Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2340,2,Mod(1621,2340)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2340, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2340.1621");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2340 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2340.q (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(18.6849940730\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 260) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 2161.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2340.2161 |
Dual form | 2340.2.q.a.1621.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2340\mathbb{Z}\right)^\times\).
\(n\) | \(937\) | \(1081\) | \(1171\) | \(2081\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.50000 | + | 2.59808i | −0.566947 | + | 0.981981i | 0.429919 | + | 0.902867i | \(0.358542\pi\) |
−0.996866 | + | 0.0791130i | \(0.974791\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.50000 | + | 2.59808i | 0.452267 | + | 0.783349i | 0.998526 | − | 0.0542666i | \(-0.0172821\pi\) |
−0.546259 | + | 0.837616i | \(0.683949\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | − | 3.46410i | 0.277350 | − | 0.960769i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.50000 | + | 6.06218i | −0.848875 | + | 1.47029i | 0.0333386 | + | 0.999444i | \(0.489386\pi\) |
−0.882213 | + | 0.470850i | \(0.843947\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.500000 | + | 0.866025i | −0.114708 | + | 0.198680i | −0.917663 | − | 0.397360i | \(-0.869927\pi\) |
0.802955 | + | 0.596040i | \(0.203260\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.50000 | − | 6.06218i | −0.729800 | − | 1.26405i | −0.956967 | − | 0.290196i | \(-0.906280\pi\) |
0.227167 | − | 0.973856i | \(-0.427054\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.50000 | − | 4.33013i | −0.464238 | − | 0.804084i | 0.534928 | − | 0.844897i | \(-0.320339\pi\) |
−0.999167 | + | 0.0408130i | \(0.987005\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.00000 | −0.718421 | −0.359211 | − | 0.933257i | \(-0.616954\pi\) | ||||
−0.359211 | + | 0.933257i | \(0.616954\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.50000 | − | 2.59808i | 0.253546 | − | 0.439155i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.50000 | + | 2.59808i | 0.246598 | + | 0.427121i | 0.962580 | − | 0.270998i | \(-0.0873538\pi\) |
−0.715981 | + | 0.698119i | \(0.754020\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.50000 | + | 6.06218i | 0.546608 | + | 0.946753i | 0.998504 | + | 0.0546823i | \(0.0174146\pi\) |
−0.451896 | + | 0.892071i | \(0.649252\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.50000 | − | 7.79423i | 0.686244 | − | 1.18861i | −0.286801 | − | 0.957990i | \(-0.592592\pi\) |
0.973044 | − | 0.230618i | \(-0.0740749\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.00000 | −1.16692 | −0.583460 | − | 0.812142i | \(-0.698301\pi\) | ||||
−0.583460 | + | 0.812142i | \(0.698301\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | − | 1.73205i | −0.142857 | − | 0.247436i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.00000 | 0.824163 | 0.412082 | − | 0.911147i | \(-0.364802\pi\) | ||||
0.412082 | + | 0.911147i | \(0.364802\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.50000 | − | 2.59808i | −0.202260 | − | 0.350325i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.50000 | − | 4.33013i | 0.325472 | − | 0.563735i | −0.656136 | − | 0.754643i | \(-0.727810\pi\) |
0.981608 | + | 0.190909i | \(0.0611434\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.50000 | − | 4.33013i | 0.320092 | − | 0.554416i | −0.660415 | − | 0.750901i | \(-0.729619\pi\) |
0.980507 | + | 0.196485i | \(0.0629528\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.00000 | + | 3.46410i | −0.124035 | + | 0.429669i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.50000 | − | 11.2583i | −0.794101 | − | 1.37542i | −0.923408 | − | 0.383819i | \(-0.874609\pi\) |
0.129307 | − | 0.991605i | \(-0.458725\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.50000 | + | 2.59808i | −0.178017 | + | 0.308335i | −0.941201 | − | 0.337846i | \(-0.890302\pi\) |
0.763184 | + | 0.646181i | \(0.223635\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −14.0000 | −1.63858 | −0.819288 | − | 0.573382i | \(-0.805631\pi\) | ||||
−0.819288 | + | 0.573382i | \(0.805631\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −9.00000 | −1.02565 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.00000 | −0.900070 | −0.450035 | − | 0.893011i | \(-0.648589\pi\) | ||||
−0.450035 | + | 0.893011i | \(0.648589\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.0000 | −1.31717 | −0.658586 | − | 0.752506i | \(-0.728845\pi\) | ||||
−0.658586 | + | 0.752506i | \(0.728845\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.50000 | − | 6.06218i | 0.379628 | − | 0.657536i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.50000 | + | 6.06218i | 0.370999 | + | 0.642590i | 0.989720 | − | 0.143022i | \(-0.0456819\pi\) |
−0.618720 | + | 0.785611i | \(0.712349\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.50000 | + | 7.79423i | 0.786214 | + | 0.817057i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.500000 | − | 0.866025i | 0.0512989 | − | 0.0888523i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.50000 | − | 9.52628i | 0.558440 | − | 0.967247i | −0.439187 | − | 0.898396i | \(-0.644733\pi\) |
0.997627 | − | 0.0688512i | \(-0.0219334\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.50000 | − | 7.79423i | −0.447767 | − | 0.775555i | 0.550474 | − | 0.834853i | \(-0.314447\pi\) |
−0.998240 | + | 0.0592978i | \(0.981114\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.0000 | −1.57653 | −0.788263 | − | 0.615338i | \(-0.789020\pi\) | ||||
−0.788263 | + | 0.615338i | \(0.789020\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.50000 | − | 2.59808i | −0.145010 | − | 0.251166i | 0.784366 | − | 0.620298i | \(-0.212988\pi\) |
−0.929377 | + | 0.369132i | \(0.879655\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14.0000 | −1.34096 | −0.670478 | − | 0.741929i | \(-0.733911\pi\) | ||||
−0.670478 | + | 0.741929i | \(0.733911\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.50000 | − | 11.2583i | 0.611469 | − | 1.05909i | −0.379525 | − | 0.925182i | \(-0.623912\pi\) |
0.990993 | − | 0.133913i | \(-0.0427543\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.50000 | + | 6.06218i | 0.326377 | + | 0.565301i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −10.5000 | − | 18.1865i | −0.962533 | − | 1.66716i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | − | 1.73205i | 0.0909091 | − | 0.157459i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.500000 | − | 0.866025i | −0.0443678 | − | 0.0768473i | 0.842989 | − | 0.537931i | \(-0.180794\pi\) |
−0.887357 | + | 0.461084i | \(0.847461\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.00000 | −0.349482 | −0.174741 | − | 0.984614i | \(-0.555909\pi\) | ||||
−0.174741 | + | 0.984614i | \(0.555909\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.50000 | − | 2.59808i | −0.130066 | − | 0.225282i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.50000 | + | 2.59808i | −0.128154 | + | 0.221969i | −0.922961 | − | 0.384893i | \(-0.874238\pi\) |
0.794808 | + | 0.606861i | \(0.207572\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.50000 | + | 11.2583i | −0.551323 | + | 0.954919i | 0.446857 | + | 0.894606i | \(0.352543\pi\) |
−0.998179 | + | 0.0603135i | \(0.980790\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 10.5000 | − | 2.59808i | 0.878054 | − | 0.217262i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.50000 | + | 4.33013i | 0.207614 | + | 0.359597i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.50000 | − | 2.59808i | 0.122885 | − | 0.212843i | −0.798019 | − | 0.602632i | \(-0.794119\pi\) |
0.920904 | + | 0.389789i | \(0.127452\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.00000 | −0.651031 | −0.325515 | − | 0.945537i | \(-0.605538\pi\) | ||||
−0.325515 | + | 0.945537i | \(0.605538\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.00000 | 0.321288 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.00000 | 0.478852 | 0.239426 | − | 0.970915i | \(-0.423041\pi\) | ||||
0.239426 | + | 0.970915i | \(0.423041\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 21.0000 | 1.65503 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.50000 | + | 9.52628i | −0.430793 | + | 0.746156i | −0.996942 | − | 0.0781474i | \(-0.975100\pi\) |
0.566149 | + | 0.824303i | \(0.308433\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.500000 | + | 0.866025i | 0.0386912 | + | 0.0670151i | 0.884723 | − | 0.466118i | \(-0.154348\pi\) |
−0.846031 | + | 0.533133i | \(0.821014\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.0000 | − | 6.92820i | −0.846154 | − | 0.532939i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.50000 | + | 12.9904i | −0.570214 | + | 0.987640i | 0.426329 | + | 0.904568i | \(0.359807\pi\) |
−0.996544 | + | 0.0830722i | \(0.973527\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.50000 | + | 2.59808i | −0.113389 | + | 0.196396i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.50000 | + | 16.4545i | 0.710063 | + | 1.22987i | 0.964833 | + | 0.262864i | \(0.0846670\pi\) |
−0.254770 | + | 0.967002i | \(0.582000\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.0000 | −1.04061 | −0.520306 | − | 0.853980i | \(-0.674182\pi\) | ||||
−0.520306 | + | 0.853980i | \(0.674182\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.50000 | − | 2.59808i | −0.110282 | − | 0.191014i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −21.0000 | −1.53567 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.50000 | + | 2.59808i | −0.108536 | + | 0.187990i | −0.915177 | − | 0.403051i | \(-0.867950\pi\) |
0.806641 | + | 0.591041i | \(0.201283\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.50000 | + | 12.9904i | 0.539862 | + | 0.935068i | 0.998911 | + | 0.0466572i | \(0.0148568\pi\) |
−0.459049 | + | 0.888411i | \(0.651810\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.5000 | − | 19.9186i | −0.819341 | − | 1.41914i | −0.906168 | − | 0.422917i | \(-0.861006\pi\) |
0.0868274 | − | 0.996223i | \(-0.472327\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.50000 | + | 7.79423i | −0.318997 | + | 0.552518i | −0.980279 | − | 0.197619i | \(-0.936679\pi\) |
0.661282 | + | 0.750137i | \(0.270013\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 15.0000 | 1.05279 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.50000 | − | 6.06218i | −0.244451 | − | 0.423401i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.00000 | −0.207514 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.50000 | + | 4.33013i | 0.172107 | + | 0.298098i | 0.939156 | − | 0.343490i | \(-0.111609\pi\) |
−0.767049 | + | 0.641588i | \(0.778276\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.50000 | + | 7.79423i | −0.306897 | + | 0.531562i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.00000 | − | 10.3923i | 0.407307 | − | 0.705476i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 17.5000 | + | 18.1865i | 1.17718 | + | 1.22336i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.5000 | + | 19.9186i | 0.770097 | + | 1.33385i | 0.937509 | + | 0.347960i | \(0.113126\pi\) |
−0.167412 | + | 0.985887i | \(0.553541\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.500000 | + | 0.866025i | −0.0331862 | + | 0.0574801i | −0.882141 | − | 0.470985i | \(-0.843899\pi\) |
0.848955 | + | 0.528465i | \(0.177232\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 26.0000 | 1.71813 | 0.859064 | − | 0.511868i | \(-0.171046\pi\) | ||||
0.859064 | + | 0.511868i | \(0.171046\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −18.0000 | −1.17922 | −0.589610 | − | 0.807688i | \(-0.700718\pi\) | ||||
−0.589610 | + | 0.807688i | \(0.700718\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.00000 | 0.521862 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 16.0000 | 1.03495 | 0.517477 | − | 0.855697i | \(-0.326871\pi\) | ||||
0.517477 | + | 0.855697i | \(0.326871\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.500000 | − | 0.866025i | 0.0322078 | − | 0.0557856i | −0.849472 | − | 0.527633i | \(-0.823079\pi\) |
0.881680 | + | 0.471848i | \(0.156413\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.00000 | + | 1.73205i | 0.0638877 | + | 0.110657i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.50000 | + | 2.59808i | 0.159071 | + | 0.165312i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.50000 | − | 4.33013i | 0.157799 | − | 0.273315i | −0.776276 | − | 0.630393i | \(-0.782894\pi\) |
0.934075 | + | 0.357078i | \(0.116227\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10.5000 | − | 18.1865i | 0.660129 | − | 1.14338i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −9.50000 | − | 16.4545i | −0.592594 | − | 1.02640i | −0.993882 | − | 0.110450i | \(-0.964771\pi\) |
0.401288 | − | 0.915952i | \(-0.368563\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.00000 | −0.559233 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.50000 | − | 6.06218i | −0.215819 | − | 0.373810i | 0.737706 | − | 0.675122i | \(-0.235909\pi\) |
−0.953526 | + | 0.301312i | \(0.902576\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.00000 | −0.368577 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.50000 | − | 2.59808i | 0.0914566 | − | 0.158408i | −0.816668 | − | 0.577108i | \(-0.804181\pi\) |
0.908124 | + | 0.418701i | \(0.137514\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.5000 | − | 19.9186i | −0.698575 | − | 1.20997i | −0.968960 | − | 0.247216i | \(-0.920484\pi\) |
0.270385 | − | 0.962752i | \(-0.412849\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.50000 | + | 2.59808i | 0.0904534 | + | 0.156670i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.5000 | − | 19.9186i | 0.690968 | − | 1.19679i | −0.280553 | − | 0.959839i | \(-0.590518\pi\) |
0.971521 | − | 0.236953i | \(-0.0761488\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.0000 | 0.596550 | 0.298275 | − | 0.954480i | \(-0.403589\pi\) | ||||
0.298275 | + | 0.954480i | \(0.403589\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.500000 | − | 0.866025i | −0.0297219 | − | 0.0514799i | 0.850782 | − | 0.525519i | \(-0.176129\pi\) |
−0.880504 | + | 0.474039i | \(0.842796\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −21.0000 | −1.23959 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.0000 | − | 27.7128i | −0.941176 | − | 1.63017i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.50000 | − | 7.79423i | 0.262893 | − | 0.455344i | −0.704117 | − | 0.710084i | \(-0.748657\pi\) |
0.967009 | + | 0.254741i | \(0.0819901\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.50000 | + | 4.33013i | −0.145556 | + | 0.252110i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −24.5000 | + | 6.06218i | −1.41687 | + | 0.350585i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 13.5000 | + | 23.3827i | 0.778127 | + | 1.34776i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.50000 | + | 4.33013i | −0.143150 | + | 0.247942i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 28.0000 | 1.59804 | 0.799022 | − | 0.601302i | \(-0.205351\pi\) | ||||
0.799022 | + | 0.601302i | \(0.205351\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 24.0000 | 1.36092 | 0.680458 | − | 0.732787i | \(-0.261781\pi\) | ||||
0.680458 | + | 0.732787i | \(0.261781\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.00000 | −0.339140 | −0.169570 | − | 0.985518i | \(-0.554238\pi\) | ||||
−0.169570 | + | 0.985518i | \(0.554238\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.00000 | 0.112331 | 0.0561656 | − | 0.998421i | \(-0.482113\pi\) | ||||
0.0561656 | + | 0.998421i | \(0.482113\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.50000 | − | 12.9904i | 0.419919 | − | 0.727322i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.50000 | − | 6.06218i | −0.194745 | − | 0.337309i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.00000 | − | 3.46410i | 0.0554700 | − | 0.192154i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 12.0000 | − | 20.7846i | 0.661581 | − | 1.14589i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.50000 | + | 11.2583i | −0.357272 | + | 0.618814i | −0.987504 | − | 0.157593i | \(-0.949627\pi\) |
0.630232 | + | 0.776407i | \(0.282960\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.50000 | + | 11.2583i | 0.355133 | + | 0.615108i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −18.0000 | −0.980522 | −0.490261 | − | 0.871576i | \(-0.663099\pi\) | ||||
−0.490261 | + | 0.871576i | \(0.663099\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.00000 | − | 10.3923i | −0.324918 | − | 0.562775i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.0000 | −0.809924 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6.50000 | + | 11.2583i | −0.348938 | + | 0.604379i | −0.986061 | − | 0.166383i | \(-0.946791\pi\) |
0.637123 | + | 0.770762i | \(0.280124\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.5000 | + | 21.6506i | 0.669110 | + | 1.15893i | 0.978153 | + | 0.207884i | \(0.0666577\pi\) |
−0.309044 | + | 0.951048i | \(0.600009\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.5000 | + | 18.1865i | 0.558859 | + | 0.967972i | 0.997592 | + | 0.0693543i | \(0.0220939\pi\) |
−0.438733 | + | 0.898617i | \(0.644573\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.50000 | − | 2.59808i | 0.0796117 | − | 0.137892i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.00000 | 0.422224 | 0.211112 | − | 0.977462i | \(-0.432292\pi\) | ||||
0.211112 | + | 0.977462i | \(0.432292\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.00000 | + | 15.5885i | 0.473684 | + | 0.820445i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 14.0000 | 0.732793 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.50000 | − | 7.79423i | −0.234898 | − | 0.406855i | 0.724345 | − | 0.689438i | \(-0.242142\pi\) |
−0.959243 | + | 0.282582i | \(0.908809\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9.00000 | + | 15.5885i | −0.467257 | + | 0.809312i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.5000 | − | 23.3827i | 0.699004 | − | 1.21071i | −0.269809 | − | 0.962914i | \(-0.586961\pi\) |
0.968812 | − | 0.247796i | \(-0.0797062\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −17.5000 | + | 4.33013i | −0.901296 | + | 0.223013i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.50000 | + | 7.79423i | 0.231149 | + | 0.400363i | 0.958147 | − | 0.286278i | \(-0.0924180\pi\) |
−0.726997 | + | 0.686640i | \(0.759085\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.50000 | + | 11.2583i | −0.332134 | + | 0.575274i | −0.982930 | − | 0.183979i | \(-0.941102\pi\) |
0.650796 | + | 0.759253i | \(0.274435\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9.00000 | 0.458682 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −18.0000 | −0.912636 | −0.456318 | − | 0.889817i | \(-0.650832\pi\) | ||||
−0.456318 | + | 0.889817i | \(0.650832\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 49.0000 | 2.47804 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.00000 | 0.402524 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −16.5000 | + | 28.5788i | −0.828111 | + | 1.43433i | 0.0714068 | + | 0.997447i | \(0.477251\pi\) |
−0.899518 | + | 0.436884i | \(0.856082\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.50000 | + | 12.9904i | 0.374532 | + | 0.648709i | 0.990257 | − | 0.139253i | \(-0.0444700\pi\) |
−0.615725 | + | 0.787961i | \(0.711137\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.00000 | + | 13.8564i | −0.199254 | + | 0.690237i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.50000 | + | 7.79423i | −0.223057 | + | 0.386346i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.500000 | − | 0.866025i | 0.0247234 | − | 0.0428222i | −0.853399 | − | 0.521258i | \(-0.825463\pi\) |
0.878122 | + | 0.478436i | \(0.158796\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.50000 | + | 12.9904i | 0.369051 | + | 0.639215i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12.0000 | 0.589057 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −16.5000 | − | 28.5788i | −0.806078 | − | 1.39617i | −0.915561 | − | 0.402179i | \(-0.868253\pi\) |
0.109483 | − | 0.993989i | \(-0.465080\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 34.0000 | 1.65706 | 0.828529 | − | 0.559946i | \(-0.189178\pi\) | ||||
0.828529 | + | 0.559946i | \(0.189178\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.50000 | + | 6.06218i | −0.169775 | + | 0.294059i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.50000 | + | 12.9904i | 0.362950 | + | 0.628649i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.50000 | − | 7.79423i | −0.216757 | − | 0.375435i | 0.737057 | − | 0.675830i | \(-0.236215\pi\) |
−0.953815 | + | 0.300395i | \(0.902881\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.500000 | + | 0.866025i | −0.0240285 | + | 0.0416185i | −0.877790 | − | 0.479046i | \(-0.840983\pi\) |
0.853761 | + | 0.520665i | \(0.174316\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.00000 | 0.334855 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.50000 | − | 2.59808i | −0.0715911 | − | 0.123999i | 0.828008 | − | 0.560717i | \(-0.189474\pi\) |
−0.899599 | + | 0.436717i | \(0.856141\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −24.0000 | −1.14027 | −0.570137 | − | 0.821549i | \(-0.693110\pi\) | ||||
−0.570137 | + | 0.821549i | \(0.693110\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.50000 | − | 6.06218i | −0.165916 | − | 0.287375i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10.5000 | + | 18.1865i | −0.495526 | + | 0.858276i | −0.999987 | − | 0.00515887i | \(-0.998358\pi\) |
0.504461 | + | 0.863434i | \(0.331691\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.5000 | + | 18.1865i | −0.494426 | + | 0.856370i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −7.50000 | − | 7.79423i | −0.351605 | − | 0.365399i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.5000 | + | 19.9186i | 0.537947 | + | 0.931752i | 0.999014 | + | 0.0443868i | \(0.0141334\pi\) |
−0.461067 | + | 0.887365i | \(0.652533\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.50000 | − | 9.52628i | 0.256161 | − | 0.443683i | −0.709050 | − | 0.705159i | \(-0.750876\pi\) |
0.965210 | + | 0.261476i | \(0.0842091\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −28.0000 | −1.30127 | −0.650635 | − | 0.759390i | \(-0.725497\pi\) | ||||
−0.650635 | + | 0.759390i | \(0.725497\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −20.0000 | −0.925490 | −0.462745 | − | 0.886492i | \(-0.653135\pi\) | ||||
−0.462745 | + | 0.886492i | \(0.653135\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 39.0000 | 1.80085 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 27.0000 | 1.24146 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.500000 | + | 0.866025i | −0.0229416 | + | 0.0397360i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −0.500000 | − | 0.866025i | −0.0228456 | − | 0.0395697i | 0.854377 | − | 0.519654i | \(-0.173939\pi\) |
−0.877222 | + | 0.480085i | \(0.840606\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.5000 | − | 2.59808i | 0.478759 | − | 0.118462i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5.50000 | + | 9.52628i | −0.249742 | + | 0.432566i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.50000 | − | 14.7224i | 0.385172 | − | 0.667137i | −0.606621 | − | 0.794991i | \(-0.707476\pi\) |
0.991793 | + | 0.127854i | \(0.0408089\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11.5000 | + | 19.9186i | 0.518988 | + | 0.898913i | 0.999757 | + | 0.0220657i | \(0.00702431\pi\) |
−0.480769 | + | 0.876847i | \(0.659642\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 35.0000 | 1.57632 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.50000 | − | 7.79423i | −0.201853 | − | 0.349619i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.0000 | −0.716258 | −0.358129 | − | 0.933672i | \(-0.616585\pi\) | ||||
−0.358129 | + | 0.933672i | \(0.616585\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.50000 | − | 9.52628i | 0.245233 | − | 0.424756i | −0.716964 | − | 0.697110i | \(-0.754469\pi\) |
0.962197 | + | 0.272354i | \(0.0878022\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.50000 | + | 7.79423i | 0.200247 | + | 0.346839i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7.50000 | + | 12.9904i | 0.332432 | + | 0.575789i | 0.982988 | − | 0.183669i | \(-0.0587976\pi\) |
−0.650556 | + | 0.759458i | \(0.725464\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 21.0000 | − | 36.3731i | 0.928985 | − | 1.60905i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 16.0000 | 0.705044 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −12.0000 | − | 20.7846i | −0.527759 | − | 0.914106i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 34.0000 | 1.48957 | 0.744784 | − | 0.667306i | \(-0.232553\pi\) | ||||
0.744784 | + | 0.667306i | \(0.232553\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.5000 | + | 19.9186i | 0.502860 | + | 0.870979i | 0.999995 | + | 0.00330547i | \(0.00105217\pi\) |
−0.497135 | + | 0.867673i | \(0.665615\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 14.0000 | − | 24.2487i | 0.609850 | − | 1.05629i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −13.0000 | + | 22.5167i | −0.565217 | + | 0.978985i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 24.5000 | − | 6.06218i | 1.06121 | − | 0.262582i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.50000 | + | 2.59808i | 0.0648507 | + | 0.112325i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.00000 | − | 5.19615i | 0.129219 | − | 0.223814i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.0000 | 0.429934 | 0.214967 | − | 0.976621i | \(-0.431036\pi\) | ||||
0.214967 | + | 0.976621i | \(0.431036\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 14.0000 | 0.599694 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.0000 | −0.684111 | −0.342055 | − | 0.939680i | \(-0.611123\pi\) | ||||
−0.342055 | + | 0.939680i | \(0.611123\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.00000 | 0.213007 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.0000 | − | 20.7846i | 0.510292 | − | 0.883852i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −9.50000 | − | 16.4545i | −0.402528 | − | 0.697199i | 0.591502 | − | 0.806303i | \(-0.298535\pi\) |
−0.994030 | + | 0.109104i | \(0.965202\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −22.5000 | − | 23.3827i | −0.951649 | − | 0.988982i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −22.5000 | + | 38.9711i | −0.948262 | + | 1.64244i | −0.199177 | + | 0.979963i | \(0.563827\pi\) |
−0.749085 | + | 0.662474i | \(0.769506\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.50000 | + | 11.2583i | −0.273457 | + | 0.473642i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9.50000 | + | 16.4545i | 0.398261 | + | 0.689808i | 0.993511 | − | 0.113732i | \(-0.0362806\pi\) |
−0.595251 | + | 0.803540i | \(0.702947\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −40.0000 | −1.67395 | −0.836974 | − | 0.547243i | \(-0.815677\pi\) | ||||
−0.836974 | + | 0.547243i | \(0.815677\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.50000 | − | 6.06218i | −0.145960 | − | 0.252810i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.00000 | 0.0832611 | 0.0416305 | − | 0.999133i | \(-0.486745\pi\) | ||||
0.0416305 | + | 0.999133i | \(0.486745\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 18.0000 | − | 31.1769i | 0.746766 | − | 1.29344i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.00000 | + | 15.5885i | 0.372742 | + | 0.645608i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 18.5000 | + | 32.0429i | 0.763577 | + | 1.32255i | 0.940996 | + | 0.338418i | \(0.109892\pi\) |
−0.177419 | + | 0.984135i | \(0.556775\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.00000 | − | 3.46410i | 0.0824086 | − | 0.142736i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −26.0000 | −1.06769 | −0.533846 | − | 0.845582i | \(-0.679254\pi\) | ||||
−0.533846 | + | 0.845582i | \(0.679254\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 10.5000 | + | 18.1865i | 0.430458 | + | 0.745575i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8.00000 | −0.326871 | −0.163436 | − | 0.986554i | \(-0.552258\pi\) | ||||
−0.163436 | + | 0.986554i | \(0.552258\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.50000 | + | 11.2583i | 0.265141 | + | 0.459237i | 0.967600 | − | 0.252486i | \(-0.0812483\pi\) |
−0.702460 | + | 0.711723i | \(0.747915\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.00000 | + | 1.73205i | −0.0406558 | + | 0.0704179i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.50000 | − | 7.79423i | 0.182649 | − | 0.316358i | −0.760133 | − | 0.649768i | \(-0.774866\pi\) |
0.942782 | + | 0.333410i | \(0.108199\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.00000 | + | 27.7128i | −0.323645 | + | 1.12114i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15.5000 | + | 26.8468i | 0.626039 | + | 1.08433i | 0.988339 | + | 0.152270i | \(0.0486583\pi\) |
−0.362300 | + | 0.932062i | \(0.618008\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 14.5000 | − | 25.1147i | 0.583748 | − | 1.01108i | −0.411282 | − | 0.911508i | \(-0.634919\pi\) |
0.995030 | − | 0.0995732i | \(-0.0317477\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12.0000 | 0.482321 | 0.241160 | − | 0.970485i | \(-0.422472\pi\) | ||||
0.241160 | + | 0.970485i | \(0.422472\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −21.0000 | −0.841347 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −21.0000 | −0.837325 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.50000 | − | 12.9904i | 0.298570 | − | 0.517139i | −0.677239 | − | 0.735763i | \(-0.736824\pi\) |
0.975809 | + | 0.218624i | \(0.0701569\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.500000 | + | 0.866025i | 0.0198419 | + | 0.0343672i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7.00000 | + | 1.73205i | −0.277350 | + | 0.0686264i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.5000 | + | 18.1865i | −0.414725 | + | 0.718325i | −0.995400 | − | 0.0958109i | \(-0.969456\pi\) |
0.580674 | + | 0.814136i | \(0.302789\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.50000 | + | 6.06218i | −0.138027 | + | 0.239069i | −0.926750 | − | 0.375680i | \(-0.877409\pi\) |
0.788723 | + | 0.614749i | \(0.210743\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8.50000 | + | 14.7224i | 0.334169 | + | 0.578799i | 0.983325 | − | 0.181857i | \(-0.0582109\pi\) |
−0.649155 | + | 0.760656i | \(0.724878\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 15.0000 | 0.588802 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −5.50000 | − | 9.52628i | −0.215232 | − | 0.372792i | 0.738113 | − | 0.674678i | \(-0.235717\pi\) |
−0.953344 | + | 0.301885i | \(0.902384\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.00000 | 0.156293 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.50000 | + | 12.9904i | −0.292159 | + | 0.506033i | −0.974320 | − | 0.225168i | \(-0.927707\pi\) |
0.682161 | + | 0.731202i | \(0.261040\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.50000 | + | 14.7224i | 0.330612 | + | 0.572636i | 0.982632 | − | 0.185565i | \(-0.0594116\pi\) |
−0.652020 | + | 0.758202i | \(0.726078\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.50000 | + | 2.59808i | 0.0581675 | + | 0.100749i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −17.5000 | + | 30.3109i | −0.677603 | + | 1.17364i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 15.0000 | 0.579069 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.50000 | − | 11.2583i | −0.250557 | − | 0.433977i | 0.713123 | − | 0.701039i | \(-0.247280\pi\) |
−0.963679 | + | 0.267063i | \(0.913947\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −22.0000 | −0.845529 | −0.422764 | − | 0.906240i | \(-0.638940\pi\) | ||||
−0.422764 | + | 0.906240i | \(0.638940\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 16.5000 | + | 28.5788i | 0.633212 | + | 1.09676i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 15.5000 | − | 26.8468i | 0.593091 | − | 1.02726i | −0.400722 | − | 0.916200i | \(-0.631241\pi\) |
0.993813 | − | 0.111064i | \(-0.0354259\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.50000 | − | 2.59808i | 0.0573121 | − | 0.0992674i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.00000 | − | 20.7846i | 0.228582 | − | 0.791831i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.5000 | + | 21.6506i | 0.475522 | + | 0.823629i | 0.999607 | − | 0.0280373i | \(-0.00892572\pi\) |
−0.524084 | + | 0.851666i | \(0.675592\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.50000 | − | 11.2583i | 0.246559 | − | 0.427053i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −49.0000 | −1.85601 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.00000 | −0.0755390 | −0.0377695 | − | 0.999286i | \(-0.512025\pi\) | ||||
−0.0377695 | + | 0.999286i | \(0.512025\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.00000 | −0.113147 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 27.0000 | 1.01544 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17.5000 | + | 30.3109i | −0.657226 | + | 1.13835i | 0.324104 | + | 0.946021i | \(0.394937\pi\) |
−0.981331 | + | 0.192328i | \(0.938396\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 14.0000 | + | 24.2487i | 0.524304 | + | 0.908121i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10.5000 | + | 2.59808i | −0.392678 | + | 0.0971625i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0.500000 | − | 0.866025i | 0.0186469 | − | 0.0322973i | −0.856551 | − | 0.516062i | \(-0.827398\pi\) |
0.875198 | + | 0.483764i | \(0.160731\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 24.0000 | − | 41.5692i | 0.893807 | − | 1.54812i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.50000 | − | 4.33013i | −0.0928477 | − | 0.160817i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −28.0000 | −1.03846 | −0.519231 | − | 0.854634i | \(-0.673782\pi\) | ||||
−0.519231 | + | 0.854634i | \(0.673782\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 31.5000 | + | 54.5596i | 1.16507 | + | 2.01796i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14.0000 | 0.517102 | 0.258551 | − | 0.965998i | \(-0.416755\pi\) | ||||
0.258551 | + | 0.965998i | \(0.416755\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 19.5000 | − | 33.7750i | 0.718292 | − | 1.24412i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −19.5000 | − | 33.7750i | −0.717319 | − | 1.24243i | −0.962058 | − | 0.272844i | \(-0.912036\pi\) |
0.244739 | − | 0.969589i | \(-0.421298\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0.500000 | + | 0.866025i | 0.0183432 | + | 0.0317714i | 0.875051 | − | 0.484030i | \(-0.160828\pi\) |
−0.856708 | + | 0.515802i | \(0.827494\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.50000 | + | 2.59808i | −0.0549557 | + | 0.0951861i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.00000 | 0.328853 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.50000 | + | 11.2583i | 0.237188 | + | 0.410822i | 0.959906 | − | 0.280321i | \(-0.0904408\pi\) |
−0.722718 | + | 0.691143i | \(0.757107\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.00000 | 0.291150 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −0.500000 | − | 0.866025i | −0.0181728 | − | 0.0314762i | 0.856796 | − | 0.515656i | \(-0.172452\pi\) |
−0.874969 | + | 0.484179i | \(0.839118\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 25.5000 | − | 44.1673i | 0.924374 | − | 1.60106i | 0.131810 | − | 0.991275i | \(-0.457921\pi\) |
0.792564 | − | 0.609788i | \(-0.208745\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 21.0000 | − | 36.3731i | 0.760251 | − | 1.31679i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −12.5000 | − | 12.9904i | −0.451349 | − | 0.469055i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.50000 | + | 4.33013i | 0.0901523 | + | 0.156148i | 0.907575 | − | 0.419890i | \(-0.137931\pi\) |
−0.817423 | + | 0.576038i | \(0.804598\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 12.5000 | − | 21.6506i | 0.449594 | − | 0.778719i | −0.548766 | − | 0.835976i | \(-0.684902\pi\) |
0.998359 | + | 0.0572570i | \(0.0182354\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.00000 | −0.143684 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −7.00000 | −0.250801 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.00000 | −0.322045 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.00000 | −0.214149 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.500000 | − | 0.866025i | 0.0178231 | − | 0.0308705i | −0.856976 | − | 0.515356i | \(-0.827660\pi\) |
0.874799 | + | 0.484485i | \(0.160993\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 19.5000 | + | 33.7750i | 0.693340 | + | 1.20090i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −12.5000 | − | 12.9904i | −0.443888 | − | 0.461302i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.50000 | + | 6.06218i | −0.123976 | + | 0.214733i | −0.921332 | − | 0.388776i | \(-0.872898\pi\) |
0.797356 | + | 0.603509i | \(0.206231\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 28.0000 | − | 48.4974i | 0.990569 | − | 1.71572i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −21.0000 | − | 36.3731i | −0.741074 | − | 1.28358i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −21.0000 | −0.740153 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −12.5000 | − | 21.6506i | −0.439477 | − | 0.761196i | 0.558173 | − | 0.829725i | \(-0.311503\pi\) |
−0.997649 | + | 0.0685291i | \(0.978169\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.50000 | − | 9.52628i | 0.192657 | − | 0.333691i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.50000 | + | 7.79423i | 0.157435 | + | 0.272686i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.50000 | + | 12.9904i | 0.261752 | + | 0.453367i | 0.966708 | − | 0.255884i | \(-0.0823665\pi\) |
−0.704956 | + | 0.709251i | \(0.749033\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −23.5000 | + | 40.7032i | −0.819159 | + | 1.41882i | 0.0871445 | + | 0.996196i | \(0.472226\pi\) |
−0.906303 | + | 0.422628i | \(0.861108\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −12.0000 | −0.417281 | −0.208640 | − | 0.977992i | \(-0.566904\pi\) | ||||
−0.208640 | + | 0.977992i | \(0.566904\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.50000 | + | 11.2583i | 0.225754 | + | 0.391018i | 0.956545 | − | 0.291583i | \(-0.0941820\pi\) |
−0.730791 | + | 0.682601i | \(0.760849\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 14.0000 | 0.485071 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.500000 | − | 0.866025i | −0.0173032 | − | 0.0299700i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6.50000 | − | 11.2583i | 0.224405 | − | 0.388681i | −0.731736 | − | 0.681588i | \(-0.761290\pi\) |
0.956141 | + | 0.292908i | \(0.0946228\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.00000 | − | 3.46410i | 0.0689655 | − | 0.119452i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 11.0000 | + | 6.92820i | 0.378412 | + | 0.238337i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.00000 | + | 5.19615i | 0.103081 | + | 0.178542i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10.5000 | − | 18.1865i | 0.359935 | − | 0.623426i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10.0000 | 0.342393 | 0.171197 | − | 0.985237i | \(-0.445237\pi\) | ||||
0.171197 | + | 0.985237i | \(0.445237\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −18.0000 | −0.614868 | −0.307434 | − | 0.951569i | \(-0.599470\pi\) | ||||
−0.307434 | + | 0.951569i | \(0.599470\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 44.0000 | 1.50126 | 0.750630 | − | 0.660722i | \(-0.229750\pi\) | ||||
0.750630 | + | 0.660722i | \(0.229750\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −16.0000 | −0.544646 | −0.272323 | − | 0.962206i | \(-0.587792\pi\) | ||||
−0.272323 | + | 0.962206i | \(0.587792\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.50000 | − | 12.9904i | 0.255008 | − | 0.441686i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −12.0000 | − | 20.7846i | −0.407072 | − | 0.705070i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −45.5000 | + | 11.2583i | −1.54171 | + | 0.381474i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.50000 | − | 2.59808i | 0.0507093 | − | 0.0878310i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.50000 | + | 4.33013i | −0.0844190 | + | 0.146218i | −0.905143 | − | 0.425106i | \(-0.860237\pi\) |
0.820724 | + | 0.571324i | \(0.193570\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5.50000 | + | 9.52628i | 0.185300 | + | 0.320949i | 0.943677 | − | 0.330867i | \(-0.107341\pi\) |
−0.758378 | + | 0.651815i | \(0.774008\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −44.0000 | −1.48072 | −0.740359 | − | 0.672212i | \(-0.765344\pi\) | ||||
−0.740359 | + | 0.672212i | \(0.765344\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −9.50000 | − | 16.4545i | −0.318979 | − | 0.552487i | 0.661296 | − | 0.750125i | \(-0.270007\pi\) |
−0.980275 | + | 0.197637i | \(0.936673\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.00000 | 0.100617 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.00000 | − | 6.92820i | 0.133855 | − | 0.231843i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9.50000 | − | 16.4545i | −0.317550 | − | 0.550013i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 10.0000 | + | 17.3205i | 0.333519 | + | 0.577671i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −21.0000 | + | 36.3731i | −0.699611 | + | 1.21176i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 14.0000 | 0.465376 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.50000 | − | 14.7224i | −0.282238 | − | 0.488850i | 0.689698 | − | 0.724097i | \(-0.257743\pi\) |
−0.971936 | + | 0.235247i | \(0.924410\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.0000 | 0.397578 | 0.198789 | − | 0.980042i | \(-0.436299\pi\) | ||||
0.198789 | + | 0.980042i | \(0.436299\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −18.0000 | − | 31.1769i | −0.595713 | − | 1.03181i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6.00000 | − | 10.3923i | 0.198137 | − | 0.343184i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 21.5000 | − | 37.2391i | 0.709220 | − | 1.22840i | −0.255927 | − | 0.966696i | \(-0.582381\pi\) |
0.965147 | − | 0.261708i | \(-0.0842858\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 7.50000 | + | 7.79423i | 0.246866 | + | 0.256550i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.50000 | + | 2.59808i | 0.0493197 | + | 0.0854242i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −26.5000 | + | 45.8993i | −0.869437 | + | 1.50591i | −0.00686358 | + | 0.999976i | \(0.502185\pi\) |
−0.862573 | + | 0.505932i | \(0.831149\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.00000 | 0.0655474 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 21.0000 | 0.686773 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 50.0000 | 1.63343 | 0.816714 | − | 0.577042i | \(-0.195793\pi\) | ||||
0.816714 | + | 0.577042i | \(0.195793\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −42.0000 | −1.36916 | −0.684580 | − | 0.728937i | \(-0.740015\pi\) | ||||
−0.684580 | + | 0.728937i | \(0.740015\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 24.5000 | − | 42.4352i | 0.797830 | − | 1.38188i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −27.5000 | − | 47.6314i | −0.893630 | − | 1.54781i | −0.835491 | − | 0.549504i | \(-0.814817\pi\) |
−0.0581388 | − | 0.998309i | \(-0.518517\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −14.0000 | + | 48.4974i | −0.454459 | + | 1.57429i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −15.5000 | + | 26.8468i | −0.502094 | + | 0.869653i | 0.497903 | + | 0.867233i | \(0.334104\pi\) |
−0.999997 | + | 0.00241992i | \(0.999230\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.50000 | − | 2.59808i | 0.0485389 | − | 0.0840718i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.50000 | − | 7.79423i | −0.145313 | − | 0.251689i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −7.50000 | − | 12.9904i | −0.241434 | − | 0.418175i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −48.0000 | −1.54358 | −0.771788 | − | 0.635880i | \(-0.780637\pi\) | ||||
−0.771788 | + | 0.635880i | \(0.780637\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −21.5000 | + | 37.2391i | −0.689968 | + | 1.19506i | 0.281880 | + | 0.959450i | \(0.409042\pi\) |
−0.971848 | + | 0.235610i | \(0.924291\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −19.5000 | − | 33.7750i | −0.625141 | − | 1.08278i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.50000 | − | 2.59808i | −0.0479893 | − | 0.0831198i | 0.841033 | − | 0.540984i | \(-0.181948\pi\) |
−0.889022 | + | 0.457864i | \(0.848615\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −10.5000 | + | 18.1865i | −0.335581 | + | 0.581244i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −36.0000 | −1.14822 | −0.574111 | − | 0.818778i | \(-0.694652\pi\) | ||||
−0.574111 | + | 0.818778i | \(0.694652\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11.5000 | + | 19.9186i | 0.366420 | + | 0.634659i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −63.0000 | −2.00328 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.50000 | + | 11.2583i | 0.206479 | + | 0.357633i | 0.950603 | − | 0.310409i | \(-0.100466\pi\) |
−0.744124 | + | 0.668042i | \(0.767133\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.50000 | − | 7.79423i | 0.142660 | − | 0.247094i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −6.50000 | + | 11.2583i | −0.205857 | + | 0.356555i | −0.950405 | − | 0.311014i | \(-0.899332\pi\) |
0.744548 | + | 0.667568i | \(0.232665\pi\) | |||||||
\(998\) | 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 | 2340.2.q.a.2161.1 | 2 | ||
3.2 | odd | 2 | 260.2.i.d.81.1 | yes | 2 | ||
12.11 | even | 2 | 1040.2.q.b.81.1 | 2 | |||
13.9 | even | 3 | inner | 2340.2.q.a.1621.1 | 2 | ||
15.2 | even | 4 | 1300.2.bb.e.549.2 | 4 | |||
15.8 | even | 4 | 1300.2.bb.e.549.1 | 4 | |||
15.14 | odd | 2 | 1300.2.i.a.601.1 | 2 | |||
39.2 | even | 12 | 3380.2.f.a.3041.1 | 2 | |||
39.11 | even | 12 | 3380.2.f.a.3041.2 | 2 | |||
39.23 | odd | 6 | 3380.2.a.a.1.1 | 1 | |||
39.29 | odd | 6 | 3380.2.a.b.1.1 | 1 | |||
39.35 | odd | 6 | 260.2.i.d.61.1 | ✓ | 2 | ||
156.35 | even | 6 | 1040.2.q.b.321.1 | 2 | |||
195.74 | odd | 6 | 1300.2.i.a.1101.1 | 2 | |||
195.113 | even | 12 | 1300.2.bb.e.1049.2 | 4 | |||
195.152 | even | 12 | 1300.2.bb.e.1049.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
260.2.i.d.61.1 | ✓ | 2 | 39.35 | odd | 6 | ||
260.2.i.d.81.1 | yes | 2 | 3.2 | odd | 2 | ||
1040.2.q.b.81.1 | 2 | 12.11 | even | 2 | |||
1040.2.q.b.321.1 | 2 | 156.35 | even | 6 | |||
1300.2.i.a.601.1 | 2 | 15.14 | odd | 2 | |||
1300.2.i.a.1101.1 | 2 | 195.74 | odd | 6 | |||
1300.2.bb.e.549.1 | 4 | 15.8 | even | 4 | |||
1300.2.bb.e.549.2 | 4 | 15.2 | even | 4 | |||
1300.2.bb.e.1049.1 | 4 | 195.152 | even | 12 | |||
1300.2.bb.e.1049.2 | 4 | 195.113 | even | 12 | |||
2340.2.q.a.1621.1 | 2 | 13.9 | even | 3 | inner | ||
2340.2.q.a.2161.1 | 2 | 1.1 | even | 1 | trivial | ||
3380.2.a.a.1.1 | 1 | 39.23 | odd | 6 | |||
3380.2.a.b.1.1 | 1 | 39.29 | odd | 6 | |||
3380.2.f.a.3041.1 | 2 | 39.2 | even | 12 | |||
3380.2.f.a.3041.2 | 2 | 39.11 | even | 12 |