Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1800,2,Mod(1549,1800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1800, 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("1800.1549");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1800.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: | \(14.3730723638\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 120) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1549.2 | ||
Root | \(0.264658 + 1.38923i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1800.1549 |
Dual form | 1800.2.d.q.1549.1 |
$q$-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 \(\left(\mathbb{Z}/1800\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1001\) | \(1351\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.38923 | + | 0.264658i | −0.982333 | + | 0.187142i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.85991 | − | 0.735342i | 0.929956 | − | 0.367671i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 0.941367i | − | 0.355803i | −0.984048 | − | 0.177902i | \(-0.943069\pi\) | ||
0.984048 | − | 0.177902i | \(-0.0569309\pi\) | |||||||
\(8\) | −2.38923 | + | 1.51380i | −0.844720 | + | 0.535209i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 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 | \(0.219954\pi\) | |||||||
\(14\) | 0.249141 | + | 1.30777i | 0.0665856 | + | 0.349517i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.91855 | − | 2.73534i | 0.729636 | − | 0.683835i | ||||
\(17\) | 7.55691i | 1.83282i | 0.400240 | + | 0.916410i | \(0.368927\pi\) | ||||
−0.400240 | + | 0.916410i | \(0.631073\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 1.05863i | − | 0.242867i | −0.992600 | − | 0.121434i | \(-0.961251\pi\) | ||
0.992600 | − | 0.121434i | \(-0.0387491\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.19051 | + | 6.24914i | 0.253817 | + | 1.33232i | ||||
\(23\) | 1.05863i | 0.220740i | 0.993891 | + | 0.110370i | \(0.0352036\pi\) | ||||
−0.993891 | + | 0.110370i | \(0.964796\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −7.71982 | + | 1.47068i | −1.51398 | + | 0.288425i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.692226 | − | 1.75086i | −0.130818 | − | 0.330881i | ||||
\(29\) | − | 2.00000i | − | 0.371391i | −0.982607 | − | 0.185695i | \(-0.940546\pi\) | ||
0.982607 | − | 0.185695i | \(-0.0594537\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.55691 | 0.638841 | 0.319420 | − | 0.947613i | \(-0.396512\pi\) | ||||
0.319420 | + | 0.947613i | \(0.396512\pi\) | |||||||
\(32\) | −3.33060 | + | 4.57243i | −0.588772 | + | 0.808299i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.00000 | − | 10.4983i | −0.342997 | − | 1.80044i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.43965 | −1.22307 | −0.611535 | − | 0.791217i | \(-0.709448\pi\) | ||||
−0.611535 | + | 0.791217i | \(0.709448\pi\) | |||||||
\(38\) | 0.280176 | + | 1.47068i | 0.0454506 | + | 0.238576i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.88273 | 0.606381 | 0.303191 | − | 0.952930i | \(-0.401948\pi\) | ||||
0.303191 | + | 0.952930i | \(0.401948\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.88273 | 0.287114 | 0.143557 | − | 0.989642i | \(-0.454146\pi\) | ||||
0.143557 | + | 0.989642i | \(0.454146\pi\) | |||||||
\(44\) | −3.30777 | − | 8.36641i | −0.498666 | − | 1.26128i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.280176 | − | 1.47068i | −0.0413097 | − | 0.216840i | ||||
\(47\) | − | 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 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 10.3354 | − | 4.08623i | 1.43326 | − | 0.566658i | ||||
\(53\) | 2.00000 | 0.274721 | 0.137361 | − | 0.990521i | \(-0.456138\pi\) | ||||
0.137361 | + | 0.990521i | \(0.456138\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.42504 | + | 2.24914i | 0.190429 | + | 0.300554i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.529317 | + | 2.77846i | 0.0695027 | + | 0.364829i | ||||
\(59\) | − | 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 | \(0.804634\pi\) | |||||||
\(62\) | −4.94137 | + | 0.941367i | −0.627554 | + | 0.119554i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 3.41683 | − | 7.23362i | 0.427103 | − | 0.904203i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.00000 | −0.488678 | −0.244339 | − | 0.969690i | \(-0.578571\pi\) | ||||
−0.244339 | + | 0.969690i | \(0.578571\pi\) | |||||||
\(68\) | 5.55691 | + | 14.0552i | 0.673875 | + | 1.70444i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 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 | \(-0.114200\pi\) | |||||||
\(74\) | 10.3354 | − | 1.96896i | 1.20146 | − | 0.228887i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.778457 | − | 1.96896i | −0.0892952 | − | 0.225856i | ||||
\(77\) | −4.23453 | −0.482570 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.5569 | −1.30025 | −0.650127 | − | 0.759825i | \(-0.725284\pi\) | ||||
−0.650127 | + | 0.759825i | \(0.725284\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −5.39400 | + | 1.02760i | −0.595668 | + | 0.113479i | ||||
\(83\) | 5.88273 | 0.645714 | 0.322857 | − | 0.946448i | \(-0.395357\pi\) | ||||
0.322857 | + | 0.946448i | \(0.395357\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.61555 | + | 0.498281i | −0.282042 | + | 0.0537310i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 6.80949 | + | 10.7474i | 0.725894 | + | 1.14568i | ||||
\(89\) | −4.11727 | −0.436429 | −0.218215 | − | 0.975901i | \(-0.570023\pi\) | ||||
−0.218215 | + | 0.975901i | \(0.570023\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 5.23109i | − | 0.548368i | ||||||
\(92\) | 0.778457 | + | 1.96896i | 0.0811598 | + | 0.205279i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.66119 | + | 13.9690i | 0.274481 | + | 1.44079i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 17.1138i | − | 1.73765i | −0.495123 | − | 0.868823i | \(-0.664877\pi\) | ||
0.495123 | − | 0.868823i | \(-0.335123\pi\) | |||||||
\(98\) | −8.49351 | + | 1.61808i | −0.857974 | + | 0.163450i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 2.00000i | − | 0.199007i | −0.995037 | − | 0.0995037i | \(-0.968274\pi\) | ||
0.995037 | − | 0.0995037i | \(-0.0317255\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.1725i | 1.00232i | 0.865354 | + | 0.501161i | \(0.167094\pi\) | ||||
−0.865354 | + | 0.501161i | \(0.832906\pi\) | |||||||
\(104\) | −13.2767 | + | 8.41205i | −1.30189 | + | 0.824869i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.77846 | + | 0.529317i | −0.269868 | + | 0.0514118i | ||||
\(107\) | 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 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.57496 | − | 2.74742i | −0.243311 | − | 0.259607i | ||||
\(113\) | − | 15.3224i | − | 1.44141i | −0.693243 | − | 0.720704i | \(-0.743819\pi\) | ||
0.693243 | − | 0.720704i | \(-0.256181\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.47068 | − | 3.71982i | −0.136550 | − | 0.345377i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.24914 | + | 11.8061i | 0.207050 | + | 1.08684i | ||||
\(119\) | 7.11383 | 0.652124 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.23453 | −0.839503 | ||||||||
\(122\) | −2.38101 | − | 12.4983i | −0.215567 | − | 1.13154i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 6.61555 | − | 2.61555i | 0.594094 | − | 0.234883i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18.1725i | 1.61255i | 0.591544 | + | 0.806273i | \(0.298519\pi\) | ||||
−0.591544 | + | 0.806273i | \(0.701481\pi\) | |||||||
\(128\) | −2.83231 | + | 10.9534i | −0.250344 | + | 0.968157i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 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 | ||||||||
\(134\) | 5.55691 | − | 1.05863i | 0.480044 | − | 0.0914520i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −11.4396 | − | 18.0552i | −0.980942 | − | 1.54822i | ||||
\(137\) | − | 4.44309i | − | 0.379598i | −0.981823 | − | 0.189799i | \(-0.939216\pi\) | ||
0.981823 | − | 0.189799i | \(-0.0607837\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 20.1725i | − | 1.71101i | −0.517798 | − | 0.855503i | \(-0.673248\pi\) | ||
0.517798 | − | 0.855503i | \(-0.326752\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −18.0552 | + | 3.43965i | −1.51516 | + | 0.288649i | ||||
\(143\) | − | 24.9966i | − | 2.09032i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.58795 | + | 8.33537i | 0.131420 | + | 0.689840i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −13.8371 | + | 5.47068i | −1.13740 | + | 0.449687i | ||||
\(149\) | − | 2.00000i | − | 0.163846i | −0.996639 | − | 0.0819232i | \(-0.973894\pi\) | ||
0.996639 | − | 0.0819232i | \(-0.0261062\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.67418 | 0.787274 | 0.393637 | − | 0.919266i | \(-0.371217\pi\) | ||||
0.393637 | + | 0.919266i | \(0.371217\pi\) | |||||||
\(152\) | 1.60256 | + | 2.52932i | 0.129985 | + | 0.205155i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 5.88273 | − | 1.12070i | 0.474044 | − | 0.0903089i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.32582 | 0.345238 | 0.172619 | − | 0.984989i | \(-0.444777\pi\) | ||||
0.172619 | + | 0.984989i | \(0.444777\pi\) | |||||||
\(158\) | 16.0552 | − | 3.05863i | 1.27728 | − | 0.243332i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.996562 | 0.0785401 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.11727 | 0.479141 | 0.239571 | − | 0.970879i | \(-0.422993\pi\) | ||||
0.239571 | + | 0.970879i | \(0.422993\pi\) | |||||||
\(164\) | 7.22154 | − | 2.85514i | 0.563908 | − | 0.222949i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.17246 | + | 1.55691i | −0.634306 | + | 0.120840i | ||||
\(167\) | − | 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 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.50172 | − | 1.38445i | 0.267004 | − | 0.105564i | ||||
\(173\) | 16.8793 | 1.28331 | 0.641655 | − | 0.766994i | \(-0.278248\pi\) | ||||
0.641655 | + | 0.766994i | \(0.278248\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −12.3043 | − | 13.1284i | −0.927474 | − | 0.989593i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 5.71982 | − | 1.08967i | 0.428719 | − | 0.0816741i | ||||
\(179\) | 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 | \(0.824191\pi\) | |||||||
\(182\) | 1.38445 | + | 7.26719i | 0.102622 | + | 0.538680i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.60256 | − | 2.52932i | −0.118142 | − | 0.186464i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 33.9931 | 2.48582 | ||||||||
\(188\) | −7.39400 | − | 18.7018i | −0.539263 | − | 1.36397i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 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 | \(-0.0561897\pi\) | |||||||
\(194\) | 4.52932 | + | 23.7750i | 0.325186 | + | 1.70695i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 11.3712 | − | 4.49575i | 0.812227 | − | 0.321125i | ||||
\(197\) | 2.88617 | 0.205631 | 0.102816 | − | 0.994700i | \(-0.467215\pi\) | ||||
0.102816 | + | 0.994700i | \(0.467215\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 17.6742 | 1.25289 | 0.626445 | − | 0.779466i | \(-0.284509\pi\) | ||||
0.626445 | + | 0.779466i | \(0.284509\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0.529317 | + | 2.77846i | 0.0372426 | + | 0.195492i | ||||
\(203\) | −1.88273 | −0.132142 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2.69223 | − | 14.1319i | −0.187576 | − | 0.984614i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 16.2181 | − | 15.2001i | 1.12452 | − | 1.05393i | ||||
\(209\) | −4.76203 | −0.329396 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 23.9379i | − | 1.64795i | −0.566623 | − | 0.823977i | \(-0.691750\pi\) | ||
0.566623 | − | 0.823977i | \(-0.308250\pi\) | |||||||
\(212\) | 3.71982 | − | 1.47068i | 0.255479 | − | 0.101007i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −23.9379 | + | 4.56035i | −1.63636 | + | 0.311739i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 3.34836i | − | 0.227302i | ||||||
\(218\) | 0.498281 | + | 2.61555i | 0.0337479 | + | 0.177147i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 41.9931i | 2.82476i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 24.0552i | − | 1.61086i | −0.592694 | − | 0.805428i | \(-0.701936\pi\) | ||
0.592694 | − | 0.805428i | \(-0.298064\pi\) | |||||||
\(224\) | 4.30434 | + | 3.13531i | 0.287596 | + | 0.209487i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.05520 | + | 21.2863i | 0.269748 | + | 1.41594i | ||||
\(227\) | −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 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.02760 | + | 4.77846i | 0.198772 | + | 0.313721i | ||||
\(233\) | 8.44309i | 0.553125i | 0.960996 | + | 0.276562i | \(0.0891953\pi\) | ||||
−0.960996 | + | 0.276562i | \(0.910805\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −6.24914 | − | 15.8061i | −0.406784 | − | 1.02889i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −9.88273 | + | 1.88273i | −0.640602 | + | 0.122039i | ||||
\(239\) | 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 | \(0.317044\pi\) | |||||||
\(242\) | 12.8289 | − | 2.44400i | 0.824671 | − | 0.157106i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 6.61555 | + | 16.7328i | 0.423517 | + | 1.07121i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 5.88273i | − | 0.374309i | ||||||
\(248\) | −8.49828 | + | 5.38445i | −0.539641 | + | 0.341913i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 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 | ||||||||
\(254\) | −4.80949 | − | 25.2457i | −0.301774 | − | 1.58406i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.03581 | − | 15.9664i | 0.0647382 | − | 0.997902i | ||||
\(257\) | − | 10.6707i | − | 0.665623i | −0.942993 | − | 0.332811i | \(-0.892003\pi\) | ||
0.942993 | − | 0.332811i | \(-0.107997\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.00344i | 0.435172i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.68879 | − | 8.86469i | −0.104334 | − | 0.547662i | ||||
\(263\) | 1.94480i | 0.119922i | 0.998201 | + | 0.0599609i | \(0.0190976\pi\) | ||||
−0.998201 | + | 0.0599609i | \(0.980902\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.38445 | − | 0.263748i | 0.0848862 | − | 0.0161715i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −7.43965 | + | 2.94137i | −0.454449 | + | 0.179673i | ||||
\(269\) | 9.76547i | 0.595411i | 0.954658 | + | 0.297706i | \(0.0962214\pi\) | ||||
−0.954658 | + | 0.297706i | \(0.903779\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.44652 | 0.209361 | 0.104681 | − | 0.994506i | \(-0.466618\pi\) | ||||
0.104681 | + | 0.994506i | \(0.466618\pi\) | |||||||
\(272\) | 20.6707 | + | 22.0552i | 1.25335 | + | 1.33729i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.17590 | + | 6.17246i | 0.0710387 | + | 0.372892i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18.7880 | −1.12886 | −0.564431 | − | 0.825480i | \(-0.690904\pi\) | ||||
−0.564431 | + | 0.825480i | \(0.690904\pi\) | |||||||
\(278\) | 5.33881 | + | 28.0242i | 0.320200 | + | 1.68078i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.8793 | 1.00693 | 0.503467 | − | 0.864014i | \(-0.332057\pi\) | ||||
0.503467 | + | 0.864014i | \(0.332057\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −20.0000 | −1.18888 | −0.594438 | − | 0.804141i | \(-0.702626\pi\) | ||||
−0.594438 | + | 0.804141i | \(0.702626\pi\) | |||||||
\(284\) | 24.1725 | − | 9.55691i | 1.43437 | − | 0.567099i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6.61555 | + | 34.7259i | 0.391186 | + | 2.05339i | ||||
\(287\) | − | 3.65508i | − | 0.215752i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −40.1070 | −2.35923 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4.41205 | − | 11.1595i | −0.258196 | − | 0.653059i | ||||
\(293\) | −20.2277 | −1.18171 | −0.590856 | − | 0.806777i | \(-0.701210\pi\) | ||||
−0.590856 | + | 0.806777i | \(0.701210\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 17.7750 | − | 11.2621i | 1.03315 | − | 0.654598i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0.529317 | + | 2.77846i | 0.0306625 | + | 0.160952i | ||||
\(299\) | 5.88273i | 0.340207i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 1.77234i | − | 0.102156i | ||||||
\(302\) | −13.4396 | + | 2.56035i | −0.773365 | + | 0.147332i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.89572 | − | 3.08967i | −0.166081 | − | 0.177205i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.11039 | 0.462884 | 0.231442 | − | 0.972849i | \(-0.425656\pi\) | ||||
0.231442 | + | 0.972849i | \(0.425656\pi\) | |||||||
\(308\) | −7.87586 | + | 3.11383i | −0.448769 | + | 0.177427i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 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 | \(-0.0461655\pi\) | |||||||
\(314\) | −6.00955 | + | 1.14486i | −0.339139 | + | 0.0646084i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −21.4948 | + | 8.49828i | −1.20918 | + | 0.478066i | ||||
\(317\) | −24.6448 | −1.38419 | −0.692094 | − | 0.721807i | \(-0.743312\pi\) | ||||
−0.692094 | + | 0.721807i | \(0.743312\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.99656 | −0.503711 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.38445 | + | 0.263748i | −0.0771525 | + | 0.0146981i | ||||
\(323\) | 8.00000 | 0.445132 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −8.49828 | + | 1.61899i | −0.470676 | + | 0.0896673i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −9.27674 | + | 5.87768i | −0.512222 | + | 0.324540i | ||||
\(329\) | −9.46563 | −0.521857 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 11.0518i | − | 0.607460i | −0.952758 | − | 0.303730i | \(-0.901768\pi\) | ||
0.952758 | − | 0.303730i | \(-0.0982320\pi\) | |||||||
\(332\) | 10.9414 | − | 4.32582i | 0.600486 | − | 0.237410i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.60256 | + | 8.41205i | 0.0876881 | + | 0.460287i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 19.9931i | 1.08909i | 0.838730 | + | 0.544547i | \(0.183299\pi\) | ||||
−0.838730 | + | 0.544547i | \(0.816701\pi\) | |||||||
\(338\) | −24.8384 | + | 4.73190i | −1.35103 | + | 0.257382i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 16.0000i | − | 0.866449i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 12.3449i | − | 0.666563i | ||||||
\(344\) | −4.49828 | + | 2.85008i | −0.242531 | + | 0.153666i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −23.4492 | + | 4.46725i | −1.26064 | + | 0.240161i | ||||
\(347\) | 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 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 20.5681 | + | 14.9820i | 1.09628 | + | 0.798541i | ||||
\(353\) | 3.79145i | 0.201798i | 0.994897 | + | 0.100899i | \(0.0321720\pi\) | ||||
−0.994897 | + | 0.100899i | \(0.967828\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −7.65775 | + | 3.02760i | −0.405860 | + | 0.160462i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.80949 | − | 14.7474i | −0.148486 | − | 0.779425i | ||||
\(359\) | −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 | ||||||||
\(362\) | −3.73625 | − | 19.6121i | −0.196373 | − | 1.03079i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3.84664 | − | 9.72938i | −0.201619 | − | 0.509958i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 22.9345i | − | 1.19717i | −0.801059 | − | 0.598585i | \(-0.795730\pi\) | ||
0.801059 | − | 0.598585i | \(-0.204270\pi\) | |||||||
\(368\) | 2.89572 | + | 3.08967i | 0.150950 | + | 0.161060i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 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 | \(0.630892\pi\) | |||||||
\(374\) | −47.2242 | + | 8.99656i | −2.44191 | + | 0.465201i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 15.2215 | + | 24.0242i | 0.784991 | + | 1.23895i | ||||
\(377\) | − | 11.1138i | − | 0.572391i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.28973i | 0.323082i | 0.986866 | + | 0.161541i | \(0.0516463\pi\) | ||||
−0.986866 | + | 0.161541i | \(0.948354\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −11.1138 | + | 2.11727i | −0.568633 | + | 0.108329i | ||||
\(383\) | − | 2.94137i | − | 0.150297i | −0.997172 | − | 0.0751484i | \(-0.976057\pi\) | ||
0.997172 | − | 0.0751484i | \(-0.0239431\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.29135 | + | 6.77846i | 0.0657278 | + | 0.345014i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −12.5845 | − | 31.8302i | −0.638882 | − | 1.61593i | ||||
\(389\) | 12.2277i | 0.619967i | 0.950742 | + | 0.309983i | \(0.100324\pi\) | ||||
−0.950742 | + | 0.309983i | \(0.899676\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.00000 | −0.404577 | ||||||||
\(392\) | −14.6073 | + | 9.25511i | −0.737782 | + | 0.467453i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −4.00955 | + | 0.763849i | −0.201998 | + | 0.0384822i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.32238 | −0.267123 | −0.133561 | − | 0.991041i | \(-0.542641\pi\) | ||||
−0.133561 | + | 0.991041i | \(0.542641\pi\) | |||||||
\(398\) | −24.5535 | + | 4.67762i | −1.23075 | + | 0.234468i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.99656 | −0.349392 | −0.174696 | − | 0.984622i | \(-0.555894\pi\) | ||||
−0.174696 | + | 0.984622i | \(0.555894\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 19.7655 | 0.984588 | ||||||||
\(404\) | −1.47068 | − | 3.71982i | −0.0731692 | − | 0.185068i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.61555 | − | 0.498281i | 0.129807 | − | 0.0247293i | ||||
\(407\) | 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 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 7.48024 | + | 18.9199i | 0.368525 | + | 0.932116i | ||||
\(413\) | −8.00000 | −0.393654 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −18.5078 | + | 25.4086i | −0.907421 | + | 1.24576i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 6.61555 | − | 1.26031i | 0.323577 | − | 0.0616438i | ||||
\(419\) | − | 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 | \(0.699580\pi\) | |||||||
\(422\) | 6.33537 | + | 33.2553i | 0.308401 | + | 1.61884i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4.77846 | + | 3.02760i | −0.232062 | + | 0.147033i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.46907 | 0.409847 | ||||||||
\(428\) | 32.0483 | − | 12.6707i | 1.54911 | − | 0.612463i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 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 | \(0.838441\pi\) | |||||||
\(434\) | 0.886172 | + | 4.65164i | 0.0425376 | + | 0.223286i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.38445 | − | 3.50172i | −0.0663033 | − | 0.167702i | ||||
\(437\) | 1.12070 | 0.0536106 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.43965 | 0.259620 | 0.129810 | − | 0.991539i | \(-0.458563\pi\) | ||||
0.129810 | + | 0.991539i | \(0.458563\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −11.1138 | − | 58.3380i | −0.528631 | − | 2.77486i | ||||
\(443\) | −15.3484 | −0.729223 | −0.364611 | − | 0.931160i | \(-0.618798\pi\) | ||||
−0.364611 | + | 0.931160i | \(0.618798\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 6.36641 | + | 33.4182i | 0.301458 | + | 1.58240i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −6.80949 | − | 3.21649i | −0.321718 | − | 0.151965i | ||||
\(449\) | 4.22766 | 0.199515 | 0.0997577 | − | 0.995012i | \(-0.468193\pi\) | ||||
0.0997577 | + | 0.995012i | \(0.468193\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 17.4656i | − | 0.822424i | ||||||
\(452\) | −11.2672 | − | 28.4983i | −0.529964 | − | 1.34045i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 15.4396 | − | 2.94137i | 0.724619 | − | 0.138045i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 2.65164i | − | 0.124038i | −0.998075 | − | 0.0620192i | \(-0.980246\pi\) | ||
0.998075 | − | 0.0620192i | \(-0.0197540\pi\) | |||||||
\(458\) | −4.56035 | − | 23.9379i | −0.213091 | − | 1.11855i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.2345i | 0.476670i | 0.971183 | + | 0.238335i | \(0.0766016\pi\) | ||||
−0.971183 | + | 0.238335i | \(0.923398\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19.0586i | 0.885730i | 0.896588 | + | 0.442865i | \(0.146038\pi\) | ||||
−0.896588 | + | 0.442865i | \(0.853962\pi\) | |||||||
\(464\) | −5.47068 | − | 5.83709i | −0.253970 | − | 0.270980i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.23453 | − | 11.7294i | −0.103513 | − | 0.543353i | ||||
\(467\) | 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 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 12.8647 | + | 20.3043i | 0.592145 | + | 0.934583i | ||||
\(473\) | − | 8.46907i | − | 0.389408i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 13.2311 | − | 5.23109i | 0.606446 | − | 0.239767i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −14.0552 | + | 2.67762i | −0.642870 | + | 0.122471i | ||||
\(479\) | −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 | ||||||||
\(482\) | −23.4492 | + | 4.46725i | −1.06808 | + | 0.203477i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −17.1754 | + | 6.79054i | −0.780701 | + | 0.308661i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 21.9379i | 0.994102i | 0.867721 | + | 0.497051i | \(0.165584\pi\) | ||||
−0.867721 | + | 0.497051i | \(0.834416\pi\) | |||||||
\(488\) | −13.6190 | − | 21.4948i | −0.616502 | − | 0.973026i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 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 | ||||||||
\(494\) | 1.55691 | + | 8.17246i | 0.0700489 | + | 0.367696i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 10.3810 | − | 9.72938i | 0.466121 | − | 0.436862i | ||||
\(497\) | − | 12.2345i | − | 0.548794i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 29.1690i | 1.30578i | 0.757451 | + | 0.652892i | \(0.226445\pi\) | ||||
−0.757451 | + | 0.652892i | \(0.773555\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3.13531 | + | 16.4577i | 0.139936 | + | 0.734543i | ||||
\(503\) | 23.9379i | 1.06734i | 0.845693 | + | 0.533670i | \(0.179187\pi\) | ||||
−0.845693 | + | 0.533670i | \(0.820813\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −6.61555 | + | 1.26031i | −0.294097 | + | 0.0560276i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 13.3630 | + | 33.7992i | 0.592886 | + | 1.49960i | ||||
\(509\) | 28.6967i | 1.27196i | 0.771706 | + | 0.635980i | \(0.219404\pi\) | ||||
−0.771706 | + | 0.635980i | \(0.780596\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.64820 | −0.249862 | ||||||||
\(512\) | 2.78667 | + | 22.4552i | 0.123155 | + | 0.992387i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2.82410 | + | 14.8241i | 0.124566 | + | 0.653863i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −45.2311 | −1.98926 | ||||||||
\(518\) | −1.85352 | − | 9.72938i | −0.0814389 | − | 0.427484i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.0000 | −0.438108 | −0.219054 | − | 0.975713i | \(-0.570297\pi\) | ||||
−0.219054 | + | 0.975713i | \(0.570297\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −25.7586 | −1.12634 | −0.563172 | − | 0.826340i | \(-0.690419\pi\) | ||||
−0.563172 | + | 0.826340i | \(0.690419\pi\) | |||||||
\(524\) | 4.69223 | + | 11.8681i | 0.204981 | + | 0.518461i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.514709 | − | 2.70178i | −0.0224424 | − | 0.117803i | ||||
\(527\) | 26.8793i | 1.17088i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.8793 | 0.951274 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.85352 | + | 0.732814i | −0.0803602 | + | 0.0317715i | ||||
\(533\) | 21.5760 | 0.934561 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 9.55691 | − | 6.05520i | 0.412796 | − | 0.261545i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −2.58451 | − | 13.5665i | −0.111426 | − | 0.584892i | ||||
\(539\) | − | 27.5017i | − | 1.18458i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.3449i | 0.530750i | 0.964145 | + | 0.265375i | \(0.0854957\pi\) | ||||
−0.964145 | + | 0.265375i | \(0.914504\pi\) | |||||||
\(542\) | −4.78801 | + | 0.912151i | −0.205663 | + | 0.0391802i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −34.5535 | − | 25.1690i | −1.48147 | − | 1.07911i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19.8759 | −0.849830 | −0.424915 | − | 0.905233i | \(-0.639696\pi\) | ||||
−0.424915 | + | 0.905233i | \(0.639696\pi\) | |||||||
\(548\) | −3.26719 | − | 8.26375i | −0.139567 | − | 0.353010i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.11727 | −0.0901986 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10.8793i | 0.462635i | ||||||||
\(554\) | 26.1008 | − | 4.97240i | 1.10892 | − | 0.211257i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −14.8337 | − | 37.5190i | −0.629087 | − | 1.59116i | ||||
\(557\) | −3.12070 | −0.132228 | −0.0661142 | − | 0.997812i | \(-0.521060\pi\) | ||||
−0.0661142 | + | 0.997812i | \(0.521060\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10.4622 | 0.442503 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −23.4492 | + | 4.46725i | −0.989145 | + | 0.188439i | ||||
\(563\) | −0.651639 | −0.0274633 | −0.0137317 | − | 0.999906i | \(-0.504371\pi\) | ||||
−0.0137317 | + | 0.999906i | \(0.504371\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 27.7846 | − | 5.29317i | 1.16787 | − | 0.222488i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −31.0518 | + | 19.6742i | −1.30290 | + | 0.825510i | ||||
\(569\) | 26.9966 | 1.13175 | 0.565877 | − | 0.824489i | \(-0.308538\pi\) | ||||
0.565877 | + | 0.824489i | \(0.308538\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.9414i | 0.625277i | 0.949872 | + | 0.312638i | \(0.101213\pi\) | ||||
−0.949872 | + | 0.312638i | \(0.898787\pi\) | |||||||
\(572\) | −18.3810 | − | 46.4914i | −0.768549 | − | 1.94390i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0.967346 | + | 5.07774i | 0.0403763 | + | 0.211941i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.87930i | 0.369650i | 0.982771 | + | 0.184825i | \(0.0591718\pi\) | ||||
−0.982771 | + | 0.184825i | \(0.940828\pi\) | |||||||
\(578\) | 55.7177 | − | 10.6146i | 2.31755 | − | 0.441511i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 5.53781i | − | 0.229747i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 8.99656i | − | 0.372600i | ||||||
\(584\) | 9.08279 | + | 14.3354i | 0.375849 | + | 0.593202i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 28.1008 | − | 5.35342i | 1.16083 | − | 0.221148i | ||||
\(587\) | −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 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −21.7129 | + | 20.3500i | −0.892397 | + | 0.836379i | ||||
\(593\) | − | 3.55691i | − | 0.146065i | −0.997330 | − | 0.0730325i | \(-0.976732\pi\) | ||
0.997330 | − | 0.0730325i | \(-0.0232677\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.47068 | − | 3.71982i | −0.0602415 | − | 0.152370i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.55691 | − | 8.17246i | −0.0636670 | − | 0.334197i | ||||
\(599\) | −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 | \(0.691567\pi\) | |||||||
\(602\) | 0.469065 | + | 2.46219i | 0.0191177 | + | 0.100351i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 17.9931 | − | 7.11383i | 0.732130 | − | 0.289458i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 7.16902i | − | 0.290982i | −0.989360 | − | 0.145491i | \(-0.953524\pi\) | ||
0.989360 | − | 0.145491i | \(-0.0464761\pi\) | |||||||
\(608\) | 4.84053 | + | 3.52588i | 0.196309 | + | 0.142993i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 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 | \(0.561822\pi\) | |||||||
\(614\) | −11.2672 | + | 2.14648i | −0.454707 | + | 0.0866250i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 10.1173 | − | 6.41023i | 0.407636 | − | 0.258276i | ||||
\(617\) | 1.32926i | 0.0535139i | 0.999642 | + | 0.0267569i | \(0.00851802\pi\) | ||||
−0.999642 | + | 0.0267569i | \(0.991482\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 28.1725i | − | 1.13235i | −0.824286 | − | 0.566173i | \(-0.808423\pi\) | ||
0.824286 | − | 0.566173i | \(-0.191577\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 44.2829 | − | 8.43621i | 1.77558 | − | 0.338261i | ||||
\(623\) | 3.87586i | 0.155283i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 1.35342 | + | 7.10428i | 0.0540934 | + | 0.283944i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 8.04564 | − | 3.18096i | 0.321056 | − | 0.126934i | ||||
\(629\) | − | 56.2208i | − | 2.24167i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.3224 | −0.928449 | −0.464225 | − | 0.885717i | \(-0.653667\pi\) | ||||
−0.464225 | + | 0.885717i | \(0.653667\pi\) | |||||||
\(632\) | 27.6121 | − | 17.4948i | 1.09835 | − | 0.695907i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 34.2372 | − | 6.52244i | 1.35973 | − | 0.259039i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 33.9740 | 1.34610 | ||||||||
\(638\) | 12.4983 | − | 2.38101i | 0.494812 | − | 0.0942653i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −27.1070 | −1.07066 | −0.535330 | − | 0.844643i | \(-0.679813\pi\) | ||||
−0.535330 | + | 0.844643i | \(0.679813\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −20.3449 | −0.802325 | −0.401163 | − | 0.916007i | \(-0.631394\pi\) | ||||
−0.401163 | + | 0.916007i | \(0.631394\pi\) | |||||||
\(644\) | 1.85352 | − | 0.732814i | 0.0730388 | − | 0.0288769i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −11.1138 | + | 2.11727i | −0.437268 | + | 0.0833027i | ||||
\(647\) | 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 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 11.3776 | − | 4.49828i | 0.445580 | − | 0.176166i | ||||
\(653\) | −8.64476 | −0.338296 | −0.169148 | − | 0.985591i | \(-0.554102\pi\) | ||||
−0.169148 | + | 0.985591i | \(0.554102\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 11.3319 | − | 10.6206i | 0.442438 | − | 0.414665i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 13.1499 | − | 2.50516i | 0.512637 | − | 0.0976612i | ||||
\(659\) | 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 | \(0.811048\pi\) | |||||||
\(662\) | 2.92494 | + | 15.3534i | 0.113681 | + | 0.596728i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −14.0552 | + | 8.90528i | −0.545447 | + | 0.345592i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.11727 | 0.0819809 | ||||||||
\(668\) | −4.45264 | − | 11.2621i | −0.172278 | − | 0.435745i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 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 | \(-0.112774\pi\) | |||||||
\(674\) | −5.29135 | − | 27.7750i | −0.203815 | − | 1.06985i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 33.2539 | − | 13.1474i | 1.27900 | − | 0.505669i | ||||
\(677\) | 42.8724 | 1.64772 | 0.823860 | − | 0.566793i | \(-0.191816\pi\) | ||||
0.823860 | + | 0.566793i | \(0.191816\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −16.1104 | −0.618260 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 4.23453 | + | 22.2277i | 0.162149 | + | 0.851141i | ||||
\(683\) | −26.1173 | −0.999349 | −0.499675 | − | 0.866213i | \(-0.666547\pi\) | ||||
−0.499675 | + | 0.866213i | \(0.666547\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 3.26719 | + | 17.1499i | 0.124742 | + | 0.654787i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5.49484 | − | 5.14992i | 0.209489 | − | 0.196339i | ||||
\(689\) | 11.1138 | 0.423403 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 5.29317i | − | 0.201362i | −0.994919 | − | 0.100681i | \(-0.967898\pi\) | ||
0.994919 | − | 0.100681i | \(-0.0321021\pi\) | |||||||
\(692\) | 31.3940 | − | 12.4121i | 1.19342 | − | 0.471835i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −9.55691 | + | 1.82066i | −0.362776 | + | 0.0691114i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 29.3415i | 1.11139i | ||||||||
\(698\) | −1.26031 | − | 6.61555i | −0.0477035 | − | 0.250402i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 7.99312i | − | 0.301896i | −0.988542 | − | 0.150948i | \(-0.951767\pi\) | ||
0.988542 | − | 0.150948i | \(-0.0482326\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.87586i | 0.297044i | ||||||||
\(704\) | −32.5389 | − | 15.3698i | −1.22635 | − | 0.579273i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.00344 | − | 5.26719i | −0.0377649 | − | 0.198233i | ||||
\(707\) | −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 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 9.83709 | − | 6.23271i | 0.368661 | − | 0.233581i | ||||
\(713\) | 3.76547i | 0.141018i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 7.80605 | + | 19.7440i | 0.291726 | + | 0.737867i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 18.0552 | − | 3.43965i | 0.673814 | − | 0.128367i | ||||
\(719\) | 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 | ||||||||
\(722\) | −24.8384 | + | 4.73190i | −0.924391 | + | 0.176103i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 10.3810 | + | 26.2569i | 0.385807 | + | 0.975829i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 41.8138i | − | 1.55079i | −0.631478 | − | 0.775394i | \(-0.717551\pi\) | ||
0.631478 | − | 0.775394i | \(-0.282449\pi\) | |||||||
\(728\) | 7.91883 | + | 12.4983i | 0.293491 | + | 0.463217i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 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 | \(0.687510\pi\) | |||||||
\(734\) | 6.06980 | + | 31.8613i | 0.224041 | + | 1.17602i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.84053 | − | 3.52588i | −0.178424 | − | 0.129966i | ||||
\(737\) | 17.9931i | 0.662785i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 29.0449i | − | 1.06843i | −0.845348 | − | 0.534217i | \(-0.820607\pi\) | ||
0.845348 | − | 0.534217i | \(-0.179393\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.498281 | + | 2.61555i | 0.0182925 | + | 0.0960198i | ||||
\(743\) | 43.2863i | 1.58802i | 0.607905 | + | 0.794010i | \(0.292010\pi\) | ||||
−0.607905 | + | 0.794010i | \(0.707990\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 21.4492 | − | 4.08623i | 0.785311 | − | 0.149608i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 63.2242 | − | 24.9966i | 2.31171 | − | 0.913965i | ||||
\(749\) | − | 16.2208i | − | 0.592694i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 41.7846 | 1.52474 | 0.762370 | − | 0.647141i | \(-0.224036\pi\) | ||||
0.762370 | + | 0.647141i | \(0.224036\pi\) | |||||||
\(752\) | −27.5044 | − | 29.3465i | −1.00298 | − | 1.07016i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.94137 | + | 15.4396i | 0.107118 | + | 0.562279i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16.3258 | −0.593372 | −0.296686 | − | 0.954975i | \(-0.595881\pi\) | ||||
−0.296686 | + | 0.954975i | \(0.595881\pi\) | |||||||
\(758\) | −1.66463 | − | 8.73787i | −0.0604620 | − | 0.317374i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −50.2208 | −1.82050 | −0.910251 | − | 0.414057i | \(-0.864111\pi\) | ||||
−0.910251 | + | 0.414057i | \(0.864111\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.77234 | −0.0641631 | ||||||||
\(764\) | 14.8793 | − | 5.88273i | 0.538314 | − | 0.212830i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0.778457 | + | 4.08623i | 0.0281268 | + | 0.147642i | ||||
\(767\) | − | 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 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −3.58795 | − | 9.07506i | −0.129133 | − | 0.326619i | ||||
\(773\) | −9.11383 | −0.327802 | −0.163901 | − | 0.986477i | \(-0.552408\pi\) | ||||
−0.163901 | + | 0.986477i | \(0.552408\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 25.9069 | + | 40.8888i | 0.930003 | + | 1.46782i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −3.23615 | − | 16.9870i | −0.116022 | − | 0.609014i | ||||
\(779\) | − | 4.11039i | − | 0.147270i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 58.4622i | − | 2.09194i | ||||||
\(782\) | 11.1138 | − | 2.11727i | 0.397430 | − | 0.0757133i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 17.8435 | − | 16.7234i | 0.637267 | − | 0.597265i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 36.2208 | 1.29113 | 0.645566 | − | 0.763705i | \(-0.276622\pi\) | ||||
0.645566 | + | 0.763705i | \(0.276622\pi\) | |||||||
\(788\) | 5.36802 | − | 2.12232i | 0.191228 | − | 0.0756046i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −14.4240 | −0.512858 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 49.9931i | 1.77531i | ||||||||
\(794\) | 7.39400 | − | 1.40861i | 0.262403 | − | 0.0499898i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 32.8724 | − | 12.9966i | 1.16513 | − | 0.460651i | ||||
\(797\) | −10.0000 | −0.354218 | −0.177109 | − | 0.984191i | \(-0.556675\pi\) | ||||
−0.177109 | + | 0.984191i | \(0.556675\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 75.9862 | 2.68820 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 9.71982 | − | 1.85170i | 0.343219 | − | 0.0653857i | ||||
\(803\) | −26.9897 | −0.952445 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −27.4588 | + | 5.23109i | −0.967193 | + | 0.184257i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 3.02760 | + | 4.77846i | 0.106511 | + | 0.168106i | ||||
\(809\) | 47.5760 | 1.67268 | 0.836342 | − | 0.548208i | \(-0.184690\pi\) | ||||
0.836342 | + | 0.548208i | \(0.184690\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.5174i | 0.720463i | 0.932863 | + | 0.360231i | \(0.117302\pi\) | ||||
−0.932863 | + | 0.360231i | \(0.882698\pi\) | |||||||
\(812\) | −3.50172 | + | 1.38445i | −0.122886 | + | 0.0485848i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −8.85696 | − | 46.4914i | −0.310436 | − | 1.62952i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 1.99312i | − | 0.0697306i | ||||||
\(818\) | 22.5439 | − | 4.29478i | 0.788230 | − | 0.150164i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 44.4622i | − | 1.55174i | −0.630892 | − | 0.775871i | \(-0.717311\pi\) | ||
0.630892 | − | 0.775871i | \(-0.282689\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 32.1656i | 1.12122i | 0.828079 | + | 0.560611i | \(0.189434\pi\) | ||||
−0.828079 | + | 0.560611i | \(0.810566\pi\) | |||||||
\(824\) | −15.3991 | − | 24.3043i | −0.536452 | − | 0.846682i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 11.1138 | − | 2.11727i | 0.386700 | − | 0.0736691i | ||||
\(827\) | 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 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 18.9870 | − | 40.1966i | 0.658256 | − | 1.39357i | ||||
\(833\) | 46.2017i | 1.60079i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −8.85696 | + | 3.50172i | −0.306324 | + | 0.121109i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 4.13187 | + | 21.6888i | 0.142733 | + | 0.749227i | ||||
\(839\) | 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 | ||||||||
\(842\) | −8.79488 | − | 46.1656i | −0.303092 | − | 1.59097i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −17.6026 | − | 44.5224i | −0.605905 | − | 1.53253i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.69308i | 0.298698i | ||||||||
\(848\) | 5.83709 | − | 5.47068i | 0.200447 | − | 0.187864i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 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 | \(0.168372\pi\) | |||||||
\(854\) | −11.7655 | + | 2.24141i | −0.402606 | + | 0.0766994i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −41.1690 | + | 26.0844i | −1.40713 | + | 0.891547i | ||||
\(857\) | 26.4362i | 0.903044i | 0.892260 | + | 0.451522i | \(0.149119\pi\) | ||||
−0.892260 | + | 0.451522i | \(0.850881\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 0.406994i | − | 0.0138865i | −0.999976 | − | 0.00694323i | \(-0.997790\pi\) | ||
0.999976 | − | 0.00694323i | \(-0.00221012\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −18.0552 | + | 3.43965i | −0.614962 | + | 0.117155i | ||||
\(863\) | 29.9311i | 1.01886i | 0.860511 | + | 0.509432i | \(0.170145\pi\) | ||||
−0.860511 | + | 0.509432i | \(0.829855\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −5.35342 | − | 28.1008i | −0.181917 | − | 0.954905i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.46219 | − | 6.22766i | −0.0835722 | − | 0.211380i | ||||
\(869\) | 51.9862i | 1.76351i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −22.2277 | −0.753155 | ||||||||
\(872\) | 2.85008 | + | 4.49828i | 0.0965159 | + | 0.152331i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1.55691 | + | 0.296604i | −0.0526634 | + | 0.0100328i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −11.2051 | −0.378370 | −0.189185 | − | 0.981941i | \(-0.560585\pi\) | ||||
−0.189185 | + | 0.981941i | \(0.560585\pi\) | |||||||
\(878\) | −7.55691 | + | 1.43965i | −0.255034 | + | 0.0485858i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 48.3380 | 1.62855 | 0.814275 | − | 0.580479i | \(-0.197135\pi\) | ||||
0.814275 | + | 0.580479i | \(0.197135\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 50.5726 | 1.70190 | 0.850951 | − | 0.525244i | \(-0.176026\pi\) | ||||
0.850951 | + | 0.525244i | \(0.176026\pi\) | |||||||
\(884\) | 30.8793 | + | 78.1035i | 1.03858 | + | 2.62691i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 21.3224 | − | 4.06207i | 0.716339 | − | 0.136468i | ||||
\(887\) | − | 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 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −17.6888 | − | 44.7405i | −0.592264 | − | 1.49802i | ||||
\(893\) | −10.6448 | −0.356213 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 10.3112 | + | 2.66625i | 0.344473 | + | 0.0890731i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −5.87318 | + | 1.11888i | −0.195991 | + | 0.0373377i | ||||
\(899\) | − | 7.11383i | − | 0.237259i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15.1138i | 0.503515i | ||||||||
\(902\) | 4.62242 | + | 24.2637i | 0.153910 | + | 0.807894i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 23.1950 | + | 36.6087i | 0.771454 | + | 1.21759i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6.46219 | −0.214573 | −0.107287 | − | 0.994228i | \(-0.534216\pi\) | ||||
−0.107287 | + | 0.994228i | \(0.534216\pi\) | |||||||
\(908\) | −20.6707 | + | 8.17246i | −0.685983 | + | 0.271213i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 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 | ||||||
\(914\) | 0.701778 | + | 3.68373i | 0.0232128 | + | 0.121847i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 12.6707 | + | 32.0483i | 0.418653 | + | 1.05891i | ||||
\(917\) | 6.00688 | 0.198365 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −46.4362 | −1.53179 | −0.765895 | − | 0.642966i | \(-0.777704\pi\) | ||||
−0.765895 | + | 0.642966i | \(0.777704\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −2.70865 | − | 14.2181i | −0.0892048 | − | 0.468248i | ||||
\(923\) | 72.2208 | 2.37718 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −5.04403 | − | 26.4768i | −0.165757 | − | 0.870082i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 9.14486 | + | 6.66119i | 0.300195 | + | 0.218664i | ||||
\(929\) | −35.9931 | −1.18090 | −0.590448 | − | 0.807076i | \(-0.701049\pi\) | ||||
−0.590448 | + | 0.807076i | \(0.701049\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 6.47230i | − | 0.212121i | ||||||
\(932\) | 6.20855 | + | 15.7034i | 0.203368 | + | 0.514382i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −5.71027 | + | 1.08785i | −0.186846 | + | 0.0355955i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 2.70360i | − | 0.0883227i | −0.999024 | − | 0.0441613i | \(-0.985938\pi\) | ||
0.999024 | − | 0.0441613i | \(-0.0140616\pi\) | |||||||
\(938\) | −0.996562 | − | 5.23109i | −0.0325389 | − | 0.170801i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 17.7655i | 0.579138i | 0.957157 | + | 0.289569i | \(0.0935119\pi\) | ||||
−0.957157 | + | 0.289569i | \(0.906488\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.11039i | 0.133853i | ||||||||
\(944\) | −23.2457 | − | 24.8026i | −0.756583 | − | 0.807256i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.24141 | + | 11.7655i | 0.0728745 | + | 0.382528i | ||||
\(947\) | 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 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −16.9966 | + | 10.7689i | −0.550862 | + | 0.349022i | ||||
\(953\) | − | 9.09472i | − | 0.294607i | −0.989091 | − | 0.147304i | \(-0.952941\pi\) | ||
0.989091 | − | 0.147304i | \(-0.0470594\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 18.8172 | − | 7.43965i | 0.608593 | − | 0.240615i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 35.0518 | − | 6.67762i | 1.13247 | − | 0.215744i | ||||
\(959\) | −4.18257 | −0.135062 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −18.3484 | −0.591883 | ||||||||
\(962\) | 57.4328 | − | 10.9414i | 1.85171 | − | 0.352764i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 31.3940 | − | 12.4121i | 1.01113 | − | 0.399765i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.47574i | 0.240404i | 0.992749 | + | 0.120202i | \(0.0383542\pi\) | ||||
−0.992749 | + | 0.120202i | \(0.961646\pi\) | |||||||
\(968\) | 22.0634 | − | 13.9792i | 0.709145 | − | 0.449309i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 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 | ||||||||
\(974\) | −5.80605 | − | 30.4768i | −0.186038 | − | 0.976540i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 24.6087 | + | 26.2569i | 0.787704 | + | 0.840462i | ||||
\(977\) | − | 4.20855i | − | 0.134644i | −0.997731 | − | 0.0673218i | \(-0.978555\pi\) | ||
0.997731 | − | 0.0673218i | \(-0.0214454\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 18.5206i | 0.591922i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.98539 | − | 10.4216i | −0.0633564 | − | 0.332567i | ||||
\(983\) | 8.35504i | 0.266484i | 0.991084 | + | 0.133242i | \(0.0425388\pi\) | ||||
−0.991084 | + | 0.133242i | \(0.957461\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −20.9966 | + | 4.00000i | −0.668667 | + | 0.127386i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −4.32582 | − | 10.9414i | −0.137623 | − | 0.348091i | ||||
\(989\) | 1.99312i | 0.0633777i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13.9087 | −0.441825 | −0.220912 | − | 0.975294i | \(-0.570903\pi\) | ||||
−0.220912 | + | 0.975294i | \(0.570903\pi\) | |||||||
\(992\) | −11.8466 | + | 16.2637i | −0.376131 | + | 0.516375i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 3.23797 | + | 16.9966i | 0.102702 | + | 0.539098i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 34.8984 | 1.10524 | 0.552622 | − | 0.833432i | \(-0.313627\pi\) | ||||
0.552622 | + | 0.833432i | \(0.313627\pi\) | |||||||
\(998\) | −7.71982 | − | 40.5224i | −0.244367 | − | 1.28272i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))