Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2268,2,Mod(109,2268)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2268, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2268.109");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2268.l (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: | \(18.1100711784\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 28) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 109.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2268.109 |
Dual form | 2268.2.l.h.541.1 |
$q$-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 \(\left(\mathbb{Z}/2268\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(1135\) | \(1541\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||||||
\(5\) | 3.00000 | 1.34164 | 0.670820 | − | 0.741620i | \(-0.265942\pi\) | ||||
0.670820 | + | 0.741620i | \(0.265942\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.50000 | + | 0.866025i | 0.944911 | + | 0.327327i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.00000 | −0.904534 | −0.452267 | − | 0.891883i | \(-0.649385\pi\) | ||||
−0.452267 | + | 0.891883i | \(0.649385\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | + | 1.73205i | −0.277350 | + | 0.480384i | −0.970725 | − | 0.240192i | \(-0.922790\pi\) |
0.693375 | + | 0.720577i | \(0.256123\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.50000 | + | 2.59808i | −0.363803 | + | 0.630126i | −0.988583 | − | 0.150675i | \(-0.951855\pi\) |
0.624780 | + | 0.780801i | \(0.285189\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.500000 | + | 0.866025i | 0.114708 | + | 0.198680i | 0.917663 | − | 0.397360i | \(-0.130073\pi\) |
−0.802955 | + | 0.596040i | \(0.796740\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.00000 | 0.625543 | 0.312772 | − | 0.949828i | \(-0.398743\pi\) | ||||
0.312772 | + | 0.949828i | \(0.398743\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.00000 | 0.800000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.00000 | + | 5.19615i | 0.557086 | + | 0.964901i | 0.997738 | + | 0.0672232i | \(0.0214140\pi\) |
−0.440652 | + | 0.897678i | \(0.645253\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.50000 | + | 6.06218i | 0.628619 | + | 1.08880i | 0.987829 | + | 0.155543i | \(0.0497126\pi\) |
−0.359211 | + | 0.933257i | \(0.616954\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 7.50000 | + | 2.59808i | 1.26773 | + | 0.439155i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.500000 | + | 0.866025i | 0.0821995 | + | 0.142374i | 0.904194 | − | 0.427121i | \(-0.140472\pi\) |
−0.821995 | + | 0.569495i | \(0.807139\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.00000 | + | 5.19615i | −0.468521 | + | 0.811503i | −0.999353 | − | 0.0359748i | \(-0.988546\pi\) |
0.530831 | + | 0.847477i | \(0.321880\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.00000 | + | 3.46410i | 0.304997 | + | 0.528271i | 0.977261 | − | 0.212041i | \(-0.0680112\pi\) |
−0.672264 | + | 0.740312i | \(0.734678\pi\) | |||||||
\(44\) | 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 | ||||||||
\(49\) | 5.50000 | + | 4.33013i | 0.785714 | + | 0.618590i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.50000 | + | 2.59808i | −0.206041 | + | 0.356873i | −0.950464 | − | 0.310835i | \(-0.899391\pi\) |
0.744423 | + | 0.667708i | \(0.232725\pi\) | |||||||
\(54\) | 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 | −0.832240 | − | 0.554416i | \(-0.812942\pi\) |
0.896258 | + | 0.443533i | \(0.146275\pi\) | |||||||
\(62\) | 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 | \(-0.814695\pi\) |
0.893801 | + | 0.448463i | \(0.148028\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.50000 | − | 2.59808i | −0.854704 | − | 0.296078i | ||||
\(78\) | 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 | ||||||||
\(83\) | −6.00000 | − | 10.3923i | −0.658586 | − | 1.14070i | −0.980982 | − | 0.194099i | \(-0.937822\pi\) |
0.322396 | − | 0.946605i | \(-0.395512\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.50000 | + | 7.79423i | −0.488094 | + | 0.845403i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.50000 | − | 12.9904i | −0.794998 | − | 1.37698i | −0.922840 | − | 0.385183i | \(-0.874138\pi\) |
0.127842 | − | 0.991795i | \(-0.459195\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.00000 | + | 3.46410i | −0.419314 | + | 0.363137i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.50000 | + | 2.59808i | 0.153897 | + | 0.266557i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.00000 | + | 8.66025i | 0.507673 | + | 0.879316i | 0.999961 | + | 0.00888289i | \(0.00282755\pi\) |
−0.492287 | + | 0.870433i | \(0.663839\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15.0000 | 1.49256 | 0.746278 | − | 0.665635i | \(-0.231839\pi\) | ||||
0.746278 | + | 0.665635i | \(0.231839\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.0000 | 1.08386 | 0.541931 | − | 0.840423i | \(-0.317693\pi\) | ||||
0.541931 | + | 0.840423i | \(0.317693\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.50000 | − | 12.9904i | −0.725052 | − | 1.25583i | −0.958952 | − | 0.283567i | \(-0.908482\pi\) |
0.233900 | − | 0.972261i | \(-0.424851\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.500000 | − | 0.866025i | 0.0478913 | − | 0.0829502i | −0.841086 | − | 0.540901i | \(-0.818083\pi\) |
0.888977 | + | 0.457951i | \(0.151417\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.00000 | + | 5.19615i | −0.282216 | + | 0.488813i | −0.971930 | − | 0.235269i | \(-0.924403\pi\) |
0.689714 | + | 0.724082i | \(0.257736\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.00000 | 0.839254 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.00000 | + | 5.19615i | −0.550019 | + | 0.476331i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.00000 | −0.181818 | ||||||||
\(122\) | 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 | ||||||||
\(131\) | 3.00000 | 0.262111 | 0.131056 | − | 0.991375i | \(-0.458163\pi\) | ||||
0.131056 | + | 0.991375i | \(0.458163\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.500000 | + | 2.59808i | 0.0433555 | + | 0.225282i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −21.0000 | −1.79415 | −0.897076 | − | 0.441877i | \(-0.854313\pi\) | ||||
−0.897076 | + | 0.441877i | \(0.854313\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.0000 | + | 17.3205i | −0.848189 | + | 1.46911i | 0.0346338 | + | 0.999400i | \(0.488974\pi\) |
−0.882823 | + | 0.469706i | \(0.844360\pi\) | |||||||
\(140\) | 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 | ||||||||
\(149\) | 3.00000 | 0.245770 | 0.122885 | − | 0.992421i | \(-0.460785\pi\) | ||||
0.122885 | + | 0.992421i | \(0.460785\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.0000 | 1.38344 | 0.691720 | − | 0.722166i | \(-0.256853\pi\) | ||||
0.691720 | + | 0.722166i | \(0.256853\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 10.5000 | + | 18.1865i | 0.843380 | + | 1.46078i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.50000 | + | 11.2583i | 0.518756 | + | 0.898513i | 0.999762 | + | 0.0217953i | \(0.00693820\pi\) |
−0.481006 | + | 0.876717i | \(0.659728\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.50000 | + | 2.59808i | 0.591083 | + | 0.204757i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.50000 | − | 9.52628i | −0.430793 | − | 0.746156i | 0.566149 | − | 0.824303i | \(-0.308433\pi\) |
−0.996942 | + | 0.0781474i | \(0.975100\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.00000 | − | 10.3923i | 0.464294 | − | 0.804181i | −0.534875 | − | 0.844931i | \(-0.679641\pi\) |
0.999169 | + | 0.0407502i | \(0.0129748\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.50000 | + | 7.79423i | 0.346154 | + | 0.599556i | ||||
\(170\) | 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 | ||||||||
\(175\) | 10.0000 | + | 3.46410i | 0.755929 | + | 0.261861i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.5000 | + | 18.1865i | −0.784807 | + | 1.35933i | 0.144308 | + | 0.989533i | \(0.453905\pi\) |
−0.929114 | + | 0.369792i | \(0.879429\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.0000 | −0.743294 | −0.371647 | − | 0.928374i | \(-0.621207\pi\) | ||||
−0.371647 | + | 0.928374i | \(0.621207\pi\) | |||||||
\(182\) | 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 | −0.656027 | − | 0.754738i | \(-0.727764\pi\) |
0.981635 | + | 0.190767i | \(0.0610975\pi\) | |||||||
\(192\) | 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 | \(-0.278427\pi\) | ||||
0.641223 | + | 0.767354i | \(0.278427\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.50000 | − | 6.06218i | 0.248108 | − | 0.429736i | −0.714893 | − | 0.699234i | \(-0.753524\pi\) |
0.963001 | + | 0.269498i | \(0.0868577\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.00000 | + | 15.5885i | 0.210559 | + | 1.09410i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.00000 | + | 15.5885i | −0.628587 | + | 1.08875i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.50000 | − | 2.59808i | −0.103757 | − | 0.179713i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.00000 | − | 3.46410i | 0.137686 | − | 0.238479i | −0.788935 | − | 0.614477i | \(-0.789367\pi\) |
0.926620 | + | 0.375999i | \(0.122700\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.00000 | + | 10.3923i | 0.409197 | + | 0.708749i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.50000 | + | 18.1865i | 0.237595 | + | 1.23458i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.00000 | − | 5.19615i | −0.201802 | − | 0.349531i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.00000 | − | 6.92820i | −0.267860 | − | 0.463947i | 0.700449 | − | 0.713702i | \(-0.252983\pi\) |
−0.968309 | + | 0.249756i | \(0.919650\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.00000 | −0.199117 | −0.0995585 | − | 0.995032i | \(-0.531743\pi\) | ||||
−0.0995585 | + | 0.995032i | \(0.531743\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.0000 | 0.726900 | 0.363450 | − | 0.931614i | \(-0.381599\pi\) | ||||
0.363450 | + | 0.931614i | \(0.381599\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.5000 | + | 18.1865i | 0.687878 | + | 1.19144i | 0.972523 | + | 0.232806i | \(0.0747909\pi\) |
−0.284645 | + | 0.958633i | \(0.591876\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 13.5000 | − | 23.3827i | 0.880643 | − | 1.52532i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.00000 | − | 10.3923i | 0.388108 | − | 0.672222i | −0.604087 | − | 0.796918i | \(-0.706462\pi\) |
0.992195 | + | 0.124696i | \(0.0397955\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.00000 | −0.0644157 | −0.0322078 | − | 0.999481i | \(-0.510254\pi\) | ||||
−0.0322078 | + | 0.999481i | \(0.510254\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 16.5000 | + | 12.9904i | 1.05415 | + | 0.829925i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.00000 | −0.127257 | ||||||||
\(248\) | 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 | ||||||||
\(257\) | 3.00000 | 0.187135 | 0.0935674 | − | 0.995613i | \(-0.470173\pi\) | ||||
0.0935674 | + | 0.995613i | \(0.470173\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.500000 | + | 2.59808i | 0.0310685 | + | 0.161437i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.00000 | −0.184988 | −0.0924940 | − | 0.995713i | \(-0.529484\pi\) | ||||
−0.0924940 | + | 0.995713i | \(0.529484\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.50000 | + | 7.79423i | −0.276433 | + | 0.478796i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.50000 | + | 2.59808i | −0.0914566 | + | 0.158408i | −0.908124 | − | 0.418701i | \(-0.862486\pi\) |
0.816668 | + | 0.577108i | \(0.195819\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.50000 | − | 9.52628i | −0.334101 | − | 0.578680i | 0.649211 | − | 0.760609i | \(-0.275099\pi\) |
−0.983312 | + | 0.181928i | \(0.941766\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −12.0000 | −0.723627 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13.0000 | −0.781094 | −0.390547 | − | 0.920583i | \(-0.627714\pi\) | ||||
−0.390547 | + | 0.920583i | \(0.627714\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −15.0000 | − | 25.9808i | −0.894825 | − | 1.54988i | −0.834021 | − | 0.551733i | \(-0.813967\pi\) |
−0.0608039 | − | 0.998150i | \(-0.519366\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −14.5000 | − | 25.1147i | −0.861936 | − | 1.49292i | −0.870058 | − | 0.492949i | \(-0.835919\pi\) |
0.00812260 | − | 0.999967i | \(-0.497414\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12.0000 | + | 10.3923i | −0.708338 | + | 0.613438i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.00000 | + | 6.92820i | 0.235294 | + | 0.407541i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3.00000 | + | 5.19615i | −0.175262 | + | 0.303562i | −0.940252 | − | 0.340480i | \(-0.889411\pi\) |
0.764990 | + | 0.644042i | \(0.222744\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −13.5000 | − | 23.3827i | −0.786000 | − | 1.36139i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.00000 | + | 5.19615i | −0.173494 | + | 0.300501i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.00000 | + | 10.3923i | 0.115278 | + | 0.599002i | ||||
\(302\) | 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 | \(-0.794649\pi\) | ||||
−0.799022 | + | 0.601302i | \(0.794649\pi\) | |||||||
\(308\) | 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 | \(0.391906\pi\) |
−0.983118 | + | 0.182973i | \(0.941428\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.50000 | − | 7.79423i | 0.252745 | − | 0.437767i | −0.711535 | − | 0.702650i | \(-0.752000\pi\) |
0.964281 | + | 0.264883i | \(0.0853332\pi\) | |||||||
\(318\) | 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 | ||||||||
\(329\) | 18.0000 | − | 15.5885i | 0.992372 | − | 0.859419i | ||||
\(330\) | 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 | ||||||||
\(335\) | 10.5000 | + | 18.1865i | 0.573676 | + | 0.993636i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.0000 | − | 29.4449i | 0.926049 | − | 1.60396i | 0.136184 | − | 0.990684i | \(-0.456516\pi\) |
0.789865 | − | 0.613280i | \(-0.210150\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10.5000 | − | 18.1865i | −0.568607 | − | 0.984856i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.0000 | + | 15.5885i | 0.539949 | + | 0.841698i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.50000 | − | 7.79423i | −0.241573 | − | 0.418416i | 0.719590 | − | 0.694399i | \(-0.244330\pi\) |
−0.961162 | + | 0.275983i | \(0.910997\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −13.0000 | − | 22.5167i | −0.695874 | − | 1.20529i | −0.969885 | − | 0.243563i | \(-0.921684\pi\) |
0.274011 | − | 0.961727i | \(-0.411649\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −21.0000 | −1.11772 | −0.558859 | − | 0.829263i | \(-0.688761\pi\) | ||||
−0.558859 | + | 0.829263i | \(0.688761\pi\) | |||||||
\(354\) | 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 | \(-0.296211\pi\) |
−0.993207 | + | 0.116358i | \(0.962878\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.00000 | − | 15.5885i | 0.473684 | − | 0.820445i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.50000 | − | 2.59808i | 0.0785136 | − | 0.135990i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.00000 | 0.260998 | 0.130499 | − | 0.991448i | \(-0.458342\pi\) | ||||
0.130499 | + | 0.991448i | \(0.458342\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.00000 | + | 5.19615i | −0.311504 | + | 0.269771i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −25.0000 | −1.29445 | −0.647225 | − | 0.762299i | \(-0.724071\pi\) | ||||
−0.647225 | + | 0.762299i | \(0.724071\pi\) | |||||||
\(374\) | 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 | ||||||||
\(383\) | −33.0000 | −1.68622 | −0.843111 | − | 0.537740i | \(-0.819278\pi\) | ||||
−0.843111 | + | 0.537740i | \(0.819278\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −22.5000 | − | 7.79423i | −1.14671 | − | 0.397231i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 15.0000 | 0.760530 | 0.380265 | − | 0.924878i | \(-0.375833\pi\) | ||||
0.380265 | + | 0.924878i | \(0.375833\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.50000 | + | 7.79423i | −0.227575 | + | 0.394171i | ||||
\(392\) | 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 | 0.785853 | + | 0.618414i | \(0.212224\pi\) |
0.142636 | + | 0.989775i | \(0.454442\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.00000 | 0.149813 | 0.0749064 | − | 0.997191i | \(-0.476134\pi\) | ||||
0.0749064 | + | 0.997191i | \(0.476134\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −14.0000 | −0.697390 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.50000 | − | 2.59808i | −0.0743522 | − | 0.128782i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.50000 | − | 9.52628i | −0.271957 | − | 0.471044i | 0.697406 | − | 0.716677i | \(-0.254338\pi\) |
−0.969363 | + | 0.245633i | \(0.921004\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.50000 | − | 23.3827i | −0.221431 | − | 1.15059i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −18.0000 | − | 31.1769i | −0.883585 | − | 1.53041i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.00000 | − | 10.3923i | 0.293119 | − | 0.507697i | −0.681426 | − | 0.731887i | \(-0.738640\pi\) |
0.974546 | + | 0.224189i | \(0.0719734\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.0000 | + | 19.0526i | 0.536107 | + | 0.928565i | 0.999109 | + | 0.0422075i | \(0.0134391\pi\) |
−0.463002 | + | 0.886357i | \(0.653228\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.00000 | + | 10.3923i | −0.291043 | + | 0.504101i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.00000 | − | 1.73205i | 0.0967868 | − | 0.0838198i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.50000 | − | 12.9904i | 0.361262 | − | 0.625725i | −0.626907 | − | 0.779094i | \(-0.715679\pi\) |
0.988169 | + | 0.153370i | \(0.0490126\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10.0000 | −0.480569 | −0.240285 | − | 0.970702i | \(-0.577241\pi\) | ||||
−0.240285 | + | 0.970702i | \(0.577241\pi\) | |||||||
\(434\) | 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 | −0.853847 | − | 0.520524i | \(-0.825737\pi\) |
0.877711 | + | 0.479191i | \(0.159070\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.50000 | − | 7.79423i | 0.213801 | − | 0.370315i | −0.739100 | − | 0.673596i | \(-0.764749\pi\) |
0.952901 | + | 0.303281i | \(0.0980821\pi\) | |||||||
\(444\) | 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 | \(-0.639633\pi\) | ||||
−0.424736 | + | 0.905317i | \(0.639633\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.00000 | − | 15.5885i | 0.423793 | − | 0.734032i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −12.0000 | + | 10.3923i | −0.562569 | + | 0.487199i | ||||
\(456\) | 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 | ||||||||
\(461\) | 3.00000 | + | 5.19615i | 0.139724 | + | 0.242009i | 0.927392 | − | 0.374091i | \(-0.122045\pi\) |
−0.787668 | + | 0.616100i | \(0.788712\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.00000 | − | 13.8564i | 0.371792 | − | 0.643962i | −0.618050 | − | 0.786139i | \(-0.712077\pi\) |
0.989841 | + | 0.142177i | \(0.0454103\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10.5000 | + | 18.1865i | 0.485882 | + | 0.841572i | 0.999868 | − | 0.0162260i | \(-0.00516512\pi\) |
−0.513986 | + | 0.857798i | \(0.671832\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.50000 | + | 18.1865i | 0.161615 | + | 0.839776i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.00000 | − | 10.3923i | −0.275880 | − | 0.477839i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.00000 | + | 3.46410i | 0.0917663 | + | 0.158944i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.00000 | −0.137073 | −0.0685367 | − | 0.997649i | \(-0.521833\pi\) | ||||
−0.0685367 | + | 0.997649i | \(0.521833\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.00000 | −0.0911922 | ||||||||
\(482\) | 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 | −0.566429 | − | 0.824110i | \(-0.691675\pi\) |
0.996915 | + | 0.0784867i | \(0.0250088\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.0000 | + | 20.7846i | −0.541552 | + | 0.937996i | 0.457263 | + | 0.889332i | \(0.348830\pi\) |
−0.998815 | + | 0.0486647i | \(0.984503\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −18.0000 | −0.810679 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11.0000 | 0.492428 | 0.246214 | − | 0.969216i | \(-0.420813\pi\) | ||||
0.246214 | + | 0.969216i | \(0.420813\pi\) | |||||||
\(500\) | 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 | ||||||||
\(509\) | 3.00000 | 0.132973 | 0.0664863 | − | 0.997787i | \(-0.478821\pi\) | ||||
0.0664863 | + | 0.997787i | \(0.478821\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.00000 | − | 1.73205i | 0.0884748 | − | 0.0766214i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 33.0000 | 1.45415 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −13.5000 | + | 23.3827i | −0.593729 | + | 1.02837i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −19.5000 | + | 33.7750i | −0.854311 | + | 1.47971i | 0.0229727 | + | 0.999736i | \(0.492687\pi\) |
−0.877283 | + | 0.479973i | \(0.840646\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.500000 | + | 0.866025i | 0.0218635 | + | 0.0378686i | 0.876750 | − | 0.480946i | \(-0.159707\pi\) |
−0.854887 | + | 0.518815i | \(0.826373\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −21.0000 | −0.914774 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −14.0000 | −0.608696 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.00000 | − | 10.3923i | −0.259889 | − | 0.450141i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −22.5000 | − | 38.9711i | −0.972760 | − | 1.68487i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −16.5000 | − | 12.9904i | −0.710705 | − | 0.559535i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.5000 | − | 30.3109i | −0.752384 | − | 1.30317i | −0.946664 | − | 0.322221i | \(-0.895571\pi\) |
0.194281 | − | 0.980946i | \(-0.437763\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.50000 | − | 2.59808i | 0.0642529 | − | 0.111289i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.00000 | − | 6.92820i | −0.171028 | − | 0.296229i | 0.767752 | − | 0.640747i | \(-0.221375\pi\) |
−0.938779 | + | 0.344519i | \(0.888042\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.00000 | + | 5.19615i | −0.127804 | + | 0.221364i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 26.0000 | − | 22.5167i | 1.10563 | − | 0.957506i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 16.5000 | − | 28.5788i | 0.699127 | − | 1.21092i | −0.269642 | − | 0.962961i | \(-0.586905\pi\) |
0.968769 | − | 0.247964i | \(-0.0797613\pi\) | |||||||
\(558\) | 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 | −0.756151 | − | 0.654398i | \(-0.772922\pi\) |
0.944800 | + | 0.327647i | \(0.106256\pi\) | |||||||
\(570\) | 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 | \(-0.826707\pi\) |
0.876245 | + | 0.481865i | \(0.160040\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.00000 | − | 31.1769i | −0.248922 | − | 1.29344i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.50000 | − | 7.79423i | 0.186371 | − | 0.322804i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6.00000 | − | 10.3923i | −0.247647 | − | 0.428936i | 0.715226 | − | 0.698893i | \(-0.246324\pi\) |
−0.962872 | + | 0.269957i | \(0.912990\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.50000 | + | 6.06218i | −0.144215 | + | 0.249788i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 10.5000 | + | 18.1865i | 0.431183 | + | 0.746831i | 0.996976 | − | 0.0777165i | \(-0.0247629\pi\) |
−0.565792 | + | 0.824548i | \(0.691430\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −18.0000 | + | 15.5885i | −0.737928 | + | 0.639064i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 13.5000 | + | 23.3827i | 0.551595 | + | 0.955391i | 0.998160 | + | 0.0606393i | \(0.0193139\pi\) |
−0.446565 | + | 0.894751i | \(0.647353\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.00000 | − | 12.1244i | −0.285536 | − | 0.494563i | 0.687203 | − | 0.726465i | \(-0.258838\pi\) |
−0.972739 | + | 0.231903i | \(0.925505\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6.00000 | −0.243935 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 47.0000 | 1.90767 | 0.953836 | − | 0.300329i | \(-0.0970966\pi\) | ||||
0.953836 | + | 0.300329i | \(0.0970966\pi\) | |||||||
\(608\) | 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 | −0.495114 | − | 0.868828i | \(-0.664874\pi\) |
0.999984 | − | 0.00563283i | \(-0.00179300\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.00000 | + | 5.19615i | −0.120775 | + | 0.209189i | −0.920074 | − | 0.391745i | \(-0.871871\pi\) |
0.799298 | + | 0.600935i | \(0.205205\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −31.0000 | −1.24600 | −0.622998 | − | 0.782224i | \(-0.714085\pi\) | ||||
−0.622998 | + | 0.782224i | \(0.714085\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −7.50000 | − | 38.9711i | −0.300481 | − | 1.56135i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.0000 | −1.16000 | ||||||||
\(626\) | 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 | ||||||||
\(635\) | 24.0000 | 0.952411 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −13.0000 | + | 5.19615i | −0.515079 | + | 0.205879i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15.0000 | 0.592464 | 0.296232 | − | 0.955116i | \(-0.404270\pi\) | ||||
0.296232 | + | 0.955116i | \(0.404270\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10.0000 | + | 17.3205i | −0.394362 | + | 0.683054i | −0.993019 | − | 0.117951i | \(-0.962368\pi\) |
0.598658 | + | 0.801005i | \(0.295701\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −10.5000 | + | 18.1865i | −0.412798 | + | 0.714986i | −0.995194 | − | 0.0979182i | \(-0.968782\pi\) |
0.582397 | + | 0.812905i | \(0.302115\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13.5000 | + | 23.3827i | 0.529921 | + | 0.917851i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 39.0000 | 1.52619 | 0.763094 | − | 0.646288i | \(-0.223679\pi\) | ||||
0.763094 | + | 0.646288i | \(0.223679\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.00000 | 0.351659 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6.00000 | − | 10.3923i | −0.233727 | − | 0.404827i | 0.725175 | − | 0.688565i | \(-0.241759\pi\) |
−0.958902 | + | 0.283738i | \(0.908425\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.50000 | − | 9.52628i | −0.213925 | − | 0.370529i | 0.739014 | − | 0.673690i | \(-0.235292\pi\) |
−0.952940 | + | 0.303160i | \(0.901958\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.50000 | + | 7.79423i | 0.0581675 | + | 0.302247i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.00000 | + | 15.5885i | 0.348481 | + | 0.603587i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.50000 | + | 2.59808i | −0.0579069 | + | 0.100298i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.00000 | − | 12.1244i | −0.269830 | − | 0.467360i | 0.698988 | − | 0.715134i | \(-0.253634\pi\) |
−0.968818 | + | 0.247774i | \(0.920301\pi\) | |||||||
\(674\) | 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 | ||||||||
\(679\) | 5.00000 | + | 25.9808i | 0.191882 | + | 0.997050i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −10.5000 | + | 18.1865i | −0.401771 | + | 0.695888i | −0.993940 | − | 0.109926i | \(-0.964939\pi\) |
0.592168 | + | 0.805814i | \(0.298272\pi\) | |||||||
\(684\) | 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 | −0.715496 | − | 0.698617i | \(-0.753799\pi\) |
0.962768 | + | 0.270330i | \(0.0871327\pi\) | |||||||
\(692\) | 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 | \(-0.610402\pi\) | ||||
−0.339925 | + | 0.940452i | \(0.610402\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.500000 | + | 0.866025i | −0.0188579 | + | 0.0326628i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 37.5000 | + | 12.9904i | 1.41033 | + | 0.488554i | ||||
\(708\) | 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 | ||||||||
\(713\) | 10.5000 | + | 18.1865i | 0.393228 | + | 0.681091i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.00000 | − | 15.5885i | 0.336581 | − | 0.582975i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 10.5000 | + | 18.1865i | 0.391584 | + | 0.678243i | 0.992659 | − | 0.120950i | \(-0.0385939\pi\) |
−0.601075 | + | 0.799193i | \(0.705261\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 27.5000 | + | 9.52628i | 1.02415 | + | 0.354777i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 12.0000 | + | 20.7846i | 0.445669 | + | 0.771921i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −16.0000 | − | 27.7128i | −0.593407 | − | 1.02781i | −0.993770 | − | 0.111454i | \(-0.964449\pi\) |
0.400362 | − | 0.916357i | \(-0.368884\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12.0000 | −0.443836 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −25.0000 | −0.923396 | −0.461698 | − | 0.887037i | \(-0.652760\pi\) | ||||
−0.461698 | + | 0.887037i | \(0.652760\pi\) | |||||||
\(734\) | 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 | −0.636691 | − | 0.771119i | \(-0.719697\pi\) |
0.986154 | + | 0.165831i | \(0.0530307\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 24.0000 | − | 41.5692i | 0.880475 | − | 1.52503i | 0.0296605 | − | 0.999560i | \(-0.490557\pi\) |
0.850814 | − | 0.525467i | \(-0.176109\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.00000 | 0.329734 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −7.50000 | − | 38.9711i | −0.274044 | − | 1.42397i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −25.0000 | −0.912263 | −0.456131 | − | 0.889912i | \(-0.650765\pi\) | ||||
−0.456131 | + | 0.889912i | \(0.650765\pi\) | |||||||
\(752\) | 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 | ||||||||
\(761\) | 3.00000 | 0.108750 | 0.0543750 | − | 0.998521i | \(-0.482683\pi\) | ||||
0.0543750 | + | 0.998521i | \(0.482683\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.00000 | − | 1.73205i | 0.0724049 | − | 0.0627044i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 18.0000 | 0.649942 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17.0000 | − | 29.4449i | 0.613036 | − | 1.06181i | −0.377690 | − | 0.925932i | \(-0.623282\pi\) |
0.990726 | − | 0.135877i | \(-0.0433852\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 16.5000 | − | 28.5788i | 0.593464 | − | 1.02791i | −0.400298 | − | 0.916385i | \(-0.631093\pi\) |
0.993762 | − | 0.111524i | \(-0.0355733\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 14.0000 | + | 24.2487i | 0.502895 | + | 0.871039i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.00000 | −0.214972 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 19.5000 | + | 33.7750i | 0.695985 | + | 1.20548i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15.5000 | + | 26.8468i | 0.552515 | + | 0.956985i | 0.998092 | + | 0.0617409i | \(0.0196653\pi\) |
−0.445577 | + | 0.895244i | \(0.647001\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12.0000 | + | 10.3923i | −0.426671 | + | 0.369508i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.00000 | + | 1.73205i | 0.0355110 | + | 0.0615069i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −21.0000 | + | 36.3731i | −0.743858 | + | 1.28840i | 0.206868 | + | 0.978369i | \(0.433673\pi\) |
−0.950726 | + | 0.310031i | \(0.899660\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13.5000 | + | 23.3827i | 0.477596 | + | 0.827220i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.50000 | + | 2.59808i | −0.0529339 | + | 0.0916841i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 22.5000 | + | 7.79423i | 0.793021 | + | 0.274710i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 16.5000 | − | 28.5788i | 0.580109 | − | 1.00478i | −0.415357 | − | 0.909659i | \(-0.636343\pi\) |
0.995466 | − | 0.0951198i | \(-0.0303234\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −52.0000 | −1.82597 | −0.912983 | − | 0.407997i | \(-0.866228\pi\) | ||||
−0.912983 | + | 0.407997i | \(0.866228\pi\) | |||||||
\(812\) | 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 | −0.999456 | − | 0.0329950i | \(-0.989495\pi\) |
0.528302 | + | 0.849056i | \(0.322829\pi\) | |||||||
\(822\) | 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 | \(-0.715277\pi\) | ||||
−0.625921 | + | 0.779886i | \(0.715277\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.500000 | − | 0.866025i | 0.0173657 | − | 0.0300783i | −0.857212 | − | 0.514964i | \(-0.827805\pi\) |
0.874578 | + | 0.484885i | \(0.161139\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −19.5000 | + | 7.79423i | −0.675635 | + | 0.270054i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 18.0000 | − | 31.1769i | 0.622916 | − | 1.07892i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 12.0000 | + | 20.7846i | 0.414286 | + | 0.717564i | 0.995353 | − | 0.0962912i | \(-0.0306980\pi\) |
−0.581067 | + | 0.813856i | \(0.697365\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.50000 | + | 6.06218i | −0.120690 | + | 0.209041i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 13.5000 | + | 23.3827i | 0.464414 | + | 0.804389i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.00000 | − | 1.73205i | −0.171802 | − | 0.0595140i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.50000 | + | 2.59808i | 0.0514193 | + | 0.0890609i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11.0000 | + | 19.0526i | 0.376633 | + | 0.652347i | 0.990570 | − | 0.137008i | \(-0.0437485\pi\) |
−0.613937 | + | 0.789355i | \(0.710415\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 15.0000 | 0.512390 | 0.256195 | − | 0.966625i | \(-0.417531\pi\) | ||||
0.256195 | + | 0.966625i | \(0.417531\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 23.0000 | 0.784750 | 0.392375 | − | 0.919805i | \(-0.371654\pi\) | ||||
0.392375 | + | 0.919805i | \(0.371654\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −25.5000 | − | 44.1673i | −0.868030 | − | 1.50347i | −0.864007 | − | 0.503480i | \(-0.832053\pi\) |
−0.00402340 | − | 0.999992i | \(-0.501281\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 13.5000 | − | 23.3827i | 0.459014 | − | 0.795035i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −19.5000 | + | 33.7750i | −0.661492 | + | 1.14574i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14.0000 | −0.474372 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −7.50000 | − | 2.59808i | −0.253546 | − | 0.0878310i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −13.0000 | −0.438979 | −0.219489 | − | 0.975615i | \(-0.570439\pi\) | ||||
−0.219489 | + | 0.975615i | \(0.570439\pi\) | |||||||
\(878\) | 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 | ||||||||
\(887\) | 39.0000 | 1.30949 | 0.654746 | − | 0.755849i | \(-0.272776\pi\) | ||||
0.654746 | + | 0.755849i | \(0.272776\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 20.0000 | + | 6.92820i | 0.670778 | + | 0.232364i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 9.00000 | 0.301174 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −31.5000 | + | 54.5596i | −1.05293 | + | 1.82373i | ||||
\(896\) | 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 | ||||||||
\(905\) | −30.0000 | −0.997234 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 41.0000 | 1.36138 | 0.680691 | − | 0.732570i | \(-0.261680\pi\) | ||||
0.680691 | + | 0.732570i | \(0.261680\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24.0000 | − | 41.5692i | −0.795155 | − | 1.37725i | −0.922740 | − | 0.385422i | \(-0.874056\pi\) |
0.127585 | − | 0.991828i | \(-0.459277\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 18.0000 | + | 31.1769i | 0.595713 | + | 1.03181i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7.50000 | + | 2.59808i | 0.247672 | + | 0.0857960i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.500000 | + | 0.866025i | 0.0164935 | + | 0.0285675i | 0.874154 | − | 0.485648i | \(-0.161416\pi\) |
−0.857661 | + | 0.514216i | \(0.828083\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.00000 | + | 3.46410i | 0.0657596 | + | 0.113899i | ||||
\(926\) | 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 | ||||||||
\(931\) | −1.00000 | + | 6.92820i | −0.0327737 | + | 0.227063i | ||||
\(932\) | 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 | \(-0.360383\pi\) | ||||
0.424691 | + | 0.905338i | \(0.360383\pi\) | |||||||
\(938\) | 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 | \(-0.572316\pi\) |
0.956391 | − | 0.292089i | \(-0.0943502\pi\) | |||||||
\(948\) | 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 | \(-0.594167\pi\) | ||||
−0.291539 | + | 0.956559i | \(0.594167\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 13.5000 | − | 23.3827i | 0.436850 | − | 0.756646i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −52.5000 | − | 18.1865i | −1.69531 | − | 0.587274i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.00000 | + | 15.5885i | −0.290323 | + | 0.502853i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −16.5000 | − | 28.5788i | −0.531154 | − | 0.919985i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.00000 | − | 13.8564i | 0.257263 | − | 0.445592i | −0.708245 | − | 0.705967i | \(-0.750513\pi\) |
0.965508 | + | 0.260375i | \(0.0838461\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −25.5000 | − | 44.1673i | −0.818334 | − | 1.41740i | −0.906909 | − | 0.421326i | \(-0.861565\pi\) |
0.0885751 | − | 0.996070i | \(-0.471769\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −40.0000 | + | 34.6410i | −1.28234 | + | 1.11054i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −13.5000 | − | 23.3827i | −0.431903 | − | 0.748078i | 0.565134 | − | 0.824999i | \(-0.308824\pi\) |
−0.997037 | + | 0.0769208i | \(0.975491\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 22.5000 | + | 38.9711i | 0.719103 | + | 1.24552i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 33.0000 | 1.05254 | 0.526268 | − | 0.850319i | \(-0.323591\pi\) | ||||
0.526268 | + | 0.850319i | \(0.323591\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 54.0000 | 1.72058 | ||||||||
\(986\) | 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 | −0.674761 | − | 0.738036i | \(-0.735753\pi\) |
0.976539 | + | 0.215342i | \(0.0690867\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 10.5000 | − | 18.1865i | 0.332872 | − | 0.576552i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 59.0000 | 1.86855 | 0.934274 | − | 0.356555i | \(-0.116049\pi\) | ||||
0.934274 | + | 0.356555i | \(0.116049\pi\) | |||||||
\(998\) | 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 \(a_p\))