Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2400,2,Mod(49,2400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2400, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2400.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2400 = 2^{5} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2400.d (of order \(2\), degree \(1\), 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: | \(19.1640964851\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.399424.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{6} - 2x^{5} + 3x^{4} - 6x^{3} + 6x^{2} - 8x + 8 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | no (minimal twist has level 120) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 49.4 | ||
Root | \(0.264658 - 1.38923i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2400.49 |
Dual form | 2400.2.d.f.49.3 |
$q$-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 \(\left(\mathbb{Z}/2400\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1601\) | \(1951\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.941367i | 0.355803i | 0.984048 | + | 0.177902i | \(0.0569309\pi\) | ||||
−0.984048 | + | 0.177902i | \(0.943069\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 4.49828i | − 1.35628i | −0.734931 | − | 0.678141i | \(-0.762786\pi\) | ||||
0.734931 | − | 0.678141i | \(-0.237214\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.55691 | 1.54121 | 0.770605 | − | 0.637313i | \(-0.219954\pi\) | ||||
0.770605 | + | 0.637313i | \(0.219954\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 7.55691i | − 1.83282i | −0.400240 | − | 0.916410i | \(-0.631073\pi\) | ||||
0.400240 | − | 0.916410i | \(-0.368927\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.05863i | 0.242867i | 0.992600 | + | 0.121434i | \(0.0387491\pi\) | ||||
−0.992600 | + | 0.121434i | \(0.961251\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.941367i | 0.205423i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.05863i | 0.220740i | 0.993891 | + | 0.110370i | \(0.0352036\pi\) | ||||
−0.993891 | + | 0.110370i | \(0.964796\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.00000i | 0.371391i | 0.982607 | + | 0.185695i | \(0.0594537\pi\) | ||||
−0.982607 | + | 0.185695i | \(0.940546\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.55691 | −0.638841 | −0.319420 | − | 0.947613i | \(-0.603488\pi\) | ||||
−0.319420 | + | 0.947613i | \(0.603488\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 4.49828i | − 0.783050i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.43965 | −1.22307 | −0.611535 | − | 0.791217i | \(-0.709448\pi\) | ||||
−0.611535 | + | 0.791217i | \(0.709448\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.55691 | 0.889818 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.88273 | −0.606381 | −0.303191 | − | 0.952930i | \(-0.598052\pi\) | ||||
−0.303191 | + | 0.952930i | \(0.598052\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.88273 | −0.287114 | −0.143557 | − | 0.989642i | \(-0.545854\pi\) | ||||
−0.143557 | + | 0.989642i | \(0.545854\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 10.0552i | − 1.46670i | −0.679851 | − | 0.733350i | \(-0.737955\pi\) | ||||
0.679851 | − | 0.733350i | \(-0.262045\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.11383 | 0.873404 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 7.55691i | − 1.05818i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.00000 | −0.274721 | −0.137361 | − | 0.990521i | \(-0.543862\pi\) | ||||
−0.137361 | + | 0.990521i | \(0.543862\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.05863i | 0.140219i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 8.49828i | − 1.10638i | −0.833054 | − | 0.553191i | \(-0.813410\pi\) | ||||
0.833054 | − | 0.553191i | \(-0.186590\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.99656i | 1.15189i | 0.817488 | + | 0.575946i | \(0.195366\pi\) | ||||
−0.817488 | + | 0.575946i | \(0.804634\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.941367i | 0.118601i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.00000 | 0.488678 | 0.244339 | − | 0.969690i | \(-0.421429\pi\) | ||||
0.244339 | + | 0.969690i | \(0.421429\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.05863i | 0.127444i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.9966 | 1.54241 | 0.771204 | − | 0.636588i | \(-0.219655\pi\) | ||||
0.771204 | + | 0.636588i | \(0.219655\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 6.00000i | − 0.702247i | −0.936329 | − | 0.351123i | \(-0.885800\pi\) | ||||
0.936329 | − | 0.351123i | \(-0.114200\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.23453 | 0.482570 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.5569 | 1.30025 | 0.650127 | − | 0.759825i | \(-0.274716\pi\) | ||||
0.650127 | + | 0.759825i | \(0.274716\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.88273 | 0.645714 | 0.322857 | − | 0.946448i | \(-0.395357\pi\) | ||||
0.322857 | + | 0.946448i | \(0.395357\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.00000i | 0.214423i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.11727 | 0.436429 | 0.218215 | − | 0.975901i | \(-0.429977\pi\) | ||||
0.218215 | + | 0.975901i | \(0.429977\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.23109i | 0.548368i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.55691 | −0.368835 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 17.1138i | − 1.73765i | −0.495123 | − | 0.868823i | \(-0.664877\pi\) | ||||
0.495123 | − | 0.868823i | \(-0.335123\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 4.49828i | − 0.452094i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.00000i | 0.199007i | 0.995037 | + | 0.0995037i | \(0.0317255\pi\) | ||||
−0.995037 | + | 0.0995037i | \(0.968274\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 10.1725i | − 1.00232i | −0.865354 | − | 0.501161i | \(-0.832906\pi\) | ||||
0.865354 | − | 0.501161i | \(-0.167094\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 17.2311 | 1.66579 | 0.832896 | − | 0.553429i | \(-0.186681\pi\) | ||||
0.832896 | + | 0.553429i | \(0.186681\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 1.88273i | − 0.180333i | −0.995927 | − | 0.0901666i | \(-0.971260\pi\) | ||||
0.995927 | − | 0.0901666i | \(-0.0287399\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.43965 | −0.706140 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 15.3224i | 1.44141i | 0.693243 | + | 0.720704i | \(0.256181\pi\) | ||||
−0.693243 | + | 0.720704i | \(0.743819\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.55691 | 0.513737 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.11383 | 0.652124 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.23453 | −0.839503 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.88273 | −0.350094 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 18.1725i | − 1.61255i | −0.591544 | − | 0.806273i | \(-0.701481\pi\) | ||||
0.591544 | − | 0.806273i | \(-0.298519\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.88273 | −0.165765 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.38101i | 0.557512i | 0.960362 | + | 0.278756i | \(0.0899220\pi\) | ||||
−0.960362 | + | 0.278756i | \(0.910078\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.996562 | −0.0864129 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.44309i | 0.379598i | 0.981823 | + | 0.189799i | \(0.0607837\pi\) | ||||
−0.981823 | + | 0.189799i | \(0.939216\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 20.1725i | 1.71101i | 0.517798 | + | 0.855503i | \(0.326752\pi\) | ||||
−0.517798 | + | 0.855503i | \(0.673248\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 10.0552i | − 0.846800i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 24.9966i | − 2.09032i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.11383 | 0.504260 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.00000i | 0.163846i | 0.996639 | + | 0.0819232i | \(0.0261062\pi\) | ||||
−0.996639 | + | 0.0819232i | \(0.973894\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.67418 | −0.787274 | −0.393637 | − | 0.919266i | \(-0.628783\pi\) | ||||
−0.393637 | + | 0.919266i | \(0.628783\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 7.55691i | − 0.610940i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.32582 | 0.345238 | 0.172619 | − | 0.984989i | \(-0.444777\pi\) | ||||
0.172619 | + | 0.984989i | \(0.444777\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.00000 | −0.158610 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.996562 | −0.0785401 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.11727 | −0.479141 | −0.239571 | − | 0.970879i | \(-0.577007\pi\) | ||||
−0.239571 | + | 0.970879i | \(0.577007\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 6.05520i | − 0.468565i | −0.972169 | − | 0.234283i | \(-0.924726\pi\) | ||||
0.972169 | − | 0.234283i | \(-0.0752741\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 17.8793 | 1.37533 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.05863i | 0.0809557i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −16.8793 | −1.28331 | −0.641655 | − | 0.766994i | \(-0.721752\pi\) | ||||
−0.641655 | + | 0.766994i | \(0.721752\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − 8.49828i | − 0.638770i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.6155i | 0.793443i | 0.917939 | + | 0.396722i | \(0.129852\pi\) | ||||
−0.917939 | + | 0.396722i | \(0.870148\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.1173i | 1.04933i | 0.851309 | + | 0.524664i | \(0.175809\pi\) | ||||
−0.851309 | + | 0.524664i | \(0.824191\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.99656i | 0.665045i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −33.9931 | −2.48582 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.941367i | 0.0684744i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.00000 | 0.578860 | 0.289430 | − | 0.957199i | \(-0.406534\pi\) | ||||
0.289430 | + | 0.957199i | \(0.406534\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 4.87930i | − 0.351219i | −0.984460 | − | 0.175610i | \(-0.943810\pi\) | ||||
0.984460 | − | 0.175610i | \(-0.0561897\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.88617 | −0.205631 | −0.102816 | − | 0.994700i | \(-0.532785\pi\) | ||||
−0.102816 | + | 0.994700i | \(0.532785\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −17.6742 | −1.25289 | −0.626445 | − | 0.779466i | \(-0.715491\pi\) | ||||
−0.626445 | + | 0.779466i | \(0.715491\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.00000 | 0.282138 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.88273 | −0.132142 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.05863i | 0.0735801i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.76203 | 0.329396 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.9379i | 1.64795i | 0.566623 | + | 0.823977i | \(0.308250\pi\) | ||||
−0.566623 | + | 0.823977i | \(0.691750\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 12.9966 | 0.890510 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 3.34836i | − 0.227302i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 6.00000i | − 0.405442i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 41.9931i | − 2.82476i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 24.0552i | 1.61086i | 0.592694 | + | 0.805428i | \(0.298064\pi\) | ||||
−0.592694 | + | 0.805428i | \(0.701936\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.1138 | −0.737651 | −0.368825 | − | 0.929499i | \(-0.620240\pi\) | ||||
−0.368825 | + | 0.929499i | \(0.620240\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.2311i | 1.13866i | 0.822108 | + | 0.569331i | \(0.192798\pi\) | ||||
−0.822108 | + | 0.569331i | \(0.807202\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.23453 | 0.278612 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 8.44309i | − 0.553125i | −0.960996 | − | 0.276562i | \(-0.910805\pi\) | ||||
0.960996 | − | 0.276562i | \(-0.0891953\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 11.5569 | 0.750702 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.1173 | 0.654432 | 0.327216 | − | 0.944950i | \(-0.393890\pi\) | ||||
0.327216 | + | 0.944950i | \(0.393890\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.8793 | 1.08729 | 0.543646 | − | 0.839315i | \(-0.317044\pi\) | ||||
0.543646 | + | 0.839315i | \(0.317044\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.88273i | 0.374309i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.88273 | 0.372803 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 11.8466i | − 0.747753i | −0.927478 | − | 0.373877i | \(-0.878028\pi\) | ||||
0.927478 | − | 0.373877i | \(-0.121972\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.76203 | 0.299386 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.6707i | 0.665623i | 0.942993 | + | 0.332811i | \(0.107997\pi\) | ||||
−0.942993 | + | 0.332811i | \(0.892003\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 7.00344i | − 0.435172i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.00000i | 0.123797i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.94480i | 0.119922i | 0.998201 | + | 0.0599609i | \(0.0190976\pi\) | ||||
−0.998201 | + | 0.0599609i | \(0.980902\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.11727 | 0.251973 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 9.76547i | − 0.595411i | −0.954658 | − | 0.297706i | \(-0.903779\pi\) | ||||
0.954658 | − | 0.297706i | \(-0.0962214\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.44652 | −0.209361 | −0.104681 | − | 0.994506i | \(-0.533382\pi\) | ||||
−0.104681 | + | 0.994506i | \(0.533382\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.23109i | 0.316600i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18.7880 | −1.12886 | −0.564431 | − | 0.825480i | \(-0.690904\pi\) | ||||
−0.564431 | + | 0.825480i | \(0.690904\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.55691 | −0.212947 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.8793 | −1.00693 | −0.503467 | − | 0.864014i | \(-0.667943\pi\) | ||||
−0.503467 | + | 0.864014i | \(0.667943\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 20.0000 | 1.18888 | 0.594438 | − | 0.804141i | \(-0.297374\pi\) | ||||
0.594438 | + | 0.804141i | \(0.297374\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 3.65508i | − 0.215752i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −40.1070 | −2.35923 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 17.1138i | − 1.00323i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 20.2277 | 1.18171 | 0.590856 | − | 0.806777i | \(-0.298790\pi\) | ||||
0.590856 | + | 0.806777i | \(0.298790\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 4.49828i | − 0.261017i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.88273i | 0.340207i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 1.77234i | − 0.102156i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.00000i | 0.114897i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.11039 | −0.462884 | −0.231442 | − | 0.972849i | \(-0.574344\pi\) | ||||
−0.231442 | + | 0.972849i | \(0.574344\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 10.1725i | − 0.578691i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −31.8759 | −1.80751 | −0.903757 | − | 0.428046i | \(-0.859202\pi\) | ||||
−0.903757 | + | 0.428046i | \(0.859202\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 5.11383i | − 0.289051i | −0.989501 | − | 0.144525i | \(-0.953834\pi\) | ||||
0.989501 | − | 0.144525i | \(-0.0461655\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 24.6448 | 1.38419 | 0.692094 | − | 0.721807i | \(-0.256688\pi\) | ||||
0.692094 | + | 0.721807i | \(0.256688\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.99656 | 0.503711 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 17.2311 | 0.961746 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.00000 | 0.445132 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 1.88273i | − 0.104115i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 9.46563 | 0.521857 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.0518i | 0.607460i | 0.952758 | + | 0.303730i | \(0.0982320\pi\) | ||||
−0.952758 | + | 0.303730i | \(0.901768\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −7.43965 | −0.407690 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 19.9931i | 1.08909i | 0.838730 | + | 0.544547i | \(0.183299\pi\) | ||||
−0.838730 | + | 0.544547i | \(0.816701\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 15.3224i | 0.832198i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 16.0000i | 0.866449i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.3449i | 0.666563i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.87930 | 0.369300 | 0.184650 | − | 0.982804i | \(-0.440885\pi\) | ||||
0.184650 | + | 0.982804i | \(0.440885\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.76203i | 0.254906i | 0.991845 | + | 0.127453i | \(0.0406801\pi\) | ||||
−0.991845 | + | 0.127453i | \(0.959320\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.55691 | 0.296606 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 3.79145i | − 0.201798i | −0.994897 | − | 0.100899i | \(-0.967828\pi\) | ||||
0.994897 | − | 0.100899i | \(-0.0321720\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 7.11383 | 0.376504 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −12.9966 | −0.685932 | −0.342966 | − | 0.939348i | \(-0.611432\pi\) | ||||
−0.342966 | + | 0.939348i | \(0.611432\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.8793 | 0.941016 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −9.23453 | −0.484687 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 22.9345i | 1.19717i | 0.801059 | + | 0.598585i | \(0.204270\pi\) | ||||
−0.801059 | + | 0.598585i | \(0.795730\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.88273 | −0.202127 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 1.88273i | − 0.0977467i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −15.4396 | −0.799435 | −0.399717 | − | 0.916638i | \(-0.630892\pi\) | ||||
−0.399717 | + | 0.916638i | \(0.630892\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 11.1138i | 0.572391i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 6.28973i | − 0.323082i | −0.986866 | − | 0.161541i | \(-0.948354\pi\) | ||||
0.986866 | − | 0.161541i | \(-0.0516463\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 18.1725i | − 0.931003i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 2.94137i | − 0.150297i | −0.997172 | − | 0.0751484i | \(-0.976057\pi\) | ||||
0.997172 | − | 0.0751484i | \(-0.0239431\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.88273 | −0.0957047 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 12.2277i | − 0.619967i | −0.950742 | − | 0.309983i | \(-0.899676\pi\) | ||||
0.950742 | − | 0.309983i | \(-0.100324\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.00000 | 0.404577 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.38101i | 0.321880i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.32238 | −0.267123 | −0.133561 | − | 0.991041i | \(-0.542641\pi\) | ||||
−0.133561 | + | 0.991041i | \(0.542641\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.996562 | −0.0498905 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.99656 | 0.349392 | 0.174696 | − | 0.984622i | \(-0.444106\pi\) | ||||
0.174696 | + | 0.984622i | \(0.444106\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −19.7655 | −0.984588 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 33.4656i | 1.65883i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −16.2277 | −0.802406 | −0.401203 | − | 0.915989i | \(-0.631408\pi\) | ||||
−0.401203 | + | 0.915989i | \(0.631408\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.44309i | 0.219161i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.00000 | 0.393654 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 20.1725i | 0.987850i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 15.6121i | − 0.762701i | −0.924430 | − | 0.381351i | \(-0.875459\pi\) | ||||
0.924430 | − | 0.381351i | \(-0.124541\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 33.2311i | 1.61958i | 0.586717 | + | 0.809792i | \(0.300420\pi\) | ||||
−0.586717 | + | 0.809792i | \(0.699580\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 10.0552i | − 0.488900i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.46907 | −0.409847 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 24.9966i | − 1.20685i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.9966 | 0.626022 | 0.313011 | − | 0.949749i | \(-0.398662\pi\) | ||||
0.313011 | + | 0.949749i | \(0.398662\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 20.2277i | 0.972079i | 0.873937 | + | 0.486040i | \(0.161559\pi\) | ||||
−0.873937 | + | 0.486040i | \(0.838441\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.12070 | −0.0536106 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.43965 | −0.259620 | −0.129810 | − | 0.991539i | \(-0.541437\pi\) | ||||
−0.129810 | + | 0.991539i | \(0.541437\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.11383 | 0.291135 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −15.3484 | −0.729223 | −0.364611 | − | 0.931160i | \(-0.618798\pi\) | ||||
−0.364611 | + | 0.931160i | \(0.618798\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.00000i | 0.0945968i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4.22766 | −0.199515 | −0.0997577 | − | 0.995012i | \(-0.531807\pi\) | ||||
−0.0997577 | + | 0.995012i | \(0.531807\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 17.4656i | 0.822424i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −9.67418 | −0.454533 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 2.65164i | − 0.124038i | −0.998075 | − | 0.0620192i | \(-0.980246\pi\) | ||||
0.998075 | − | 0.0620192i | \(-0.0197540\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 7.55691i | − 0.352727i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 10.2345i | − 0.476670i | −0.971183 | − | 0.238335i | \(-0.923398\pi\) | ||||
0.971183 | − | 0.238335i | \(-0.0766016\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 19.0586i | − 0.885730i | −0.896588 | − | 0.442865i | \(-0.853962\pi\) | ||||
0.896588 | − | 0.442865i | \(-0.146038\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.11039 | 0.190206 | 0.0951031 | − | 0.995467i | \(-0.469682\pi\) | ||||
0.0951031 | + | 0.995467i | \(0.469682\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.76547i | 0.173873i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.32582 | 0.199323 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.46907i | 0.389408i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.00000 | −0.0915737 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −25.2311 | −1.15284 | −0.576419 | − | 0.817154i | \(-0.695550\pi\) | ||||
−0.576419 | + | 0.817154i | \(0.695550\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −41.3415 | −1.88501 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.996562 | −0.0453451 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 21.9379i | − 0.994102i | −0.867721 | − | 0.497051i | \(-0.834416\pi\) | ||||
0.867721 | − | 0.497051i | \(-0.165584\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6.11727 | −0.276632 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.50172i | 0.338548i | 0.985569 | + | 0.169274i | \(0.0541423\pi\) | ||||
−0.985569 | + | 0.169274i | \(0.945858\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 15.1138 | 0.680693 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 12.2345i | 0.548794i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 29.1690i | − 1.30578i | −0.757451 | − | 0.652892i | \(-0.773555\pi\) | ||||
0.757451 | − | 0.652892i | \(-0.226445\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 6.05520i | − 0.270526i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 23.9379i | 1.06734i | 0.845693 | + | 0.533670i | \(0.179187\pi\) | ||||
−0.845693 | + | 0.533670i | \(0.820813\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 17.8793 | 0.794047 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 28.6967i | − 1.27196i | −0.771706 | − | 0.635980i | \(-0.780596\pi\) | ||||
0.771706 | − | 0.635980i | \(-0.219404\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.64820 | 0.249862 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.05863i | 0.0467398i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −45.2311 | −1.98926 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −16.8793 | −0.740919 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10.0000 | 0.438108 | 0.219054 | − | 0.975713i | \(-0.429703\pi\) | ||||
0.219054 | + | 0.975713i | \(0.429703\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 25.7586 | 1.12634 | 0.563172 | − | 0.826340i | \(-0.309581\pi\) | ||||
0.563172 | + | 0.826340i | \(0.309581\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 26.8793i | 1.17088i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.8793 | 0.951274 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 8.49828i | − 0.368794i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −21.5760 | −0.934561 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 10.6155i | 0.458095i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 27.5017i | − 1.18458i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.3449i | 0.530750i | 0.964145 | + | 0.265375i | \(0.0854957\pi\) | ||||
−0.964145 | + | 0.265375i | \(0.914504\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 14.1173i | 0.605830i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.8759 | 0.849830 | 0.424915 | − | 0.905233i | \(-0.360304\pi\) | ||||
0.424915 | + | 0.905233i | \(0.360304\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 8.99656i | 0.383964i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.11727 | −0.0901986 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10.8793i | 0.462635i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.12070 | 0.132228 | 0.0661142 | − | 0.997812i | \(-0.478940\pi\) | ||||
0.0661142 | + | 0.997812i | \(0.478940\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −10.4622 | −0.442503 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −33.9931 | −1.43519 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −0.651639 | −0.0274633 | −0.0137317 | − | 0.999906i | \(-0.504371\pi\) | ||||
−0.0137317 | + | 0.999906i | \(0.504371\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.941367i | 0.0395337i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −26.9966 | −1.13175 | −0.565877 | − | 0.824489i | \(-0.691462\pi\) | ||||
−0.565877 | + | 0.824489i | \(0.691462\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 14.9414i | − 0.625277i | −0.949872 | − | 0.312638i | \(-0.898787\pi\) | ||||
0.949872 | − | 0.312638i | \(-0.101213\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.00000 | 0.334205 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.87930i | 0.369650i | 0.982771 | + | 0.184825i | \(0.0591718\pi\) | ||||
−0.982771 | + | 0.184825i | \(0.940828\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 4.87930i | − 0.202777i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.53781i | 0.229747i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.99656i | 0.372600i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.23109 | −0.0508127 | −0.0254064 | − | 0.999677i | \(-0.508088\pi\) | ||||
−0.0254064 | + | 0.999677i | \(0.508088\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 3.76547i | − 0.155153i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.88617 | −0.118721 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.55691i | 0.146065i | 0.997330 | + | 0.0730325i | \(0.0232677\pi\) | ||||
−0.997330 | + | 0.0730325i | \(0.976732\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −17.6742 | −0.723356 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −19.2242 | −0.785480 | −0.392740 | − | 0.919649i | \(-0.628473\pi\) | ||||
−0.392740 | + | 0.919649i | \(0.628473\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −27.7586 | −1.13230 | −0.566148 | − | 0.824303i | \(-0.691567\pi\) | ||||
−0.566148 | + | 0.824303i | \(0.691567\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.00000 | 0.162893 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.16902i | 0.290982i | 0.989360 | + | 0.145491i | \(0.0464761\pi\) | ||||
−0.989360 | + | 0.145491i | \(0.953524\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.88273 | −0.0762922 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 55.8759i | − 2.26050i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.55691 | −0.386000 | −0.193000 | − | 0.981199i | \(-0.561822\pi\) | ||||
−0.193000 | + | 0.981199i | \(0.561822\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 1.32926i | − 0.0535139i | −0.999642 | − | 0.0267569i | \(-0.991482\pi\) | ||||
0.999642 | − | 0.0267569i | \(-0.00851802\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 28.1725i | 1.13235i | 0.824286 | + | 0.566173i | \(0.191577\pi\) | ||||
−0.824286 | + | 0.566173i | \(0.808423\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.05863i | 0.0424815i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.87586i | 0.155283i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.76203 | 0.190177 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 56.2208i | 2.24167i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23.3224 | 0.928449 | 0.464225 | − | 0.885717i | \(-0.346333\pi\) | ||||
0.464225 | + | 0.885717i | \(0.346333\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 23.9379i | 0.951447i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 33.9740 | 1.34610 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 12.9966 | 0.514136 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 27.1070 | 1.07066 | 0.535330 | − | 0.844643i | \(-0.320187\pi\) | ||||
0.535330 | + | 0.844643i | \(0.320187\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20.3449 | 0.802325 | 0.401163 | − | 0.916007i | \(-0.368606\pi\) | ||||
0.401163 | + | 0.916007i | \(0.368606\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 37.6965i | 1.48200i | 0.671503 | + | 0.741002i | \(0.265649\pi\) | ||||
−0.671503 | + | 0.741002i | \(0.734351\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −38.2277 | −1.50057 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 3.34836i | − 0.131233i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 8.64476 | 0.338296 | 0.169148 | − | 0.985591i | \(-0.445898\pi\) | ||||
0.169148 | + | 0.985591i | \(0.445898\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 6.00000i | − 0.234082i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 29.2603i | 1.13982i | 0.821707 | + | 0.569910i | \(0.193022\pi\) | ||||
−0.821707 | + | 0.569910i | \(0.806978\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 28.7620i | 1.11871i | 0.828927 | + | 0.559357i | \(0.188952\pi\) | ||||
−0.828927 | + | 0.559357i | \(0.811048\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 41.9931i | − 1.63088i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.11727 | −0.0819809 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 24.0552i | 0.930028i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 40.4691 | 1.56229 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 18.0000i | − 0.693849i | −0.937893 | − | 0.346925i | \(-0.887226\pi\) | ||||
0.937893 | − | 0.346925i | \(-0.112774\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −42.8724 | −1.64772 | −0.823860 | − | 0.566793i | \(-0.808184\pi\) | ||||
−0.823860 | + | 0.566793i | \(0.808184\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 16.1104 | 0.618260 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −11.1138 | −0.425883 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −26.1173 | −0.999349 | −0.499675 | − | 0.866213i | \(-0.666547\pi\) | ||||
−0.499675 | + | 0.866213i | \(0.666547\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 17.2311i | 0.657407i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −11.1138 | −0.423403 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.29317i | 0.201362i | 0.994919 | + | 0.100681i | \(0.0321021\pi\) | ||||
−0.994919 | + | 0.100681i | \(0.967898\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.23453 | 0.160857 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 29.3415i | 1.11139i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 8.44309i | − 0.319347i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.99312i | 0.301896i | 0.988542 | + | 0.150948i | \(0.0482326\pi\) | ||||
−0.988542 | + | 0.150948i | \(0.951767\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 7.87586i | − 0.297044i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.88273 | −0.0708075 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 28.9966i | 1.08899i | 0.838764 | + | 0.544494i | \(0.183278\pi\) | ||||
−0.838764 | + | 0.544494i | \(0.816722\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 11.5569 | 0.433418 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 3.76547i | − 0.141018i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 10.1173 | 0.377836 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 26.8793 | 1.00243 | 0.501214 | − | 0.865323i | \(-0.332887\pi\) | ||||
0.501214 | + | 0.865323i | \(0.332887\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.57602 | 0.356630 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 16.8793 | 0.627748 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 41.8138i | 1.55079i | 0.631478 | + | 0.775394i | \(0.282449\pi\) | ||||
−0.631478 | + | 0.775394i | \(0.717551\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 14.2277i | 0.526229i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −30.0844 | −1.11119 | −0.555597 | − | 0.831452i | \(-0.687510\pi\) | ||||
−0.555597 | + | 0.831452i | \(0.687510\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 17.9931i | − 0.662785i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 29.0449i | 1.06843i | 0.845348 | + | 0.534217i | \(0.179393\pi\) | ||||
−0.845348 | + | 0.534217i | \(0.820607\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.88273i | 0.216108i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 43.2863i | 1.58802i | 0.607905 | + | 0.794010i | \(0.292010\pi\) | ||||
−0.607905 | + | 0.794010i | \(0.707990\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.88273 | 0.215238 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 16.2208i | 0.592694i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −41.7846 | −1.52474 | −0.762370 | − | 0.647141i | \(-0.775964\pi\) | ||||
−0.762370 | + | 0.647141i | \(0.775964\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − 11.8466i | − 0.431716i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16.3258 | −0.593372 | −0.296686 | − | 0.954975i | \(-0.595881\pi\) | ||||
−0.296686 | + | 0.954975i | \(0.595881\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.76203 | 0.172851 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 50.2208 | 1.82050 | 0.910251 | − | 0.414057i | \(-0.135889\pi\) | ||||
0.910251 | + | 0.414057i | \(0.135889\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.77234 | 0.0641631 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 47.2242i | − 1.70517i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 31.3415 | 1.13020 | 0.565101 | − | 0.825021i | \(-0.308837\pi\) | ||||
0.565101 | + | 0.825021i | \(0.308837\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.6707i | 0.384297i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 9.11383 | 0.327802 | 0.163901 | − | 0.986477i | \(-0.447592\pi\) | ||||
0.163901 | + | 0.986477i | \(0.447592\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − 7.00344i | − 0.251247i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 4.11039i | − 0.147270i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 58.4622i | − 2.09194i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.00000i | 0.0714742i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −36.2208 | −1.29113 | −0.645566 | − | 0.763705i | \(-0.723378\pi\) | ||||
−0.645566 | + | 0.763705i | \(0.723378\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.94480i | 0.0692369i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −14.4240 | −0.512858 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 49.9931i | 1.77531i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 10.0000 | 0.354218 | 0.177109 | − | 0.984191i | \(-0.443325\pi\) | ||||
0.177109 | + | 0.984191i | \(0.443325\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −75.9862 | −2.68820 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.11727 | 0.145476 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −26.9897 | −0.952445 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 9.76547i | − 0.343761i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −47.5760 | −1.67268 | −0.836342 | − | 0.548208i | \(-0.815310\pi\) | ||||
−0.836342 | + | 0.548208i | \(0.815310\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 20.5174i | − 0.720463i | −0.932863 | − | 0.360231i | \(-0.882698\pi\) | ||||
0.932863 | − | 0.360231i | \(-0.117302\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.44652 | −0.120875 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 1.99312i | − 0.0697306i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.23109i | 0.182789i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 44.4622i | 1.55174i | 0.630892 | + | 0.775871i | \(0.282689\pi\) | ||||
−0.630892 | + | 0.775871i | \(0.717311\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 32.1656i | − 1.12122i | −0.828079 | − | 0.560611i | \(-0.810566\pi\) | ||||
0.828079 | − | 0.560611i | \(-0.189434\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 20.0000 | 0.695468 | 0.347734 | − | 0.937593i | \(-0.386951\pi\) | ||||
0.347734 | + | 0.937593i | \(0.386951\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 33.8827i | − 1.17680i | −0.808571 | − | 0.588398i | \(-0.799759\pi\) | ||||
0.808571 | − | 0.588398i | \(-0.200241\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −18.7880 | −0.651749 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 46.2017i | − 1.60079i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.55691 | −0.122945 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4.52750 | 0.156307 | 0.0781533 | − | 0.996941i | \(-0.475098\pi\) | ||||
0.0781533 | + | 0.996941i | \(0.475098\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25.0000 | 0.862069 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −16.8793 | −0.581354 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 8.69308i | − 0.298698i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 20.0000 | 0.686398 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 7.87586i | − 0.269981i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 50.4293 | 1.72667 | 0.863334 | − | 0.504633i | \(-0.168372\pi\) | ||||
0.863334 | + | 0.504633i | \(0.168372\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 26.4362i | − 0.903044i | −0.892260 | − | 0.451522i | \(-0.850881\pi\) | ||||
0.892260 | − | 0.451522i | \(-0.149119\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.406994i | 0.0138865i | 0.999976 | + | 0.00694323i | \(0.00221012\pi\) | ||||
−0.999976 | + | 0.00694323i | \(0.997790\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 3.65508i | − 0.124565i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 29.9311i | 1.01886i | 0.860511 | + | 0.509432i | \(0.170145\pi\) | ||||
−0.860511 | + | 0.509432i | \(0.829855\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −40.1070 | −1.36210 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 51.9862i | − 1.76351i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 22.2277 | 0.753155 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 17.1138i | − 0.579215i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −11.2051 | −0.378370 | −0.189185 | − | 0.981941i | \(-0.560585\pi\) | ||||
−0.189185 | + | 0.981941i | \(0.560585\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 20.2277 | 0.682262 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −48.3380 | −1.62855 | −0.814275 | − | 0.580479i | \(-0.802865\pi\) | ||||
−0.814275 | + | 0.580479i | \(0.802865\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −50.5726 | −1.70190 | −0.850951 | − | 0.525244i | \(-0.823974\pi\) | ||||
−0.850951 | + | 0.525244i | \(0.823974\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 48.0483i | − 1.61330i | −0.591026 | − | 0.806652i | \(-0.701277\pi\) | ||||
0.591026 | − | 0.806652i | \(-0.298723\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 17.1070 | 0.573749 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 4.49828i | − 0.150698i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 10.6448 | 0.356213 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.88273i | 0.196419i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 7.11383i | − 0.237259i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15.1138i | 0.503515i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 1.77234i | − 0.0589799i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.46219 | 0.214573 | 0.107287 | − | 0.994228i | \(-0.465784\pi\) | ||||
0.107287 | + | 0.994228i | \(0.465784\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.00000i | 0.0663358i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −50.3380 | −1.66777 | −0.833887 | − | 0.551935i | \(-0.813890\pi\) | ||||
−0.833887 | + | 0.551935i | \(0.813890\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 26.4622i | − 0.875771i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −6.00688 | −0.198365 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 46.4362 | 1.53179 | 0.765895 | − | 0.642966i | \(-0.222296\pi\) | ||||
0.765895 | + | 0.642966i | \(0.222296\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8.11039 | −0.267246 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 72.2208 | 2.37718 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 10.1725i | − 0.334107i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 35.9931 | 1.18090 | 0.590448 | − | 0.807076i | \(-0.298951\pi\) | ||||
0.590448 | + | 0.807076i | \(0.298951\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.47230i | 0.212121i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −31.8759 | −1.04357 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 2.70360i | − 0.0883227i | −0.999024 | − | 0.0441613i | \(-0.985938\pi\) | ||||
0.999024 | − | 0.0441613i | \(-0.0140616\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 5.11383i | − 0.166883i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 17.7655i | − 0.579138i | −0.957157 | − | 0.289569i | \(-0.906488\pi\) | ||||
0.957157 | − | 0.289569i | \(-0.0935119\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 4.11039i | − 0.133853i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 26.2277 | 0.852284 | 0.426142 | − | 0.904656i | \(-0.359872\pi\) | ||||
0.426142 | + | 0.904656i | \(0.359872\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 33.3415i | − 1.08231i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 24.6448 | 0.799161 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 9.09472i | 0.294607i | 0.989091 | + | 0.147304i | \(0.0470594\pi\) | ||||
−0.989091 | + | 0.147304i | \(0.952941\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 8.99656 | 0.290818 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.18257 | −0.135062 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −18.3484 | −0.591883 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 17.2311 | 0.555264 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 7.47574i | − 0.240404i | −0.992749 | − | 0.120202i | \(-0.961646\pi\) | ||||
0.992749 | − | 0.120202i | \(-0.0383542\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8.00000 | 0.256997 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 41.0777i | 1.31825i | 0.752035 | + | 0.659124i | \(0.229073\pi\) | ||||
−0.752035 | + | 0.659124i | \(0.770927\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −18.9897 | −0.608781 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.20855i | 0.134644i | 0.997731 | + | 0.0673218i | \(0.0214454\pi\) | ||||
−0.997731 | + | 0.0673218i | \(0.978555\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 18.5206i | − 0.591922i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 1.88273i | − 0.0601111i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 8.35504i | 0.266484i | 0.991084 | + | 0.133242i | \(0.0425388\pi\) | ||||
−0.991084 | + | 0.133242i | \(0.957461\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 9.46563 | 0.301294 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 1.99312i | − 0.0633777i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13.9087 | 0.441825 | 0.220912 | − | 0.975294i | \(-0.429097\pi\) | ||||
0.220912 | + | 0.975294i | \(0.429097\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 11.0518i | 0.350717i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 34.8984 | 1.10524 | 0.552622 | − | 0.833432i | \(-0.313627\pi\) | ||||
0.552622 | + | 0.833432i | \(0.313627\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7.43965 | −0.235380 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))