Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1014,2,Mod(361,1014)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1014, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1014.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1014 = 2 \cdot 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1014.i (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.09683076496\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 78) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 823.2 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1014.823 |
Dual form | 1014.2.i.d.361.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times\).
\(n\) | \(677\) | \(847\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | + | 0.500000i | 0.612372 | + | 0.353553i | ||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | ||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | 2.00000i | 0.894427i | 0.894427 | + | 0.447214i | \(0.147584\pi\) | ||||
−0.894427 | + | 0.447214i | \(0.852416\pi\) | |||||||
\(6\) | 0.866025 | − | 0.500000i | 0.353553 | − | 0.204124i | ||||
\(7\) | −3.46410 | + | 2.00000i | −1.30931 | + | 0.755929i | −0.981981 | − | 0.188982i | \(-0.939481\pi\) |
−0.327327 | + | 0.944911i | \(0.606148\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | −1.00000 | + | 1.73205i | −0.316228 | + | 0.547723i | ||||
\(11\) | −3.46410 | − | 2.00000i | −1.04447 | − | 0.603023i | −0.123371 | − | 0.992361i | \(-0.539370\pi\) |
−0.921095 | + | 0.389338i | \(0.872704\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −4.00000 | −1.06904 | ||||||||
\(15\) | 1.73205 | + | 1.00000i | 0.447214 | + | 0.258199i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 1.00000 | + | 1.73205i | 0.242536 | + | 0.420084i | 0.961436 | − | 0.275029i | \(-0.0886875\pi\) |
−0.718900 | + | 0.695113i | \(0.755354\pi\) | |||||||
\(18\) | − | 1.00000i | − | 0.235702i | ||||||
\(19\) | −6.92820 | + | 4.00000i | −1.58944 | + | 0.917663i | −0.596040 | + | 0.802955i | \(0.703260\pi\) |
−0.993399 | + | 0.114708i | \(0.963407\pi\) | |||||||
\(20\) | −1.73205 | + | 1.00000i | −0.387298 | + | 0.223607i | ||||
\(21\) | 4.00000i | 0.872872i | ||||||||
\(22\) | −2.00000 | − | 3.46410i | −0.426401 | − | 0.738549i | ||||
\(23\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(24\) | 0.866025 | + | 0.500000i | 0.176777 | + | 0.102062i | ||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −3.46410 | − | 2.00000i | −0.654654 | − | 0.377964i | ||||
\(29\) | −3.00000 | + | 5.19615i | −0.557086 | + | 0.964901i | 0.440652 | + | 0.897678i | \(0.354747\pi\) |
−0.997738 | + | 0.0672232i | \(0.978586\pi\) | |||||||
\(30\) | 1.00000 | + | 1.73205i | 0.182574 | + | 0.316228i | ||||
\(31\) | − | 4.00000i | − | 0.718421i | −0.933257 | − | 0.359211i | \(-0.883046\pi\) | ||
0.933257 | − | 0.359211i | \(-0.116954\pi\) | |||||||
\(32\) | −0.866025 | + | 0.500000i | −0.153093 | + | 0.0883883i | ||||
\(33\) | −3.46410 | + | 2.00000i | −0.603023 | + | 0.348155i | ||||
\(34\) | 2.00000i | 0.342997i | ||||||||
\(35\) | −4.00000 | − | 6.92820i | −0.676123 | − | 1.17108i | ||||
\(36\) | 0.500000 | − | 0.866025i | 0.0833333 | − | 0.144338i | ||||
\(37\) | −1.73205 | − | 1.00000i | −0.284747 | − | 0.164399i | 0.350823 | − | 0.936442i | \(-0.385902\pi\) |
−0.635571 | + | 0.772043i | \(0.719235\pi\) | |||||||
\(38\) | −8.00000 | −1.29777 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.00000 | −0.316228 | ||||||||
\(41\) | 8.66025 | + | 5.00000i | 1.35250 | + | 0.780869i | 0.988600 | − | 0.150567i | \(-0.0481100\pi\) |
0.363905 | + | 0.931436i | \(0.381443\pi\) | |||||||
\(42\) | −2.00000 | + | 3.46410i | −0.308607 | + | 0.534522i | ||||
\(43\) | 2.00000 | + | 3.46410i | 0.304997 | + | 0.528271i | 0.977261 | − | 0.212041i | \(-0.0680112\pi\) |
−0.672264 | + | 0.740312i | \(0.734678\pi\) | |||||||
\(44\) | − | 4.00000i | − | 0.603023i | ||||||
\(45\) | 1.73205 | − | 1.00000i | 0.258199 | − | 0.149071i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 8.00000i | − | 1.16692i | −0.812142 | − | 0.583460i | \(-0.801699\pi\) | ||
0.812142 | − | 0.583460i | \(-0.198301\pi\) | |||||||
\(48\) | 0.500000 | + | 0.866025i | 0.0721688 | + | 0.125000i | ||||
\(49\) | 4.50000 | − | 7.79423i | 0.642857 | − | 1.11346i | ||||
\(50\) | 0.866025 | + | 0.500000i | 0.122474 | + | 0.0707107i | ||||
\(51\) | 2.00000 | 0.280056 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.0000 | −1.37361 | −0.686803 | − | 0.726844i | \(-0.740986\pi\) | ||||
−0.686803 | + | 0.726844i | \(0.740986\pi\) | |||||||
\(54\) | −0.866025 | − | 0.500000i | −0.117851 | − | 0.0680414i | ||||
\(55\) | 4.00000 | − | 6.92820i | 0.539360 | − | 0.934199i | ||||
\(56\) | −2.00000 | − | 3.46410i | −0.267261 | − | 0.462910i | ||||
\(57\) | 8.00000i | 1.05963i | ||||||||
\(58\) | −5.19615 | + | 3.00000i | −0.682288 | + | 0.393919i | ||||
\(59\) | −3.46410 | + | 2.00000i | −0.450988 | + | 0.260378i | −0.708247 | − | 0.705965i | \(-0.750514\pi\) |
0.257260 | + | 0.966342i | \(0.417180\pi\) | |||||||
\(60\) | 2.00000i | 0.258199i | ||||||||
\(61\) | 1.00000 | + | 1.73205i | 0.128037 | + | 0.221766i | 0.922916 | − | 0.385002i | \(-0.125799\pi\) |
−0.794879 | + | 0.606768i | \(0.792466\pi\) | |||||||
\(62\) | 2.00000 | − | 3.46410i | 0.254000 | − | 0.439941i | ||||
\(63\) | 3.46410 | + | 2.00000i | 0.436436 | + | 0.251976i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −4.00000 | −0.492366 | ||||||||
\(67\) | 13.8564 | + | 8.00000i | 1.69283 | + | 0.977356i | 0.952217 | + | 0.305424i | \(0.0987981\pi\) |
0.740613 | + | 0.671932i | \(0.234535\pi\) | |||||||
\(68\) | −1.00000 | + | 1.73205i | −0.121268 | + | 0.210042i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | − | 8.00000i | − | 0.956183i | ||||||
\(71\) | −6.92820 | + | 4.00000i | −0.822226 | + | 0.474713i | −0.851184 | − | 0.524868i | \(-0.824115\pi\) |
0.0289572 | + | 0.999581i | \(0.490781\pi\) | |||||||
\(72\) | 0.866025 | − | 0.500000i | 0.102062 | − | 0.0589256i | ||||
\(73\) | − | 2.00000i | − | 0.234082i | −0.993127 | − | 0.117041i | \(-0.962659\pi\) | ||
0.993127 | − | 0.117041i | \(-0.0373409\pi\) | |||||||
\(74\) | −1.00000 | − | 1.73205i | −0.116248 | − | 0.201347i | ||||
\(75\) | 0.500000 | − | 0.866025i | 0.0577350 | − | 0.100000i | ||||
\(76\) | −6.92820 | − | 4.00000i | −0.794719 | − | 0.458831i | ||||
\(77\) | 16.0000 | 1.82337 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.00000 | 0.900070 | 0.450035 | − | 0.893011i | \(-0.351411\pi\) | ||||
0.450035 | + | 0.893011i | \(0.351411\pi\) | |||||||
\(80\) | −1.73205 | − | 1.00000i | −0.193649 | − | 0.111803i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 5.00000 | + | 8.66025i | 0.552158 | + | 0.956365i | ||||
\(83\) | 12.0000i | 1.31717i | 0.752506 | + | 0.658586i | \(0.228845\pi\) | ||||
−0.752506 | + | 0.658586i | \(0.771155\pi\) | |||||||
\(84\) | −3.46410 | + | 2.00000i | −0.377964 | + | 0.218218i | ||||
\(85\) | −3.46410 | + | 2.00000i | −0.375735 | + | 0.216930i | ||||
\(86\) | 4.00000i | 0.431331i | ||||||||
\(87\) | 3.00000 | + | 5.19615i | 0.321634 | + | 0.557086i | ||||
\(88\) | 2.00000 | − | 3.46410i | 0.213201 | − | 0.369274i | ||||
\(89\) | 12.1244 | + | 7.00000i | 1.28518 | + | 0.741999i | 0.977790 | − | 0.209585i | \(-0.0672115\pi\) |
0.307389 | + | 0.951584i | \(0.400545\pi\) | |||||||
\(90\) | 2.00000 | 0.210819 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.46410 | − | 2.00000i | −0.359211 | − | 0.207390i | ||||
\(94\) | 4.00000 | − | 6.92820i | 0.412568 | − | 0.714590i | ||||
\(95\) | −8.00000 | − | 13.8564i | −0.820783 | − | 1.42164i | ||||
\(96\) | 1.00000i | 0.102062i | ||||||||
\(97\) | 8.66025 | − | 5.00000i | 0.879316 | − | 0.507673i | 0.00888289 | − | 0.999961i | \(-0.497172\pi\) |
0.870433 | + | 0.492287i | \(0.163839\pi\) | |||||||
\(98\) | 7.79423 | − | 4.50000i | 0.787336 | − | 0.454569i | ||||
\(99\) | 4.00000i | 0.402015i | ||||||||
\(100\) | 0.500000 | + | 0.866025i | 0.0500000 | + | 0.0866025i | ||||
\(101\) | −1.00000 | + | 1.73205i | −0.0995037 | + | 0.172345i | −0.911479 | − | 0.411346i | \(-0.865059\pi\) |
0.811976 | + | 0.583691i | \(0.198392\pi\) | |||||||
\(102\) | 1.73205 | + | 1.00000i | 0.171499 | + | 0.0990148i | ||||
\(103\) | −16.0000 | −1.57653 | −0.788263 | − | 0.615338i | \(-0.789020\pi\) | ||||
−0.788263 | + | 0.615338i | \(0.789020\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −8.00000 | −0.780720 | ||||||||
\(106\) | −8.66025 | − | 5.00000i | −0.841158 | − | 0.485643i | ||||
\(107\) | −6.00000 | + | 10.3923i | −0.580042 | + | 1.00466i | 0.415432 | + | 0.909624i | \(0.363630\pi\) |
−0.995474 | + | 0.0950377i | \(0.969703\pi\) | |||||||
\(108\) | −0.500000 | − | 0.866025i | −0.0481125 | − | 0.0833333i | ||||
\(109\) | − | 2.00000i | − | 0.191565i | −0.995402 | − | 0.0957826i | \(-0.969465\pi\) | ||
0.995402 | − | 0.0957826i | \(-0.0305354\pi\) | |||||||
\(110\) | 6.92820 | − | 4.00000i | 0.660578 | − | 0.381385i | ||||
\(111\) | −1.73205 | + | 1.00000i | −0.164399 | + | 0.0949158i | ||||
\(112\) | − | 4.00000i | − | 0.377964i | ||||||
\(113\) | 3.00000 | + | 5.19615i | 0.282216 | + | 0.488813i | 0.971930 | − | 0.235269i | \(-0.0755971\pi\) |
−0.689714 | + | 0.724082i | \(0.742264\pi\) | |||||||
\(114\) | −4.00000 | + | 6.92820i | −0.374634 | + | 0.648886i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −6.00000 | −0.557086 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −4.00000 | −0.368230 | ||||||||
\(119\) | −6.92820 | − | 4.00000i | −0.635107 | − | 0.366679i | ||||
\(120\) | −1.00000 | + | 1.73205i | −0.0912871 | + | 0.158114i | ||||
\(121\) | 2.50000 | + | 4.33013i | 0.227273 | + | 0.393648i | ||||
\(122\) | 2.00000i | 0.181071i | ||||||||
\(123\) | 8.66025 | − | 5.00000i | 0.780869 | − | 0.450835i | ||||
\(124\) | 3.46410 | − | 2.00000i | 0.311086 | − | 0.179605i | ||||
\(125\) | 12.0000i | 1.07331i | ||||||||
\(126\) | 2.00000 | + | 3.46410i | 0.178174 | + | 0.308607i | ||||
\(127\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(128\) | −0.866025 | − | 0.500000i | −0.0765466 | − | 0.0441942i | ||||
\(129\) | 4.00000 | 0.352180 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.00000 | 0.349482 | 0.174741 | − | 0.984614i | \(-0.444091\pi\) | ||||
0.174741 | + | 0.984614i | \(0.444091\pi\) | |||||||
\(132\) | −3.46410 | − | 2.00000i | −0.301511 | − | 0.174078i | ||||
\(133\) | 16.0000 | − | 27.7128i | 1.38738 | − | 2.40301i | ||||
\(134\) | 8.00000 | + | 13.8564i | 0.691095 | + | 1.19701i | ||||
\(135\) | − | 2.00000i | − | 0.172133i | ||||||
\(136\) | −1.73205 | + | 1.00000i | −0.148522 | + | 0.0857493i | ||||
\(137\) | 8.66025 | − | 5.00000i | 0.739895 | − | 0.427179i | −0.0821359 | − | 0.996621i | \(-0.526174\pi\) |
0.822031 | + | 0.569442i | \(0.192841\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.00000 | − | 10.3923i | −0.508913 | − | 0.881464i | −0.999947 | − | 0.0103230i | \(-0.996714\pi\) |
0.491033 | − | 0.871141i | \(-0.336619\pi\) | |||||||
\(140\) | 4.00000 | − | 6.92820i | 0.338062 | − | 0.585540i | ||||
\(141\) | −6.92820 | − | 4.00000i | −0.583460 | − | 0.336861i | ||||
\(142\) | −8.00000 | −0.671345 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −10.3923 | − | 6.00000i | −0.863034 | − | 0.498273i | ||||
\(146\) | 1.00000 | − | 1.73205i | 0.0827606 | − | 0.143346i | ||||
\(147\) | −4.50000 | − | 7.79423i | −0.371154 | − | 0.642857i | ||||
\(148\) | − | 2.00000i | − | 0.164399i | ||||||
\(149\) | −5.19615 | + | 3.00000i | −0.425685 | + | 0.245770i | −0.697507 | − | 0.716578i | \(-0.745707\pi\) |
0.271821 | + | 0.962348i | \(0.412374\pi\) | |||||||
\(150\) | 0.866025 | − | 0.500000i | 0.0707107 | − | 0.0408248i | ||||
\(151\) | − | 12.0000i | − | 0.976546i | −0.872691 | − | 0.488273i | \(-0.837627\pi\) | ||
0.872691 | − | 0.488273i | \(-0.162373\pi\) | |||||||
\(152\) | −4.00000 | − | 6.92820i | −0.324443 | − | 0.561951i | ||||
\(153\) | 1.00000 | − | 1.73205i | 0.0808452 | − | 0.140028i | ||||
\(154\) | 13.8564 | + | 8.00000i | 1.11658 | + | 0.644658i | ||||
\(155\) | 8.00000 | 0.642575 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.0000 | 1.11732 | 0.558661 | − | 0.829396i | \(-0.311315\pi\) | ||||
0.558661 | + | 0.829396i | \(0.311315\pi\) | |||||||
\(158\) | 6.92820 | + | 4.00000i | 0.551178 | + | 0.318223i | ||||
\(159\) | −5.00000 | + | 8.66025i | −0.396526 | + | 0.686803i | ||||
\(160\) | −1.00000 | − | 1.73205i | −0.0790569 | − | 0.136931i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −0.866025 | + | 0.500000i | −0.0680414 | + | 0.0392837i | ||||
\(163\) | 13.8564 | − | 8.00000i | 1.08532 | − | 0.626608i | 0.152992 | − | 0.988227i | \(-0.451109\pi\) |
0.932326 | + | 0.361619i | \(0.117776\pi\) | |||||||
\(164\) | 10.0000i | 0.780869i | ||||||||
\(165\) | −4.00000 | − | 6.92820i | −0.311400 | − | 0.539360i | ||||
\(166\) | −6.00000 | + | 10.3923i | −0.465690 | + | 0.806599i | ||||
\(167\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(168\) | −4.00000 | −0.308607 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −4.00000 | −0.306786 | ||||||||
\(171\) | 6.92820 | + | 4.00000i | 0.529813 | + | 0.305888i | ||||
\(172\) | −2.00000 | + | 3.46410i | −0.152499 | + | 0.264135i | ||||
\(173\) | −5.00000 | − | 8.66025i | −0.380143 | − | 0.658427i | 0.610939 | − | 0.791677i | \(-0.290792\pi\) |
−0.991082 | + | 0.133250i | \(0.957459\pi\) | |||||||
\(174\) | 6.00000i | 0.454859i | ||||||||
\(175\) | −3.46410 | + | 2.00000i | −0.261861 | + | 0.151186i | ||||
\(176\) | 3.46410 | − | 2.00000i | 0.261116 | − | 0.150756i | ||||
\(177\) | 4.00000i | 0.300658i | ||||||||
\(178\) | 7.00000 | + | 12.1244i | 0.524672 | + | 0.908759i | ||||
\(179\) | −6.00000 | + | 10.3923i | −0.448461 | + | 0.776757i | −0.998286 | − | 0.0585225i | \(-0.981361\pi\) |
0.549825 | + | 0.835280i | \(0.314694\pi\) | |||||||
\(180\) | 1.73205 | + | 1.00000i | 0.129099 | + | 0.0745356i | ||||
\(181\) | 10.0000 | 0.743294 | 0.371647 | − | 0.928374i | \(-0.378793\pi\) | ||||
0.371647 | + | 0.928374i | \(0.378793\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.00000 | 0.147844 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.00000 | − | 3.46410i | 0.147043 | − | 0.254686i | ||||
\(186\) | −2.00000 | − | 3.46410i | −0.146647 | − | 0.254000i | ||||
\(187\) | − | 8.00000i | − | 0.585018i | ||||||
\(188\) | 6.92820 | − | 4.00000i | 0.505291 | − | 0.291730i | ||||
\(189\) | 3.46410 | − | 2.00000i | 0.251976 | − | 0.145479i | ||||
\(190\) | − | 16.0000i | − | 1.16076i | ||||||
\(191\) | 4.00000 | + | 6.92820i | 0.289430 | + | 0.501307i | 0.973674 | − | 0.227946i | \(-0.0732010\pi\) |
−0.684244 | + | 0.729253i | \(0.739868\pi\) | |||||||
\(192\) | −0.500000 | + | 0.866025i | −0.0360844 | + | 0.0625000i | ||||
\(193\) | −12.1244 | − | 7.00000i | −0.872730 | − | 0.503871i | −0.00447566 | − | 0.999990i | \(-0.501425\pi\) |
−0.868255 | + | 0.496119i | \(0.834758\pi\) | |||||||
\(194\) | 10.0000 | 0.717958 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 9.00000 | 0.642857 | ||||||||
\(197\) | −15.5885 | − | 9.00000i | −1.11063 | − | 0.641223i | −0.171639 | − | 0.985160i | \(-0.554906\pi\) |
−0.938993 | + | 0.343937i | \(0.888239\pi\) | |||||||
\(198\) | −2.00000 | + | 3.46410i | −0.142134 | + | 0.246183i | ||||
\(199\) | −4.00000 | − | 6.92820i | −0.283552 | − | 0.491127i | 0.688705 | − | 0.725042i | \(-0.258180\pi\) |
−0.972257 | + | 0.233915i | \(0.924846\pi\) | |||||||
\(200\) | 1.00000i | 0.0707107i | ||||||||
\(201\) | 13.8564 | − | 8.00000i | 0.977356 | − | 0.564276i | ||||
\(202\) | −1.73205 | + | 1.00000i | −0.121867 | + | 0.0703598i | ||||
\(203\) | − | 24.0000i | − | 1.68447i | ||||||
\(204\) | 1.00000 | + | 1.73205i | 0.0700140 | + | 0.121268i | ||||
\(205\) | −10.0000 | + | 17.3205i | −0.698430 | + | 1.20972i | ||||
\(206\) | −13.8564 | − | 8.00000i | −0.965422 | − | 0.557386i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 32.0000 | 2.21349 | ||||||||
\(210\) | −6.92820 | − | 4.00000i | −0.478091 | − | 0.276026i | ||||
\(211\) | −6.00000 | + | 10.3923i | −0.413057 | + | 0.715436i | −0.995222 | − | 0.0976347i | \(-0.968872\pi\) |
0.582165 | + | 0.813070i | \(0.302206\pi\) | |||||||
\(212\) | −5.00000 | − | 8.66025i | −0.343401 | − | 0.594789i | ||||
\(213\) | 8.00000i | 0.548151i | ||||||||
\(214\) | −10.3923 | + | 6.00000i | −0.710403 | + | 0.410152i | ||||
\(215\) | −6.92820 | + | 4.00000i | −0.472500 | + | 0.272798i | ||||
\(216\) | − | 1.00000i | − | 0.0680414i | ||||||
\(217\) | 8.00000 | + | 13.8564i | 0.543075 | + | 0.940634i | ||||
\(218\) | 1.00000 | − | 1.73205i | 0.0677285 | − | 0.117309i | ||||
\(219\) | −1.73205 | − | 1.00000i | −0.117041 | − | 0.0675737i | ||||
\(220\) | 8.00000 | 0.539360 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −2.00000 | −0.134231 | ||||||||
\(223\) | 3.46410 | + | 2.00000i | 0.231973 | + | 0.133930i | 0.611482 | − | 0.791258i | \(-0.290574\pi\) |
−0.379509 | + | 0.925188i | \(0.623907\pi\) | |||||||
\(224\) | 2.00000 | − | 3.46410i | 0.133631 | − | 0.231455i | ||||
\(225\) | −0.500000 | − | 0.866025i | −0.0333333 | − | 0.0577350i | ||||
\(226\) | 6.00000i | 0.399114i | ||||||||
\(227\) | 17.3205 | − | 10.0000i | 1.14960 | − | 0.663723i | 0.200812 | − | 0.979630i | \(-0.435642\pi\) |
0.948790 | + | 0.315906i | \(0.102309\pi\) | |||||||
\(228\) | −6.92820 | + | 4.00000i | −0.458831 | + | 0.264906i | ||||
\(229\) | − | 22.0000i | − | 1.45380i | −0.686743 | − | 0.726900i | \(-0.740960\pi\) | ||
0.686743 | − | 0.726900i | \(-0.259040\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.00000 | − | 13.8564i | 0.526361 | − | 0.911685i | ||||
\(232\) | −5.19615 | − | 3.00000i | −0.341144 | − | 0.196960i | ||||
\(233\) | −18.0000 | −1.17922 | −0.589610 | − | 0.807688i | \(-0.700718\pi\) | ||||
−0.589610 | + | 0.807688i | \(0.700718\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 16.0000 | 1.04372 | ||||||||
\(236\) | −3.46410 | − | 2.00000i | −0.225494 | − | 0.130189i | ||||
\(237\) | 4.00000 | − | 6.92820i | 0.259828 | − | 0.450035i | ||||
\(238\) | −4.00000 | − | 6.92820i | −0.259281 | − | 0.449089i | ||||
\(239\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(240\) | −1.73205 | + | 1.00000i | −0.111803 | + | 0.0645497i | ||||
\(241\) | −8.66025 | + | 5.00000i | −0.557856 | + | 0.322078i | −0.752285 | − | 0.658838i | \(-0.771048\pi\) |
0.194429 | + | 0.980917i | \(0.437715\pi\) | |||||||
\(242\) | 5.00000i | 0.321412i | ||||||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | −1.00000 | + | 1.73205i | −0.0640184 | + | 0.110883i | ||||
\(245\) | 15.5885 | + | 9.00000i | 0.995910 | + | 0.574989i | ||||
\(246\) | 10.0000 | 0.637577 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 4.00000 | 0.254000 | ||||||||
\(249\) | 10.3923 | + | 6.00000i | 0.658586 | + | 0.380235i | ||||
\(250\) | −6.00000 | + | 10.3923i | −0.379473 | + | 0.657267i | ||||
\(251\) | 2.00000 | + | 3.46410i | 0.126239 | + | 0.218652i | 0.922217 | − | 0.386674i | \(-0.126376\pi\) |
−0.795978 | + | 0.605326i | \(0.793043\pi\) | |||||||
\(252\) | 4.00000i | 0.251976i | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.00000i | 0.250490i | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −3.00000 | + | 5.19615i | −0.187135 | + | 0.324127i | −0.944294 | − | 0.329104i | \(-0.893253\pi\) |
0.757159 | + | 0.653231i | \(0.226587\pi\) | |||||||
\(258\) | 3.46410 | + | 2.00000i | 0.215666 | + | 0.124515i | ||||
\(259\) | 8.00000 | 0.497096 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.00000 | 0.371391 | ||||||||
\(262\) | 3.46410 | + | 2.00000i | 0.214013 | + | 0.123560i | ||||
\(263\) | −4.00000 | + | 6.92820i | −0.246651 | + | 0.427211i | −0.962594 | − | 0.270947i | \(-0.912663\pi\) |
0.715944 | + | 0.698158i | \(0.245997\pi\) | |||||||
\(264\) | −2.00000 | − | 3.46410i | −0.123091 | − | 0.213201i | ||||
\(265\) | − | 20.0000i | − | 1.22859i | ||||||
\(266\) | 27.7128 | − | 16.0000i | 1.69918 | − | 0.981023i | ||||
\(267\) | 12.1244 | − | 7.00000i | 0.741999 | − | 0.428393i | ||||
\(268\) | 16.0000i | 0.977356i | ||||||||
\(269\) | 13.0000 | + | 22.5167i | 0.792624 | + | 1.37287i | 0.924337 | + | 0.381577i | \(0.124619\pi\) |
−0.131713 | + | 0.991288i | \(0.542048\pi\) | |||||||
\(270\) | 1.00000 | − | 1.73205i | 0.0608581 | − | 0.105409i | ||||
\(271\) | −3.46410 | − | 2.00000i | −0.210429 | − | 0.121491i | 0.391082 | − | 0.920356i | \(-0.372101\pi\) |
−0.601511 | + | 0.798865i | \(0.705434\pi\) | |||||||
\(272\) | −2.00000 | −0.121268 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 10.0000 | 0.604122 | ||||||||
\(275\) | −3.46410 | − | 2.00000i | −0.208893 | − | 0.120605i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.0000 | + | 19.0526i | 0.660926 | + | 1.14476i | 0.980373 | + | 0.197153i | \(0.0631696\pi\) |
−0.319447 | + | 0.947604i | \(0.603497\pi\) | |||||||
\(278\) | − | 12.0000i | − | 0.719712i | ||||||
\(279\) | −3.46410 | + | 2.00000i | −0.207390 | + | 0.119737i | ||||
\(280\) | 6.92820 | − | 4.00000i | 0.414039 | − | 0.239046i | ||||
\(281\) | 26.0000i | 1.55103i | 0.631329 | + | 0.775515i | \(0.282510\pi\) | ||||
−0.631329 | + | 0.775515i | \(0.717490\pi\) | |||||||
\(282\) | −4.00000 | − | 6.92820i | −0.238197 | − | 0.412568i | ||||
\(283\) | −2.00000 | + | 3.46410i | −0.118888 | + | 0.205919i | −0.919327 | − | 0.393494i | \(-0.871266\pi\) |
0.800439 | + | 0.599414i | \(0.204600\pi\) | |||||||
\(284\) | −6.92820 | − | 4.00000i | −0.411113 | − | 0.237356i | ||||
\(285\) | −16.0000 | −0.947758 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −40.0000 | −2.36113 | ||||||||
\(288\) | 0.866025 | + | 0.500000i | 0.0510310 | + | 0.0294628i | ||||
\(289\) | 6.50000 | − | 11.2583i | 0.382353 | − | 0.662255i | ||||
\(290\) | −6.00000 | − | 10.3923i | −0.352332 | − | 0.610257i | ||||
\(291\) | − | 10.0000i | − | 0.586210i | ||||||
\(292\) | 1.73205 | − | 1.00000i | 0.101361 | − | 0.0585206i | ||||
\(293\) | −22.5167 | + | 13.0000i | −1.31544 | + | 0.759468i | −0.982991 | − | 0.183654i | \(-0.941207\pi\) |
−0.332446 | + | 0.943122i | \(0.607874\pi\) | |||||||
\(294\) | − | 9.00000i | − | 0.524891i | ||||||
\(295\) | −4.00000 | − | 6.92820i | −0.232889 | − | 0.403376i | ||||
\(296\) | 1.00000 | − | 1.73205i | 0.0581238 | − | 0.100673i | ||||
\(297\) | 3.46410 | + | 2.00000i | 0.201008 | + | 0.116052i | ||||
\(298\) | −6.00000 | −0.347571 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 1.00000 | 0.0577350 | ||||||||
\(301\) | −13.8564 | − | 8.00000i | −0.798670 | − | 0.461112i | ||||
\(302\) | 6.00000 | − | 10.3923i | 0.345261 | − | 0.598010i | ||||
\(303\) | 1.00000 | + | 1.73205i | 0.0574485 | + | 0.0995037i | ||||
\(304\) | − | 8.00000i | − | 0.458831i | ||||||
\(305\) | −3.46410 | + | 2.00000i | −0.198354 | + | 0.114520i | ||||
\(306\) | 1.73205 | − | 1.00000i | 0.0990148 | − | 0.0571662i | ||||
\(307\) | 8.00000i | 0.456584i | 0.973593 | + | 0.228292i | \(0.0733141\pi\) | ||||
−0.973593 | + | 0.228292i | \(0.926686\pi\) | |||||||
\(308\) | 8.00000 | + | 13.8564i | 0.455842 | + | 0.789542i | ||||
\(309\) | −8.00000 | + | 13.8564i | −0.455104 | + | 0.788263i | ||||
\(310\) | 6.92820 | + | 4.00000i | 0.393496 | + | 0.227185i | ||||
\(311\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.00000 | −0.339140 | −0.169570 | − | 0.985518i | \(-0.554238\pi\) | ||||
−0.169570 | + | 0.985518i | \(0.554238\pi\) | |||||||
\(314\) | 12.1244 | + | 7.00000i | 0.684217 | + | 0.395033i | ||||
\(315\) | −4.00000 | + | 6.92820i | −0.225374 | + | 0.390360i | ||||
\(316\) | 4.00000 | + | 6.92820i | 0.225018 | + | 0.389742i | ||||
\(317\) | − | 6.00000i | − | 0.336994i | −0.985702 | − | 0.168497i | \(-0.946109\pi\) | ||
0.985702 | − | 0.168497i | \(-0.0538913\pi\) | |||||||
\(318\) | −8.66025 | + | 5.00000i | −0.485643 | + | 0.280386i | ||||
\(319\) | 20.7846 | − | 12.0000i | 1.16371 | − | 0.671871i | ||||
\(320\) | − | 2.00000i | − | 0.111803i | ||||||
\(321\) | 6.00000 | + | 10.3923i | 0.334887 | + | 0.580042i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −13.8564 | − | 8.00000i | −0.770991 | − | 0.445132i | ||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 16.0000 | 0.886158 | ||||||||
\(327\) | −1.73205 | − | 1.00000i | −0.0957826 | − | 0.0553001i | ||||
\(328\) | −5.00000 | + | 8.66025i | −0.276079 | + | 0.478183i | ||||
\(329\) | 16.0000 | + | 27.7128i | 0.882109 | + | 1.52786i | ||||
\(330\) | − | 8.00000i | − | 0.440386i | ||||||
\(331\) | 6.92820 | − | 4.00000i | 0.380808 | − | 0.219860i | −0.297361 | − | 0.954765i | \(-0.596107\pi\) |
0.678170 | + | 0.734905i | \(0.262773\pi\) | |||||||
\(332\) | −10.3923 | + | 6.00000i | −0.570352 | + | 0.329293i | ||||
\(333\) | 2.00000i | 0.109599i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −16.0000 | + | 27.7128i | −0.874173 | + | 1.51411i | ||||
\(336\) | −3.46410 | − | 2.00000i | −0.188982 | − | 0.109109i | ||||
\(337\) | −18.0000 | −0.980522 | −0.490261 | − | 0.871576i | \(-0.663099\pi\) | ||||
−0.490261 | + | 0.871576i | \(0.663099\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.00000 | 0.325875 | ||||||||
\(340\) | −3.46410 | − | 2.00000i | −0.187867 | − | 0.108465i | ||||
\(341\) | −8.00000 | + | 13.8564i | −0.433224 | + | 0.750366i | ||||
\(342\) | 4.00000 | + | 6.92820i | 0.216295 | + | 0.374634i | ||||
\(343\) | 8.00000i | 0.431959i | ||||||||
\(344\) | −3.46410 | + | 2.00000i | −0.186772 | + | 0.107833i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 10.0000i | − | 0.537603i | ||||||
\(347\) | 6.00000 | + | 10.3923i | 0.322097 | + | 0.557888i | 0.980921 | − | 0.194409i | \(-0.0622790\pi\) |
−0.658824 | + | 0.752297i | \(0.728946\pi\) | |||||||
\(348\) | −3.00000 | + | 5.19615i | −0.160817 | + | 0.278543i | ||||
\(349\) | 5.19615 | + | 3.00000i | 0.278144 | + | 0.160586i | 0.632583 | − | 0.774493i | \(-0.281995\pi\) |
−0.354439 | + | 0.935079i | \(0.615328\pi\) | |||||||
\(350\) | −4.00000 | −0.213809 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.00000 | 0.213201 | ||||||||
\(353\) | −12.1244 | − | 7.00000i | −0.645314 | − | 0.372572i | 0.141344 | − | 0.989960i | \(-0.454858\pi\) |
−0.786659 | + | 0.617388i | \(0.788191\pi\) | |||||||
\(354\) | −2.00000 | + | 3.46410i | −0.106299 | + | 0.184115i | ||||
\(355\) | −8.00000 | − | 13.8564i | −0.424596 | − | 0.735422i | ||||
\(356\) | 14.0000i | 0.741999i | ||||||||
\(357\) | −6.92820 | + | 4.00000i | −0.366679 | + | 0.211702i | ||||
\(358\) | −10.3923 | + | 6.00000i | −0.549250 | + | 0.317110i | ||||
\(359\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(360\) | 1.00000 | + | 1.73205i | 0.0527046 | + | 0.0912871i | ||||
\(361\) | 22.5000 | − | 38.9711i | 1.18421 | − | 2.05111i | ||||
\(362\) | 8.66025 | + | 5.00000i | 0.455173 | + | 0.262794i | ||||
\(363\) | 5.00000 | 0.262432 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.00000 | 0.209370 | ||||||||
\(366\) | 1.73205 | + | 1.00000i | 0.0905357 | + | 0.0522708i | ||||
\(367\) | −8.00000 | + | 13.8564i | −0.417597 | + | 0.723299i | −0.995697 | − | 0.0926670i | \(-0.970461\pi\) |
0.578101 | + | 0.815966i | \(0.303794\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 10.0000i | − | 0.520579i | ||||||
\(370\) | 3.46410 | − | 2.00000i | 0.180090 | − | 0.103975i | ||||
\(371\) | 34.6410 | − | 20.0000i | 1.79847 | − | 1.03835i | ||||
\(372\) | − | 4.00000i | − | 0.207390i | ||||||
\(373\) | −3.00000 | − | 5.19615i | −0.155334 | − | 0.269047i | 0.777847 | − | 0.628454i | \(-0.216312\pi\) |
−0.933181 | + | 0.359408i | \(0.882979\pi\) | |||||||
\(374\) | 4.00000 | − | 6.92820i | 0.206835 | − | 0.358249i | ||||
\(375\) | 10.3923 | + | 6.00000i | 0.536656 | + | 0.309839i | ||||
\(376\) | 8.00000 | 0.412568 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 4.00000 | 0.205738 | ||||||||
\(379\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(380\) | 8.00000 | − | 13.8564i | 0.410391 | − | 0.710819i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 8.00000i | 0.409316i | ||||||||
\(383\) | −20.7846 | + | 12.0000i | −1.06204 | + | 0.613171i | −0.925997 | − | 0.377531i | \(-0.876773\pi\) |
−0.136047 | + | 0.990702i | \(0.543440\pi\) | |||||||
\(384\) | −0.866025 | + | 0.500000i | −0.0441942 | + | 0.0255155i | ||||
\(385\) | 32.0000i | 1.63087i | ||||||||
\(386\) | −7.00000 | − | 12.1244i | −0.356291 | − | 0.617113i | ||||
\(387\) | 2.00000 | − | 3.46410i | 0.101666 | − | 0.176090i | ||||
\(388\) | 8.66025 | + | 5.00000i | 0.439658 | + | 0.253837i | ||||
\(389\) | 26.0000 | 1.31825 | 0.659126 | − | 0.752032i | \(-0.270926\pi\) | ||||
0.659126 | + | 0.752032i | \(0.270926\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 7.79423 | + | 4.50000i | 0.393668 | + | 0.227284i | ||||
\(393\) | 2.00000 | − | 3.46410i | 0.100887 | − | 0.174741i | ||||
\(394\) | −9.00000 | − | 15.5885i | −0.453413 | − | 0.785335i | ||||
\(395\) | 16.0000i | 0.805047i | ||||||||
\(396\) | −3.46410 | + | 2.00000i | −0.174078 | + | 0.100504i | ||||
\(397\) | −5.19615 | + | 3.00000i | −0.260787 | + | 0.150566i | −0.624694 | − | 0.780870i | \(-0.714776\pi\) |
0.363906 | + | 0.931436i | \(0.381443\pi\) | |||||||
\(398\) | − | 8.00000i | − | 0.401004i | ||||||
\(399\) | −16.0000 | − | 27.7128i | −0.801002 | − | 1.38738i | ||||
\(400\) | −0.500000 | + | 0.866025i | −0.0250000 | + | 0.0433013i | ||||
\(401\) | 5.19615 | + | 3.00000i | 0.259483 | + | 0.149813i | 0.624099 | − | 0.781345i | \(-0.285466\pi\) |
−0.364615 | + | 0.931158i | \(0.618800\pi\) | |||||||
\(402\) | 16.0000 | 0.798007 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −2.00000 | −0.0995037 | ||||||||
\(405\) | −1.73205 | − | 1.00000i | −0.0860663 | − | 0.0496904i | ||||
\(406\) | 12.0000 | − | 20.7846i | 0.595550 | − | 1.03152i | ||||
\(407\) | 4.00000 | + | 6.92820i | 0.198273 | + | 0.343418i | ||||
\(408\) | 2.00000i | 0.0990148i | ||||||||
\(409\) | 1.73205 | − | 1.00000i | 0.0856444 | − | 0.0494468i | −0.456566 | − | 0.889689i | \(-0.650921\pi\) |
0.542211 | + | 0.840243i | \(0.317588\pi\) | |||||||
\(410\) | −17.3205 | + | 10.0000i | −0.855399 | + | 0.493865i | ||||
\(411\) | − | 10.0000i | − | 0.493264i | ||||||
\(412\) | −8.00000 | − | 13.8564i | −0.394132 | − | 0.682656i | ||||
\(413\) | 8.00000 | − | 13.8564i | 0.393654 | − | 0.681829i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −24.0000 | −1.17811 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −12.0000 | −0.587643 | ||||||||
\(418\) | 27.7128 | + | 16.0000i | 1.35548 | + | 0.782586i | ||||
\(419\) | −2.00000 | + | 3.46410i | −0.0977064 | + | 0.169232i | −0.910735 | − | 0.412991i | \(-0.864484\pi\) |
0.813029 | + | 0.582224i | \(0.197817\pi\) | |||||||
\(420\) | −4.00000 | − | 6.92820i | −0.195180 | − | 0.338062i | ||||
\(421\) | 22.0000i | 1.07221i | 0.844150 | + | 0.536107i | \(0.180106\pi\) | ||||
−0.844150 | + | 0.536107i | \(0.819894\pi\) | |||||||
\(422\) | −10.3923 | + | 6.00000i | −0.505889 | + | 0.292075i | ||||
\(423\) | −6.92820 | + | 4.00000i | −0.336861 | + | 0.194487i | ||||
\(424\) | − | 10.0000i | − | 0.485643i | ||||||
\(425\) | 1.00000 | + | 1.73205i | 0.0485071 | + | 0.0840168i | ||||
\(426\) | −4.00000 | + | 6.92820i | −0.193801 | + | 0.335673i | ||||
\(427\) | −6.92820 | − | 4.00000i | −0.335279 | − | 0.193574i | ||||
\(428\) | −12.0000 | −0.580042 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −8.00000 | −0.385794 | ||||||||
\(431\) | 6.92820 | + | 4.00000i | 0.333720 | + | 0.192673i | 0.657491 | − | 0.753462i | \(-0.271618\pi\) |
−0.323772 | + | 0.946135i | \(0.604951\pi\) | |||||||
\(432\) | 0.500000 | − | 0.866025i | 0.0240563 | − | 0.0416667i | ||||
\(433\) | −15.0000 | − | 25.9808i | −0.720854 | − | 1.24856i | −0.960658 | − | 0.277734i | \(-0.910416\pi\) |
0.239804 | − | 0.970821i | \(-0.422917\pi\) | |||||||
\(434\) | 16.0000i | 0.768025i | ||||||||
\(435\) | −10.3923 | + | 6.00000i | −0.498273 | + | 0.287678i | ||||
\(436\) | 1.73205 | − | 1.00000i | 0.0829502 | − | 0.0478913i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −1.00000 | − | 1.73205i | −0.0477818 | − | 0.0827606i | ||||
\(439\) | 8.00000 | − | 13.8564i | 0.381819 | − | 0.661330i | −0.609503 | − | 0.792784i | \(-0.708631\pi\) |
0.991322 | + | 0.131453i | \(0.0419644\pi\) | |||||||
\(440\) | 6.92820 | + | 4.00000i | 0.330289 | + | 0.190693i | ||||
\(441\) | −9.00000 | −0.428571 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.00000 | −0.190046 | −0.0950229 | − | 0.995475i | \(-0.530292\pi\) | ||||
−0.0950229 | + | 0.995475i | \(0.530292\pi\) | |||||||
\(444\) | −1.73205 | − | 1.00000i | −0.0821995 | − | 0.0474579i | ||||
\(445\) | −14.0000 | + | 24.2487i | −0.663664 | + | 1.14950i | ||||
\(446\) | 2.00000 | + | 3.46410i | 0.0947027 | + | 0.164030i | ||||
\(447\) | 6.00000i | 0.283790i | ||||||||
\(448\) | 3.46410 | − | 2.00000i | 0.163663 | − | 0.0944911i | ||||
\(449\) | −5.19615 | + | 3.00000i | −0.245222 | + | 0.141579i | −0.617574 | − | 0.786513i | \(-0.711885\pi\) |
0.372353 | + | 0.928091i | \(0.378551\pi\) | |||||||
\(450\) | − | 1.00000i | − | 0.0471405i | ||||||
\(451\) | −20.0000 | − | 34.6410i | −0.941763 | − | 1.63118i | ||||
\(452\) | −3.00000 | + | 5.19615i | −0.141108 | + | 0.244406i | ||||
\(453\) | −10.3923 | − | 6.00000i | −0.488273 | − | 0.281905i | ||||
\(454\) | 20.0000 | 0.938647 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −8.00000 | −0.374634 | ||||||||
\(457\) | 25.9808 | + | 15.0000i | 1.21533 | + | 0.701670i | 0.963915 | − | 0.266209i | \(-0.0857713\pi\) |
0.251414 | + | 0.967880i | \(0.419105\pi\) | |||||||
\(458\) | 11.0000 | − | 19.0526i | 0.513996 | − | 0.890268i | ||||
\(459\) | −1.00000 | − | 1.73205i | −0.0466760 | − | 0.0808452i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.19615 | + | 3.00000i | −0.242009 | + | 0.139724i | −0.616100 | − | 0.787668i | \(-0.711288\pi\) |
0.374091 | + | 0.927392i | \(0.377955\pi\) | |||||||
\(462\) | 13.8564 | − | 8.00000i | 0.644658 | − | 0.372194i | ||||
\(463\) | 20.0000i | 0.929479i | 0.885448 | + | 0.464739i | \(0.153852\pi\) | ||||
−0.885448 | + | 0.464739i | \(0.846148\pi\) | |||||||
\(464\) | −3.00000 | − | 5.19615i | −0.139272 | − | 0.241225i | ||||
\(465\) | 4.00000 | − | 6.92820i | 0.185496 | − | 0.321288i | ||||
\(466\) | −15.5885 | − | 9.00000i | −0.722121 | − | 0.416917i | ||||
\(467\) | 4.00000 | 0.185098 | 0.0925490 | − | 0.995708i | \(-0.470499\pi\) | ||||
0.0925490 | + | 0.995708i | \(0.470499\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −64.0000 | −2.95525 | ||||||||
\(470\) | 13.8564 | + | 8.00000i | 0.639148 | + | 0.369012i | ||||
\(471\) | 7.00000 | − | 12.1244i | 0.322543 | − | 0.558661i | ||||
\(472\) | −2.00000 | − | 3.46410i | −0.0920575 | − | 0.159448i | ||||
\(473\) | − | 16.0000i | − | 0.735681i | ||||||
\(474\) | 6.92820 | − | 4.00000i | 0.318223 | − | 0.183726i | ||||
\(475\) | −6.92820 | + | 4.00000i | −0.317888 | + | 0.183533i | ||||
\(476\) | − | 8.00000i | − | 0.366679i | ||||||
\(477\) | 5.00000 | + | 8.66025i | 0.228934 | + | 0.396526i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −13.8564 | − | 8.00000i | −0.633115 | − | 0.365529i | 0.148842 | − | 0.988861i | \(-0.452445\pi\) |
−0.781958 | + | 0.623332i | \(0.785779\pi\) | |||||||
\(480\) | −2.00000 | −0.0912871 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −10.0000 | −0.455488 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.50000 | + | 4.33013i | −0.113636 | + | 0.196824i | ||||
\(485\) | 10.0000 | + | 17.3205i | 0.454077 | + | 0.786484i | ||||
\(486\) | 1.00000i | 0.0453609i | ||||||||
\(487\) | 3.46410 | − | 2.00000i | 0.156973 | − | 0.0906287i | −0.419456 | − | 0.907776i | \(-0.637779\pi\) |
0.576429 | + | 0.817147i | \(0.304446\pi\) | |||||||
\(488\) | −1.73205 | + | 1.00000i | −0.0784063 | + | 0.0452679i | ||||
\(489\) | − | 16.0000i | − | 0.723545i | ||||||
\(490\) | 9.00000 | + | 15.5885i | 0.406579 | + | 0.704215i | ||||
\(491\) | 18.0000 | − | 31.1769i | 0.812329 | − | 1.40699i | −0.0989017 | − | 0.995097i | \(-0.531533\pi\) |
0.911230 | − | 0.411897i | \(-0.135134\pi\) | |||||||
\(492\) | 8.66025 | + | 5.00000i | 0.390434 | + | 0.225417i | ||||
\(493\) | −12.0000 | −0.540453 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −8.00000 | −0.359573 | ||||||||
\(496\) | 3.46410 | + | 2.00000i | 0.155543 | + | 0.0898027i | ||||
\(497\) | 16.0000 | − | 27.7128i | 0.717698 | − | 1.24309i | ||||
\(498\) | 6.00000 | + | 10.3923i | 0.268866 | + | 0.465690i | ||||
\(499\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(500\) | −10.3923 | + | 6.00000i | −0.464758 | + | 0.268328i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 4.00000i | 0.178529i | ||||||||
\(503\) | −20.0000 | − | 34.6410i | −0.891756 | − | 1.54457i | −0.837769 | − | 0.546025i | \(-0.816140\pi\) |
−0.0539870 | − | 0.998542i | \(-0.517193\pi\) | |||||||
\(504\) | −2.00000 | + | 3.46410i | −0.0890871 | + | 0.154303i | ||||
\(505\) | −3.46410 | − | 2.00000i | −0.154150 | − | 0.0889988i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −36.3731 | − | 21.0000i | −1.61221 | − | 0.930809i | −0.988857 | − | 0.148866i | \(-0.952438\pi\) |
−0.623350 | − | 0.781943i | \(-0.714229\pi\) | |||||||
\(510\) | −2.00000 | + | 3.46410i | −0.0885615 | + | 0.153393i | ||||
\(511\) | 4.00000 | + | 6.92820i | 0.176950 | + | 0.306486i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 6.92820 | − | 4.00000i | 0.305888 | − | 0.176604i | ||||
\(514\) | −5.19615 | + | 3.00000i | −0.229192 | + | 0.132324i | ||||
\(515\) | − | 32.0000i | − | 1.41009i | ||||||
\(516\) | 2.00000 | + | 3.46410i | 0.0880451 | + | 0.152499i | ||||
\(517\) | −16.0000 | + | 27.7128i | −0.703679 | + | 1.21881i | ||||
\(518\) | 6.92820 | + | 4.00000i | 0.304408 | + | 0.175750i | ||||
\(519\) | −10.0000 | −0.438951 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14.0000 | −0.613351 | −0.306676 | − | 0.951814i | \(-0.599217\pi\) | ||||
−0.306676 | + | 0.951814i | \(0.599217\pi\) | |||||||
\(522\) | 5.19615 | + | 3.00000i | 0.227429 | + | 0.131306i | ||||
\(523\) | 10.0000 | − | 17.3205i | 0.437269 | − | 0.757373i | −0.560208 | − | 0.828352i | \(-0.689279\pi\) |
0.997478 | + | 0.0709788i | \(0.0226123\pi\) | |||||||
\(524\) | 2.00000 | + | 3.46410i | 0.0873704 | + | 0.151330i | ||||
\(525\) | 4.00000i | 0.174574i | ||||||||
\(526\) | −6.92820 | + | 4.00000i | −0.302084 | + | 0.174408i | ||||
\(527\) | 6.92820 | − | 4.00000i | 0.301797 | − | 0.174243i | ||||
\(528\) | − | 4.00000i | − | 0.174078i | ||||||
\(529\) | 11.5000 | + | 19.9186i | 0.500000 | + | 0.866025i | ||||
\(530\) | 10.0000 | − | 17.3205i | 0.434372 | − | 0.752355i | ||||
\(531\) | 3.46410 | + | 2.00000i | 0.150329 | + | 0.0867926i | ||||
\(532\) | 32.0000 | 1.38738 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 14.0000 | 0.605839 | ||||||||
\(535\) | −20.7846 | − | 12.0000i | −0.898597 | − | 0.518805i | ||||
\(536\) | −8.00000 | + | 13.8564i | −0.345547 | + | 0.598506i | ||||
\(537\) | 6.00000 | + | 10.3923i | 0.258919 | + | 0.448461i | ||||
\(538\) | 26.0000i | 1.12094i | ||||||||
\(539\) | −31.1769 | + | 18.0000i | −1.34288 | + | 0.775315i | ||||
\(540\) | 1.73205 | − | 1.00000i | 0.0745356 | − | 0.0430331i | ||||
\(541\) | 34.0000i | 1.46177i | 0.682498 | + | 0.730887i | \(0.260893\pi\) | ||||
−0.682498 | + | 0.730887i | \(0.739107\pi\) | |||||||
\(542\) | −2.00000 | − | 3.46410i | −0.0859074 | − | 0.148796i | ||||
\(543\) | 5.00000 | − | 8.66025i | 0.214571 | − | 0.371647i | ||||
\(544\) | −1.73205 | − | 1.00000i | −0.0742611 | − | 0.0428746i | ||||
\(545\) | 4.00000 | 0.171341 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −28.0000 | −1.19719 | −0.598597 | − | 0.801050i | \(-0.704275\pi\) | ||||
−0.598597 | + | 0.801050i | \(0.704275\pi\) | |||||||
\(548\) | 8.66025 | + | 5.00000i | 0.369948 | + | 0.213589i | ||||
\(549\) | 1.00000 | − | 1.73205i | 0.0426790 | − | 0.0739221i | ||||
\(550\) | −2.00000 | − | 3.46410i | −0.0852803 | − | 0.147710i | ||||
\(551\) | − | 48.0000i | − | 2.04487i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −27.7128 | + | 16.0000i | −1.17847 | + | 0.680389i | ||||
\(554\) | 22.0000i | 0.934690i | ||||||||
\(555\) | −2.00000 | − | 3.46410i | −0.0848953 | − | 0.147043i | ||||
\(556\) | 6.00000 | − | 10.3923i | 0.254457 | − | 0.440732i | ||||
\(557\) | 15.5885 | + | 9.00000i | 0.660504 | + | 0.381342i | 0.792469 | − | 0.609912i | \(-0.208795\pi\) |
−0.131965 | + | 0.991254i | \(0.542129\pi\) | |||||||
\(558\) | −4.00000 | −0.169334 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 8.00000 | 0.338062 | ||||||||
\(561\) | −6.92820 | − | 4.00000i | −0.292509 | − | 0.168880i | ||||
\(562\) | −13.0000 | + | 22.5167i | −0.548372 | + | 0.949808i | ||||
\(563\) | 2.00000 | + | 3.46410i | 0.0842900 | + | 0.145994i | 0.905088 | − | 0.425223i | \(-0.139804\pi\) |
−0.820798 | + | 0.571218i | \(0.806471\pi\) | |||||||
\(564\) | − | 8.00000i | − | 0.336861i | ||||||
\(565\) | −10.3923 | + | 6.00000i | −0.437208 | + | 0.252422i | ||||
\(566\) | −3.46410 | + | 2.00000i | −0.145607 | + | 0.0840663i | ||||
\(567\) | − | 4.00000i | − | 0.167984i | ||||||
\(568\) | −4.00000 | − | 6.92820i | −0.167836 | − | 0.290701i | ||||
\(569\) | −15.0000 | + | 25.9808i | −0.628833 | + | 1.08917i | 0.358954 | + | 0.933355i | \(0.383134\pi\) |
−0.987786 | + | 0.155815i | \(0.950200\pi\) | |||||||
\(570\) | −13.8564 | − | 8.00000i | −0.580381 | − | 0.335083i | ||||
\(571\) | 20.0000 | 0.836974 | 0.418487 | − | 0.908223i | \(-0.362561\pi\) | ||||
0.418487 | + | 0.908223i | \(0.362561\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.00000 | 0.334205 | ||||||||
\(574\) | −34.6410 | − | 20.0000i | −1.44589 | − | 0.834784i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.500000 | + | 0.866025i | 0.0208333 | + | 0.0360844i | ||||
\(577\) | 18.0000i | 0.749350i | 0.927156 | + | 0.374675i | \(0.122246\pi\) | ||||
−0.927156 | + | 0.374675i | \(0.877754\pi\) | |||||||
\(578\) | 11.2583 | − | 6.50000i | 0.468285 | − | 0.270364i | ||||
\(579\) | −12.1244 | + | 7.00000i | −0.503871 | + | 0.290910i | ||||
\(580\) | − | 12.0000i | − | 0.498273i | ||||||
\(581\) | −24.0000 | − | 41.5692i | −0.995688 | − | 1.72458i | ||||
\(582\) | 5.00000 | − | 8.66025i | 0.207257 | − | 0.358979i | ||||
\(583\) | 34.6410 | + | 20.0000i | 1.43468 | + | 0.828315i | ||||
\(584\) | 2.00000 | 0.0827606 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −26.0000 | −1.07405 | ||||||||
\(587\) | −3.46410 | − | 2.00000i | −0.142979 | − | 0.0825488i | 0.426804 | − | 0.904344i | \(-0.359639\pi\) |
−0.569783 | + | 0.821795i | \(0.692973\pi\) | |||||||
\(588\) | 4.50000 | − | 7.79423i | 0.185577 | − | 0.321429i | ||||
\(589\) | 16.0000 | + | 27.7128i | 0.659269 | + | 1.14189i | ||||
\(590\) | − | 8.00000i | − | 0.329355i | ||||||
\(591\) | −15.5885 | + | 9.00000i | −0.641223 | + | 0.370211i | ||||
\(592\) | 1.73205 | − | 1.00000i | 0.0711868 | − | 0.0410997i | ||||
\(593\) | 42.0000i | 1.72473i | 0.506284 | + | 0.862367i | \(0.331019\pi\) | ||||
−0.506284 | + | 0.862367i | \(0.668981\pi\) | |||||||
\(594\) | 2.00000 | + | 3.46410i | 0.0820610 | + | 0.142134i | ||||
\(595\) | 8.00000 | − | 13.8564i | 0.327968 | − | 0.568057i | ||||
\(596\) | −5.19615 | − | 3.00000i | −0.212843 | − | 0.122885i | ||||
\(597\) | −8.00000 | −0.327418 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −24.0000 | −0.980613 | −0.490307 | − | 0.871550i | \(-0.663115\pi\) | ||||
−0.490307 | + | 0.871550i | \(0.663115\pi\) | |||||||
\(600\) | 0.866025 | + | 0.500000i | 0.0353553 | + | 0.0204124i | ||||
\(601\) | −13.0000 | + | 22.5167i | −0.530281 | + | 0.918474i | 0.469095 | + | 0.883148i | \(0.344580\pi\) |
−0.999376 | + | 0.0353259i | \(0.988753\pi\) | |||||||
\(602\) | −8.00000 | − | 13.8564i | −0.326056 | − | 0.564745i | ||||
\(603\) | − | 16.0000i | − | 0.651570i | ||||||
\(604\) | 10.3923 | − | 6.00000i | 0.422857 | − | 0.244137i | ||||
\(605\) | −8.66025 | + | 5.00000i | −0.352089 | + | 0.203279i | ||||
\(606\) | 2.00000i | 0.0812444i | ||||||||
\(607\) | 8.00000 | + | 13.8564i | 0.324710 | + | 0.562414i | 0.981454 | − | 0.191700i | \(-0.0614000\pi\) |
−0.656744 | + | 0.754114i | \(0.728067\pi\) | |||||||
\(608\) | 4.00000 | − | 6.92820i | 0.162221 | − | 0.280976i | ||||
\(609\) | −20.7846 | − | 12.0000i | −0.842235 | − | 0.486265i | ||||
\(610\) | −4.00000 | −0.161955 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 2.00000 | 0.0808452 | ||||||||
\(613\) | 1.73205 | + | 1.00000i | 0.0699569 | + | 0.0403896i | 0.534570 | − | 0.845124i | \(-0.320473\pi\) |
−0.464614 | + | 0.885514i | \(0.653807\pi\) | |||||||
\(614\) | −4.00000 | + | 6.92820i | −0.161427 | + | 0.279600i | ||||
\(615\) | 10.0000 | + | 17.3205i | 0.403239 | + | 0.698430i | ||||
\(616\) | 16.0000i | 0.644658i | ||||||||
\(617\) | 5.19615 | − | 3.00000i | 0.209189 | − | 0.120775i | −0.391745 | − | 0.920074i | \(-0.628129\pi\) |
0.600935 | + | 0.799298i | \(0.294795\pi\) | |||||||
\(618\) | −13.8564 | + | 8.00000i | −0.557386 | + | 0.321807i | ||||
\(619\) | − | 32.0000i | − | 1.28619i | −0.765787 | − | 0.643094i | \(-0.777650\pi\) | ||
0.765787 | − | 0.643094i | \(-0.222350\pi\) | |||||||
\(620\) | 4.00000 | + | 6.92820i | 0.160644 | + | 0.278243i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −56.0000 | −2.24359 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.0000 | −0.760000 | ||||||||
\(626\) | −5.19615 | − | 3.00000i | −0.207680 | − | 0.119904i | ||||
\(627\) | 16.0000 | − | 27.7128i | 0.638978 | − | 1.10674i | ||||
\(628\) | 7.00000 | + | 12.1244i | 0.279330 | + | 0.483814i | ||||
\(629\) | − | 4.00000i | − | 0.159490i | ||||||
\(630\) | −6.92820 | + | 4.00000i | −0.276026 | + | 0.159364i | ||||
\(631\) | 31.1769 | − | 18.0000i | 1.24113 | − | 0.716569i | 0.271808 | − | 0.962351i | \(-0.412378\pi\) |
0.969325 | + | 0.245783i | \(0.0790450\pi\) | |||||||
\(632\) | 8.00000i | 0.318223i | ||||||||
\(633\) | 6.00000 | + | 10.3923i | 0.238479 | + | 0.413057i | ||||
\(634\) | 3.00000 | − | 5.19615i | 0.119145 | − | 0.206366i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −10.0000 | −0.396526 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 24.0000 | 0.950169 | ||||||||
\(639\) | 6.92820 | + | 4.00000i | 0.274075 | + | 0.158238i | ||||
\(640\) | 1.00000 | − | 1.73205i | 0.0395285 | − | 0.0684653i | ||||
\(641\) | 1.00000 | + | 1.73205i | 0.0394976 | + | 0.0684119i | 0.885098 | − | 0.465404i | \(-0.154091\pi\) |
−0.845601 | + | 0.533816i | \(0.820758\pi\) | |||||||
\(642\) | 12.0000i | 0.473602i | ||||||||
\(643\) | −13.8564 | + | 8.00000i | −0.546443 | + | 0.315489i | −0.747686 | − | 0.664052i | \(-0.768835\pi\) |
0.201243 | + | 0.979541i | \(0.435502\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.00000i | 0.315000i | ||||||||
\(646\) | −8.00000 | − | 13.8564i | −0.314756 | − | 0.545173i | ||||
\(647\) | 12.0000 | − | 20.7846i | 0.471769 | − | 0.817127i | −0.527710 | − | 0.849425i | \(-0.676949\pi\) |
0.999478 | + | 0.0322975i | \(0.0102824\pi\) | |||||||
\(648\) | −0.866025 | − | 0.500000i | −0.0340207 | − | 0.0196419i | ||||
\(649\) | 16.0000 | 0.628055 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 16.0000 | 0.627089 | ||||||||
\(652\) | 13.8564 | + | 8.00000i | 0.542659 | + | 0.313304i | ||||
\(653\) | 5.00000 | − | 8.66025i | 0.195665 | − | 0.338902i | −0.751453 | − | 0.659786i | \(-0.770647\pi\) |
0.947118 | + | 0.320884i | \(0.103980\pi\) | |||||||
\(654\) | −1.00000 | − | 1.73205i | −0.0391031 | − | 0.0677285i | ||||
\(655\) | 8.00000i | 0.312586i | ||||||||
\(656\) | −8.66025 | + | 5.00000i | −0.338126 | + | 0.195217i | ||||
\(657\) | −1.73205 | + | 1.00000i | −0.0675737 | + | 0.0390137i | ||||
\(658\) | 32.0000i | 1.24749i | ||||||||
\(659\) | 18.0000 | + | 31.1769i | 0.701180 | + | 1.21448i | 0.968052 | + | 0.250748i | \(0.0806766\pi\) |
−0.266872 | + | 0.963732i | \(0.585990\pi\) | |||||||
\(660\) | 4.00000 | − | 6.92820i | 0.155700 | − | 0.269680i | ||||
\(661\) | −1.73205 | − | 1.00000i | −0.0673690 | − | 0.0388955i | 0.465937 | − | 0.884818i | \(-0.345717\pi\) |
−0.533306 | + | 0.845922i | \(0.679051\pi\) | |||||||
\(662\) | 8.00000 | 0.310929 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −12.0000 | −0.465690 | ||||||||
\(665\) | 55.4256 | + | 32.0000i | 2.14931 | + | 1.24091i | ||||
\(666\) | −1.00000 | + | 1.73205i | −0.0387492 | + | 0.0671156i | ||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3.46410 | − | 2.00000i | 0.133930 | − | 0.0773245i | ||||
\(670\) | −27.7128 | + | 16.0000i | −1.07064 | + | 0.618134i | ||||
\(671\) | − | 8.00000i | − | 0.308837i | ||||||
\(672\) | −2.00000 | − | 3.46410i | −0.0771517 | − | 0.133631i | ||||
\(673\) | −7.00000 | + | 12.1244i | −0.269830 | + | 0.467360i | −0.968818 | − | 0.247774i | \(-0.920301\pi\) |
0.698988 | + | 0.715134i | \(0.253634\pi\) | |||||||
\(674\) | −15.5885 | − | 9.00000i | −0.600445 | − | 0.346667i | ||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 38.0000 | 1.46046 | 0.730229 | − | 0.683202i | \(-0.239413\pi\) | ||||
0.730229 | + | 0.683202i | \(0.239413\pi\) | |||||||
\(678\) | 5.19615 | + | 3.00000i | 0.199557 | + | 0.115214i | ||||
\(679\) | −20.0000 | + | 34.6410i | −0.767530 | + | 1.32940i | ||||
\(680\) | −2.00000 | − | 3.46410i | −0.0766965 | − | 0.132842i | ||||
\(681\) | − | 20.0000i | − | 0.766402i | ||||||
\(682\) | −13.8564 | + | 8.00000i | −0.530589 | + | 0.306336i | ||||
\(683\) | −38.1051 | + | 22.0000i | −1.45805 | + | 0.841807i | −0.998916 | − | 0.0465592i | \(-0.985174\pi\) |
−0.459136 | + | 0.888366i | \(0.651841\pi\) | |||||||
\(684\) | 8.00000i | 0.305888i | ||||||||
\(685\) | 10.0000 | + | 17.3205i | 0.382080 | + | 0.661783i | ||||
\(686\) | −4.00000 | + | 6.92820i | −0.152721 | + | 0.264520i | ||||
\(687\) | −19.0526 | − | 11.0000i | −0.726900 | − | 0.419676i | ||||
\(688\) | −4.00000 | −0.152499 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 27.7128 | + | 16.0000i | 1.05425 | + | 0.608669i | 0.923835 | − | 0.382791i | \(-0.125037\pi\) |
0.130410 | + | 0.991460i | \(0.458371\pi\) | |||||||
\(692\) | 5.00000 | − | 8.66025i | 0.190071 | − | 0.329213i | ||||
\(693\) | −8.00000 | − | 13.8564i | −0.303895 | − | 0.526361i | ||||
\(694\) | 12.0000i | 0.455514i | ||||||||
\(695\) | 20.7846 | − | 12.0000i | 0.788405 | − | 0.455186i | ||||
\(696\) | −5.19615 | + | 3.00000i | −0.196960 | + | 0.113715i | ||||
\(697\) | 20.0000i | 0.757554i | ||||||||
\(698\) | 3.00000 | + | 5.19615i | 0.113552 | + | 0.196677i | ||||
\(699\) | −9.00000 | + | 15.5885i | −0.340411 | + | 0.589610i | ||||
\(700\) | −3.46410 | − | 2.00000i | −0.130931 | − | 0.0755929i | ||||
\(701\) | 50.0000 | 1.88847 | 0.944237 | − | 0.329267i | \(-0.106802\pi\) | ||||
0.944237 | + | 0.329267i | \(0.106802\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.0000 | 0.603451 | ||||||||
\(704\) | 3.46410 | + | 2.00000i | 0.130558 | + | 0.0753778i | ||||
\(705\) | 8.00000 | − | 13.8564i | 0.301297 | − | 0.521862i | ||||
\(706\) | −7.00000 | − | 12.1244i | −0.263448 | − | 0.456306i | ||||
\(707\) | − | 8.00000i | − | 0.300871i | ||||||
\(708\) | −3.46410 | + | 2.00000i | −0.130189 | + | 0.0751646i | ||||
\(709\) | −5.19615 | + | 3.00000i | −0.195146 | + | 0.112667i | −0.594389 | − | 0.804178i | \(-0.702606\pi\) |
0.399244 | + | 0.916845i | \(0.369273\pi\) | |||||||
\(710\) | − | 16.0000i | − | 0.600469i | ||||||
\(711\) | −4.00000 | − | 6.92820i | −0.150012 | − | 0.259828i | ||||
\(712\) | −7.00000 | + | 12.1244i | −0.262336 | + | 0.454379i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | −8.00000 | −0.299392 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −12.0000 | −0.448461 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −12.0000 | − | 20.7846i | −0.447524 | − | 0.775135i | 0.550700 | − | 0.834703i | \(-0.314361\pi\) |
−0.998224 | + | 0.0595683i | \(0.981028\pi\) | |||||||
\(720\) | 2.00000i | 0.0745356i | ||||||||
\(721\) | 55.4256 | − | 32.0000i | 2.06416 | − | 1.19174i | ||||
\(722\) | 38.9711 | − | 22.5000i | 1.45036 | − | 0.837363i | ||||
\(723\) | 10.0000i | 0.371904i | ||||||||
\(724\) | 5.00000 | + | 8.66025i | 0.185824 | + | 0.321856i | ||||
\(725\) | −3.00000 | + | 5.19615i | −0.111417 | + | 0.192980i | ||||
\(726\) | 4.33013 | + | 2.50000i | 0.160706 | + | 0.0927837i | ||||
\(727\) | 40.0000 | 1.48352 | 0.741759 | − | 0.670667i | \(-0.233992\pi\) | ||||
0.741759 | + | 0.670667i | \(0.233992\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 3.46410 | + | 2.00000i | 0.128212 | + | 0.0740233i | ||||
\(731\) | −4.00000 | + | 6.92820i | −0.147945 | + | 0.256249i | ||||
\(732\) | 1.00000 | + | 1.73205i | 0.0369611 | + | 0.0640184i | ||||
\(733\) | − | 2.00000i | − | 0.0738717i | −0.999318 | − | 0.0369358i | \(-0.988240\pi\) | ||
0.999318 | − | 0.0369358i | \(-0.0117597\pi\) | |||||||
\(734\) | −13.8564 | + | 8.00000i | −0.511449 | + | 0.295285i | ||||
\(735\) | 15.5885 | − | 9.00000i | 0.574989 | − | 0.331970i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −32.0000 | − | 55.4256i | −1.17874 | − | 2.04163i | ||||
\(738\) | 5.00000 | − | 8.66025i | 0.184053 | − | 0.318788i | ||||
\(739\) | 34.6410 | + | 20.0000i | 1.27429 | + | 0.735712i | 0.975793 | − | 0.218698i | \(-0.0701811\pi\) |
0.298498 | + | 0.954410i | \(0.403514\pi\) | |||||||
\(740\) | 4.00000 | 0.147043 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 40.0000 | 1.46845 | ||||||||
\(743\) | 20.7846 | + | 12.0000i | 0.762513 | + | 0.440237i | 0.830197 | − | 0.557470i | \(-0.188228\pi\) |
−0.0676840 | + | 0.997707i | \(0.521561\pi\) | |||||||
\(744\) | 2.00000 | − | 3.46410i | 0.0733236 | − | 0.127000i | ||||
\(745\) | −6.00000 | − | 10.3923i | −0.219823 | − | 0.380745i | ||||
\(746\) | − | 6.00000i | − | 0.219676i | ||||||
\(747\) | 10.3923 | − | 6.00000i | 0.380235 | − | 0.219529i | ||||
\(748\) | 6.92820 | − | 4.00000i | 0.253320 | − | 0.146254i | ||||
\(749\) | − | 48.0000i | − | 1.75388i | ||||||
\(750\) | 6.00000 | + | 10.3923i | 0.219089 | + | 0.379473i | ||||
\(751\) | −20.0000 | + | 34.6410i | −0.729810 | + | 1.26407i | 0.227153 | + | 0.973859i | \(0.427058\pi\) |
−0.956963 | + | 0.290209i | \(0.906275\pi\) | |||||||
\(752\) | 6.92820 | + | 4.00000i | 0.252646 | + | 0.145865i | ||||
\(753\) | 4.00000 | 0.145768 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 24.0000 | 0.873449 | ||||||||
\(756\) | 3.46410 | + | 2.00000i | 0.125988 | + | 0.0727393i | ||||
\(757\) | −27.0000 | + | 46.7654i | −0.981332 | + | 1.69972i | −0.324109 | + | 0.946020i | \(0.605065\pi\) |
−0.657222 | + | 0.753697i | \(0.728269\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 13.8564 | − | 8.00000i | 0.502625 | − | 0.290191i | ||||
\(761\) | 22.5167 | − | 13.0000i | 0.816228 | − | 0.471250i | −0.0328858 | − | 0.999459i | \(-0.510470\pi\) |
0.849114 | + | 0.528209i | \(0.177136\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.00000 | + | 6.92820i | 0.144810 | + | 0.250818i | ||||
\(764\) | −4.00000 | + | 6.92820i | −0.144715 | + | 0.250654i | ||||
\(765\) | 3.46410 | + | 2.00000i | 0.125245 | + | 0.0723102i | ||||
\(766\) | −24.0000 | −0.867155 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −1.73205 | − | 1.00000i | −0.0624593 | − | 0.0360609i | 0.468445 | − | 0.883493i | \(-0.344814\pi\) |
−0.530904 | + | 0.847432i | \(0.678148\pi\) | |||||||
\(770\) | −16.0000 | + | 27.7128i | −0.576600 | + | 0.998700i | ||||
\(771\) | 3.00000 | + | 5.19615i | 0.108042 | + | 0.187135i | ||||
\(772\) | − | 14.0000i | − | 0.503871i | ||||||
\(773\) | −46.7654 | + | 27.0000i | −1.68203 | + | 0.971123i | −0.721726 | + | 0.692179i | \(0.756651\pi\) |
−0.960307 | + | 0.278944i | \(0.910016\pi\) | |||||||
\(774\) | 3.46410 | − | 2.00000i | 0.124515 | − | 0.0718885i | ||||
\(775\) | − | 4.00000i | − | 0.143684i | ||||||
\(776\) | 5.00000 | + | 8.66025i | 0.179490 | + | 0.310885i | ||||
\(777\) | 4.00000 | − | 6.92820i | 0.143499 | − | 0.248548i | ||||
\(778\) | 22.5167 | + | 13.0000i | 0.807261 | + | 0.466073i | ||||
\(779\) | −80.0000 | −2.86630 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 32.0000 | 1.14505 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.00000 | − | 5.19615i | 0.107211 | − | 0.185695i | ||||
\(784\) | 4.50000 | + | 7.79423i | 0.160714 | + | 0.278365i | ||||
\(785\) | 28.0000i | 0.999363i | ||||||||
\(786\) | 3.46410 | − | 2.00000i | 0.123560 | − | 0.0713376i | ||||
\(787\) | −34.6410 | + | 20.0000i | −1.23482 | + | 0.712923i | −0.968031 | − | 0.250832i | \(-0.919296\pi\) |
−0.266788 | + | 0.963755i | \(0.585962\pi\) | |||||||
\(788\) | − | 18.0000i | − | 0.641223i | ||||||
\(789\) | 4.00000 | + | 6.92820i | 0.142404 | + | 0.246651i | ||||
\(790\) | −8.00000 | + | 13.8564i | −0.284627 | + | 0.492989i | ||||
\(791\) | −20.7846 | − | 12.0000i | −0.739016 | − | 0.426671i | ||||
\(792\) | −4.00000 | −0.142134 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −6.00000 | −0.212932 | ||||||||
\(795\) | −17.3205 | − | 10.0000i | −0.614295 | − | 0.354663i | ||||
\(796\) | 4.00000 | − | 6.92820i | 0.141776 | − | 0.245564i | ||||
\(797\) | −1.00000 | − | 1.73205i | −0.0354218 | − | 0.0613524i | 0.847771 | − | 0.530362i | \(-0.177944\pi\) |
−0.883193 | + | 0.469010i | \(0.844611\pi\) | |||||||
\(798\) | − | 32.0000i | − | 1.13279i | ||||||
\(799\) | 13.8564 | − | 8.00000i | 0.490204 | − | 0.283020i | ||||
\(800\) | −0.866025 | + | 0.500000i | −0.0306186 | + | 0.0176777i | ||||
\(801\) | − | 14.0000i | − | 0.494666i | ||||||
\(802\) | 3.00000 | + | 5.19615i | 0.105934 | + | 0.183483i | ||||
\(803\) | −4.00000 | + | 6.92820i | −0.141157 | + | 0.244491i | ||||
\(804\) | 13.8564 | + | 8.00000i | 0.488678 | + | 0.282138i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 26.0000 | 0.915243 | ||||||||
\(808\) | −1.73205 | − | 1.00000i | −0.0609333 | − | 0.0351799i | ||||
\(809\) | −1.00000 | + | 1.73205i | −0.0351581 | + | 0.0608957i | −0.883069 | − | 0.469243i | \(-0.844527\pi\) |
0.847911 | + | 0.530139i | \(0.177860\pi\) | |||||||
\(810\) | −1.00000 | − | 1.73205i | −0.0351364 | − | 0.0608581i | ||||
\(811\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(812\) | 20.7846 | − | 12.0000i | 0.729397 | − | 0.421117i | ||||
\(813\) | −3.46410 | + | 2.00000i | −0.121491 | + | 0.0701431i | ||||
\(814\) | 8.00000i | 0.280400i | ||||||||
\(815\) | 16.0000 | + | 27.7128i | 0.560456 | + | 0.970737i | ||||
\(816\) | −1.00000 | + | 1.73205i | −0.0350070 | + | 0.0606339i | ||||
\(817\) | −27.7128 | − | 16.0000i | −0.969549 | − | 0.559769i | ||||
\(818\) | 2.00000 | 0.0699284 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −20.0000 | −0.698430 | ||||||||
\(821\) | −36.3731 | − | 21.0000i | −1.26943 | − | 0.732905i | −0.294549 | − | 0.955636i | \(-0.595169\pi\) |
−0.974880 | + | 0.222731i | \(0.928503\pi\) | |||||||
\(822\) | 5.00000 | − | 8.66025i | 0.174395 | − | 0.302061i | ||||
\(823\) | −8.00000 | − | 13.8564i | −0.278862 | − | 0.483004i | 0.692240 | − | 0.721668i | \(-0.256624\pi\) |
−0.971102 | + | 0.238664i | \(0.923291\pi\) | |||||||
\(824\) | − | 16.0000i | − | 0.557386i | ||||||
\(825\) | −3.46410 | + | 2.00000i | −0.120605 | + | 0.0696311i | ||||
\(826\) | 13.8564 | − | 8.00000i | 0.482126 | − | 0.278356i | ||||
\(827\) | − | 28.0000i | − | 0.973655i | −0.873498 | − | 0.486828i | \(-0.838154\pi\) | ||
0.873498 | − | 0.486828i | \(-0.161846\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.00000 | + | 1.73205i | −0.0347314 | + | 0.0601566i | −0.882869 | − | 0.469620i | \(-0.844391\pi\) |
0.848137 | + | 0.529777i | \(0.177724\pi\) | |||||||
\(830\) | −20.7846 | − | 12.0000i | −0.721444 | − | 0.416526i | ||||
\(831\) | 22.0000 | 0.763172 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 18.0000 | 0.623663 | ||||||||
\(834\) | −10.3923 | − | 6.00000i | −0.359856 | − | 0.207763i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 16.0000 | + | 27.7128i | 0.553372 | + | 0.958468i | ||||
\(837\) | 4.00000i | 0.138260i | ||||||||
\(838\) | −3.46410 | + | 2.00000i | −0.119665 | + | 0.0690889i | ||||
\(839\) | 34.6410 | − | 20.0000i | 1.19594 | − | 0.690477i | 0.236293 | − | 0.971682i | \(-0.424067\pi\) |
0.959648 | + | 0.281205i | \(0.0907341\pi\) | |||||||
\(840\) | − | 8.00000i | − | 0.276026i | ||||||
\(841\) | −3.50000 | − | 6.06218i | −0.120690 | − | 0.209041i | ||||
\(842\) | −11.0000 | + | 19.0526i | −0.379085 | + | 0.656595i | ||||
\(843\) | 22.5167 | + | 13.0000i | 0.775515 | + | 0.447744i | ||||
\(844\) | −12.0000 | −0.413057 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −8.00000 | −0.275046 | ||||||||
\(847\) | −17.3205 | − | 10.0000i | −0.595140 | − | 0.343604i | ||||
\(848\) | 5.00000 | − | 8.66025i | 0.171701 | − | 0.297394i | ||||
\(849\) | 2.00000 | + | 3.46410i | 0.0686398 | + | 0.118888i | ||||
\(850\) | 2.00000i | 0.0685994i | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | −6.92820 | + | 4.00000i | −0.237356 | + | 0.137038i | ||||
\(853\) | 2.00000i | 0.0684787i | 0.999414 | + | 0.0342393i | \(0.0109009\pi\) | ||||
−0.999414 | + | 0.0342393i | \(0.989099\pi\) | |||||||
\(854\) | −4.00000 | − | 6.92820i | −0.136877 | − | 0.237078i | ||||
\(855\) | −8.00000 | + | 13.8564i | −0.273594 | + | 0.473879i | ||||
\(856\) | −10.3923 | − | 6.00000i | −0.355202 | − | 0.205076i | ||||
\(857\) | −18.0000 | −0.614868 | −0.307434 | − | 0.951569i | \(-0.599470\pi\) | ||||
−0.307434 | + | 0.951569i | \(0.599470\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −44.0000 | −1.50126 | −0.750630 | − | 0.660722i | \(-0.770250\pi\) | ||||
−0.750630 | + | 0.660722i | \(0.770250\pi\) | |||||||
\(860\) | −6.92820 | − | 4.00000i | −0.236250 | − | 0.136399i | ||||
\(861\) | −20.0000 | + | 34.6410i | −0.681598 | + | 1.18056i | ||||
\(862\) | 4.00000 | + | 6.92820i | 0.136241 | + | 0.235976i | ||||
\(863\) | 40.0000i | 1.36162i | 0.732462 | + | 0.680808i | \(0.238371\pi\) | ||||
−0.732462 | + | 0.680808i | \(0.761629\pi\) | |||||||
\(864\) | 0.866025 | − | 0.500000i | 0.0294628 | − | 0.0170103i | ||||
\(865\) | 17.3205 | − | 10.0000i | 0.588915 | − | 0.340010i | ||||
\(866\) | − | 30.0000i | − | 1.01944i | ||||||
\(867\) | −6.50000 | − | 11.2583i | −0.220752 | − | 0.382353i | ||||
\(868\) | −8.00000 | + | 13.8564i | −0.271538 | + | 0.470317i | ||||
\(869\) | −27.7128 | − | 16.0000i | −0.940093 | − | 0.542763i | ||||
\(870\) | −12.0000 | −0.406838 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 2.00000 | 0.0677285 | ||||||||
\(873\) | −8.66025 | − | 5.00000i | −0.293105 | − | 0.169224i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −24.0000 | − | 41.5692i | −0.811348 | − | 1.40530i | ||||
\(876\) | − | 2.00000i | − | 0.0675737i | ||||||
\(877\) | 19.0526 | − | 11.0000i | 0.643359 | − | 0.371444i | −0.142548 | − | 0.989788i | \(-0.545530\pi\) |
0.785907 | + | 0.618344i | \(0.212196\pi\) | |||||||
\(878\) | 13.8564 | − | 8.00000i | 0.467631 | − | 0.269987i | ||||
\(879\) | 26.0000i | 0.876958i | ||||||||
\(880\) | 4.00000 | + | 6.92820i | 0.134840 | + | 0.233550i | ||||
\(881\) | 13.0000 | − | 22.5167i | 0.437981 | − | 0.758606i | −0.559553 | − | 0.828795i | \(-0.689027\pi\) |
0.997534 | + | 0.0701893i | \(0.0223603\pi\) | |||||||
\(882\) | −7.79423 | − | 4.50000i | −0.262445 | − | 0.151523i | ||||
\(883\) | −4.00000 | −0.134611 | −0.0673054 | − | 0.997732i | \(-0.521440\pi\) | ||||
−0.0673054 | + | 0.997732i | \(0.521440\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −8.00000 | −0.268917 | ||||||||
\(886\) | −3.46410 | − | 2.00000i | −0.116379 | − | 0.0671913i | ||||
\(887\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(888\) | −1.00000 | − | 1.73205i | −0.0335578 | − | 0.0581238i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −24.2487 | + | 14.0000i | −0.812819 | + | 0.469281i | ||||
\(891\) | 3.46410 | − | 2.00000i | 0.116052 | − | 0.0670025i | ||||
\(892\) | 4.00000i | 0.133930i | ||||||||
\(893\) | 32.0000 | + | 55.4256i | 1.07084 | + | 1.85475i | ||||
\(894\) | −3.00000 | + | 5.19615i | −0.100335 | + | 0.173785i | ||||
\(895\) | −20.7846 | − | 12.0000i | −0.694753 | − | 0.401116i | ||||
\(896\) | 4.00000 | 0.133631 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −6.00000 | −0.200223 | ||||||||
\(899\) | 20.7846 | + | 12.0000i | 0.693206 | + | 0.400222i | ||||
\(900\) | 0.500000 | − | 0.866025i | 0.0166667 | − | 0.0288675i | ||||
\(901\) | −10.0000 | − | 17.3205i | −0.333148 | − | 0.577030i | ||||
\(902\) | − | 40.0000i | − | 1.33185i | ||||||
\(903\) | −13.8564 | + | 8.00000i | −0.461112 | + | 0.266223i | ||||
\(904\) | −5.19615 | + | 3.00000i | −0.172821 | + | 0.0997785i | ||||
\(905\) | 20.0000i | 0.664822i | ||||||||
\(906\) | −6.00000 | − | 10.3923i | −0.199337 | − | 0.345261i | ||||
\(907\) | 14.0000 | − | 24.2487i | 0.464862 | − | 0.805165i | −0.534333 | − | 0.845274i | \(-0.679437\pi\) |
0.999195 | + | 0.0401089i | \(0.0127705\pi\) | |||||||
\(908\) | 17.3205 | + | 10.0000i | 0.574801 | + | 0.331862i | ||||
\(909\) | 2.00000 | 0.0663358 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 40.0000 | 1.32526 | 0.662630 | − | 0.748947i | \(-0.269440\pi\) | ||||
0.662630 | + | 0.748947i | \(0.269440\pi\) | |||||||
\(912\) | −6.92820 | − | 4.00000i | −0.229416 | − | 0.132453i | ||||
\(913\) | 24.0000 | − | 41.5692i | 0.794284 | − | 1.37574i | ||||
\(914\) | 15.0000 | + | 25.9808i | 0.496156 | + | 0.859367i | ||||
\(915\) | 4.00000i | 0.132236i | ||||||||
\(916\) | 19.0526 | − | 11.0000i | 0.629514 | − | 0.363450i | ||||
\(917\) | −13.8564 | + | 8.00000i | −0.457579 | + | 0.264183i | ||||
\(918\) | − | 2.00000i | − | 0.0660098i | ||||||
\(919\) | 8.00000 | + | 13.8564i | 0.263896 | + | 0.457081i | 0.967274 | − | 0.253735i | \(-0.0816592\pi\) |
−0.703378 | + | 0.710816i | \(0.748326\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.92820 | + | 4.00000i | 0.228292 | + | 0.131804i | ||||
\(922\) | −6.00000 | −0.197599 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 16.0000 | 0.526361 | ||||||||
\(925\) | −1.73205 | − | 1.00000i | −0.0569495 | − | 0.0328798i | ||||
\(926\) | −10.0000 | + | 17.3205i | −0.328620 | + | 0.569187i | ||||
\(927\) | 8.00000 | + | 13.8564i | 0.262754 | + | 0.455104i | ||||
\(928\) | − | 6.00000i | − | 0.196960i | ||||||
\(929\) | 39.8372 | − | 23.0000i | 1.30702 | − | 0.754606i | 0.325418 | − | 0.945570i | \(-0.394495\pi\) |
0.981597 | + | 0.190965i | \(0.0611616\pi\) | |||||||
\(930\) | 6.92820 | − | 4.00000i | 0.227185 | − | 0.131165i | ||||
\(931\) | 72.0000i | 2.35970i | ||||||||
\(932\) | −9.00000 | − | 15.5885i | −0.294805 | − | 0.510617i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 3.46410 | + | 2.00000i | 0.113349 | + | 0.0654420i | ||||
\(935\) | 16.0000 | 0.523256 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 26.0000 | 0.849383 | 0.424691 | − | 0.905338i | \(-0.360383\pi\) | ||||
0.424691 | + | 0.905338i | \(0.360383\pi\) | |||||||
\(938\) | −55.4256 | − | 32.0000i | −1.80971 | − | 1.04484i | ||||
\(939\) | −3.00000 | + | 5.19615i | −0.0979013 | + | 0.169570i | ||||
\(940\) | 8.00000 | + | 13.8564i | 0.260931 | + | 0.451946i | ||||
\(941\) | − | 46.0000i | − | 1.49956i | −0.661689 | − | 0.749779i | \(-0.730160\pi\) | ||
0.661689 | − | 0.749779i | \(-0.269840\pi\) | |||||||
\(942\) | 12.1244 | − | 7.00000i | 0.395033 | − | 0.228072i | ||||
\(943\) | 0 | 0 | ||||||||
\(944\) | − | 4.00000i | − | 0.130189i | ||||||
\(945\) | 4.00000 | + | 6.92820i | 0.130120 | + | 0.225374i | ||||
\(946\) | 8.00000 | − | 13.8564i | 0.260102 | − | 0.450511i | ||||
\(947\) | −3.46410 | − | 2.00000i | −0.112568 | − | 0.0649913i | 0.442659 | − | 0.896690i | \(-0.354035\pi\) |
−0.555227 | + | 0.831699i | \(0.687369\pi\) | |||||||
\(948\) | 8.00000 | 0.259828 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −8.00000 | −0.259554 | ||||||||
\(951\) | −5.19615 | − | 3.00000i | −0.168497 | − | 0.0972817i | ||||
\(952\) | 4.00000 | − | 6.92820i | 0.129641 | − | 0.224544i | ||||
\(953\) | −15.0000 | − | 25.9808i | −0.485898 | − | 0.841599i | 0.513971 | − | 0.857808i | \(-0.328174\pi\) |
−0.999869 | + | 0.0162081i | \(0.994841\pi\) | |||||||
\(954\) | 10.0000i | 0.323762i | ||||||||
\(955\) | −13.8564 | + | 8.00000i | −0.448383 | + | 0.258874i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 24.0000i | − | 0.775810i | ||||||
\(958\) | −8.00000 | − | 13.8564i | −0.258468 | − | 0.447680i | ||||
\(959\) | −20.0000 | + | 34.6410i | −0.645834 | + | 1.11862i | ||||
\(960\) | −1.73205 | − | 1.00000i | −0.0559017 | − | 0.0322749i | ||||
\(961\) | 15.0000 | 0.483871 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 12.0000 | 0.386695 | ||||||||
\(964\) | −8.66025 | − | 5.00000i | −0.278928 | − | 0.161039i | ||||
\(965\) | 14.0000 | − | 24.2487i | 0.450676 | − | 0.780594i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.00000i | 0.128631i | 0.997930 | + | 0.0643157i | \(0.0204865\pi\) | ||||
−0.997930 | + | 0.0643157i | \(0.979514\pi\) | |||||||
\(968\) | −4.33013 | + | 2.50000i | −0.139176 | + | 0.0803530i | ||||
\(969\) | −13.8564 | + | 8.00000i | −0.445132 | + | 0.256997i | ||||
\(970\) | 20.0000i | 0.642161i | ||||||||
\(971\) | 14.0000 | + | 24.2487i | 0.449281 | + | 0.778178i | 0.998339 | − | 0.0576061i | \(-0.0183467\pi\) |
−0.549058 | + | 0.835784i | \(0.685013\pi\) | |||||||
\(972\) | −0.500000 | + | 0.866025i | −0.0160375 | + | 0.0277778i | ||||
\(973\) | 41.5692 | + | 24.0000i | 1.33265 | + | 0.769405i | ||||
\(974\) | 4.00000 | 0.128168 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.00000 | −0.0640184 | ||||||||
\(977\) | −5.19615 | − | 3.00000i | −0.166240 | − | 0.0959785i | 0.414572 | − | 0.910017i | \(-0.363931\pi\) |
−0.580812 | + | 0.814038i | \(0.697265\pi\) | |||||||
\(978\) | 8.00000 | − | 13.8564i | 0.255812 | − | 0.443079i | ||||
\(979\) | −28.0000 | − | 48.4974i | −0.894884 | − | 1.54998i | ||||
\(980\) | 18.0000i | 0.574989i | ||||||||
\(981\) | −1.73205 | + | 1.00000i | −0.0553001 | + | 0.0319275i | ||||
\(982\) | 31.1769 | − | 18.0000i | 0.994895 | − | 0.574403i | ||||
\(983\) | − | 24.0000i | − | 0.765481i | −0.923856 | − | 0.382741i | \(-0.874980\pi\) | ||
0.923856 | − | 0.382741i | \(-0.125020\pi\) | |||||||
\(984\) | 5.00000 | + | 8.66025i | 0.159394 | + | 0.276079i | ||||
\(985\) | 18.0000 | − | 31.1769i | 0.573528 | − | 0.993379i | ||||
\(986\) | −10.3923 | − | 6.00000i | −0.330958 | − | 0.191079i | ||||
\(987\) | 32.0000 | 1.01857 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −6.92820 | − | 4.00000i | −0.220193 | − | 0.127128i | ||||
\(991\) | 24.0000 | − | 41.5692i | 0.762385 | − | 1.32049i | −0.179233 | − | 0.983807i | \(-0.557362\pi\) |
0.941618 | − | 0.336683i | \(-0.109305\pi\) | |||||||
\(992\) | 2.00000 | + | 3.46410i | 0.0635001 | + | 0.109985i | ||||
\(993\) | − | 8.00000i | − | 0.253872i | ||||||
\(994\) | 27.7128 | − | 16.0000i | 0.878997 | − | 0.507489i | ||||
\(995\) | 13.8564 | − | 8.00000i | 0.439278 | − | 0.253617i | ||||
\(996\) | 12.0000i | 0.380235i | ||||||||
\(997\) | 13.0000 | + | 22.5167i | 0.411714 | + | 0.713110i | 0.995077 | − | 0.0991016i | \(-0.0315969\pi\) |
−0.583363 | + | 0.812211i | \(0.698264\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.73205 | + | 1.00000i | 0.0547997 | + | 0.0316386i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))