Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1764,2,Mod(361,1764)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1764, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1764.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1764.k (of order \(3\), 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: | \(14.0856109166\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 28) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1549.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1764.1549 |
Dual form | 1764.2.k.b.361.1 |
$q$-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 \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(883\) | \(1081\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.50000 | + | 2.59808i | −0.670820 | + | 1.16190i | 0.306851 | + | 0.951757i | \(0.400725\pi\) |
−0.977672 | + | 0.210138i | \(0.932609\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.50000 | − | 2.59808i | −0.452267 | − | 0.783349i | 0.546259 | − | 0.837616i | \(-0.316051\pi\) |
−0.998526 | + | 0.0542666i | \(0.982718\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.00000 | −0.554700 | −0.277350 | − | 0.960769i | \(-0.589456\pi\) | ||||
−0.277350 | + | 0.960769i | \(0.589456\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.50000 | − | 2.59808i | −0.363803 | − | 0.630126i | 0.624780 | − | 0.780801i | \(-0.285189\pi\) |
−0.988583 | + | 0.150675i | \(0.951855\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.500000 | + | 0.866025i | −0.114708 | + | 0.198680i | −0.917663 | − | 0.397360i | \(-0.869927\pi\) |
0.802955 | + | 0.596040i | \(0.203260\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.50000 | − | 2.59808i | 0.312772 | − | 0.541736i | −0.666190 | − | 0.745782i | \(-0.732076\pi\) |
0.978961 | + | 0.204046i | \(0.0654092\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.00000 | − | 3.46410i | −0.400000 | − | 0.692820i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.00000 | 1.11417 | 0.557086 | − | 0.830455i | \(-0.311919\pi\) | ||||
0.557086 | + | 0.830455i | \(0.311919\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.50000 | − | 6.06218i | −0.628619 | − | 1.08880i | −0.987829 | − | 0.155543i | \(-0.950287\pi\) |
0.359211 | − | 0.933257i | \(-0.383046\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.500000 | − | 0.866025i | 0.0821995 | − | 0.142374i | −0.821995 | − | 0.569495i | \(-0.807139\pi\) |
0.904194 | + | 0.427121i | \(0.140472\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.00000 | 0.937043 | 0.468521 | − | 0.883452i | \(-0.344787\pi\) | ||||
0.468521 | + | 0.883452i | \(0.344787\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.00000 | −0.609994 | −0.304997 | − | 0.952353i | \(-0.598656\pi\) | ||||
−0.304997 | + | 0.952353i | \(0.598656\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.50000 | − | 7.79423i | 0.656392 | − | 1.13691i | −0.325150 | − | 0.945662i | \(-0.605415\pi\) |
0.981543 | − | 0.191243i | \(-0.0612518\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.50000 | + | 2.59808i | 0.206041 | + | 0.356873i | 0.950464 | − | 0.310835i | \(-0.100609\pi\) |
−0.744423 | + | 0.667708i | \(0.767275\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 9.00000 | 1.21356 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.50000 | − | 7.79423i | −0.585850 | − | 1.01472i | −0.994769 | − | 0.102151i | \(-0.967427\pi\) |
0.408919 | − | 0.912571i | \(-0.365906\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.500000 | + | 0.866025i | −0.0640184 | + | 0.110883i | −0.896258 | − | 0.443533i | \(-0.853725\pi\) |
0.832240 | + | 0.554416i | \(0.187058\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.00000 | − | 5.19615i | 0.372104 | − | 0.644503i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.50000 | + | 6.06218i | 0.427593 | + | 0.740613i | 0.996659 | − | 0.0816792i | \(-0.0260283\pi\) |
−0.569066 | + | 0.822292i | \(0.692695\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.500000 | − | 0.866025i | −0.0585206 | − | 0.101361i | 0.835281 | − | 0.549823i | \(-0.185305\pi\) |
−0.893801 | + | 0.448463i | \(0.851972\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.50000 | − | 11.2583i | 0.731307 | − | 1.26666i | −0.225018 | − | 0.974355i | \(-0.572244\pi\) |
0.956325 | − | 0.292306i | \(-0.0944227\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.0000 | 1.31717 | 0.658586 | − | 0.752506i | \(-0.271155\pi\) | ||||
0.658586 | + | 0.752506i | \(0.271155\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.00000 | 0.976187 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.50000 | + | 12.9904i | −0.794998 | + | 1.37698i | 0.127842 | + | 0.991795i | \(0.459195\pi\) |
−0.922840 | + | 0.385183i | \(0.874138\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.50000 | − | 2.59808i | −0.153897 | − | 0.266557i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.0000 | 1.01535 | 0.507673 | − | 0.861550i | \(-0.330506\pi\) | ||||
0.507673 | + | 0.861550i | \(0.330506\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.50000 | − | 12.9904i | −0.746278 | − | 1.29259i | −0.949595 | − | 0.313478i | \(-0.898506\pi\) |
0.203317 | − | 0.979113i | \(-0.434828\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.50000 | − | 9.52628i | 0.541931 | − | 0.938652i | −0.456862 | − | 0.889538i | \(-0.651027\pi\) |
0.998793 | − | 0.0491146i | \(-0.0156400\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.50000 | − | 12.9904i | 0.725052 | − | 1.25583i | −0.233900 | − | 0.972261i | \(-0.575149\pi\) |
0.958952 | − | 0.283567i | \(-0.0915178\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.500000 | + | 0.866025i | 0.0478913 | + | 0.0829502i | 0.888977 | − | 0.457951i | \(-0.151417\pi\) |
−0.841086 | + | 0.540901i | \(0.818083\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.00000 | −0.564433 | −0.282216 | − | 0.959351i | \(-0.591070\pi\) | ||||
−0.282216 | + | 0.959351i | \(0.591070\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.50000 | + | 7.79423i | 0.419627 | + | 0.726816i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | − | 1.73205i | 0.0909091 | − | 0.157459i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3.00000 | −0.268328 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.00000 | 0.709885 | 0.354943 | − | 0.934888i | \(-0.384500\pi\) | ||||
0.354943 | + | 0.934888i | \(0.384500\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.50000 | + | 2.59808i | −0.131056 | + | 0.226995i | −0.924084 | − | 0.382190i | \(-0.875170\pi\) |
0.793028 | + | 0.609185i | \(0.208503\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.5000 | − | 18.1865i | −0.897076 | − | 1.55378i | −0.831215 | − | 0.555952i | \(-0.812354\pi\) |
−0.0658609 | − | 0.997829i | \(-0.520979\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −20.0000 | −1.69638 | −0.848189 | − | 0.529694i | \(-0.822307\pi\) | ||||
−0.848189 | + | 0.529694i | \(0.822307\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.00000 | + | 5.19615i | 0.250873 | + | 0.434524i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.00000 | + | 15.5885i | −0.747409 | + | 1.29455i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.50000 | − | 2.59808i | 0.122885 | − | 0.212843i | −0.798019 | − | 0.602632i | \(-0.794119\pi\) |
0.920904 | + | 0.389789i | \(0.127452\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.50000 | − | 14.7224i | −0.691720 | − | 1.19809i | −0.971274 | − | 0.237964i | \(-0.923520\pi\) |
0.279554 | − | 0.960130i | \(-0.409814\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 21.0000 | 1.68676 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.50000 | − | 11.2583i | −0.518756 | − | 0.898513i | −0.999762 | − | 0.0217953i | \(-0.993062\pi\) |
0.481006 | − | 0.876717i | \(-0.340272\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.50000 | + | 9.52628i | −0.430793 | + | 0.746156i | −0.996942 | − | 0.0781474i | \(-0.975100\pi\) |
0.566149 | + | 0.824303i | \(0.308433\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −12.0000 | −0.928588 | −0.464294 | − | 0.885681i | \(-0.653692\pi\) | ||||
−0.464294 | + | 0.885681i | \(0.653692\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.50000 | − | 7.79423i | 0.342129 | − | 0.592584i | −0.642699 | − | 0.766119i | \(-0.722185\pi\) |
0.984828 | + | 0.173534i | \(0.0555188\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.5000 | + | 18.1865i | 0.784807 | + | 1.35933i | 0.929114 | + | 0.369792i | \(0.120571\pi\) |
−0.144308 | + | 0.989533i | \(0.546095\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.0000 | 0.743294 | 0.371647 | − | 0.928374i | \(-0.378793\pi\) | ||||
0.371647 | + | 0.928374i | \(0.378793\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.50000 | + | 2.59808i | 0.110282 | + | 0.191014i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.50000 | + | 7.79423i | −0.329073 | + | 0.569970i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.50000 | + | 7.79423i | −0.325609 | + | 0.563971i | −0.981635 | − | 0.190767i | \(-0.938902\pi\) |
0.656027 | + | 0.754738i | \(0.272236\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.50000 | − | 9.52628i | −0.395899 | − | 0.685717i | 0.597317 | − | 0.802005i | \(-0.296234\pi\) |
−0.993215 | + | 0.116289i | \(0.962900\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −18.0000 | −1.28245 | −0.641223 | − | 0.767354i | \(-0.721573\pi\) | ||||
−0.641223 | + | 0.767354i | \(0.721573\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.50000 | − | 6.06218i | −0.248108 | − | 0.429736i | 0.714893 | − | 0.699234i | \(-0.246476\pi\) |
−0.963001 | + | 0.269498i | \(0.913142\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.00000 | + | 15.5885i | −0.628587 | + | 1.08875i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.00000 | 0.207514 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.00000 | −0.275371 | −0.137686 | − | 0.990476i | \(-0.543966\pi\) | ||||
−0.137686 | + | 0.990476i | \(0.543966\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.00000 | − | 10.3923i | 0.409197 | − | 0.708749i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.00000 | + | 5.19615i | 0.201802 | + | 0.349531i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.00000 | −0.535720 | −0.267860 | − | 0.963458i | \(-0.586316\pi\) | ||||
−0.267860 | + | 0.963458i | \(0.586316\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.50000 | + | 2.59808i | 0.0995585 | + | 0.172440i | 0.911502 | − | 0.411296i | \(-0.134924\pi\) |
−0.811943 | + | 0.583736i | \(0.801590\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.50000 | − | 9.52628i | 0.363450 | − | 0.629514i | −0.625076 | − | 0.780564i | \(-0.714932\pi\) |
0.988526 | + | 0.151050i | \(0.0482653\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −10.5000 | + | 18.1865i | −0.687878 | + | 1.19144i | 0.284645 | + | 0.958633i | \(0.408124\pi\) |
−0.972523 | + | 0.232806i | \(0.925209\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 13.5000 | + | 23.3827i | 0.880643 | + | 1.52532i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.0000 | 0.776215 | 0.388108 | − | 0.921614i | \(-0.373129\pi\) | ||||
0.388108 | + | 0.921614i | \(0.373129\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.500000 | − | 0.866025i | −0.0322078 | − | 0.0557856i | 0.849472 | − | 0.527633i | \(-0.176921\pi\) |
−0.881680 | + | 0.471848i | \(0.843587\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.00000 | − | 1.73205i | 0.0636285 | − | 0.110208i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.00000 | −0.565825 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.50000 | + | 2.59808i | −0.0935674 | + | 0.162064i | −0.909010 | − | 0.416775i | \(-0.863160\pi\) |
0.815442 | + | 0.578838i | \(0.196494\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.50000 | − | 2.59808i | −0.0924940 | − | 0.160204i | 0.816066 | − | 0.577959i | \(-0.196151\pi\) |
−0.908560 | + | 0.417755i | \(0.862817\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.00000 | −0.552866 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.50000 | − | 2.59808i | −0.0914566 | − | 0.158408i | 0.816668 | − | 0.577108i | \(-0.195819\pi\) |
−0.908124 | + | 0.418701i | \(0.862486\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.50000 | − | 9.52628i | 0.334101 | − | 0.578680i | −0.649211 | − | 0.760609i | \(-0.724901\pi\) |
0.983312 | + | 0.181928i | \(0.0582339\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6.00000 | + | 10.3923i | −0.361814 | + | 0.626680i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.50000 | + | 11.2583i | 0.390547 | + | 0.676448i | 0.992522 | − | 0.122068i | \(-0.0389525\pi\) |
−0.601975 | + | 0.798515i | \(0.705619\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −30.0000 | −1.78965 | −0.894825 | − | 0.446417i | \(-0.852700\pi\) | ||||
−0.894825 | + | 0.446417i | \(0.852700\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.5000 | + | 25.1147i | 0.861936 | + | 1.49292i | 0.870058 | + | 0.492949i | \(0.164081\pi\) |
−0.00812260 | + | 0.999967i | \(0.502586\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.00000 | − | 6.92820i | 0.235294 | − | 0.407541i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.00000 | 0.350524 | 0.175262 | − | 0.984522i | \(-0.443923\pi\) | ||||
0.175262 | + | 0.984522i | \(0.443923\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 27.0000 | 1.57200 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.00000 | + | 5.19615i | −0.173494 | + | 0.300501i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.50000 | − | 2.59808i | −0.0858898 | − | 0.148765i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 28.0000 | 1.59804 | 0.799022 | − | 0.601302i | \(-0.205351\pi\) | ||||
0.799022 | + | 0.601302i | \(0.205351\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.5000 | + | 23.3827i | 0.765515 | + | 1.32591i | 0.939974 | + | 0.341246i | \(0.110849\pi\) |
−0.174459 | + | 0.984664i | \(0.555818\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.5000 | − | 19.9186i | 0.650018 | − | 1.12586i | −0.333099 | − | 0.942892i | \(-0.608094\pi\) |
0.983118 | − | 0.182973i | \(-0.0585722\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.50000 | + | 7.79423i | −0.252745 | + | 0.437767i | −0.964281 | − | 0.264883i | \(-0.914667\pi\) |
0.711535 | + | 0.702650i | \(0.248000\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.00000 | − | 15.5885i | −0.503903 | − | 0.872786i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.00000 | 0.166924 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.00000 | + | 6.92820i | 0.221880 | + | 0.384308i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.50000 | − | 11.2583i | 0.357272 | − | 0.618814i | −0.630232 | − | 0.776407i | \(-0.717040\pi\) |
0.987504 | + | 0.157593i | \(0.0503735\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −21.0000 | −1.14735 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −34.0000 | −1.85210 | −0.926049 | − | 0.377403i | \(-0.876817\pi\) | ||||
−0.926049 | + | 0.377403i | \(0.876817\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10.5000 | + | 18.1865i | −0.568607 | + | 0.984856i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.50000 | + | 7.79423i | 0.241573 | + | 0.418416i | 0.961162 | − | 0.275983i | \(-0.0890035\pi\) |
−0.719590 | + | 0.694399i | \(0.755670\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −26.0000 | −1.39175 | −0.695874 | − | 0.718164i | \(-0.744983\pi\) | ||||
−0.695874 | + | 0.718164i | \(0.744983\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.5000 | + | 18.1865i | 0.558859 | + | 0.967972i | 0.997592 | + | 0.0693543i | \(0.0220939\pi\) |
−0.438733 | + | 0.898617i | \(0.644573\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7.50000 | − | 12.9904i | 0.395835 | − | 0.685606i | −0.597372 | − | 0.801964i | \(-0.703789\pi\) |
0.993207 | + | 0.116358i | \(0.0371219\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.00000 | + | 15.5885i | 0.473684 | + | 0.820445i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.00000 | 0.157027 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.50000 | + | 4.33013i | 0.130499 | + | 0.226031i | 0.923869 | − | 0.382709i | \(-0.125009\pi\) |
−0.793370 | + | 0.608740i | \(0.791675\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.5000 | − | 21.6506i | 0.647225 | − | 1.12103i | −0.336557 | − | 0.941663i | \(-0.609263\pi\) |
0.983783 | − | 0.179364i | \(-0.0574041\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −12.0000 | −0.618031 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.00000 | 0.410932 | 0.205466 | − | 0.978664i | \(-0.434129\pi\) | ||||
0.205466 | + | 0.978664i | \(0.434129\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 16.5000 | − | 28.5788i | 0.843111 | − | 1.46031i | −0.0441413 | − | 0.999025i | \(-0.514055\pi\) |
0.887252 | − | 0.461285i | \(-0.152611\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.50000 | + | 12.9904i | 0.380265 | + | 0.658638i | 0.991100 | − | 0.133120i | \(-0.0424994\pi\) |
−0.610835 | + | 0.791758i | \(0.709166\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.00000 | −0.455150 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 19.5000 | + | 33.7750i | 0.981151 | + | 1.69940i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −18.5000 | + | 32.0429i | −0.928488 | + | 1.60819i | −0.142636 | + | 0.989775i | \(0.545558\pi\) |
−0.785853 | + | 0.618414i | \(0.787776\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.50000 | − | 2.59808i | 0.0749064 | − | 0.129742i | −0.826139 | − | 0.563466i | \(-0.809468\pi\) |
0.901046 | + | 0.433724i | \(0.142801\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.00000 | + | 12.1244i | 0.348695 | + | 0.603957i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.00000 | −0.148704 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.50000 | + | 9.52628i | 0.271957 | + | 0.471044i | 0.969363 | − | 0.245633i | \(-0.0789957\pi\) |
−0.697406 | + | 0.716677i | \(0.745662\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −18.0000 | + | 31.1769i | −0.883585 | + | 1.53041i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12.0000 | −0.586238 | −0.293119 | − | 0.956076i | \(-0.594693\pi\) | ||||
−0.293119 | + | 0.956076i | \(0.594693\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −22.0000 | −1.07221 | −0.536107 | − | 0.844150i | \(-0.680106\pi\) | ||||
−0.536107 | + | 0.844150i | \(0.680106\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.00000 | + | 10.3923i | −0.291043 | + | 0.504101i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.50000 | − | 12.9904i | −0.361262 | − | 0.625725i | 0.626907 | − | 0.779094i | \(-0.284321\pi\) |
−0.988169 | + | 0.153370i | \(0.950987\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10.0000 | 0.480569 | 0.240285 | − | 0.970702i | \(-0.422759\pi\) | ||||
0.240285 | + | 0.970702i | \(0.422759\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.50000 | + | 2.59808i | 0.0717547 | + | 0.124283i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.500000 | + | 0.866025i | −0.0238637 | + | 0.0413331i | −0.877711 | − | 0.479191i | \(-0.840930\pi\) |
0.853847 | + | 0.520524i | \(0.174263\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.50000 | + | 7.79423i | −0.213801 | + | 0.370315i | −0.952901 | − | 0.303281i | \(-0.901918\pi\) |
0.739100 | + | 0.673596i | \(0.235251\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −22.5000 | − | 38.9711i | −1.06660 | − | 1.84741i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.0000 | 0.849473 | 0.424736 | − | 0.905317i | \(-0.360367\pi\) | ||||
0.424736 | + | 0.905317i | \(0.360367\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.00000 | − | 15.5885i | −0.423793 | − | 0.734032i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.5000 | + | 19.9186i | −0.537947 | + | 0.931752i | 0.461067 | + | 0.887365i | \(0.347467\pi\) |
−0.999014 | + | 0.0443868i | \(0.985867\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.00000 | −0.279448 | −0.139724 | − | 0.990190i | \(-0.544622\pi\) | ||||
−0.139724 | + | 0.990190i | \(0.544622\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.0000 | −0.743583 | −0.371792 | − | 0.928316i | \(-0.621256\pi\) | ||||
−0.371792 | + | 0.928316i | \(0.621256\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10.5000 | − | 18.1865i | 0.485882 | − | 0.841572i | −0.513986 | − | 0.857798i | \(-0.671832\pi\) |
0.999868 | + | 0.0162260i | \(0.00516512\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.00000 | + | 10.3923i | 0.275880 | + | 0.477839i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.00000 | 0.183533 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.50000 | + | 2.59808i | 0.0685367 | + | 0.118709i | 0.898257 | − | 0.439470i | \(-0.144834\pi\) |
−0.829721 | + | 0.558179i | \(0.811500\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.00000 | + | 1.73205i | −0.0455961 | + | 0.0789747i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −15.0000 | + | 25.9808i | −0.681115 | + | 1.17973i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.50000 | + | 16.4545i | 0.430486 | + | 0.745624i | 0.996915 | − | 0.0784867i | \(-0.0250088\pi\) |
−0.566429 | + | 0.824110i | \(0.691675\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −24.0000 | −1.08310 | −0.541552 | − | 0.840667i | \(-0.682163\pi\) | ||||
−0.541552 | + | 0.840667i | \(0.682163\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.00000 | − | 15.5885i | −0.405340 | − | 0.702069i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.50000 | + | 9.52628i | −0.246214 | + | 0.426455i | −0.962472 | − | 0.271380i | \(-0.912520\pi\) |
0.716258 | + | 0.697835i | \(0.245853\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 45.0000 | 2.00247 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.50000 | + | 2.59808i | −0.0664863 | + | 0.115158i | −0.897352 | − | 0.441315i | \(-0.854512\pi\) |
0.830866 | + | 0.556473i | \(0.187846\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 16.5000 | + | 28.5788i | 0.727077 | + | 1.25933i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −27.0000 | −1.18746 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −19.5000 | − | 33.7750i | −0.854311 | − | 1.47971i | −0.877283 | − | 0.479973i | \(-0.840646\pi\) |
0.0229727 | − | 0.999736i | \(-0.492687\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.500000 | + | 0.866025i | −0.0218635 | + | 0.0378686i | −0.876750 | − | 0.480946i | \(-0.840293\pi\) |
0.854887 | + | 0.518815i | \(0.173627\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −10.5000 | + | 18.1865i | −0.457387 | + | 0.792218i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.00000 | + | 12.1244i | 0.304348 | + | 0.527146i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −12.0000 | −0.519778 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 22.5000 | + | 38.9711i | 0.972760 | + | 1.68487i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.5000 | + | 30.3109i | −0.752384 | + | 1.30317i | 0.194281 | + | 0.980946i | \(0.437763\pi\) |
−0.946664 | + | 0.322221i | \(0.895571\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.00000 | −0.128506 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.00000 | 0.342055 | 0.171028 | − | 0.985266i | \(-0.445291\pi\) | ||||
0.171028 | + | 0.985266i | \(0.445291\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.00000 | + | 5.19615i | −0.127804 | + | 0.221364i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −16.5000 | − | 28.5788i | −0.699127 | − | 1.21092i | −0.968769 | − | 0.247964i | \(-0.920239\pi\) |
0.269642 | − | 0.962961i | \(-0.413095\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.00000 | 0.338364 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.50000 | − | 7.79423i | −0.189652 | − | 0.328488i | 0.755482 | − | 0.655169i | \(-0.227403\pi\) |
−0.945134 | + | 0.326682i | \(0.894069\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.00000 | − | 15.5885i | 0.378633 | − | 0.655811i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.50000 | + | 7.79423i | −0.188650 | + | 0.326751i | −0.944800 | − | 0.327647i | \(-0.893744\pi\) |
0.756151 | + | 0.654398i | \(0.227078\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.5000 | − | 25.1147i | −0.606806 | − | 1.05102i | −0.991763 | − | 0.128085i | \(-0.959117\pi\) |
0.384957 | − | 0.922934i | \(-0.374216\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −12.0000 | −0.500435 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −0.500000 | − | 0.866025i | −0.0208153 | − | 0.0360531i | 0.855430 | − | 0.517918i | \(-0.173293\pi\) |
−0.876245 | + | 0.481865i | \(0.839960\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.50000 | − | 7.79423i | 0.186371 | − | 0.322804i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 12.0000 | 0.495293 | 0.247647 | − | 0.968850i | \(-0.420343\pi\) | ||||
0.247647 | + | 0.968850i | \(0.420343\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.00000 | 0.288430 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 10.5000 | − | 18.1865i | 0.431183 | − | 0.746831i | −0.565792 | − | 0.824548i | \(-0.691430\pi\) |
0.996976 | + | 0.0777165i | \(0.0247629\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −13.5000 | − | 23.3827i | −0.551595 | − | 0.955391i | −0.998160 | − | 0.0606393i | \(-0.980686\pi\) |
0.446565 | − | 0.894751i | \(-0.352647\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14.0000 | −0.571072 | −0.285536 | − | 0.958368i | \(-0.592172\pi\) | ||||
−0.285536 | + | 0.958368i | \(0.592172\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.00000 | + | 5.19615i | 0.121967 | + | 0.211254i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 23.5000 | − | 40.7032i | 0.953836 | − | 1.65209i | 0.216825 | − | 0.976210i | \(-0.430430\pi\) |
0.737011 | − | 0.675881i | \(-0.236237\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.00000 | + | 15.5885i | −0.364101 | + | 0.630641i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.5000 | + | 21.6506i | 0.504870 | + | 0.874461i | 0.999984 | + | 0.00563283i | \(0.00179300\pi\) |
−0.495114 | + | 0.868828i | \(0.664874\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.00000 | −0.241551 | −0.120775 | − | 0.992680i | \(-0.538538\pi\) | ||||
−0.120775 | + | 0.992680i | \(0.538538\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −15.5000 | − | 26.8468i | −0.622998 | − | 1.07906i | −0.988924 | − | 0.148420i | \(-0.952581\pi\) |
0.365927 | − | 0.930644i | \(-0.380752\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.5000 | − | 25.1147i | 0.580000 | − | 1.00459i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.00000 | −0.119618 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.0000 | −0.636950 | −0.318475 | − | 0.947931i | \(-0.603171\pi\) | ||||
−0.318475 | + | 0.947931i | \(0.603171\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −12.0000 | + | 20.7846i | −0.476205 | + | 0.824812i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.50000 | + | 12.9904i | 0.296232 | + | 0.513089i | 0.975271 | − | 0.221013i | \(-0.0709364\pi\) |
−0.679039 | + | 0.734103i | \(0.737603\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −20.0000 | −0.788723 | −0.394362 | − | 0.918955i | \(-0.629034\pi\) | ||||
−0.394362 | + | 0.918955i | \(0.629034\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −10.5000 | − | 18.1865i | −0.412798 | − | 0.714986i | 0.582397 | − | 0.812905i | \(-0.302115\pi\) |
−0.995194 | + | 0.0979182i | \(0.968782\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13.5000 | + | 23.3827i | −0.529921 | + | 0.917851i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 19.5000 | − | 33.7750i | 0.763094 | − | 1.32172i | −0.178154 | − | 0.984003i | \(-0.557013\pi\) |
0.941248 | − | 0.337715i | \(-0.109654\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.50000 | − | 7.79423i | −0.175830 | − | 0.304546i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12.0000 | −0.467454 | −0.233727 | − | 0.972302i | \(-0.575092\pi\) | ||||
−0.233727 | + | 0.972302i | \(0.575092\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.50000 | + | 9.52628i | 0.213925 | + | 0.370529i | 0.952940 | − | 0.303160i | \(-0.0980418\pi\) |
−0.739014 | + | 0.673690i | \(0.764708\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.00000 | − | 15.5885i | 0.348481 | − | 0.603587i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.00000 | 0.115814 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14.0000 | 0.539660 | 0.269830 | − | 0.962908i | \(-0.413032\pi\) | ||||
0.269830 | + | 0.962908i | \(0.413032\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −13.5000 | + | 23.3827i | −0.518847 | + | 0.898670i | 0.480913 | + | 0.876768i | \(0.340305\pi\) |
−0.999760 | + | 0.0219013i | \(0.993028\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 10.5000 | + | 18.1865i | 0.401771 | + | 0.695888i | 0.993940 | − | 0.109926i | \(-0.0350613\pi\) |
−0.592168 | + | 0.805814i | \(0.701728\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 63.0000 | 2.40711 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.00000 | − | 5.19615i | −0.114291 | − | 0.197958i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.50000 | + | 11.2583i | −0.247272 | + | 0.428287i | −0.962768 | − | 0.270330i | \(-0.912867\pi\) |
0.715496 | + | 0.698617i | \(0.246201\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 30.0000 | − | 51.9615i | 1.13796 | − | 1.97101i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.00000 | − | 15.5885i | −0.340899 | − | 0.590455i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18.0000 | 0.679851 | 0.339925 | − | 0.940452i | \(-0.389598\pi\) | ||||
0.339925 | + | 0.940452i | \(0.389598\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.500000 | + | 0.866025i | 0.0188579 | + | 0.0326628i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.500000 | − | 0.866025i | 0.0187779 | − | 0.0325243i | −0.856484 | − | 0.516174i | \(-0.827356\pi\) |
0.875262 | + | 0.483650i | \(0.160689\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −21.0000 | −0.786456 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −18.0000 | −0.673162 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 10.5000 | − | 18.1865i | 0.391584 | − | 0.678243i | −0.601075 | − | 0.799193i | \(-0.705261\pi\) |
0.992659 | + | 0.120950i | \(0.0385939\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −12.0000 | − | 20.7846i | −0.445669 | − | 0.771921i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −32.0000 | −1.18681 | −0.593407 | − | 0.804902i | \(-0.702218\pi\) | ||||
−0.593407 | + | 0.804902i | \(0.702218\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.00000 | + | 10.3923i | 0.221918 | + | 0.384373i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12.5000 | + | 21.6506i | −0.461698 | + | 0.799684i | −0.999046 | − | 0.0436764i | \(-0.986093\pi\) |
0.537348 | + | 0.843361i | \(0.319426\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 10.5000 | − | 18.1865i | 0.386772 | − | 0.669910i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.50000 | + | 16.4545i | 0.349463 | + | 0.605288i | 0.986154 | − | 0.165831i | \(-0.0530307\pi\) |
−0.636691 | + | 0.771119i | \(0.719697\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 48.0000 | 1.76095 | 0.880475 | − | 0.474093i | \(-0.157224\pi\) | ||||
0.880475 | + | 0.474093i | \(0.157224\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.50000 | + | 7.79423i | 0.164867 | + | 0.285558i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.5000 | − | 21.6506i | 0.456131 | − | 0.790043i | −0.542621 | − | 0.839978i | \(-0.682568\pi\) |
0.998752 | + | 0.0499348i | \(0.0159013\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 51.0000 | 1.85608 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.00000 | 0.0726912 | 0.0363456 | − | 0.999339i | \(-0.488428\pi\) | ||||
0.0363456 | + | 0.999339i | \(0.488428\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.50000 | + | 2.59808i | −0.0543750 | + | 0.0941802i | −0.891932 | − | 0.452170i | \(-0.850650\pi\) |
0.837557 | + | 0.546350i | \(0.183983\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9.00000 | + | 15.5885i | 0.324971 | + | 0.562867i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 34.0000 | 1.22607 | 0.613036 | − | 0.790055i | \(-0.289948\pi\) | ||||
0.613036 | + | 0.790055i | \(0.289948\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 16.5000 | + | 28.5788i | 0.593464 | + | 1.02791i | 0.993762 | + | 0.111524i | \(0.0355733\pi\) |
−0.400298 | + | 0.916385i | \(0.631093\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −14.0000 | + | 24.2487i | −0.502895 | + | 0.871039i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.00000 | + | 5.19615i | −0.107486 | + | 0.186171i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 39.0000 | 1.39197 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −15.5000 | − | 26.8468i | −0.552515 | − | 0.956985i | −0.998092 | − | 0.0617409i | \(-0.980335\pi\) |
0.445577 | − | 0.895244i | \(-0.352999\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.00000 | − | 1.73205i | 0.0355110 | − | 0.0615069i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 42.0000 | 1.48772 | 0.743858 | − | 0.668338i | \(-0.232994\pi\) | ||||
0.743858 | + | 0.668338i | \(0.232994\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −27.0000 | −0.955191 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.50000 | + | 2.59808i | −0.0529339 | + | 0.0916841i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −16.5000 | − | 28.5788i | −0.580109 | − | 1.00478i | −0.995466 | − | 0.0951198i | \(-0.969677\pi\) |
0.415357 | − | 0.909659i | \(-0.363657\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 52.0000 | 1.82597 | 0.912983 | − | 0.407997i | \(-0.133772\pi\) | ||||
0.912983 | + | 0.407997i | \(0.133772\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −16.5000 | − | 28.5788i | −0.577970 | − | 1.00107i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.00000 | − | 3.46410i | 0.0699711 | − | 0.121194i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13.5000 | − | 23.3827i | 0.471153 | − | 0.816061i | −0.528302 | − | 0.849056i | \(-0.677171\pi\) |
0.999456 | + | 0.0329950i | \(0.0105045\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.50000 | − | 4.33013i | −0.0871445 | − | 0.150939i | 0.819159 | − | 0.573567i | \(-0.194441\pi\) |
−0.906303 | + | 0.422628i | \(0.861108\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 36.0000 | 1.25184 | 0.625921 | − | 0.779886i | \(-0.284723\pi\) | ||||
0.625921 | + | 0.779886i | \(0.284723\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −0.500000 | − | 0.866025i | −0.0173657 | − | 0.0300783i | 0.857212 | − | 0.514964i | \(-0.172195\pi\) |
−0.874578 | + | 0.484885i | \(0.838861\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 18.0000 | − | 31.1769i | 0.622916 | − | 1.07892i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −24.0000 | −0.828572 | −0.414286 | − | 0.910147i | \(-0.635969\pi\) | ||||
−0.414286 | + | 0.910147i | \(0.635969\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 13.5000 | − | 23.3827i | 0.464414 | − | 0.804389i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.50000 | − | 2.59808i | −0.0514193 | − | 0.0890609i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.0000 | 0.753266 | 0.376633 | − | 0.926363i | \(-0.377082\pi\) | ||||
0.376633 | + | 0.926363i | \(0.377082\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −7.50000 | − | 12.9904i | −0.256195 | − | 0.443743i | 0.709024 | − | 0.705184i | \(-0.249136\pi\) |
−0.965219 | + | 0.261441i | \(0.915802\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.5000 | − | 19.9186i | 0.392375 | − | 0.679613i | −0.600387 | − | 0.799709i | \(-0.704987\pi\) |
0.992762 | + | 0.120096i | \(0.0383202\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 25.5000 | − | 44.1673i | 0.868030 | − | 1.50347i | 0.00402340 | − | 0.999992i | \(-0.498719\pi\) |
0.864007 | − | 0.503480i | \(-0.167947\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 13.5000 | + | 23.3827i | 0.459014 | + | 0.795035i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −39.0000 | −1.32298 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.00000 | − | 12.1244i | −0.237186 | − | 0.410818i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.50000 | − | 11.2583i | 0.219489 | − | 0.380167i | −0.735163 | − | 0.677891i | \(-0.762894\pi\) |
0.954652 | + | 0.297724i | \(0.0962275\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 18.0000 | 0.606435 | 0.303218 | − | 0.952921i | \(-0.401939\pi\) | ||||
0.303218 | + | 0.952921i | \(0.401939\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 44.0000 | 1.48072 | 0.740359 | − | 0.672212i | \(-0.234656\pi\) | ||||
0.740359 | + | 0.672212i | \(0.234656\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −19.5000 | + | 33.7750i | −0.654746 | + | 1.13405i | 0.327212 | + | 0.944951i | \(0.393891\pi\) |
−0.981957 | + | 0.189102i | \(0.939442\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.50000 | + | 7.79423i | 0.150587 | + | 0.260824i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −63.0000 | −2.10586 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −21.0000 | − | 36.3731i | −0.700389 | − | 1.21311i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.50000 | − | 7.79423i | 0.149917 | − | 0.259663i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −15.0000 | + | 25.9808i | −0.498617 | + | 0.863630i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −20.5000 | − | 35.5070i | −0.680691 | − | 1.17899i | −0.974770 | − | 0.223211i | \(-0.928346\pi\) |
0.294079 | − | 0.955781i | \(-0.404987\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −48.0000 | −1.59031 | −0.795155 | − | 0.606406i | \(-0.792611\pi\) | ||||
−0.795155 | + | 0.606406i | \(0.792611\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −18.0000 | − | 31.1769i | −0.595713 | − | 1.03181i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.500000 | − | 0.866025i | 0.0164935 | − | 0.0285675i | −0.857661 | − | 0.514216i | \(-0.828083\pi\) |
0.874154 | + | 0.485648i | \(0.161416\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.00000 | −0.131519 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.50000 | − | 7.79423i | 0.147640 | − | 0.255720i | −0.782715 | − | 0.622381i | \(-0.786166\pi\) |
0.930355 | + | 0.366660i | \(0.119499\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −13.5000 | − | 23.3827i | −0.441497 | − | 0.764696i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −26.0000 | −0.849383 | −0.424691 | − | 0.905338i | \(-0.639617\pi\) | ||||
−0.424691 | + | 0.905338i | \(0.639617\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −13.5000 | − | 23.3827i | −0.440087 | − | 0.762254i | 0.557608 | − | 0.830104i | \(-0.311719\pi\) |
−0.997695 | + | 0.0678506i | \(0.978386\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.00000 | − | 15.5885i | 0.293080 | − | 0.507630i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −22.5000 | + | 38.9711i | −0.731152 | + | 1.26639i | 0.225240 | + | 0.974303i | \(0.427684\pi\) |
−0.956391 | + | 0.292089i | \(0.905650\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.00000 | + | 1.73205i | 0.0324614 | + | 0.0562247i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 18.0000 | 0.583077 | 0.291539 | − | 0.956559i | \(-0.405833\pi\) | ||||
0.291539 | + | 0.956559i | \(0.405833\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −13.5000 | − | 23.3827i | −0.436850 | − | 0.756646i | ||||
\(956\) | 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 | ||||||||
\(965\) | 33.0000 | 1.06231 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −16.0000 | −0.514525 | −0.257263 | − | 0.966342i | \(-0.582821\pi\) | ||||
−0.257263 | + | 0.966342i | \(0.582821\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −25.5000 | + | 44.1673i | −0.818334 | + | 1.41740i | 0.0885751 | + | 0.996070i | \(0.471769\pi\) |
−0.906909 | + | 0.421326i | \(0.861565\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 13.5000 | + | 23.3827i | 0.431903 | + | 0.748078i | 0.997037 | − | 0.0769208i | \(-0.0245089\pi\) |
−0.565134 | + | 0.824999i | \(0.691176\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 45.0000 | 1.43821 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −16.5000 | − | 28.5788i | −0.526268 | − | 0.911523i | −0.999532 | − | 0.0306024i | \(-0.990257\pi\) |
0.473263 | − | 0.880921i | \(-0.343076\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 27.0000 | − | 46.7654i | 0.860292 | − | 1.49007i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6.00000 | + | 10.3923i | −0.190789 | + | 0.330456i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.50000 | + | 16.4545i | 0.301777 | + | 0.522694i | 0.976539 | − | 0.215342i | \(-0.0690867\pi\) |
−0.674761 | + | 0.738036i | \(0.735753\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 21.0000 | 0.665745 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 29.5000 | + | 51.0955i | 0.934274 | + | 1.61821i | 0.775923 | + | 0.630828i | \(0.217285\pi\) |
0.158352 | + | 0.987383i | \(0.449382\pi\) | |||||||
\(998\) | 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 \(a_p\))