Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [260,2,Mod(61,260)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(260, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([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("260.61");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 260 = 2^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 260.i (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: | \(2.07611045255\) |
Analytic rank: | \(0\) |
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: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 81.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 260.81 |
Dual form | 260.2.i.d.61.1 |
$q$-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 \(\left(\mathbb{Z}/260\mathbb{Z}\right)^\times\).
\(n\) | \(41\) | \(131\) | \(157\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 1.50000 | + | 2.59808i | 0.866025 | + | 1.50000i | 0.866025 | + | 0.500000i | \(0.166667\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(4\) | 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 | ||||||||
\(9\) | −3.00000 | + | 5.19615i | −1.00000 | + | 1.73205i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.50000 | − | 2.59808i | −0.452267 | − | 0.783349i | 0.546259 | − | 0.837616i | \(-0.316051\pi\) |
−0.998526 | + | 0.0542666i | \(0.982718\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | − | 3.46410i | 0.277350 | − | 0.960769i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.50000 | + | 2.59808i | 0.387298 | + | 0.670820i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.50000 | − | 6.06218i | 0.848875 | − | 1.47029i | −0.0333386 | − | 0.999444i | \(-0.510614\pi\) |
0.882213 | − | 0.470850i | \(-0.156053\pi\) | |||||||
\(18\) | 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 | ||||||||
\(21\) | −9.00000 | −1.96396 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.50000 | + | 6.06218i | 0.729800 | + | 1.26405i | 0.956967 | + | 0.290196i | \(0.0937204\pi\) |
−0.227167 | + | 0.973856i | \(0.572946\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −9.00000 | −1.73205 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.50000 | + | 4.33013i | 0.464238 | + | 0.804084i | 0.999167 | − | 0.0408130i | \(-0.0129948\pi\) |
−0.534928 | + | 0.844897i | \(0.679661\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.00000 | −0.718421 | −0.359211 | − | 0.933257i | \(-0.616954\pi\) | ||||
−0.359211 | + | 0.933257i | \(0.616954\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.50000 | − | 7.79423i | 0.783349 | − | 1.35680i | ||||
\(34\) | 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 | ||||||||
\(39\) | 10.5000 | − | 2.59808i | 1.68135 | − | 0.416025i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.50000 | − | 6.06218i | −0.546608 | − | 0.946753i | −0.998504 | − | 0.0546823i | \(-0.982585\pi\) |
0.451896 | − | 0.892071i | \(-0.350748\pi\) | |||||||
\(42\) | 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 | ||||||||
\(45\) | −3.00000 | + | 5.19615i | −0.447214 | + | 0.774597i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.00000 | 1.16692 | 0.583460 | − | 0.812142i | \(-0.301699\pi\) | ||||
0.583460 | + | 0.812142i | \(0.301699\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | − | 1.73205i | −0.142857 | − | 0.247436i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 21.0000 | 2.94059 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.00000 | −0.824163 | −0.412082 | − | 0.911147i | \(-0.635198\pi\) | ||||
−0.412082 | + | 0.911147i | \(0.635198\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.50000 | − | 2.59808i | −0.202260 | − | 0.350325i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.00000 | −0.397360 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.50000 | + | 4.33013i | −0.325472 | + | 0.563735i | −0.981608 | − | 0.190909i | \(-0.938857\pi\) |
0.656136 | + | 0.754643i | \(0.272190\pi\) | |||||||
\(60\) | 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 | ||||||||
\(63\) | −9.00000 | − | 15.5885i | −1.13389 | − | 1.96396i | ||||
\(64\) | 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 | ||||||||
\(69\) | −10.5000 | + | 18.1865i | −1.26405 | + | 2.18940i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.50000 | − | 2.59808i | 0.178017 | − | 0.308335i | −0.763184 | − | 0.646181i | \(-0.776365\pi\) |
0.941201 | + | 0.337846i | \(0.109698\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −14.0000 | −1.63858 | −0.819288 | − | 0.573382i | \(-0.805631\pi\) | ||||
−0.819288 | + | 0.573382i | \(0.805631\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.50000 | + | 2.59808i | 0.173205 | + | 0.300000i | ||||
\(76\) | 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 | ||||||||
\(81\) | −4.50000 | − | 7.79423i | −0.500000 | − | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.0000 | 1.31717 | 0.658586 | − | 0.752506i | \(-0.271155\pi\) | ||||
0.658586 | + | 0.752506i | \(0.271155\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.50000 | − | 6.06218i | 0.379628 | − | 0.657536i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −7.50000 | + | 12.9904i | −0.804084 | + | 1.39272i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.50000 | − | 6.06218i | −0.370999 | − | 0.642590i | 0.618720 | − | 0.785611i | \(-0.287651\pi\) |
−0.989720 | + | 0.143022i | \(0.954318\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.50000 | + | 7.79423i | 0.786214 | + | 0.817057i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.00000 | − | 10.3923i | −0.622171 | − | 1.07763i | ||||
\(94\) | 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 | ||||||||
\(99\) | 18.0000 | 1.80907 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.50000 | + | 7.79423i | 0.447767 | + | 0.775555i | 0.998240 | − | 0.0592978i | \(-0.0188862\pi\) |
−0.550474 | + | 0.834853i | \(0.685553\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.0000 | −1.57653 | −0.788263 | − | 0.615338i | \(-0.789020\pi\) | ||||
−0.788263 | + | 0.615338i | \(0.789020\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −9.00000 | −0.878310 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.50000 | + | 2.59808i | 0.145010 | + | 0.251166i | 0.929377 | − | 0.369132i | \(-0.120345\pi\) |
−0.784366 | + | 0.620298i | \(0.787012\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14.0000 | −1.34096 | −0.670478 | − | 0.741929i | \(-0.733911\pi\) | ||||
−0.670478 | + | 0.741929i | \(0.733911\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.50000 | + | 7.79423i | −0.427121 | + | 0.739795i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.50000 | + | 11.2583i | −0.611469 | + | 1.05909i | 0.379525 | + | 0.925182i | \(0.376088\pi\) |
−0.990993 | + | 0.133913i | \(0.957246\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.50000 | + | 6.06218i | 0.326377 | + | 0.565301i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 15.0000 | + | 15.5885i | 1.38675 | + | 1.44115i | ||||
\(118\) | 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 | ||||||||
\(123\) | 10.5000 | − | 18.1865i | 0.946753 | − | 1.63982i | ||||
\(124\) | 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 | ||||||||
\(129\) | 27.0000 | 2.37722 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.00000 | 0.349482 | 0.174741 | − | 0.984614i | \(-0.444091\pi\) | ||||
0.174741 | + | 0.984614i | \(0.444091\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.50000 | − | 2.59808i | −0.130066 | − | 0.225282i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −9.00000 | −0.774597 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.50000 | − | 2.59808i | 0.128154 | − | 0.221969i | −0.794808 | − | 0.606861i | \(-0.792428\pi\) |
0.922961 | + | 0.384893i | \(0.125762\pi\) | |||||||
\(138\) | 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 | ||||||||
\(141\) | 12.0000 | + | 20.7846i | 1.01058 | + | 1.75038i | ||||
\(142\) | 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 | ||||||||
\(147\) | 3.00000 | − | 5.19615i | 0.247436 | − | 0.428571i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.50000 | + | 2.59808i | −0.122885 | + | 0.212843i | −0.920904 | − | 0.389789i | \(-0.872548\pi\) |
0.798019 | + | 0.602632i | \(0.205881\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.00000 | −0.651031 | −0.325515 | − | 0.945537i | \(-0.605538\pi\) | ||||
−0.325515 | + | 0.945537i | \(0.605538\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 21.0000 | + | 36.3731i | 1.69775 | + | 2.94059i | ||||
\(154\) | 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 | ||||||||
\(159\) | −9.00000 | − | 15.5885i | −0.713746 | − | 1.23625i | ||||
\(160\) | 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 | ||||||||
\(165\) | 4.50000 | − | 7.79423i | 0.350325 | − | 0.606780i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.500000 | − | 0.866025i | −0.0386912 | − | 0.0670151i | 0.846031 | − | 0.533133i | \(-0.178986\pi\) |
−0.884723 | + | 0.466118i | \(0.845652\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.0000 | − | 6.92820i | −0.846154 | − | 0.532939i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.00000 | − | 5.19615i | −0.229416 | − | 0.397360i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.50000 | − | 12.9904i | 0.570214 | − | 0.987640i | −0.426329 | − | 0.904568i | \(-0.640193\pi\) |
0.996544 | − | 0.0830722i | \(-0.0264732\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.50000 | + | 2.59808i | −0.113389 | + | 0.196396i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −15.0000 | −1.12747 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.50000 | − | 16.4545i | −0.710063 | − | 1.22987i | −0.964833 | − | 0.262864i | \(-0.915333\pi\) |
0.254770 | − | 0.967002i | \(-0.418000\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.0000 | −1.04061 | −0.520306 | − | 0.853980i | \(-0.674182\pi\) | ||||
−0.520306 | + | 0.853980i | \(0.674182\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 15.0000 | 1.10883 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.50000 | + | 2.59808i | 0.110282 | + | 0.191014i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −21.0000 | −1.53567 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 13.5000 | − | 23.3827i | 0.981981 | − | 1.70084i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.50000 | − | 2.59808i | 0.108536 | − | 0.187990i | −0.806641 | − | 0.591041i | \(-0.798717\pi\) |
0.915177 | + | 0.403051i | \(0.132050\pi\) | |||||||
\(192\) | 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 | ||||||||
\(195\) | 10.5000 | − | 2.59808i | 0.751921 | − | 0.186052i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.5000 | + | 19.9186i | 0.819341 | + | 1.41914i | 0.906168 | + | 0.422917i | \(0.138994\pi\) |
−0.0868274 | + | 0.996223i | \(0.527673\pi\) | |||||||
\(198\) | 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 | ||||||||
\(201\) | 19.5000 | − | 33.7750i | 1.37542 | − | 2.38230i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −15.0000 | −1.05279 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.50000 | − | 6.06218i | −0.244451 | − | 0.423401i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −42.0000 | −2.91920 | ||||||||
\(208\) | 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 | ||||||||
\(213\) | 9.00000 | 0.616670 | ||||||||
\(214\) | 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 | ||||||||
\(219\) | −21.0000 | − | 36.3731i | −1.41905 | − | 2.45786i | ||||
\(220\) | 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 | ||||||||
\(225\) | −3.00000 | + | 5.19615i | −0.200000 | + | 0.346410i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.500000 | − | 0.866025i | 0.0331862 | − | 0.0574801i | −0.848955 | − | 0.528465i | \(-0.822768\pi\) |
0.882141 | + | 0.470985i | \(0.156101\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 26.0000 | 1.71813 | 0.859064 | − | 0.511868i | \(-0.171046\pi\) | ||||
0.859064 | + | 0.511868i | \(0.171046\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 13.5000 | + | 23.3827i | 0.888235 | + | 1.53847i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 18.0000 | 1.17922 | 0.589610 | − | 0.807688i | \(-0.299282\pi\) | ||||
0.589610 | + | 0.807688i | \(0.299282\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.00000 | 0.521862 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −12.0000 | − | 20.7846i | −0.779484 | − | 1.35011i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −16.0000 | −1.03495 | −0.517477 | − | 0.855697i | \(-0.673129\pi\) | ||||
−0.517477 | + | 0.855697i | \(0.673129\pi\) | |||||||
\(240\) | 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 | ||||||||
\(249\) | 18.0000 | + | 31.1769i | 1.14070 | + | 1.97576i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.50000 | + | 4.33013i | −0.157799 | + | 0.273315i | −0.934075 | − | 0.357078i | \(-0.883773\pi\) |
0.776276 | + | 0.630393i | \(0.217106\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10.5000 | − | 18.1865i | 0.660129 | − | 1.14338i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 21.0000 | 1.31507 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 9.50000 | + | 16.4545i | 0.592594 | + | 1.02640i | 0.993882 | + | 0.110450i | \(0.0352294\pi\) |
−0.401288 | + | 0.915952i | \(0.631437\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.00000 | −0.559233 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −30.0000 | −1.85695 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.50000 | + | 6.06218i | 0.215819 | + | 0.373810i | 0.953526 | − | 0.301312i | \(-0.0974245\pi\) |
−0.737706 | + | 0.675122i | \(0.764091\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.00000 | −0.368577 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 10.5000 | − | 18.1865i | 0.642590 | − | 1.11300i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.50000 | + | 2.59808i | −0.0914566 | + | 0.158408i | −0.908124 | − | 0.418701i | \(-0.862486\pi\) |
0.816668 | + | 0.577108i | \(0.195819\pi\) | |||||||
\(270\) | 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 | ||||||||
\(273\) | −9.00000 | + | 31.1769i | −0.544705 | + | 1.88691i | ||||
\(274\) | 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 | ||||||||
\(279\) | 12.0000 | − | 20.7846i | 0.718421 | − | 1.24434i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.0000 | −0.596550 | −0.298275 | − | 0.954480i | \(-0.596411\pi\) | ||||
−0.298275 | + | 0.954480i | \(0.596411\pi\) | |||||||
\(282\) | 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 | ||||||||
\(285\) | −3.00000 | −0.177705 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 21.0000 | 1.23959 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.0000 | − | 27.7128i | −0.941176 | − | 1.63017i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 33.0000 | 1.93449 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4.50000 | + | 7.79423i | −0.262893 | + | 0.455344i | −0.967009 | − | 0.254741i | \(-0.918010\pi\) |
0.704117 | + | 0.710084i | \(0.251343\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.50000 | + | 4.33013i | −0.145556 | + | 0.252110i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 13.5000 | + | 23.3827i | 0.783349 | + | 1.35680i | ||||
\(298\) | 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 | ||||||||
\(303\) | −13.5000 | + | 23.3827i | −0.775555 | + | 1.34330i | ||||
\(304\) | 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 | ||||||||
\(309\) | −24.0000 | − | 41.5692i | −1.36531 | − | 2.36479i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −24.0000 | −1.36092 | −0.680458 | − | 0.732787i | \(-0.738219\pi\) | ||||
−0.680458 | + | 0.732787i | \(0.738219\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.00000 | −0.339140 | −0.169570 | − | 0.985518i | \(-0.554238\pi\) | ||||
−0.169570 | + | 0.985518i | \(0.554238\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −9.00000 | − | 15.5885i | −0.507093 | − | 0.878310i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.00000 | −0.112331 | −0.0561656 | − | 0.998421i | \(-0.517887\pi\) | ||||
−0.0561656 | + | 0.998421i | \(0.517887\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.50000 | − | 12.9904i | 0.419919 | − | 0.727322i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.50000 | + | 7.79423i | −0.251166 | + | 0.435031i | ||||
\(322\) | 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 | ||||||||
\(327\) | −21.0000 | − | 36.3731i | −1.16130 | − | 2.01144i | ||||
\(328\) | 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 | ||||||||
\(333\) | −18.0000 | −0.986394 | ||||||||
\(334\) | 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 | ||||||||
\(339\) | −39.0000 | −2.11819 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.00000 | + | 10.3923i | 0.324918 | + | 0.562775i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.0000 | −0.809924 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −10.5000 | + | 18.1865i | −0.565301 | + | 0.979130i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.50000 | − | 11.2583i | 0.348938 | − | 0.604379i | −0.637123 | − | 0.770762i | \(-0.719876\pi\) |
0.986061 | + | 0.166383i | \(0.0532089\pi\) | |||||||
\(348\) | 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 | ||||||||
\(351\) | −9.00000 | + | 31.1769i | −0.480384 | + | 1.66410i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.5000 | − | 18.1865i | −0.558859 | − | 0.967972i | −0.997592 | − | 0.0693543i | \(-0.977906\pi\) |
0.438733 | − | 0.898617i | \(-0.355427\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.50000 | − | 2.59808i | 0.0796117 | − | 0.137892i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −31.5000 | + | 54.5596i | −1.66716 | + | 2.88760i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8.00000 | −0.422224 | −0.211112 | − | 0.977462i | \(-0.567708\pi\) | ||||
−0.211112 | + | 0.977462i | \(0.567708\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.00000 | + | 15.5885i | 0.473684 | + | 0.820445i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6.00000 | 0.314918 | ||||||||
\(364\) | 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 | ||||||||
\(369\) | 42.0000 | 2.18643 | ||||||||
\(370\) | 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 | ||||||||
\(375\) | 1.50000 | + | 2.59808i | 0.0774597 | + | 0.134164i | ||||
\(376\) | 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 | ||||||||
\(381\) | 1.50000 | − | 2.59808i | 0.0768473 | − | 0.133103i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6.50000 | − | 11.2583i | 0.332134 | − | 0.575274i | −0.650796 | − | 0.759253i | \(-0.725565\pi\) |
0.982930 | + | 0.183979i | \(0.0588979\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9.00000 | 0.458682 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 27.0000 | + | 46.7654i | 1.37249 | + | 2.37722i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 18.0000 | 0.912636 | 0.456318 | − | 0.889817i | \(-0.349168\pi\) | ||||
0.456318 | + | 0.889817i | \(0.349168\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 49.0000 | 2.47804 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.00000 | + | 10.3923i | 0.302660 | + | 0.524222i | ||||
\(394\) | 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 | ||||||||
\(399\) | 4.50000 | − | 7.79423i | 0.225282 | − | 0.390199i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.50000 | − | 12.9904i | −0.374532 | − | 0.648709i | 0.615725 | − | 0.787961i | \(-0.288863\pi\) |
−0.990257 | + | 0.139253i | \(0.955530\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.00000 | + | 13.8564i | −0.199254 | + | 0.690237i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4.50000 | − | 7.79423i | −0.223607 | − | 0.387298i | ||||
\(406\) | 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 | ||||||||
\(411\) | 9.00000 | 0.443937 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7.50000 | − | 12.9904i | −0.369051 | − | 0.639215i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12.0000 | 0.589057 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −39.0000 | −1.90984 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 16.5000 | + | 28.5788i | 0.806078 | + | 1.39617i | 0.915561 | + | 0.402179i | \(0.131747\pi\) |
−0.109483 | + | 0.993989i | \(0.534920\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 34.0000 | 1.65706 | 0.828529 | − | 0.559946i | \(-0.189178\pi\) | ||||
0.828529 | + | 0.559946i | \(0.189178\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −24.0000 | + | 41.5692i | −1.16692 | + | 2.02116i | ||||
\(424\) | 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 | ||||||||
\(429\) | −22.5000 | − | 23.3827i | −1.08631 | − | 1.12893i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.50000 | + | 7.79423i | 0.216757 | + | 0.375435i | 0.953815 | − | 0.300395i | \(-0.0971186\pi\) |
−0.737057 | + | 0.675830i | \(0.763785\pi\) | |||||||
\(432\) | 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 | ||||||||
\(435\) | −7.50000 | + | 12.9904i | −0.359597 | + | 0.622841i | ||||
\(436\) | 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 | ||||||||
\(441\) | 12.0000 | 0.571429 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 24.0000 | 1.14027 | 0.570137 | − | 0.821549i | \(-0.306890\pi\) | ||||
0.570137 | + | 0.821549i | \(0.306890\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.50000 | − | 6.06218i | −0.165916 | − | 0.287375i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −9.00000 | −0.425685 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.5000 | − | 18.1865i | 0.495526 | − | 0.858276i | −0.504461 | − | 0.863434i | \(-0.668309\pi\) |
0.999987 | + | 0.00515887i | \(0.00164213\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.5000 | + | 18.1865i | −0.494426 | + | 0.856370i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −12.0000 | − | 20.7846i | −0.563809 | − | 0.976546i | ||||
\(454\) | 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 | ||||||||
\(459\) | −31.5000 | + | 54.5596i | −1.47029 | + | 2.54662i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.50000 | + | 9.52628i | −0.256161 | + | 0.443683i | −0.965210 | − | 0.261476i | \(-0.915791\pi\) |
0.709050 | + | 0.705159i | \(0.249124\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −28.0000 | −1.30127 | −0.650635 | − | 0.759390i | \(-0.725497\pi\) | ||||
−0.650635 | + | 0.759390i | \(0.725497\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −6.00000 | − | 10.3923i | −0.278243 | − | 0.481932i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 20.0000 | 0.925490 | 0.462745 | − | 0.886492i | \(-0.346865\pi\) | ||||
0.462745 | + | 0.886492i | \(0.346865\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 39.0000 | 1.80085 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.00000 | + | 15.5885i | 0.414698 | + | 0.718278i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −27.0000 | −1.24146 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.500000 | + | 0.866025i | −0.0229416 | + | 0.0397360i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 18.0000 | − | 31.1769i | 0.824163 | − | 1.42749i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0.500000 | + | 0.866025i | 0.0228456 | + | 0.0395697i | 0.877222 | − | 0.480085i | \(-0.159394\pi\) |
−0.854377 | + | 0.519654i | \(0.826061\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.5000 | − | 2.59808i | 0.478759 | − | 0.118462i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −31.5000 | − | 54.5596i | −1.43330 | − | 2.48255i | ||||
\(484\) | 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 | ||||||||
\(489\) | −33.0000 | −1.49231 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11.5000 | − | 19.9186i | −0.518988 | − | 0.898913i | −0.999757 | − | 0.0220657i | \(-0.992976\pi\) |
0.480769 | − | 0.876847i | \(-0.340358\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 35.0000 | 1.57632 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 18.0000 | 0.809040 | ||||||||
\(496\) | 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 | ||||||||
\(501\) | 1.50000 | − | 2.59808i | 0.0670151 | − | 0.116073i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5.50000 | + | 9.52628i | −0.245233 | + | 0.424756i | −0.962197 | − | 0.272354i | \(-0.912198\pi\) |
0.716964 | + | 0.697110i | \(0.245531\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.50000 | + | 7.79423i | 0.200247 | + | 0.346839i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.50000 | − | 38.9711i | 0.0666173 | − | 1.73077i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7.50000 | − | 12.9904i | −0.332432 | − | 0.575789i | 0.650556 | − | 0.759458i | \(-0.274536\pi\) |
−0.982988 | + | 0.183669i | \(0.941202\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 21.0000 | − | 36.3731i | 0.928985 | − | 1.60905i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.50000 | − | 7.79423i | 0.198680 | − | 0.344124i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −16.0000 | −0.705044 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −12.0000 | − | 20.7846i | −0.527759 | − | 0.914106i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 45.0000 | 1.97528 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −34.0000 | −1.48957 | −0.744784 | − | 0.667306i | \(-0.767447\pi\) | ||||
−0.744784 | + | 0.667306i | \(0.767447\pi\) | |||||||
\(522\) | 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 | ||||||||
\(525\) | −9.00000 | −0.392792 | ||||||||
\(526\) | 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 | ||||||||
\(531\) | −15.0000 | − | 25.9808i | −0.650945 | − | 1.12747i | ||||
\(532\) | 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 | ||||||||
\(537\) | 28.5000 | − | 49.3634i | 1.22987 | − | 2.13019i | ||||
\(538\) | 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 | ||||||||
\(543\) | −21.0000 | − | 36.3731i | −0.901196 | − | 1.56092i | ||||
\(544\) | 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 | ||||||||
\(549\) | 15.0000 | + | 25.9808i | 0.640184 | + | 1.10883i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.00000 | −0.213007 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.0000 | − | 20.7846i | 0.510292 | − | 0.883852i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.50000 | + | 7.79423i | −0.191014 | + | 0.330847i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9.50000 | + | 16.4545i | 0.402528 | + | 0.697199i | 0.994030 | − | 0.109104i | \(-0.0347983\pi\) |
−0.591502 | + | 0.806303i | \(0.701465\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −22.5000 | − | 23.3827i | −0.951649 | − | 0.988982i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −31.5000 | − | 54.5596i | −1.32993 | − | 2.30351i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 22.5000 | − | 38.9711i | 0.948262 | − | 1.64244i | 0.199177 | − | 0.979963i | \(-0.436173\pi\) |
0.749085 | − | 0.662474i | \(-0.230494\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.50000 | + | 11.2583i | −0.273457 | + | 0.473642i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 27.0000 | 1.13389 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9.50000 | − | 16.4545i | −0.398261 | − | 0.689808i | 0.595251 | − | 0.803540i | \(-0.297053\pi\) |
−0.993511 | + | 0.113732i | \(0.963719\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −40.0000 | −1.67395 | −0.836974 | − | 0.547243i | \(-0.815677\pi\) | ||||
−0.836974 | + | 0.547243i | \(0.815677\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9.00000 | 0.375980 | ||||||||
\(574\) | 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 | ||||||||
\(579\) | −22.5000 | + | 38.9711i | −0.935068 | + | 1.61959i | ||||
\(580\) | 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 | ||||||||
\(585\) | 15.0000 | + | 15.5885i | 0.620174 | + | 0.644503i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −18.5000 | − | 32.0429i | −0.763577 | − | 1.32255i | −0.940996 | − | 0.338418i | \(-0.890108\pi\) |
0.177419 | − | 0.984135i | \(-0.443225\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.00000 | − | 3.46410i | 0.0824086 | − | 0.142736i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −34.5000 | + | 59.7558i | −1.41914 | + | 2.45802i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 26.0000 | 1.06769 | 0.533846 | − | 0.845582i | \(-0.320746\pi\) | ||||
0.533846 | + | 0.845582i | \(0.320746\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 10.5000 | + | 18.1865i | 0.430458 | + | 0.745575i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −27.0000 | −1.10504 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.00000 | 0.326871 | 0.163436 | − | 0.986554i | \(-0.447742\pi\) | ||||
0.163436 | + | 0.986554i | \(0.447742\pi\) | |||||||
\(600\) | 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 | ||||||||
\(603\) | 78.0000 | 3.17641 | ||||||||
\(604\) | 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 | ||||||||
\(609\) | −22.5000 | − | 38.9711i | −0.911746 | − | 1.57919i | ||||
\(610\) | 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 | ||||||||
\(615\) | 10.5000 | − | 18.1865i | 0.423401 | − | 0.733352i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14.5000 | + | 25.1147i | −0.583748 | + | 1.01108i | 0.411282 | + | 0.911508i | \(0.365081\pi\) |
−0.995030 | + | 0.0995732i | \(0.968252\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12.0000 | 0.482321 | 0.241160 | − | 0.970485i | \(-0.422472\pi\) | ||||
0.241160 | + | 0.970485i | \(0.422472\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −31.5000 | − | 54.5596i | −1.26405 | − | 2.18940i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 21.0000 | 0.841347 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.50000 | + | 7.79423i | 0.179713 | + | 0.311272i | ||||
\(628\) | 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 | ||||||||
\(633\) | −7.50000 | + | 12.9904i | −0.298098 | + | 0.516321i | ||||
\(634\) | 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 | ||||||||
\(639\) | 9.00000 | + | 15.5885i | 0.356034 | + | 0.616670i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10.5000 | − | 18.1865i | 0.414725 | − | 0.718325i | −0.580674 | − | 0.814136i | \(-0.697211\pi\) |
0.995400 | + | 0.0958109i | \(0.0305444\pi\) | |||||||
\(642\) | 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 | ||||||||
\(645\) | 27.0000 | 1.06312 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8.50000 | − | 14.7224i | −0.334169 | − | 0.578799i | 0.649155 | − | 0.760656i | \(-0.275122\pi\) |
−0.983325 | + | 0.181857i | \(0.941789\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 15.0000 | 0.588802 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 36.0000 | 1.41095 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.50000 | + | 9.52628i | 0.215232 | + | 0.372792i | 0.953344 | − | 0.301885i | \(-0.0976160\pi\) |
−0.738113 | + | 0.674678i | \(0.764283\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.00000 | 0.156293 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 42.0000 | − | 72.7461i | 1.63858 | − | 2.83810i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.50000 | − | 12.9904i | 0.292159 | − | 0.506033i | −0.682161 | − | 0.731202i | \(-0.738960\pi\) |
0.974320 | + | 0.225168i | \(0.0722932\pi\) | |||||||
\(660\) | 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 | ||||||||
\(663\) | 21.0000 | − | 72.7461i | 0.815572 | − | 2.82523i | ||||
\(664\) | 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 | ||||||||
\(669\) | −34.5000 | + | 59.7558i | −1.33385 | + | 2.31029i | ||||
\(670\) | 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 | ||||||||
\(675\) | −9.00000 | −0.346410 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 22.0000 | 0.845529 | 0.422764 | − | 0.906240i | \(-0.361060\pi\) | ||||
0.422764 | + | 0.906240i | \(0.361060\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 16.5000 | + | 28.5788i | 0.633212 | + | 1.09676i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.00000 | 0.114960 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −15.5000 | + | 26.8468i | −0.593091 | + | 1.02726i | 0.400722 | + | 0.916200i | \(0.368759\pi\) |
−0.993813 | + | 0.111064i | \(0.964574\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.50000 | − | 2.59808i | 0.0573121 | − | 0.0992674i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 39.0000 | + | 67.5500i | 1.48794 | + | 2.57719i | ||||
\(688\) | 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 | ||||||||
\(693\) | −27.0000 | + | 46.7654i | −1.02565 | + | 1.77647i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.50000 | + | 11.2583i | −0.246559 | + | 0.427053i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −49.0000 | −1.85601 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 27.0000 | + | 46.7654i | 1.02123 | + | 1.76883i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.00000 | 0.0755390 | 0.0377695 | − | 0.999286i | \(-0.487975\pi\) | ||||
0.0377695 | + | 0.999286i | \(0.487975\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.00000 | −0.113147 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 12.0000 | + | 20.7846i | 0.451946 | + | 0.782794i | ||||
\(706\) | 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 | ||||||||
\(711\) | 24.0000 | − | 41.5692i | 0.900070 | − | 1.55897i | ||||
\(712\) | 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 | ||||||||
\(717\) | −24.0000 | − | 41.5692i | −0.896296 | − | 1.55243i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −0.500000 | + | 0.866025i | −0.0186469 | + | 0.0322973i | −0.875198 | − | 0.483764i | \(-0.839269\pi\) |
0.856551 | + | 0.516062i | \(0.172602\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 24.0000 | − | 41.5692i | 0.893807 | − | 1.54812i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.00000 | 0.111571 | ||||||||
\(724\) | 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 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 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 | ||||||||
\(735\) | 3.00000 | − | 5.19615i | 0.110657 | − | 0.191663i | ||||
\(736\) | 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 | ||||||||
\(741\) | −3.00000 | + | 10.3923i | −0.110208 | + | 0.381771i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −0.500000 | − | 0.866025i | −0.0183432 | − | 0.0317714i | 0.856708 | − | 0.515802i | \(-0.172506\pi\) |
−0.875051 | + | 0.484030i | \(0.839172\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.50000 | + | 2.59808i | −0.0549557 | + | 0.0951861i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −36.0000 | + | 62.3538i | −1.31717 | + | 2.28141i | ||||
\(748\) | 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 | ||||||||
\(753\) | −15.0000 | −0.546630 | ||||||||
\(754\) | 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 | ||||||||
\(759\) | 63.0000 | 2.28676 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −25.5000 | + | 44.1673i | −0.924374 | + | 1.60106i | −0.131810 | + | 0.991275i | \(0.542079\pi\) |
−0.792564 | + | 0.609788i | \(0.791255\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 21.0000 | − | 36.3731i | 0.760251 | − | 1.31679i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 21.0000 | + | 36.3731i | 0.759257 | + | 1.31507i | ||||
\(766\) | 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 | ||||||||
\(771\) | −28.5000 | + | 49.3634i | −1.02640 | + | 1.77778i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −12.5000 | + | 21.6506i | −0.449594 | + | 0.778719i | −0.998359 | − | 0.0572570i | \(-0.981765\pi\) |
0.548766 | + | 0.835976i | \(0.315098\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.00000 | −0.143684 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −13.5000 | − | 23.3827i | −0.484310 | − | 0.838849i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.00000 | 0.250801 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.00000 | −0.322045 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −22.5000 | − | 38.9711i | −0.804084 | − | 1.39272i | ||||
\(784\) | 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 | ||||||||
\(789\) | −10.5000 | + | 18.1865i | −0.373810 | + | 0.647458i | ||||
\(790\) | 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 | ||||||||
\(795\) | −9.00000 | − | 15.5885i | −0.319197 | − | 0.552866i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.50000 | − | 6.06218i | 0.123976 | − | 0.214733i | −0.797356 | − | 0.603509i | \(-0.793769\pi\) |
0.921332 | + | 0.388776i | \(0.127102\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 28.0000 | − | 48.4974i | 0.990569 | − | 1.71572i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 42.0000 | 1.48400 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 21.0000 | + | 36.3731i | 0.741074 | + | 1.28358i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −21.0000 | −0.740153 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −9.00000 | −0.316815 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 12.5000 | + | 21.6506i | 0.439477 | + | 0.761196i | 0.997649 | − | 0.0685291i | \(-0.0218306\pi\) |
−0.558173 | + | 0.829725i | \(0.688497\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 34.5000 | − | 59.7558i | 1.20997 | − | 2.09573i | ||||
\(814\) | 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 | ||||||||
\(819\) | −63.0000 | + | 15.5885i | −2.20140 | + | 0.544705i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.50000 | − | 12.9904i | −0.261752 | − | 0.453367i | 0.704956 | − | 0.709251i | \(-0.250967\pi\) |
−0.966708 | + | 0.255884i | \(0.917634\pi\) | |||||||
\(822\) | 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 | ||||||||
\(825\) | 4.50000 | − | 7.79423i | 0.156670 | − | 0.271360i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12.0000 | 0.417281 | 0.208640 | − | 0.977992i | \(-0.433096\pi\) | ||||
0.208640 | + | 0.977992i | \(0.433096\pi\) | |||||||
\(828\) | 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 | ||||||||
\(831\) | 69.0000 | 2.39358 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −14.0000 | −0.485071 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.500000 | − | 0.866025i | −0.0173032 | − | 0.0299700i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 36.0000 | 1.24434 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −6.50000 | + | 11.2583i | −0.224405 | + | 0.388681i | −0.956141 | − | 0.292908i | \(-0.905377\pi\) |
0.731736 | + | 0.681588i | \(0.238710\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.00000 | − | 3.46410i | 0.0689655 | − | 0.119452i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −15.0000 | − | 25.9808i | −0.516627 | − | 0.894825i | ||||
\(844\) | 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 | ||||||||
\(849\) | 1.50000 | − | 2.59808i | 0.0514799 | − | 0.0891657i | ||||
\(850\) | 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 | ||||||||
\(855\) | −3.00000 | − | 5.19615i | −0.102598 | − | 0.177705i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 18.0000 | 0.614868 | 0.307434 | − | 0.951569i | \(-0.400530\pi\) | ||||
0.307434 | + | 0.951569i | \(0.400530\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 44.0000 | 1.50126 | 0.750630 | − | 0.660722i | \(-0.229750\pi\) | ||||
0.750630 | + | 0.660722i | \(0.229750\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 31.5000 | + | 54.5596i | 1.07352 | + | 1.85939i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 16.0000 | 0.544646 | 0.272323 | − | 0.962206i | \(-0.412208\pi\) | ||||
0.272323 | + | 0.962206i | \(0.412208\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.50000 | − | 12.9904i | 0.255008 | − | 0.441686i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 48.0000 | − | 83.1384i | 1.63017 | − | 2.82353i | ||||
\(868\) | 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 | ||||||||
\(873\) | 33.0000 | + | 57.1577i | 1.11688 | + | 1.93449i | ||||
\(874\) | 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 | ||||||||
\(879\) | −27.0000 | −0.910687 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −5.50000 | − | 9.52628i | −0.185300 | − | 0.320949i | 0.758378 | − | 0.651815i | \(-0.225992\pi\) |
−0.943677 | + | 0.330867i | \(0.892659\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −44.0000 | −1.48072 | −0.740359 | − | 0.672212i | \(-0.765344\pi\) | ||||
−0.740359 | + | 0.672212i | \(0.765344\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −15.0000 | −0.504219 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 9.50000 | + | 16.4545i | 0.318979 | + | 0.552487i | 0.980275 | − | 0.197637i | \(-0.0633268\pi\) |
−0.661296 | + | 0.750125i | \(0.729993\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.00000 | 0.100617 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −13.5000 | + | 23.3827i | −0.452267 | + | 0.783349i | ||||
\(892\) | 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 | ||||||||
\(897\) | 52.5000 | + | 54.5596i | 1.75292 | + | 1.82169i | ||||
\(898\) | 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 | ||||||||
\(903\) | −40.5000 | + | 70.1481i | −1.34776 | + | 2.33438i | ||||
\(904\) | 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 | ||||||||
\(909\) | −54.0000 | −1.79107 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12.0000 | −0.397578 | −0.198789 | − | 0.980042i | \(-0.563701\pi\) | ||||
−0.198789 | + | 0.980042i | \(0.563701\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −18.0000 | − | 31.1769i | −0.595713 | − | 1.03181i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 15.0000 | 0.495885 | ||||||||
\(916\) | 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 | ||||||||
\(921\) | 42.0000 | + | 72.7461i | 1.38395 | + | 2.39707i | ||||
\(922\) | 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 | ||||||||
\(927\) | 48.0000 | − | 83.1384i | 1.57653 | − | 2.73062i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 26.5000 | − | 45.8993i | 0.869437 | − | 1.50591i | 0.00686358 | − | 0.999976i | \(-0.497815\pi\) |
0.862573 | − | 0.505932i | \(-0.168851\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.00000 | 0.0655474 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −36.0000 | − | 62.3538i | −1.17859 | − | 2.04137i | ||||
\(934\) | 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 | ||||||||
\(939\) | −9.00000 | − | 15.5885i | −0.293704 | − | 0.508710i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 42.0000 | 1.36916 | 0.684580 | − | 0.728937i | \(-0.259985\pi\) | ||||
0.684580 | + | 0.728937i | \(0.259985\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 24.5000 | − | 42.4352i | 0.797830 | − | 1.38188i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 13.5000 | − | 23.3827i | 0.439155 | − | 0.760639i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 27.5000 | + | 47.6314i | 0.893630 | + | 1.54781i | 0.835491 | + | 0.549504i | \(0.185183\pi\) |
0.0581388 | + | 0.998309i | \(0.481483\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −14.0000 | + | 48.4974i | −0.454459 | + | 1.57429i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.00000 | − | 5.19615i | −0.0972817 | − | 0.168497i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 15.5000 | − | 26.8468i | 0.502094 | − | 0.869653i | −0.497903 | − | 0.867233i | \(-0.665896\pi\) |
0.999997 | − | 0.00241992i | \(-0.000770286\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.50000 | − | 2.59808i | 0.0485389 | − | 0.0840718i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 45.0000 | 1.45464 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.50000 | + | 7.79423i | 0.145313 | + | 0.251689i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −18.0000 | −0.580042 | ||||||||
\(964\) | 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 | ||||||||
\(969\) | −10.5000 | + | 18.1865i | −0.337309 | + | 0.584236i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21.5000 | − | 37.2391i | 0.689968 | − | 1.19506i | −0.281880 | − | 0.959450i | \(-0.590958\pi\) |
0.971848 | − | 0.235610i | \(-0.0757087\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −19.5000 | − | 33.7750i | −0.625141 | − | 1.08278i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 10.5000 | − | 2.59808i | 0.336269 | − | 0.0832050i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.50000 | + | 2.59808i | 0.0479893 | + | 0.0831198i | 0.889022 | − | 0.457864i | \(-0.151385\pi\) |
−0.841033 | + | 0.540984i | \(0.818052\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −10.5000 | + | 18.1865i | −0.335581 | + | 0.581244i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 42.0000 | − | 72.7461i | 1.34096 | − | 2.32261i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 36.0000 | 1.14822 | 0.574111 | − | 0.818778i | \(-0.305348\pi\) | ||||
0.574111 | + | 0.818778i | \(0.305348\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11.5000 | + | 19.9186i | 0.366420 | + | 0.634659i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −72.0000 | −2.29179 | ||||||||
\(988\) | 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 | ||||||||
\(993\) | −39.0000 | −1.23763 | ||||||||
\(994\) | 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 | ||||||||
\(999\) | −13.5000 | − | 23.3827i | −0.427121 | − | 0.739795i |
(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 | 260.2.i.d.81.1 | yes | 2 | |
3.2 | odd | 2 | 2340.2.q.a.2161.1 | 2 | |||
4.3 | odd | 2 | 1040.2.q.b.81.1 | 2 | |||
5.2 | odd | 4 | 1300.2.bb.e.549.2 | 4 | |||
5.3 | odd | 4 | 1300.2.bb.e.549.1 | 4 | |||
5.4 | even | 2 | 1300.2.i.a.601.1 | 2 | |||
13.2 | odd | 12 | 3380.2.f.a.3041.1 | 2 | |||
13.3 | even | 3 | 3380.2.a.b.1.1 | 1 | |||
13.9 | even | 3 | inner | 260.2.i.d.61.1 | ✓ | 2 | |
13.10 | even | 6 | 3380.2.a.a.1.1 | 1 | |||
13.11 | odd | 12 | 3380.2.f.a.3041.2 | 2 | |||
39.35 | odd | 6 | 2340.2.q.a.1621.1 | 2 | |||
52.35 | odd | 6 | 1040.2.q.b.321.1 | 2 | |||
65.9 | even | 6 | 1300.2.i.a.1101.1 | 2 | |||
65.22 | odd | 12 | 1300.2.bb.e.1049.1 | 4 | |||
65.48 | odd | 12 | 1300.2.bb.e.1049.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
260.2.i.d.61.1 | ✓ | 2 | 13.9 | even | 3 | inner | |
260.2.i.d.81.1 | yes | 2 | 1.1 | even | 1 | trivial | |
1040.2.q.b.81.1 | 2 | 4.3 | odd | 2 | |||
1040.2.q.b.321.1 | 2 | 52.35 | odd | 6 | |||
1300.2.i.a.601.1 | 2 | 5.4 | even | 2 | |||
1300.2.i.a.1101.1 | 2 | 65.9 | even | 6 | |||
1300.2.bb.e.549.1 | 4 | 5.3 | odd | 4 | |||
1300.2.bb.e.549.2 | 4 | 5.2 | odd | 4 | |||
1300.2.bb.e.1049.1 | 4 | 65.22 | odd | 12 | |||
1300.2.bb.e.1049.2 | 4 | 65.48 | odd | 12 | |||
2340.2.q.a.1621.1 | 2 | 39.35 | odd | 6 | |||
2340.2.q.a.2161.1 | 2 | 3.2 | odd | 2 | |||
3380.2.a.a.1.1 | 1 | 13.10 | even | 6 | |||
3380.2.a.b.1.1 | 1 | 13.3 | even | 3 | |||
3380.2.f.a.3041.1 | 2 | 13.2 | odd | 12 | |||
3380.2.f.a.3041.2 | 2 | 13.11 | odd | 12 |