Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2028,2,Mod(361,2028)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2028, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 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("2028.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2028 = 2^{2} \cdot 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2028.q (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: | \(16.1936615299\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 156) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 361.2 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2028.361 |
Dual form | 2028.2.q.h.1837.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2028\mathbb{Z}\right)^\times\).
\(n\) | \(677\) | \(1015\) | \(1861\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 | 0 | ||||||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.00000i | 1.78885i | 0.447214 | + | 0.894427i | \(0.352416\pi\) | ||||
−0.447214 | + | 0.894427i | \(0.647584\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.73205 | + | 1.00000i | 0.654654 | + | 0.377964i | 0.790237 | − | 0.612801i | \(-0.209957\pi\) |
−0.135583 | + | 0.990766i | \(0.543291\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.46410 | + | 2.00000i | −1.04447 | + | 0.603023i | −0.921095 | − | 0.389338i | \(-0.872704\pi\) |
−0.123371 | + | 0.992361i | \(0.539370\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.46410 | + | 2.00000i | −0.894427 | + | 0.516398i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.00000 | − | 1.73205i | 0.242536 | − | 0.420084i | −0.718900 | − | 0.695113i | \(-0.755354\pi\) |
0.961436 | + | 0.275029i | \(0.0886875\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.73205 | − | 1.00000i | −0.397360 | − | 0.229416i | 0.287984 | − | 0.957635i | \(-0.407015\pi\) |
−0.685344 | + | 0.728219i | \(0.740348\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.00000i | 0.436436i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −11.0000 | −2.20000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.00000 | + | 5.19615i | 0.557086 | + | 0.964901i | 0.997738 | + | 0.0672232i | \(0.0214140\pi\) |
−0.440652 | + | 0.897678i | \(0.645253\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.0000i | 1.79605i | 0.439941 | + | 0.898027i | \(0.354999\pi\) | ||||
−0.439941 | + | 0.898027i | \(0.645001\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.46410 | − | 2.00000i | −0.603023 | − | 0.348155i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.00000 | + | 6.92820i | −0.676123 | + | 1.17108i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.66025 | − | 5.00000i | 1.42374 | − | 0.821995i | 0.427121 | − | 0.904194i | \(-0.359528\pi\) |
0.996616 | + | 0.0821995i | \(0.0261945\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.92820 | + | 4.00000i | −1.08200 | + | 0.624695i | −0.931436 | − | 0.363905i | \(-0.881443\pi\) |
−0.150567 | + | 0.988600i | \(0.548110\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.00000 | − | 3.46410i | 0.304997 | − | 0.528271i | −0.672264 | − | 0.740312i | \(-0.734678\pi\) |
0.977261 | + | 0.212041i | \(0.0680112\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.46410 | − | 2.00000i | −0.516398 | − | 0.298142i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 4.00000i | − | 0.583460i | −0.956501 | − | 0.291730i | \(-0.905769\pi\) | ||
0.956501 | − | 0.291730i | \(-0.0942309\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.50000 | − | 2.59808i | −0.214286 | − | 0.371154i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 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 | 0 | ||||||||
\(55\) | −8.00000 | − | 13.8564i | −1.07872 | − | 1.86840i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 2.00000i | − | 0.264906i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.92820 | + | 4.00000i | 0.901975 | + | 0.520756i | 0.877841 | − | 0.478953i | \(-0.158984\pi\) |
0.0241347 | + | 0.999709i | \(0.492317\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.00000 | − | 12.1244i | 0.896258 | − | 1.55236i | 0.0640184 | − | 0.997949i | \(-0.479608\pi\) |
0.832240 | − | 0.554416i | \(-0.187058\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.73205 | + | 1.00000i | −0.218218 | + | 0.125988i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.73205 | + | 1.00000i | −0.211604 | + | 0.122169i | −0.602056 | − | 0.798454i | \(-0.705652\pi\) |
0.390453 | + | 0.920623i | \(0.372318\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.8564 | + | 8.00000i | 1.64445 | + | 0.949425i | 0.979223 | + | 0.202787i | \(0.0649998\pi\) |
0.665230 | + | 0.746639i | \(0.268333\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 10.0000i | − | 1.17041i | −0.810885 | − | 0.585206i | \(-0.801014\pi\) | ||
0.810885 | − | 0.585206i | \(-0.198986\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.50000 | − | 9.52628i | −0.635085 | − | 1.10000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −8.00000 | −0.911685 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −16.0000 | −1.80014 | −0.900070 | − | 0.435745i | \(-0.856485\pi\) | ||||
−0.900070 | + | 0.435745i | \(0.856485\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.92820 | + | 4.00000i | 0.751469 | + | 0.433861i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.00000 | + | 5.19615i | −0.321634 | + | 0.557086i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.46410 | + | 2.00000i | −0.367194 | + | 0.212000i | −0.672232 | − | 0.740341i | \(-0.734664\pi\) |
0.305038 | + | 0.952340i | \(0.401331\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.66025 | + | 5.00000i | −0.898027 | + | 0.518476i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.00000 | − | 6.92820i | 0.410391 | − | 0.710819i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.73205 | − | 1.00000i | −0.175863 | − | 0.101535i | 0.409484 | − | 0.912317i | \(-0.365709\pi\) |
−0.585348 | + | 0.810782i | \(0.699042\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 4.00000i | − | 0.402015i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.00000 | + | 8.66025i | 0.497519 | + | 0.861727i | 0.999996 | − | 0.00286291i | \(-0.000911295\pi\) |
−0.502477 | + | 0.864590i | \(0.667578\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.00000 | 0.788263 | 0.394132 | − | 0.919054i | \(-0.371045\pi\) | ||||
0.394132 | + | 0.919054i | \(0.371045\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −8.00000 | −0.780720 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.00000 | − | 10.3923i | −0.580042 | − | 1.00466i | −0.995474 | − | 0.0950377i | \(-0.969703\pi\) |
0.415432 | − | 0.909624i | \(-0.363630\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.00000i | 0.191565i | 0.995402 | + | 0.0957826i | \(0.0305354\pi\) | ||||
−0.995402 | + | 0.0957826i | \(0.969465\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.66025 | + | 5.00000i | 0.821995 | + | 0.474579i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.00000 | + | 5.19615i | −0.282216 | + | 0.488813i | −0.971930 | − | 0.235269i | \(-0.924403\pi\) |
0.689714 | + | 0.724082i | \(0.257736\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.46410 | − | 2.00000i | 0.317554 | − | 0.183340i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.50000 | − | 4.33013i | 0.227273 | − | 0.393648i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6.92820 | − | 4.00000i | −0.624695 | − | 0.360668i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 24.0000i | − | 2.14663i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.00000 | + | 10.3923i | 0.532414 | + | 0.922168i | 0.999284 | + | 0.0378419i | \(0.0120483\pi\) |
−0.466870 | + | 0.884326i | \(0.654618\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.00000 | 0.352180 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.00000 | 0.349482 | 0.174741 | − | 0.984614i | \(-0.444091\pi\) | ||||
0.174741 | + | 0.984614i | \(0.444091\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.00000 | − | 3.46410i | −0.173422 | − | 0.300376i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 4.00000i | − | 0.344265i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.92820 | − | 4.00000i | −0.591916 | − | 0.341743i | 0.173939 | − | 0.984757i | \(-0.444351\pi\) |
−0.765855 | + | 0.643013i | \(0.777684\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.46410 | − | 2.00000i | 0.291730 | − | 0.168430i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −20.7846 | + | 12.0000i | −1.72607 | + | 0.996546i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.50000 | − | 2.59808i | 0.123718 | − | 0.214286i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.0000i | 1.46482i | 0.680864 | + | 0.732410i | \(0.261604\pi\) | ||||
−0.680864 | + | 0.732410i | \(0.738396\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.00000 | + | 1.73205i | 0.0808452 | + | 0.140028i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −40.0000 | −3.21288 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.00000 | 0.159617 | 0.0798087 | − | 0.996810i | \(-0.474569\pi\) | ||||
0.0798087 | + | 0.996810i | \(0.474569\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.00000 | − | 8.66025i | −0.396526 | − | 0.686803i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.73205 | − | 1.00000i | −0.135665 | − | 0.0783260i | 0.430632 | − | 0.902528i | \(-0.358291\pi\) |
−0.566296 | + | 0.824202i | \(0.691624\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 8.00000 | − | 13.8564i | 0.622799 | − | 1.07872i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −10.3923 | + | 6.00000i | −0.804181 | + | 0.464294i | −0.844931 | − | 0.534875i | \(-0.820359\pi\) |
0.0407502 | + | 0.999169i | \(0.487025\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.73205 | − | 1.00000i | 0.132453 | − | 0.0764719i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.00000 | − | 1.73205i | 0.0760286 | − | 0.131685i | −0.825505 | − | 0.564396i | \(-0.809109\pi\) |
0.901533 | + | 0.432710i | \(0.142443\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −19.0526 | − | 11.0000i | −1.44024 | − | 0.831522i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.00000i | 0.601317i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.00000 | + | 10.3923i | 0.448461 | + | 0.776757i | 0.998286 | − | 0.0585225i | \(-0.0186389\pi\) |
−0.549825 | + | 0.835280i | \(0.685306\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.00000 | −0.148659 | −0.0743294 | − | 0.997234i | \(-0.523682\pi\) | ||||
−0.0743294 | + | 0.997234i | \(0.523682\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 14.0000 | 1.03491 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 20.0000 | + | 34.6410i | 1.47043 | + | 2.54686i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.00000i | 0.585018i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.73205 | − | 1.00000i | −0.125988 | − | 0.0727393i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.00000 | − | 6.92820i | 0.289430 | − | 0.501307i | −0.684244 | − | 0.729253i | \(-0.739868\pi\) |
0.973674 | + | 0.227946i | \(0.0732010\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.1244 | + | 7.00000i | −0.872730 | + | 0.503871i | −0.868255 | − | 0.496119i | \(-0.834758\pi\) |
−0.00447566 | + | 0.999990i | \(0.501425\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.3923 | − | 6.00000i | 0.740421 | − | 0.427482i | −0.0818013 | − | 0.996649i | \(-0.526067\pi\) |
0.822222 | + | 0.569166i | \(0.192734\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.00000 | − | 3.46410i | 0.141776 | − | 0.245564i | −0.786389 | − | 0.617731i | \(-0.788052\pi\) |
0.928166 | + | 0.372168i | \(0.121385\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.73205 | − | 1.00000i | −0.122169 | − | 0.0705346i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 12.0000i | 0.842235i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −16.0000 | − | 27.7128i | −1.11749 | − | 1.93555i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.00000 | 0.553372 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.00000 | + | 10.3923i | 0.413057 | + | 0.715436i | 0.995222 | − | 0.0976347i | \(-0.0311277\pi\) |
−0.582165 | + | 0.813070i | \(0.697794\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 16.0000i | 1.09630i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 13.8564 | + | 8.00000i | 0.944999 | + | 0.545595i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.0000 | + | 17.3205i | −0.678844 | + | 1.17579i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8.66025 | − | 5.00000i | 0.585206 | − | 0.337869i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.1244 | + | 7.00000i | −0.811907 | + | 0.468755i | −0.847618 | − | 0.530607i | \(-0.821964\pi\) |
0.0357107 | + | 0.999362i | \(0.488630\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.50000 | − | 9.52628i | 0.366667 | − | 0.635085i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.46410 | − | 2.00000i | −0.229920 | − | 0.132745i | 0.380615 | − | 0.924734i | \(-0.375712\pi\) |
−0.610535 | + | 0.791989i | \(0.709046\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 2.00000i | − | 0.132164i | −0.997814 | − | 0.0660819i | \(-0.978950\pi\) | ||
0.997814 | − | 0.0660819i | \(-0.0210498\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.00000 | − | 6.92820i | −0.263181 | − | 0.455842i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 18.0000 | 1.17922 | 0.589610 | − | 0.807688i | \(-0.299282\pi\) | ||||
0.589610 | + | 0.807688i | \(0.299282\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 16.0000 | 1.04372 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.00000 | − | 13.8564i | −0.519656 | − | 0.900070i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 24.0000i | 1.55243i | 0.630468 | + | 0.776215i | \(0.282863\pi\) | ||||
−0.630468 | + | 0.776215i | \(0.717137\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.73205 | + | 1.00000i | 0.111571 | + | 0.0644157i | 0.554747 | − | 0.832019i | \(-0.312815\pi\) |
−0.443176 | + | 0.896435i | \(0.646148\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.500000 | − | 0.866025i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 10.3923 | − | 6.00000i | 0.663940 | − | 0.383326i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.0000 | + | 17.3205i | −0.631194 | + | 1.09326i | 0.356113 | + | 0.934443i | \(0.384102\pi\) |
−0.987308 | + | 0.158818i | \(0.949232\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 8.00000i | 0.500979i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 15.0000 | + | 25.9808i | 0.935674 | + | 1.62064i | 0.773427 | + | 0.633885i | \(0.218541\pi\) |
0.162247 | + | 0.986750i | \(0.448126\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 20.0000 | 1.24274 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.00000 | −0.371391 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 8.00000 | + | 13.8564i | 0.493301 | + | 0.854423i | 0.999970 | − | 0.00771799i | \(-0.00245674\pi\) |
−0.506669 | + | 0.862141i | \(0.669123\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 40.0000i | − | 2.45718i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.46410 | − | 2.00000i | −0.212000 | − | 0.122398i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.00000 | − | 12.1244i | 0.426798 | − | 0.739235i | −0.569789 | − | 0.821791i | \(-0.692975\pi\) |
0.996586 | + | 0.0825561i | \(0.0263084\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.66025 | + | 5.00000i | −0.526073 | + | 0.303728i | −0.739416 | − | 0.673249i | \(-0.764898\pi\) |
0.213343 | + | 0.976977i | \(0.431565\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 38.1051 | − | 22.0000i | 2.29783 | − | 1.32665i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.0000 | − | 19.0526i | 0.660926 | − | 1.14476i | −0.319447 | − | 0.947604i | \(-0.603497\pi\) |
0.980373 | − | 0.197153i | \(-0.0631696\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −8.66025 | − | 5.00000i | −0.518476 | − | 0.299342i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 8.00000i | − | 0.477240i | −0.971113 | − | 0.238620i | \(-0.923305\pi\) | ||
0.971113 | − | 0.238620i | \(-0.0766950\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.00000 | − | 13.8564i | −0.475551 | − | 0.823678i | 0.524057 | − | 0.851683i | \(-0.324418\pi\) |
−0.999608 | + | 0.0280052i | \(0.991084\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 8.00000 | 0.473879 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −16.0000 | −0.944450 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.50000 | + | 11.2583i | 0.382353 | + | 0.662255i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 2.00000i | − | 0.117242i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6.92820 | − | 4.00000i | −0.404750 | − | 0.233682i | 0.283782 | − | 0.958889i | \(-0.408411\pi\) |
−0.688531 | + | 0.725206i | \(0.741744\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −16.0000 | + | 27.7128i | −0.931556 | + | 1.61350i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.46410 | − | 2.00000i | 0.201008 | − | 0.116052i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.92820 | − | 4.00000i | 0.399335 | − | 0.230556i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.00000 | + | 8.66025i | −0.287242 | + | 0.497519i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 48.4974 | + | 28.0000i | 2.77695 | + | 1.60328i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 22.0000i | 1.25561i | 0.778372 | + | 0.627803i | \(0.216046\pi\) | ||||
−0.778372 | + | 0.627803i | \(0.783954\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.00000 | + | 6.92820i | 0.227552 | + | 0.394132i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −24.0000 | −1.36092 | −0.680458 | − | 0.732787i | \(-0.738219\pi\) | ||||
−0.680458 | + | 0.732787i | \(0.738219\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.00000 | −0.339140 | −0.169570 | − | 0.985518i | \(-0.554238\pi\) | ||||
−0.169570 | + | 0.985518i | \(0.554238\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.00000 | − | 6.92820i | −0.225374 | − | 0.390360i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 12.0000i | 0.673987i | 0.941507 | + | 0.336994i | \(0.109410\pi\) | ||||
−0.941507 | + | 0.336994i | \(0.890590\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −20.7846 | − | 12.0000i | −1.16371 | − | 0.671871i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.00000 | − | 10.3923i | 0.334887 | − | 0.580042i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.46410 | + | 2.00000i | −0.192748 | + | 0.111283i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.73205 | + | 1.00000i | −0.0957826 | + | 0.0553001i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.00000 | − | 6.92820i | 0.220527 | − | 0.381964i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.73205 | + | 1.00000i | 0.0952021 | + | 0.0549650i | 0.546845 | − | 0.837234i | \(-0.315829\pi\) |
−0.451643 | + | 0.892199i | \(0.649162\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 10.0000i | 0.547997i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.00000 | − | 6.92820i | −0.218543 | − | 0.378528i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 30.0000 | 1.63420 | 0.817102 | − | 0.576493i | \(-0.195579\pi\) | ||||
0.817102 | + | 0.576493i | \(0.195579\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.00000 | −0.325875 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −20.0000 | − | 34.6410i | −1.08306 | − | 1.87592i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 20.0000i | − | 1.07990i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6.00000 | + | 10.3923i | −0.322097 | + | 0.557888i | −0.980921 | − | 0.194409i | \(-0.937721\pi\) |
0.658824 | + | 0.752297i | \(0.271054\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.5885 | − | 9.00000i | 0.834431 | − | 0.481759i | −0.0209364 | − | 0.999781i | \(-0.506665\pi\) |
0.855367 | + | 0.518022i | \(0.173331\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.8564 | − | 8.00000i | 0.737502 | − | 0.425797i | −0.0836583 | − | 0.996495i | \(-0.526660\pi\) |
0.821160 | + | 0.570697i | \(0.193327\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −32.0000 | + | 55.4256i | −1.69838 | + | 2.94169i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.46410 | + | 2.00000i | 0.183340 | + | 0.105851i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 12.0000i | − | 0.633336i | −0.948536 | − | 0.316668i | \(-0.897436\pi\) | ||
0.948536 | − | 0.316668i | \(-0.102564\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.50000 | − | 12.9904i | −0.394737 | − | 0.683704i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.00000 | 0.262432 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 40.0000 | 2.09370 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.00000 | − | 3.46410i | −0.104399 | − | 0.180825i | 0.809093 | − | 0.587680i | \(-0.199959\pi\) |
−0.913493 | + | 0.406855i | \(0.866625\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 8.00000i | − | 0.416463i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −17.3205 | − | 10.0000i | −0.899236 | − | 0.519174i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.00000 | − | 15.5885i | 0.466002 | − | 0.807140i | −0.533244 | − | 0.845962i | \(-0.679027\pi\) |
0.999246 | + | 0.0388219i | \(0.0123605\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 20.7846 | − | 12.0000i | 1.07331 | − | 0.619677i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.19615 | + | 3.00000i | −0.266908 | + | 0.154100i | −0.627482 | − | 0.778631i | \(-0.715914\pi\) |
0.360573 | + | 0.932731i | \(0.382581\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.00000 | + | 10.3923i | −0.307389 | + | 0.532414i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10.3923 | + | 6.00000i | 0.531022 | + | 0.306586i | 0.741433 | − | 0.671027i | \(-0.234147\pi\) |
−0.210411 | + | 0.977613i | \(0.567480\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 32.0000i | − | 1.63087i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.00000 | + | 3.46410i | 0.101666 | + | 0.176090i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 26.0000 | 1.31825 | 0.659126 | − | 0.752032i | \(-0.270926\pi\) | ||||
0.659126 | + | 0.752032i | \(0.270926\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.00000 | + | 3.46410i | 0.100887 | + | 0.174741i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 64.0000i | − | 3.22019i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −15.5885 | − | 9.00000i | −0.782362 | − | 0.451697i | 0.0549046 | − | 0.998492i | \(-0.482515\pi\) |
−0.837267 | + | 0.546795i | \(0.815848\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.00000 | − | 3.46410i | 0.100125 | − | 0.173422i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10.3923 | + | 6.00000i | −0.518967 | + | 0.299626i | −0.736512 | − | 0.676425i | \(-0.763528\pi\) |
0.217545 | + | 0.976050i | \(0.430195\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.46410 | − | 2.00000i | 0.172133 | − | 0.0993808i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −20.0000 | + | 34.6410i | −0.991363 | + | 1.71709i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.1244 | + | 7.00000i | 0.599511 | + | 0.346128i | 0.768849 | − | 0.639430i | \(-0.220830\pi\) |
−0.169338 | + | 0.985558i | \(0.554163\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 8.00000i | − | 0.394611i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.00000 | + | 13.8564i | 0.393654 | + | 0.681829i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.0000 | + | 17.3205i | 0.488532 | + | 0.846162i | 0.999913 | − | 0.0131919i | \(-0.00419923\pi\) |
−0.511381 | + | 0.859354i | \(0.670866\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.00000i | 0.0974740i | 0.998812 | + | 0.0487370i | \(0.0155196\pi\) | ||||
−0.998812 | + | 0.0487370i | \(0.984480\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.46410 | + | 2.00000i | 0.168430 | + | 0.0972433i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −11.0000 | + | 19.0526i | −0.533578 | + | 0.924185i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 24.2487 | − | 14.0000i | 1.17348 | − | 0.677507i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 17.3205 | − | 10.0000i | 0.834300 | − | 0.481683i | −0.0210230 | − | 0.999779i | \(-0.506692\pi\) |
0.855323 | + | 0.518096i | \(0.173359\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.00000 | + | 15.5885i | −0.432512 | + | 0.749133i | −0.997089 | − | 0.0762473i | \(-0.975706\pi\) |
0.564577 | + | 0.825381i | \(0.309039\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −20.7846 | − | 12.0000i | −0.996546 | − | 0.575356i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.00000 | + | 13.8564i | 0.381819 | + | 0.661330i | 0.991322 | − | 0.131453i | \(-0.0419644\pi\) |
−0.609503 | + | 0.792784i | \(0.708631\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.00000 | 0.142857 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.00000 | −0.190046 | −0.0950229 | − | 0.995475i | \(-0.530292\pi\) | ||||
−0.0950229 | + | 0.995475i | \(0.530292\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.00000 | − | 13.8564i | −0.379236 | − | 0.656857i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10.3923 | − | 6.00000i | −0.490443 | − | 0.283158i | 0.234315 | − | 0.972161i | \(-0.424715\pi\) |
−0.724758 | + | 0.689003i | \(0.758049\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 16.0000 | − | 27.7128i | 0.753411 | − | 1.30495i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −15.5885 | + | 9.00000i | −0.732410 | + | 0.422857i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.5885 | − | 9.00000i | 0.729197 | − | 0.421002i | −0.0889312 | − | 0.996038i | \(-0.528345\pi\) |
0.818128 | + | 0.575036i | \(0.195012\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.00000 | + | 1.73205i | −0.0466760 | + | 0.0808452i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.3923 | + | 6.00000i | 0.484018 | + | 0.279448i | 0.722089 | − | 0.691800i | \(-0.243182\pi\) |
−0.238071 | + | 0.971248i | \(0.576515\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 22.0000i | 1.02243i | 0.859454 | + | 0.511213i | \(0.170804\pi\) | ||||
−0.859454 | + | 0.511213i | \(0.829196\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −20.0000 | − | 34.6410i | −0.927478 | − | 1.60644i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 28.0000 | 1.29569 | 0.647843 | − | 0.761774i | \(-0.275671\pi\) | ||||
0.647843 | + | 0.761774i | \(0.275671\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.00000 | −0.184703 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.00000 | + | 1.73205i | 0.0460776 | + | 0.0798087i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 16.0000i | 0.735681i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 19.0526 | + | 11.0000i | 0.874191 | + | 0.504715i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.00000 | − | 8.66025i | 0.228934 | − | 0.396526i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −13.8564 | + | 8.00000i | −0.633115 | + | 0.365529i | −0.781958 | − | 0.623332i | \(-0.785779\pi\) |
0.148842 | + | 0.988861i | \(0.452445\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.00000 | − | 6.92820i | 0.181631 | − | 0.314594i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −22.5167 | − | 13.0000i | −1.02033 | − | 0.589086i | −0.106129 | − | 0.994352i | \(-0.533846\pi\) |
−0.914199 | + | 0.405266i | \(0.867179\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 2.00000i | − | 0.0904431i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.00000 | + | 10.3923i | 0.270776 | + | 0.468998i | 0.969061 | − | 0.246822i | \(-0.0793863\pi\) |
−0.698285 | + | 0.715820i | \(0.746053\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.0000 | 0.540453 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 16.0000 | 0.719147 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 16.0000 | + | 27.7128i | 0.717698 | + | 1.24309i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.00000i | 0.268597i | 0.990941 | + | 0.134298i | \(0.0428781\pi\) | ||||
−0.990941 | + | 0.134298i | \(0.957122\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −10.3923 | − | 6.00000i | −0.464294 | − | 0.268060i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −8.00000 | + | 13.8564i | −0.356702 | + | 0.617827i | −0.987408 | − | 0.158196i | \(-0.949432\pi\) |
0.630705 | + | 0.776022i | \(0.282766\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −34.6410 | + | 20.0000i | −1.54150 | + | 0.889988i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10.3923 | + | 6.00000i | −0.460631 | + | 0.265945i | −0.712309 | − | 0.701866i | \(-0.752351\pi\) |
0.251679 | + | 0.967811i | \(0.419017\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.0000 | − | 17.3205i | 0.442374 | − | 0.766214i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.73205 | + | 1.00000i | 0.0764719 | + | 0.0441511i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 32.0000i | 1.41009i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.00000 | + | 13.8564i | 0.351840 | + | 0.609404i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.00000 | 0.0877903 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.00000 | −0.0876216 | −0.0438108 | − | 0.999040i | \(-0.513950\pi\) | ||||
−0.0438108 | + | 0.999040i | \(0.513950\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.00000 | − | 13.8564i | −0.349816 | − | 0.605898i | 0.636401 | − | 0.771358i | \(-0.280422\pi\) |
−0.986216 | + | 0.165460i | \(0.947089\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 22.0000i | − | 0.960159i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 17.3205 | + | 10.0000i | 0.754493 | + | 0.435607i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.5000 | − | 19.9186i | 0.500000 | − | 0.866025i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.92820 | + | 4.00000i | −0.300658 | + | 0.173585i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 41.5692 | − | 24.0000i | 1.79719 | − | 1.03761i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6.00000 | + | 10.3923i | −0.258919 | + | 0.448461i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 10.3923 | + | 6.00000i | 0.447628 | + | 0.258438i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 38.0000i | 1.63375i | 0.576816 | + | 0.816874i | \(0.304295\pi\) | ||||
−0.576816 | + | 0.816874i | \(0.695705\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.00000 | − | 1.73205i | −0.0429141 | − | 0.0743294i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8.00000 | −0.342682 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 32.0000 | 1.36822 | 0.684111 | − | 0.729378i | \(-0.260191\pi\) | ||||
0.684111 | + | 0.729378i | \(0.260191\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7.00000 | + | 12.1244i | 0.298753 | + | 0.517455i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 12.0000i | − | 0.511217i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −27.7128 | − | 16.0000i | −1.17847 | − | 0.680389i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −20.0000 | + | 34.6410i | −0.848953 | + | 1.47043i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 20.7846 | − | 12.0000i | 0.880672 | − | 0.508456i | 0.00979220 | − | 0.999952i | \(-0.496883\pi\) |
0.870880 | + | 0.491496i | \(0.163550\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.92820 | + | 4.00000i | −0.292509 | + | 0.168880i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 14.0000 | − | 24.2487i | 0.590030 | − | 1.02196i | −0.404198 | − | 0.914671i | \(-0.632449\pi\) |
0.994228 | − | 0.107290i | \(-0.0342173\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −20.7846 | − | 12.0000i | −0.874415 | − | 0.504844i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 2.00000i | − | 0.0839921i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.00000 | + | 5.19615i | 0.125767 | + | 0.217834i | 0.922032 | − | 0.387113i | \(-0.126528\pi\) |
−0.796266 | + | 0.604947i | \(0.793194\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.00000 | 0.334790 | 0.167395 | − | 0.985890i | \(-0.446465\pi\) | ||||
0.167395 | + | 0.985890i | \(0.446465\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.00000 | 0.334205 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 30.0000i | 1.24892i | 0.781058 | + | 0.624458i | \(0.214680\pi\) | ||||
−0.781058 | + | 0.624458i | \(0.785320\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −12.1244 | − | 7.00000i | −0.503871 | − | 0.290910i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 34.6410 | − | 20.0000i | 1.43468 | − | 0.828315i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.92820 | − | 4.00000i | 0.285958 | − | 0.165098i | −0.350160 | − | 0.936690i | \(-0.613873\pi\) |
0.636117 | + | 0.771592i | \(0.280539\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.0000 | − | 17.3205i | 0.412043 | − | 0.713679i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 10.3923 | + | 6.00000i | 0.427482 | + | 0.246807i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 36.0000i | − | 1.47834i | −0.673517 | − | 0.739171i | \(-0.735217\pi\) | ||
0.673517 | − | 0.739171i | \(-0.264783\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.00000 | + | 13.8564i | 0.327968 | + | 0.568057i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4.00000 | 0.163709 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 24.0000 | 0.980613 | 0.490307 | − | 0.871550i | \(-0.336885\pi\) | ||||
0.490307 | + | 0.871550i | \(0.336885\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.0000 | + | 19.0526i | 0.448699 | + | 0.777170i | 0.998302 | − | 0.0582563i | \(-0.0185541\pi\) |
−0.549602 | + | 0.835426i | \(0.685221\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 2.00000i | − | 0.0814463i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 17.3205 | + | 10.0000i | 0.704179 | + | 0.406558i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.00000 | − | 3.46410i | 0.0811775 | − | 0.140604i | −0.822578 | − | 0.568652i | \(-0.807465\pi\) |
0.903756 | + | 0.428048i | \(0.140799\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −10.3923 | + | 6.00000i | −0.421117 | + | 0.243132i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.1244 | − | 7.00000i | 0.489698 | − | 0.282727i | −0.234751 | − | 0.972056i | \(-0.575428\pi\) |
0.724449 | + | 0.689328i | \(0.242094\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 16.0000 | − | 27.7128i | 0.645182 | − | 1.11749i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −41.5692 | − | 24.0000i | −1.67351 | − | 0.966204i | −0.965647 | − | 0.259858i | \(-0.916324\pi\) |
−0.707867 | − | 0.706346i | \(-0.750342\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14.0000i | 0.562708i | 0.959604 | + | 0.281354i | \(0.0907834\pi\) | ||||
−0.959604 | + | 0.281354i | \(0.909217\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8.00000 | −0.320513 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 41.0000 | 1.64000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.00000 | + | 6.92820i | 0.159745 | + | 0.276686i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 20.0000i | − | 0.797452i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25.9808 | + | 15.0000i | 1.03428 | + | 0.597141i | 0.918207 | − | 0.396100i | \(-0.129637\pi\) |
0.116071 | + | 0.993241i | \(0.462970\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6.00000 | + | 10.3923i | −0.238479 | + | 0.413057i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −41.5692 | + | 24.0000i | −1.64962 | + | 0.952411i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −13.8564 | + | 8.00000i | −0.548151 | + | 0.316475i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 13.0000 | − | 22.5167i | 0.513469 | − | 0.889355i | −0.486409 | − | 0.873731i | \(-0.661693\pi\) |
0.999878 | − | 0.0156233i | \(-0.00497325\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22.5167 | + | 13.0000i | 0.887970 | + | 0.512670i | 0.873278 | − | 0.487222i | \(-0.161990\pi\) |
0.0146923 | + | 0.999892i | \(0.495323\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 16.0000i | 0.629999i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −12.0000 | − | 20.7846i | −0.471769 | − | 0.817127i | 0.527710 | − | 0.849425i | \(-0.323051\pi\) |
−0.999478 | + | 0.0322975i | \(0.989718\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −32.0000 | −1.25611 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −20.0000 | −0.783862 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 23.0000 | + | 39.8372i | 0.900060 | + | 1.55895i | 0.827415 | + | 0.561591i | \(0.189811\pi\) |
0.0726446 | + | 0.997358i | \(0.476856\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 16.0000i | 0.625172i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.66025 | + | 5.00000i | 0.337869 | + | 0.195069i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.00000 | − | 10.3923i | 0.233727 | − | 0.404827i | −0.725175 | − | 0.688565i | \(-0.758241\pi\) |
0.958902 | + | 0.283738i | \(0.0915745\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.66025 | − | 5.00000i | 0.336845 | − | 0.194477i | −0.322031 | − | 0.946729i | \(-0.604366\pi\) |
0.658876 | + | 0.752252i | \(0.271032\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 13.8564 | − | 8.00000i | 0.537328 | − | 0.310227i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −12.1244 | − | 7.00000i | −0.468755 | − | 0.270636i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 56.0000i | 2.16186i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.0000 | + | 19.0526i | 0.424019 | + | 0.734422i | 0.996328 | − | 0.0856156i | \(-0.0272857\pi\) |
−0.572309 | + | 0.820038i | \(0.693952\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 11.0000 | 0.423390 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 38.0000 | 1.46046 | 0.730229 | − | 0.683202i | \(-0.239413\pi\) | ||||
0.730229 | + | 0.683202i | \(0.239413\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.00000 | − | 3.46410i | −0.0767530 | − | 0.132940i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 4.00000i | − | 0.153280i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −17.3205 | − | 10.0000i | −0.662751 | − | 0.382639i | 0.130573 | − | 0.991439i | \(-0.458318\pi\) |
−0.793324 | + | 0.608799i | \(0.791651\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 16.0000 | − | 27.7128i | 0.611329 | − | 1.05885i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.73205 | − | 1.00000i | 0.0660819 | − | 0.0381524i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.66025 | + | 5.00000i | −0.329452 | + | 0.190209i | −0.655598 | − | 0.755110i | \(-0.727583\pi\) |
0.326146 | + | 0.945319i | \(0.394250\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.00000 | − | 6.92820i | 0.151947 | − | 0.263181i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 16.0000i | 0.606043i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 9.00000 | + | 15.5885i | 0.340411 | + | 0.589610i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.00000 | 0.0755390 | 0.0377695 | − | 0.999286i | \(-0.487975\pi\) | ||||
0.0377695 | + | 0.999286i | \(0.487975\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −20.0000 | −0.754314 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 8.00000 | + | 13.8564i | 0.301297 | + | 0.521862i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 20.0000i | 0.752177i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.19615 | − | 3.00000i | −0.195146 | − | 0.112667i | 0.399244 | − | 0.916845i | \(-0.369273\pi\) |
−0.594389 | + | 0.804178i | \(0.702606\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.00000 | − | 13.8564i | 0.300023 | − | 0.519656i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −20.7846 | + | 12.0000i | −0.776215 | + | 0.448148i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −24.0000 | + | 41.5692i | −0.895049 | + | 1.55027i | −0.0613050 | + | 0.998119i | \(0.519526\pi\) |
−0.833744 | + | 0.552151i | \(0.813807\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13.8564 | + | 8.00000i | 0.516040 | + | 0.297936i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.00000i | 0.0743808i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −33.0000 | − | 57.1577i | −1.22559 | − | 2.12278i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −44.0000 | −1.63187 | −0.815935 | − | 0.578144i | \(-0.803777\pi\) | ||||
−0.815935 | + | 0.578144i | \(0.803777\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.00000 | − | 6.92820i | −0.147945 | − | 0.256249i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 22.0000i | − | 0.812589i | −0.913742 | − | 0.406294i | \(-0.866821\pi\) | ||
0.913742 | − | 0.406294i | \(-0.133179\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 10.3923 | + | 6.00000i | 0.383326 | + | 0.221313i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.00000 | − | 6.92820i | 0.147342 | − | 0.255204i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19.0526 | − | 11.0000i | 0.700860 | − | 0.404642i | −0.106808 | − | 0.994280i | \(-0.534063\pi\) |
0.807668 | + | 0.589638i | \(0.200730\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −41.5692 | + | 24.0000i | −1.52503 | + | 0.880475i | −0.525467 | + | 0.850814i | \(0.676109\pi\) |
−0.999560 | + | 0.0296605i | \(0.990557\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 24.0000i | − | 0.876941i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 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 | ||||||||
\(753\) | −20.0000 | −0.728841 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −72.0000 | −2.62035 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.00000 | − | 15.5885i | −0.327111 | − | 0.566572i | 0.654827 | − | 0.755779i | \(-0.272742\pi\) |
−0.981937 | + | 0.189207i | \(0.939408\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −34.6410 | − | 20.0000i | −1.25574 | − | 0.724999i | −0.283493 | − | 0.958974i | \(-0.591493\pi\) |
−0.972243 | + | 0.233975i | \(0.924827\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.00000 | + | 3.46410i | −0.0724049 | + | 0.125409i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6.92820 | + | 4.00000i | −0.250490 | + | 0.144620i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 19.0526 | − | 11.0000i | 0.687053 | − | 0.396670i | −0.115454 | − | 0.993313i | \(-0.536832\pi\) |
0.802507 | + | 0.596643i | \(0.203499\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −15.0000 | + | 25.9808i | −0.540212 | + | 0.935674i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −41.5692 | − | 24.0000i | −1.49514 | − | 0.863220i | −0.495156 | − | 0.868804i | \(-0.664889\pi\) |
−0.999984 | + | 0.00558380i | \(0.998223\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 110.000i | − | 3.95132i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 10.0000 | + | 17.3205i | 0.358748 | + | 0.621370i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 16.0000 | 0.573259 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −64.0000 | −2.29010 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.00000 | − | 5.19615i | −0.107211 | − | 0.185695i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 8.00000i | 0.285532i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 43.3013 | + | 25.0000i | 1.54352 | + | 0.891154i | 0.998613 | + | 0.0526599i | \(0.0167699\pi\) |
0.544911 | + | 0.838494i | \(0.316563\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −8.00000 | + | 13.8564i | −0.284808 | + | 0.493301i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.3923 | + | 6.00000i | −0.369508 | + | 0.213335i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 34.6410 | − | 20.0000i | 1.22859 | − | 0.709327i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −13.0000 | + | 22.5167i | −0.460484 | + | 0.797581i | −0.998985 | − | 0.0450436i | \(-0.985657\pi\) |
0.538501 | + | 0.842625i | \(0.318991\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.92820 | − | 4.00000i | −0.245102 | − | 0.141510i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 4.00000i | − | 0.141333i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 20.0000 | + | 34.6410i | 0.705785 | + | 1.22245i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 14.0000 | 0.492823 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −19.0000 | − | 32.9090i | −0.668004 | − | 1.15702i | −0.978461 | − | 0.206430i | \(-0.933815\pi\) |
0.310457 | − | 0.950587i | \(-0.399518\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 6.00000i | − | 0.210688i | −0.994436 | − | 0.105344i | \(-0.966406\pi\) | ||
0.994436 | − | 0.105344i | \(-0.0335944\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8.66025 | − | 5.00000i | −0.303728 | − | 0.175358i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.00000 | − | 6.92820i | 0.140114 | − | 0.242684i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.92820 | + | 4.00000i | −0.242387 | + | 0.139942i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −20.7846 | + | 12.0000i | −0.725388 | + | 0.418803i | −0.816733 | − | 0.577016i | \(-0.804217\pi\) |
0.0913446 | + | 0.995819i | \(0.470884\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16.0000 | − | 27.7128i | 0.557725 | − | 0.966008i | −0.439961 | − | 0.898017i | \(-0.645008\pi\) |
0.997686 | − | 0.0679910i | \(-0.0216589\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 38.1051 | + | 22.0000i | 1.32665 | + | 0.765942i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 20.0000i | − | 0.695468i | −0.937593 | − | 0.347734i | \(-0.886951\pi\) | ||
0.937593 | − | 0.347734i | \(-0.113049\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.00000 | − | 12.1244i | −0.243120 | − | 0.421096i | 0.718481 | − | 0.695546i | \(-0.244838\pi\) |
−0.961601 | + | 0.274450i | \(0.911504\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 22.0000 | 0.763172 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.00000 | −0.207888 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −24.0000 | − | 41.5692i | −0.830554 | − | 1.43856i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 10.0000i | − | 0.345651i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 13.8564 | + | 8.00000i | 0.478376 | + | 0.276191i | 0.719740 | − | 0.694244i | \(-0.244261\pi\) |
−0.241363 | + | 0.970435i | \(0.577595\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.50000 | + | 6.06218i | −0.120690 | + | 0.209041i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 6.92820 | − | 4.00000i | 0.238620 | − | 0.137767i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.66025 | − | 5.00000i | 0.297570 | − | 0.171802i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 8.00000 | − | 13.8564i | 0.274559 | − | 0.475551i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 14.0000i | − | 0.479351i | −0.970853 | − | 0.239675i | \(-0.922959\pi\) | ||
0.970853 | − | 0.239675i | \(-0.0770410\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.00000 | + | 6.92820i | 0.136797 | + | 0.236940i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 18.0000 | 0.614868 | 0.307434 | − | 0.951569i | \(-0.400530\pi\) | ||||
0.307434 | + | 0.951569i | \(0.400530\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 52.0000 | 1.77422 | 0.887109 | − | 0.461561i | \(-0.152710\pi\) | ||||
0.887109 | + | 0.461561i | \(0.152710\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.00000 | − | 13.8564i | −0.272639 | − | 0.472225i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 4.00000i | − | 0.136162i | −0.997680 | − | 0.0680808i | \(-0.978312\pi\) | ||
0.997680 | − | 0.0680808i | \(-0.0216876\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.92820 | + | 4.00000i | 0.235566 | + | 0.136004i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −6.50000 | + | 11.2583i | −0.220752 | + | 0.382353i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 55.4256 | − | 32.0000i | 1.88019 | − | 1.08553i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.73205 | − | 1.00000i | 0.0586210 | − | 0.0338449i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 24.0000 | − | 41.5692i | 0.811348 | − | 1.40530i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8.66025 | + | 5.00000i | 0.292436 | + | 0.168838i | 0.639040 | − | 0.769174i | \(-0.279332\pi\) |
−0.346604 | + | 0.938012i | \(0.612665\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 8.00000i | − | 0.269833i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.00000 | + | 12.1244i | 0.235836 | + | 0.408480i | 0.959515 | − | 0.281656i | \(-0.0908839\pi\) |
−0.723679 | + | 0.690136i | \(0.757551\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 32.0000 | 1.07689 | 0.538443 | − | 0.842662i | \(-0.319013\pi\) | ||||
0.538443 | + | 0.842662i | \(0.319013\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −32.0000 | −1.07567 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −24.0000 | − | 41.5692i | −0.805841 | − | 1.39576i | −0.915722 | − | 0.401813i | \(-0.868380\pi\) |
0.109881 | − | 0.993945i | \(-0.464953\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 24.0000i | 0.804934i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.46410 | + | 2.00000i | 0.116052 | + | 0.0670025i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.00000 | + | 6.92820i | −0.133855 | + | 0.231843i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −41.5692 | + | 24.0000i | −1.38951 | + | 0.802232i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −51.9615 | + | 30.0000i | −1.73301 | + | 1.00056i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10.0000 | + | 17.3205i | −0.333148 | + | 0.577030i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6.92820 | + | 4.00000i | 0.230556 | + | 0.133112i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 8.00000i | − | 0.265929i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −28.0000 | − | 48.4974i | −0.929725 | − | 1.61033i | −0.783781 | − | 0.621038i | \(-0.786711\pi\) |
−0.145944 | − | 0.989293i | \(-0.546622\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −10.0000 | −0.331679 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −56.0000 | −1.85536 | −0.927681 | − | 0.373373i | \(-0.878201\pi\) | ||||
−0.927681 | + | 0.373373i | \(0.878201\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 56.0000i | 1.85130i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6.92820 | + | 4.00000i | 0.228789 | + | 0.132092i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −28.0000 | + | 48.4974i | −0.923635 | + | 1.59978i | −0.129893 | + | 0.991528i | \(0.541463\pi\) |
−0.793742 | + | 0.608254i | \(0.791870\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −19.0526 | + | 11.0000i | −0.627803 | + | 0.362462i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −95.2628 | + | 55.0000i | −3.13222 | + | 1.80839i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4.00000 | + | 6.92820i | −0.131377 | + | 0.227552i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 13.8564 | + | 8.00000i | 0.454614 | + | 0.262471i | 0.709777 | − | 0.704427i | \(-0.248796\pi\) |
−0.255163 | + | 0.966898i | \(0.582129\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.00000i | 0.196642i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −12.0000 | − | 20.7846i | −0.392862 | − | 0.680458i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −32.0000 | −1.04651 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −34.0000 | −1.11073 | −0.555366 | − | 0.831606i | \(-0.687422\pi\) | ||||
−0.555366 | + | 0.831606i | \(0.687422\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.00000 | − | 5.19615i | −0.0979013 | − | 0.169570i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 8.00000i | − | 0.260793i | −0.991462 | − | 0.130396i | \(-0.958375\pi\) | ||
0.991462 | − | 0.130396i | \(-0.0416250\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.00000 | − | 6.92820i | 0.130120 | − | 0.225374i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6.92820 | − | 4.00000i | 0.225136 | − | 0.129983i | −0.383190 | − | 0.923670i | \(-0.625175\pi\) |
0.608326 | + | 0.793687i | \(0.291841\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −10.3923 | + | 6.00000i | −0.336994 | + | 0.194563i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −21.0000 | + | 36.3731i | −0.680257 | + | 1.17824i | 0.294646 | + | 0.955607i | \(0.404798\pi\) |
−0.974902 | + | 0.222633i | \(0.928535\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 27.7128 | + | 16.0000i | 0.896766 | + | 0.517748i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 24.0000i | − | 0.775810i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −8.00000 | − | 13.8564i | −0.258333 | − | 0.447447i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −69.0000 | −2.22581 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 12.0000 | 0.386695 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −28.0000 | − | 48.4974i | −0.901352 | − | 1.56119i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 22.0000i | − | 0.707472i | −0.935345 | − | 0.353736i | \(-0.884911\pi\) | ||
0.935345 | − | 0.353736i | \(-0.115089\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.46410 | − | 2.00000i | −0.111283 | − | 0.0642493i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 14.0000 | − | 24.2487i | 0.449281 | − | 0.778178i | −0.549058 | − | 0.835784i | \(-0.685013\pi\) |
0.998339 | + | 0.0576061i | \(0.0183467\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 10.3923 | − | 6.00000i | 0.332479 | − | 0.191957i | −0.324462 | − | 0.945899i | \(-0.605183\pi\) |
0.656941 | + | 0.753942i | \(0.271850\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.00000 | − | 13.8564i | 0.255681 | − | 0.442853i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.73205 | − | 1.00000i | −0.0553001 | − | 0.0319275i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 24.0000i | 0.765481i | 0.923856 | + | 0.382741i | \(0.125020\pi\) | ||||
−0.923856 | + | 0.382741i | \(0.874980\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 24.0000 | + | 41.5692i | 0.764704 | + | 1.32451i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 8.00000 | 0.254643 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 18.0000 | + | 31.1769i | 0.571789 | + | 0.990367i | 0.996382 | + | 0.0849833i | \(0.0270837\pi\) |
−0.424594 | + | 0.905384i | \(0.639583\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.00000i | 0.0634681i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 13.8564 | + | 8.00000i | 0.439278 | + | 0.253617i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −11.0000 | + | 19.0526i | −0.348373 | + | 0.603401i | −0.985961 | − | 0.166978i | \(-0.946599\pi\) |
0.637587 | + | 0.770378i | \(0.279933\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8.66025 | + | 5.00000i | −0.273998 | + | 0.158193i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))