Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [507,2,Mod(316,507)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(507, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("507.316");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 507 = 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 507.j (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: | \(4.04841538248\) |
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 39) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 361.2 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 507.361 |
Dual form | 507.2.j.e.316.2 |
$q$-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 \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).
\(n\) | \(170\) | \(340\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 | −0.161521 | − | 0.986869i | \(-0.551640\pi\) |
0.773893 | + | 0.633316i | \(0.218307\pi\) | |||||||
\(3\) | 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 | −0.327327 | − | 0.944911i | \(-0.606148\pi\) |
−0.981981 | + | 0.188982i | \(0.939481\pi\) | |||||||
\(8\) | 3.00000i | 1.06066i | ||||||||
\(9\) | −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 | −0.921095 | − | 0.389338i | \(-0.872704\pi\) |
−0.123371 | + | 0.992361i | \(0.539370\pi\) | |||||||
\(12\) | −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 | −0.718900 | − | 0.695113i | \(-0.755354\pi\) |
0.961436 | + | 0.275029i | \(0.0886875\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(20\) | −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 | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(24\) | −2.59808 | + | 1.50000i | −0.530330 | + | 0.306186i | ||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 3.46410 | − | 2.00000i | 0.654654 | − | 0.377964i | ||||
\(29\) | 5.00000 | + | 8.66025i | 0.928477 | + | 1.60817i | 0.785872 | + | 0.618389i | \(0.212214\pi\) |
0.142605 | + | 0.989780i | \(0.454452\pi\) | |||||||
\(30\) | −1.00000 | + | 1.73205i | −0.182574 | + | 0.316228i | ||||
\(31\) | 4.00000i | 0.718421i | 0.933257 | + | 0.359211i | \(0.116954\pi\) | ||||
−0.933257 | + | 0.359211i | \(0.883046\pi\) | |||||||
\(32\) | −4.33013 | − | 2.50000i | −0.765466 | − | 0.441942i | ||||
\(33\) | −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 | \(-0.614098\pi\) |
0.635571 | + | 0.772043i | \(0.280765\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −6.00000 | −0.948683 | ||||||||
\(41\) | 5.19615 | − | 3.00000i | 0.811503 | − | 0.468521i | −0.0359748 | − | 0.999353i | \(-0.511454\pi\) |
0.847477 | + | 0.530831i | \(0.178120\pi\) | |||||||
\(42\) | −2.00000 | − | 3.46410i | −0.308607 | − | 0.534522i | ||||
\(43\) | −6.00000 | + | 10.3923i | −0.914991 | + | 1.58481i | −0.108078 | + | 0.994142i | \(0.534469\pi\) |
−0.806914 | + | 0.590669i | \(0.798864\pi\) | |||||||
\(44\) | − | 4.00000i | − | 0.603023i | ||||||
\(45\) | −1.73205 | − | 1.00000i | −0.258199 | − | 0.149071i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(48\) | −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 | ||||||||
\(53\) | 6.00000 | 0.824163 | 0.412082 | − | 0.911147i | \(-0.364802\pi\) | ||||
0.412082 | + | 0.911147i | \(0.364802\pi\) | |||||||
\(54\) | −0.866025 | + | 0.500000i | −0.117851 | + | 0.0680414i | ||||
\(55\) | −4.00000 | − | 6.92820i | −0.539360 | − | 0.934199i | ||||
\(56\) | 6.00000 | − | 10.3923i | 0.801784 | − | 1.38873i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 8.66025 | + | 5.00000i | 1.13715 | + | 0.656532i | ||||
\(59\) | 10.3923 | + | 6.00000i | 1.35296 | + | 0.781133i | 0.988663 | − | 0.150148i | \(-0.0479752\pi\) |
0.364299 | + | 0.931282i | \(0.381308\pi\) | |||||||
\(60\) | − | 2.00000i | − | 0.258199i | ||||||
\(61\) | 1.00000 | − | 1.73205i | 0.128037 | − | 0.221766i | −0.794879 | − | 0.606768i | \(-0.792466\pi\) |
0.922916 | + | 0.385002i | \(0.125799\pi\) | |||||||
\(62\) | 2.00000 | + | 3.46410i | 0.254000 | + | 0.439941i | ||||
\(63\) | 3.46410 | − | 2.00000i | 0.436436 | − | 0.251976i | ||||
\(64\) | −7.00000 | −0.875000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −4.00000 | −0.492366 | ||||||||
\(67\) | −6.92820 | + | 4.00000i | −0.846415 | + | 0.488678i | −0.859440 | − | 0.511237i | \(-0.829187\pi\) |
0.0130248 | + | 0.999915i | \(0.495854\pi\) | |||||||
\(68\) | 1.00000 | + | 1.73205i | 0.121268 | + | 0.210042i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | − | 8.00000i | − | 0.956183i | ||||||
\(71\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(72\) | −2.59808 | − | 1.50000i | −0.306186 | − | 0.176777i | ||||
\(73\) | − | 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 | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 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 | ||||
\(82\) | 3.00000 | − | 5.19615i | 0.331295 | − | 0.573819i | ||||
\(83\) | 4.00000i | 0.439057i | 0.975606 | + | 0.219529i | \(0.0704519\pi\) | ||||
−0.975606 | + | 0.219529i | \(0.929548\pi\) | |||||||
\(84\) | 3.46410 | + | 2.00000i | 0.377964 | + | 0.218218i | ||||
\(85\) | 3.46410 | + | 2.00000i | 0.375735 | + | 0.216930i | ||||
\(86\) | 12.0000i | 1.29399i | ||||||||
\(87\) | −5.00000 | + | 8.66025i | −0.536056 | + | 0.928477i | ||||
\(88\) | −6.00000 | − | 10.3923i | −0.639602 | − | 1.10782i | ||||
\(89\) | 1.73205 | − | 1.00000i | 0.183597 | − | 0.106000i | −0.405385 | − | 0.914146i | \(-0.632862\pi\) |
0.588982 | + | 0.808146i | \(0.299529\pi\) | |||||||
\(90\) | −2.00000 | −0.210819 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.46410 | + | 2.00000i | −0.359211 | + | 0.207390i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | − | 5.00000i | − | 0.510310i | ||||||
\(97\) | −8.66025 | − | 5.00000i | −0.879316 | − | 0.507673i | −0.00888289 | − | 0.999961i | \(-0.502828\pi\) |
−0.870433 | + | 0.492287i | \(0.836161\pi\) | |||||||
\(98\) | 7.79423 | + | 4.50000i | 0.787336 | + | 0.454569i | ||||
\(99\) | − | 4.00000i | − | 0.402015i | ||||||
\(100\) | −0.500000 | + | 0.866025i | −0.0500000 | + | 0.0866025i | ||||
\(101\) | −9.00000 | − | 15.5885i | −0.895533 | − | 1.55111i | −0.833143 | − | 0.553058i | \(-0.813461\pi\) |
−0.0623905 | − | 0.998052i | \(-0.519872\pi\) | |||||||
\(102\) | 1.73205 | − | 1.00000i | 0.171499 | − | 0.0990148i | ||||
\(103\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 8.00000 | 0.780720 | ||||||||
\(106\) | 5.19615 | − | 3.00000i | 0.504695 | − | 0.291386i | ||||
\(107\) | −6.00000 | − | 10.3923i | −0.580042 | − | 1.00466i | −0.995474 | − | 0.0950377i | \(-0.969703\pi\) |
0.415432 | − | 0.909624i | \(-0.363630\pi\) | |||||||
\(108\) | 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 | −0.689714 | − | 0.724082i | \(-0.742264\pi\) |
0.971930 | + | 0.235269i | \(0.0755971\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −10.0000 | −0.928477 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 12.0000 | 1.10469 | ||||||||
\(119\) | −6.92820 | + | 4.00000i | −0.635107 | + | 0.366679i | ||||
\(120\) | −3.00000 | − | 5.19615i | −0.273861 | − | 0.474342i | ||||
\(121\) | 2.50000 | − | 4.33013i | 0.227273 | − | 0.393648i | ||||
\(122\) | − | 2.00000i | − | 0.181071i | ||||||
\(123\) | 5.19615 | + | 3.00000i | 0.468521 | + | 0.270501i | ||||
\(124\) | −3.46410 | − | 2.00000i | −0.311086 | − | 0.179605i | ||||
\(125\) | 12.0000i | 1.07331i | ||||||||
\(126\) | 2.00000 | − | 3.46410i | 0.178174 | − | 0.308607i | ||||
\(127\) | −8.00000 | − | 13.8564i | −0.709885 | − | 1.22956i | −0.964899 | − | 0.262620i | \(-0.915413\pi\) |
0.255014 | − | 0.966937i | \(-0.417920\pi\) | |||||||
\(128\) | 2.59808 | − | 1.50000i | 0.229640 | − | 0.132583i | ||||
\(129\) | −12.0000 | −1.05654 | ||||||||
\(130\) | 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 | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −4.00000 | + | 6.92820i | −0.345547 | + | 0.598506i | ||||
\(135\) | − | 2.00000i | − | 0.172133i | ||||||
\(136\) | 5.19615 | + | 3.00000i | 0.445566 | + | 0.257248i | ||||
\(137\) | 5.19615 | + | 3.00000i | 0.443937 | + | 0.256307i | 0.705266 | − | 0.708942i | \(-0.250827\pi\) |
−0.261329 | + | 0.965250i | \(0.584161\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.00000 | + | 10.3923i | −0.508913 | + | 0.881464i | 0.491033 | + | 0.871141i | \(0.336619\pi\) |
−0.999947 | + | 0.0103230i | \(0.996714\pi\) | |||||||
\(140\) | 4.00000 | + | 6.92820i | 0.338062 | + | 0.585540i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | −17.3205 | + | 10.0000i | −1.43839 | + | 0.830455i | ||||
\(146\) | −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 | \(-0.254293\pi\) |
−0.271821 | + | 0.962348i | \(0.587626\pi\) | |||||||
\(150\) | 0.866025 | + | 0.500000i | 0.0707107 | + | 0.0408248i | ||||
\(151\) | − | 4.00000i | − | 0.325515i | −0.986666 | − | 0.162758i | \(-0.947961\pi\) | ||
0.986666 | − | 0.162758i | \(-0.0520389\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 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 | ||||||||
\(157\) | −18.0000 | −1.43656 | −0.718278 | − | 0.695756i | \(-0.755069\pi\) | ||||
−0.718278 | + | 0.695756i | \(0.755069\pi\) | |||||||
\(158\) | 6.92820 | − | 4.00000i | 0.551178 | − | 0.318223i | ||||
\(159\) | 3.00000 | + | 5.19615i | 0.237915 | + | 0.412082i | ||||
\(160\) | 5.00000 | − | 8.66025i | 0.395285 | − | 0.684653i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −0.866025 | − | 0.500000i | −0.0680414 | − | 0.0392837i | ||||
\(163\) | 6.92820 | + | 4.00000i | 0.542659 | + | 0.313304i | 0.746156 | − | 0.665771i | \(-0.231897\pi\) |
−0.203497 | + | 0.979076i | \(0.565231\pi\) | |||||||
\(164\) | 6.00000i | 0.468521i | ||||||||
\(165\) | 4.00000 | − | 6.92820i | 0.311400 | − | 0.539360i | ||||
\(166\) | 2.00000 | + | 3.46410i | 0.155230 | + | 0.268866i | ||||
\(167\) | 6.92820 | − | 4.00000i | 0.536120 | − | 0.309529i | −0.207385 | − | 0.978259i | \(-0.566495\pi\) |
0.743505 | + | 0.668730i | \(0.233162\pi\) | |||||||
\(168\) | 12.0000 | 0.925820 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 4.00000 | 0.306786 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −6.00000 | − | 10.3923i | −0.457496 | − | 0.792406i | ||||
\(173\) | 3.00000 | − | 5.19615i | 0.228086 | − | 0.395056i | −0.729155 | − | 0.684349i | \(-0.760087\pi\) |
0.957241 | + | 0.289292i | \(0.0934200\pi\) | |||||||
\(174\) | 10.0000i | 0.758098i | ||||||||
\(175\) | −3.46410 | − | 2.00000i | −0.261861 | − | 0.151186i | ||||
\(176\) | −3.46410 | − | 2.00000i | −0.261116 | − | 0.150756i | ||||
\(177\) | 12.0000i | 0.901975i | ||||||||
\(178\) | 1.00000 | − | 1.73205i | 0.0749532 | − | 0.129823i | ||||
\(179\) | 2.00000 | + | 3.46410i | 0.149487 | + | 0.258919i | 0.931038 | − | 0.364922i | \(-0.118904\pi\) |
−0.781551 | + | 0.623841i | \(0.785571\pi\) | |||||||
\(180\) | 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 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.46410 | + | 2.00000i | 0.251976 | + | 0.145479i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.00000 | + | 6.92820i | −0.289430 | + | 0.501307i | −0.973674 | − | 0.227946i | \(-0.926799\pi\) |
0.684244 | + | 0.729253i | \(0.260132\pi\) | |||||||
\(192\) | −3.50000 | − | 6.06218i | −0.252591 | − | 0.437500i | ||||
\(193\) | −15.5885 | + | 9.00000i | −1.12208 | + | 0.647834i | −0.941932 | − | 0.335805i | \(-0.890992\pi\) |
−0.180150 | + | 0.983639i | \(0.557658\pi\) | |||||||
\(194\) | −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 | \(-0.445094\pi\) |
0.938993 | + | 0.343937i | \(0.111761\pi\) | |||||||
\(198\) | −2.00000 | − | 3.46410i | −0.142134 | − | 0.246183i | ||||
\(199\) | 4.00000 | − | 6.92820i | 0.283552 | − | 0.491127i | −0.688705 | − | 0.725042i | \(-0.741820\pi\) |
0.972257 | + | 0.233915i | \(0.0751537\pi\) | |||||||
\(200\) | 3.00000i | 0.212132i | ||||||||
\(201\) | −6.92820 | − | 4.00000i | −0.488678 | − | 0.282138i | ||||
\(202\) | −15.5885 | − | 9.00000i | −1.09680 | − | 0.633238i | ||||
\(203\) | − | 40.0000i | − | 2.80745i | ||||||
\(204\) | −1.00000 | + | 1.73205i | −0.0700140 | + | 0.121268i | ||||
\(205\) | 6.00000 | + | 10.3923i | 0.419058 | + | 0.725830i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 6.92820 | − | 4.00000i | 0.478091 | − | 0.276026i | ||||
\(211\) | 10.0000 | + | 17.3205i | 0.688428 | + | 1.19239i | 0.972346 | + | 0.233544i | \(0.0750324\pi\) |
−0.283918 | + | 0.958849i | \(0.591634\pi\) | |||||||
\(212\) | −3.00000 | + | 5.19615i | −0.206041 | + | 0.356873i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −10.3923 | − | 6.00000i | −0.710403 | − | 0.410152i | ||||
\(215\) | −20.7846 | − | 12.0000i | −1.41750 | − | 0.818393i | ||||
\(216\) | − | 3.00000i | − | 0.204124i | ||||||
\(217\) | 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 | −0.379509 | − | 0.925188i | \(-0.623907\pi\) |
0.611482 | + | 0.791258i | \(0.290574\pi\) | |||||||
\(224\) | 10.0000 | + | 17.3205i | 0.668153 | + | 1.15728i | ||||
\(225\) | −0.500000 | + | 0.866025i | −0.0333333 | + | 0.0577350i | ||||
\(226\) | − | 6.00000i | − | 0.399114i | ||||||
\(227\) | 17.3205 | + | 10.0000i | 1.14960 | + | 0.663723i | 0.948790 | − | 0.315906i | \(-0.102309\pi\) |
0.200812 | + | 0.979630i | \(0.435642\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.0000i | 0.660819i | 0.943838 | + | 0.330409i | \(0.107187\pi\) | ||||
−0.943838 | + | 0.330409i | \(0.892813\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.00000 | + | 13.8564i | 0.526361 | + | 0.911685i | ||||
\(232\) | −25.9808 | + | 15.0000i | −1.70572 | + | 0.984798i | ||||
\(233\) | 14.0000 | 0.917170 | 0.458585 | − | 0.888650i | \(-0.348356\pi\) | ||||
0.458585 | + | 0.888650i | \(0.348356\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −10.3923 | + | 6.00000i | −0.676481 | + | 0.390567i | ||||
\(237\) | 4.00000 | + | 6.92820i | 0.259828 | + | 0.450035i | ||||
\(238\) | −4.00000 | + | 6.92820i | −0.259281 | + | 0.449089i | ||||
\(239\) | − | 24.0000i | − | 1.55243i | −0.630468 | − | 0.776215i | \(-0.717137\pi\) | ||
0.630468 | − | 0.776215i | \(-0.282863\pi\) | |||||||
\(240\) | −1.73205 | − | 1.00000i | −0.111803 | − | 0.0645497i | ||||
\(241\) | 8.66025 | + | 5.00000i | 0.557856 | + | 0.322078i | 0.752285 | − | 0.658838i | \(-0.228952\pi\) |
−0.194429 | + | 0.980917i | \(0.562285\pi\) | |||||||
\(242\) | − | 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 | ||||
\(246\) | 6.00000 | 0.382546 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −12.0000 | −0.762001 | ||||||||
\(249\) | −3.46410 | + | 2.00000i | −0.219529 | + | 0.126745i | ||||
\(250\) | 6.00000 | + | 10.3923i | 0.379473 | + | 0.657267i | ||||
\(251\) | −6.00000 | + | 10.3923i | −0.378717 | + | 0.655956i | −0.990876 | − | 0.134778i | \(-0.956968\pi\) |
0.612159 | + | 0.790735i | \(0.290301\pi\) | |||||||
\(252\) | 4.00000i | 0.251976i | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −13.8564 | − | 8.00000i | −0.869428 | − | 0.501965i | ||||
\(255\) | 4.00000i | 0.250490i | ||||||||
\(256\) | 8.50000 | − | 14.7224i | 0.531250 | − | 0.920152i | ||||
\(257\) | 13.0000 | + | 22.5167i | 0.810918 | + | 1.40455i | 0.912222 | + | 0.409695i | \(0.134365\pi\) |
−0.101305 | + | 0.994855i | \(0.532302\pi\) | |||||||
\(258\) | −10.3923 | + | 6.00000i | −0.646997 | + | 0.373544i | ||||
\(259\) | −8.00000 | −0.497096 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −10.0000 | −0.618984 | ||||||||
\(262\) | 3.46410 | − | 2.00000i | 0.214013 | − | 0.123560i | ||||
\(263\) | −12.0000 | − | 20.7846i | −0.739952 | − | 1.28163i | −0.952517 | − | 0.304487i | \(-0.901515\pi\) |
0.212565 | − | 0.977147i | \(-0.431818\pi\) | |||||||
\(264\) | 6.00000 | − | 10.3923i | 0.369274 | − | 0.639602i | ||||
\(265\) | 12.0000i | 0.737154i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.73205 | + | 1.00000i | 0.106000 | + | 0.0611990i | ||||
\(268\) | − | 8.00000i | − | 0.488678i | ||||||
\(269\) | −11.0000 | + | 19.0526i | −0.670682 | + | 1.16166i | 0.307029 | + | 0.951700i | \(0.400665\pi\) |
−0.977711 | + | 0.209955i | \(0.932668\pi\) | |||||||
\(270\) | −1.00000 | − | 1.73205i | −0.0608581 | − | 0.105409i | ||||
\(271\) | 10.3923 | − | 6.00000i | 0.631288 | − | 0.364474i | −0.149963 | − | 0.988692i | \(-0.547915\pi\) |
0.781251 | + | 0.624218i | \(0.214582\pi\) | |||||||
\(272\) | 2.00000 | 0.121268 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.00000 | 0.362473 | ||||||||
\(275\) | −3.46410 | + | 2.00000i | −0.208893 | + | 0.120605i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.00000 | + | 8.66025i | −0.300421 | + | 0.520344i | −0.976231 | − | 0.216731i | \(-0.930460\pi\) |
0.675810 | + | 0.737075i | \(0.263794\pi\) | |||||||
\(278\) | 12.0000i | 0.719712i | ||||||||
\(279\) | −3.46410 | − | 2.00000i | −0.207390 | − | 0.119737i | ||||
\(280\) | 20.7846 | + | 12.0000i | 1.24212 | + | 0.717137i | ||||
\(281\) | 10.0000i | 0.596550i | 0.954480 | + | 0.298275i | \(0.0964112\pi\) | ||||
−0.954480 | + | 0.298275i | \(0.903589\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.00000 | + | 10.3923i | 0.356663 | + | 0.617758i | 0.987401 | − | 0.158237i | \(-0.0505811\pi\) |
−0.630738 | + | 0.775996i | \(0.717248\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −24.0000 | −1.41668 | ||||||||
\(288\) | 4.33013 | − | 2.50000i | 0.255155 | − | 0.147314i | ||||
\(289\) | 6.50000 | + | 11.2583i | 0.382353 | + | 0.662255i | ||||
\(290\) | −10.0000 | + | 17.3205i | −0.587220 | + | 1.01710i | ||||
\(291\) | − | 10.0000i | − | 0.586210i | ||||||
\(292\) | 1.73205 | + | 1.00000i | 0.101361 | + | 0.0585206i | ||||
\(293\) | −5.19615 | − | 3.00000i | −0.303562 | − | 0.175262i | 0.340480 | − | 0.940252i | \(-0.389411\pi\) |
−0.644042 | + | 0.764990i | \(0.722744\pi\) | |||||||
\(294\) | 9.00000i | 0.524891i | ||||||||
\(295\) | −12.0000 | + | 20.7846i | −0.698667 | + | 1.21013i | ||||
\(296\) | 3.00000 | + | 5.19615i | 0.174371 | + | 0.302020i | ||||
\(297\) | 3.46410 | − | 2.00000i | 0.201008 | − | 0.116052i | ||||
\(298\) | 6.00000 | 0.347571 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −1.00000 | −0.0577350 | ||||||||
\(301\) | 41.5692 | − | 24.0000i | 2.39601 | − | 1.38334i | ||||
\(302\) | −2.00000 | − | 3.46410i | −0.115087 | − | 0.199337i | ||||
\(303\) | 9.00000 | − | 15.5885i | 0.517036 | − | 0.895533i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.46410 | + | 2.00000i | 0.198354 | + | 0.114520i | ||||
\(306\) | 1.73205 | + | 1.00000i | 0.0990148 | + | 0.0571662i | ||||
\(307\) | 16.0000i | 0.913168i | 0.889680 | + | 0.456584i | \(0.150927\pi\) | ||||
−0.889680 | + | 0.456584i | \(0.849073\pi\) | |||||||
\(308\) | −8.00000 | + | 13.8564i | −0.455842 | + | 0.789542i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −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 | \(0.554238\pi\) | |||||||
\(314\) | −15.5885 | + | 9.00000i | −0.879708 | + | 0.507899i | ||||
\(315\) | 4.00000 | + | 6.92820i | 0.225374 | + | 0.390360i | ||||
\(316\) | −4.00000 | + | 6.92820i | −0.225018 | + | 0.389742i | ||||
\(317\) | 26.0000i | 1.46031i | 0.683284 | + | 0.730153i | \(0.260551\pi\) | ||||
−0.683284 | + | 0.730153i | \(0.739449\pi\) | |||||||
\(318\) | 5.19615 | + | 3.00000i | 0.291386 | + | 0.168232i | ||||
\(319\) | −34.6410 | − | 20.0000i | −1.93952 | − | 1.11979i | ||||
\(320\) | − | 14.0000i | − | 0.782624i | ||||||
\(321\) | 6.00000 | − | 10.3923i | 0.334887 | − | 0.580042i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 8.00000 | 0.443079 | ||||||||
\(327\) | 1.73205 | − | 1.00000i | 0.0957826 | − | 0.0553001i | ||||
\(328\) | 9.00000 | + | 15.5885i | 0.496942 | + | 0.860729i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | − | 8.00000i | − | 0.440386i | ||||||
\(331\) | 13.8564 | + | 8.00000i | 0.761617 | + | 0.439720i | 0.829876 | − | 0.557948i | \(-0.188411\pi\) |
−0.0682590 | + | 0.997668i | \(0.521744\pi\) | |||||||
\(332\) | −3.46410 | − | 2.00000i | −0.190117 | − | 0.109764i | ||||
\(333\) | 2.00000i | 0.109599i | ||||||||
\(334\) | 4.00000 | − | 6.92820i | 0.218870 | − | 0.379094i | ||||
\(335\) | −8.00000 | − | 13.8564i | −0.437087 | − | 0.757056i | ||||
\(336\) | 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 | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 8.00000i | − | 0.431959i | ||||||
\(344\) | −31.1769 | − | 18.0000i | −1.68095 | − | 0.970495i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 6.00000i | − | 0.322562i | ||||||
\(347\) | 6.00000 | − | 10.3923i | 0.322097 | − | 0.557888i | −0.658824 | − | 0.752297i | \(-0.728946\pi\) |
0.980921 | + | 0.194409i | \(0.0622790\pi\) | |||||||
\(348\) | −5.00000 | − | 8.66025i | −0.268028 | − | 0.464238i | ||||
\(349\) | 22.5167 | − | 13.0000i | 1.20529 | − | 0.695874i | 0.243563 | − | 0.969885i | \(-0.421684\pi\) |
0.961727 | + | 0.274011i | \(0.0883505\pi\) | |||||||
\(350\) | −4.00000 | −0.213809 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 20.0000 | 1.06600 | ||||||||
\(353\) | −1.73205 | + | 1.00000i | −0.0921878 | + | 0.0532246i | −0.545385 | − | 0.838186i | \(-0.683617\pi\) |
0.453197 | + | 0.891410i | \(0.350283\pi\) | |||||||
\(354\) | 6.00000 | + | 10.3923i | 0.318896 | + | 0.552345i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 2.00000i | 0.106000i | ||||||||
\(357\) | −6.92820 | − | 4.00000i | −0.366679 | − | 0.211702i | ||||
\(358\) | 3.46410 | + | 2.00000i | 0.183083 | + | 0.105703i | ||||
\(359\) | − | 24.0000i | − | 1.26667i | −0.773877 | − | 0.633336i | \(-0.781685\pi\) | ||
0.773877 | − | 0.633336i | \(-0.218315\pi\) | |||||||
\(360\) | 3.00000 | − | 5.19615i | 0.158114 | − | 0.273861i | ||||
\(361\) | −9.50000 | − | 16.4545i | −0.500000 | − | 0.866025i | ||||
\(362\) | 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 | 0.578101 | − | 0.815966i | \(-0.303794\pi\) |
−0.995697 | + | 0.0926670i | \(0.970461\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.00000i | 0.312348i | ||||||||
\(370\) | 3.46410 | + | 2.00000i | 0.180090 | + | 0.103975i | ||||
\(371\) | −20.7846 | − | 12.0000i | −1.07908 | − | 0.623009i | ||||
\(372\) | − | 4.00000i | − | 0.207390i | ||||||
\(373\) | 13.0000 | − | 22.5167i | 0.673114 | − | 1.16587i | −0.303902 | − | 0.952703i | \(-0.598289\pi\) |
0.977016 | − | 0.213165i | \(-0.0683772\pi\) | |||||||
\(374\) | 4.00000 | + | 6.92820i | 0.206835 | + | 0.358249i | ||||
\(375\) | −10.3923 | + | 6.00000i | −0.536656 | + | 0.309839i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 4.00000 | 0.205738 | ||||||||
\(379\) | −20.7846 | + | 12.0000i | −1.06763 | + | 0.616399i | −0.927534 | − | 0.373739i | \(-0.878076\pi\) |
−0.140100 | + | 0.990137i | \(0.544742\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.00000 | − | 13.8564i | 0.409852 | − | 0.709885i | ||||
\(382\) | 8.00000i | 0.409316i | ||||||||
\(383\) | 13.8564 | + | 8.00000i | 0.708029 | + | 0.408781i | 0.810331 | − | 0.585973i | \(-0.199287\pi\) |
−0.102302 | + | 0.994753i | \(0.532621\pi\) | |||||||
\(384\) | 2.59808 | + | 1.50000i | 0.132583 | + | 0.0765466i | ||||
\(385\) | 32.0000i | 1.63087i | ||||||||
\(386\) | −9.00000 | + | 15.5885i | −0.458088 | + | 0.793432i | ||||
\(387\) | −6.00000 | − | 10.3923i | −0.304997 | − | 0.528271i | ||||
\(388\) | 8.66025 | − | 5.00000i | 0.439658 | − | 0.253837i | ||||
\(389\) | −22.0000 | −1.11544 | −0.557722 | − | 0.830028i | \(-0.688325\pi\) | ||||
−0.557722 | + | 0.830028i | \(0.688325\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −23.3827 | + | 13.5000i | −1.18100 | + | 0.681853i | ||||
\(393\) | 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 | ||||
\(397\) | 32.9090 | + | 19.0000i | 1.65165 | + | 0.953583i | 0.976392 | + | 0.216004i | \(0.0693024\pi\) |
0.675261 | + | 0.737579i | \(0.264031\pi\) | |||||||
\(398\) | − | 8.00000i | − | 0.401004i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.500000 | + | 0.866025i | 0.0250000 | + | 0.0433013i | ||||
\(401\) | −19.0526 | + | 11.0000i | −0.951439 | + | 0.549314i | −0.893528 | − | 0.449008i | \(-0.851777\pi\) |
−0.0579116 | + | 0.998322i | \(0.518444\pi\) | |||||||
\(402\) | −8.00000 | −0.399004 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 18.0000 | 0.895533 | ||||||||
\(405\) | 1.73205 | − | 1.00000i | 0.0860663 | − | 0.0496904i | ||||
\(406\) | −20.0000 | − | 34.6410i | −0.992583 | − | 1.71920i | ||||
\(407\) | −4.00000 | + | 6.92820i | −0.198273 | + | 0.343418i | ||||
\(408\) | 6.00000i | 0.297044i | ||||||||
\(409\) | −29.4449 | − | 17.0000i | −1.45595 | − | 0.840596i | −0.457146 | − | 0.889392i | \(-0.651128\pi\) |
−0.998809 | + | 0.0487958i | \(0.984462\pi\) | |||||||
\(410\) | 10.3923 | + | 6.00000i | 0.513239 | + | 0.296319i | ||||
\(411\) | 6.00000i | 0.295958i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −24.0000 | − | 41.5692i | −1.18096 | − | 2.04549i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.00000 | −0.392705 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −12.0000 | −0.587643 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.00000 | − | 3.46410i | −0.0977064 | − | 0.169232i | 0.813029 | − | 0.582224i | \(-0.197817\pi\) |
−0.910735 | + | 0.412991i | \(0.864484\pi\) | |||||||
\(420\) | −4.00000 | + | 6.92820i | −0.195180 | + | 0.338062i | ||||
\(421\) | − | 10.0000i | − | 0.487370i | −0.969854 | − | 0.243685i | \(-0.921644\pi\) | ||
0.969854 | − | 0.243685i | \(-0.0783563\pi\) | |||||||
\(422\) | 17.3205 | + | 10.0000i | 0.843149 | + | 0.486792i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 18.0000i | 0.874157i | ||||||||
\(425\) | 1.00000 | − | 1.73205i | 0.0485071 | − | 0.0840168i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.92820 | + | 4.00000i | −0.335279 | + | 0.193574i | ||||
\(428\) | 12.0000 | 0.580042 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −24.0000 | −1.15738 | ||||||||
\(431\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(432\) | −0.500000 | − | 0.866025i | −0.0240563 | − | 0.0416667i | ||||
\(433\) | 17.0000 | − | 29.4449i | 0.816968 | − | 1.41503i | −0.0909384 | − | 0.995857i | \(-0.528987\pi\) |
0.907906 | − | 0.419173i | \(-0.137680\pi\) | |||||||
\(434\) | − | 16.0000i | − | 0.768025i | ||||||
\(435\) | −17.3205 | − | 10.0000i | −0.830455 | − | 0.479463i | ||||
\(436\) | 1.73205 | + | 1.00000i | 0.0829502 | + | 0.0478913i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 1.00000 | − | 1.73205i | 0.0477818 | − | 0.0827606i | ||||
\(439\) | 16.0000 | + | 27.7128i | 0.763638 | + | 1.32266i | 0.940963 | + | 0.338508i | \(0.109922\pi\) |
−0.177325 | + | 0.984152i | \(0.556744\pi\) | |||||||
\(440\) | 20.7846 | − | 12.0000i | 0.990867 | − | 0.572078i | ||||
\(441\) | −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 | ||||
\(445\) | 2.00000 | + | 3.46410i | 0.0948091 | + | 0.164214i | ||||
\(446\) | 2.00000 | − | 3.46410i | 0.0947027 | − | 0.164030i | ||||
\(447\) | 6.00000i | 0.283790i | ||||||||
\(448\) | 24.2487 | + | 14.0000i | 1.14564 | + | 0.661438i | ||||
\(449\) | 19.0526 | + | 11.0000i | 0.899146 | + | 0.519122i | 0.876923 | − | 0.480631i | \(-0.159592\pi\) |
0.0222229 | + | 0.999753i | \(0.492926\pi\) | |||||||
\(450\) | 1.00000i | 0.0471405i | ||||||||
\(451\) | −12.0000 | + | 20.7846i | −0.565058 | + | 0.978709i | ||||
\(452\) | 3.00000 | + | 5.19615i | 0.141108 | + | 0.244406i | ||||
\(453\) | 3.46410 | − | 2.00000i | 0.162758 | − | 0.0939682i | ||||
\(454\) | 20.0000 | 0.938647 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.73205 | − | 1.00000i | 0.0810219 | − | 0.0467780i | −0.458942 | − | 0.888466i | \(-0.651771\pi\) |
0.539964 | + | 0.841688i | \(0.318438\pi\) | |||||||
\(458\) | 5.00000 | + | 8.66025i | 0.233635 | + | 0.404667i | ||||
\(459\) | −1.00000 | + | 1.73205i | −0.0466760 | + | 0.0808452i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 32.9090 | + | 19.0000i | 1.53272 | + | 0.884918i | 0.999235 | + | 0.0391109i | \(0.0124526\pi\) |
0.533488 | + | 0.845807i | \(0.320881\pi\) | |||||||
\(462\) | 13.8564 | + | 8.00000i | 0.644658 | + | 0.372194i | ||||
\(463\) | − | 4.00000i | − | 0.185896i | −0.995671 | − | 0.0929479i | \(-0.970371\pi\) | ||
0.995671 | − | 0.0929479i | \(-0.0296290\pi\) | |||||||
\(464\) | −5.00000 | + | 8.66025i | −0.232119 | + | 0.402042i | ||||
\(465\) | −4.00000 | − | 6.92820i | −0.185496 | − | 0.321288i | ||||
\(466\) | 12.1244 | − | 7.00000i | 0.561650 | − | 0.324269i | ||||
\(467\) | −12.0000 | −0.555294 | −0.277647 | − | 0.960683i | \(-0.589555\pi\) | ||||
−0.277647 | + | 0.960683i | \(0.589555\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 32.0000 | 1.47762 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.00000 | − | 15.5885i | −0.414698 | − | 0.718278i | ||||
\(472\) | −18.0000 | + | 31.1769i | −0.828517 | + | 1.43503i | ||||
\(473\) | − | 48.0000i | − | 2.20704i | ||||||
\(474\) | 6.92820 | + | 4.00000i | 0.318223 | + | 0.183726i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 8.00000i | − | 0.366679i | ||||||
\(477\) | −3.00000 | + | 5.19615i | −0.137361 | + | 0.237915i | ||||
\(478\) | −12.0000 | − | 20.7846i | −0.548867 | − | 0.950666i | ||||
\(479\) | 20.7846 | − | 12.0000i | 0.949673 | − | 0.548294i | 0.0566937 | − | 0.998392i | \(-0.481944\pi\) |
0.892979 | + | 0.450098i | \(0.148611\pi\) | |||||||
\(480\) | 10.0000 | 0.456435 | ||||||||
\(481\) | 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 | ||||||
\(487\) | −10.3923 | − | 6.00000i | −0.470920 | − | 0.271886i | 0.245705 | − | 0.969345i | \(-0.420981\pi\) |
−0.716625 | + | 0.697459i | \(0.754314\pi\) | |||||||
\(488\) | 5.19615 | + | 3.00000i | 0.235219 | + | 0.135804i | ||||
\(489\) | 8.00000i | 0.361773i | ||||||||
\(490\) | −9.00000 | + | 15.5885i | −0.406579 | + | 0.704215i | ||||
\(491\) | −6.00000 | − | 10.3923i | −0.270776 | − | 0.468998i | 0.698285 | − | 0.715820i | \(-0.253947\pi\) |
−0.969061 | + | 0.246822i | \(0.920614\pi\) | |||||||
\(492\) | −5.19615 | + | 3.00000i | −0.234261 | + | 0.135250i | ||||
\(493\) | 20.0000 | 0.900755 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 8.00000 | 0.359573 | ||||||||
\(496\) | −3.46410 | + | 2.00000i | −0.155543 | + | 0.0898027i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −2.00000 | + | 3.46410i | −0.0896221 | + | 0.155230i | ||||
\(499\) | − | 24.0000i | − | 1.07439i | −0.843459 | − | 0.537194i | \(-0.819484\pi\) | ||
0.843459 | − | 0.537194i | \(-0.180516\pi\) | |||||||
\(500\) | −10.3923 | − | 6.00000i | −0.464758 | − | 0.268328i | ||||
\(501\) | 6.92820 | + | 4.00000i | 0.309529 | + | 0.178707i | ||||
\(502\) | 12.0000i | 0.535586i | ||||||||
\(503\) | 4.00000 | − | 6.92820i | 0.178351 | − | 0.308913i | −0.762965 | − | 0.646440i | \(-0.776257\pi\) |
0.941316 | + | 0.337527i | \(0.109590\pi\) | |||||||
\(504\) | 6.00000 | + | 10.3923i | 0.267261 | + | 0.462910i | ||||
\(505\) | 31.1769 | − | 18.0000i | 1.38735 | − | 0.800989i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 16.0000 | 0.709885 | ||||||||
\(509\) | 8.66025 | − | 5.00000i | 0.383859 | − | 0.221621i | −0.295637 | − | 0.955300i | \(-0.595532\pi\) |
0.679496 | + | 0.733679i | \(0.262199\pi\) | |||||||
\(510\) | 2.00000 | + | 3.46410i | 0.0885615 | + | 0.153393i | ||||
\(511\) | −4.00000 | + | 6.92820i | −0.176950 | + | 0.306486i | ||||
\(512\) | − | 11.0000i | − | 0.486136i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 22.5167 | + | 13.0000i | 0.993167 | + | 0.573405i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 6.00000 | − | 10.3923i | 0.264135 | − | 0.457496i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −6.92820 | + | 4.00000i | −0.304408 | + | 0.175750i | ||||
\(519\) | 6.00000 | 0.263371 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18.0000 | 0.788594 | 0.394297 | − | 0.918983i | \(-0.370988\pi\) | ||||
0.394297 | + | 0.918983i | \(0.370988\pi\) | |||||||
\(522\) | −8.66025 | + | 5.00000i | −0.379049 | + | 0.218844i | ||||
\(523\) | −22.0000 | − | 38.1051i | −0.961993 | − | 1.66622i | −0.717486 | − | 0.696573i | \(-0.754707\pi\) |
−0.244507 | − | 0.969648i | \(-0.578626\pi\) | |||||||
\(524\) | −2.00000 | + | 3.46410i | −0.0873704 | + | 0.151330i | ||||
\(525\) | − | 4.00000i | − | 0.174574i | ||||||
\(526\) | −20.7846 | − | 12.0000i | −0.906252 | − | 0.523225i | ||||
\(527\) | 6.92820 | + | 4.00000i | 0.301797 | + | 0.174243i | ||||
\(528\) | − | 4.00000i | − | 0.174078i | ||||||
\(529\) | 11.5000 | − | 19.9186i | 0.500000 | − | 0.866025i | ||||
\(530\) | 6.00000 | + | 10.3923i | 0.260623 | + | 0.451413i | ||||
\(531\) | −10.3923 | + | 6.00000i | −0.450988 | + | 0.260378i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 2.00000 | 0.0865485 | ||||||||
\(535\) | 20.7846 | − | 12.0000i | 0.898597 | − | 0.518805i | ||||
\(536\) | −12.0000 | − | 20.7846i | −0.518321 | − | 0.897758i | ||||
\(537\) | −2.00000 | + | 3.46410i | −0.0863064 | + | 0.149487i | ||||
\(538\) | 22.0000i | 0.948487i | ||||||||
\(539\) | −31.1769 | − | 18.0000i | −1.34288 | − | 0.775315i | ||||
\(540\) | 1.73205 | + | 1.00000i | 0.0745356 | + | 0.0430331i | ||||
\(541\) | − | 30.0000i | − | 1.28980i | −0.764267 | − | 0.644900i | \(-0.776899\pi\) | ||
0.764267 | − | 0.644900i | \(-0.223101\pi\) | |||||||
\(542\) | 6.00000 | − | 10.3923i | 0.257722 | − | 0.446388i | ||||
\(543\) | 5.00000 | + | 8.66025i | 0.214571 | + | 0.371647i | ||||
\(544\) | −8.66025 | + | 5.00000i | −0.371305 | + | 0.214373i | ||||
\(545\) | 4.00000 | 0.171341 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.00000 | 0.171028 | 0.0855138 | − | 0.996337i | \(-0.472747\pi\) | ||||
0.0855138 | + | 0.996337i | \(0.472747\pi\) | |||||||
\(548\) | −5.19615 | + | 3.00000i | −0.221969 | + | 0.128154i | ||||
\(549\) | 1.00000 | + | 1.73205i | 0.0426790 | + | 0.0739221i | ||||
\(550\) | −2.00000 | + | 3.46410i | −0.0852803 | + | 0.147710i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −27.7128 | − | 16.0000i | −1.17847 | − | 0.680389i | ||||
\(554\) | 10.0000i | 0.424859i | ||||||||
\(555\) | −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 | \(-0.791205\pi\) |
0.131965 | + | 0.991254i | \(0.457871\pi\) | |||||||
\(558\) | −4.00000 | −0.169334 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 8.00000 | 0.338062 | ||||||||
\(561\) | −6.92820 | + | 4.00000i | −0.292509 | + | 0.168880i | ||||
\(562\) | 5.00000 | + | 8.66025i | 0.210912 | + | 0.365311i | ||||
\(563\) | −6.00000 | + | 10.3923i | −0.252870 | + | 0.437983i | −0.964315 | − | 0.264758i | \(-0.914708\pi\) |
0.711445 | + | 0.702742i | \(0.248041\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.3923 | + | 6.00000i | 0.437208 | + | 0.252422i | ||||
\(566\) | 10.3923 | + | 6.00000i | 0.436821 | + | 0.252199i | ||||
\(567\) | 4.00000i | 0.167984i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 17.0000 | + | 29.4449i | 0.712677 | + | 1.23439i | 0.963849 | + | 0.266450i | \(0.0858508\pi\) |
−0.251172 | + | 0.967943i | \(0.580816\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.00000 | 0.167395 | 0.0836974 | − | 0.996491i | \(-0.473327\pi\) | ||||
0.0836974 | + | 0.996491i | \(0.473327\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8.00000 | −0.334205 | ||||||||
\(574\) | −20.7846 | + | 12.0000i | −0.867533 | + | 0.500870i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 3.50000 | − | 6.06218i | 0.145833 | − | 0.252591i | ||||
\(577\) | − | 46.0000i | − | 1.91501i | −0.288425 | − | 0.957503i | \(-0.593132\pi\) | ||
0.288425 | − | 0.957503i | \(-0.406868\pi\) | |||||||
\(578\) | 11.2583 | + | 6.50000i | 0.468285 | + | 0.270364i | ||||
\(579\) | −15.5885 | − | 9.00000i | −0.647834 | − | 0.374027i | ||||
\(580\) | − | 20.0000i | − | 0.830455i | ||||||
\(581\) | 8.00000 | − | 13.8564i | 0.331896 | − | 0.574861i | ||||
\(582\) | −5.00000 | − | 8.66025i | −0.207257 | − | 0.358979i | ||||
\(583\) | −20.7846 | + | 12.0000i | −0.860811 | + | 0.496989i | ||||
\(584\) | 6.00000 | 0.248282 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6.00000 | −0.247858 | ||||||||
\(587\) | 24.2487 | − | 14.0000i | 1.00085 | − | 0.577842i | 0.0923513 | − | 0.995726i | \(-0.470562\pi\) |
0.908500 | + | 0.417885i | \(0.137228\pi\) | |||||||
\(588\) | −4.50000 | − | 7.79423i | −0.185577 | − | 0.321429i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 24.0000i | 0.988064i | ||||||||
\(591\) | 15.5885 | + | 9.00000i | 0.641223 | + | 0.370211i | ||||
\(592\) | 1.73205 | + | 1.00000i | 0.0711868 | + | 0.0410997i | ||||
\(593\) | 26.0000i | 1.06769i | 0.845582 | + | 0.533846i | \(0.179254\pi\) | ||||
−0.845582 | + | 0.533846i | \(0.820746\pi\) | |||||||
\(594\) | 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 | ||||||||
\(599\) | −40.0000 | −1.63436 | −0.817178 | − | 0.576386i | \(-0.804463\pi\) | ||||
−0.817178 | + | 0.576386i | \(0.804463\pi\) | |||||||
\(600\) | −2.59808 | + | 1.50000i | −0.106066 | + | 0.0612372i | ||||
\(601\) | 19.0000 | + | 32.9090i | 0.775026 | + | 1.34238i | 0.934780 | + | 0.355228i | \(0.115597\pi\) |
−0.159754 | + | 0.987157i | \(0.551070\pi\) | |||||||
\(602\) | 24.0000 | − | 41.5692i | 0.978167 | − | 1.69423i | ||||
\(603\) | − | 8.00000i | − | 0.325785i | ||||||
\(604\) | 3.46410 | + | 2.00000i | 0.140952 | + | 0.0813788i | ||||
\(605\) | 8.66025 | + | 5.00000i | 0.352089 | + | 0.203279i | ||||
\(606\) | − | 18.0000i | − | 0.731200i | ||||||
\(607\) | 8.00000 | − | 13.8564i | 0.324710 | − | 0.562414i | −0.656744 | − | 0.754114i | \(-0.728067\pi\) |
0.981454 | + | 0.191700i | \(0.0614000\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 34.6410 | − | 20.0000i | 1.40372 | − | 0.810441i | ||||
\(610\) | 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 | \(-0.679527\pi\) |
0.464614 | + | 0.885514i | \(0.346193\pi\) | |||||||
\(614\) | 8.00000 | + | 13.8564i | 0.322854 | + | 0.559199i | ||||
\(615\) | −6.00000 | + | 10.3923i | −0.241943 | + | 0.419058i | ||||
\(616\) | 48.0000i | 1.93398i | ||||||||
\(617\) | −19.0526 | − | 11.0000i | −0.767027 | − | 0.442843i | 0.0647859 | − | 0.997899i | \(-0.479364\pi\) |
−0.831813 | + | 0.555056i | \(0.812697\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 24.0000i | − | 0.964641i | −0.875995 | − | 0.482321i | \(-0.839794\pi\) | ||
0.875995 | − | 0.482321i | \(-0.160206\pi\) | |||||||
\(620\) | 4.00000 | − | 6.92820i | 0.160644 | − | 0.278243i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8.00000 | −0.320513 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.0000 | −0.760000 | ||||||||
\(626\) | −5.19615 | + | 3.00000i | −0.207680 | + | 0.119904i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 9.00000 | − | 15.5885i | 0.359139 | − | 0.622047i | ||||
\(629\) | − | 4.00000i | − | 0.159490i | ||||||
\(630\) | 6.92820 | + | 4.00000i | 0.276026 | + | 0.159364i | ||||
\(631\) | 17.3205 | + | 10.0000i | 0.689519 | + | 0.398094i | 0.803432 | − | 0.595397i | \(-0.203005\pi\) |
−0.113913 | + | 0.993491i | \(0.536339\pi\) | |||||||
\(632\) | 24.0000i | 0.954669i | ||||||||
\(633\) | −10.0000 | + | 17.3205i | −0.397464 | + | 0.688428i | ||||
\(634\) | 13.0000 | + | 22.5167i | 0.516296 | + | 0.894251i | ||||
\(635\) | 27.7128 | − | 16.0000i | 1.09975 | − | 0.634941i | ||||
\(636\) | −6.00000 | −0.237915 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −40.0000 | −1.58362 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 3.00000 | + | 5.19615i | 0.118585 | + | 0.205396i | ||||
\(641\) | 1.00000 | − | 1.73205i | 0.0394976 | − | 0.0684119i | −0.845601 | − | 0.533816i | \(-0.820758\pi\) |
0.885098 | + | 0.465404i | \(0.154091\pi\) | |||||||
\(642\) | − | 12.0000i | − | 0.473602i | ||||||
\(643\) | 34.6410 | + | 20.0000i | 1.36611 | + | 0.788723i | 0.990429 | − | 0.138027i | \(-0.0440759\pi\) |
0.375680 | + | 0.926750i | \(0.377409\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 24.0000i | − | 0.944999i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4.00000 | − | 6.92820i | −0.157256 | − | 0.272376i | 0.776622 | − | 0.629967i | \(-0.216932\pi\) |
−0.933878 | + | 0.357591i | \(0.883598\pi\) | |||||||
\(648\) | 2.59808 | − | 1.50000i | 0.102062 | − | 0.0589256i | ||||
\(649\) | −48.0000 | −1.88416 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 16.0000 | 0.627089 | ||||||||
\(652\) | −6.92820 | + | 4.00000i | −0.271329 | + | 0.156652i | ||||
\(653\) | −3.00000 | − | 5.19615i | −0.117399 | − | 0.203341i | 0.801337 | − | 0.598213i | \(-0.204122\pi\) |
−0.918736 | + | 0.394872i | \(0.870789\pi\) | |||||||
\(654\) | 1.00000 | − | 1.73205i | 0.0391031 | − | 0.0677285i | ||||
\(655\) | 8.00000i | 0.312586i | ||||||||
\(656\) | 5.19615 | + | 3.00000i | 0.202876 | + | 0.117130i | ||||
\(657\) | 1.73205 | + | 1.00000i | 0.0675737 | + | 0.0390137i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −14.0000 | + | 24.2487i | −0.545363 | + | 0.944596i | 0.453221 | + | 0.891398i | \(0.350275\pi\) |
−0.998584 | + | 0.0531977i | \(0.983059\pi\) | |||||||
\(660\) | 4.00000 | + | 6.92820i | 0.155700 | + | 0.269680i | ||||
\(661\) | −25.9808 | + | 15.0000i | −1.01053 | + | 0.583432i | −0.911348 | − | 0.411636i | \(-0.864957\pi\) |
−0.0991864 | + | 0.995069i | \(0.531624\pi\) | |||||||
\(662\) | 16.0000 | 0.621858 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −12.0000 | −0.465690 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.00000 | + | 1.73205i | 0.0387492 | + | 0.0671156i | ||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 8.00000i | 0.309529i | ||||||||
\(669\) | 3.46410 | + | 2.00000i | 0.133930 | + | 0.0773245i | ||||
\(670\) | −13.8564 | − | 8.00000i | −0.535320 | − | 0.309067i | ||||
\(671\) | 8.00000i | 0.308837i | ||||||||
\(672\) | −10.0000 | + | 17.3205i | −0.385758 | + | 0.668153i | ||||
\(673\) | −7.00000 | − | 12.1244i | −0.269830 | − | 0.467360i | 0.698988 | − | 0.715134i | \(-0.253634\pi\) |
−0.968818 | + | 0.247774i | \(0.920301\pi\) | |||||||
\(674\) | −15.5885 | + | 9.00000i | −0.600445 | + | 0.346667i | ||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 22.0000 | 0.845529 | 0.422764 | − | 0.906240i | \(-0.361060\pi\) | ||||
0.422764 | + | 0.906240i | \(0.361060\pi\) | |||||||
\(678\) | 5.19615 | − | 3.00000i | 0.199557 | − | 0.115214i | ||||
\(679\) | 20.0000 | + | 34.6410i | 0.767530 | + | 1.32940i | ||||
\(680\) | −6.00000 | + | 10.3923i | −0.230089 | + | 0.398527i | ||||
\(681\) | 20.0000i | 0.766402i | ||||||||
\(682\) | −13.8564 | − | 8.00000i | −0.530589 | − | 0.306336i | ||||
\(683\) | −10.3923 | − | 6.00000i | −0.397650 | − | 0.229584i | 0.287819 | − | 0.957685i | \(-0.407070\pi\) |
−0.685470 | + | 0.728101i | \(0.740403\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.00000 | + | 10.3923i | −0.229248 | + | 0.397070i | ||||
\(686\) | −4.00000 | − | 6.92820i | −0.152721 | − | 0.264520i | ||||
\(687\) | −8.66025 | + | 5.00000i | −0.330409 | + | 0.190762i | ||||
\(688\) | −12.0000 | −0.457496 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20.7846 | + | 12.0000i | −0.790684 | + | 0.456502i | −0.840203 | − | 0.542272i | \(-0.817564\pi\) |
0.0495194 | + | 0.998773i | \(0.484231\pi\) | |||||||
\(692\) | 3.00000 | + | 5.19615i | 0.114043 | + | 0.197528i | ||||
\(693\) | −8.00000 | + | 13.8564i | −0.303895 | + | 0.526361i | ||||
\(694\) | − | 12.0000i | − | 0.455514i | ||||||
\(695\) | −20.7846 | − | 12.0000i | −0.788405 | − | 0.455186i | ||||
\(696\) | −25.9808 | − | 15.0000i | −0.984798 | − | 0.568574i | ||||
\(697\) | − | 12.0000i | − | 0.454532i | ||||||
\(698\) | 13.0000 | − | 22.5167i | 0.492057 | − | 0.852268i | ||||
\(699\) | 7.00000 | + | 12.1244i | 0.264764 | + | 0.458585i | ||||
\(700\) | 3.46410 | − | 2.00000i | 0.130931 | − | 0.0755929i | ||||
\(701\) | 34.0000 | 1.28416 | 0.642081 | − | 0.766637i | \(-0.278071\pi\) | ||||
0.642081 | + | 0.766637i | \(0.278071\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 24.2487 | − | 14.0000i | 0.913908 | − | 0.527645i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.00000 | + | 1.73205i | −0.0376355 | + | 0.0651866i | ||||
\(707\) | 72.0000i | 2.70784i | ||||||||
\(708\) | −10.3923 | − | 6.00000i | −0.390567 | − | 0.225494i | ||||
\(709\) | −22.5167 | − | 13.0000i | −0.845631 | − | 0.488225i | 0.0135434 | − | 0.999908i | \(-0.495689\pi\) |
−0.859174 | + | 0.511683i | \(0.829022\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.00000 | + | 6.92820i | −0.150012 | + | 0.259828i | ||||
\(712\) | 3.00000 | + | 5.19615i | 0.112430 | + | 0.194734i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | −8.00000 | −0.299392 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −4.00000 | −0.149487 | ||||||||
\(717\) | 20.7846 | − | 12.0000i | 0.776215 | − | 0.448148i | ||||
\(718\) | −12.0000 | − | 20.7846i | −0.447836 | − | 0.775675i | ||||
\(719\) | −12.0000 | + | 20.7846i | −0.447524 | + | 0.775135i | −0.998224 | − | 0.0595683i | \(-0.981028\pi\) |
0.550700 | + | 0.834703i | \(0.314361\pi\) | |||||||
\(720\) | − | 2.00000i | − | 0.0745356i | ||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −16.4545 | − | 9.50000i | −0.612372 | − | 0.353553i | ||||
\(723\) | 10.0000i | 0.371904i | ||||||||
\(724\) | −5.00000 | + | 8.66025i | −0.185824 | + | 0.321856i | ||||
\(725\) | 5.00000 | + | 8.66025i | 0.185695 | + | 0.321634i | ||||
\(726\) | 4.33013 | − | 2.50000i | 0.160706 | − | 0.0927837i | ||||
\(727\) | −8.00000 | −0.296704 | −0.148352 | − | 0.988935i | \(-0.547397\pi\) | ||||
−0.148352 | + | 0.988935i | \(0.547397\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 3.46410 | − | 2.00000i | 0.128212 | − | 0.0740233i | ||||
\(731\) | 12.0000 | + | 20.7846i | 0.443836 | + | 0.768747i | ||||
\(732\) | −1.00000 | + | 1.73205i | −0.0369611 | + | 0.0640184i | ||||
\(733\) | 30.0000i | 1.10808i | 0.832492 | + | 0.554038i | \(0.186914\pi\) | ||||
−0.832492 | + | 0.554038i | \(0.813086\pi\) | |||||||
\(734\) | −13.8564 | − | 8.00000i | −0.511449 | − | 0.295285i | ||||
\(735\) | −15.5885 | − | 9.00000i | −0.574989 | − | 0.331970i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 16.0000 | − | 27.7128i | 0.589368 | − | 1.02081i | ||||
\(738\) | 3.00000 | + | 5.19615i | 0.110432 | + | 0.191273i | ||||
\(739\) | −27.7128 | + | 16.0000i | −1.01943 | + | 0.588570i | −0.913939 | − | 0.405851i | \(-0.866975\pi\) |
−0.105493 | + | 0.994420i | \(0.533642\pi\) | |||||||
\(740\) | −4.00000 | −0.147043 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −24.0000 | −0.881068 | ||||||||
\(743\) | 41.5692 | − | 24.0000i | 1.52503 | − | 0.880475i | 0.525467 | − | 0.850814i | \(-0.323891\pi\) |
0.999560 | − | 0.0296605i | \(-0.00944260\pi\) | |||||||
\(744\) | −6.00000 | − | 10.3923i | −0.219971 | − | 0.381000i | ||||
\(745\) | −6.00000 | + | 10.3923i | −0.219823 | + | 0.380745i | ||||
\(746\) | − | 26.0000i | − | 0.951928i | ||||||
\(747\) | −3.46410 | − | 2.00000i | −0.126745 | − | 0.0731762i | ||||
\(748\) | −6.92820 | − | 4.00000i | −0.253320 | − | 0.146254i | ||||
\(749\) | 48.0000i | 1.75388i | ||||||||
\(750\) | −6.00000 | + | 10.3923i | −0.219089 | + | 0.379473i | ||||
\(751\) | 4.00000 | + | 6.92820i | 0.145962 | + | 0.252814i | 0.929731 | − | 0.368238i | \(-0.120039\pi\) |
−0.783769 | + | 0.621052i | \(0.786706\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −12.0000 | −0.437304 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.00000 | 0.291150 | ||||||||
\(756\) | −3.46410 | + | 2.00000i | −0.125988 | + | 0.0727393i | ||||
\(757\) | −11.0000 | − | 19.0526i | −0.399802 | − | 0.692477i | 0.593899 | − | 0.804539i | \(-0.297588\pi\) |
−0.993701 | + | 0.112062i | \(0.964254\pi\) | |||||||
\(758\) | −12.0000 | + | 20.7846i | −0.435860 | + | 0.754931i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8.66025 | − | 5.00000i | −0.313934 | − | 0.181250i | 0.334752 | − | 0.942306i | \(-0.391348\pi\) |
−0.648686 | + | 0.761057i | \(0.724681\pi\) | |||||||
\(762\) | − | 16.0000i | − | 0.579619i | ||||||
\(763\) | −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 | ||||
\(766\) | 16.0000 | 0.578103 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 17.0000 | 0.613435 | ||||||||
\(769\) | −25.9808 | + | 15.0000i | −0.936890 | + | 0.540914i | −0.888984 | − | 0.457938i | \(-0.848588\pi\) |
−0.0479061 | + | 0.998852i | \(0.515255\pi\) | |||||||
\(770\) | 16.0000 | + | 27.7128i | 0.576600 | + | 0.998700i | ||||
\(771\) | −13.0000 | + | 22.5167i | −0.468184 | + | 0.810918i | ||||
\(772\) | − | 18.0000i | − | 0.647834i | ||||||
\(773\) | −8.66025 | − | 5.00000i | −0.311488 | − | 0.179838i | 0.336104 | − | 0.941825i | \(-0.390891\pi\) |
−0.647592 | + | 0.761987i | \(0.724224\pi\) | |||||||
\(774\) | −10.3923 | − | 6.00000i | −0.373544 | − | 0.215666i | ||||
\(775\) | 4.00000i | 0.143684i | ||||||||
\(776\) | 15.0000 | − | 25.9808i | 0.538469 | − | 0.932655i | ||||
\(777\) | −4.00000 | − | 6.92820i | −0.143499 | − | 0.248548i | ||||
\(778\) | −19.0526 | + | 11.0000i | −0.683067 | + | 0.394369i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.00000 | − | 8.66025i | −0.178685 | − | 0.309492i | ||||
\(784\) | −4.50000 | + | 7.79423i | −0.160714 | + | 0.278365i | ||||
\(785\) | − | 36.0000i | − | 1.28490i | ||||||
\(786\) | 3.46410 | + | 2.00000i | 0.123560 | + | 0.0713376i | ||||
\(787\) | −27.7128 | − | 16.0000i | −0.987855 | − | 0.570338i | −0.0832226 | − | 0.996531i | \(-0.526521\pi\) |
−0.904632 | + | 0.426193i | \(0.859855\pi\) | |||||||
\(788\) | 18.0000i | 0.641223i | ||||||||
\(789\) | 12.0000 | − | 20.7846i | 0.427211 | − | 0.739952i | ||||
\(790\) | 8.00000 | + | 13.8564i | 0.284627 | + | 0.492989i | ||||
\(791\) | −20.7846 | + | 12.0000i | −0.739016 | + | 0.426671i | ||||
\(792\) | 12.0000 | 0.426401 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 38.0000 | 1.34857 | ||||||||
\(795\) | −10.3923 | + | 6.00000i | −0.368577 | + | 0.212798i | ||||
\(796\) | 4.00000 | + | 6.92820i | 0.141776 | + | 0.245564i | ||||
\(797\) | 23.0000 | − | 39.8372i | 0.814702 | − | 1.41110i | −0.0948400 | − | 0.995493i | \(-0.530234\pi\) |
0.909542 | − | 0.415612i | \(-0.136433\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −4.33013 | − | 2.50000i | −0.153093 | − | 0.0883883i | ||||
\(801\) | 2.00000i | 0.0706665i | ||||||||
\(802\) | −11.0000 | + | 19.0526i | −0.388424 | + | 0.672769i | ||||
\(803\) | 4.00000 | + | 6.92820i | 0.141157 | + | 0.244491i | ||||
\(804\) | 6.92820 | − | 4.00000i | 0.244339 | − | 0.141069i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −22.0000 | −0.774437 | ||||||||
\(808\) | 46.7654 | − | 27.0000i | 1.64520 | − | 0.949857i | ||||
\(809\) | 15.0000 | + | 25.9808i | 0.527372 | + | 0.913435i | 0.999491 | + | 0.0319002i | \(0.0101559\pi\) |
−0.472119 | + | 0.881535i | \(0.656511\pi\) | |||||||
\(810\) | 1.00000 | − | 1.73205i | 0.0351364 | − | 0.0608581i | ||||
\(811\) | 8.00000i | 0.280918i | 0.990086 | + | 0.140459i | \(0.0448578\pi\) | ||||
−0.990086 | + | 0.140459i | \(0.955142\pi\) | |||||||
\(812\) | 34.6410 | + | 20.0000i | 1.21566 | + | 0.701862i | ||||
\(813\) | 10.3923 | + | 6.00000i | 0.364474 | + | 0.210429i | ||||
\(814\) | 8.00000i | 0.280400i | ||||||||
\(815\) | −8.00000 | + | 13.8564i | −0.280228 | + | 0.485369i | ||||
\(816\) | 1.00000 | + | 1.73205i | 0.0350070 | + | 0.0606339i | ||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −34.0000 | −1.18878 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −12.0000 | −0.419058 | ||||||||
\(821\) | −19.0526 | + | 11.0000i | −0.664939 | + | 0.383903i | −0.794156 | − | 0.607714i | \(-0.792087\pi\) |
0.129217 | + | 0.991616i | \(0.458754\pi\) | |||||||
\(822\) | 3.00000 | + | 5.19615i | 0.104637 | + | 0.181237i | ||||
\(823\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.46410 | − | 2.00000i | −0.120605 | − | 0.0696311i | ||||
\(826\) | −41.5692 | − | 24.0000i | −1.44638 | − | 0.835067i | ||||
\(827\) | − | 4.00000i | − | 0.139094i | −0.997579 | − | 0.0695468i | \(-0.977845\pi\) | ||
0.997579 | − | 0.0695468i | \(-0.0221553\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −17.0000 | − | 29.4449i | −0.590434 | − | 1.02266i | −0.994174 | − | 0.107788i | \(-0.965623\pi\) |
0.403739 | − | 0.914874i | \(-0.367710\pi\) | |||||||
\(830\) | −6.92820 | + | 4.00000i | −0.240481 | + | 0.138842i | ||||
\(831\) | −10.0000 | −0.346896 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 18.0000 | 0.623663 | ||||||||
\(834\) | −10.3923 | + | 6.00000i | −0.359856 | + | 0.207763i | ||||
\(835\) | 8.00000 | + | 13.8564i | 0.276851 | + | 0.479521i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 4.00000i | − | 0.138260i | ||||||
\(838\) | −3.46410 | − | 2.00000i | −0.119665 | − | 0.0690889i | ||||
\(839\) | 41.5692 | + | 24.0000i | 1.43513 | + | 0.828572i | 0.997506 | − | 0.0705865i | \(-0.0224871\pi\) |
0.437623 | + | 0.899158i | \(0.355820\pi\) | |||||||
\(840\) | 24.0000i | 0.828079i | ||||||||
\(841\) | −35.5000 | + | 61.4878i | −1.22414 | + | 2.12027i | ||||
\(842\) | −5.00000 | − | 8.66025i | −0.172311 | − | 0.298452i | ||||
\(843\) | −8.66025 | + | 5.00000i | −0.298275 | + | 0.172209i | ||||
\(844\) | −20.0000 | −0.688428 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −17.3205 | + | 10.0000i | −0.595140 | + | 0.343604i | ||||
\(848\) | 3.00000 | + | 5.19615i | 0.103020 | + | 0.178437i | ||||
\(849\) | −6.00000 | + | 10.3923i | −0.205919 | + | 0.356663i | ||||
\(850\) | − | 2.00000i | − | 0.0685994i | ||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 30.0000i | − | 1.02718i | −0.858036 | − | 0.513590i | \(-0.828315\pi\) | ||
0.858036 | − | 0.513590i | \(-0.171685\pi\) | |||||||
\(854\) | −4.00000 | + | 6.92820i | −0.136877 | + | 0.237078i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 31.1769 | − | 18.0000i | 1.06561 | − | 0.615227i | ||||
\(857\) | 46.0000 | 1.57133 | 0.785665 | − | 0.618652i | \(-0.212321\pi\) | ||||
0.785665 | + | 0.618652i | \(0.212321\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −44.0000 | −1.50126 | −0.750630 | − | 0.660722i | \(-0.770250\pi\) | ||||
−0.750630 | + | 0.660722i | \(0.770250\pi\) | |||||||
\(860\) | 20.7846 | − | 12.0000i | 0.708749 | − | 0.409197i | ||||
\(861\) | −12.0000 | − | 20.7846i | −0.408959 | − | 0.708338i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 16.0000i | 0.544646i | 0.962206 | + | 0.272323i | \(0.0877920\pi\) | ||||
−0.962206 | + | 0.272323i | \(0.912208\pi\) | |||||||
\(864\) | 4.33013 | + | 2.50000i | 0.147314 | + | 0.0850517i | ||||
\(865\) | 10.3923 | + | 6.00000i | 0.353349 | + | 0.204006i | ||||
\(866\) | − | 34.0000i | − | 1.15537i | ||||||
\(867\) | −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 | ||||
\(870\) | −20.0000 | −0.678064 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 6.00000 | 0.203186 | ||||||||
\(873\) | 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 | ||||||||
\(877\) | 8.66025 | + | 5.00000i | 0.292436 | + | 0.168838i | 0.639040 | − | 0.769174i | \(-0.279332\pi\) |
−0.346604 | + | 0.938012i | \(0.612665\pi\) | |||||||
\(878\) | 27.7128 | + | 16.0000i | 0.935262 | + | 0.539974i | ||||
\(879\) | − | 6.00000i | − | 0.202375i | ||||||
\(880\) | 4.00000 | − | 6.92820i | 0.134840 | − | 0.233550i | ||||
\(881\) | 29.0000 | + | 50.2295i | 0.977035 | + | 1.69227i | 0.673050 | + | 0.739597i | \(0.264984\pi\) |
0.303985 | + | 0.952677i | \(0.401683\pi\) | |||||||
\(882\) | −7.79423 | + | 4.50000i | −0.262445 | + | 0.151523i | ||||
\(883\) | 44.0000 | 1.48072 | 0.740359 | − | 0.672212i | \(-0.234656\pi\) | ||||
0.740359 | + | 0.672212i | \(0.234656\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −24.0000 | −0.806751 | ||||||||
\(886\) | −3.46410 | + | 2.00000i | −0.116379 | + | 0.0671913i | ||||
\(887\) | 24.0000 | + | 41.5692i | 0.805841 | + | 1.39576i | 0.915722 | + | 0.401813i | \(0.131620\pi\) |
−0.109881 | + | 0.993945i | \(0.535047\pi\) | |||||||
\(888\) | −3.00000 | + | 5.19615i | −0.100673 | + | 0.174371i | ||||
\(889\) | 64.0000i | 2.14649i | ||||||||
\(890\) | 3.46410 | + | 2.00000i | 0.116117 | + | 0.0670402i | ||||
\(891\) | 3.46410 | + | 2.00000i | 0.116052 | + | 0.0670025i | ||||
\(892\) | 4.00000i | 0.133930i | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 3.00000 | + | 5.19615i | 0.100335 | + | 0.173785i | ||||
\(895\) | −6.92820 | + | 4.00000i | −0.231584 | + | 0.133705i | ||||
\(896\) | −12.0000 | −0.400892 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 22.0000 | 0.734150 | ||||||||
\(899\) | −34.6410 | + | 20.0000i | −1.15534 | + | 0.667037i | ||||
\(900\) | −0.500000 | − | 0.866025i | −0.0166667 | − | 0.0288675i | ||||
\(901\) | 6.00000 | − | 10.3923i | 0.199889 | − | 0.346218i | ||||
\(902\) | 24.0000i | 0.799113i | ||||||||
\(903\) | 41.5692 | + | 24.0000i | 1.38334 | + | 0.798670i | ||||
\(904\) | 15.5885 | + | 9.00000i | 0.518464 | + | 0.299336i | ||||
\(905\) | 20.0000i | 0.664822i | ||||||||
\(906\) | 2.00000 | − | 3.46410i | 0.0664455 | − | 0.115087i | ||||
\(907\) | 6.00000 | + | 10.3923i | 0.199227 | + | 0.345071i | 0.948278 | − | 0.317441i | \(-0.102824\pi\) |
−0.749051 | + | 0.662512i | \(0.769490\pi\) | |||||||
\(908\) | −17.3205 | + | 10.0000i | −0.574801 | + | 0.331862i | ||||
\(909\) | 18.0000 | 0.597022 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −40.0000 | −1.32526 | −0.662630 | − | 0.748947i | \(-0.730560\pi\) | ||||
−0.662630 | + | 0.748947i | \(0.730560\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.00000 | − | 13.8564i | −0.264761 | − | 0.458580i | ||||
\(914\) | 1.00000 | − | 1.73205i | 0.0330771 | − | 0.0572911i | ||||
\(915\) | 4.00000i | 0.132236i | ||||||||
\(916\) | −8.66025 | − | 5.00000i | −0.286143 | − | 0.165205i | ||||
\(917\) | −13.8564 | − | 8.00000i | −0.457579 | − | 0.264183i | ||||
\(918\) | 2.00000i | 0.0660098i | ||||||||
\(919\) | 24.0000 | − | 41.5692i | 0.791687 | − | 1.37124i | −0.133235 | − | 0.991084i | \(-0.542536\pi\) |
0.924922 | − | 0.380158i | \(-0.124130\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −13.8564 | + | 8.00000i | −0.456584 | + | 0.263609i | ||||
\(922\) | 38.0000 | 1.25146 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −16.0000 | −0.526361 | ||||||||
\(925\) | 1.73205 | − | 1.00000i | 0.0569495 | − | 0.0328798i | ||||
\(926\) | −2.00000 | − | 3.46410i | −0.0657241 | − | 0.113837i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − | 50.0000i | − | 1.64133i | ||||||
\(929\) | −25.9808 | − | 15.0000i | −0.852401 | − | 0.492134i | 0.00905914 | − | 0.999959i | \(-0.497116\pi\) |
−0.861460 | + | 0.507825i | \(0.830450\pi\) | |||||||
\(930\) | −6.92820 | − | 4.00000i | −0.227185 | − | 0.131165i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −7.00000 | + | 12.1244i | −0.229293 | + | 0.397146i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −10.3923 | + | 6.00000i | −0.340047 | + | 0.196326i | ||||
\(935\) | −16.0000 | −0.523256 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 26.0000 | 0.849383 | 0.424691 | − | 0.905338i | \(-0.360383\pi\) | ||||
0.424691 | + | 0.905338i | \(0.360383\pi\) | |||||||
\(938\) | 27.7128 | − | 16.0000i | 0.904855 | − | 0.522419i | ||||
\(939\) | −3.00000 | − | 5.19615i | −0.0979013 | − | 0.169570i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 14.0000i | − | 0.456387i | −0.973616 | − | 0.228193i | \(-0.926718\pi\) | ||
0.973616 | − | 0.228193i | \(-0.0732819\pi\) | |||||||
\(942\) | −15.5885 | − | 9.00000i | −0.507899 | − | 0.293236i | ||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 12.0000i | 0.390567i | ||||||||
\(945\) | −4.00000 | + | 6.92820i | −0.130120 | + | 0.225374i | ||||
\(946\) | −24.0000 | − | 41.5692i | −0.780307 | − | 1.35153i | ||||
\(947\) | 51.9615 | − | 30.0000i | 1.68852 | − | 0.974869i | 0.732872 | − | 0.680367i | \(-0.238179\pi\) |
0.955651 | − | 0.294502i | \(-0.0951539\pi\) | |||||||
\(948\) | −8.00000 | −0.259828 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −22.5167 | + | 13.0000i | −0.730153 | + | 0.421554i | ||||
\(952\) | −12.0000 | − | 20.7846i | −0.388922 | − | 0.673633i | ||||
\(953\) | −15.0000 | + | 25.9808i | −0.485898 | + | 0.841599i | −0.999869 | − | 0.0162081i | \(-0.994841\pi\) |
0.513971 | + | 0.857808i | \(0.328174\pi\) | |||||||
\(954\) | 6.00000i | 0.194257i | ||||||||
\(955\) | −13.8564 | − | 8.00000i | −0.448383 | − | 0.258874i | ||||
\(956\) | 20.7846 | + | 12.0000i | 0.672222 | + | 0.388108i | ||||
\(957\) | − | 40.0000i | − | 1.29302i | ||||||
\(958\) | 12.0000 | − | 20.7846i | 0.387702 | − | 0.671520i | ||||
\(959\) | −12.0000 | − | 20.7846i | −0.387500 | − | 0.671170i | ||||
\(960\) | 12.1244 | − | 7.00000i | 0.391312 | − | 0.225924i | ||||
\(961\) | 15.0000 | 0.483871 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 12.0000 | 0.386695 | ||||||||
\(964\) | −8.66025 | + | 5.00000i | −0.278928 | + | 0.161039i | ||||
\(965\) | −18.0000 | − | 31.1769i | −0.579441 | − | 1.00362i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 52.0000i | − | 1.67221i | −0.548572 | − | 0.836104i | \(-0.684828\pi\) | ||
0.548572 | − | 0.836104i | \(-0.315172\pi\) | |||||||
\(968\) | 12.9904 | + | 7.50000i | 0.417527 | + | 0.241059i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | − | 20.0000i | − | 0.642161i | ||||||
\(971\) | 30.0000 | − | 51.9615i | 0.962746 | − | 1.66752i | 0.247193 | − | 0.968966i | \(-0.420492\pi\) |
0.715553 | − | 0.698558i | \(-0.246175\pi\) | |||||||
\(972\) | 0.500000 | + | 0.866025i | 0.0160375 | + | 0.0277778i | ||||
\(973\) | 41.5692 | − | 24.0000i | 1.33265 | − | 0.769405i | ||||
\(974\) | −12.0000 | −0.384505 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.00000 | 0.0640184 | ||||||||
\(977\) | −36.3731 | + | 21.0000i | −1.16368 | + | 0.671850i | −0.952183 | − | 0.305530i | \(-0.901167\pi\) |
−0.211495 | + | 0.977379i | \(0.567833\pi\) | |||||||
\(978\) | 4.00000 | + | 6.92820i | 0.127906 | + | 0.221540i | ||||
\(979\) | −4.00000 | + | 6.92820i | −0.127841 | + | 0.221426i | ||||
\(980\) | − | 18.0000i | − | 0.574989i | ||||||
\(981\) | 1.73205 | + | 1.00000i | 0.0553001 | + | 0.0319275i | ||||
\(982\) | −10.3923 | − | 6.00000i | −0.331632 | − | 0.191468i | ||||
\(983\) | − | 16.0000i | − | 0.510321i | −0.966899 | − | 0.255160i | \(-0.917872\pi\) | ||
0.966899 | − | 0.255160i | \(-0.0821283\pi\) | |||||||
\(984\) | −9.00000 | + | 15.5885i | −0.286910 | + | 0.496942i | ||||
\(985\) | 18.0000 | + | 31.1769i | 0.573528 | + | 0.993379i | ||||
\(986\) | 17.3205 | − | 10.0000i | 0.551597 | − | 0.318465i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 6.92820 | − | 4.00000i | 0.220193 | − | 0.127128i | ||||
\(991\) | −8.00000 | − | 13.8564i | −0.254128 | − | 0.440163i | 0.710530 | − | 0.703667i | \(-0.248455\pi\) |
−0.964658 | + | 0.263504i | \(0.915122\pi\) | |||||||
\(992\) | 10.0000 | − | 17.3205i | 0.317500 | − | 0.549927i | ||||
\(993\) | 16.0000i | 0.507745i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 13.8564 | + | 8.00000i | 0.439278 | + | 0.253617i | ||||
\(996\) | − | 4.00000i | − | 0.126745i | ||||||
\(997\) | 13.0000 | − | 22.5167i | 0.411714 | − | 0.713110i | −0.583363 | − | 0.812211i | \(-0.698264\pi\) |
0.995077 | + | 0.0991016i | \(0.0315969\pi\) | |||||||
\(998\) | −12.0000 | − | 20.7846i | −0.379853 | − | 0.657925i | ||||
\(999\) | −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 \(a_p\))