Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,9,Mod(73,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.73");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.z (of order \(6\), 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: | \(102.659409735\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - x^{9} + 1442 x^{8} + 59551 x^{7} + 2229058 x^{6} + 41253567 x^{5} + 582209889 x^{4} + \cdots + 63214027776 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{9}\cdot 7^{6} \) |
Twist minimal: | no (minimal twist has level 28) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 73.4 | ||
Root | \(-0.957903 - 1.65914i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 252.73 |
Dual form | 252.9.z.c.145.4 |
$q$-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 \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 616.084 | − | 355.696i | 0.985734 | − | 0.569114i | 0.0817374 | − | 0.996654i | \(-0.473953\pi\) |
0.903996 | + | 0.427540i | \(0.140620\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2382.47 | − | 297.754i | −0.992281 | − | 0.124013i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1141.87 | − | 1977.78i | 0.0779913 | − | 0.135085i | −0.824392 | − | 0.566019i | \(-0.808483\pi\) |
0.902383 | + | 0.430935i | \(0.141816\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 8314.85i | − | 0.291126i | −0.989349 | − | 0.145563i | \(-0.953501\pi\) | ||
0.989349 | − | 0.145563i | \(-0.0464994\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 63255.0 | + | 36520.3i | 0.757355 | + | 0.437259i | 0.828345 | − | 0.560218i | \(-0.189283\pi\) |
−0.0709904 | + | 0.997477i | \(0.522616\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −218262. | + | 126014.i | −1.67481 | + | 0.966949i | −0.709918 | + | 0.704284i | \(0.751268\pi\) |
−0.964887 | + | 0.262665i | \(0.915398\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −142303. | − | 246477.i | −0.508515 | − | 0.880773i | −0.999951 | − | 0.00986012i | \(-0.996861\pi\) |
0.491437 | − | 0.870913i | \(-0.336472\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 57726.8 | − | 99985.8i | 0.147781 | − | 0.255964i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 105335. | 0.148930 | 0.0744649 | − | 0.997224i | \(-0.476275\pi\) | ||||
0.0744649 | + | 0.997224i | \(0.476275\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 743496. | + | 429258.i | 0.805067 | + | 0.464805i | 0.845240 | − | 0.534387i | \(-0.179458\pi\) |
−0.0401732 | + | 0.999193i | \(0.512791\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.57371e6 | + | 663992.i | −1.04870 | + | 0.442477i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.41911e6 | + | 2.45797e6i | 0.757196 | + | 1.31150i | 0.944275 | + | 0.329157i | \(0.106765\pi\) |
−0.187079 | + | 0.982345i | \(0.559902\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.75485e6i | 0.621017i | 0.950571 | + | 0.310509i | \(0.100499\pi\) | ||||
−0.950571 | + | 0.310509i | \(0.899501\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.66109e6 | −0.485868 | −0.242934 | − | 0.970043i | \(-0.578110\pi\) | ||||
−0.242934 | + | 0.970043i | \(0.578110\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.13716e6 | + | 1.81124e6i | −0.642904 | + | 0.371181i | −0.785732 | − | 0.618567i | \(-0.787714\pi\) |
0.142829 | + | 0.989747i | \(0.454380\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.58749e6 | + | 1.41878e6i | 0.969242 | + | 0.246111i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.68440e6 | − | 9.84568e6i | 0.720413 | − | 1.24779i | −0.240422 | − | 0.970669i | \(-0.577286\pi\) |
0.960834 | − | 0.277123i | \(-0.0893810\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 1.62464e6i | − | 0.177544i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.15832e7 | + | 6.68757e6i | 0.955919 | + | 0.551900i | 0.894915 | − | 0.446237i | \(-0.147236\pi\) |
0.0610044 | + | 0.998137i | \(0.480570\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.24328e7 | + | 7.17810e6i | −0.897947 | + | 0.518430i | −0.876533 | − | 0.481341i | \(-0.840150\pi\) |
−0.0214132 | + | 0.999771i | \(0.506817\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.95756e6 | − | 5.12265e6i | −0.165684 | − | 0.286973i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.55171e7 | − | 2.68764e7i | 0.770036 | − | 1.33374i | −0.167507 | − | 0.985871i | \(-0.553572\pi\) |
0.937543 | − | 0.347870i | \(-0.113095\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.33725e7 | −1.31327 | −0.656637 | − | 0.754207i | \(-0.728022\pi\) | ||||
−0.656637 | + | 0.754207i | \(0.728022\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.19825e6 | − | 4.15591e6i | −0.253475 | − | 0.146344i | 0.367879 | − | 0.929874i | \(-0.380084\pi\) |
−0.621354 | + | 0.783530i | \(0.713417\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.30936e6 | + | 4.37199e6i | −0.0941415 | + | 0.124370i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.40981e6 | + | 5.90597e6i | 0.0875431 | + | 0.151629i | 0.906472 | − | 0.422266i | \(-0.138765\pi\) |
−0.818929 | + | 0.573895i | \(0.805432\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 4.05040e7i | − | 0.853465i | −0.904378 | − | 0.426732i | \(-0.859665\pi\) | ||
0.904378 | − | 0.426732i | \(-0.140335\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.19605e7 | 0.995400 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.65699e7 | − | 2.11136e7i | 0.582860 | − | 0.336514i | −0.179409 | − | 0.983774i | \(-0.557419\pi\) |
0.762269 | + | 0.647260i | \(0.224085\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.47578e6 | + | 1.98099e7i | −0.0361033 | + | 0.288879i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −8.96452e7 | + | 1.55270e8i | −1.10061 | + | 1.90631i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.29688e7i | 1.05015i | 0.851057 | + | 0.525074i | \(0.175962\pi\) | ||||
−0.851057 | + | 0.525074i | \(0.824038\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.75882e8 | + | 1.01545e8i | 1.69019 | + | 0.975832i | 0.954356 | + | 0.298670i | \(0.0965431\pi\) |
0.735834 | + | 0.677162i | \(0.236790\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.00729e7 | + | 2.31361e7i | −0.356042 | + | 0.205561i | −0.667343 | − | 0.744750i | \(-0.732569\pi\) |
0.311301 | + | 0.950311i | \(0.399235\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.08056e8 | + | 1.87159e8i | 0.824357 | + | 1.42783i | 0.902410 | + | 0.430878i | \(0.141796\pi\) |
−0.0780533 | + | 0.996949i | \(0.524870\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.17692e7 | + | 8.96669e7i | −0.366746 | + | 0.635223i | −0.989055 | − | 0.147549i | \(-0.952862\pi\) |
0.622309 | + | 0.782772i | \(0.286195\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.87471e8 | 1.76311 | 0.881556 | − | 0.472079i | \(-0.156496\pi\) | ||||
0.881556 | + | 0.472079i | \(0.156496\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.75341e8 | − | 1.01233e8i | −1.00252 | − | 0.578805i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.39829e8 | − | 1.05843e8i | −0.697283 | − | 0.527805i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.04572e8 | + | 1.81123e8i | 0.487835 | + | 0.844954i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.95755e8i | 0.801811i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.09348e8 | −0.420336 | −0.210168 | − | 0.977665i | \(-0.567401\pi\) | ||||
−0.210168 | + | 0.977665i | \(0.567401\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.61254e8 | − | 9.31002e7i | 0.547553 | − | 0.316130i | −0.200582 | − | 0.979677i | \(-0.564283\pi\) |
0.748134 | + | 0.663547i | \(0.230950\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.57524e8 | − | 2.35235e8i | 1.78179 | − | 0.751788i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.19189e8 | + | 5.52852e8i | −0.906078 | + | 1.56937i | −0.0866147 | + | 0.996242i | \(0.527605\pi\) |
−0.819463 | + | 0.573132i | \(0.805728\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.54755e8i | 0.950318i | 0.879900 | + | 0.475159i | \(0.157609\pi\) | ||||
−0.879900 | + | 0.475159i | \(0.842391\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.64449e7 | − | 9.49449e6i | −0.0393268 | − | 0.0227053i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.48953e7 | − | 3.74673e7i | 0.146805 | − | 0.0847580i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.47313e8 | − | 2.55154e8i | −0.298880 | − | 0.517675i | 0.677000 | − | 0.735983i | \(-0.263280\pi\) |
−0.975880 | + | 0.218308i | \(0.929946\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.80004e8 | − | 3.11777e8i | 0.346238 | − | 0.599702i | −0.639340 | − | 0.768925i | \(-0.720792\pi\) |
0.985578 | + | 0.169222i | \(0.0541255\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.10741e8 | 1.05811 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.46689e8 | − | 3.15631e8i | −0.899790 | − | 0.519494i | −0.0226582 | − | 0.999743i | \(-0.507213\pi\) |
−0.877132 | + | 0.480249i | \(0.840546\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.65643e8 | + | 6.29593e8i | 0.395362 | + | 0.937037i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.28000e8 | + | 5.68113e8i | 0.464648 | + | 0.804793i | 0.999186 | − | 0.0403513i | \(-0.0128477\pi\) |
−0.534538 | + | 0.845144i | \(0.679514\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.33854e8i | 0.300662i | 0.988636 | + | 0.150331i | \(0.0480340\pi\) | ||||
−0.988636 | + | 0.150331i | \(0.951966\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.46594e8 | 0.915246 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.00353e8 | − | 1.15674e8i | 0.223672 | − | 0.129137i | −0.383977 | − | 0.923343i | \(-0.625446\pi\) |
0.607649 | + | 0.794205i | \(0.292113\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.67303e8 | + | 2.21024e8i | −0.178383 | + | 0.235661i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.67392e8 | + | 6.36342e8i | −0.357864 | + | 0.619838i | −0.987604 | − | 0.156968i | \(-0.949828\pi\) |
0.629740 | + | 0.776806i | \(0.283161\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.76795e9i | 1.64723i | 0.567147 | + | 0.823616i | \(0.308047\pi\) | ||||
−0.567147 | + | 0.823616i | \(0.691953\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.74858e9 | + | 1.00954e9i | 1.49279 | + | 0.861861i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.44458e8 | − | 8.34030e7i | 0.118134 | − | 0.0682048i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.15726e9 | + | 2.00444e9i | 0.869558 | + | 1.50612i | 0.862449 | + | 0.506144i | \(0.168929\pi\) |
0.00710853 | + | 0.999975i | \(0.497737\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.41515e8 | + | 1.28434e9i | −0.534430 | + | 0.925660i | 0.464761 | + | 0.885436i | \(0.346140\pi\) |
−0.999191 | + | 0.0402236i | \(0.987193\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −9.91728e8 | −0.658458 | −0.329229 | − | 0.944250i | \(-0.606789\pi\) | ||||
−0.329229 | + | 0.944250i | \(0.606789\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.44567e8 | + | 5.45346e8i | 0.602310 | + | 0.347744i | 0.769950 | − | 0.638104i | \(-0.220281\pi\) |
−0.167640 | + | 0.985848i | \(0.553614\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.50958e8 | − | 3.13640e7i | −0.147780 | − | 0.0184692i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.24192e8 | + | 1.08113e9i | 0.353429 | + | 0.612158i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.75566e8i | 0.301655i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.72265e9 | 1.37361 | 0.686804 | − | 0.726843i | \(-0.259013\pi\) | ||||
0.686804 | + | 0.726843i | \(0.259013\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.02337e9 | + | 5.90842e8i | −0.478937 | + | 0.276514i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.64354e9 | − | 1.24407e9i | −0.741210 | − | 0.561056i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.03661e8 | − | 5.25956e8i | 0.127298 | − | 0.220486i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 2.79895e9i | − | 1.13181i | −0.824469 | − | 0.565907i | \(-0.808526\pi\) | ||
0.824469 | − | 0.565907i | \(-0.191474\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.83318e9 | − | 1.63574e9i | −1.06702 | − | 0.616042i | −0.139651 | − | 0.990201i | \(-0.544598\pi\) |
−0.927365 | + | 0.374159i | \(0.877932\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.31582e8 | + | 2.49174e8i | −0.156936 | + | 0.0906068i | −0.576411 | − | 0.817160i | \(-0.695547\pi\) |
0.419476 | + | 0.907767i | \(0.362214\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.05020e8 | − | 3.55106e8i | −0.0695622 | − | 0.120485i | 0.829146 | − | 0.559031i | \(-0.188827\pi\) |
−0.898709 | + | 0.438546i | \(0.855494\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.28850e9 | + | 2.23175e9i | −0.422488 | + | 0.731770i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.65129e9 | 0.812578 | 0.406289 | − | 0.913745i | \(-0.366823\pi\) | ||||
0.406289 | + | 0.913745i | \(0.366823\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.98398e9 | − | 1.14545e9i | −0.588125 | − | 0.339554i | 0.176231 | − | 0.984349i | \(-0.443610\pi\) |
−0.764356 | + | 0.644795i | \(0.776943\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.94701e9 | − | 1.11336e9i | 1.09548 | − | 0.309009i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.04779e9 | + | 1.81482e9i | 0.281504 | + | 0.487580i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.86113e9i | 1.72862i | 0.502956 | + | 0.864312i | \(0.332246\pi\) | ||||
−0.502956 | + | 0.864312i | \(0.667754\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.49968e8 | −0.158639 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.96090e9 | − | 2.86418e9i | 1.13718 | − | 0.656550i | 0.191447 | − | 0.981503i | \(-0.438682\pi\) |
0.945730 | + | 0.324953i | \(0.105349\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.64910e9 | − | 6.27857e9i | −0.588708 | − | 1.39528i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 8.97165e8 | − | 1.55394e9i | 0.187521 | − | 0.324796i | −0.756902 | − | 0.653528i | \(-0.773288\pi\) |
0.944423 | + | 0.328733i | \(0.106621\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 8.08768e9i | − | 1.63999i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.31848e9 | − | 4.22532e9i | −1.39769 | − | 0.806958i | −0.403542 | − | 0.914961i | \(-0.632221\pi\) |
−0.994151 | + | 0.108003i | \(0.965554\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.03480e8 | − | 4.63890e8i | 0.148970 | − | 0.0860077i | −0.423662 | − | 0.905820i | \(-0.639256\pi\) |
0.572632 | + | 0.819812i | \(0.305922\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.31833e8 | − | 2.28342e8i | −0.0230512 | − | 0.0399259i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.40624e9 | + | 7.63184e9i | −0.748427 | + | 1.29631i | 0.200150 | + | 0.979765i | \(0.435857\pi\) |
−0.948576 | + | 0.316548i | \(0.897476\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.34848e8 | 0.149939 | 0.0749697 | − | 0.997186i | \(-0.476114\pi\) | ||||
0.0749697 | + | 0.997186i | \(0.476114\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.07905e9 | − | 1.20034e9i | −0.324130 | − | 0.187137i | 0.329102 | − | 0.944294i | \(-0.393254\pi\) |
−0.653232 | + | 0.757158i | \(0.726587\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.22513e8 | − | 4.18086e9i | 0.0770140 | − | 0.616223i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.20413e8 | − | 1.42100e9i | −0.117609 | − | 0.203705i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 1.88044e9i | − | 0.255146i | −0.991829 | − | 0.127573i | \(-0.959281\pi\) | ||
0.991829 | − | 0.127573i | \(-0.0407187\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.51497e9 | 1.25638 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.04942e9 | + | 1.18323e9i | −0.256416 | + | 0.148042i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.95748e9 | + | 4.94596e8i | 0.482118 | + | 0.0602538i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.10644e9 | + | 8.84461e9i | −0.590091 | + | 1.02207i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.12605e10i | 1.26766i | 0.773471 | + | 0.633832i | \(0.218519\pi\) | ||||
−0.773471 | + | 0.633832i | \(0.781481\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.00193e10 | − | 5.78466e9i | −1.07102 | − | 0.618353i | −0.142559 | − | 0.989786i | \(-0.545533\pi\) |
−0.928459 | + | 0.371434i | \(0.878866\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.74494e9 | − | 3.31684e9i | 0.598561 | − | 0.345579i | −0.169914 | − | 0.985459i | \(-0.554349\pi\) |
0.768475 | + | 0.639880i | \(0.221016\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6.66436e9 | − | 1.15430e10i | −0.659966 | − | 1.14310i | −0.980624 | − | 0.195900i | \(-0.937237\pi\) |
0.320658 | − | 0.947195i | \(-0.396096\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.20279e8 | − | 2.08330e8i | 0.0116152 | − | 0.0201182i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.84083e10 | −1.69123 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −8.31367e8 | − | 4.79990e8i | −0.0745177 | − | 0.0430228i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.01349e9 | − | 3.38112e9i | 0.683972 | − | 0.288587i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.10229e9 | − | 5.37332e9i | −0.258446 | − | 0.447642i | 0.707380 | − | 0.706834i | \(-0.249877\pi\) |
−0.965826 | + | 0.259192i | \(0.916544\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 2.20775e10i | − | 1.75295i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.25909e10 | −0.976196 | −0.488098 | − | 0.872789i | \(-0.662309\pi\) | ||||
−0.488098 | + | 0.872789i | \(0.662309\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.69795e9 | − | 9.80314e8i | 0.125576 | − | 0.0725016i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.28895e10 | − | 5.04389e9i | −0.931239 | − | 0.364409i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8.11191e9 | − | 1.40502e10i | 0.559507 | − | 0.969094i | −0.438031 | − | 0.898960i | \(-0.644324\pi\) |
0.997538 | − | 0.0701340i | \(-0.0223427\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 1.03313e9i | − | 0.0696391i | −0.999394 | − | 0.0348196i | \(-0.988914\pi\) | ||
0.999394 | − | 0.0348196i | \(-0.0110857\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.02373e10 | + | 5.91051e9i | 0.659306 | + | 0.380651i | 0.792013 | − | 0.610505i | \(-0.209033\pi\) |
−0.132706 | + | 0.991155i | \(0.542367\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.05602e10 | + | 1.18705e10i | −1.29454 | + | 0.747402i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7.42552e9 | − | 1.28614e10i | −0.447042 | − | 0.774300i | 0.551149 | − | 0.834407i | \(-0.314189\pi\) |
−0.998192 | + | 0.0601062i | \(0.980856\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.32672e10 | − | 4.02999e10i | 1.36998 | − | 2.37288i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.91296e9 | −0.333145 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.92235e8 | + | 1.10987e8i | 0.0105966 | + | 0.00611796i | 0.505289 | − | 0.862950i | \(-0.331386\pi\) |
−0.494692 | + | 0.869068i | \(0.664719\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.64745e10 | + | 2.17644e10i | −0.869594 | + | 1.14882i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.16778e10 | + | 2.02265e10i | 0.603288 | + | 1.04493i | 0.992319 | + | 0.123701i | \(0.0394765\pi\) |
−0.389031 | + | 0.921225i | \(0.627190\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 8.75847e8i | − | 0.0433574i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.13272e8 | 0.0200299 | 0.0100150 | − | 0.999950i | \(-0.496812\pi\) | ||||
0.0100150 | + | 0.999950i | \(0.496812\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.36941e10 | − | 7.90631e9i | 0.636414 | − | 0.367434i | −0.146818 | − | 0.989164i | \(-0.546903\pi\) |
0.783232 | + | 0.621730i | \(0.213570\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.83743e8 | + | 3.87064e9i | −0.0220177 | + | 0.176173i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.91657e8 | + | 3.31960e8i | −0.00837001 | + | 0.0144973i | −0.870180 | − | 0.492734i | \(-0.835998\pi\) |
0.861810 | + | 0.507231i | \(0.169331\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 2.07878e10i | − | 0.889411i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.20146e9 | + | 2.42571e9i | 0.172588 | + | 0.0996440i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.61525e9 | − | 2.08727e9i | 0.145538 | − | 0.0840265i | −0.425463 | − | 0.904976i | \(-0.639889\pi\) |
0.571001 | + | 0.820949i | \(0.306555\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.51066e10 | − | 2.61654e10i | −0.584238 | − | 1.01193i | −0.994970 | − | 0.100174i | \(-0.968060\pi\) |
0.410732 | − | 0.911756i | \(-0.365273\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.56921e9 | − | 6.18206e9i | 0.135317 | − | 0.234376i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.48175e9 | 0.236219 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.37437e9 | + | 1.37084e9i | 0.0848507 | + | 0.0489886i | 0.541825 | − | 0.840491i | \(-0.317734\pi\) |
−0.456974 | + | 0.889480i | \(0.651067\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.56054e10 | − | 1.93819e10i | −0.880097 | − | 0.666186i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.44071e10 | − | 2.49538e10i | −0.485718 | − | 0.841289i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.48634e9i | 0.113113i | 0.998399 | + | 0.0565567i | \(0.0180122\pi\) | ||||
−0.998399 | + | 0.0565567i | \(0.981988\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.91451e10 | −0.609438 | −0.304719 | − | 0.952442i | \(-0.598563\pi\) | ||||
−0.304719 | + | 0.952442i | \(0.598563\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.30302e9 | − | 4.21640e9i | 0.223845 | − | 0.129237i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.17581e10 | − | 1.33996e10i | 0.955307 | − | 0.403071i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.38075e10 | + | 4.12358e10i | −0.689930 | + | 1.19499i | 0.281931 | + | 0.959435i | \(0.409025\pi\) |
−0.971860 | + | 0.235558i | \(0.924308\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.83719e10i | 0.522640i | 0.965252 | + | 0.261320i | \(0.0841579\pi\) | ||||
−0.965252 | + | 0.261320i | \(0.915842\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.21189e10 | + | 3.58644e10i | 1.70333 | + | 0.983416i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.33233e10 | + | 3.07862e10i | −1.43568 | + | 0.828892i | −0.997546 | − | 0.0700162i | \(-0.977695\pi\) |
−0.438137 | + | 0.898908i | \(0.644362\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8.71680e8 | + | 1.50979e9i | 0.0226330 | + | 0.0392015i | 0.877120 | − | 0.480271i | \(-0.159462\pi\) |
−0.854487 | + | 0.519473i | \(0.826128\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.50201e10 | − | 2.60155e10i | 0.383030 | − | 0.663427i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.37418e10 | 0.584156 | 0.292078 | − | 0.956395i | \(-0.405653\pi\) | ||||
0.292078 | + | 0.956395i | \(0.405653\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.47070e9 | + | 2.00381e9i | 0.0838901 | + | 0.0484340i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5.52100e9 | + | 1.30852e10i | 0.128817 | + | 0.305305i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.05435e10 | + | 5.29030e10i | 0.700253 | + | 1.21287i | 0.968378 | + | 0.249489i | \(0.0802626\pi\) |
−0.268125 | + | 0.963384i | \(0.586404\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.26327e10i | 0.722518i | 0.932465 | + | 0.361259i | \(0.117653\pi\) | ||||
−0.932465 | + | 0.361259i | \(0.882347\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.98874e10 | −1.08559 | −0.542797 | − | 0.839864i | \(-0.682635\pi\) | ||||
−0.542797 | + | 0.839864i | \(0.682635\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.22519e10 | − | 3.59412e10i | 1.30884 | − | 0.755657i | 0.326934 | − | 0.945047i | \(-0.393985\pi\) |
0.981902 | + | 0.189391i | \(0.0606513\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.49715e10 | + | 5.94118e10i | −0.929492 | + | 1.22795i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.89675e9 | + | 3.28526e9i | −0.0378935 | + | 0.0656335i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.90975e10i | 0.571586i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.14306e10 | − | 2.39199e10i | −0.787007 | − | 0.454379i | 0.0519006 | − | 0.998652i | \(-0.483472\pi\) |
−0.838908 | + | 0.544273i | \(0.816805\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.04376e10 | − | 1.17997e10i | 0.381813 | − | 0.220440i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.30686e10 | + | 5.72766e10i | 0.597653 | + | 1.03517i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.96693e10 | − | 3.40683e10i | 0.349683 | − | 0.605668i | −0.636510 | − | 0.771268i | \(-0.719623\pi\) |
0.986193 | + | 0.165600i | \(0.0529561\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.00258e11 | −1.72502 | −0.862509 | − | 0.506041i | \(-0.831108\pi\) | ||||
−0.862509 | + | 0.506041i | \(0.831108\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.66298e9 | + | 3.84688e9i | 0.112793 | + | 0.0651209i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.95088e10 | + | 9.93681e9i | 1.30314 | + | 0.162863i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.63552e9 | + | 1.32251e10i | 0.123151 | + | 0.213303i | 0.921009 | − | 0.389542i | \(-0.127367\pi\) |
−0.797858 | + | 0.602846i | \(0.794034\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.70851e10i | 0.735549i | 0.929915 | + | 0.367774i | \(0.119880\pi\) | ||||
−0.929915 | + | 0.367774i | \(0.880120\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.44477e11 | 2.22144 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.97031e10 | + | 2.86961e10i | −0.740478 | + | 0.427515i | −0.822243 | − | 0.569136i | \(-0.807278\pi\) |
0.0817648 | + | 0.996652i | \(0.473944\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.59121e10 | + | 1.20446e10i | 0.233370 | + | 0.176648i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.64588e10 | + | 2.85075e10i | −0.233975 | + | 0.405257i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.27282e9i | 0.115795i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.54486e10 | + | 2.62397e10i | 0.616836 | + | 0.356130i | 0.775636 | − | 0.631181i | \(-0.217429\pi\) |
−0.158800 | + | 0.987311i | \(0.550763\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.95547e10 | + | 1.12899e10i | −0.261363 | + | 0.150898i | −0.624956 | − | 0.780660i | \(-0.714883\pi\) |
0.363593 | + | 0.931558i | \(0.381550\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.13532e10 | + | 5.43054e10i | 0.406481 | + | 0.704045i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.34496e9 | + | 2.32954e9i | −0.0171746 | + | 0.0297473i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.45913e10 | 0.180794 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.33143e11 | + | 7.68704e10i | 1.62519 | + | 0.938305i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 9.18622e9 | − | 9.43075e9i | 0.108838 | − | 0.111735i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.77813e10 | − | 6.54391e10i | −0.441050 | − | 0.763920i | 0.556718 | − | 0.830702i | \(-0.312060\pi\) |
−0.997768 | + | 0.0667812i | \(0.978727\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.36564e10i | 0.834881i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.03691e11 | −1.15823 | −0.579113 | − | 0.815247i | \(-0.696601\pi\) | ||||
−0.579113 | + | 0.815247i | \(0.696601\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.29907e10 | + | 1.32737e10i | −0.249428 | + | 0.144008i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.36523e9 | − | 1.50861e10i | −0.0680634 | − | 0.161315i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8.78292e10 | − | 1.52125e11i | 0.912469 | − | 1.58044i | 0.101905 | − | 0.994794i | \(-0.467506\pi\) |
0.810565 | − | 0.585649i | \(-0.199160\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.38117e10i | 0.141449i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.89713e8 | + | 5.71411e8i | 0.00985089 | + | 0.00568741i | 0.504917 | − | 0.863168i | \(-0.331523\pi\) |
−0.495066 | + | 0.868855i | \(0.664856\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.77106e11 | − | 1.02252e11i | 1.73796 | − | 1.00341i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2.53958e10 | − | 4.39868e10i | −0.242277 | − | 0.419636i | 0.719085 | − | 0.694922i | \(-0.244561\pi\) |
−0.961363 | + | 0.275285i | \(0.911228\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.58711e10 | + | 9.67715e10i | −0.525584 | + | 0.910339i | 0.473972 | + | 0.880540i | \(0.342820\pi\) |
−0.999556 | + | 0.0297987i | \(0.990513\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.28589e10 | −0.300595 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.57318e10 | + | 3.79503e10i | 0.593024 | + | 0.342382i | 0.766292 | − | 0.642492i | \(-0.222100\pi\) |
−0.173269 | + | 0.984875i | \(0.555433\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.20602e10 | + | 9.64994e10i | −0.105840 | + | 0.846876i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.29817e10 | − | 2.24850e10i | −0.112372 | − | 0.194634i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.81096e10i | 0.236756i | 0.992969 | + | 0.118378i | \(0.0377695\pi\) | ||||
−0.992969 | + | 0.118378i | \(0.962230\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.16369e11 | −1.79777 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.48692e10 | − | 4.32257e10i | 0.605458 | − | 0.349561i | −0.165728 | − | 0.986172i | \(-0.552997\pi\) |
0.771186 | + | 0.636610i | \(0.219664\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.23794e11 | − | 1.54715e10i | −0.987716 | − | 0.123442i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.30484e10 | − | 3.99210e10i | 0.179033 | − | 0.310094i | −0.762517 | − | 0.646969i | \(-0.776036\pi\) |
0.941550 | + | 0.336874i | \(0.109370\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 1.65816e11i | − | 1.27095i | −0.772120 | − | 0.635476i | \(-0.780804\pi\) | ||
0.772120 | − | 0.635476i | \(-0.219196\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.28850e11 | + | 7.43915e10i | 0.961750 | + | 0.555267i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.04541e11 | + | 6.03566e10i | −0.770071 | + | 0.444601i | −0.832900 | − | 0.553424i | \(-0.813321\pi\) |
0.0628290 | + | 0.998024i | \(0.479988\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.50602e10 | + | 2.60851e10i | 0.108060 | + | 0.187166i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.32931e10 | + | 1.26947e11i | −0.519064 | + | 0.899045i | 0.480691 | + | 0.876890i | \(0.340386\pi\) |
−0.999755 | + | 0.0221550i | \(0.992947\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.34126e9 | 0.0299554 | 0.0149777 | − | 0.999888i | \(-0.495232\pi\) | ||||
0.0149777 | + | 0.999888i | \(0.495232\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.46823e11 | + | 8.47685e10i | 1.00007 | + | 0.577394i | 0.908270 | − | 0.418384i | \(-0.137403\pi\) |
0.0918045 | + | 0.995777i | \(0.470737\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −9.34133e10 | + | 3.94137e10i | −0.620092 | + | 0.261634i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.21787e10 | + | 1.59658e11i | 0.604102 | + | 1.04634i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.07305e11i | 1.32436i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.67082e11 | 1.05393 | 0.526967 | − | 0.849886i | \(-0.323329\pi\) | ||||
0.526967 | + | 0.849886i | \(0.323329\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.73677e10 | + | 3.88947e10i | −0.414340 | + | 0.239219i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.17969e10 | − | 4.64591e10i | 0.0716493 | − | 0.282172i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.44089e10 | + | 2.49570e10i | −0.0853491 | + | 0.147829i | −0.905540 | − | 0.424261i | \(-0.860534\pi\) |
0.820191 | + | 0.572090i | \(0.193867\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.88987e9i | 0.0578558i | 0.999582 | + | 0.0289279i | \(0.00920931\pi\) | ||||
−0.999582 | + | 0.0289279i | \(0.990791\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.71054e11 | − | 9.87580e10i | −0.976148 | − | 0.563579i | −0.0750432 | − | 0.997180i | \(-0.523909\pi\) |
−0.901105 | + | 0.433601i | \(0.857243\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.64531e10 | − | 1.52727e10i | 0.149107 | − | 0.0860869i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.38657e8 | + | 9.32982e8i | 0.00296251 | + | 0.00513122i | 0.867503 | − | 0.497432i | \(-0.165724\pi\) |
−0.864540 | + | 0.502563i | \(0.832390\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.62307e10 | − | 1.14715e11i | 0.359828 | − | 0.623240i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.24072e11 | −0.657859 | −0.328929 | − | 0.944355i | \(-0.606688\pi\) | ||||
−0.328929 | + | 0.944355i | \(0.606688\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.51218e11 | − | 8.73060e10i | −0.792134 | − | 0.457339i | 0.0485793 | − | 0.998819i | \(-0.484531\pi\) |
−0.840713 | + | 0.541481i | \(0.817864\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.59809e11 | − | 3.43233e11i | 1.32852 | − | 1.75510i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.49896e10 | − | 2.59627e10i | −0.0757330 | − | 0.131173i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.27858e10i | 0.161732i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.01995e11 | 0.497184 | 0.248592 | − | 0.968608i | \(-0.420032\pi\) | ||||
0.248592 | + | 0.968608i | \(0.420032\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.52406e10 | − | 4.34402e10i | 0.358177 | − | 0.206794i | −0.310104 | − | 0.950703i | \(-0.600364\pi\) |
0.668281 | + | 0.743909i | \(0.267031\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.76819e10 | − | 2.21495e11i | 0.130232 | − | 1.04204i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8.12762e9 | − | 1.40774e10i | 0.0373491 | − | 0.0646906i | −0.846747 | − | 0.531996i | \(-0.821442\pi\) |
0.884096 | + | 0.467306i | \(0.154775\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.54137e11i | 2.06265i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −8.18654e10 | − | 4.72650e10i | −0.363265 | − | 0.209731i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.95833e10 | − | 1.70800e10i | 0.129758 | − | 0.0749160i | −0.433716 | − | 0.901050i | \(-0.642798\pi\) |
0.563474 | + | 0.826134i | \(0.309464\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.26185e11 | + | 2.18558e11i | 0.540839 | + | 0.936760i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.40875e10 | + | 1.11003e11i | −0.271545 | + | 0.470330i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.18076e11 | 0.903100 | 0.451550 | − | 0.892246i | \(-0.350871\pi\) | ||||
0.451550 | + | 0.892246i | \(0.350871\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.19475e11 | − | 3.57654e11i | −2.53631 | − | 1.46434i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.88797e11 | − | 2.94298e11i | −1.55613 | − | 1.17790i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.33656e11 | − | 4.04704e11i | −0.924681 | − | 1.60159i | −0.792074 | − | 0.610425i | \(-0.790999\pi\) |
−0.132606 | − | 0.991169i | \(-0.542335\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 2.44339e11i | − | 0.945442i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.35086e10 | −0.0516876 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4.77167e10 | + | 2.75492e10i | −0.178548 | + | 0.103085i | −0.586610 | − | 0.809869i | \(-0.699538\pi\) |
0.408062 | + | 0.912954i | \(0.366205\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.02361e11 | − | 4.31890e10i | 0.378786 | − | 0.159821i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6.08067e9 | − | 1.05320e10i | 0.0220089 | − | 0.0381206i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.20385e10i | 0.0430957i | 0.999768 | + | 0.0215478i | \(0.00685942\pi\) | ||||
−0.999768 | + | 0.0215478i | \(0.993141\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.05072e11 | − | 6.06634e10i | −0.367975 | − | 0.212450i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.82913e11 | − | 1.63340e11i | 0.980023 | − | 0.565817i | 0.0777461 | − | 0.996973i | \(-0.475228\pi\) |
0.902277 | + | 0.431157i | \(0.141894\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.54370e10 | − | 6.13787e10i | −0.120112 | − | 0.208040i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.01067e11 | − | 1.75053e11i | 0.338869 | − | 0.586938i | −0.645351 | − | 0.763886i | \(-0.723289\pi\) |
0.984220 | + | 0.176948i | \(0.0566224\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.17987e11 | −1.37154 | −0.685768 | − | 0.727820i | \(-0.740534\pi\) | ||||
−0.685768 | + | 0.727820i | \(0.740534\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.81514e11 | − | 1.04797e11i | −0.589232 | − | 0.340193i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.01713e11 | − | 4.78074e11i | −0.640924 | − | 1.51904i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.43927e11 | + | 2.49289e11i | 0.452462 | + | 0.783688i | 0.998538 | − | 0.0540477i | \(-0.0172123\pi\) |
−0.546076 | + | 0.837736i | \(0.683879\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 2.56107e11i | − | 0.788196i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.76242e9 | −0.0114574 | −0.00572868 | − | 0.999984i | \(-0.501824\pi\) | ||||
−0.00572868 | + | 0.999984i | \(0.501824\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.20846e11 | − | 3.00710e11i | 1.55300 | − | 0.896623i | 0.555100 | − | 0.831783i | \(-0.312680\pi\) |
0.997896 | − | 0.0648394i | \(-0.0206535\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.50037e11 | − | 1.98214e11i | 0.442691 | − | 0.584838i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.56062e10 | − | 9.63128e10i | 0.160673 | − | 0.278293i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 2.32644e10i | − | 0.0665252i | −0.999447 | − | 0.0332626i | \(-0.989410\pi\) | ||
0.999447 | − | 0.0332626i | \(-0.0105898\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.95209e10 | − | 1.70439e10i | −0.0826820 | − | 0.0477365i | 0.458089 | − | 0.888906i | \(-0.348534\pi\) |
−0.540771 | + | 0.841170i | \(0.681867\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.58393e10 | − | 4.95593e10i | 0.237946 | − | 0.137378i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.21135e11 | − | 3.83017e11i | −0.600492 | − | 1.04008i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.81071e10 | + | 6.60034e10i | −0.102424 | + | 0.177404i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.49074e11 | −1.18260 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.83036e10 | − | 3.94351e10i | −0.178051 | − | 0.102798i | 0.408326 | − | 0.912836i | \(-0.366113\pi\) |
−0.586377 | + | 0.810039i | \(0.699446\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.84890e11 | − | 8.55957e10i | −1.74950 | − | 0.218648i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.96848e10 | + | 1.03377e11i | 0.150928 | + | 0.261416i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.31195e11i | 0.572988i | 0.958082 | + | 0.286494i | \(0.0924898\pi\) | ||||
−0.958082 | + | 0.286494i | \(0.907510\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.64589e11 | −0.649208 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.64389e10 | + | 9.49103e9i | −0.0395377 | + | 0.0228271i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.87602e11 | + | 2.93394e11i | 0.923002 | + | 0.698663i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.77818e11 | + | 6.54400e11i | −0.882040 | + | 1.52774i | −0.0329710 | + | 0.999456i | \(0.510497\pi\) |
−0.849069 | + | 0.528282i | \(0.822836\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.12335e10i | 0.0953162i | 0.998864 | + | 0.0476581i | \(0.0151758\pi\) | ||||
−0.998864 | + | 0.0476581i | \(0.984824\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.04151e11 | + | 2.33337e11i | 0.916037 | + | 0.528874i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.62553e11 | − | 2.09320e11i | 0.813735 | − | 0.469810i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.04220e10 | − | 1.21974e11i | −0.155001 | − | 0.268470i | 0.778058 | − | 0.628192i | \(-0.216205\pi\) |
−0.933060 | + | 0.359722i | \(0.882872\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.94058e11 | + | 5.09323e11i | −0.640964 | + | 1.11018i | 0.344254 | + | 0.938876i | \(0.388132\pi\) |
−0.985218 | + | 0.171305i | \(0.945202\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.48519e10 | 0.0531297 | 0.0265648 | − | 0.999647i | \(-0.491543\pi\) | ||||
0.0265648 | + | 0.999647i | \(0.491543\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4.39196e11 | + | 2.53570e11i | 0.929909 | + | 0.536883i | 0.886783 | − | 0.462186i | \(-0.152935\pi\) |
0.0431265 | + | 0.999070i | \(0.486268\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.01622e11 | + | 2.93802e11i | 0.626446 | + | 0.610203i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.31810e10 | + | 1.44074e11i | 0.171111 | + | 0.296373i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 5.64346e11i | 1.13893i | 0.822015 | + | 0.569465i | \(0.192850\pi\) | ||||
−0.822015 | + | 0.569465i | \(0.807150\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.89151e11 | −0.977820 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.59964e11 | − | 2.65560e11i | 0.902188 | − | 0.520879i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.95208e11 | − | 4.62657e11i | −0.379284 | − | 0.898930i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.03887e11 | − | 6.99553e11i | 0.770091 | − | 1.33384i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.33682e11i | 0.819173i | 0.912271 | + | 0.409586i | \(0.134327\pi\) | ||||
−0.912271 | + | 0.409586i | \(0.865673\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 5.92795e11 | + | 3.42250e11i | 1.09896 | + | 0.634484i | 0.935947 | − | 0.352141i | \(-0.114546\pi\) |
0.163011 | + | 0.986624i | \(0.447879\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.14525e11 | + | 2.39326e11i | −0.761339 | + | 0.439559i | −0.829776 | − | 0.558096i | \(-0.811532\pi\) |
0.0684372 | + | 0.997655i | \(0.478199\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4.96342e10 | + | 8.59690e10i | 0.0894825 | + | 0.154988i | 0.907292 | − | 0.420500i | \(-0.138145\pi\) |
−0.817810 | + | 0.575488i | \(0.804812\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.22896e10 | − | 1.42530e11i | 0.146987 | − | 0.254590i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.55743e10 | 0.0273104 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.23473e11 | − | 1.29022e11i | −0.388287 | − | 0.224177i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 5.82868e10 | − | 4.66379e11i | 0.0994348 | − | 0.795622i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.51149e11 | − | 6.08207e11i | −0.593598 | − | 1.02814i | −0.993743 | − | 0.111691i | \(-0.964373\pi\) |
0.400145 | − | 0.916452i | \(-0.368960\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5.35262e10i | 0.0888512i | 0.999013 | + | 0.0444256i | \(0.0141458\pi\) | ||||
−0.999013 | + | 0.0444256i | \(0.985854\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.23059e11 | −1.18941 | −0.594704 | − | 0.803945i | \(-0.702731\pi\) | ||||
−0.594704 | + | 0.803945i | \(0.702731\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −7.11223e11 | + | 4.10625e11i | −1.14898 | + | 0.663362i | −0.948638 | − | 0.316365i | \(-0.897538\pi\) |
−0.200339 | + | 0.979727i | \(0.564204\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.60518e11 | + | 3.25589e10i | 0.417092 | + | 0.0521270i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.56483e11 | − | 7.90652e11i | 0.717825 | − | 1.24331i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.22720e11i | 0.814660i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 7.83163e10 | + | 4.52159e10i | 0.119898 | + | 0.0692234i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.19134e11 | − | 4.15192e11i | 1.09122 | − | 0.630014i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6.28852e11 | + | 1.08920e12i | 0.937463 | + | 1.62373i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.58264e11 | − | 7.93736e11i | 0.677153 | − | 1.17286i | −0.298682 | − | 0.954353i | \(-0.596547\pi\) |
0.975835 | − | 0.218510i | \(-0.0701196\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.64275e11 | −0.964438 | −0.482219 | − | 0.876051i | \(-0.660169\pi\) | ||||
−0.482219 | + | 0.876051i | \(0.660169\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.01079e10 | − | 4.62503e10i | −0.115290 | − | 0.0665628i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.11904e11 | + | 1.73794e11i | −0.582530 | + | 0.245786i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.26364e10 | + | 9.11688e10i | 0.0737945 | + | 0.127816i | 0.900561 | − | 0.434729i | \(-0.143156\pi\) |
−0.826767 | + | 0.562545i | \(0.809822\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.77487e11i | 0.382328i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.27682e11 | 0.447596 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.33087e11 | − | 2.50043e11i | 0.581449 | − | 0.335700i | −0.180260 | − | 0.983619i | \(-0.557694\pi\) |
0.761709 | + | 0.647919i | \(0.224361\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.39832e12 | + | 3.94434e11i | −1.86127 | + | 0.525020i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.93322e10 | − | 1.02766e11i | 0.0776326 | − | 0.134464i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 3.30356e11i | − | 0.428572i | −0.976771 | − | 0.214286i | \(-0.931258\pi\) | ||
0.976771 | − | 0.214286i | \(-0.0687424\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.89310e11 | − | 1.09298e11i | −0.241444 | − | 0.139398i | 0.374396 | − | 0.927269i | \(-0.377850\pi\) |
−0.615840 | + | 0.787871i | \(0.711183\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.32528e11 | − | 2.49720e11i | 0.546975 | − | 0.315796i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.29630e11 | + | 7.44142e11i | 0.534189 | + | 0.925243i | 0.999202 | + | 0.0399390i | \(0.0127164\pi\) |
−0.465013 | + | 0.885304i | \(0.653950\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.45558e10 | + | 5.98524e10i | −0.0426046 | + | 0.0737933i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.26575e12 | −1.53453 | −0.767265 | − | 0.641330i | \(-0.778383\pi\) | ||||
−0.767265 | + | 0.641330i | \(0.778383\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.42594e12 | + | 8.23267e11i | 1.71430 | + | 0.989754i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9.25071e11 | − | 1.22211e12i | 1.09371 | − | 1.44489i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.79215e10 | − | 1.00323e11i | −0.0679119 | − | 0.117627i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.05502e12i | 1.21661i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.22731e11 | 0.826553 | 0.413276 | − | 0.910606i | \(-0.364384\pi\) | ||||
0.413276 | + | 0.910606i | \(0.364384\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.64175e11 | + | 1.52522e11i | −0.297177 | + | 0.171575i | −0.641174 | − | 0.767395i | \(-0.721552\pi\) |
0.343997 | + | 0.938971i | \(0.388219\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.05630e11 | − | 8.45191e11i | 0.117851 | − | 0.942982i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.67849e10 | − | 6.37133e10i | 0.0403730 | − | 0.0699282i | −0.845133 | − | 0.534556i | \(-0.820479\pi\) |
0.885506 | + | 0.464628i | \(0.153812\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 9.64363e10i | − | 0.104981i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 5.99150e11 | + | 3.45919e11i | 0.641685 | + | 0.370477i | 0.785263 | − | 0.619162i | \(-0.212528\pi\) |
−0.143579 | + | 0.989639i | \(0.545861\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.10987e11 | + | 3.52754e11i | −0.649064 | + | 0.374737i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.36378e11 | + | 4.09419e11i | 0.247071 | + | 0.427940i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.34640e9 | + | 9.26023e9i | −0.00554328 | + | 0.00960124i | −0.868784 | − | 0.495192i | \(-0.835098\pi\) |
0.863240 | + | 0.504793i | \(0.168431\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7.75909e11 | 0.791623 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.71798e11 | + | 3.30128e11i | 0.578711 | + | 0.334119i | 0.760621 | − | 0.649196i | \(-0.224895\pi\) |
−0.181910 | + | 0.983315i | \(0.558228\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 252.9.z.c.73.4 | 10 | ||
3.2 | odd | 2 | 28.9.h.a.17.4 | yes | 10 | ||
7.5 | odd | 6 | inner | 252.9.z.c.145.4 | 10 | ||
12.11 | even | 2 | 112.9.s.b.17.2 | 10 | |||
21.2 | odd | 6 | 196.9.h.a.117.2 | 10 | |||
21.5 | even | 6 | 28.9.h.a.5.4 | ✓ | 10 | ||
21.11 | odd | 6 | 196.9.b.a.97.4 | 10 | |||
21.17 | even | 6 | 196.9.b.a.97.7 | 10 | |||
21.20 | even | 2 | 196.9.h.a.129.2 | 10 | |||
84.47 | odd | 6 | 112.9.s.b.33.2 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
28.9.h.a.5.4 | ✓ | 10 | 21.5 | even | 6 | ||
28.9.h.a.17.4 | yes | 10 | 3.2 | odd | 2 | ||
112.9.s.b.17.2 | 10 | 12.11 | even | 2 | |||
112.9.s.b.33.2 | 10 | 84.47 | odd | 6 | |||
196.9.b.a.97.4 | 10 | 21.11 | odd | 6 | |||
196.9.b.a.97.7 | 10 | 21.17 | even | 6 | |||
196.9.h.a.117.2 | 10 | 21.2 | odd | 6 | |||
196.9.h.a.129.2 | 10 | 21.20 | even | 2 | |||
252.9.z.c.73.4 | 10 | 1.1 | even | 1 | trivial | ||
252.9.z.c.145.4 | 10 | 7.5 | odd | 6 | inner |