Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1300,2,Mod(549,1300)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1300, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1300.549");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1300 = 2^{2} \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1300.bb (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(10.3805522628\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 260) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 549.2 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1300.549 |
Dual form | 1300.2.bb.e.1049.2 |
$q$-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 \(\left(\mathbb{Z}/1300\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(651\) | \(677\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 2.59808 | − | 1.50000i | 1.50000 | − | 0.866025i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
1.00000 | \(0\) | |||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.59808 | − | 1.50000i | −0.981981 | − | 0.566947i | −0.0791130 | − | 0.996866i | \(-0.525209\pi\) |
−0.902867 | + | 0.429919i | \(0.858542\pi\) | |||||||
\(8\) | 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 | ||||||||
\(13\) | −3.46410 | − | 1.00000i | −0.960769 | − | 0.277350i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.06218 | + | 3.50000i | 1.47029 | + | 0.848875i | 0.999444 | − | 0.0333386i | \(-0.0106140\pi\) |
0.470850 | + | 0.882213i | \(0.343947\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.500000 | − | 0.866025i | 0.114708 | − | 0.198680i | −0.802955 | − | 0.596040i | \(-0.796740\pi\) |
0.917663 | + | 0.397360i | \(0.130073\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −9.00000 | −1.96396 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.06218 | − | 3.50000i | 1.26405 | − | 0.729800i | 0.290196 | − | 0.956967i | \(-0.406280\pi\) |
0.973856 | + | 0.227167i | \(0.0729463\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 9.00000i | − | 1.73205i | ||||||
\(28\) | 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 | ||||||||
\(33\) | −7.79423 | − | 4.50000i | −1.35680 | − | 0.783349i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.59808 | + | 1.50000i | −0.427121 | + | 0.246598i | −0.698119 | − | 0.715981i | \(-0.745980\pi\) |
0.270998 | + | 0.962580i | \(0.412646\pi\) | |||||||
\(38\) | 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 | ||||||||
\(43\) | −7.79423 | − | 4.50000i | −1.18861 | − | 0.686244i | −0.230618 | − | 0.973044i | \(-0.574075\pi\) |
−0.957990 | + | 0.286801i | \(0.907408\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.00000i | 1.16692i | 0.812142 | + | 0.583460i | \(0.198301\pi\) | ||||
−0.812142 | + | 0.583460i | \(0.801699\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | + | 1.73205i | 0.142857 | + | 0.247436i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 21.0000 | 2.94059 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.00000i | 0.824163i | 0.911147 | + | 0.412082i | \(0.135198\pi\) | ||||
−0.911147 | + | 0.412082i | \(0.864802\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 3.00000i | − | 0.397360i | ||||||
\(58\) | 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 | ||||||||
\(63\) | −15.5885 | + | 9.00000i | −1.96396 | + | 1.13389i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.2583 | − | 6.50000i | 1.37542 | − | 0.794101i | 0.383819 | − | 0.923408i | \(-0.374609\pi\) |
0.991605 | + | 0.129307i | \(0.0412752\pi\) | |||||||
\(68\) | 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 | ||||||||
\(73\) | 14.0000i | 1.63858i | 0.573382 | + | 0.819288i | \(0.305631\pi\) | ||||
−0.573382 | + | 0.819288i | \(0.694369\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 9.00000i | 1.02565i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.00000 | 0.900070 | 0.450035 | − | 0.893011i | \(-0.351411\pi\) | ||||
0.450035 | + | 0.893011i | \(0.351411\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | − | 7.79423i | −0.500000 | − | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 12.0000i | − | 1.31717i | −0.752506 | − | 0.658586i | \(-0.771155\pi\) | ||
0.752506 | − | 0.658586i | \(-0.228845\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −12.9904 | − | 7.50000i | −1.39272 | − | 0.804084i | ||||
\(88\) | 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 | ||||||||
\(93\) | −10.3923 | + | 6.00000i | −1.07763 | + | 0.622171i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.52628 | + | 5.50000i | 0.967247 | + | 0.558440i | 0.898396 | − | 0.439187i | \(-0.144733\pi\) |
0.0688512 | + | 0.997627i | \(0.478067\pi\) | |||||||
\(98\) | 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 | ||||||||
\(103\) | 16.0000i | 1.57653i | 0.615338 | + | 0.788263i | \(0.289020\pi\) | ||||
−0.615338 | + | 0.788263i | \(0.710980\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.59808 | + | 1.50000i | −0.251166 | + | 0.145010i | −0.620298 | − | 0.784366i | \(-0.712988\pi\) |
0.369132 | + | 0.929377i | \(0.379655\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.0000 | 1.34096 | 0.670478 | − | 0.741929i | \(-0.266089\pi\) | ||||
0.670478 | + | 0.741929i | \(0.266089\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.50000 | + | 7.79423i | −0.427121 | + | 0.739795i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.2583 | + | 6.50000i | 1.05909 | + | 0.611469i | 0.925182 | − | 0.379525i | \(-0.123912\pi\) |
0.133913 | + | 0.990993i | \(0.457246\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −15.5885 | + | 15.0000i | −1.44115 | + | 1.38675i | ||||
\(118\) | 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 | ||||||||
\(123\) | −18.1865 | − | 10.5000i | −1.63982 | − | 0.946753i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.866025 | − | 0.500000i | 0.0768473 | − | 0.0443678i | −0.461084 | − | 0.887357i | \(-0.652539\pi\) |
0.537931 | + | 0.842989i | \(0.319206\pi\) | |||||||
\(128\) | 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 | ||||||||
\(133\) | −2.59808 | + | 1.50000i | −0.225282 | + | 0.130066i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.59808 | + | 1.50000i | 0.221969 | + | 0.128154i | 0.606861 | − | 0.794808i | \(-0.292428\pi\) |
−0.384893 | + | 0.922961i | \(0.625762\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.50000 | − | 11.2583i | 0.551323 | − | 0.954919i | −0.446857 | − | 0.894606i | \(-0.647457\pi\) |
0.998179 | − | 0.0603135i | \(-0.0192101\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.0000 | + | 20.7846i | 1.01058 | + | 1.75038i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.59808 | + | 10.5000i | 0.217262 | + | 0.878054i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.19615 | + | 3.00000i | 0.428571 | + | 0.247436i | ||||
\(148\) | 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 | ||||||||
\(153\) | 36.3731 | − | 21.0000i | 2.94059 | − | 1.69775i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.00000i | 0.478852i | 0.970915 | + | 0.239426i | \(0.0769593\pi\) | ||||
−0.970915 | + | 0.239426i | \(0.923041\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 9.00000 | + | 15.5885i | 0.713746 | + | 1.23625i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −21.0000 | −1.65503 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.52628 | + | 5.50000i | 0.746156 | + | 0.430793i | 0.824303 | − | 0.566149i | \(-0.191567\pi\) |
−0.0781474 | + | 0.996942i | \(0.524900\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.866025 | − | 0.500000i | 0.0670151 | − | 0.0386912i | −0.466118 | − | 0.884723i | \(-0.654348\pi\) |
0.533133 | + | 0.846031i | \(0.321014\pi\) | |||||||
\(168\) | 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 | ||||||||
\(173\) | −12.9904 | − | 7.50000i | −0.987640 | − | 0.570214i | −0.0830722 | − | 0.996544i | \(-0.526473\pi\) |
−0.904568 | + | 0.426329i | \(0.859807\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 15.0000i | − | 1.12747i | ||||||
\(178\) | 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 | ||||||||
\(183\) | − | 15.0000i | − | 1.10883i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 21.0000i | − | 1.53567i | ||||||
\(188\) | 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 | ||||||||
\(193\) | 12.9904 | − | 7.50000i | 0.935068 | − | 0.539862i | 0.0466572 | − | 0.998911i | \(-0.485143\pi\) |
0.888411 | + | 0.459049i | \(0.151810\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −19.9186 | + | 11.5000i | −1.41914 | + | 0.819341i | −0.996223 | − | 0.0868274i | \(-0.972327\pi\) |
−0.422917 | + | 0.906168i | \(0.638994\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.50000 | − | 7.79423i | 0.318997 | − | 0.552518i | −0.661282 | − | 0.750137i | \(-0.729987\pi\) |
0.980279 | + | 0.197619i | \(0.0633208\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 19.5000 | − | 33.7750i | 1.37542 | − | 2.38230i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 15.0000i | 1.05279i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 42.0000i | − | 2.91920i | ||||||
\(208\) | 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 | ||||||||
\(213\) | − | 9.00000i | − | 0.616670i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.3923 | + | 6.00000i | 0.705476 | + | 0.407307i | ||||
\(218\) | 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 | ||||||||
\(223\) | 19.9186 | − | 11.5000i | 1.33385 | − | 0.770097i | 0.347960 | − | 0.937509i | \(-0.386874\pi\) |
0.985887 | + | 0.167412i | \(0.0535411\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.866025 | + | 0.500000i | 0.0574801 | + | 0.0331862i | 0.528465 | − | 0.848955i | \(-0.322768\pi\) |
−0.470985 | + | 0.882141i | \(0.656101\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −26.0000 | −1.71813 | −0.859064 | − | 0.511868i | \(-0.828954\pi\) | ||||
−0.859064 | + | 0.511868i | \(0.828954\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 13.5000 | + | 23.3827i | 0.888235 | + | 1.53847i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 18.0000i | − | 1.17922i | −0.807688 | − | 0.589610i | \(-0.799282\pi\) | ||
0.807688 | − | 0.589610i | \(-0.200718\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 20.7846 | − | 12.0000i | 1.35011 | − | 0.779484i | ||||
\(238\) | 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 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.59808 | + | 2.50000i | −0.165312 | + | 0.159071i | ||||
\(248\) | 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 | ||||||||
\(253\) | −18.1865 | − | 10.5000i | −1.14338 | − | 0.660129i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −16.4545 | + | 9.50000i | −1.02640 | + | 0.592594i | −0.915952 | − | 0.401288i | \(-0.868563\pi\) |
−0.110450 | + | 0.993882i | \(0.535229\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.00000 | 0.559233 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −30.0000 | −1.85695 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.06218 | − | 3.50000i | 0.373810 | − | 0.215819i | −0.301312 | − | 0.953526i | \(-0.597424\pi\) |
0.675122 | + | 0.737706i | \(0.264091\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 18.1865 | + | 10.5000i | 1.11300 | + | 0.642590i | ||||
\(268\) | 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 | ||||||||
\(273\) | 31.1769 | + | 9.00000i | 1.88691 | + | 0.544705i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19.9186 | + | 11.5000i | 1.19679 | + | 0.690968i | 0.959839 | − | 0.280553i | \(-0.0905179\pi\) |
0.236953 | + | 0.971521i | \(0.423851\pi\) | |||||||
\(278\) | 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 | ||||||||
\(283\) | −0.866025 | + | 0.500000i | −0.0514799 | + | 0.0297219i | −0.525519 | − | 0.850782i | \(-0.676129\pi\) |
0.474039 | + | 0.880504i | \(0.342796\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 21.0000i | 1.23959i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.0000 | + | 27.7128i | 0.941176 | + | 1.63017i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 33.0000 | 1.93449 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.79423 | + | 4.50000i | 0.455344 | + | 0.262893i | 0.710084 | − | 0.704117i | \(-0.248657\pi\) |
−0.254741 | + | 0.967009i | \(0.581990\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −23.3827 | + | 13.5000i | −1.35680 | + | 0.783349i | ||||
\(298\) | 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 | ||||||||
\(303\) | 23.3827 | + | 13.5000i | 1.34330 | + | 0.775555i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 28.0000i | 1.59804i | 0.601302 | + | 0.799022i | \(0.294649\pi\) | ||||
−0.601302 | + | 0.799022i | \(0.705351\pi\) | |||||||
\(308\) | 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 | ||||||||
\(313\) | 6.00000i | 0.339140i | 0.985518 | + | 0.169570i | \(0.0542379\pi\) | ||||
−0.985518 | + | 0.169570i | \(0.945762\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 2.00000i | − | 0.112331i | −0.998421 | − | 0.0561656i | \(-0.982113\pi\) | ||
0.998421 | − | 0.0561656i | \(-0.0178875\pi\) | |||||||
\(318\) | 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 | ||||||||
\(323\) | 6.06218 | − | 3.50000i | 0.337309 | − | 0.194745i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 36.3731 | − | 21.0000i | 2.01144 | − | 1.16130i | ||||
\(328\) | 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 | ||||||||
\(333\) | 18.0000i | 0.986394i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 18.0000i | − | 0.980522i | −0.871576 | − | 0.490261i | \(-0.836901\pi\) | ||
0.871576 | − | 0.490261i | \(-0.163099\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 39.0000 | 2.11819 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.00000 | + | 10.3923i | 0.324918 | + | 0.562775i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.0000i | 0.809924i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 11.2583 | + | 6.50000i | 0.604379 | + | 0.348938i | 0.770762 | − | 0.637123i | \(-0.219876\pi\) |
−0.166383 | + | 0.986061i | \(0.553209\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12.5000 | − | 21.6506i | −0.669110 | − | 1.15893i | −0.978153 | − | 0.207884i | \(-0.933342\pi\) |
0.309044 | − | 0.951048i | \(-0.399991\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −9.00000 | + | 31.1769i | −0.480384 | + | 1.66410i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −18.1865 | + | 10.5000i | −0.967972 | + | 0.558859i | −0.898617 | − | 0.438733i | \(-0.855427\pi\) |
−0.0693543 | + | 0.997592i | \(0.522094\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −54.5596 | − | 31.5000i | −2.88760 | − | 1.66716i | ||||
\(358\) | 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 | ||||||||
\(363\) | − | 6.00000i | − | 0.314918i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.79423 | − | 4.50000i | 0.406855 | − | 0.234898i | −0.282582 | − | 0.959243i | \(-0.591191\pi\) |
0.689438 | + | 0.724345i | \(0.257858\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −42.0000 | −2.18643 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.00000 | − | 15.5885i | 0.467257 | − | 0.809312i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −23.3827 | − | 13.5000i | −1.21071 | − | 0.699004i | −0.247796 | − | 0.968812i | \(-0.579706\pi\) |
−0.962914 | + | 0.269809i | \(0.913039\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.33013 | + | 17.5000i | 0.223013 | + | 0.901296i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.50000 | − | 7.79423i | −0.231149 | − | 0.400363i | 0.726997 | − | 0.686640i | \(-0.240915\pi\) |
−0.958147 | + | 0.286278i | \(0.907582\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.50000 | − | 2.59808i | 0.0768473 | − | 0.133103i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11.2583 | − | 6.50000i | −0.575274 | − | 0.332134i | 0.183979 | − | 0.982930i | \(-0.441102\pi\) |
−0.759253 | + | 0.650796i | \(0.774435\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −46.7654 | + | 27.0000i | −2.37722 | + | 1.37249i | ||||
\(388\) | 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 | ||||||||
\(393\) | 10.3923 | − | 6.00000i | 0.524222 | − | 0.302660i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −28.5788 | − | 16.5000i | −1.43433 | − | 0.828111i | −0.436884 | − | 0.899518i | \(-0.643918\pi\) |
−0.997447 | + | 0.0714068i | \(0.977251\pi\) | |||||||
\(398\) | 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 | ||||||||
\(403\) | 13.8564 | + | 4.00000i | 0.690237 | + | 0.199254i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.79423 | + | 4.50000i | 0.386346 | + | 0.223057i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.500000 | + | 0.866025i | −0.0247234 | + | 0.0428222i | −0.878122 | − | 0.478436i | \(-0.841204\pi\) |
0.853399 | + | 0.521258i | \(0.174537\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9.00000 | 0.443937 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −12.9904 | + | 7.50000i | −0.639215 | + | 0.369051i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 39.0000i | − | 1.90984i | ||||||
\(418\) | 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 | ||||||||
\(423\) | 41.5692 | + | 24.0000i | 2.02116 | + | 1.16692i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −12.9904 | + | 7.50000i | −0.628649 | + | 0.362950i | ||||
\(428\) | 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 | ||||||||
\(433\) | 0.866025 | + | 0.500000i | 0.0416185 | + | 0.0240285i | 0.520665 | − | 0.853761i | \(-0.325684\pi\) |
−0.479046 | + | 0.877790i | \(0.659017\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 7.00000i | − | 0.334855i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.50000 | + | 2.59808i | 0.0715911 | + | 0.123999i | 0.899599 | − | 0.436717i | \(-0.143859\pi\) |
−0.828008 | + | 0.560717i | \(0.810526\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 12.0000 | 0.571429 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 24.0000i | − | 1.14027i | −0.821549 | − | 0.570137i | \(-0.806890\pi\) | ||
0.821549 | − | 0.570137i | \(-0.193110\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 9.00000i | − | 0.425685i | ||||||
\(448\) | 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 | ||||||||
\(453\) | −20.7846 | + | 12.0000i | −0.976546 | + | 0.563809i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −19.9186 | + | 11.5000i | −0.931752 | + | 0.537947i | −0.887365 | − | 0.461067i | \(-0.847467\pi\) |
−0.0443868 | + | 0.999014i | \(0.514133\pi\) | |||||||
\(458\) | 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 | ||||||||
\(463\) | 28.0000i | 1.30127i | 0.759390 | + | 0.650635i | \(0.225497\pi\) | ||||
−0.759390 | + | 0.650635i | \(0.774503\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 20.0000i | 0.925490i | 0.886492 | + | 0.462745i | \(0.153135\pi\) | ||||
−0.886492 | + | 0.462745i | \(0.846865\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −39.0000 | −1.80085 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.00000 | + | 15.5885i | 0.414698 | + | 0.718278i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 27.0000i | 1.24146i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 31.1769 | + | 18.0000i | 1.42749 | + | 0.824163i | ||||
\(478\) | 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 | ||||||||
\(483\) | −54.5596 | + | 31.5000i | −2.48255 | + | 1.43330i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.7224 | + | 8.50000i | 0.667137 | + | 0.385172i | 0.794991 | − | 0.606621i | \(-0.207476\pi\) |
−0.127854 | + | 0.991793i | \(0.540809\pi\) | |||||||
\(488\) | 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 | ||||||||
\(493\) | − | 35.0000i | − | 1.57632i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7.79423 | + | 4.50000i | −0.349619 | + | 0.201853i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.0000 | 0.716258 | 0.358129 | − | 0.933672i | \(-0.383415\pi\) | ||||
0.358129 | + | 0.933672i | \(0.383415\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.50000 | − | 2.59808i | 0.0670151 | − | 0.116073i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.52628 | + | 5.50000i | 0.424756 | + | 0.245233i | 0.697110 | − | 0.716964i | \(-0.254469\pi\) |
−0.272354 | + | 0.962197i | \(0.587802\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 38.9711 | + | 1.50000i | 1.73077 | + | 0.0666173i | ||||
\(508\) | 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 | ||||||||
\(513\) | −7.79423 | − | 4.50000i | −0.344124 | − | 0.198680i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 20.7846 | − | 12.0000i | 0.914106 | − | 0.527759i | ||||
\(518\) | 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 | ||||||||
\(523\) | 19.9186 | − | 11.5000i | 0.870979 | − | 0.502860i | 0.00330547 | − | 0.999995i | \(-0.498948\pi\) |
0.867673 | + | 0.497135i | \(0.165615\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −24.2487 | − | 14.0000i | −1.05629 | − | 0.609850i | ||||
\(528\) | 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 | ||||||||
\(533\) | 6.06218 | + | 24.5000i | 0.262582 | + | 1.06121i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 49.3634 | + | 28.5000i | 2.13019 | + | 1.22987i | ||||
\(538\) | 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 | ||||||||
\(543\) | −36.3731 | + | 21.0000i | −1.56092 | + | 0.901196i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 16.0000i | − | 0.684111i | −0.939680 | − | 0.342055i | \(-0.888877\pi\) | ||
0.939680 | − | 0.342055i | \(-0.111123\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −15.0000 | − | 25.9808i | −0.640184 | − | 1.10883i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.00000 | −0.213007 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −20.7846 | − | 12.0000i | −0.883852 | − | 0.510292i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −16.4545 | + | 9.50000i | −0.697199 | + | 0.402528i | −0.806303 | − | 0.591502i | \(-0.798535\pi\) |
0.109104 | + | 0.994030i | \(0.465202\pi\) | |||||||
\(558\) | 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 | ||||||||
\(563\) | −38.9711 | − | 22.5000i | −1.64244 | − | 0.948262i | −0.979963 | − | 0.199177i | \(-0.936173\pi\) |
−0.662474 | − | 0.749085i | \(-0.730494\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 27.0000i | 1.13389i | ||||||||
\(568\) | 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 | ||||||||
\(573\) | − | 9.00000i | − | 0.375980i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.00000i | 0.0832611i | 0.999133 | + | 0.0416305i | \(0.0132552\pi\) | ||||
−0.999133 | + | 0.0416305i | \(0.986745\pi\) | |||||||
\(578\) | 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 | ||||||||
\(583\) | 15.5885 | − | 9.00000i | 0.645608 | − | 0.372742i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 32.0429 | − | 18.5000i | 1.32255 | − | 0.763577i | 0.338418 | − | 0.940996i | \(-0.390108\pi\) |
0.984135 | + | 0.177419i | \(0.0567748\pi\) | |||||||
\(588\) | 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 | ||||||||
\(593\) | − | 26.0000i | − | 1.06769i | −0.845582 | − | 0.533846i | \(-0.820746\pi\) | ||
0.845582 | − | 0.533846i | \(-0.179254\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 27.0000i | − | 1.10504i | ||||||
\(598\) | 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 | ||||||||
\(603\) | − | 78.0000i | − | 3.17641i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.79423 | + | 4.50000i | 0.316358 | + | 0.182649i | 0.649768 | − | 0.760133i | \(-0.274866\pi\) |
−0.333410 | + | 0.942782i | \(0.608199\pi\) | |||||||
\(608\) | 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 | ||||||||
\(613\) | 26.8468 | − | 15.5000i | 1.08433 | − | 0.626039i | 0.152270 | − | 0.988339i | \(-0.451342\pi\) |
0.932062 | + | 0.362300i | \(0.118008\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −25.1147 | − | 14.5000i | −1.01108 | − | 0.583748i | −0.0995732 | − | 0.995030i | \(-0.531748\pi\) |
−0.911508 | + | 0.411282i | \(0.865081\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12.0000 | −0.482321 | −0.241160 | − | 0.970485i | \(-0.577528\pi\) | ||||
−0.241160 | + | 0.970485i | \(0.577528\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −31.5000 | − | 54.5596i | −1.26405 | − | 2.18940i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 21.0000i | − | 0.841347i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −7.79423 | + | 4.50000i | −0.311272 | + | 0.179713i | ||||
\(628\) | 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 | ||||||||
\(633\) | 12.9904 | + | 7.50000i | 0.516321 | + | 0.298098i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.73205 | − | 7.00000i | −0.0686264 | − | 0.277350i | ||||
\(638\) | 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 | ||||||||
\(643\) | 6.06218 | + | 3.50000i | 0.239069 | + | 0.138027i | 0.614749 | − | 0.788723i | \(-0.289257\pi\) |
−0.375680 | + | 0.926750i | \(0.622591\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 14.7224 | − | 8.50000i | 0.578799 | − | 0.334169i | −0.181857 | − | 0.983325i | \(-0.558211\pi\) |
0.760656 | + | 0.649155i | \(0.224878\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −15.0000 | −0.588802 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 36.0000 | 1.41095 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.52628 | − | 5.50000i | 0.372792 | − | 0.215232i | −0.301885 | − | 0.953344i | \(-0.597616\pi\) |
0.674678 | + | 0.738113i | \(0.264283\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 72.7461 | + | 42.0000i | 2.83810 | + | 1.63858i | ||||
\(658\) | 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 | ||||||||
\(663\) | −72.7461 | − | 21.0000i | −2.82523 | − | 0.815572i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −30.3109 | − | 17.5000i | −1.17364 | − | 0.677603i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 34.5000 | − | 59.7558i | 1.33385 | − | 2.31029i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −15.0000 | −0.579069 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.2583 | + | 6.50000i | −0.433977 | + | 0.250557i | −0.701039 | − | 0.713123i | \(-0.747280\pi\) |
0.267063 | + | 0.963679i | \(0.413947\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 22.0000i | 0.845529i | 0.906240 | + | 0.422764i | \(0.138940\pi\) | ||||
−0.906240 | + | 0.422764i | \(0.861060\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −16.5000 | − | 28.5788i | −0.633212 | − | 1.09676i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.00000 | 0.114960 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 26.8468 | + | 15.5000i | 1.02726 | + | 0.593091i | 0.916200 | − | 0.400722i | \(-0.131241\pi\) |
0.111064 | + | 0.993813i | \(0.464574\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −67.5500 | + | 39.0000i | −2.57719 | + | 1.48794i | ||||
\(688\) | 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 | ||||||||
\(693\) | 46.7654 | + | 27.0000i | 1.77647 | + | 1.02565i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 49.0000i | − | 1.85601i | ||||||
\(698\) | 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 | ||||||||
\(703\) | 3.00000i | 0.113147i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 27.0000i | − | 1.01544i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17.5000 | − | 30.3109i | 0.657226 | − | 1.13835i | −0.324104 | − | 0.946021i | \(-0.605063\pi\) |
0.981331 | − | 0.192328i | \(-0.0616038\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 24.0000 | − | 41.5692i | 0.900070 | − | 1.55897i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −24.2487 | + | 14.0000i | −0.908121 | + | 0.524304i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 41.5692 | − | 24.0000i | 1.55243 | − | 0.896296i | ||||
\(718\) | 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 | ||||||||
\(723\) | − | 3.00000i | − | 0.111571i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 28.0000i | − | 1.03846i | −0.854634 | − | 0.519231i | \(-0.826218\pi\) | ||
0.854634 | − | 0.519231i | \(-0.173782\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −31.5000 | − | 54.5596i | −1.16507 | − | 2.01796i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 14.0000i | − | 0.517102i | −0.965998 | − | 0.258551i | \(-0.916755\pi\) | ||
0.965998 | − | 0.258551i | \(-0.0832450\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −33.7750 | − | 19.5000i | −1.24412 | − | 0.718292i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19.5000 | + | 33.7750i | 0.717319 | + | 1.24243i | 0.962058 | + | 0.272844i | \(0.0879643\pi\) |
−0.244739 | + | 0.969589i | \(0.578702\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.00000 | + | 10.3923i | −0.110208 | + | 0.381771i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −0.866025 | + | 0.500000i | −0.0317714 | + | 0.0183432i | −0.515802 | − | 0.856708i | \(-0.672506\pi\) |
0.484030 | + | 0.875051i | \(0.339172\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −62.3538 | − | 36.0000i | −2.28141 | − | 1.31717i | ||||
\(748\) | 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 | ||||||||
\(753\) | 15.0000i | 0.546630i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0.866025 | − | 0.500000i | 0.0314762 | − | 0.0181728i | −0.484179 | − | 0.874969i | \(-0.660882\pi\) |
0.515656 | + | 0.856796i | \(0.327548\pi\) | |||||||
\(758\) | 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 | ||||||||
\(763\) | −36.3731 | − | 21.0000i | −1.31679 | − | 0.760251i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −12.9904 | + | 12.5000i | −0.469055 | + | 0.451349i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.50000 | − | 4.33013i | −0.0901523 | − | 0.156148i | 0.817423 | − | 0.576038i | \(-0.195402\pi\) |
−0.907575 | + | 0.419890i | \(0.862069\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −28.5000 | + | 49.3634i | −1.02640 | + | 1.77778i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 21.6506 | + | 12.5000i | 0.778719 | + | 0.449594i | 0.835976 | − | 0.548766i | \(-0.184902\pi\) |
−0.0572570 | + | 0.998359i | \(0.518235\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 23.3827 | − | 13.5000i | 0.838849 | − | 0.484310i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −7.00000 | −0.250801 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.00000 | −0.322045 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −38.9711 | + | 22.5000i | −1.39272 | + | 0.804084i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.866025 | + | 0.500000i | 0.0308705 | + | 0.0178231i | 0.515356 | − | 0.856976i | \(-0.327660\pi\) |
−0.484485 | + | 0.874799i | \(0.660993\pi\) | |||||||
\(788\) | 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 | ||||||||
\(793\) | −12.9904 | + | 12.5000i | −0.461302 | + | 0.443888i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6.06218 | + | 3.50000i | 0.214733 | + | 0.123976i | 0.603509 | − | 0.797356i | \(-0.293769\pi\) |
−0.388776 | + | 0.921332i | \(0.627102\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −28.0000 | + | 48.4974i | −0.990569 | + | 1.71572i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 42.0000 | 1.48400 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 36.3731 | − | 21.0000i | 1.28358 | − | 0.741074i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 9.00000i | − | 0.316815i | ||||||
\(808\) | 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 | ||||||||
\(813\) | −59.7558 | − | 34.5000i | −2.09573 | − | 1.20997i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.79423 | + | 4.50000i | −0.272686 | + | 0.157435i | ||||
\(818\) | 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 | ||||||||
\(823\) | 40.7032 | + | 23.5000i | 1.41882 | + | 0.819159i | 0.996196 | − | 0.0871445i | \(-0.0277742\pi\) |
0.422628 | + | 0.906303i | \(0.361108\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12.0000i | 0.417281i | 0.977992 | + | 0.208640i | \(0.0669038\pi\) | ||||
−0.977992 | + | 0.208640i | \(0.933096\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.50000 | − | 11.2583i | −0.225754 | − | 0.391018i | 0.730791 | − | 0.682601i | \(-0.239151\pi\) |
−0.956545 | + | 0.291583i | \(0.905818\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 69.0000 | 2.39358 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 14.0000i | 0.485071i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 36.0000i | 1.24434i | ||||||||
\(838\) | 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 | ||||||||
\(843\) | −25.9808 | + | 15.0000i | −0.894825 | + | 0.516627i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.19615 | + | 3.00000i | −0.178542 | + | 0.103081i | ||||
\(848\) | 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 | ||||||||
\(853\) | − | 10.0000i | − | 0.342393i | −0.985237 | − | 0.171197i | \(-0.945237\pi\) | ||
0.985237 | − | 0.171197i | \(-0.0547634\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 18.0000i | 0.614868i | 0.951569 | + | 0.307434i | \(0.0994704\pi\) | ||||
−0.951569 | + | 0.307434i | \(0.900530\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −44.0000 | −1.50126 | −0.750630 | − | 0.660722i | \(-0.770250\pi\) | ||||
−0.750630 | + | 0.660722i | \(0.770250\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 31.5000 | + | 54.5596i | 1.07352 | + | 1.85939i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 16.0000i | − | 0.544646i | −0.962206 | − | 0.272323i | \(-0.912208\pi\) | ||
0.962206 | − | 0.272323i | \(-0.0877920\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 83.1384 | + | 48.0000i | 2.82353 | + | 1.63017i | ||||
\(868\) | 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 | ||||||||
\(873\) | 57.1577 | − | 33.0000i | 1.93449 | − | 1.11688i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.33013 | − | 2.50000i | −0.146218 | − | 0.0844190i | 0.425106 | − | 0.905143i | \(-0.360237\pi\) |
−0.571324 | + | 0.820724i | \(0.693570\pi\) | |||||||
\(878\) | 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 | ||||||||
\(883\) | 44.0000i | 1.48072i | 0.672212 | + | 0.740359i | \(0.265344\pi\) | ||||
−0.672212 | + | 0.740359i | \(0.734656\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −16.4545 | + | 9.50000i | −0.552487 | + | 0.318979i | −0.750125 | − | 0.661296i | \(-0.770007\pi\) |
0.197637 | + | 0.980275i | \(0.436673\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.00000 | −0.100617 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −13.5000 | + | 23.3827i | −0.452267 | + | 0.783349i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.92820 | + | 4.00000i | 0.231843 | + | 0.133855i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −54.5596 | + | 52.5000i | −1.82169 | + | 1.75292i | ||||
\(898\) | 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 | ||||||||
\(903\) | 70.1481 | + | 40.5000i | 2.33438 | + | 1.34776i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 14.7224 | − | 8.50000i | 0.488850 | − | 0.282238i | −0.235247 | − | 0.971936i | \(-0.575590\pi\) |
0.724097 | + | 0.689698i | \(0.242257\pi\) | |||||||
\(908\) | 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 | ||||||||
\(913\) | −31.1769 | + | 18.0000i | −1.03181 | + | 0.595713i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −10.3923 | − | 6.00000i | −0.343184 | − | 0.198137i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −21.5000 | + | 37.2391i | −0.709220 | + | 1.22840i | 0.255927 | + | 0.966696i | \(0.417619\pi\) |
−0.965147 | + | 0.261708i | \(0.915714\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 42.0000 | + | 72.7461i | 1.38395 | + | 2.39707i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −7.79423 | + | 7.50000i | −0.256550 | + | 0.246866i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 83.1384 | + | 48.0000i | 2.73062 | + | 1.57653i | ||||
\(928\) | 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 | ||||||||
\(933\) | −62.3538 | + | 36.0000i | −2.04137 | + | 1.17859i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 50.0000i | 1.63343i | 0.577042 | + | 0.816714i | \(0.304207\pi\) | ||||
−0.577042 | + | 0.816714i | \(0.695793\pi\) | |||||||
\(938\) | 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 | ||||||||
\(943\) | −42.4352 | − | 24.5000i | −1.38188 | − | 0.797830i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −47.6314 | + | 27.5000i | −1.54781 | + | 0.893630i | −0.549504 | + | 0.835491i | \(0.685183\pi\) |
−0.998309 | + | 0.0581388i | \(0.981483\pi\) | |||||||
\(948\) | 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 | ||||||||
\(953\) | −26.8468 | − | 15.5000i | −0.869653 | − | 0.502094i | −0.00241992 | − | 0.999997i | \(-0.500770\pi\) |
−0.867233 | + | 0.497903i | \(0.834104\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 45.0000i | 1.45464i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.50000 | − | 7.79423i | −0.145313 | − | 0.251689i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 18.0000i | 0.580042i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 48.0000i | − | 1.54358i | −0.635880 | − | 0.771788i | \(-0.719363\pi\) | ||
0.635880 | − | 0.771788i | \(-0.280637\pi\) | |||||||
\(968\) | 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 | ||||||||
\(973\) | −33.7750 | + | 19.5000i | −1.08278 | + | 0.625141i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.59808 | + | 1.50000i | −0.0831198 | + | 0.0479893i | −0.540984 | − | 0.841033i | \(-0.681948\pi\) |
0.457864 | + | 0.889022i | \(0.348615\pi\) | |||||||
\(978\) | 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 | ||||||||
\(983\) | − | 36.0000i | − | 1.14822i | −0.818778 | − | 0.574111i | \(-0.805348\pi\) | ||
0.818778 | − | 0.574111i | \(-0.194652\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 72.0000i | − | 2.29179i | ||||||
\(988\) | 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 | ||||||||
\(993\) | 39.0000i | 1.23763i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −11.2583 | − | 6.50000i | −0.356555 | − | 0.205857i | 0.311014 | − | 0.950405i | \(-0.399332\pi\) |
−0.667568 | + | 0.744548i | \(0.732665\pi\) | |||||||
\(998\) | 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 | 1300.2.bb.e.549.2 | 4 | ||
5.2 | odd | 4 | 1300.2.i.a.601.1 | 2 | |||
5.3 | odd | 4 | 260.2.i.d.81.1 | yes | 2 | ||
5.4 | even | 2 | inner | 1300.2.bb.e.549.1 | 4 | ||
13.9 | even | 3 | inner | 1300.2.bb.e.1049.1 | 4 | ||
15.8 | even | 4 | 2340.2.q.a.2161.1 | 2 | |||
20.3 | even | 4 | 1040.2.q.b.81.1 | 2 | |||
65.3 | odd | 12 | 3380.2.a.b.1.1 | 1 | |||
65.9 | even | 6 | inner | 1300.2.bb.e.1049.2 | 4 | ||
65.22 | odd | 12 | 1300.2.i.a.1101.1 | 2 | |||
65.23 | odd | 12 | 3380.2.a.a.1.1 | 1 | |||
65.28 | even | 12 | 3380.2.f.a.3041.1 | 2 | |||
65.48 | odd | 12 | 260.2.i.d.61.1 | ✓ | 2 | ||
65.63 | even | 12 | 3380.2.f.a.3041.2 | 2 | |||
195.113 | even | 12 | 2340.2.q.a.1621.1 | 2 | |||
260.243 | even | 12 | 1040.2.q.b.321.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
260.2.i.d.61.1 | ✓ | 2 | 65.48 | odd | 12 | ||
260.2.i.d.81.1 | yes | 2 | 5.3 | odd | 4 | ||
1040.2.q.b.81.1 | 2 | 20.3 | even | 4 | |||
1040.2.q.b.321.1 | 2 | 260.243 | even | 12 | |||
1300.2.i.a.601.1 | 2 | 5.2 | odd | 4 | |||
1300.2.i.a.1101.1 | 2 | 65.22 | odd | 12 | |||
1300.2.bb.e.549.1 | 4 | 5.4 | even | 2 | inner | ||
1300.2.bb.e.549.2 | 4 | 1.1 | even | 1 | trivial | ||
1300.2.bb.e.1049.1 | 4 | 13.9 | even | 3 | inner | ||
1300.2.bb.e.1049.2 | 4 | 65.9 | even | 6 | inner | ||
2340.2.q.a.1621.1 | 2 | 195.113 | even | 12 | |||
2340.2.q.a.2161.1 | 2 | 15.8 | even | 4 | |||
3380.2.a.a.1.1 | 1 | 65.23 | odd | 12 | |||
3380.2.a.b.1.1 | 1 | 65.3 | odd | 12 | |||
3380.2.f.a.3041.1 | 2 | 65.28 | even | 12 | |||
3380.2.f.a.3041.2 | 2 | 65.63 | even | 12 |