0.500000 | + | 0.866025i | −0.0192450 | + | 0.0333333i | ||||
\(676\) | −12.0000 | −0.461538 | ||||||||
\(677\) | 6.00000 | 0.230599 | 0.115299 | − | 0.993331i | \(-0.463217\pi\) | ||||
0.115299 | + | 0.993331i | \(0.463217\pi\) | |||||||
\(678\) | 4.50000 | − | 7.79423i | 0.172821 | − | 0.299336i | ||||
\(679\) | 4.00000 | + | 6.92820i | 0.153506 | + | 0.265880i | ||||
\(680\) | −3.00000 | −0.115045 | ||||||||
\(681\) | 12.0000 | − | 20.7846i | 0.459841 | − | 0.796468i | ||||
\(682\) | 6.00000 | − | 10.3923i | 0.229752 | − | 0.397942i | ||||
\(683\) | −9.00000 | + | 15.5885i | −0.344375 | + | 0.596476i | −0.985240 | − | 0.171178i | \(-0.945243\pi\) |
0.640865 | + | 0.767654i | \(0.278576\pi\) | |||||||
\(684\) | −1.00000 | − | 1.73205i | −0.0382360 | − | 0.0662266i | ||||
\(685\) | 4.50000 | + | 7.79423i | 0.171936 | + | 0.297802i | ||||
\(686\) | 4.00000 | − | 6.92820i | 0.152721 | − | 0.264520i | ||||
\(687\) | −7.00000 | + | 12.1244i | −0.267067 | + | 0.462573i | ||||
\(688\) | −4.00000 | + | 6.92820i | −0.152499 | + | 0.264135i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.00000 | − | 8.66025i | 0.190209 | − | 0.329452i | −0.755110 | − | 0.655598i | \(-0.772417\pi\) |
0.945319 | + | 0.326146i | \(0.105750\pi\) | |||||||
\(692\) | −12.0000 | −0.456172 | ||||||||
\(693\) | −12.0000 | −0.455842 | ||||||||
\(694\) | −3.00000 | + | 5.19615i | −0.113878 | + | 0.197243i | ||||
\(695\) | −20.0000 | −0.758643 | ||||||||
\(696\) | 1.50000 | + | 2.59808i | 0.0568574 | + | 0.0984798i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 14.0000 | + | 24.2487i | 0.529908 | + | 0.917827i | ||||
\(699\) | −3.00000 | − | 5.19615i | −0.113470 | − | 0.196537i | ||||
\(700\) | 2.00000 | + | 3.46410i | 0.0755929 | + | 0.130931i | ||||
\(701\) | 1.50000 | − | 2.59808i | 0.0566542 | − | 0.0981280i | −0.836307 | − | 0.548261i | \(-0.815290\pi\) |
0.892962 | + | 0.450133i | \(0.148623\pi\) | |||||||
\(702\) | −1.00000 | −0.0377426 | ||||||||
\(703\) | −1.00000 | − | 12.1244i | −0.0377157 | − | 0.457279i | ||||
\(704\) | 3.00000 | 0.113067 | ||||||||
\(705\) | −4.50000 | + | 7.79423i | −0.169480 | + | 0.293548i | ||||
\(706\) | 3.00000 | + | 5.19615i | 0.112906 | + | 0.195560i | ||||
\(707\) | −18.0000 | − | 31.1769i | −0.676960 | − | 1.17253i | ||||
\(708\) | −1.50000 | − | 2.59808i | −0.0563735 | − | 0.0976417i | ||||
\(709\) | 38.0000 | 1.42712 | 0.713560 | − | 0.700594i | \(-0.247082\pi\) | ||||
0.713560 | + | 0.700594i | \(0.247082\pi\) | |||||||
\(710\) | 3.00000 | + | 5.19615i | 0.112588 | + | 0.195008i | ||||
\(711\) | −16.0000 | −0.600047 | ||||||||
\(712\) | 3.00000 | − | 5.19615i | 0.112430 | − | 0.194734i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | −12.0000 | −0.449089 | ||||||||
\(715\) | −1.50000 | + | 2.59808i | −0.0560968 | + | 0.0971625i | ||||
\(716\) | 6.00000 | + | 10.3923i | 0.224231 | + | 0.388379i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 15.0000 | − | 25.9808i | 0.559795 | − | 0.969593i | ||||
\(719\) | −24.0000 | + | 41.5692i | −0.895049 | + | 1.55027i | −0.0613050 | + | 0.998119i | \(0.519526\pi\) |
−0.833744 | + | 0.552151i | \(0.813807\pi\) | |||||||
\(720\) | 0.500000 | − | 0.866025i | 0.0186339 | − | 0.0322749i | ||||
\(721\) | 28.0000 | + | 48.4974i | 1.04277 | + | 1.80614i | ||||
\(722\) | 7.50000 | + | 12.9904i | 0.279121 | + | 0.483452i | ||||
\(723\) | −2.50000 | + | 4.33013i | −0.0929760 | + | 0.161039i | ||||
\(724\) | −13.0000 | + | 22.5167i | −0.483141 | + | 0.836825i | ||||
\(725\) | 1.50000 | − | 2.59808i | 0.0557086 | − | 0.0964901i | ||||
\(726\) | −2.00000 | −0.0742270 | ||||||||
\(727\) | 2.00000 | + | 3.46410i | 0.0741759 | + | 0.128476i | 0.900728 | − | 0.434384i | \(-0.143034\pi\) |
−0.826552 | + | 0.562861i | \(0.809701\pi\) | |||||||
\(728\) | −2.00000 | + | 3.46410i | −0.0741249 | + | 0.128388i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 4.00000 | 0.148047 | ||||||||
\(731\) | −12.0000 | + | 20.7846i | −0.443836 | + | 0.768747i | ||||
\(732\) | −10.0000 | −0.369611 | ||||||||
\(733\) | −2.50000 | − | 4.33013i | −0.0923396 | − | 0.159937i | 0.816156 | − | 0.577832i | \(-0.196101\pi\) |
−0.908495 | + | 0.417895i | \(0.862768\pi\) | |||||||
\(734\) | 20.0000 | 0.738213 | ||||||||
\(735\) | 4.50000 | + | 7.79423i | 0.165985 | + | 0.287494i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 19.5000 | + | 33.7750i | 0.718292 | + | 1.24412i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 38.0000 | 1.39785 | 0.698926 | − | 0.715194i | \(-0.253662\pi\) | ||||
0.698926 | + | 0.715194i | \(0.253662\pi\) | |||||||
\(740\) | 5.00000 | − | 3.46410i | 0.183804 | − | 0.127343i | ||||
\(741\) | −2.00000 | −0.0734718 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 25.5000 | + | 44.1673i | 0.935504 | + | 1.62034i | 0.773732 | + | 0.633513i | \(0.218388\pi\) |
0.161772 | + | 0.986828i | \(0.448279\pi\) | |||||||
\(744\) | 2.00000 | + | 3.46410i | 0.0733236 | + | 0.127000i | ||||
\(745\) | −7.50000 | − | 12.9904i | −0.274779 | − | 0.475931i | ||||
\(746\) | −22.0000 | −0.805477 | ||||||||
\(747\) | −6.00000 | − | 10.3923i | −0.219529 | − | 0.380235i | ||||
\(748\) | 9.00000 | 0.329073 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −1.00000 | −0.0365148 | ||||||||
\(751\) | −43.0000 | −1.56909 | −0.784546 | − | 0.620070i | \(-0.787104\pi\) | ||||
−0.784546 | + | 0.620070i | \(0.787104\pi\) | |||||||
\(752\) | 4.50000 | − | 7.79423i | 0.164098 | − | 0.284226i | ||||
\(753\) | −4.50000 | − | 7.79423i | −0.163989 | − | 0.284037i | ||||
\(754\) | 3.00000 | 0.109254 | ||||||||
\(755\) | 4.00000 | − | 6.92820i | 0.145575 | − | 0.252143i | ||||
\(756\) | 2.00000 | − | 3.46410i | 0.0727393 | − | 0.125988i | ||||
\(757\) | 11.0000 | − | 19.0526i | 0.399802 | − | 0.692477i | −0.593899 | − | 0.804539i | \(-0.702412\pi\) |
0.993701 | + | 0.112062i | \(0.0357456\pi\) | |||||||
\(758\) | 8.00000 | + | 13.8564i | 0.290573 | + | 0.503287i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.00000 | − | 1.73205i | 0.0362738 | − | 0.0628281i | ||||
\(761\) | 3.00000 | − | 5.19615i | 0.108750 | − | 0.188360i | −0.806514 | − | 0.591215i | \(-0.798649\pi\) |
0.915264 | + | 0.402854i | \(0.131982\pi\) | |||||||
\(762\) | 2.00000 | − | 3.46410i | 0.0724524 | − | 0.125491i | ||||
\(763\) | 16.0000 | 0.579239 | ||||||||
\(764\) | −12.0000 | − | 20.7846i | −0.434145 | − | 0.751961i | ||||
\(765\) | 1.50000 | − | 2.59808i | 0.0542326 | − | 0.0939336i | ||||
\(766\) | −9.00000 | −0.325183 | ||||||||
\(767\) | −3.00000 | −0.108324 | ||||||||
\(768\) | −0.500000 | + | 0.866025i | −0.0180422 | + | 0.0312500i | ||||
\(769\) | −13.0000 | −0.468792 | −0.234396 | − | 0.972141i | \(-0.575311\pi\) | ||||
−0.234396 | + | 0.972141i | \(0.575311\pi\) | |||||||
\(770\) | −6.00000 | − | 10.3923i | −0.216225 | − | 0.374513i | ||||
\(771\) | 3.00000 | 0.108042 | ||||||||
\(772\) | −4.00000 | − | 6.92820i | −0.143963 | − | 0.249351i | ||||
\(773\) | −6.00000 | − | 10.3923i | −0.215805 | − | 0.373785i | 0.737716 | − | 0.675111i | \(-0.235904\pi\) |
−0.953521 | + | 0.301326i | \(0.902571\pi\) | |||||||
\(774\) | −4.00000 | − | 6.92820i |