Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1728,3,Mod(127,1728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1728, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1728.127");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.o (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(47.0845896815\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 10 x^{19} + 50 x^{18} - 130 x^{17} + 203 x^{16} - 296 x^{15} + 1260 x^{14} - 3380 x^{13} + \cdots + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{26}\cdot 3^{8} \) |
Twist minimal: | no (minimal twist has level 288) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 127.3 | ||
Root | \(0.810930 + 0.810930i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1728.127 |
Dual form | 1728.3.o.h.1279.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(703\) | \(1217\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.966952 | − | 1.67481i | −0.193390 | − | 0.334962i | 0.752981 | − | 0.658042i | \(-0.228615\pi\) |
−0.946372 | + | 0.323080i | \(0.895282\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −8.96285 | − | 5.17470i | −1.28041 | − | 0.739243i | −0.303484 | − | 0.952837i | \(-0.598150\pi\) |
−0.976923 | + | 0.213593i | \(0.931483\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −18.2506 | − | 10.5370i | −1.65915 | − | 0.957910i | −0.973109 | − | 0.230347i | \(-0.926014\pi\) |
−0.686040 | − | 0.727564i | \(-0.740653\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 7.47096 | + | 12.9401i | 0.574690 | + | 0.995391i | 0.996075 | + | 0.0885100i | \(0.0282105\pi\) |
−0.421386 | + | 0.906881i | \(0.638456\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.89794 | −0.346938 | −0.173469 | − | 0.984839i | \(-0.555498\pi\) | ||||
−0.173469 | + | 0.984839i | \(0.555498\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 32.7678i | − | 1.72462i | −0.506382 | − | 0.862309i | \(-0.669017\pi\) | ||
0.506382 | − | 0.862309i | \(-0.330983\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.30154 | − | 2.48349i | 0.187023 | − | 0.107978i | −0.403565 | − | 0.914951i | \(-0.632229\pi\) |
0.590588 | + | 0.806973i | \(0.298896\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 10.6300 | − | 18.4117i | 0.425200 | − | 0.736469i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −9.34387 | + | 16.1841i | −0.322202 | + | 0.558071i | −0.980942 | − | 0.194300i | \(-0.937756\pi\) |
0.658740 | + | 0.752371i | \(0.271090\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.55802 | − | 4.94098i | 0.276065 | − | 0.159386i | −0.355576 | − | 0.934648i | \(-0.615715\pi\) |
0.631641 | + | 0.775261i | \(0.282382\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 20.0147i | 0.571850i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −43.5347 | −1.17661 | −0.588307 | − | 0.808638i | \(-0.700205\pi\) | ||||
−0.588307 | + | 0.808638i | \(0.700205\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.82699 | + | 13.5567i | 0.190902 | + | 0.330652i | 0.945549 | − | 0.325478i | \(-0.105525\pi\) |
−0.754647 | + | 0.656131i | \(0.772192\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.26635 | + | 4.19523i | 0.168985 | + | 0.0975635i | 0.582107 | − | 0.813112i | \(-0.302228\pi\) |
−0.413122 | + | 0.910676i | \(0.635562\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 43.2309 | + | 24.9594i | 0.919807 | + | 0.531051i | 0.883574 | − | 0.468292i | \(-0.155131\pi\) |
0.0362337 | + | 0.999343i | \(0.488464\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 29.0551 | + | 50.3249i | 0.592961 | + | 1.02704i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −75.8512 | −1.43115 | −0.715577 | − | 0.698534i | \(-0.753836\pi\) | ||||
−0.715577 | + | 0.698534i | \(0.753836\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 40.7551i | 0.741002i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −58.8809 | + | 33.9949i | −0.997981 | + | 0.576185i | −0.907650 | − | 0.419727i | \(-0.862126\pi\) |
−0.0903307 | + | 0.995912i | \(0.528792\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.64421 | + | 16.7043i | −0.158102 | + | 0.273840i | −0.934184 | − | 0.356791i | \(-0.883871\pi\) |
0.776082 | + | 0.630632i | \(0.217204\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 14.4481 | − | 25.0249i | 0.222279 | − | 0.384998i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 32.2998 | − | 18.6483i | 0.482086 | − | 0.278333i | −0.239199 | − | 0.970971i | \(-0.576885\pi\) |
0.721286 | + | 0.692638i | \(0.243552\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 95.4928i | 1.34497i | 0.740111 | + | 0.672485i | \(0.234773\pi\) | ||||
−0.740111 | + | 0.672485i | \(0.765227\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 68.3482 | 0.936277 | 0.468138 | − | 0.883655i | \(-0.344925\pi\) | ||||
0.468138 | + | 0.883655i | \(0.344925\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 109.052 | + | 188.883i | 1.41626 | + | 2.45303i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 73.2208 | + | 42.2741i | 0.926846 | + | 0.535115i | 0.885813 | − | 0.464043i | \(-0.153602\pi\) |
0.0410333 | + | 0.999158i | \(0.486935\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 14.0131 | + | 8.09049i | 0.168833 | + | 0.0974758i | 0.582035 | − | 0.813163i | \(-0.302256\pi\) |
−0.413202 | + | 0.910639i | \(0.635590\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.70303 | + | 9.87793i | 0.0670944 | + | 0.116211i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −42.9444 | −0.482521 | −0.241260 | − | 0.970460i | \(-0.577561\pi\) | ||||
−0.241260 | + | 0.970460i | \(0.577561\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 154.640i | − | 1.69934i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −54.8798 | + | 31.6848i | −0.577682 | + | 0.333525i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15.8988 | − | 27.5376i | 0.163905 | − | 0.283893i | −0.772361 | − | 0.635184i | \(-0.780924\pi\) |
0.936266 | + | 0.351292i | \(0.114257\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −56.1229 | + | 97.2077i | −0.555672 | + | 0.962452i | 0.442179 | + | 0.896927i | \(0.354206\pi\) |
−0.997851 | + | 0.0655252i | \(0.979128\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 48.3175 | − | 27.8961i | 0.469101 | − | 0.270836i | −0.246762 | − | 0.969076i | \(-0.579367\pi\) |
0.715864 | + | 0.698240i | \(0.246033\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 89.4882i | − | 0.836338i | −0.908369 | − | 0.418169i | \(-0.862672\pi\) | ||
0.908369 | − | 0.418169i | \(-0.137328\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 158.842 | 1.45727 | 0.728634 | − | 0.684904i | \(-0.240156\pi\) | ||||
0.728634 | + | 0.684904i | \(0.240156\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 25.4171 | + | 44.0237i | 0.224930 | + | 0.389591i | 0.956298 | − | 0.292392i | \(-0.0944513\pi\) |
−0.731368 | + | 0.681983i | \(0.761118\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.31876 | − | 4.80284i | −0.0723371 | − | 0.0417638i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 52.8624 | + | 30.5201i | 0.444222 | + | 0.256471i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 161.557 | + | 279.825i | 1.33518 | + | 2.31261i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −89.4624 | −0.715699 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 20.1417i | 0.158596i | 0.996851 | + | 0.0792979i | \(0.0252678\pi\) | ||||
−0.996851 | + | 0.0792979i | \(0.974732\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −55.2586 | + | 31.9036i | −0.421821 | + | 0.243539i | −0.695856 | − | 0.718181i | \(-0.744975\pi\) |
0.274035 | + | 0.961720i | \(0.411642\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −169.563 | + | 293.692i | −1.27491 | + | 2.20821i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.48134 | − | 9.49396i | 0.0400098 | − | 0.0692990i | −0.845327 | − | 0.534249i | \(-0.820594\pi\) |
0.885337 | + | 0.464950i | \(0.153928\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −180.759 | + | 104.361i | −1.30042 | + | 0.750799i | −0.980476 | − | 0.196638i | \(-0.936998\pi\) |
−0.319945 | + | 0.947436i | \(0.603664\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 314.887i | − | 2.20200i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 36.1403 | 0.249243 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −81.2800 | − | 140.781i | −0.545503 | − | 0.944839i | −0.998575 | − | 0.0533652i | \(-0.983005\pi\) |
0.453072 | − | 0.891474i | \(-0.350328\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −96.3636 | − | 55.6356i | −0.638170 | − | 0.368447i | 0.145739 | − | 0.989323i | \(-0.453444\pi\) |
−0.783909 | + | 0.620876i | \(0.786777\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −16.5504 | − | 9.55537i | −0.106777 | − | 0.0616476i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −47.0780 | − | 81.5415i | −0.299860 | − | 0.519373i | 0.676244 | − | 0.736678i | \(-0.263607\pi\) |
−0.976104 | + | 0.217305i | \(0.930273\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −51.4054 | −0.319288 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 151.014i | 0.926468i | 0.886236 | + | 0.463234i | \(0.153311\pi\) | ||||
−0.886236 | + | 0.463234i | \(0.846689\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 72.7991 | − | 42.0306i | 0.435923 | − | 0.251680i | −0.265944 | − | 0.963989i | \(-0.585684\pi\) |
0.701867 | + | 0.712308i | \(0.252350\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −27.1306 | + | 46.9916i | −0.160536 | + | 0.278057i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −131.671 | + | 228.060i | −0.761102 | + | 1.31827i | 0.181180 | + | 0.983450i | \(0.442008\pi\) |
−0.942283 | + | 0.334818i | \(0.891325\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −190.550 | + | 110.014i | −1.08886 | + | 0.628653i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 215.534i | − | 1.20410i | −0.798458 | − | 0.602050i | \(-0.794351\pi\) | ||
0.798458 | − | 0.602050i | \(-0.205649\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 332.798 | 1.83866 | 0.919332 | − | 0.393482i | \(-0.128730\pi\) | ||||
0.919332 | + | 0.393482i | \(0.128730\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 42.0960 | + | 72.9123i | 0.227546 | + | 0.394121i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 107.641 | + | 62.1467i | 0.575622 | + | 0.332335i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 114.364 | + | 66.0279i | 0.598763 | + | 0.345696i | 0.768555 | − | 0.639784i | \(-0.220976\pi\) |
−0.169792 | + | 0.985480i | \(0.554310\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −87.6264 | − | 151.773i | −0.454023 | − | 0.786391i | 0.544609 | − | 0.838690i | \(-0.316678\pi\) |
−0.998631 | + | 0.0522997i | \(0.983345\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 308.985 | 1.56845 | 0.784227 | − | 0.620475i | \(-0.213060\pi\) | ||||
0.784227 | + | 0.620475i | \(0.213060\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 310.934i | 1.56248i | 0.624229 | + | 0.781241i | \(0.285413\pi\) | ||||
−0.624229 | + | 0.781241i | \(0.714587\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 167.495 | − | 96.7035i | 0.825100 | − | 0.476372i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 15.1366 | − | 26.2174i | 0.0738373 | − | 0.127890i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −345.274 | + | 598.032i | −1.65203 | + | 2.86140i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.05601 | + | 4.65114i | −0.0381802 | + | 0.0220433i | −0.518969 | − | 0.854793i | \(-0.673684\pi\) |
0.480788 | + | 0.876837i | \(0.340351\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 16.2263i | − | 0.0754714i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −102.272 | −0.471301 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −44.0633 | − | 76.3199i | −0.199382 | − | 0.345339i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −360.713 | − | 208.258i | −1.61755 | − | 0.933891i | −0.987552 | − | 0.157292i | \(-0.949724\pi\) |
−0.629995 | − | 0.776599i | \(-0.716943\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 308.860 | + | 178.321i | 1.36062 | + | 0.785553i | 0.989706 | − | 0.143114i | \(-0.0457117\pi\) |
0.370912 | + | 0.928668i | \(0.379045\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 164.486 | + | 284.898i | 0.718280 | + | 1.24410i | 0.961681 | + | 0.274172i | \(0.0884036\pi\) |
−0.243401 | + | 0.969926i | \(0.578263\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 65.3289 | 0.280382 | 0.140191 | − | 0.990124i | \(-0.455228\pi\) | ||||
0.140191 | + | 0.990124i | \(0.455228\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 96.5381i | − | 0.410801i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −81.9440 | + | 47.3104i | −0.342862 | + | 0.197951i | −0.661537 | − | 0.749913i | \(-0.730095\pi\) |
0.318675 | + | 0.947864i | \(0.396762\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 42.2962 | − | 73.2591i | 0.175503 | − | 0.303980i | −0.764832 | − | 0.644229i | \(-0.777178\pi\) |
0.940335 | + | 0.340250i | \(0.110512\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 56.1897 | − | 97.3235i | 0.229346 | − | 0.397239i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 424.018 | − | 244.807i | 1.71667 | − | 0.991120i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.43066i | 0.00569986i | 0.999996 | + | 0.00284993i | \(0.000907162\pi\) | ||||
−0.999996 | + | 0.00284993i | \(0.999093\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −104.674 | −0.413733 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 69.7372 | + | 120.788i | 0.271351 | + | 0.469994i | 0.969208 | − | 0.246243i | \(-0.0791962\pi\) |
−0.697857 | + | 0.716237i | \(0.745863\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 390.195 | + | 225.279i | 1.50654 | + | 0.869804i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −234.380 | − | 135.319i | −0.891178 | − | 0.514522i | −0.0168501 | − | 0.999858i | \(-0.505364\pi\) |
−0.874327 | + | 0.485336i | \(0.838697\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 73.3444 | + | 127.036i | 0.276771 | + | 0.479382i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −176.888 | −0.657577 | −0.328788 | − | 0.944404i | \(-0.606640\pi\) | ||||
−0.328788 | + | 0.944404i | \(0.606640\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 205.187i | − | 0.757147i | −0.925571 | − | 0.378574i | \(-0.876415\pi\) | ||
0.925571 | − | 0.378574i | \(-0.123585\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −388.009 | + | 224.017i | −1.41094 | + | 0.814607i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 120.995 | − | 209.569i | 0.436805 | − | 0.756568i | −0.560636 | − | 0.828062i | \(-0.689443\pi\) |
0.997441 | + | 0.0714943i | \(0.0227768\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −21.4562 | + | 37.1632i | −0.0763566 | + | 0.132253i | −0.901675 | − | 0.432414i | \(-0.857662\pi\) |
0.825319 | + | 0.564667i | \(0.190995\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −328.185 | + | 189.478i | −1.15966 | + | 0.669533i | −0.951224 | − | 0.308502i | \(-0.900172\pi\) |
−0.208441 | + | 0.978035i | \(0.566839\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 162.009i | − | 0.564492i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −254.214 | −0.879634 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 56.2663 | + | 97.4561i | 0.192035 | + | 0.332615i | 0.945925 | − | 0.324387i | \(-0.105158\pi\) |
−0.753889 | + | 0.657001i | \(0.771825\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 113.870 | + | 65.7428i | 0.386000 | + | 0.222857i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 64.2733 | + | 37.1082i | 0.214961 | + | 0.124108i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −43.4181 | − | 75.2024i | −0.144246 | − | 0.249842i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 37.3020 | 0.122301 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 109.964i | 0.358189i | 0.983832 | + | 0.179094i | \(0.0573167\pi\) | ||||
−0.983832 | + | 0.179094i | \(0.942683\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −462.400 | + | 266.967i | −1.48682 | + | 0.858413i | −0.999887 | − | 0.0150284i | \(-0.995216\pi\) |
−0.486929 | + | 0.873442i | \(0.661883\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −78.8728 | + | 136.612i | −0.251990 | + | 0.436459i | −0.964074 | − | 0.265635i | \(-0.914418\pi\) |
0.712084 | + | 0.702095i | \(0.247752\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 111.823 | − | 193.683i | 0.352753 | − | 0.610987i | −0.633977 | − | 0.773352i | \(-0.718579\pi\) |
0.986731 | + | 0.162365i | \(0.0519121\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 341.063 | − | 196.913i | 1.06916 | − | 0.617282i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 193.262i | 0.598336i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 317.666 | 0.977433 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −258.315 | − | 447.414i | −0.785152 | − | 1.35992i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −177.292 | − | 102.360i | −0.535625 | − | 0.309243i | 0.207679 | − | 0.978197i | \(-0.433409\pi\) |
−0.743304 | + | 0.668954i | \(0.766742\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −62.4647 | − | 36.0640i | −0.186462 | − | 0.107654i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 251.883 | + | 436.275i | 0.747428 | + | 1.29458i | 0.949052 | + | 0.315120i | \(0.102045\pi\) |
−0.201624 | + | 0.979463i | \(0.564622\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −208.252 | −0.610711 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 94.2847i | − | 0.274883i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 256.064 | − | 147.839i | 0.737938 | − | 0.426049i | −0.0833813 | − | 0.996518i | \(-0.526572\pi\) |
0.821319 | + | 0.570469i | \(0.193239\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 29.0465 | − | 50.3101i | 0.0832279 | − | 0.144155i | −0.821407 | − | 0.570343i | \(-0.806810\pi\) |
0.904635 | + | 0.426188i | \(0.140144\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 250.158 | − | 433.286i | 0.708662 | − | 1.22744i | −0.256692 | − | 0.966493i | \(-0.582633\pi\) |
0.965354 | − | 0.260945i | \(-0.0840341\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 159.932 | − | 92.3370i | 0.450514 | − | 0.260104i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 204.499i | 0.569636i | 0.958582 | + | 0.284818i | \(0.0919332\pi\) | ||||
−0.958582 | + | 0.284818i | \(0.908067\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −712.726 | −1.97431 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −66.0894 | − | 114.470i | −0.181067 | − | 0.313617i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −152.383 | − | 87.9782i | −0.415212 | − | 0.239723i | 0.277815 | − | 0.960635i | \(-0.410390\pi\) |
−0.693027 | + | 0.720912i | \(0.743723\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 679.842 | + | 392.507i | 1.83246 | + | 1.05797i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −175.334 | − | 303.688i | −0.470065 | − | 0.814177i | 0.529349 | − | 0.848404i | \(-0.322436\pi\) |
−0.999414 | + | 0.0342271i | \(0.989103\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −279.231 | −0.740665 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 79.8445i | − | 0.210672i | −0.994437 | − | 0.105336i | \(-0.966408\pi\) | ||
0.994437 | − | 0.105336i | \(-0.0335917\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −256.795 | + | 148.261i | −0.670482 | + | 0.387103i | −0.796259 | − | 0.604955i | \(-0.793191\pi\) |
0.125777 | + | 0.992059i | \(0.459858\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 210.896 | − | 365.282i | 0.547781 | − | 0.948784i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 63.0249 | − | 109.162i | 0.162018 | − | 0.280623i | −0.773574 | − | 0.633705i | \(-0.781533\pi\) |
0.935592 | + | 0.353082i | \(0.114866\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −25.3702 | + | 14.6475i | −0.0648855 | + | 0.0374617i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 163.508i | − | 0.413944i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.66640 | 0.00419748 | 0.00209874 | − | 0.999998i | \(-0.499332\pi\) | ||||
0.00209874 | + | 0.999998i | \(0.499332\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 279.021 | + | 483.278i | 0.695813 | + | 1.20518i | 0.969906 | + | 0.243480i | \(0.0782890\pi\) |
−0.274093 | + | 0.961703i | \(0.588378\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 127.873 | + | 73.8277i | 0.317304 | + | 0.183195i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 794.536 | + | 458.726i | 1.95218 | + | 1.12709i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −99.7341 | − | 172.744i | −0.243849 | − | 0.422358i | 0.717959 | − | 0.696086i | \(-0.245077\pi\) |
−0.961807 | + | 0.273728i | \(0.911743\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 703.654 | 1.70376 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 31.2925i | − | 0.0754035i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −299.782 | + | 173.079i | −0.715469 | + | 0.413076i | −0.813083 | − | 0.582148i | \(-0.802212\pi\) |
0.0976136 | + | 0.995224i | \(0.468879\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −160.593 | + | 278.155i | −0.381456 | + | 0.660702i | −0.991271 | − | 0.131842i | \(-0.957911\pi\) |
0.609814 | + | 0.792544i | \(0.291244\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −62.6952 | + | 108.591i | −0.147518 | + | 0.255509i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 172.879 | − | 99.8118i | 0.404869 | − | 0.233751i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 734.565i | − | 1.70433i | −0.523276 | − | 0.852163i | \(-0.675290\pi\) | ||
0.523276 | − | 0.852163i | \(-0.324710\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 400.407 | 0.924729 | 0.462364 | − | 0.886690i | \(-0.347001\pi\) | ||||
0.462364 | + | 0.886690i | \(0.347001\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −81.3785 | − | 140.952i | −0.186221 | − | 0.322544i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 143.545 | + | 82.8758i | 0.326982 | + | 0.188783i | 0.654500 | − | 0.756062i | \(-0.272879\pi\) |
−0.327518 | + | 0.944845i | \(0.606212\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −492.357 | − | 284.262i | −1.11141 | − | 0.641675i | −0.172219 | − | 0.985059i | \(-0.555094\pi\) |
−0.939195 | + | 0.343383i | \(0.888427\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 41.5251 | + | 71.9236i | 0.0933149 | + | 0.161626i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 183.191 | 0.407999 | 0.203999 | − | 0.978971i | \(-0.434606\pi\) | ||||
0.203999 | + | 0.978971i | \(0.434606\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 329.892i | − | 0.731468i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −258.993 | + | 149.529i | −0.569215 | + | 0.328636i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 194.840 | − | 337.473i | 0.426346 | − | 0.738453i | −0.570199 | − | 0.821507i | \(-0.693134\pi\) |
0.996545 | + | 0.0830536i | \(0.0264673\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 234.336 | − | 405.883i | 0.508322 | − | 0.880439i | −0.491632 | − | 0.870803i | \(-0.663599\pi\) |
0.999954 | − | 0.00963620i | \(-0.00306735\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −381.289 | + | 220.137i | −0.823518 | + | 0.475458i | −0.851628 | − | 0.524146i | \(-0.824384\pi\) |
0.0281101 | + | 0.999605i | \(0.491051\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 232.287i | − | 0.497403i | −0.968580 | − | 0.248701i | \(-0.919996\pi\) | ||
0.968580 | − | 0.248701i | \(-0.0800038\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −385.997 | −0.823022 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −88.4104 | − | 153.131i | −0.186914 | − | 0.323745i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −603.311 | − | 348.322i | −1.27013 | − | 0.733308i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −54.7737 | − | 31.6236i | −0.114350 | − | 0.0660200i | 0.441734 | − | 0.897146i | \(-0.354363\pi\) |
−0.556084 | + | 0.831126i | \(0.687697\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −325.246 | − | 563.343i | −0.676188 | − | 1.17119i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −61.4936 | −0.126791 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 65.1317i | − | 0.133741i | −0.997762 | − | 0.0668704i | \(-0.978699\pi\) | ||
0.997762 | − | 0.0668704i | \(-0.0213014\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −593.177 | + | 342.471i | −1.20810 | + | 0.697496i | −0.962344 | − | 0.271835i | \(-0.912369\pi\) |
−0.245755 | + | 0.969332i | \(0.579036\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 55.1096 | − | 95.4526i | 0.111784 | − | 0.193616i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 494.147 | − | 855.888i | 0.994259 | − | 1.72211i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 233.586 | − | 134.861i | 0.468108 | − | 0.270262i | −0.247340 | − | 0.968929i | \(-0.579556\pi\) |
0.715447 | + | 0.698667i | \(0.246223\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 182.143i | − | 0.362114i | −0.983473 | − | 0.181057i | \(-0.942048\pi\) | ||
0.983473 | − | 0.181057i | \(-0.0579518\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 217.072 | 0.429846 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 121.872 | + | 211.088i | 0.239433 | + | 0.414711i | 0.960552 | − | 0.278101i | \(-0.0897050\pi\) |
−0.721119 | + | 0.692812i | \(0.756372\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −612.595 | − | 353.682i | −1.19882 | − | 0.692136i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −93.4413 | − | 53.9484i | −0.181439 | − | 0.104754i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −525.995 | − | 911.050i | −1.01740 | − | 1.76219i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 698.539 | 1.34077 | 0.670383 | − | 0.742016i | \(-0.266130\pi\) | ||||
0.670383 | + | 0.742016i | \(0.266130\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 76.4187i | 0.146116i | 0.997328 | + | 0.0730580i | \(0.0232758\pi\) | ||||
−0.997328 | + | 0.0730580i | \(0.976724\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −50.4747 | + | 29.1416i | −0.0957775 | + | 0.0552972i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −252.165 | + | 436.762i | −0.476681 | + | 0.825637i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −116.950 | + | 202.564i | −0.219419 | + | 0.380045i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −149.876 | + | 86.5308i | −0.280142 | + | 0.161740i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 1224.61i | − | 2.27201i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −319.631 | −0.590816 | −0.295408 | − | 0.955371i | \(-0.595456\pi\) | ||||
−0.295408 | + | 0.955371i | \(0.595456\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −153.593 | − | 266.030i | −0.281821 | − | 0.488129i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 21.7181 | + | 12.5389i | 0.0397040 | + | 0.0229231i | 0.519721 | − | 0.854336i | \(-0.326036\pi\) |
−0.480017 | + | 0.877259i | \(0.659369\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 530.315 | + | 306.178i | 0.962459 | + | 0.555676i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −437.511 | − | 757.792i | −0.791160 | − | 1.37033i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −993.726 | −1.78407 | −0.892035 | − | 0.451967i | \(-0.850722\pi\) | ||||
−0.892035 | + | 0.451967i | \(0.850722\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 125.370i | 0.224275i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −792.494 | + | 457.546i | −1.40763 | + | 0.812693i | −0.995159 | − | 0.0982790i | \(-0.968666\pi\) |
−0.412467 | + | 0.910972i | \(0.635333\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 49.1542 | − | 85.1377i | 0.0869987 | − | 0.150686i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 86.7437 | − | 150.245i | 0.152449 | − | 0.264050i | −0.779678 | − | 0.626181i | \(-0.784617\pi\) |
0.932127 | + | 0.362131i | \(0.117951\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 516.243 | − | 298.053i | 0.904103 | − | 0.521984i | 0.0255737 | − | 0.999673i | \(-0.491859\pi\) |
0.878529 | + | 0.477689i | \(0.158525\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 105.598i | − | 0.183649i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −121.875 | −0.211222 | −0.105611 | − | 0.994408i | \(-0.533680\pi\) | ||||
−0.105611 | + | 0.994408i | \(0.533680\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −83.7317 | − | 145.028i | −0.144117 | − | 0.249617i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1384.33 | + | 799.245i | 2.37450 | + | 1.37092i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 281.323 | + | 162.422i | 0.479256 | + | 0.276698i | 0.720106 | − | 0.693864i | \(-0.244093\pi\) |
−0.240851 | + | 0.970562i | \(0.577426\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −161.905 | − | 280.427i | −0.274881 | − | 0.476107i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −785.829 | −1.32518 | −0.662588 | − | 0.748984i | \(-0.730542\pi\) | ||||
−0.662588 | + | 0.748984i | \(0.730542\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 118.046i | − | 0.198396i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 623.633 | − | 360.054i | 1.04112 | − | 0.601093i | 0.120972 | − | 0.992656i | \(-0.461399\pi\) |
0.920151 | + | 0.391563i | \(0.128066\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 283.454 | − | 490.956i | 0.471637 | − | 0.816899i | −0.527837 | − | 0.849346i | \(-0.676997\pi\) |
0.999473 | + | 0.0324471i | \(0.0103300\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 312.436 | − | 541.155i | 0.516423 | − | 0.894471i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −68.5352 | + | 39.5688i | −0.112908 | + | 0.0651875i | −0.555391 | − | 0.831590i | \(-0.687431\pi\) |
0.442483 | + | 0.896777i | \(0.354098\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 745.883i | 1.22076i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −951.491 | −1.55219 | −0.776094 | − | 0.630617i | \(-0.782802\pi\) | ||||
−0.776094 | + | 0.630617i | \(0.782802\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −152.435 | − | 264.025i | −0.247059 | − | 0.427918i | 0.715650 | − | 0.698459i | \(-0.246131\pi\) |
−0.962708 | + | 0.270541i | \(0.912797\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 44.3755 | + | 25.6202i | 0.0716891 | + | 0.0413897i | 0.535416 | − | 0.844588i | \(-0.320155\pi\) |
−0.463727 | + | 0.885978i | \(0.653488\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 384.904 | + | 222.224i | 0.617823 | + | 0.356700i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −179.244 | − | 310.460i | −0.286791 | − | 0.496737i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 256.765 | 0.408212 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 316.484i | 0.501560i | 0.968044 | + | 0.250780i | \(0.0806871\pi\) | ||||
−0.968044 | + | 0.250780i | \(0.919313\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 33.7335 | − | 19.4760i | 0.0531236 | − | 0.0306709i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −434.139 | + | 751.951i | −0.681537 | + | 1.18046i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 608.032 | − | 1053.14i | 0.948568 | − | 1.64297i | 0.200124 | − | 0.979770i | \(-0.435865\pi\) |
0.748444 | − | 0.663198i | \(-0.230801\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −696.018 | + | 401.846i | −1.08245 | + | 0.624955i | −0.931557 | − | 0.363595i | \(-0.881549\pi\) |
−0.150896 | + | 0.988550i | \(0.548216\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1091.43i | 1.68690i | 0.537205 | + | 0.843452i | \(0.319480\pi\) | ||||
−0.537205 | + | 0.843452i | \(0.680520\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1432.82 | 2.20773 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −25.8433 | − | 44.7619i | −0.0395762 | − | 0.0685480i | 0.845559 | − | 0.533882i | \(-0.179267\pi\) |
−0.885135 | + | 0.465334i | \(0.845934\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 106.865 | + | 61.6984i | 0.163152 | + | 0.0941961i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 440.684 | + | 254.429i | 0.668716 | + | 0.386083i | 0.795590 | − | 0.605836i | \(-0.207161\pi\) |
−0.126874 | + | 0.991919i | \(0.540494\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 163.945 | + | 283.961i | 0.248026 | + | 0.429593i | 0.962978 | − | 0.269580i | \(-0.0868849\pi\) |
−0.714952 | + | 0.699173i | \(0.753552\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 655.838 | 0.986223 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 92.8218i | 0.139163i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 352.026 | − | 203.242i | 0.524629 | − | 0.302895i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −341.446 | + | 591.401i | −0.507349 | + | 0.878754i | 0.492615 | + | 0.870247i | \(0.336041\pi\) |
−0.999964 | + | 0.00850630i | \(0.997292\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 178.474 | − | 309.125i | 0.263624 | − | 0.456611i | −0.703578 | − | 0.710618i | \(-0.748415\pi\) |
0.967202 | + | 0.254007i | \(0.0817488\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −284.998 | + | 164.543i | −0.419731 | + | 0.242332i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 1099.06i | − | 1.60917i | −0.593839 | − | 0.804584i | \(-0.702388\pi\) | ||
0.593839 | − | 0.804584i | \(-0.297612\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −21.2008 | −0.0309500 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −566.681 | − | 981.521i | −0.822469 | − | 1.42456i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 823.701 | + | 475.564i | 1.19204 | + | 0.688226i | 0.958769 | − | 0.284186i | \(-0.0917232\pi\) |
0.233273 | + | 0.972411i | \(0.425056\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 349.570 | + | 201.824i | 0.502978 | + | 0.290394i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −46.1631 | − | 79.9569i | −0.0662312 | − | 0.114716i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 99.5247 | 0.141975 | 0.0709876 | − | 0.997477i | \(-0.477385\pi\) | ||||
0.0709876 | + | 0.997477i | \(0.477385\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1426.53i | 2.02921i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1006.04 | − | 580.838i | 1.42297 | − | 0.821553i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 631.369 | − | 1093.56i | 0.890506 | − | 1.54240i | 0.0512359 | − | 0.998687i | \(-0.483684\pi\) |
0.839270 | − | 0.543715i | \(-0.182983\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 24.5418 | − | 42.5076i | 0.0344204 | − | 0.0596180i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −527.375 | + | 304.480i | −0.737587 | + | 0.425846i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 875.064i | − | 1.21706i | −0.793532 | − | 0.608528i | \(-0.791760\pi\) | ||
0.793532 | − | 0.608528i | \(-0.208240\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −577.416 | −0.800854 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 198.651 | + | 344.073i | 0.274001 | + | 0.474584i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 129.425 | + | 74.7236i | 0.178026 | + | 0.102784i | 0.586365 | − | 0.810047i | \(-0.300558\pi\) |
−0.408339 | + | 0.912830i | \(0.633892\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −42.8565 | − | 24.7432i | −0.0586273 | − | 0.0338485i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 114.030 | + | 197.506i | 0.155566 | + | 0.269449i | 0.933265 | − | 0.359188i | \(-0.116946\pi\) |
−0.777699 | + | 0.628637i | \(0.783613\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −785.989 | −1.06647 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 283.397i | 0.383487i | 0.981445 | + | 0.191744i | \(0.0614142\pi\) | ||||
−0.981445 | + | 0.191744i | \(0.938586\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −755.841 | + | 436.385i | −1.01728 | + | 0.587328i | −0.913316 | − | 0.407253i | \(-0.866487\pi\) |
−0.103967 | + | 0.994581i | \(0.533154\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −157.188 | + | 272.257i | −0.210990 | + | 0.365446i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −463.075 | + | 802.069i | −0.618257 | + | 1.07085i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −699.693 | + | 403.968i | −0.931682 | + | 0.537907i | −0.887343 | − | 0.461110i | \(-0.847451\pi\) |
−0.0443390 | + | 0.999017i | \(0.514118\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 215.188i | 0.285017i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −447.804 | −0.591551 | −0.295775 | − | 0.955258i | \(-0.595578\pi\) | ||||
−0.295775 | + | 0.955258i | \(0.595578\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 650.854 | + | 1127.31i | 0.855261 | + | 1.48136i | 0.876403 | + | 0.481579i | \(0.159937\pi\) |
−0.0211418 | + | 0.999776i | \(0.506730\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1423.68 | − | 821.961i | −1.86589 | − | 1.07727i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −879.794 | − | 507.949i | −1.14706 | − | 0.662255i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 58.7699 | + | 101.792i | 0.0764238 | + | 0.132370i | 0.901705 | − | 0.432353i | \(-0.142316\pi\) |
−0.825281 | + | 0.564723i | \(0.808983\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 748.233 | 0.967960 | 0.483980 | − | 0.875079i | \(-0.339191\pi\) | ||||
0.483980 | + | 0.875079i | \(0.339191\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 210.090i | − | 0.271084i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 444.224 | − | 256.473i | 0.570249 | − | 0.329233i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1006.21 | − | 1742.81i | 1.28836 | − | 2.23150i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −91.0444 | + | 157.694i | −0.115980 | + | 0.200883i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 552.393 | − | 318.924i | 0.701897 | − | 0.405240i | −0.106157 | − | 0.994349i | \(-0.533855\pi\) |
0.808054 | + | 0.589109i | \(0.200521\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 526.104i | − | 0.665112i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −288.206 | −0.363438 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 85.2936 | + | 147.733i | 0.107018 | + | 0.185361i | 0.914561 | − | 0.404448i | \(-0.132536\pi\) |
−0.807543 | + | 0.589809i | \(0.799203\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −254.974 | − | 147.209i | −0.319116 | − | 0.184242i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1247.40 | − | 720.186i | −1.55342 | − | 0.896869i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 49.7065 | + | 86.0942i | 0.0617472 | + | 0.106949i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 969.433 | 1.19831 | 0.599155 | − | 0.800633i | \(-0.295503\pi\) | ||||
0.599155 | + | 0.800633i | \(0.295503\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 230.645i | 0.284396i | 0.989838 | + | 0.142198i | \(0.0454170\pi\) | ||||
−0.989838 | + | 0.142198i | \(0.954583\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 252.920 | − | 146.024i | 0.310332 | − | 0.179170i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 137.468 | − | 238.102i | 0.168260 | − | 0.291435i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −627.592 | + | 1087.02i | −0.764424 | + | 1.32402i | 0.176126 | + | 0.984368i | \(0.443643\pi\) |
−0.940551 | + | 0.339654i | \(0.889690\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 344.755 | − | 199.044i | 0.418900 | − | 0.241852i | −0.275707 | − | 0.961242i | \(-0.588912\pi\) |
0.694606 | + | 0.719390i | \(0.255579\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 406.686i | 0.491760i | 0.969300 | + | 0.245880i | \(0.0790770\pi\) | ||||
−0.969300 | + | 0.245880i | \(0.920923\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1333.85 | −1.60899 | −0.804494 | − | 0.593961i | \(-0.797563\pi\) | ||||
−0.804494 | + | 0.593961i | \(0.797563\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −171.365 | − | 296.813i | −0.205721 | − | 0.356318i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −140.786 | − | 81.2831i | −0.168607 | − | 0.0973450i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −285.181 | − | 164.649i | −0.339905 | − | 0.196244i | 0.320325 | − | 0.947308i | \(-0.396208\pi\) |
−0.660230 | + | 0.751063i | \(0.729541\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 245.884 | + | 425.884i | 0.292371 | + | 0.506402i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 104.936 | 0.124185 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 3344.04i | − | 3.94810i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −187.266 | + | 108.118i | −0.220054 | + | 0.127048i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −245.911 | + | 425.931i | −0.288290 | + | 0.499332i | −0.973402 | − | 0.229105i | \(-0.926420\pi\) |
0.685112 | + | 0.728438i | \(0.259753\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −293.484 | + | 508.329i | −0.342455 | + | 0.593149i | −0.984888 | − | 0.173192i | \(-0.944592\pi\) |
0.642433 | + | 0.766342i | \(0.277925\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −221.512 | + | 127.890i | −0.257872 | + | 0.148883i | −0.623364 | − | 0.781932i | \(-0.714234\pi\) |
0.365491 | + | 0.930815i | \(0.380901\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 1123.57i | − | 1.30193i | −0.759107 | − | 0.650966i | \(-0.774364\pi\) | ||
0.759107 | − | 0.650966i | \(-0.225636\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 509.277 | 0.588760 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −890.885 | − | 1543.06i | −1.02518 | − | 1.77567i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 482.621 | + | 278.641i | 0.554100 | + | 0.319910i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 801.838 | + | 462.941i | 0.916386 | + | 0.529076i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 498.332 | + | 863.136i | 0.568223 | + | 0.984192i | 0.996742 | + | 0.0806586i | \(0.0257024\pi\) |
−0.428518 | + | 0.903533i | \(0.640964\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 804.052 | 0.912659 | 0.456329 | − | 0.889811i | \(-0.349164\pi\) | ||||
0.456329 | + | 0.889811i | \(0.349164\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 852.030i | 0.964926i | 0.875916 | + | 0.482463i | \(0.160258\pi\) | ||||
−0.875916 | + | 0.482463i | \(0.839742\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −588.730 | + | 339.904i | −0.663732 | + | 0.383206i | −0.793697 | − | 0.608313i | \(-0.791847\pi\) |
0.129965 | + | 0.991519i | \(0.458513\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 104.227 | − | 180.527i | 0.117241 | − | 0.203067i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 817.863 | − | 1416.58i | 0.915860 | − | 1.58632i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −360.978 | + | 208.411i | −0.403328 | + | 0.232861i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 184.671i | 0.205419i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 447.366 | 0.496522 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −321.800 | − | 557.374i | −0.355580 | − | 0.615883i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1033.20 | − | 596.521i | −1.13914 | − | 0.657685i | −0.192926 | − | 0.981213i | \(-0.561798\pi\) |
−0.946219 | + | 0.323528i | \(0.895131\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 466.555 | + | 269.365i | 0.512135 | + | 0.295681i | 0.733711 | − | 0.679462i | \(-0.237787\pi\) |
−0.221576 | + | 0.975143i | \(0.571120\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −170.499 | − | 295.313i | −0.186746 | − | 0.323454i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 660.366 | 0.720137 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 1195.64i | − | 1.30102i | −0.759498 | − | 0.650509i | \(-0.774555\pi\) | ||
0.759498 | − | 0.650509i | \(-0.225445\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1235.69 | + | 713.424i | −1.33877 | + | 0.772940i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −462.774 | + | 801.549i | −0.500297 | + | 0.866539i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −706.854 | + | 1224.31i | −0.760876 | + | 1.31788i | 0.181523 | + | 0.983387i | \(0.441897\pi\) |
−0.942400 | + | 0.334489i | \(0.891436\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1649.03 | − | 952.070i | 1.77125 | − | 1.02263i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 240.371i | − | 0.257082i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1275.33 | −1.36108 | −0.680541 | − | 0.732710i | \(-0.738255\pi\) | ||||
−0.680541 | + | 0.732710i | \(0.738255\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −275.421 | − | 477.043i | −0.292690 | − | 0.506954i | 0.681755 | − | 0.731580i | \(-0.261217\pi\) |
−0.974445 | + | 0.224627i | \(0.927884\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 67.3362 | + | 38.8766i | 0.0714064 | + | 0.0412265i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 696.651 | + | 402.212i | 0.735640 | + | 0.424722i | 0.820482 | − | 0.571672i | \(-0.193705\pi\) |
−0.0848419 | + | 0.996394i | \(0.527039\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 510.627 | + | 884.432i | 0.538069 | + | 0.931962i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −721.612 | −0.757200 | −0.378600 | − | 0.925560i | \(-0.623594\pi\) | ||||
−0.378600 | + | 0.925560i | \(0.623594\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 255.383i | − | 0.267417i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −98.2568 | + | 56.7286i | −0.102458 | + | 0.0591539i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −431.674 | + | 747.680i | −0.449192 | + | 0.778023i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −169.461 | + | 293.515i | −0.175607 | + | 0.304161i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1030.73 | + | 595.091i | −1.06590 | + | 0.615400i | −0.927059 | − | 0.374915i | \(-0.877672\pi\) |
−0.138844 | + | 0.990314i | \(0.544339\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1024.09i | − | 1.05467i | −0.849657 | − | 0.527335i | \(-0.823191\pi\) | ||
0.849657 | − | 0.527335i | \(-0.176809\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2160.15 | 2.22009 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 641.906 | + | 1111.81i | 0.657018 | + | 1.13799i | 0.981384 | + | 0.192056i | \(0.0615156\pi\) |
−0.324366 | + | 0.945932i | \(0.605151\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 783.762 | + | 452.505i | 0.800574 | + | 0.462212i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −103.885 | − | 59.9782i | −0.105682 | − | 0.0610154i | 0.446227 | − | 0.894920i | \(-0.352767\pi\) |
−0.551909 | + | 0.833904i | \(0.686101\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −298.774 | − | 517.492i | −0.303324 | − | 0.525372i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 41.6753 | 0.0421389 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 549.882i | 0.554876i | 0.960744 | + | 0.277438i | \(0.0894853\pi\) | ||||
−0.960744 | + | 0.277438i | \(0.910515\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 520.755 | − | 300.658i | 0.523372 | − | 0.302169i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20.2764 | − | 35.1198i | 0.0203374 | − | 0.0352254i | −0.855678 | − | 0.517509i | \(-0.826859\pi\) |
0.876015 | + | 0.482284i | \(0.160193\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1728.3.o.h.127.3 | 20 | ||
3.2 | odd | 2 | 576.3.o.h.511.4 | 20 | |||
4.3 | odd | 2 | inner | 1728.3.o.h.127.4 | 20 | ||
8.3 | odd | 2 | 864.3.o.b.127.8 | 20 | |||
8.5 | even | 2 | 864.3.o.b.127.7 | 20 | |||
9.4 | even | 3 | inner | 1728.3.o.h.1279.4 | 20 | ||
9.5 | odd | 6 | 576.3.o.h.319.7 | 20 | |||
12.11 | even | 2 | 576.3.o.h.511.7 | 20 | |||
24.5 | odd | 2 | 288.3.o.b.223.7 | yes | 20 | ||
24.11 | even | 2 | 288.3.o.b.223.4 | yes | 20 | ||
36.23 | even | 6 | 576.3.o.h.319.4 | 20 | |||
36.31 | odd | 6 | inner | 1728.3.o.h.1279.3 | 20 | ||
72.5 | odd | 6 | 288.3.o.b.31.4 | ✓ | 20 | ||
72.11 | even | 6 | 2592.3.g.g.2431.7 | 10 | |||
72.13 | even | 6 | 864.3.o.b.415.8 | 20 | |||
72.29 | odd | 6 | 2592.3.g.g.2431.8 | 10 | |||
72.43 | odd | 6 | 2592.3.g.h.2431.3 | 10 | |||
72.59 | even | 6 | 288.3.o.b.31.7 | yes | 20 | ||
72.61 | even | 6 | 2592.3.g.h.2431.4 | 10 | |||
72.67 | odd | 6 | 864.3.o.b.415.7 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
288.3.o.b.31.4 | ✓ | 20 | 72.5 | odd | 6 | ||
288.3.o.b.31.7 | yes | 20 | 72.59 | even | 6 | ||
288.3.o.b.223.4 | yes | 20 | 24.11 | even | 2 | ||
288.3.o.b.223.7 | yes | 20 | 24.5 | odd | 2 | ||
576.3.o.h.319.4 | 20 | 36.23 | even | 6 | |||
576.3.o.h.319.7 | 20 | 9.5 | odd | 6 | |||
576.3.o.h.511.4 | 20 | 3.2 | odd | 2 | |||
576.3.o.h.511.7 | 20 | 12.11 | even | 2 | |||
864.3.o.b.127.7 | 20 | 8.5 | even | 2 | |||
864.3.o.b.127.8 | 20 | 8.3 | odd | 2 | |||
864.3.o.b.415.7 | 20 | 72.67 | odd | 6 | |||
864.3.o.b.415.8 | 20 | 72.13 | even | 6 | |||
1728.3.o.h.127.3 | 20 | 1.1 | even | 1 | trivial | ||
1728.3.o.h.127.4 | 20 | 4.3 | odd | 2 | inner | ||
1728.3.o.h.1279.3 | 20 | 36.31 | odd | 6 | inner | ||
1728.3.o.h.1279.4 | 20 | 9.4 | even | 3 | inner | ||
2592.3.g.g.2431.7 | 10 | 72.11 | even | 6 | |||
2592.3.g.g.2431.8 | 10 | 72.29 | odd | 6 | |||
2592.3.g.h.2431.3 | 10 | 72.43 | odd | 6 | |||
2592.3.g.h.2431.4 | 10 | 72.61 | even | 6 |