Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1323,2,Mod(1322,1323)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1323, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1323.1322");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1323 = 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1323.c (of order \(2\), degree \(1\), 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: | \(10.5642081874\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 24x^{14} + 212x^{12} + 872x^{10} + 1815x^{8} + 1928x^{6} + 996x^{4} + 200x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1322.5 | ||
Root | \(-0.964652i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1323.1322 |
Dual form | 1323.2.c.f.1322.11 |
$q$-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 \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 0.698626i | − 0.494003i | −0.969015 | − | 0.247001i | \(-0.920555\pi\) | ||||
0.969015 | − | 0.247001i | \(-0.0794452\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.51192 | 0.755961 | ||||||||
\(5\) | −2.26676 | −1.01372 | −0.506862 | − | 0.862027i | \(-0.669195\pi\) | ||||
−0.506862 | + | 0.862027i | \(0.669195\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − 2.45352i | − 0.867450i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.58361i | 0.500783i | ||||||||
\(11\) | 0.558767i | 0.168475i | 0.996446 | + | 0.0842373i | \(0.0268454\pi\) | ||||
−0.996446 | + | 0.0842373i | \(0.973155\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 5.53446i | − 1.53498i | −0.641060 | − | 0.767491i | \(-0.721505\pi\) | ||||
0.641060 | − | 0.767491i | \(-0.278495\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.30975 | 0.327438 | ||||||||
\(17\) | −5.74871 | −1.39427 | −0.697134 | − | 0.716941i | \(-0.745542\pi\) | ||||
−0.697134 | + | 0.716941i | \(0.745542\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 0.893030i | − 0.204875i | −0.994739 | − | 0.102438i | \(-0.967336\pi\) | ||||
0.994739 | − | 0.102438i | \(-0.0326642\pi\) | |||||||
\(20\) | −3.42716 | −0.766336 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.390369 | 0.0832269 | ||||||||
\(23\) | 6.26097i | 1.30550i | 0.757573 | + | 0.652751i | \(0.226385\pi\) | ||||
−0.757573 | + | 0.652751i | \(0.773615\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.138181 | 0.0276362 | ||||||||
\(26\) | −3.86651 | −0.758286 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 8.42510i | − 1.56450i | −0.622963 | − | 0.782251i | \(-0.714071\pi\) | ||||
0.622963 | − | 0.782251i | \(-0.285929\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 0.233422i | − 0.0419238i | −0.999780 | − | 0.0209619i | \(-0.993327\pi\) | ||||
0.999780 | − | 0.0209619i | \(-0.00667287\pi\) | |||||||
\(32\) | − 5.82206i | − 1.02921i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.01620i | 0.688772i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.37407 | 0.883492 | 0.441746 | − | 0.897140i | \(-0.354359\pi\) | ||||
0.441746 | + | 0.897140i | \(0.354359\pi\) | |||||||
\(38\) | −0.623893 | −0.101209 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 5.56153i | 0.879355i | ||||||||
\(41\) | 2.37380 | 0.370725 | 0.185363 | − | 0.982670i | \(-0.440654\pi\) | ||||
0.185363 | + | 0.982670i | \(0.440654\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.7212 | −1.78746 | −0.893731 | − | 0.448603i | \(-0.851922\pi\) | ||||
−0.893731 | + | 0.448603i | \(0.851922\pi\) | |||||||
\(44\) | 0.844812i | 0.127360i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.37407 | 0.644922 | ||||||||
\(47\) | −12.4185 | −1.81142 | −0.905711 | − | 0.423895i | \(-0.860663\pi\) | ||||
−0.905711 | + | 0.423895i | \(0.860663\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | − 0.0965369i | − 0.0136524i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − 8.36767i | − 1.16039i | ||||||||
\(53\) | − 7.77314i | − 1.06772i | −0.845572 | − | 0.533861i | \(-0.820740\pi\) | ||||
0.845572 | − | 0.533861i | \(-0.179260\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 1.26659i | − 0.170787i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.88599 | −0.772869 | ||||||||
\(59\) | 7.15404 | 0.931377 | 0.465688 | − | 0.884949i | \(-0.345807\pi\) | ||||
0.465688 | + | 0.884949i | \(0.345807\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 12.7942i | − 1.63813i | −0.573703 | − | 0.819063i | \(-0.694494\pi\) | ||||
0.573703 | − | 0.819063i | \(-0.305506\pi\) | |||||||
\(62\) | −0.163075 | −0.0207105 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.44794 | −0.180992 | ||||||||
\(65\) | 12.5453i | 1.55605i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.03093 | −0.736795 | −0.368397 | − | 0.929668i | \(-0.620093\pi\) | ||||
−0.368397 | + | 0.929668i | \(0.620093\pi\) | |||||||
\(68\) | −8.69161 | −1.05401 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 11.2259i | − 1.33227i | −0.745830 | − | 0.666137i | \(-0.767947\pi\) | ||||
0.745830 | − | 0.666137i | \(-0.232053\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.77298i | 0.207511i | 0.994603 | + | 0.103756i | \(0.0330860\pi\) | ||||
−0.994603 | + | 0.103756i | \(0.966914\pi\) | |||||||
\(74\) | − 3.75446i | − 0.436447i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − 1.35019i | − 0.154878i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.77119 | −0.649310 | −0.324655 | − | 0.945833i | \(-0.605248\pi\) | ||||
−0.324655 | + | 0.945833i | \(0.605248\pi\) | |||||||
\(80\) | −2.96889 | −0.331932 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − 1.65840i | − 0.183139i | ||||||||
\(83\) | 0.913671 | 0.100288 | 0.0501442 | − | 0.998742i | \(-0.484032\pi\) | ||||
0.0501442 | + | 0.998742i | \(0.484032\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 13.0309 | 1.41340 | ||||||||
\(86\) | 8.18871i | 0.883011i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.37094 | 0.146143 | ||||||||
\(89\) | 2.80582 | 0.297416 | 0.148708 | − | 0.988881i | \(-0.452489\pi\) | ||||
0.148708 | + | 0.988881i | \(0.452489\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 9.46610i | 0.986909i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 8.67587i | 0.894848i | ||||||||
\(95\) | 2.02428i | 0.207687i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.5775i | 1.27705i | 0.769601 | + | 0.638525i | \(0.220455\pi\) | ||||
−0.769601 | + | 0.638525i | \(0.779545\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.208919 | 0.0208919 | ||||||||
\(101\) | −0.952418 | −0.0947692 | −0.0473846 | − | 0.998877i | \(-0.515089\pi\) | ||||
−0.0473846 | + | 0.998877i | \(0.515089\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.44270i | 0.831884i | 0.909391 | + | 0.415942i | \(0.136548\pi\) | ||||
−0.909391 | + | 0.415942i | \(0.863452\pi\) | |||||||
\(104\) | −13.5789 | −1.33152 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.43051 | −0.527458 | ||||||||
\(107\) | 8.71449i | 0.842461i | 0.906954 | + | 0.421231i | \(0.138402\pi\) | ||||
−0.906954 | + | 0.421231i | \(0.861598\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.81213 | −0.173571 | −0.0867853 | − | 0.996227i | \(-0.527659\pi\) | ||||
−0.0867853 | + | 0.996227i | \(0.527659\pi\) | |||||||
\(110\) | −0.884871 | −0.0843691 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 14.0108i | − 1.31802i | −0.752133 | − | 0.659011i | \(-0.770975\pi\) | ||||
0.752133 | − | 0.659011i | \(-0.229025\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 14.1921i | − 1.32342i | ||||||||
\(116\) | − 12.7381i | − 1.18270i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − 4.99800i | − 0.460103i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.6878 | 0.971616 | ||||||||
\(122\) | −8.93834 | −0.809239 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − 0.352916i | − 0.0316928i | ||||||||
\(125\) | 11.0206 | 0.985708 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18.8192 | 1.66993 | 0.834967 | − | 0.550299i | \(-0.185486\pi\) | ||||
0.834967 | + | 0.550299i | \(0.185486\pi\) | |||||||
\(128\) | − 10.6326i | − 0.939795i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 8.76444 | 0.768692 | ||||||||
\(131\) | −0.836235 | −0.0730622 | −0.0365311 | − | 0.999333i | \(-0.511631\pi\) | ||||
−0.0365311 | + | 0.999333i | \(0.511631\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 4.21336i | 0.363979i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 14.1046i | 1.20946i | ||||||||
\(137\) | 10.2613i | 0.876678i | 0.898810 | + | 0.438339i | \(0.144433\pi\) | ||||
−0.898810 | + | 0.438339i | \(0.855567\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 12.0668i | − 1.02350i | −0.859136 | − | 0.511748i | \(-0.828998\pi\) | ||||
0.859136 | − | 0.511748i | \(-0.171002\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −7.84272 | −0.658147 | ||||||||
\(143\) | 3.09247 | 0.258605 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 19.0977i | 1.58597i | ||||||||
\(146\) | 1.23865 | 0.102511 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 8.12518 | 0.667886 | ||||||||
\(149\) | − 20.4060i | − 1.67172i | −0.548940 | − | 0.835862i | \(-0.684968\pi\) | ||||
0.548940 | − | 0.835862i | \(-0.315032\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.9337 | −1.37804 | −0.689022 | − | 0.724741i | \(-0.741960\pi\) | ||||
−0.689022 | + | 0.724741i | \(0.741960\pi\) | |||||||
\(152\) | −2.19106 | −0.177719 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.529111i | 0.0424992i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.3192i | 1.46203i | 0.682361 | + | 0.731016i | \(0.260953\pi\) | ||||
−0.682361 | + | 0.731016i | \(0.739047\pi\) | |||||||
\(158\) | 4.03190i | 0.320761i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 13.1972i | 1.04333i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.98370 | −0.547006 | −0.273503 | − | 0.961871i | \(-0.588182\pi\) | ||||
−0.273503 | + | 0.961871i | \(0.588182\pi\) | |||||||
\(164\) | 3.58900 | 0.280254 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − 0.638314i | − 0.0495427i | ||||||||
\(167\) | 11.5922 | 0.897032 | 0.448516 | − | 0.893775i | \(-0.351953\pi\) | ||||
0.448516 | + | 0.893775i | \(0.351953\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −17.6302 | −1.35617 | ||||||||
\(170\) | − 9.10374i | − 0.698225i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −17.7215 | −1.35125 | ||||||||
\(173\) | 1.66805 | 0.126820 | 0.0634098 | − | 0.997988i | \(-0.479802\pi\) | ||||
0.0634098 | + | 0.997988i | \(0.479802\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.731847i | 0.0551651i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − 1.96022i | − 0.146924i | ||||||||
\(179\) | 13.2059i | 0.987059i | 0.869729 | + | 0.493529i | \(0.164293\pi\) | ||||
−0.869729 | + | 0.493529i | \(0.835707\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.51772i | 0.410129i | 0.978748 | + | 0.205064i | \(0.0657404\pi\) | ||||
−0.978748 | + | 0.205064i | \(0.934260\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 15.3614 | 1.13246 | ||||||||
\(185\) | −12.1817 | −0.895617 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 3.21219i | − 0.234899i | ||||||||
\(188\) | −18.7758 | −1.36937 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.41421 | 0.102598 | ||||||||
\(191\) | 8.62690i | 0.624220i | 0.950046 | + | 0.312110i | \(0.101036\pi\) | ||||
−0.950046 | + | 0.312110i | \(0.898964\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.95986 | 0.572963 | 0.286482 | − | 0.958086i | \(-0.407514\pi\) | ||||
0.286482 | + | 0.958086i | \(0.407514\pi\) | |||||||
\(194\) | 8.78696 | 0.630867 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.95188i | 0.709042i | 0.935048 | + | 0.354521i | \(0.115356\pi\) | ||||
−0.935048 | + | 0.354521i | \(0.884644\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 11.3677i | − 0.805834i | −0.915236 | − | 0.402917i | \(-0.867996\pi\) | ||||
0.915236 | − | 0.402917i | \(-0.132004\pi\) | |||||||
\(200\) | − 0.339030i | − 0.0239730i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0.665384i | 0.0468162i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.38082 | −0.375813 | ||||||||
\(206\) | 5.89829 | 0.410953 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − 7.24878i | − 0.502612i | ||||||||
\(209\) | 0.498995 | 0.0345162 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.8860 | 0.955951 | 0.477976 | − | 0.878373i | \(-0.341371\pi\) | ||||
0.477976 | + | 0.878373i | \(0.341371\pi\) | |||||||
\(212\) | − 11.7524i | − 0.807157i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 6.08816 | 0.416178 | ||||||||
\(215\) | 26.5690 | 1.81199 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 1.26600i | 0.0857443i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | − 1.91498i | − 0.129108i | ||||||||
\(221\) | 31.8160i | 2.14018i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.2139i | 0.683974i | 0.939705 | + | 0.341987i | \(0.111100\pi\) | ||||
−0.939705 | + | 0.341987i | \(0.888900\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −9.78828 | −0.651107 | ||||||||
\(227\) | 6.73372 | 0.446932 | 0.223466 | − | 0.974712i | \(-0.428263\pi\) | ||||
0.223466 | + | 0.974712i | \(0.428263\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 11.1127i | − 0.734349i | −0.930152 | − | 0.367175i | \(-0.880325\pi\) | ||||
0.930152 | − | 0.367175i | \(-0.119675\pi\) | |||||||
\(230\) | −9.91495 | −0.653772 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −20.6712 | −1.35713 | ||||||||
\(233\) | 1.15453i | 0.0756356i | 0.999285 | + | 0.0378178i | \(0.0120407\pi\) | ||||
−0.999285 | + | 0.0378178i | \(0.987959\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 28.1497 | 1.83628 | ||||||||
\(236\) | 10.8164 | 0.704085 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 25.1538i | 1.62707i | 0.581518 | + | 0.813533i | \(0.302459\pi\) | ||||
−0.581518 | + | 0.813533i | \(0.697541\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − 30.3705i | − 1.95634i | −0.207812 | − | 0.978169i | \(-0.566634\pi\) | ||||
0.207812 | − | 0.978169i | \(-0.433366\pi\) | |||||||
\(242\) | − 7.46676i | − 0.479981i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − 19.3438i | − 1.23836i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.94243 | −0.314480 | ||||||||
\(248\) | −0.572705 | −0.0363668 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | − 7.69924i | − 0.486943i | ||||||||
\(251\) | 22.0663 | 1.39281 | 0.696406 | − | 0.717648i | \(-0.254781\pi\) | ||||
0.696406 | + | 0.717648i | \(0.254781\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.49842 | −0.219944 | ||||||||
\(254\) | − 13.1476i | − 0.824953i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −10.3241 | −0.645253 | ||||||||
\(257\) | 12.9488 | 0.807726 | 0.403863 | − | 0.914819i | \(-0.367667\pi\) | ||||
0.403863 | + | 0.914819i | \(0.367667\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 18.9675i | 1.17631i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0.584215i | 0.0360929i | ||||||||
\(263\) | − 9.40750i | − 0.580091i | −0.957013 | − | 0.290046i | \(-0.906330\pi\) | ||||
0.957013 | − | 0.290046i | \(-0.0936705\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 17.6198i | 1.08238i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −9.11829 | −0.556988 | ||||||||
\(269\) | 5.96896 | 0.363934 | 0.181967 | − | 0.983305i | \(-0.441754\pi\) | ||||
0.181967 | + | 0.983305i | \(0.441754\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.63814i | 0.403238i | 0.979464 | + | 0.201619i | \(0.0646204\pi\) | ||||
−0.979464 | + | 0.201619i | \(0.935380\pi\) | |||||||
\(272\) | −7.52940 | −0.456537 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 7.16878 | 0.433082 | ||||||||
\(275\) | 0.0772110i | 0.00465600i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.37374 | −0.503129 | −0.251565 | − | 0.967840i | \(-0.580945\pi\) | ||||
−0.251565 | + | 0.967840i | \(0.580945\pi\) | |||||||
\(278\) | −8.43020 | −0.505610 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 5.56729i | − 0.332117i | −0.986116 | − | 0.166058i | \(-0.946896\pi\) | ||||
0.986116 | − | 0.166058i | \(-0.0531040\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.2040i | 0.903781i | 0.892073 | + | 0.451891i | \(0.149250\pi\) | ||||
−0.892073 | + | 0.451891i | \(0.850750\pi\) | |||||||
\(284\) | − 16.9727i | − 1.00715i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − 2.16048i | − 0.127752i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.0477 | 0.943982 | ||||||||
\(290\) | 13.3421 | 0.783476 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.68060i | 0.156870i | ||||||||
\(293\) | 16.8511 | 0.984453 | 0.492226 | − | 0.870467i | \(-0.336183\pi\) | ||||
0.492226 | + | 0.870467i | \(0.336183\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −16.2165 | −0.944159 | ||||||||
\(296\) | − 13.1854i | − 0.766385i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −14.2561 | −0.825836 | ||||||||
\(299\) | 34.6510 | 2.00392 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 11.8303i | 0.680757i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − 1.16965i | − 0.0670840i | ||||||||
\(305\) | 29.0013i | 1.66061i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 13.9504i | − 0.796194i | −0.917343 | − | 0.398097i | \(-0.869671\pi\) | ||||
0.917343 | − | 0.398097i | \(-0.130329\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.369650 | 0.0209947 | ||||||||
\(311\) | 27.8051 | 1.57668 | 0.788342 | − | 0.615237i | \(-0.210940\pi\) | ||||
0.788342 | + | 0.615237i | \(0.210940\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 24.2403i | − 1.37014i | −0.728476 | − | 0.685071i | \(-0.759771\pi\) | ||||
0.728476 | − | 0.685071i | \(-0.240229\pi\) | |||||||
\(314\) | 12.7983 | 0.722248 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.72559 | −0.490853 | ||||||||
\(317\) | − 21.7139i | − 1.21958i | −0.792565 | − | 0.609788i | \(-0.791255\pi\) | ||||
0.792565 | − | 0.609788i | \(-0.208745\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.70767 | 0.263579 | ||||||||
\(320\) | 3.28212 | 0.183476 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.13377i | 0.285651i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 0.764757i | − 0.0424211i | ||||||||
\(326\) | 4.87899i | 0.270222i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − 5.82416i | − 0.321585i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.4384 | 0.683676 | 0.341838 | − | 0.939759i | \(-0.388951\pi\) | ||||
0.341838 | + | 0.939759i | \(0.388951\pi\) | |||||||
\(332\) | 1.38140 | 0.0758141 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − 8.09861i | − 0.443136i | ||||||||
\(335\) | 13.6706 | 0.746907 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.16911 | −0.172632 | −0.0863161 | − | 0.996268i | \(-0.527510\pi\) | ||||
−0.0863161 | + | 0.996268i | \(0.527510\pi\) | |||||||
\(338\) | 12.3169i | 0.669952i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 19.7017 | 1.06848 | ||||||||
\(341\) | 0.130428 | 0.00706310 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 28.7581i | 1.55053i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − 1.16534i | − 0.0626493i | ||||||||
\(347\) | − 23.5645i | − 1.26501i | −0.774558 | − | 0.632503i | \(-0.782028\pi\) | ||||
0.774558 | − | 0.632503i | \(-0.217972\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 16.0140i | − 0.857211i | −0.903492 | − | 0.428606i | \(-0.859005\pi\) | ||||
0.903492 | − | 0.428606i | \(-0.140995\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.25318 | 0.173395 | ||||||||
\(353\) | −3.36316 | −0.179003 | −0.0895015 | − | 0.995987i | \(-0.528527\pi\) | ||||
−0.0895015 | + | 0.995987i | \(0.528527\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 25.4465i | 1.35056i | ||||||||
\(356\) | 4.24218 | 0.224835 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 9.22601 | 0.487610 | ||||||||
\(359\) | 3.38359i | 0.178579i | 0.996006 | + | 0.0892896i | \(0.0284597\pi\) | ||||
−0.996006 | + | 0.0892896i | \(0.971540\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.2025 | 0.958026 | ||||||||
\(362\) | 3.85482 | 0.202605 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 4.01890i | − 0.210359i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.4675i | 0.807396i | 0.914892 | + | 0.403698i | \(0.132275\pi\) | ||||
−0.914892 | + | 0.403698i | \(0.867725\pi\) | |||||||
\(368\) | 8.20033i | 0.427472i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 8.51045i | 0.442437i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.8113 | 0.766902 | 0.383451 | − | 0.923561i | \(-0.374736\pi\) | ||||
0.383451 | + | 0.923561i | \(0.374736\pi\) | |||||||
\(374\) | −2.24412 | −0.116041 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 30.4690i | 1.57132i | ||||||||
\(377\) | −46.6284 | −2.40148 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.481657 | −0.0247410 | −0.0123705 | − | 0.999923i | \(-0.503938\pi\) | ||||
−0.0123705 | + | 0.999923i | \(0.503938\pi\) | |||||||
\(380\) | 3.06055i | 0.157003i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 6.02697 | 0.308367 | ||||||||
\(383\) | 17.8417 | 0.911669 | 0.455835 | − | 0.890065i | \(-0.349341\pi\) | ||||
0.455835 | + | 0.890065i | \(0.349341\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − 5.56096i | − 0.283045i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 19.0162i | 0.965401i | ||||||||
\(389\) | 26.0373i | 1.32014i | 0.751204 | + | 0.660071i | \(0.229474\pi\) | ||||
−0.751204 | + | 0.660071i | \(0.770526\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 35.9925i | − 1.82022i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 6.95264 | 0.350269 | ||||||||
\(395\) | 13.0819 | 0.658221 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 17.6508i | 0.885867i | 0.896554 | + | 0.442934i | \(0.146062\pi\) | ||||
−0.896554 | + | 0.442934i | \(0.853938\pi\) | |||||||
\(398\) | −7.94176 | −0.398084 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.180983 | 0.00904916 | ||||||||
\(401\) | 9.71282i | 0.485035i | 0.970147 | + | 0.242518i | \(0.0779732\pi\) | ||||
−0.970147 | + | 0.242518i | \(0.922027\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.29186 | −0.0643523 | ||||||||
\(404\) | −1.43998 | −0.0716418 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.00285i | 0.148846i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − 1.29391i | − 0.0639798i | −0.999488 | − | 0.0319899i | \(-0.989816\pi\) | ||||
0.999488 | − | 0.0319899i | \(-0.0101844\pi\) | |||||||
\(410\) | 3.75918i | 0.185653i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 12.7647i | 0.628872i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.07107 | −0.101665 | ||||||||
\(416\) | −32.2220 | −1.57981 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − 0.348611i | − 0.0170511i | ||||||||
\(419\) | 8.20815 | 0.400994 | 0.200497 | − | 0.979694i | \(-0.435744\pi\) | ||||
0.200497 | + | 0.979694i | \(0.435744\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.0477 | 0.782117 | 0.391058 | − | 0.920366i | \(-0.372109\pi\) | ||||
0.391058 | + | 0.920366i | \(0.372109\pi\) | |||||||
\(422\) | − 9.70111i | − 0.472243i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −19.0715 | −0.926196 | ||||||||
\(425\) | −0.794363 | −0.0385323 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 13.1756i | 0.636868i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | − 18.5618i | − 0.895130i | ||||||||
\(431\) | 16.2409i | 0.782296i | 0.920328 | + | 0.391148i | \(0.127922\pi\) | ||||
−0.920328 | + | 0.391148i | \(0.872078\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.47525i | 0.359238i | 0.983736 | + | 0.179619i | \(0.0574864\pi\) | ||||
−0.983736 | + | 0.179619i | \(0.942514\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.73980 | −0.131213 | ||||||||
\(437\) | 5.59123 | 0.267465 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 12.7742i | − 0.609677i | −0.952404 | − | 0.304839i | \(-0.901397\pi\) | ||||
0.952404 | − | 0.304839i | \(-0.0986026\pi\) | |||||||
\(440\) | −3.10760 | −0.148149 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 22.2275 | 1.05725 | ||||||||
\(443\) | 6.43543i | 0.305756i | 0.988245 | + | 0.152878i | \(0.0488542\pi\) | ||||
−0.988245 | + | 0.152878i | \(0.951146\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.36010 | −0.301498 | ||||||||
\(446\) | 7.13570 | 0.337885 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 6.29690i | − 0.297169i | −0.988900 | − | 0.148585i | \(-0.952528\pi\) | ||||
0.988900 | − | 0.148585i | \(-0.0474717\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.32640i | 0.0624577i | ||||||||
\(452\) | − 21.1832i | − 0.996374i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − 4.70435i | − 0.220786i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −24.0714 | −1.12601 | −0.563006 | − | 0.826453i | \(-0.690355\pi\) | ||||
−0.563006 | + | 0.826453i | \(0.690355\pi\) | |||||||
\(458\) | −7.76363 | −0.362771 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − 21.4573i | − 1.00045i | ||||||||
\(461\) | 29.8904 | 1.39213 | 0.696067 | − | 0.717977i | \(-0.254932\pi\) | ||||
0.696067 | + | 0.717977i | \(0.254932\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −25.1319 | −1.16798 | −0.583989 | − | 0.811761i | \(-0.698509\pi\) | ||||
−0.583989 | + | 0.811761i | \(0.698509\pi\) | |||||||
\(464\) | − 11.0348i | − 0.512278i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.806582 | 0.0373642 | ||||||||
\(467\) | −22.1660 | −1.02572 | −0.512860 | − | 0.858472i | \(-0.671414\pi\) | ||||
−0.512860 | + | 0.858472i | \(0.671414\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | − 19.6661i | − 0.907129i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − 17.5526i | − 0.807923i | ||||||||
\(473\) | − 6.54940i | − 0.301142i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 0.123400i | − 0.00566197i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 17.5731 | 0.803775 | ||||||||
\(479\) | −15.8987 | −0.726430 | −0.363215 | − | 0.931705i | \(-0.618321\pi\) | ||||
−0.363215 | + | 0.931705i | \(0.618321\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − 29.7426i | − 1.35614i | ||||||||
\(482\) | −21.2176 | −0.966436 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 16.1591 | 0.734504 | ||||||||
\(485\) | − 28.5101i | − 1.29458i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.39399 | 0.153797 | 0.0768983 | − | 0.997039i | \(-0.475498\pi\) | ||||
0.0768983 | + | 0.997039i | \(0.475498\pi\) | |||||||
\(488\) | −31.3908 | −1.42099 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 30.2097i | − 1.36335i | −0.731657 | − | 0.681673i | \(-0.761253\pi\) | ||||
0.731657 | − | 0.681673i | \(-0.238747\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 48.4335i | 2.18134i | ||||||||
\(494\) | 3.45291i | 0.155354i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − 0.305725i | − 0.0137275i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −36.0289 | −1.61288 | −0.806438 | − | 0.591319i | \(-0.798608\pi\) | ||||
−0.806438 | + | 0.591319i | \(0.798608\pi\) | |||||||
\(500\) | 16.6622 | 0.745157 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − 15.4161i | − 0.688053i | ||||||||
\(503\) | 9.73396 | 0.434016 | 0.217008 | − | 0.976170i | \(-0.430370\pi\) | ||||
0.217008 | + | 0.976170i | \(0.430370\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.15890 | 0.0960698 | ||||||||
\(506\) | 2.44409i | 0.108653i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 28.4532 | 1.26241 | ||||||||
\(509\) | −17.0295 | −0.754819 | −0.377410 | − | 0.926046i | \(-0.623185\pi\) | ||||
−0.377410 | + | 0.926046i | \(0.623185\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − 14.0525i | − 0.621038i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − 9.04639i | − 0.399019i | ||||||||
\(515\) | − 19.1375i | − 0.843301i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 6.93904i | − 0.305179i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 30.7800 | 1.34979 | ||||||||
\(521\) | −27.3357 | −1.19760 | −0.598799 | − | 0.800899i | \(-0.704355\pi\) | ||||
−0.598799 | + | 0.800899i | \(0.704355\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 5.82076i | − 0.254524i | −0.991869 | − | 0.127262i | \(-0.959381\pi\) | ||||
0.991869 | − | 0.127262i | \(-0.0406189\pi\) | |||||||
\(524\) | −1.26432 | −0.0552322 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.57232 | −0.286567 | ||||||||
\(527\) | 1.34188i | 0.0584530i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.1997 | −0.704335 | ||||||||
\(530\) | 12.3096 | 0.534697 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 13.1377i | − 0.569056i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 19.7536i | − 0.854023i | ||||||||
\(536\) | 14.7970i | 0.639133i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − 4.17007i | − 0.179784i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.5802 | −0.669845 | −0.334922 | − | 0.942246i | \(-0.608710\pi\) | ||||
−0.334922 | + | 0.942246i | \(0.608710\pi\) | |||||||
\(542\) | 4.63758 | 0.199201 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 33.4694i | 1.43499i | ||||||||
\(545\) | 4.10765 | 0.175953 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.86923 | −0.122679 | −0.0613397 | − | 0.998117i | \(-0.519537\pi\) | ||||
−0.0613397 | + | 0.998117i | \(0.519537\pi\) | |||||||
\(548\) | 15.5142i | 0.662735i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.0539416 | 0.00230008 | ||||||||
\(551\) | −7.52387 | −0.320528 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 5.85011i | 0.248547i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − 18.2441i | − 0.773723i | ||||||||
\(557\) | − 5.56301i | − 0.235712i | −0.993031 | − | 0.117856i | \(-0.962398\pi\) | ||||
0.993031 | − | 0.117856i | \(-0.0376022\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 64.8703i | 2.74372i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −3.88945 | −0.164067 | ||||||||
\(563\) | −13.4984 | −0.568891 | −0.284445 | − | 0.958692i | \(-0.591809\pi\) | ||||
−0.284445 | + | 0.958692i | \(0.591809\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 31.7590i | 1.33611i | ||||||||
\(566\) | 10.6219 | 0.446470 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −27.5430 | −1.15568 | ||||||||
\(569\) | 1.11892i | 0.0469074i | 0.999725 | + | 0.0234537i | \(0.00746622\pi\) | ||||
−0.999725 | + | 0.0234537i | \(0.992534\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −45.2921 | −1.89542 | −0.947709 | − | 0.319137i | \(-0.896607\pi\) | ||||
−0.947709 | + | 0.319137i | \(0.896607\pi\) | |||||||
\(572\) | 4.67558 | 0.195496 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.865147i | 0.0360791i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 28.8678i | − 1.20178i | −0.799331 | − | 0.600891i | \(-0.794813\pi\) | ||||
0.799331 | − | 0.600891i | \(-0.205187\pi\) | |||||||
\(578\) | − 11.2113i | − 0.466330i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 28.8742i | 1.19893i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.34337 | 0.179884 | ||||||||
\(584\) | 4.35003 | 0.180006 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − 11.7726i | − 0.486323i | ||||||||
\(587\) | −29.1477 | −1.20305 | −0.601527 | − | 0.798852i | \(-0.705441\pi\) | ||||
−0.601527 | + | 0.798852i | \(0.705441\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.208453 | −0.00858914 | ||||||||
\(590\) | 11.3292i | 0.466417i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 7.03871 | 0.289289 | ||||||||
\(593\) | −36.9631 | −1.51789 | −0.758946 | − | 0.651154i | \(-0.774285\pi\) | ||||
−0.758946 | + | 0.651154i | \(0.774285\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − 30.8523i | − 1.26376i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − 24.2081i | − 0.989943i | ||||||||
\(599\) | − 26.3316i | − 1.07588i | −0.842983 | − | 0.537940i | \(-0.819203\pi\) | ||||
0.842983 | − | 0.537940i | \(-0.180797\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − 7.86645i | − 0.320879i | −0.987046 | − | 0.160440i | \(-0.948709\pi\) | ||||
0.987046 | − | 0.160440i | \(-0.0512912\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −25.6024 | −1.04175 | ||||||||
\(605\) | −24.2266 | −0.984951 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 22.7603i | − 0.923812i | −0.886929 | − | 0.461906i | \(-0.847166\pi\) | ||||
0.886929 | − | 0.461906i | \(-0.152834\pi\) | |||||||
\(608\) | −5.19928 | −0.210858 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 20.2610 | 0.820345 | ||||||||
\(611\) | 68.7296i | 2.78050i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.4090 | 0.581972 | 0.290986 | − | 0.956727i | \(-0.406017\pi\) | ||||
0.290986 | + | 0.956727i | \(0.406017\pi\) | |||||||
\(614\) | −9.74614 | −0.393322 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 14.8252i | − 0.596841i | −0.954435 | − | 0.298420i | \(-0.903540\pi\) | ||||
0.954435 | − | 0.298420i | \(-0.0964597\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 34.0864i | 1.37005i | 0.728520 | + | 0.685025i | \(0.240209\pi\) | ||||
−0.728520 | + | 0.685025i | \(0.759791\pi\) | |||||||
\(620\) | 0.799974i | 0.0321277i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − 19.4254i | − 0.778886i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −25.6718 | −1.02687 | ||||||||
\(626\) | −16.9349 | −0.676855 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 27.6972i | 1.10524i | ||||||||
\(629\) | −30.8940 | −1.23182 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.10726 | −0.282935 | −0.141468 | − | 0.989943i | \(-0.545182\pi\) | ||||
−0.141468 | + | 0.989943i | \(0.545182\pi\) | |||||||
\(632\) | 14.1597i | 0.563244i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −15.1699 | −0.602474 | ||||||||
\(635\) | −42.6586 | −1.69285 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − 3.28890i | − 0.130209i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 24.1014i | 0.952693i | ||||||||
\(641\) | 8.59556i | 0.339504i | 0.985487 | + | 0.169752i | \(0.0542967\pi\) | ||||
−0.985487 | + | 0.169752i | \(0.945703\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 47.3240i | 1.86628i | 0.359516 | + | 0.933139i | \(0.382942\pi\) | ||||
−0.359516 | + | 0.933139i | \(0.617058\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.58658 | 0.141112 | ||||||||
\(647\) | 37.5030 | 1.47439 | 0.737197 | − | 0.675678i | \(-0.236149\pi\) | ||||
0.737197 | + | 0.675678i | \(0.236149\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.99744i | 0.156913i | ||||||||
\(650\) | −0.534279 | −0.0209562 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −10.5588 | −0.413515 | ||||||||
\(653\) | 2.66764i | 0.104393i | 0.998637 | + | 0.0521964i | \(0.0166222\pi\) | ||||
−0.998637 | + | 0.0521964i | \(0.983378\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.89554 | 0.0740649 | ||||||||
\(656\) | 3.10909 | 0.121390 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 39.7218i | 1.54734i | 0.633589 | + | 0.773670i | \(0.281581\pi\) | ||||
−0.633589 | + | 0.773670i | \(0.718419\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.68591i | 0.298947i | 0.988766 | + | 0.149474i | \(0.0477579\pi\) | ||||
−0.988766 | + | 0.149474i | \(0.952242\pi\) | |||||||
\(662\) | − 8.68978i | − 0.337738i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − 2.24171i | − 0.0869951i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 52.7493 | 2.04246 | ||||||||
\(668\) | 17.5265 | 0.678121 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | − 9.55065i | − 0.368974i | ||||||||
\(671\) | 7.14896 | 0.275983 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.64404 | 0.294656 | 0.147328 | − | 0.989088i | \(-0.452933\pi\) | ||||
0.147328 | + | 0.989088i | \(0.452933\pi\) | |||||||
\(674\) | 2.21402i | 0.0852808i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −26.6555 | −1.02521 | ||||||||
\(677\) | 14.8718 | 0.571571 | 0.285785 | − | 0.958294i | \(-0.407746\pi\) | ||||
0.285785 | + | 0.958294i | \(0.407746\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | − 31.9716i | − 1.22606i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − 0.0911207i | − 0.00348919i | ||||||||
\(683\) | − 38.1933i | − 1.46142i | −0.682685 | − | 0.730712i | \(-0.739188\pi\) | ||||
0.682685 | − | 0.730712i | \(-0.260812\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 23.2598i | − 0.888710i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −15.3519 | −0.585284 | ||||||||
\(689\) | −43.0201 | −1.63893 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 10.5130i | − 0.399935i | −0.979803 | − | 0.199968i | \(-0.935916\pi\) | ||||
0.979803 | − | 0.199968i | \(-0.0640837\pi\) | |||||||
\(692\) | 2.52197 | 0.0958708 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −16.4627 | −0.624917 | ||||||||
\(695\) | 27.3526i | 1.03754i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −13.6463 | −0.516890 | ||||||||
\(698\) | −11.1878 | −0.423465 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 26.6270i | − 1.00569i | −0.864378 | − | 0.502843i | \(-0.832287\pi\) | ||||
0.864378 | − | 0.502843i | \(-0.167713\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 4.79920i | − 0.181005i | ||||||||
\(704\) | − 0.809058i | − 0.0304925i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.34959i | 0.0884280i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13.5562 | 0.509114 | 0.254557 | − | 0.967058i | \(-0.418070\pi\) | ||||
0.254557 | + | 0.967058i | \(0.418070\pi\) | |||||||
\(710\) | 17.7775 | 0.667179 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − 6.88413i | − 0.257994i | ||||||||
\(713\) | 1.46145 | 0.0547316 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.00988 | −0.262155 | ||||||||
\(716\) | 19.9664i | 0.746178i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 2.36386 | 0.0882186 | ||||||||
\(719\) | −25.4247 | −0.948180 | −0.474090 | − | 0.880476i | \(-0.657223\pi\) | ||||
−0.474090 | + | 0.880476i | \(0.657223\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − 12.7167i | − 0.473268i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 8.34236i | 0.310042i | ||||||||
\(725\) | − 1.16419i | − 0.0432369i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 42.5225i | − 1.57707i | −0.614988 | − | 0.788536i | \(-0.710839\pi\) | ||||
0.614988 | − | 0.788536i | \(-0.289161\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2.80771 | −0.103918 | ||||||||
\(731\) | 67.3816 | 2.49220 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 18.4165i | 0.680229i | 0.940384 | + | 0.340114i | \(0.110466\pi\) | ||||
−0.940384 | + | 0.340114i | \(0.889534\pi\) | |||||||
\(734\) | 10.8060 | 0.398856 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 36.4518 | 1.34363 | ||||||||
\(737\) | − 3.36988i | − 0.124131i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.71395 | 0.320548 | 0.160274 | − | 0.987073i | \(-0.448762\pi\) | ||||
0.160274 | + | 0.987073i | \(0.448762\pi\) | |||||||
\(740\) | −18.4178 | −0.677052 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 1.30005i | − 0.0476941i | −0.999716 | − | 0.0238470i | \(-0.992409\pi\) | ||||
0.999716 | − | 0.0238470i | \(-0.00759147\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 46.2554i | 1.69467i | ||||||||
\(746\) | − 10.3476i | − 0.378852i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − 4.85658i | − 0.177574i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.4698 | 0.783443 | 0.391722 | − | 0.920084i | \(-0.371880\pi\) | ||||
0.391722 | + | 0.920084i | \(0.371880\pi\) | |||||||
\(752\) | −16.2652 | −0.593130 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 32.5758i | 1.18634i | ||||||||
\(755\) | 38.3845 | 1.39696 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16.7524 | 0.608877 | 0.304439 | − | 0.952532i | \(-0.401531\pi\) | ||||
0.304439 | + | 0.952532i | \(0.401531\pi\) | |||||||
\(758\) | 0.336498i | 0.0122221i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.96661 | 0.180158 | ||||||||
\(761\) | −34.3655 | −1.24575 | −0.622874 | − | 0.782322i | \(-0.714035\pi\) | ||||
−0.622874 | + | 0.782322i | \(0.714035\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 13.0432i | 0.471886i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − 12.4647i | − 0.450367i | ||||||||
\(767\) | − 39.5937i | − 1.42965i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 14.6402i | 0.527938i | 0.964531 | + | 0.263969i | \(0.0850317\pi\) | ||||
−0.964531 | + | 0.263969i | \(0.914968\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 12.0347 | 0.433138 | ||||||||
\(773\) | −43.2233 | −1.55464 | −0.777318 | − | 0.629108i | \(-0.783420\pi\) | ||||
−0.777318 | + | 0.629108i | \(0.783420\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 0.0322545i | − 0.00115862i | ||||||||
\(776\) | 30.8591 | 1.10778 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 18.1903 | 0.652154 | ||||||||
\(779\) | − 2.11987i | − 0.0759523i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.27268 | 0.224454 | ||||||||
\(782\) | −25.1453 | −0.899193 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 41.5252i | − 1.48210i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 28.5985i | − 1.01942i | −0.860345 | − | 0.509712i | \(-0.829752\pi\) | ||||
0.860345 | − | 0.509712i | \(-0.170248\pi\) | |||||||
\(788\) | 15.0465i | 0.536009i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − 9.13933i | − 0.325163i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −70.8088 | −2.51449 | ||||||||
\(794\) | 12.3313 | 0.437621 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − 17.1871i | − 0.609179i | ||||||||
\(797\) | −41.0119 | −1.45272 | −0.726358 | − | 0.687317i | \(-0.758789\pi\) | ||||
−0.726358 | + | 0.687317i | \(0.758789\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 71.3903 | 2.52561 | ||||||||
\(800\) | − 0.804499i | − 0.0284434i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 6.78562 | 0.239609 | ||||||||
\(803\) | −0.990680 | −0.0349603 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.902529i | 0.0317902i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2.33678i | 0.0822075i | ||||||||
\(809\) | − 50.4495i | − 1.77371i | −0.462048 | − | 0.886855i | \(-0.652885\pi\) | ||||
0.462048 | − | 0.886855i | \(-0.347115\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24.9315i | 0.875465i | 0.899105 | + | 0.437732i | \(0.144218\pi\) | ||||
−0.899105 | + | 0.437732i | \(0.855782\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2.09787 | 0.0735303 | ||||||||
\(815\) | 15.8303 | 0.554513 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.4674i | 0.366206i | ||||||||
\(818\) | −0.903959 | −0.0316062 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −8.13538 | −0.284100 | ||||||||
\(821\) | − 7.86728i | − 0.274570i | −0.990532 | − | 0.137285i | \(-0.956162\pi\) | ||||
0.990532 | − | 0.137285i | \(-0.0438376\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 36.7198 | 1.27997 | 0.639986 | − | 0.768386i | \(-0.278940\pi\) | ||||
0.639986 | + | 0.768386i | \(0.278940\pi\) | |||||||
\(824\) | 20.7143 | 0.721618 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 19.7296i | 0.686067i | 0.939323 | + | 0.343033i | \(0.111454\pi\) | ||||
−0.939323 | + | 0.343033i | \(0.888546\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 26.1288i | − 0.907492i | −0.891131 | − | 0.453746i | \(-0.850087\pi\) | ||||
0.891131 | − | 0.453746i | \(-0.149913\pi\) | |||||||
\(830\) | 1.44690i | 0.0502227i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 8.01353i | 0.277819i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −26.2767 | −0.909342 | ||||||||
\(836\) | 0.754442 | 0.0260929 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − 5.73442i | − 0.198092i | ||||||||
\(839\) | −53.3357 | −1.84135 | −0.920676 | − | 0.390328i | \(-0.872362\pi\) | ||||
−0.920676 | + | 0.390328i | \(0.872362\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −41.9824 | −1.44767 | ||||||||
\(842\) | − 11.2113i | − 0.386368i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 20.9945 | 0.722662 | ||||||||
\(845\) | 39.9634 | 1.37478 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − 10.1809i | − 0.349613i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0.554963i | 0.0190351i | ||||||||
\(851\) | 33.6469i | 1.15340i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 44.6277i | − 1.52802i | −0.645202 | − | 0.764012i | \(-0.723227\pi\) | ||||
0.645202 | − | 0.764012i | \(-0.276773\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 21.3812 | 0.730793 | ||||||||
\(857\) | −39.5137 | −1.34976 | −0.674882 | − | 0.737926i | \(-0.735805\pi\) | ||||
−0.674882 | + | 0.737926i | \(0.735805\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 41.5978i | − 1.41930i | −0.704555 | − | 0.709650i | \(-0.748853\pi\) | ||||
0.704555 | − | 0.709650i | \(-0.251147\pi\) | |||||||
\(860\) | 40.1703 | 1.36980 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 11.3463 | 0.386457 | ||||||||
\(863\) | 21.8415i | 0.743493i | 0.928334 | + | 0.371747i | \(0.121241\pi\) | ||||
−0.928334 | + | 0.371747i | \(0.878759\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.78107 | −0.128560 | ||||||||
\(866\) | 5.22240 | 0.177464 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 3.22475i | − 0.109392i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 33.3779i | 1.13097i | ||||||||
\(872\) | 4.44609i | 0.150564i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − 3.90617i | − 0.132128i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 39.2454 | 1.32522 | 0.662611 | − | 0.748963i | \(-0.269448\pi\) | ||||
0.662611 | + | 0.748963i | \(0.269448\pi\) | |||||||
\(878\) | −8.92436 | −0.301182 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | − 1.65892i | − 0.0559221i | ||||||||
\(881\) | 2.29892 | 0.0774524 | 0.0387262 | − | 0.999250i | \(-0.487670\pi\) | ||||
0.0387262 | + | 0.999250i | \(0.487670\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.14326 | −0.173085 | −0.0865423 | − | 0.996248i | \(-0.527582\pi\) | ||||
−0.0865423 | + | 0.996248i | \(0.527582\pi\) | |||||||
\(884\) | 48.1033i | 1.61789i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4.49595 | 0.151045 | ||||||||
\(887\) | −13.2017 | −0.443269 | −0.221634 | − | 0.975130i | \(-0.571139\pi\) | ||||
−0.221634 | + | 0.975130i | \(0.571139\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 4.44333i | 0.148941i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 15.4426i | 0.517058i | ||||||||
\(893\) | 11.0901i | 0.371115i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 29.9347i | − 1.00061i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −4.39918 | −0.146802 | ||||||||
\(899\) | −1.96660 | −0.0655899 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 44.6855i | 1.48869i | ||||||||
\(902\) | 0.926657 | 0.0308543 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −34.3757 | −1.14332 | ||||||||
\(905\) | − 12.5073i | − 0.415758i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12.1283 | 0.402714 | 0.201357 | − | 0.979518i | \(-0.435465\pi\) | ||||
0.201357 | + | 0.979518i | \(0.435465\pi\) | |||||||
\(908\) | 10.1809 | 0.337864 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.54730i | 0.250053i | 0.992153 | + | 0.125027i | \(0.0399016\pi\) | ||||
−0.992153 | + | 0.125027i | \(0.960098\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.510529i | 0.0168960i | ||||||||
\(914\) | 16.8169i | 0.556253i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − 16.8016i | − 0.555140i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.76262 | 0.124117 | 0.0620587 | − | 0.998072i | \(-0.480233\pi\) | ||||
0.0620587 | + | 0.998072i | \(0.480233\pi\) | |||||||
\(920\) | −34.8205 | −1.14800 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − 20.8822i | − 0.687718i | ||||||||
\(923\) | −62.1295 | −2.04502 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.742595 | 0.0244164 | ||||||||
\(926\) | 17.5578i | 0.576985i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −49.0515 | −1.61019 | ||||||||
\(929\) | −40.9953 | −1.34501 | −0.672507 | − | 0.740091i | \(-0.734782\pi\) | ||||
−0.672507 | + | 0.740091i | \(0.734782\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 1.74556i | 0.0571776i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 15.4857i | 0.506709i | ||||||||
\(935\) | 7.28125i | 0.238122i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 13.0152i | 0.425187i | 0.977141 | + | 0.212593i | \(0.0681910\pi\) | ||||
−0.977141 | + | 0.212593i | \(0.931809\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 42.5601 | 1.38816 | ||||||||
\(941\) | 10.7228 | 0.349554 | 0.174777 | − | 0.984608i | \(-0.444080\pi\) | ||||
0.174777 | + | 0.984608i | \(0.444080\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 14.8623i | 0.483982i | ||||||||
\(944\) | 9.37004 | 0.304969 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.57558 | −0.148765 | ||||||||
\(947\) | − 35.9063i | − 1.16680i | −0.812186 | − | 0.583398i | \(-0.801723\pi\) | ||||
0.812186 | − | 0.583398i | \(-0.198277\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.81246 | 0.318526 | ||||||||
\(950\) | −0.0862103 | −0.00279703 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 17.6691i | − 0.572360i | −0.958176 | − | 0.286180i | \(-0.907615\pi\) | ||||
0.958176 | − | 0.286180i | \(-0.0923855\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 19.5551i | − 0.632787i | ||||||||
\(956\) | 38.0307i | 1.23000i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 11.1072i | 0.358859i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.9455 | 0.998242 | ||||||||
\(962\) | −20.7789 | −0.669939 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − 45.9179i | − 1.47892i | ||||||||
\(965\) | −18.0431 | −0.580826 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −50.3563 | −1.61935 | −0.809675 | − | 0.586878i | \(-0.800357\pi\) | ||||
−0.809675 | + | 0.586878i | \(0.800357\pi\) | |||||||
\(968\) | − 26.2227i | − 0.842828i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −19.9179 | −0.639525 | ||||||||
\(971\) | 51.1649 | 1.64196 | 0.820980 | − | 0.570956i | \(-0.193427\pi\) | ||||
0.820980 | + | 0.570956i | \(0.193427\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − 2.37113i | − 0.0759759i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − 16.7572i | − 0.536386i | ||||||||
\(977\) | − 27.9975i | − 0.895720i | −0.894104 | − | 0.447860i | \(-0.852186\pi\) | ||||
0.894104 | − | 0.447860i | \(-0.147814\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.56780i | 0.0501070i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −21.1053 | −0.673497 | ||||||||
\(983\) | 24.0255 | 0.766295 | 0.383147 | − | 0.923687i | \(-0.374840\pi\) | ||||
0.383147 | + | 0.923687i | \(0.374840\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − 22.5585i | − 0.718773i | ||||||||
\(986\) | 33.8369 | 1.07759 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −7.47258 | −0.237734 | ||||||||
\(989\) | − 73.3859i | − 2.33353i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 34.2532 | 1.08809 | 0.544045 | − | 0.839056i | \(-0.316892\pi\) | ||||
0.544045 | + | 0.839056i | \(0.316892\pi\) | |||||||
\(992\) | −1.35900 | −0.0431482 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 25.7678i | 0.816893i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 39.1980i | − 1.24141i | −0.784043 | − | 0.620706i | \(-0.786846\pi\) | ||||
0.784043 | − | 0.620706i | \(-0.213154\pi\) | |||||||
\(998\) | 25.1707i | 0.796765i | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1323.2.c.f.1322.5 | ✓ | 16 | |
3.2 | odd | 2 | inner | 1323.2.c.f.1322.12 | yes | 16 | |
7.6 | odd | 2 | inner | 1323.2.c.f.1322.6 | yes | 16 | |
21.20 | even | 2 | inner | 1323.2.c.f.1322.11 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1323.2.c.f.1322.5 | ✓ | 16 | 1.1 | even | 1 | trivial | |
1323.2.c.f.1322.6 | yes | 16 | 7.6 | odd | 2 | inner | |
1323.2.c.f.1322.11 | yes | 16 | 21.20 | even | 2 | inner | |
1323.2.c.f.1322.12 | yes | 16 | 3.2 | odd | 2 | inner |