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.d.1837.2 |
$q$-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 \(\left(\mathbb{Z}/2028\mathbb{Z}\right)^\times\).
\(n\) | \(677\) | \(1015\) | \(1861\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 | ||||||||
\(5\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(6\) | 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 | ||||||||
\(11\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.00000 | + | 5.19615i | −0.727607 | + | 1.26025i | 0.230285 | + | 0.973123i | \(0.426034\pi\) |
−0.957892 | + | 0.287129i | \(0.907299\pi\) | |||||||
\(18\) | 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 | ||||||||
\(25\) | 5.00000 | 1.00000 | ||||||||
\(26\) | 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 | ||||||||
\(31\) | 2.00000i | 0.359211i | 0.983739 | + | 0.179605i | \(0.0574821\pi\) | ||||
−0.983739 | + | 0.179605i | \(0.942518\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.73205 | + | 1.00000i | −0.284747 | + | 0.164399i | −0.635571 | − | 0.772043i | \(-0.719235\pi\) |
0.350823 | + | 0.936442i | \(0.385902\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.3923 | + | 6.00000i | −1.62301 | + | 0.937043i | −0.636895 | + | 0.770950i | \(0.719782\pi\) |
−0.986110 | + | 0.166092i | \(0.946885\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.00000 | + | 3.46410i | −0.304997 | + | 0.528271i | −0.977261 | − | 0.212041i | \(-0.931989\pi\) |
0.672264 | + | 0.740312i | \(0.265322\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.50000 | − | 2.59808i | −0.214286 | − | 0.371154i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.00000 | 0.840168 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.00000 | 0.824163 | 0.412082 | − | 0.911147i | \(-0.364802\pi\) | ||||
0.412082 | + | 0.911147i | \(0.364802\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.00000i | 0.264906i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.3923 | + | 6.00000i | 1.35296 | + | 0.781133i | 0.988663 | − | 0.150148i | \(-0.0479752\pi\) |
0.364299 | + | 0.931282i | \(0.381308\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.00000 | + | 1.73205i | −0.128037 | + | 0.221766i | −0.922916 | − | 0.385002i | \(-0.874201\pi\) |
0.794879 | + | 0.606768i | \(0.207534\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.73205 | + | 1.00000i | −0.218218 | + | 0.125988i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.66025 | + | 5.00000i | −1.05802 | + | 0.610847i | −0.924883 | − | 0.380251i | \(-0.875838\pi\) |
−0.133135 | + | 0.991098i | \(0.542504\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.3923 | − | 6.00000i | −1.23334 | − | 0.712069i | −0.265615 | − | 0.964079i | \(-0.585575\pi\) |
−0.967725 | + | 0.252010i | \(0.918908\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 14.0000i | − | 1.63858i | −0.573382 | − | 0.819288i | \(-0.694369\pi\) | ||
0.573382 | − | 0.819288i | \(-0.305631\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.50000 | − | 4.33013i | −0.288675 | − | 0.500000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.00000 | 0.900070 | 0.450035 | − | 0.893011i | \(-0.351411\pi\) | ||||
0.450035 | + | 0.893011i | \(0.351411\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.0000i | 1.31717i | 0.752506 | + | 0.658586i | \(0.228845\pi\) | ||||
−0.752506 | + | 0.658586i | \(0.771155\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.00000 | − | 5.19615i | 0.321634 | − | 0.557086i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.73205 | − | 1.00000i | 0.179605 | − | 0.103695i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.66025 | + | 5.00000i | 0.879316 | + | 0.507673i | 0.870433 | − | 0.492287i | \(-0.163839\pi\) |
0.00888289 | + | 0.999961i | \(0.497172\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.00000 | + | 15.5885i | 0.895533 | + | 1.55111i | 0.833143 | + | 0.553058i | \(0.186539\pi\) |
0.0623905 | + | 0.998052i | \(0.480128\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.0000 | 1.57653 | 0.788263 | − | 0.615338i | \(-0.210980\pi\) | ||||
0.788263 | + | 0.615338i | \(0.210980\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.00000 | + | 10.3923i | 0.580042 | + | 1.00466i | 0.995474 | + | 0.0950377i | \(0.0302972\pi\) |
−0.415432 | + | 0.909624i | \(0.636370\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.0000i | 1.34096i | 0.741929 | + | 0.670478i | \(0.233911\pi\) | ||||
−0.741929 | + | 0.670478i | \(0.766089\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.73205 | + | 1.00000i | 0.164399 | + | 0.0949158i | ||||
\(112\) | 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 | ||||||||
\(119\) | −10.3923 | + | 6.00000i | −0.952661 | + | 0.550019i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.50000 | + | 9.52628i | −0.500000 | + | 0.866025i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 10.3923 | + | 6.00000i | 0.937043 | + | 0.541002i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.00000 | − | 3.46410i | −0.177471 | − | 0.307389i | 0.763542 | − | 0.645758i | \(-0.223458\pi\) |
−0.941014 | + | 0.338368i | \(0.890125\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.00000 | 0.352180 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.0000 | 1.04844 | 0.524222 | − | 0.851581i | \(-0.324356\pi\) | ||||
0.524222 | + | 0.851581i | \(0.324356\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.00000 | − | 3.46410i | −0.173422 | − | 0.300376i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.3923 | − | 6.00000i | −0.887875 | − | 0.512615i | −0.0146279 | − | 0.999893i | \(-0.504656\pi\) |
−0.873247 | + | 0.487278i | \(0.837990\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.00000 | − | 13.8564i | 0.678551 | − | 1.17529i | −0.296866 | − | 0.954919i | \(-0.595942\pi\) |
0.975417 | − | 0.220366i | \(-0.0707252\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.50000 | + | 2.59808i | −0.123718 | + | 0.214286i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −10.3923 | − | 6.00000i | −0.851371 | − | 0.491539i | 0.00974235 | − | 0.999953i | \(-0.496899\pi\) |
−0.861113 | + | 0.508413i | \(0.830232\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.0000i | 0.813788i | 0.913475 | + | 0.406894i | \(0.133388\pi\) | ||||
−0.913475 | + | 0.406894i | \(0.866612\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.00000 | − | 5.19615i | −0.242536 | − | 0.420084i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.00000 | 0.159617 | 0.0798087 | − | 0.996810i | \(-0.474569\pi\) | ||||
0.0798087 | + | 0.996810i | \(0.474569\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.00000 | − | 5.19615i | −0.237915 | − | 0.412082i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.1244 | + | 7.00000i | 0.949653 | + | 0.548282i | 0.892973 | − | 0.450110i | \(-0.148615\pi\) |
0.0566798 | + | 0.998392i | \(0.481949\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 20.7846 | − | 12.0000i | 1.60836 | − | 0.928588i | 0.618624 | − | 0.785687i | \(-0.287690\pi\) |
0.989737 | − | 0.142901i | \(-0.0456431\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.73205 | − | 1.00000i | 0.132453 | − | 0.0764719i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.00000 | + | 5.19615i | −0.228086 | + | 0.395056i | −0.957241 | − | 0.289292i | \(-0.906580\pi\) |
0.729155 | + | 0.684349i | \(0.239913\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.66025 | + | 5.00000i | 0.654654 | + | 0.377964i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 12.0000i | − | 0.901975i | ||||||
\(178\) | 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 | ||||||||
\(183\) | 2.00000 | 0.147844 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.73205 | + | 1.00000i | 0.125988 | + | 0.0727393i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.73205 | + | 1.00000i | −0.124676 | + | 0.0719816i | −0.561041 | − | 0.827788i | \(-0.689599\pi\) |
0.436365 | + | 0.899770i | \(0.356266\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −20.7846 | + | 12.0000i | −1.48084 | + | 0.854965i | −0.999764 | − | 0.0217133i | \(-0.993088\pi\) |
−0.481078 | + | 0.876678i | \(0.659755\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.0000 | − | 17.3205i | 0.708881 | − | 1.22782i | −0.256391 | − | 0.966573i | \(-0.582534\pi\) |
0.965272 | − | 0.261245i | \(-0.0841331\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.66025 | + | 5.00000i | 0.610847 | + | 0.352673i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 12.0000i | 0.842235i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.00000 | + | 3.46410i | 0.137686 | + | 0.238479i | 0.926620 | − | 0.375999i | \(-0.122700\pi\) |
−0.788935 | + | 0.614477i | \(0.789367\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 12.0000i | 0.822226i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.00000 | + | 3.46410i | −0.135769 | + | 0.235159i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −12.1244 | + | 7.00000i | −0.819288 | + | 0.473016i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 22.5167 | − | 13.0000i | 1.50783 | − | 0.870544i | 0.507869 | − | 0.861435i | \(-0.330434\pi\) |
0.999959 | − | 0.00910984i | \(-0.00289979\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.50000 | + | 4.33013i | −0.166667 | + | 0.288675i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −20.7846 | − | 12.0000i | −1.37952 | − | 0.796468i | −0.387421 | − | 0.921903i | \(-0.626634\pi\) |
−0.992102 | + | 0.125435i | \(0.959967\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 14.0000i | − | 0.925146i | −0.886581 | − | 0.462573i | \(-0.846926\pi\) | ||
0.886581 | − | 0.462573i | \(-0.153074\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.00000 | −0.393073 | −0.196537 | − | 0.980497i | \(-0.562969\pi\) | ||||
−0.196537 | + | 0.980497i | \(0.562969\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.00000 | − | 6.92820i | −0.259828 | − | 0.450035i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 12.0000i | − | 0.776215i | −0.921614 | − | 0.388108i | \(-0.873129\pi\) | ||
0.921614 | − | 0.388108i | \(-0.126871\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.66025 | − | 5.00000i | −0.557856 | − | 0.322078i | 0.194429 | − | 0.980917i | \(-0.437715\pi\) |
−0.752285 | + | 0.658838i | \(0.771048\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.500000 | + | 0.866025i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 10.3923 | − | 6.00000i | 0.658586 | − | 0.380235i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.00000 | − | 10.3923i | 0.378717 | − | 0.655956i | −0.612159 | − | 0.790735i | \(-0.709699\pi\) |
0.990876 | + | 0.134778i | \(0.0430322\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.00000 | + | 5.19615i | 0.187135 | + | 0.324127i | 0.944294 | − | 0.329104i | \(-0.106747\pi\) |
−0.757159 | + | 0.653231i | \(0.773413\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.00000 | −0.248548 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.00000 | −0.371391 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.0000 | + | 20.7846i | 0.739952 | + | 1.28163i | 0.952517 | + | 0.304487i | \(0.0984850\pi\) |
−0.212565 | + | 0.977147i | \(0.568182\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −9.00000 | + | 15.5885i | −0.548740 | + | 0.950445i | 0.449622 | + | 0.893219i | \(0.351559\pi\) |
−0.998361 | + | 0.0572259i | \(0.981774\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −22.5167 | + | 13.0000i | −1.36779 | + | 0.789694i | −0.990645 | − | 0.136461i | \(-0.956427\pi\) |
−0.377144 | + | 0.926155i | \(0.623094\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.00000 | + | 8.66025i | −0.300421 | + | 0.520344i | −0.976231 | − | 0.216731i | \(-0.930460\pi\) |
0.675810 | + | 0.737075i | \(0.263794\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.73205 | − | 1.00000i | −0.103695 | − | 0.0598684i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.0000i | 0.715860i | 0.933748 | + | 0.357930i | \(0.116517\pi\) | ||||
−0.933748 | + | 0.357930i | \(0.883483\pi\) | |||||||
\(282\) | 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 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −24.0000 | −1.41668 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.50000 | − | 16.4545i | −0.558824 | − | 0.967911i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 10.0000i | − | 0.586210i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −10.3923 | − | 6.00000i | −0.607125 | − | 0.350524i | 0.164714 | − | 0.986341i | \(-0.447330\pi\) |
−0.771839 | + | 0.635818i | \(0.780663\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.92820 | + | 4.00000i | −0.399335 | + | 0.230556i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 9.00000 | − | 15.5885i | 0.517036 | − | 0.895533i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 2.00000i | − | 0.114146i | −0.998370 | − | 0.0570730i | \(-0.981823\pi\) | ||
0.998370 | − | 0.0570730i | \(-0.0181768\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8.00000 | − | 13.8564i | −0.455104 | − | 0.788263i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −24.0000 | −1.36092 | −0.680458 | − | 0.732787i | \(-0.738219\pi\) | ||||
−0.680458 | + | 0.732787i | \(0.738219\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −22.0000 | −1.24351 | −0.621757 | − | 0.783210i | \(-0.713581\pi\) | ||||
−0.621757 | + | 0.783210i | \(0.713581\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 24.0000i | − | 1.34797i | −0.738743 | − | 0.673987i | \(-0.764580\pi\) | ||
0.738743 | − | 0.673987i | \(-0.235420\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.00000 | − | 10.3923i | 0.334887 | − | 0.580042i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 10.3923 | − | 6.00000i | 0.578243 | − | 0.333849i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 12.1244 | − | 7.00000i | 0.670478 | − | 0.387101i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.66025 | + | 5.00000i | 0.476011 | + | 0.274825i | 0.718752 | − | 0.695266i | \(-0.244713\pi\) |
−0.242742 | + | 0.970091i | \(0.578047\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 2.00000i | − | 0.109599i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.00000 | −0.108947 | −0.0544735 | − | 0.998515i | \(-0.517348\pi\) | ||||
−0.0544735 | + | 0.998515i | \(0.517348\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.00000 | 0.325875 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 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 | −0.658824 | − | 0.752297i | \(-0.728946\pi\) |
0.980921 | + | 0.194409i | \(0.0622790\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.0526 | − | 11.0000i | 1.01986 | − | 0.588817i | 0.105797 | − | 0.994388i | \(-0.466261\pi\) |
0.914063 | + | 0.405571i | \(0.132927\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.3923 | − | 6.00000i | 0.553127 | − | 0.319348i | −0.197256 | − | 0.980352i | \(-0.563203\pi\) |
0.750382 | + | 0.661004i | \(0.229870\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 10.3923 | + | 6.00000i | 0.550019 | + | 0.317554i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 24.0000i | 1.26667i | 0.773877 | + | 0.633336i | \(0.218315\pi\) | ||||
−0.773877 | + | 0.633336i | \(0.781685\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.50000 | − | 12.9904i | −0.394737 | − | 0.683704i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 11.0000 | 0.577350 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.0000 | − | 17.3205i | −0.521996 | − | 0.904123i | −0.999673 | − | 0.0255875i | \(-0.991854\pi\) |
0.477677 | − | 0.878536i | \(-0.341479\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 12.0000i | − | 0.624695i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10.3923 | + | 6.00000i | 0.539542 | + | 0.311504i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.00000 | + | 12.1244i | −0.362446 | + | 0.627775i | −0.988363 | − | 0.152115i | \(-0.951392\pi\) |
0.625917 | + | 0.779890i | \(0.284725\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 22.5167 | − | 13.0000i | 1.15660 | − | 0.667765i | 0.206116 | − | 0.978528i | \(-0.433918\pi\) |
0.950488 | + | 0.310763i | \(0.100584\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.00000 | + | 3.46410i | −0.102463 | + | 0.177471i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −20.7846 | − | 12.0000i | −1.06204 | − | 0.613171i | −0.136047 | − | 0.990702i | \(-0.543440\pi\) |
−0.925997 | + | 0.377531i | \(0.876773\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.00000 | − | 3.46410i | −0.101666 | − | 0.176090i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −30.0000 | −1.52106 | −0.760530 | − | 0.649303i | \(-0.775061\pi\) | ||||
−0.760530 | + | 0.649303i | \(0.775061\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.00000 | − | 10.3923i | −0.302660 | − | 0.524222i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −19.0526 | − | 11.0000i | −0.956221 | − | 0.552074i | −0.0612128 | − | 0.998125i | \(-0.519497\pi\) |
−0.895008 | + | 0.446051i | \(0.852830\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.00000 | + | 3.46410i | −0.100125 | + | 0.173422i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −20.7846 | + | 12.0000i | −1.03793 | + | 0.599251i | −0.919247 | − | 0.393680i | \(-0.871202\pi\) |
−0.118686 | + | 0.992932i | \(0.537868\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.66025 | + | 5.00000i | 0.428222 | + | 0.247234i | 0.698589 | − | 0.715523i | \(-0.253812\pi\) |
−0.270367 | + | 0.962757i | \(0.587145\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 12.0000i | 0.591916i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 12.0000 | + | 20.7846i | 0.590481 | + | 1.02274i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −16.0000 | −0.783523 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.00000 | + | 10.3923i | 0.293119 | + | 0.507697i | 0.974546 | − | 0.224189i | \(-0.0719734\pi\) |
−0.681426 | + | 0.731887i | \(0.738640\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 34.0000i | − | 1.65706i | −0.559946 | − | 0.828529i | \(-0.689178\pi\) | ||
0.559946 | − | 0.828529i | \(-0.310822\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −15.0000 | + | 25.9808i | −0.727607 | + | 1.26025i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.46410 | + | 2.00000i | −0.167640 | + | 0.0967868i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 20.7846 | − | 12.0000i | 1.00116 | − | 0.578020i | 0.0925683 | − | 0.995706i | \(-0.470492\pi\) |
0.908591 | + | 0.417687i | \(0.137159\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.00000 | − | 12.1244i | 0.336399 | − | 0.582659i | −0.647354 | − | 0.762190i | \(-0.724124\pi\) |
0.983752 | + | 0.179530i | \(0.0574578\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.00000 | + | 6.92820i | 0.190910 | + | 0.330665i | 0.945552 | − | 0.325471i | \(-0.105523\pi\) |
−0.754642 | + | 0.656136i | \(0.772190\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.00000 | 0.142857 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12.0000 | −0.570137 | −0.285069 | − | 0.958507i | \(-0.592016\pi\) | ||||
−0.285069 | + | 0.958507i | \(0.592016\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 12.0000i | 0.567581i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.66025 | − | 5.00000i | 0.406894 | − | 0.234920i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 32.9090 | − | 19.0000i | 1.53942 | − | 0.888783i | 0.540544 | − | 0.841316i | \(-0.318219\pi\) |
0.998873 | − | 0.0474665i | \(-0.0151147\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.00000 | + | 5.19615i | −0.140028 | + | 0.242536i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 22.0000i | 1.02243i | 0.859454 | + | 0.511213i | \(0.170804\pi\) | ||||
−0.859454 | + | 0.511213i | \(0.829196\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −36.0000 | −1.66588 | −0.832941 | − | 0.553362i | \(-0.813345\pi\) | ||||
−0.832941 | + | 0.553362i | \(0.813345\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −20.0000 | −0.923514 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.00000 | − | 1.73205i | −0.0460776 | − | 0.0798087i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.66025 | − | 5.00000i | −0.397360 | − | 0.229416i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.00000 | + | 5.19615i | −0.137361 | + | 0.237915i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10.3923 | − | 6.00000i | 0.474837 | − | 0.274147i | −0.243426 | − | 0.969920i | \(-0.578271\pi\) |
0.718262 | + | 0.695773i | \(0.244938\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.73205 | − | 1.00000i | −0.0784867 | − | 0.0453143i | 0.460243 | − | 0.887793i | \(-0.347762\pi\) |
−0.538730 | + | 0.842479i | \(0.681096\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 14.0000i | − | 0.633102i | ||||||
\(490\) | 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 | ||||||||
\(493\) | −36.0000 | −1.62136 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −12.0000 | − | 20.7846i | −0.538274 | − | 0.932317i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.0000i | 0.626726i | 0.949633 | + | 0.313363i | \(0.101456\pi\) | ||||
−0.949633 | + | 0.313363i | \(0.898544\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −20.7846 | − | 12.0000i | −0.928588 | − | 0.536120i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12.0000 | − | 20.7846i | 0.535054 | − | 0.926740i | −0.464107 | − | 0.885779i | \(-0.653625\pi\) |
0.999161 | − | 0.0409609i | \(-0.0130419\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.0000 | − | 24.2487i | 0.619324 | − | 1.07270i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.73205 | − | 1.00000i | −0.0764719 | − | 0.0441511i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.00000 | 0.263371 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 30.0000 | 1.31432 | 0.657162 | − | 0.753749i | \(-0.271757\pi\) | ||||
0.657162 | + | 0.753749i | \(0.271757\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.00000 | + | 13.8564i | 0.349816 | + | 0.605898i | 0.986216 | − | 0.165460i | \(-0.0529109\pi\) |
−0.636401 | + | 0.771358i | \(0.719578\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 10.0000i | − | 0.436436i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −10.3923 | − | 6.00000i | −0.452696 | − | 0.261364i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.5000 | − | 19.9186i | 0.500000 | − | 0.866025i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −10.3923 | + | 6.00000i | −0.450988 | + | 0.260378i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6.00000 | − | 10.3923i | 0.258919 | − | 0.448461i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.0000i | 0.429934i | 0.976621 | + | 0.214967i | \(0.0689643\pi\) | ||||
−0.976621 | + | 0.214967i | \(0.931036\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.00000 | + | 1.73205i | 0.0429141 | + | 0.0743294i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.0000 | −0.684111 | −0.342055 | − | 0.939680i | \(-0.611123\pi\) | ||||
−0.342055 | + | 0.939680i | \(0.611123\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.00000 | − | 1.73205i | −0.0426790 | − | 0.0739221i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 12.0000i | − | 0.511217i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13.8564 | + | 8.00000i | 0.589234 | + | 0.340195i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10.3923 | − | 6.00000i | 0.440336 | − | 0.254228i | −0.263404 | − | 0.964686i | \(-0.584845\pi\) |
0.703740 | + | 0.710457i | \(0.251512\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6.00000 | − | 10.3923i | 0.252870 | − | 0.437983i | −0.711445 | − | 0.702742i | \(-0.751959\pi\) |
0.964315 | + | 0.264758i | \(0.0852922\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 2.00000i | − | 0.0839921i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9.00000 | − | 15.5885i | −0.377300 | − | 0.653502i | 0.613369 | − | 0.789797i | \(-0.289814\pi\) |
−0.990668 | + | 0.136295i | \(0.956481\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 40.0000 | 1.67395 | 0.836974 | − | 0.547243i | \(-0.184323\pi\) | ||||
0.836974 | + | 0.547243i | \(0.184323\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.00000i | 0.0832611i | 0.999133 | + | 0.0416305i | \(0.0132552\pi\) | ||||
−0.999133 | + | 0.0416305i | \(0.986745\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.73205 | + | 1.00000i | 0.0719816 | + | 0.0415586i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −12.0000 | + | 20.7846i | −0.497844 | + | 0.862291i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −10.3923 | + | 6.00000i | −0.428936 | + | 0.247647i | −0.698893 | − | 0.715226i | \(-0.746324\pi\) |
0.269957 | + | 0.962872i | \(0.412990\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.00000 | − | 3.46410i | 0.0824086 | − | 0.142736i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 20.7846 | + | 12.0000i | 0.854965 | + | 0.493614i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −20.0000 | −0.818546 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −48.0000 | −1.96123 | −0.980613 | − | 0.195952i | \(-0.937220\pi\) | ||||
−0.980613 | + | 0.195952i | \(0.937220\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13.0000 | − | 22.5167i | −0.530281 | − | 0.918474i | −0.999376 | − | 0.0353259i | \(-0.988753\pi\) |
0.469095 | − | 0.883148i | \(-0.344580\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 10.0000i | − | 0.407231i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 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 | ||||||||
\(613\) | −19.0526 | + | 11.0000i | −0.769526 | + | 0.444286i | −0.832705 | − | 0.553716i | \(-0.813209\pi\) |
0.0631797 | + | 0.998002i | \(0.479876\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 31.1769 | + | 18.0000i | 1.25514 | + | 0.724653i | 0.972125 | − | 0.234464i | \(-0.0753335\pi\) |
0.283011 | + | 0.959117i | \(0.408667\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22.0000i | 0.884255i | 0.896952 | + | 0.442127i | \(0.145776\pi\) | ||||
−0.896952 | + | 0.442127i | \(0.854224\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.0000 | 1.00000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 12.0000i | − | 0.478471i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.66025 | − | 5.00000i | −0.344759 | − | 0.199047i | 0.317615 | − | 0.948220i | \(-0.397118\pi\) |
−0.662375 | + | 0.749173i | \(0.730451\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.00000 | − | 3.46410i | 0.0794929 | − | 0.137686i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 10.3923 | − | 6.00000i | 0.411113 | − | 0.237356i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.00000 | − | 15.5885i | 0.355479 | − | 0.615707i | −0.631721 | − | 0.775196i | \(-0.717651\pi\) |
0.987200 | + | 0.159489i | \(0.0509845\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12.1244 | − | 7.00000i | −0.478138 | − | 0.276053i | 0.241502 | − | 0.970400i | \(-0.422360\pi\) |
−0.719640 | + | 0.694347i | \(0.755693\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 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 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.00000 | 0.156772 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 15.0000 | + | 25.9808i | 0.586995 | + | 1.01671i | 0.994623 | + | 0.103558i | \(0.0330227\pi\) |
−0.407628 | + | 0.913148i | \(0.633644\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 12.1244 | + | 7.00000i | 0.473016 | + | 0.273096i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 18.0000 | − | 31.1769i | 0.701180 | − | 1.21448i | −0.266872 | − | 0.963732i | \(-0.585990\pi\) |
0.968052 | − | 0.250748i | \(-0.0806766\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.73205 | + | 1.00000i | −0.0673690 | + | 0.0388955i | −0.533306 | − | 0.845922i | \(-0.679051\pi\) |
0.465937 | + | 0.884818i | \(0.345717\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −22.5167 | − | 13.0000i | −0.870544 | − | 0.502609i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.00000 | − | 8.66025i | −0.192736 | − | 0.333828i | 0.753420 | − | 0.657539i | \(-0.228403\pi\) |
−0.946156 | + | 0.323711i | \(0.895069\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.00000 | 0.192450 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6.00000 | 0.230599 | 0.115299 | − | 0.993331i | \(-0.463217\pi\) | ||||
0.115299 | + | 0.993331i | \(0.463217\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.0000 | + | 17.3205i | 0.383765 | + | 0.664700i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 24.0000i | 0.919682i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −20.7846 | − | 12.0000i | −0.795301 | − | 0.459167i | 0.0465244 | − | 0.998917i | \(-0.485185\pi\) |
−0.841825 | + | 0.539750i | \(0.818519\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −12.1244 | + | 7.00000i | −0.462573 | + | 0.267067i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.1244 | − | 7.00000i | 0.461232 | − | 0.266293i | −0.251330 | − | 0.967901i | \(-0.580868\pi\) |
0.712562 | + | 0.701609i | \(0.247535\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 72.0000i | − | 2.72719i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.00000 | + | 5.19615i | 0.113470 | + | 0.196537i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 42.0000 | 1.58632 | 0.793159 | − | 0.609015i | \(-0.208435\pi\) | ||||
0.793159 | + | 0.609015i | \(0.208435\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.00000 | 0.150863 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 36.0000i | 1.35392i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.66025 | − | 5.00000i | −0.325243 | − | 0.187779i | 0.328484 | − | 0.944509i | \(-0.393462\pi\) |
−0.653727 | + | 0.756730i | \(0.726796\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.00000 | + | 6.92820i | −0.150012 | + | 0.259828i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −10.3923 | + | 6.00000i | −0.388108 | + | 0.224074i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 27.7128 | + | 16.0000i | 1.03208 | + | 0.595871i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 10.0000i | 0.371904i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 15.0000 | + | 25.9808i | 0.557086 | + | 0.964901i | ||||
\(726\) | 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 | ||||||||
\(731\) | −12.0000 | − | 20.7846i | −0.443836 | − | 0.768747i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 38.0000i | 1.40356i | 0.712393 | + | 0.701781i | \(0.247612\pi\) | ||||
−0.712393 | + | 0.701781i | \(0.752388\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.73205 | + | 1.00000i | −0.0637145 | + | 0.0367856i | −0.531519 | − | 0.847046i | \(-0.678379\pi\) |
0.467804 | + | 0.883832i | \(0.345045\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 10.3923 | − | 6.00000i | 0.381257 | − | 0.220119i | −0.297108 | − | 0.954844i | \(-0.596022\pi\) |
0.678365 | + | 0.734725i | \(0.262689\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −10.3923 | − | 6.00000i | −0.380235 | − | 0.219529i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 24.0000i | 0.876941i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16.0000 | + | 27.7128i | 0.583848 | + | 1.01125i | 0.995018 | + | 0.0996961i | \(0.0317870\pi\) |
−0.411170 | + | 0.911559i | \(0.634880\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −12.0000 | −0.437304 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.00000 | − | 1.73205i | −0.0363456 | − | 0.0629525i | 0.847280 | − | 0.531146i | \(-0.178238\pi\) |
−0.883626 | + | 0.468193i | \(0.844905\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −10.3923 | − | 6.00000i | −0.376721 | − | 0.217500i | 0.299670 | − | 0.954043i | \(-0.403123\pi\) |
−0.676391 | + | 0.736543i | \(0.736457\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −14.0000 | + | 24.2487i | −0.506834 | + | 0.877862i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −19.0526 | + | 11.0000i | −0.687053 | + | 0.396670i | −0.802507 | − | 0.596643i | \(-0.796501\pi\) |
0.115454 | + | 0.993313i | \(0.463168\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.00000 | − | 5.19615i | 0.108042 | − | 0.187135i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −10.3923 | − | 6.00000i | −0.373785 | − | 0.215805i | 0.301326 | − | 0.953521i | \(-0.402571\pi\) |
−0.675111 | + | 0.737716i | \(0.735904\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.0000i | 0.359211i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.00000 | + | 3.46410i | 0.0717496 | + | 0.124274i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 24.0000 | 0.859889 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.00000 | + | 5.19615i | 0.107211 | + | 0.185695i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 22.5167 | + | 13.0000i | 0.802632 | + | 0.463400i | 0.844391 | − | 0.535728i | \(-0.179963\pi\) |
−0.0417585 | + | 0.999128i | \(0.513296\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 12.0000 | − | 20.7846i | 0.427211 | − | 0.739952i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.3923 | + | 6.00000i | −0.369508 | + | 0.213335i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −9.00000 | + | 15.5885i | −0.318796 | + | 0.552171i | −0.980237 | − | 0.197826i | \(-0.936612\pi\) |
0.661441 | + | 0.749997i | \(0.269945\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 18.0000 | 0.633630 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.00000 | − | 5.19615i | −0.105474 | − | 0.182687i | 0.808458 | − | 0.588555i | \(-0.200303\pi\) |
−0.913932 | + | 0.405868i | \(0.866969\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 22.0000i | − | 0.772524i | −0.922389 | − | 0.386262i | \(-0.873766\pi\) | ||
0.922389 | − | 0.386262i | \(-0.126234\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 22.5167 | + | 13.0000i | 0.789694 | + | 0.455930i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.92820 | − | 4.00000i | 0.242387 | − | 0.139942i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −10.3923 | + | 6.00000i | −0.362694 | + | 0.209401i | −0.670262 | − | 0.742125i | \(-0.733818\pi\) |
0.307568 | + | 0.951526i | \(0.400485\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20.0000 | + | 34.6410i | −0.697156 | + | 1.20751i | 0.272292 | + | 0.962215i | \(0.412218\pi\) |
−0.969448 | + | 0.245295i | \(0.921115\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 48.0000i | − | 1.66912i | −0.550914 | − | 0.834562i | \(-0.685721\pi\) | ||
0.550914 | − | 0.834562i | \(-0.314279\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.00000 | + | 1.73205i | 0.0347314 | + | 0.0601566i | 0.882869 | − | 0.469620i | \(-0.155609\pi\) |
−0.848137 | + | 0.529777i | \(0.822276\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 10.0000 | 0.346896 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 18.0000 | 0.623663 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.00000i | 0.0691301i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 31.1769 | + | 18.0000i | 1.07635 | + | 0.621429i | 0.929909 | − | 0.367791i | \(-0.119886\pi\) |
0.146438 | + | 0.989220i | \(0.453219\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.50000 | + | 6.06218i | −0.120690 | + | 0.209041i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 10.3923 | − | 6.00000i | 0.357930 | − | 0.206651i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −19.0526 | + | 11.0000i | −0.654654 | + | 0.377964i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −8.00000 | + | 13.8564i | −0.274559 | + | 0.475551i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.0000i | 0.753266i | 0.926363 | + | 0.376633i | \(0.122918\pi\) | ||||
−0.926363 | + | 0.376633i | \(0.877082\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 42.0000 | 1.43469 | 0.717346 | − | 0.696717i | \(-0.245357\pi\) | ||||
0.717346 | + | 0.696717i | \(0.245357\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 44.0000 | 1.50126 | 0.750630 | − | 0.660722i | \(-0.229750\pi\) | ||||
0.750630 | + | 0.660722i | \(0.229750\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 12.0000 | + | 20.7846i | 0.408959 | + | 0.708338i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −9.50000 | + | 16.4545i | −0.322637 | + | 0.558824i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −8.66025 | + | 5.00000i | −0.293105 | + | 0.169224i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −43.3013 | − | 25.0000i | −1.46218 | − | 0.844190i | −0.463068 | − | 0.886323i | \(-0.653251\pi\) |
−0.999112 | + | 0.0421327i | \(0.986585\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 12.0000i | 0.404750i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −21.0000 | − | 36.3731i | −0.707508 | − | 1.22544i | −0.965779 | − | 0.259367i | \(-0.916486\pi\) |
0.258271 | − | 0.966073i | \(-0.416847\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 16.0000 | 0.538443 | 0.269221 | − | 0.963078i | \(-0.413234\pi\) | ||||
0.269221 | + | 0.963078i | \(0.413234\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −12.0000 | − | 20.7846i | −0.402921 | − | 0.697879i | 0.591156 | − | 0.806557i | \(-0.298672\pi\) |
−0.994077 | + | 0.108678i | \(0.965338\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 8.00000i | − | 0.268311i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −10.3923 | + | 6.00000i | −0.346603 | + | 0.200111i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −18.0000 | + | 31.1769i | −0.599667 | + | 1.03865i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6.92820 | + | 4.00000i | 0.230556 | + | 0.133112i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.00000 | + | 6.92820i | 0.132818 | + | 0.230047i | 0.924762 | − | 0.380547i | \(-0.124264\pi\) |
−0.791944 | + | 0.610594i | \(0.790931\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −18.0000 | −0.597022 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 48.0000 | 1.59031 | 0.795155 | − | 0.606406i | \(-0.207389\pi\) | ||||
0.795155 | + | 0.606406i | \(0.207389\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 20.7846 | + | 12.0000i | 0.686368 | + | 0.396275i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.00000 | − | 13.8564i | 0.263896 | − | 0.457081i | −0.703378 | − | 0.710816i | \(-0.748326\pi\) |
0.967274 | + | 0.253735i | \(0.0816592\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.73205 | + | 1.00000i | −0.0570730 | + | 0.0329511i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.66025 | + | 5.00000i | −0.284747 | + | 0.164399i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −8.00000 | + | 13.8564i | −0.262754 | + | 0.455104i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 31.1769 | + | 18.0000i | 1.02288 | + | 0.590561i | 0.914937 | − | 0.403596i | \(-0.132240\pi\) |
0.107944 | + | 0.994157i | \(0.465573\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.00000i | 0.196642i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 12.0000 | + | 20.7846i | 0.392862 | + | 0.680458i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −34.0000 | −1.11073 | −0.555366 | − | 0.831606i | \(-0.687422\pi\) | ||||
−0.555366 | + | 0.831606i | \(0.687422\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 11.0000 | + | 19.0526i | 0.358971 | + | 0.621757i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 12.0000i | − | 0.391189i | −0.980685 | − | 0.195594i | \(-0.937336\pi\) | ||
0.980685 | − | 0.195594i | \(-0.0626636\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 31.1769 | − | 18.0000i | 1.01311 | − | 0.584921i | 0.101012 | − | 0.994885i | \(-0.467792\pi\) |
0.912102 | + | 0.409964i | \(0.134459\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −20.7846 | + | 12.0000i | −0.673987 | + | 0.389127i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −9.00000 | + | 15.5885i | −0.291539 | + | 0.504960i | −0.974174 | − | 0.225800i | \(-0.927501\pi\) |
0.682635 | + | 0.730759i | \(0.260834\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −12.0000 | − | 20.7846i | −0.387500 | − | 0.671170i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 27.0000 | 0.870968 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −12.0000 | −0.386695 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 50.0000i | 1.60789i | 0.594703 | + | 0.803946i | \(0.297270\pi\) | ||||
−0.594703 | + | 0.803946i | \(0.702730\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −10.3923 | − | 6.00000i | −0.333849 | − | 0.192748i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −6.00000 | + | 10.3923i | −0.192549 | + | 0.333505i | −0.946094 | − | 0.323891i | \(-0.895009\pi\) |
0.753545 | + | 0.657396i | \(0.228342\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 27.7128 | − | 16.0000i | 0.888432 | − | 0.512936i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 20.7846 | − | 12.0000i | 0.664959 | − | 0.383914i | −0.129205 | − | 0.991618i | \(-0.541243\pi\) |
0.794164 | + | 0.607704i | \(0.207909\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −12.1244 | − | 7.00000i | −0.387101 | − | 0.223493i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 60.0000i | − | 1.91370i | −0.290578 | − | 0.956851i | \(-0.593847\pi\) | ||
0.290578 | − | 0.956851i | \(-0.406153\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 26.0000 | + | 45.0333i | 0.825917 | + | 1.43053i | 0.901216 | + | 0.433370i | \(0.142676\pi\) |
−0.0752991 | + | 0.997161i | \(0.523991\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 10.0000i | − | 0.317340i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.00000 | − | 8.66025i | 0.158352 | − | 0.274273i | −0.775923 | − | 0.630828i | \(-0.782715\pi\) |
0.934274 | + | 0.356555i | \(0.116049\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.73205 | + | 1.00000i | −0.0547997 | + | 0.0316386i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))