Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2592,2,Mod(433,2592)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2592, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2592.433");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2592 = 2^{5} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2592.r (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: | \(20.6972242039\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.49787136.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 3x^{6} + 5x^{4} + 12x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | no (minimal twist has level 216) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 433.1 | ||
Root | \(-0.228425 + 1.39564i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2592.433 |
Dual form | 2592.2.r.p.2161.1 |
$q$-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 \(\left(\mathbb{Z}/2592\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(1217\) | \(2431\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.866025 | − | 0.500000i | −0.387298 | − | 0.223607i | 0.293691 | − | 0.955901i | \(-0.405116\pi\) |
−0.680989 | + | 0.732294i | \(0.738450\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.500000 | + | 0.866025i | 0.188982 | + | 0.327327i | 0.944911 | − | 0.327327i | \(-0.106148\pi\) |
−0.755929 | + | 0.654654i | \(0.772814\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.59808 | + | 1.50000i | −0.783349 | + | 0.452267i | −0.837616 | − | 0.546259i | \(-0.816051\pi\) |
0.0542666 | + | 0.998526i | \(0.482718\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.58258 | − | 2.64575i | −1.27098 | − | 0.733799i | −0.295806 | − | 0.955248i | \(-0.595588\pi\) |
−0.975172 | + | 0.221449i | \(0.928921\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.29150 | 1.28338 | 0.641689 | − | 0.766965i | \(-0.278234\pi\) | ||||
0.641689 | + | 0.766965i | \(0.278234\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.29150i | 1.21395i | 0.794719 | + | 0.606977i | \(0.207618\pi\) | ||||
−0.794719 | + | 0.606977i | \(0.792382\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.64575 | − | 4.58258i | 0.551677 | − | 0.955533i | −0.446476 | − | 0.894795i | \(-0.647321\pi\) |
0.998154 | − | 0.0607377i | \(-0.0193453\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.00000 | − | 3.46410i | −0.400000 | − | 0.692820i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.19615 | − | 3.00000i | 0.964901 | − | 0.557086i | 0.0672232 | − | 0.997738i | \(-0.478586\pi\) |
0.897678 | + | 0.440652i | \(0.145253\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.50000 | + | 6.06218i | −0.628619 | + | 1.08880i | 0.359211 | + | 0.933257i | \(0.383046\pi\) |
−0.987829 | + | 0.155543i | \(0.950287\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 1.00000i | − | 0.169031i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.29150i | 0.869918i | 0.900450 | + | 0.434959i | \(0.143237\pi\) | ||||
−0.900450 | + | 0.434959i | \(0.856763\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.64575 | − | 4.58258i | 0.413197 | − | 0.715678i | −0.582040 | − | 0.813160i | \(-0.697745\pi\) |
0.995237 | + | 0.0974818i | \(0.0310788\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.16515 | − | 5.29150i | 1.39767 | − | 0.806947i | 0.403524 | − | 0.914969i | \(-0.367785\pi\) |
0.994148 | + | 0.108022i | \(0.0344518\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.00000 | − | 5.19615i | 0.428571 | − | 0.742307i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 9.00000i | − | 1.23625i | −0.786082 | − | 0.618123i | \(-0.787894\pi\) | ||
0.786082 | − | 0.618123i | \(-0.212106\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.00000 | 0.404520 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.46410 | − | 2.00000i | −0.450988 | − | 0.260378i | 0.257260 | − | 0.966342i | \(-0.417180\pi\) |
−0.708247 | + | 0.705965i | \(0.750514\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.64575 | + | 4.58258i | 0.328165 | + | 0.568399i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 15.8745 | 1.88396 | 0.941979 | − | 0.335673i | \(-0.108964\pi\) | ||||
0.941979 | + | 0.335673i | \(0.108964\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.00000 | 0.351123 | 0.175562 | − | 0.984468i | \(-0.443826\pi\) | ||||
0.175562 | + | 0.984468i | \(0.443826\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.59808 | − | 1.50000i | −0.296078 | − | 0.170941i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.00000 | + | 3.46410i | 0.225018 | + | 0.389742i | 0.956325 | − | 0.292306i | \(-0.0944227\pi\) |
−0.731307 | + | 0.682048i | \(0.761089\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.06218 | − | 3.50000i | 0.665410 | − | 0.384175i | −0.128925 | − | 0.991654i | \(-0.541153\pi\) |
0.794335 | + | 0.607479i | \(0.207819\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.58258 | − | 2.64575i | −0.497050 | − | 0.286972i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.5830 | 1.12180 | 0.560898 | − | 0.827885i | \(-0.310456\pi\) | ||||
0.560898 | + | 0.827885i | \(0.310456\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 5.29150i | − | 0.554700i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.64575 | − | 4.58258i | 0.271448 | − | 0.470162i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.50000 | − | 6.06218i | −0.355371 | − | 0.615521i | 0.631810 | − | 0.775123i | \(-0.282312\pi\) |
−0.987181 | + | 0.159602i | \(0.948979\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −14.7224 | + | 8.50000i | −1.46494 | + | 0.845782i | −0.999233 | − | 0.0391591i | \(-0.987532\pi\) |
−0.465704 | + | 0.884941i | \(0.654199\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 3.00000i | − | 0.290021i | −0.989430 | − | 0.145010i | \(-0.953678\pi\) | ||
0.989430 | − | 0.145010i | \(-0.0463216\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 5.29150i | − | 0.506834i | −0.967357 | − | 0.253417i | \(-0.918446\pi\) | ||
0.967357 | − | 0.253417i | \(-0.0815545\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.93725 | − | 13.7477i | 0.746674 | − | 1.29328i | −0.202735 | − | 0.979234i | \(-0.564983\pi\) |
0.949409 | − | 0.314044i | \(-0.101684\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.58258 | + | 2.64575i | −0.427327 | + | 0.246718i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.64575 | + | 4.58258i | 0.242536 | + | 0.420084i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00000 | + | 1.73205i | −0.0909091 | + | 0.157459i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.00000i | 0.804984i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.0000 | −1.15356 | −0.576782 | − | 0.816898i | \(-0.695692\pi\) | ||||
−0.576782 | + | 0.816898i | \(0.695692\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.06218 | − | 3.50000i | −0.529655 | − | 0.305796i | 0.211221 | − | 0.977438i | \(-0.432256\pi\) |
−0.740876 | + | 0.671642i | \(0.765589\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.58258 | + | 2.64575i | −0.397360 | + | 0.229416i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.16515 | + | 5.29150i | 0.777378 | + | 0.448819i | 0.835500 | − | 0.549490i | \(-0.185178\pi\) |
−0.0581222 | + | 0.998309i | \(0.518511\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 15.8745 | 1.32749 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.00000 | −0.498273 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.59808 | + | 1.50000i | 0.212843 | + | 0.122885i | 0.602632 | − | 0.798019i | \(-0.294119\pi\) |
−0.389789 | + | 0.920904i | \(0.627452\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.50000 | + | 2.59808i | 0.122068 | + | 0.211428i | 0.920583 | − | 0.390547i | \(-0.127714\pi\) |
−0.798515 | + | 0.601975i | \(0.794381\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.06218 | − | 3.50000i | 0.486926 | − | 0.281127i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.16515 | + | 5.29150i | 0.731459 | + | 0.422308i | 0.818956 | − | 0.573857i | \(-0.194553\pi\) |
−0.0874969 | + | 0.996165i | \(0.527887\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.29150 | 0.417029 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 5.29150i | − | 0.414462i | −0.978292 | − | 0.207231i | \(-0.933555\pi\) | ||
0.978292 | − | 0.207231i | \(-0.0664452\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.29150 | − | 9.16515i | 0.409469 | − | 0.709221i | −0.585361 | − | 0.810772i | \(-0.699047\pi\) |
0.994830 | + | 0.101552i | \(0.0323807\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.50000 | + | 12.9904i | 0.576923 | + | 0.999260i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.9904 | − | 7.50000i | 0.987640 | − | 0.570214i | 0.0830722 | − | 0.996544i | \(-0.473527\pi\) |
0.904568 | + | 0.426329i | \(0.140193\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.00000 | − | 3.46410i | 0.151186 | − | 0.261861i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 23.0000i | − | 1.71910i | −0.511051 | − | 0.859550i | \(-0.670744\pi\) | ||
0.511051 | − | 0.859550i | \(-0.329256\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 21.1660i | − | 1.57326i | −0.617426 | − | 0.786629i | \(-0.711825\pi\) | ||
0.617426 | − | 0.786629i | \(-0.288175\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.64575 | − | 4.58258i | 0.194520 | − | 0.336918i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −13.7477 | + | 7.93725i | −1.00533 | + | 0.580429i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.64575 | + | 4.58258i | 0.191440 | + | 0.331584i | 0.945728 | − | 0.324960i | \(-0.105351\pi\) |
−0.754288 | + | 0.656544i | \(0.772018\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.50000 | − | 2.59808i | 0.107972 | − | 0.187014i | −0.806976 | − | 0.590584i | \(-0.798898\pi\) |
0.914949 | + | 0.403570i | \(0.132231\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 13.0000i | − | 0.926212i | −0.886303 | − | 0.463106i | \(-0.846735\pi\) | ||
0.886303 | − | 0.463106i | \(-0.153265\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 17.0000 | 1.20510 | 0.602549 | − | 0.798082i | \(-0.294152\pi\) | ||||
0.602549 | + | 0.798082i | \(0.294152\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.19615 | + | 3.00000i | 0.364698 | + | 0.210559i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.58258 | + | 2.64575i | −0.320061 | + | 0.184787i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.93725 | − | 13.7477i | −0.549031 | − | 0.950950i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.58258 | + | 2.64575i | 0.315478 | + | 0.182141i | 0.649375 | − | 0.760468i | \(-0.275031\pi\) |
−0.333897 | + | 0.942609i | \(0.608364\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −10.5830 | −0.721755 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.00000 | −0.475191 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −24.2487 | − | 14.0000i | −1.63114 | − | 0.941742i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.00000 | − | 13.8564i | −0.535720 | − | 0.927894i | −0.999128 | − | 0.0417488i | \(-0.986707\pi\) |
0.463409 | − | 0.886145i | \(-0.346626\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.46410 | + | 2.00000i | −0.229920 | + | 0.132745i | −0.610535 | − | 0.791989i | \(-0.709046\pi\) |
0.380615 | + | 0.924734i | \(0.375712\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.3303 | + | 10.5830i | 1.21130 | + | 0.699345i | 0.963043 | − | 0.269349i | \(-0.0868086\pi\) |
0.248258 | + | 0.968694i | \(0.420142\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.5830 | 0.693316 | 0.346658 | − | 0.937992i | \(-0.387316\pi\) | ||||
0.346658 | + | 0.937992i | \(0.387316\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.93725 | − | 13.7477i | 0.513418 | − | 0.889267i | −0.486461 | − | 0.873703i | \(-0.661712\pi\) |
0.999879 | − | 0.0155640i | \(-0.00495438\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.00000 | + | 8.66025i | 0.322078 | + | 0.557856i | 0.980917 | − | 0.194429i | \(-0.0622852\pi\) |
−0.658838 | + | 0.752285i | \(0.728952\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.19615 | + | 3.00000i | −0.331970 | + | 0.191663i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 14.0000 | − | 24.2487i | 0.890799 | − | 1.54291i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.0000i | 0.757433i | 0.925513 | + | 0.378717i | \(0.123635\pi\) | ||||
−0.925513 | + | 0.378717i | \(0.876365\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 15.8745i | 0.998022i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.93725 | + | 13.7477i | −0.495112 | + | 0.857560i | −0.999984 | − | 0.00563467i | \(-0.998206\pi\) |
0.504872 | + | 0.863194i | \(0.331540\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.58258 | + | 2.64575i | −0.284747 | + | 0.164399i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.64575 | − | 4.58258i | −0.163144 | − | 0.282574i | 0.772851 | − | 0.634588i | \(-0.218830\pi\) |
−0.935995 | + | 0.352014i | \(0.885497\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.50000 | + | 7.79423i | −0.276433 | + | 0.478796i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 18.0000i | 1.09748i | 0.835993 | + | 0.548740i | \(0.184892\pi\) | ||||
−0.835993 | + | 0.548740i | \(0.815108\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.0000 | −0.911185 | −0.455593 | − | 0.890188i | \(-0.650573\pi\) | ||||
−0.455593 | + | 0.890188i | \(0.650573\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 10.3923 | + | 6.00000i | 0.626680 | + | 0.361814i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.16515 | − | 5.29150i | 0.550681 | − | 0.317936i | −0.198716 | − | 0.980057i | \(-0.563677\pi\) |
0.749396 | + | 0.662122i | \(0.230344\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.93725 | + | 13.7477i | 0.473497 | + | 0.820121i | 0.999540 | − | 0.0303374i | \(-0.00965819\pi\) |
−0.526043 | + | 0.850458i | \(0.676325\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −22.9129 | − | 13.2288i | −1.36203 | − | 0.786368i | −0.372135 | − | 0.928178i | \(-0.621374\pi\) |
−0.989894 | + | 0.141810i | \(0.954708\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.29150 | 0.312348 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11.0000 | 0.647059 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 25.9808 | + | 15.0000i | 1.51781 | + | 0.876309i | 0.999781 | + | 0.0209480i | \(0.00666844\pi\) |
0.518032 | + | 0.855361i | \(0.326665\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.00000 | + | 3.46410i | 0.116445 | + | 0.201688i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −24.2487 | + | 14.0000i | −1.40234 | + | 0.809641i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.16515 | + | 5.29150i | 0.528271 | + | 0.304997i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 15.8745i | − | 0.906006i | −0.891509 | − | 0.453003i | \(-0.850353\pi\) | ||
0.891509 | − | 0.453003i | \(-0.149647\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.2288 | + | 22.9129i | −0.750134 | + | 1.29927i | 0.197623 | + | 0.980278i | \(0.436678\pi\) |
−0.947757 | + | 0.318992i | \(0.896656\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.500000 | + | 0.866025i | 0.0282617 | + | 0.0489506i | 0.879810 | − | 0.475325i | \(-0.157669\pi\) |
−0.851549 | + | 0.524276i | \(0.824336\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 11.2583 | − | 6.50000i | 0.632331 | − | 0.365076i | −0.149323 | − | 0.988788i | \(-0.547710\pi\) |
0.781654 | + | 0.623712i | \(0.214376\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.00000 | + | 15.5885i | −0.503903 | + | 0.872786i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 28.0000i | 1.55796i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 21.1660i | 1.17408i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.3303 | + | 10.5830i | −1.00752 | + | 0.581695i | −0.910466 | − | 0.413584i | \(-0.864277\pi\) |
−0.0970586 | + | 0.995279i | \(0.530943\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −17.0000 | + | 29.4449i | −0.926049 | + | 1.60396i | −0.136184 | + | 0.990684i | \(0.543484\pi\) |
−0.789865 | + | 0.613280i | \(0.789850\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 21.0000i | − | 1.13721i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.0000 | 0.701934 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −19.9186 | − | 11.5000i | −1.06929 | − | 0.617352i | −0.141299 | − | 0.989967i | \(-0.545128\pi\) |
−0.927986 | + | 0.372615i | \(0.878461\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.58258 | − | 2.64575i | 0.245300 | − | 0.141624i | −0.372310 | − | 0.928108i | \(-0.621434\pi\) |
0.617610 | + | 0.786484i | \(0.288101\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.93725 | + | 13.7477i | 0.422457 | + | 0.731718i | 0.996179 | − | 0.0873325i | \(-0.0278343\pi\) |
−0.573722 | + | 0.819050i | \(0.694501\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −13.7477 | − | 7.93725i | −0.729654 | − | 0.421266i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −21.1660 | −1.11710 | −0.558550 | − | 0.829471i | \(-0.688642\pi\) | ||||
−0.558550 | + | 0.829471i | \(0.688642\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.00000 | −0.473684 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.59808 | − | 1.50000i | −0.135990 | − | 0.0785136i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.50000 | − | 2.59808i | −0.0782994 | − | 0.135618i | 0.824217 | − | 0.566274i | \(-0.191616\pi\) |
−0.902516 | + | 0.430656i | \(0.858282\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.79423 | − | 4.50000i | 0.404656 | − | 0.233628i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −22.9129 | − | 13.2288i | −1.18638 | − | 0.684959i | −0.228901 | − | 0.973450i | \(-0.573513\pi\) |
−0.957483 | + | 0.288491i | \(0.906847\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −31.7490 | −1.63516 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.1660i | 1.08722i | 0.839336 | + | 0.543612i | \(0.182944\pi\) | ||||
−0.839336 | + | 0.543612i | \(0.817056\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.93725 | + | 13.7477i | −0.405575 | + | 0.702476i | −0.994388 | − | 0.105793i | \(-0.966262\pi\) |
0.588813 | + | 0.808269i | \(0.299595\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.50000 | + | 2.59808i | 0.0764471 | + | 0.132410i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.33013 | − | 2.50000i | 0.219546 | − | 0.126755i | −0.386194 | − | 0.922418i | \(-0.626210\pi\) |
0.605740 | + | 0.795663i | \(0.292877\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.0000 | − | 24.2487i | 0.708010 | − | 1.22631i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 4.00000i | − | 0.201262i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 5.29150i | − | 0.265573i | −0.991145 | − | 0.132786i | \(-0.957608\pi\) | ||
0.991145 | − | 0.132786i | \(-0.0423924\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 32.0780 | − | 18.5203i | 1.59792 | − | 0.922560i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.93725 | − | 13.7477i | −0.393435 | − | 0.681450i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.50000 | − | 9.52628i | 0.271957 | − | 0.471044i | −0.697406 | − | 0.716677i | \(-0.745662\pi\) |
0.969363 | + | 0.245633i | \(0.0789957\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 4.00000i | − | 0.196827i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.00000 | −0.343616 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.16515 | − | 5.29150i | 0.446682 | − | 0.257892i | −0.259746 | − | 0.965677i | \(-0.583639\pi\) |
0.706428 | + | 0.707785i | \(0.250305\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −10.5830 | − | 18.3303i | −0.513351 | − | 0.889150i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −31.7490 | −1.52930 | −0.764648 | − | 0.644448i | \(-0.777087\pi\) | ||||
−0.764648 | + | 0.644448i | \(0.777087\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.00000 | 0.240285 | 0.120142 | − | 0.992757i | \(-0.461665\pi\) | ||||
0.120142 | + | 0.992757i | \(0.461665\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 24.2487 | + | 14.0000i | 1.15997 | + | 0.669711i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.5000 | − | 18.1865i | −0.501138 | − | 0.867996i | −0.999999 | − | 0.00131415i | \(-0.999582\pi\) |
0.498861 | − | 0.866682i | \(-0.333752\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 20.7846 | − | 12.0000i | 0.987507 | − | 0.570137i | 0.0829786 | − | 0.996551i | \(-0.473557\pi\) |
0.904528 | + | 0.426414i | \(0.140223\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.16515 | − | 5.29150i | −0.434470 | − | 0.250841i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −15.8745 | −0.749164 | −0.374582 | − | 0.927194i | \(-0.622214\pi\) | ||||
−0.374582 | + | 0.927194i | \(0.622214\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 15.8745i | 0.747501i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.64575 | + | 4.58258i | −0.124035 | + | 0.214834i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.50000 | − | 14.7224i | −0.397613 | − | 0.688686i | 0.595818 | − | 0.803120i | \(-0.296828\pi\) |
−0.993431 | + | 0.114433i | \(0.963495\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.79423 | + | 4.50000i | −0.363013 | + | 0.209586i | −0.670402 | − | 0.741998i | \(-0.733878\pi\) |
0.307388 | + | 0.951584i | \(0.400545\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −20.5000 | + | 35.5070i | −0.952716 | + | 1.65015i | −0.213205 | + | 0.977007i | \(0.568390\pi\) |
−0.739511 | + | 0.673145i | \(0.764943\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 1.00000i | − | 0.0462745i | −0.999732 | − | 0.0231372i | \(-0.992635\pi\) | ||
0.999732 | − | 0.0231372i | \(-0.00736547\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −15.8745 | + | 27.4955i | −0.729911 | + | 1.26424i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 18.3303 | − | 10.5830i | 0.841052 | − | 0.485582i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10.5830 | − | 18.3303i | −0.483550 | − | 0.837533i | 0.516272 | − | 0.856425i | \(-0.327319\pi\) |
−0.999822 | + | 0.0188920i | \(0.993986\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14.0000 | − | 24.2487i | 0.638345 | − | 1.10565i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.00000i | 0.317854i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 40.0000 | 1.81257 | 0.906287 | − | 0.422664i | \(-0.138905\pi\) | ||||
0.906287 | + | 0.422664i | \(0.138905\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 25.1147 | + | 14.5000i | 1.13341 | + | 0.654376i | 0.944791 | − | 0.327674i | \(-0.106265\pi\) |
0.188621 | + | 0.982050i | \(0.439598\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 27.4955 | − | 15.8745i | 1.23833 | − | 0.714952i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.93725 | + | 13.7477i | 0.356034 | + | 0.616670i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 15.8745 | 0.707809 | 0.353905 | − | 0.935282i | \(-0.384854\pi\) | ||||
0.353905 | + | 0.935282i | \(0.384854\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 17.0000 | 0.756490 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −18.1865 | − | 10.5000i | −0.806104 | − | 0.465404i | 0.0394971 | − | 0.999220i | \(-0.487424\pi\) |
−0.845601 | + | 0.533815i | \(0.820758\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.50000 | + | 2.59808i | 0.0663561 | + | 0.114932i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15.8745 | −0.695475 | −0.347737 | − | 0.937592i | \(-0.613050\pi\) | ||||
−0.347737 | + | 0.937592i | \(0.613050\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.8745i | 0.694144i | 0.937839 | + | 0.347072i | \(0.112824\pi\) | ||||
−0.937839 | + | 0.347072i | \(0.887176\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −18.5203 | + | 32.0780i | −0.806755 | + | 1.39734i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.50000 | − | 4.33013i | −0.108696 | − | 0.188266i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −24.2487 | + | 14.0000i | −1.05033 | + | 0.606407i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.50000 | + | 2.59808i | −0.0648507 | + | 0.112325i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 18.0000i | 0.775315i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 10.5830i | − | 0.454999i | −0.973778 | − | 0.227499i | \(-0.926945\pi\) | ||
0.973778 | − | 0.227499i | \(-0.0730550\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.64575 | + | 4.58258i | −0.113332 | + | 0.196296i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.58258 | − | 2.64575i | 0.195937 | − | 0.113124i | −0.398822 | − | 0.917028i | \(-0.630581\pi\) |
0.594759 | + | 0.803904i | \(0.297248\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 15.8745 | + | 27.4955i | 0.676277 | + | 1.17135i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.00000 | + | 3.46410i | −0.0850487 | + | 0.147309i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 39.0000i | 1.65248i | 0.563316 | + | 0.826242i | \(0.309525\pi\) | ||||
−0.563316 | + | 0.826242i | \(0.690475\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −56.0000 | −2.36855 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.59808 | + | 1.50000i | 0.109496 | + | 0.0632175i | 0.553748 | − | 0.832684i | \(-0.313197\pi\) |
−0.444252 | + | 0.895902i | \(0.646530\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −13.7477 | + | 7.93725i | −0.578371 | + | 0.333923i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −15.8745 | − | 27.4955i | −0.665494 | − | 1.15267i | −0.979151 | − | 0.203133i | \(-0.934888\pi\) |
0.313657 | − | 0.949536i | \(-0.398446\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 22.9129 | + | 13.2288i | 0.958874 | + | 0.553606i | 0.895826 | − | 0.444404i | \(-0.146585\pi\) |
0.0630478 | + | 0.998011i | \(0.479918\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −21.1660 | −0.882684 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18.0000 | −0.749350 | −0.374675 | − | 0.927156i | \(-0.622246\pi\) | ||||
−0.374675 | + | 0.927156i | \(0.622246\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.06218 | + | 3.50000i | 0.251502 | + | 0.145204i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 13.5000 | + | 23.3827i | 0.559113 | + | 0.968412i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −19.9186 | + | 11.5000i | −0.822128 | + | 0.474656i | −0.851150 | − | 0.524923i | \(-0.824094\pi\) |
0.0290218 | + | 0.999579i | \(0.490761\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −32.0780 | − | 18.5203i | −1.32175 | − | 0.763114i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −31.7490 | −1.30378 | −0.651888 | − | 0.758315i | \(-0.726023\pi\) | ||||
−0.651888 | + | 0.758315i | \(0.726023\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 5.29150i | − | 0.216930i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10.5830 | − | 18.3303i | 0.432410 | − | 0.748956i | −0.564670 | − | 0.825317i | \(-0.690997\pi\) |
0.997080 | + | 0.0763606i | \(0.0243300\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.50000 | − | 4.33013i | −0.101977 | − | 0.176630i | 0.810522 | − | 0.585708i | \(-0.199184\pi\) |
−0.912499 | + | 0.409079i | \(0.865850\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.73205 | − | 1.00000i | 0.0704179 | − | 0.0406558i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.00000 | + | 6.92820i | −0.162355 | + | 0.281207i | −0.935713 | − | 0.352763i | \(-0.885242\pi\) |
0.773358 | + | 0.633970i | \(0.218576\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10.5830i | 0.427444i | 0.976895 | + | 0.213722i | \(0.0685586\pi\) | ||||
−0.976895 | + | 0.213722i | \(0.931441\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.64575 | + | 4.58258i | −0.106514 | + | 0.184488i | −0.914356 | − | 0.404912i | \(-0.867302\pi\) |
0.807842 | + | 0.589399i | \(0.200636\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 13.7477 | − | 7.93725i | 0.552568 | − | 0.319025i | −0.197589 | − | 0.980285i | \(-0.563311\pi\) |
0.750157 | + | 0.661260i | \(0.229978\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.29150 | + | 9.16515i | 0.212000 | + | 0.367194i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.50000 | + | 9.52628i | −0.220000 | + | 0.381051i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 28.0000i | 1.11643i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23.0000 | 0.915616 | 0.457808 | − | 0.889051i | \(-0.348635\pi\) | ||||
0.457808 | + | 0.889051i | \(0.348635\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 11.2583 | + | 6.50000i | 0.446773 | + | 0.257945i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −27.4955 | + | 15.8745i | −1.08941 | + | 0.628971i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −18.5203 | − | 32.0780i | −0.731506 | − | 1.26701i | −0.956239 | − | 0.292586i | \(-0.905484\pi\) |
0.224733 | − | 0.974420i | \(-0.427849\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18.3303 | + | 10.5830i | 0.722877 | + | 0.417353i | 0.815811 | − | 0.578319i | \(-0.196291\pi\) |
−0.0929339 | + | 0.995672i | \(0.529625\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −31.7490 | −1.24818 | −0.624091 | − | 0.781351i | \(-0.714531\pi\) | ||||
−0.624091 | + | 0.781351i | \(0.714531\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 12.0000 | 0.471041 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.59808 | − | 1.50000i | −0.101671 | − | 0.0586995i | 0.448303 | − | 0.893882i | \(-0.352029\pi\) |
−0.549973 | + | 0.835182i | \(0.685362\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.50000 | + | 6.06218i | 0.136756 | + | 0.236869i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12.9904 | + | 7.50000i | −0.506033 | + | 0.292159i | −0.731202 | − | 0.682161i | \(-0.761040\pi\) |
0.225168 | + | 0.974320i | \(0.427707\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.9129 | + | 13.2288i | 0.891208 | + | 0.514539i | 0.874337 | − | 0.485319i | \(-0.161296\pi\) |
0.0168704 | + | 0.999858i | \(0.494630\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.29150 | 0.205196 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 31.7490i | − | 1.22933i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14.5000 | − | 25.1147i | −0.558934 | − | 0.968102i | −0.997586 | − | 0.0694449i | \(-0.977877\pi\) |
0.438652 | − | 0.898657i | \(-0.355456\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5.19615 | − | 3.00000i | 0.199704 | − | 0.115299i | −0.396813 | − | 0.917899i | \(-0.629884\pi\) |
0.596518 | + | 0.802600i | \(0.296551\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.50000 | − | 6.06218i | 0.134318 | − | 0.232645i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 44.0000i | − | 1.68361i | −0.539779 | − | 0.841807i | \(-0.681492\pi\) | ||
0.539779 | − | 0.841807i | \(-0.318508\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −23.8118 | + | 41.2432i | −0.907156 | + | 1.57124i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −36.6606 | + | 21.1660i | −1.39464 | + | 0.805193i | −0.993824 | − | 0.110968i | \(-0.964605\pi\) |
−0.400811 | + | 0.916161i | \(0.631272\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5.29150 | − | 9.16515i | −0.200718 | − | 0.347654i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14.0000 | − | 24.2487i | 0.530288 | − | 0.918485i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.00000i | 0.0377695i | 0.999822 | + | 0.0188847i | \(0.00601156\pi\) | ||||
−0.999822 | + | 0.0188847i | \(0.993988\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −28.0000 | −1.05604 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −14.7224 | − | 8.50000i | −0.553694 | − | 0.319675i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −18.3303 | + | 10.5830i | −0.688409 | + | 0.397453i | −0.803016 | − | 0.595958i | \(-0.796773\pi\) |
0.114607 | + | 0.993411i | \(0.463439\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 18.5203 | + | 32.0780i | 0.693589 | + | 1.20133i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −13.7477 | − | 7.93725i | −0.514136 | − | 0.296836i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −21.1660 | −0.789359 | −0.394679 | − | 0.918819i | \(-0.629144\pi\) | ||||
−0.394679 | + | 0.918819i | \(0.629144\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −20.7846 | − | 12.0000i | −0.771921 | − | 0.445669i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.5000 | + | 28.5788i | 0.611951 | + | 1.05993i | 0.990911 | + | 0.134517i | \(0.0429484\pi\) |
−0.378960 | + | 0.925413i | \(0.623718\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 48.4974 | − | 28.0000i | 1.79374 | − | 1.03562i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.58258 | − | 2.64575i | −0.169261 | − | 0.0977231i | 0.412976 | − | 0.910742i | \(-0.364489\pi\) |
−0.582237 | + | 0.813019i | \(0.697823\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 5.29150i | − | 0.194651i | −0.995253 | − | 0.0973255i | \(-0.968971\pi\) | ||
0.995253 | − | 0.0973255i | \(-0.0310288\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −18.5203 | + | 32.0780i | −0.679442 | + | 1.17683i | 0.295707 | + | 0.955279i | \(0.404445\pi\) |
−0.975149 | + | 0.221550i | \(0.928888\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.50000 | − | 2.59808i | −0.0549557 | − | 0.0951861i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.59808 | − | 1.50000i | 0.0949316 | − | 0.0548088i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −15.5000 | + | 26.8468i | −0.565603 | + | 0.979653i | 0.431390 | + | 0.902165i | \(0.358023\pi\) |
−0.996993 | + | 0.0774878i | \(0.975310\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 3.00000i | − | 0.109181i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.29150 | − | 9.16515i | 0.191817 | − | 0.332236i | −0.754036 | − | 0.656834i | \(-0.771895\pi\) |
0.945852 | + | 0.324597i | \(0.105229\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.58258 | − | 2.64575i | 0.165900 | − | 0.0957826i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 10.5830 | + | 18.3303i | 0.382130 | + | 0.661869i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17.5000 | − | 30.3109i | 0.631066 | − | 1.09304i | −0.356268 | − | 0.934384i | \(-0.615951\pi\) |
0.987334 | − | 0.158655i | \(-0.0507157\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 14.0000i | − | 0.503545i | −0.967786 | − | 0.251773i | \(-0.918987\pi\) | ||
0.967786 | − | 0.251773i | \(-0.0810135\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 28.0000 | 1.00579 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 24.2487 | + | 14.0000i | 0.868800 | + | 0.501602i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −41.2432 | + | 23.8118i | −1.47580 | + | 0.852052i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.29150 | − | 9.16515i | −0.188862 | − | 0.327118i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 15.8745 | 0.564433 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 42.4352 | + | 24.5000i | 1.50313 | + | 0.867835i | 0.999993 | + | 0.00362965i | \(0.00115536\pi\) |
0.503140 | + | 0.864205i | \(0.332178\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −7.79423 | + | 4.50000i | −0.275052 | + | 0.158802i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.58258 | − | 2.64575i | −0.161515 | − | 0.0932505i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −31.7490 | −1.11624 | −0.558118 | − | 0.829762i | \(-0.688476\pi\) | ||||
−0.558118 | + | 0.829762i | \(0.688476\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 37.0405i | − | 1.30067i | −0.759648 | − | 0.650334i | \(-0.774629\pi\) | ||
0.759648 | − | 0.650334i | \(-0.225371\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.64575 | + | 4.58258i | −0.0926766 | + | 0.160521i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 28.0000 | + | 48.4974i | 0.979596 | + | 1.69671i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.66025 | − | 5.00000i | 0.302245 | − | 0.174501i | −0.341206 | − | 0.939989i | \(-0.610835\pi\) |
0.643451 | + | 0.765487i | \(0.277502\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.5000 | − | 19.9186i | 0.400865 | − | 0.694318i | −0.592966 | − | 0.805228i | \(-0.702043\pi\) |
0.993831 | + | 0.110910i | \(0.0353764\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 36.0000i | 1.25184i | 0.779886 | + | 0.625921i | \(0.215277\pi\) | ||||
−0.779886 | + | 0.625921i | \(0.784723\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 21.1660i | − | 0.735126i | −0.929999 | − | 0.367563i | \(-0.880192\pi\) | ||
0.929999 | − | 0.367563i | \(-0.119808\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 15.8745 | − | 27.4955i | 0.550019 | − | 0.952661i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9.16515 | + | 5.29150i | −0.317173 | + | 0.183120i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −18.5203 | − | 32.0780i | −0.639390 | − | 1.10746i | −0.985567 | − | 0.169287i | \(-0.945853\pi\) |
0.346176 | − | 0.938169i | \(-0.387480\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.50000 | − | 6.06218i | 0.120690 | − | 0.209041i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 15.0000i | − | 0.516016i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.00000 | −0.0687208 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 24.2487 | + | 14.0000i | 0.831235 | + | 0.479914i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7.93725 | + | 13.7477i | 0.271131 | + | 0.469613i | 0.969152 | − | 0.246464i | \(-0.0792689\pi\) |
−0.698020 | + | 0.716078i | \(0.745936\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 45.8258 | + | 26.4575i | 1.56355 | + | 0.902719i | 0.996893 | + | 0.0787681i | \(0.0250987\pi\) |
0.566662 | + | 0.823951i | \(0.308235\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −15.0000 | −0.510015 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10.3923 | − | 6.00000i | −0.352535 | − | 0.203536i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −7.79423 | + | 4.50000i | −0.263493 | + | 0.152128i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 45.8258 | + | 26.4575i | 1.54743 | + | 0.893407i | 0.998337 | + | 0.0576426i | \(0.0183584\pi\) |
0.549089 | + | 0.835764i | \(0.314975\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 26.4575 | 0.891376 | 0.445688 | − | 0.895188i | \(-0.352959\pi\) | ||||
0.445688 | + | 0.895188i | \(0.352959\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 58.2065i | 1.95881i | 0.201916 | + | 0.979403i | \(0.435283\pi\) | ||||
−0.201916 | + | 0.979403i | \(0.564717\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 7.93725 | − | 13.7477i | 0.266507 | − | 0.461603i | −0.701450 | − | 0.712718i | \(-0.747464\pi\) |
0.967957 | + | 0.251115i | \(0.0807972\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.50000 | − | 11.2583i | −0.218003 | − | 0.377592i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −11.5000 | + | 19.9186i | −0.384403 | + | 0.665805i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 42.0000i | 1.40078i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 47.6235i | − | 1.58657i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −10.5830 | + | 18.3303i | −0.351791 | + | 0.609320i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.58258 | − | 2.64575i | 0.152162 | − | 0.0878507i | −0.421986 | − | 0.906602i | \(-0.638667\pi\) |
0.574148 | + | 0.818752i | \(0.305333\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15.8745 | − | 27.4955i | −0.525946 | − | 0.910965i | −0.999543 | − | 0.0302235i | \(-0.990378\pi\) |
0.473597 | − | 0.880742i | \(-0.342955\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10.5000 | + | 18.1865i | −0.347499 | + | 0.601886i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 7.00000i | − | 0.231160i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.00000 | −0.0989609 | −0.0494804 | − | 0.998775i | \(-0.515757\pi\) | ||||
−0.0494804 | + | 0.998775i | \(0.515757\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −72.7461 | − | 42.0000i | −2.39447 | − | 1.38245i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 18.3303 | − | 10.5830i | 0.602697 | − | 0.347967i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5.29150 | + | 9.16515i | 0.173609 | + | 0.300699i | 0.939679 | − | 0.342058i | \(-0.111124\pi\) |
−0.766070 | + | 0.642757i | \(0.777791\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 27.4955 | + | 15.8745i | 0.901127 | + | 0.520266i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 15.8745 | 0.519152 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −19.0000 | −0.620703 | −0.310351 | − | 0.950622i | \(-0.600447\pi\) | ||||
−0.310351 | + | 0.950622i | \(0.600447\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 18.1865 | + | 10.5000i | 0.592864 | + | 0.342290i | 0.766229 | − | 0.642567i | \(-0.222131\pi\) |
−0.173365 | + | 0.984858i | \(0.555464\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −14.0000 | − | 24.2487i | −0.455903 | − | 0.789647i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −33.7750 | + | 19.5000i | −1.09754 | + | 0.633665i | −0.935574 | − | 0.353131i | \(-0.885117\pi\) |
−0.161966 | + | 0.986796i | \(0.551783\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −13.7477 | − | 7.93725i | −0.446270 | − | 0.257654i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 31.7490 | 1.02845 | 0.514226 | − | 0.857655i | \(-0.328079\pi\) | ||||
0.514226 | + | 0.857655i | \(0.328079\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 5.29150i | − | 0.171229i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.00000 | − | 15.5885i | −0.290323 | − | 0.502853i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.59808 | + | 1.50000i | −0.0836350 | + | 0.0482867i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 20.5000 | − | 35.5070i | 0.659236 | − | 1.14183i | −0.321578 | − | 0.946883i | \(-0.604213\pi\) |
0.980814 | − | 0.194946i | \(-0.0624533\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 15.0000i | − | 0.481373i | −0.970603 | − | 0.240686i | \(-0.922627\pi\) | ||
0.970603 | − | 0.240686i | \(-0.0773725\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 10.5830i | 0.339276i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 5.29150 | − | 9.16515i | 0.169290 | − | 0.293219i | −0.768880 | − | 0.639393i | \(-0.779186\pi\) |
0.938170 | + | 0.346174i | \(0.112519\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −27.4955 | + | 15.8745i | −0.878759 | + | 0.507351i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 21.1660 | + | 36.6606i | 0.675091 | + | 1.16929i | 0.976442 | + | 0.215779i | \(0.0692289\pi\) |
−0.301351 | + | 0.953513i | \(0.597438\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.50000 | + | 11.2583i | −0.207107 | + | 0.358720i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 56.0000i | − | 1.78070i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −47.0000 | −1.49300 | −0.746502 | − | 0.665383i | \(-0.768268\pi\) | ||||
−0.746502 | + | 0.665383i | \(0.768268\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −14.7224 | − | 8.50000i | −0.466732 | − | 0.269468i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 13.7477 | − | 7.93725i | 0.435395 | − | 0.251375i | −0.266247 | − | 0.963905i | \(-0.585784\pi\) |
0.701642 | + | 0.712529i | \(0.252450\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))