Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,9,Mod(181,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, base_ring=CyclotomicField(2))
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("252.181");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.d (of order \(2\), degree \(1\), 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: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - x^{9} + 14312 x^{8} - 30343 x^{7} + 170123918 x^{6} - 875537263 x^{5} + 496509566533 x^{4} + \cdots + 39\!\cdots\!76 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{19}\cdot 3^{15}\cdot 7^{4} \) |
Twist minimal: | no (minimal twist has level 84) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 181.3 | ||
Root | \(-32.7935 - 56.7999i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 252.181 |
Dual form | 252.9.d.d.181.8 |
$q$-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 \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 429.816i | − | 0.687706i | −0.939023 | − | 0.343853i | \(-0.888268\pi\) | ||
0.939023 | − | 0.343853i | \(-0.111732\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1615.33 | − | 1776.38i | −0.672772 | − | 0.739850i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5985.37 | −0.408809 | −0.204404 | − | 0.978887i | \(-0.565526\pi\) | ||||
−0.204404 | + | 0.978887i | \(0.565526\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 10608.4i | 0.371429i | 0.982604 | + | 0.185714i | \(0.0594599\pi\) | ||||
−0.982604 | + | 0.185714i | \(0.940540\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 54416.4i | 0.651530i | 0.945451 | + | 0.325765i | \(0.105622\pi\) | ||||
−0.945451 | + | 0.325765i | \(0.894378\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 183537.i | 1.40835i | 0.710028 | + | 0.704173i | \(0.248682\pi\) | ||||
−0.710028 | + | 0.704173i | \(0.751318\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 355836. | 1.27157 | 0.635783 | − | 0.771868i | \(-0.280677\pi\) | ||||
0.635783 | + | 0.771868i | \(0.280677\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 205883. | 0.527060 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −709300. | −1.00285 | −0.501427 | − | 0.865200i | \(-0.667192\pi\) | ||||
−0.501427 | + | 0.865200i | \(0.667192\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 647270.i | 0.700872i | 0.936587 | + | 0.350436i | \(0.113967\pi\) | ||||
−0.936587 | + | 0.350436i | \(0.886033\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −763517. | + | 694293.i | −0.508799 | + | 0.462669i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.29917e6 | 1.76035 | 0.880173 | − | 0.474653i | \(-0.157426\pi\) | ||||
0.880173 | + | 0.474653i | \(0.157426\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 837610.i | − | 0.296419i | −0.988956 | − | 0.148210i | \(-0.952649\pi\) | ||
0.988956 | − | 0.148210i | \(-0.0473510\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 884577. | 0.258739 | 0.129369 | − | 0.991596i | \(-0.458705\pi\) | ||||
0.129369 | + | 0.991596i | \(0.458705\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 8.95952e6i | − | 1.83609i | −0.396480 | − | 0.918043i | \(-0.629769\pi\) | ||
0.396480 | − | 0.918043i | \(-0.370231\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −546251. | + | 5.73886e6i | −0.0947563 | + | 0.995500i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.91683e6 | −1.25681 | −0.628404 | − | 0.777887i | \(-0.716292\pi\) | ||||
−0.628404 | + | 0.777887i | \(0.716292\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.57261e6i | 0.281140i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 1.24157e7i | − | 1.02462i | −0.858801 | − | 0.512310i | \(-0.828790\pi\) | ||
0.858801 | − | 0.512310i | \(-0.171210\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 2.50177e6i | − | 0.180687i | −0.995911 | − | 0.0903437i | \(-0.971203\pi\) | ||
0.995911 | − | 0.0903437i | \(-0.0287966\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.55965e6 | 0.255434 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.92355e7 | 1.45081 | 0.725407 | − | 0.688320i | \(-0.241651\pi\) | ||||
0.725407 | + | 0.688320i | \(0.241651\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.60661e7 | −0.632233 | −0.316117 | − | 0.948720i | \(-0.602379\pi\) | ||||
−0.316117 | + | 0.948720i | \(0.602379\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.50356e6i | 0.158586i | 0.996851 | + | 0.0792929i | \(0.0252662\pi\) | ||||
−0.996851 | + | 0.0792929i | \(0.974734\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 9.66831e6 | + | 1.06323e7i | 0.275035 | + | 0.302457i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.46076e7 | −1.14525 | −0.572625 | − | 0.819817i | \(-0.694075\pi\) | ||||
−0.572625 | + | 0.819817i | \(0.694075\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 1.75410e7i | − | 0.369609i | −0.982775 | − | 0.184805i | \(-0.940835\pi\) | ||
0.982775 | − | 0.184805i | \(-0.0591652\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.33891e7 | 0.448061 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.24371e6i | 0.0835755i | 0.999127 | + | 0.0417877i | \(0.0133053\pi\) | ||||
−0.999127 | + | 0.0417877i | \(0.986695\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.88445e7 | − | 1.71360e7i | 0.274801 | − | 0.249887i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 7.88873e7 | 0.968529 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 6.69113e7i | − | 0.755810i | −0.925844 | − | 0.377905i | \(-0.876645\pi\) | ||
0.925844 | − | 0.377905i | \(-0.123355\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 2.80485e7i | − | 0.269540i | −0.990877 | − | 0.134770i | \(-0.956970\pi\) | ||
0.990877 | − | 0.134770i | \(-0.0430296\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 1.64415e7i | − | 0.146081i | −0.997329 | − | 0.0730405i | \(-0.976730\pi\) | ||
0.997329 | − | 0.0730405i | \(-0.0232702\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.32225e8 | 1.77163 | 0.885817 | − | 0.464034i | \(-0.153598\pi\) | ||||
0.885817 | + | 0.464034i | \(0.153598\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.99604e7 | −0.141404 | −0.0707022 | − | 0.997497i | \(-0.522524\pi\) | ||||
−0.0707022 | + | 0.997497i | \(0.522524\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.62616e7 | 0.467727 | 0.233863 | − | 0.972269i | \(-0.424863\pi\) | ||||
0.233863 | + | 0.972269i | \(0.424863\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 1.52944e8i | − | 0.874464i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 9.66642e7 | − | 8.79002e7i | 0.482034 | − | 0.438331i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.78534e8 | −0.832876 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 2.56389e8i | − | 1.05017i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.66167e6 | 0.0217635 | 0.0108818 | − | 0.999941i | \(-0.496536\pi\) | ||||
0.0108818 | + | 0.999941i | \(0.496536\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.29714e8i | 0.440454i | 0.975449 | + | 0.220227i | \(0.0706798\pi\) | ||||
−0.975449 | + | 0.220227i | \(0.929320\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.26032e8 | − | 2.96472e8i | 1.04197 | − | 0.947496i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.30172e8 | 0.937256 | 0.468628 | − | 0.883396i | \(-0.344749\pi\) | ||||
0.468628 | + | 0.883396i | \(0.344749\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 2.04732e8i | − | 0.548436i | −0.961668 | − | 0.274218i | \(-0.911581\pi\) | ||
0.961668 | − | 0.274218i | \(-0.0884190\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 6.34950e7i | − | 0.151843i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.04869e8i | 0.689669i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.62729e8 | 0.330157 | 0.165079 | − | 0.986280i | \(-0.447212\pi\) | ||||
0.165079 | + | 0.986280i | \(0.447212\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.71122e8 | −0.329152 | −0.164576 | − | 0.986364i | \(-0.552626\pi\) | ||||
−0.164576 | + | 0.986364i | \(0.552626\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.78207e8 | 0.481994 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 2.38413e8i | − | 0.392402i | −0.980564 | − | 0.196201i | \(-0.937139\pi\) | ||
0.980564 | − | 0.196201i | \(-0.0628605\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.74791e8 | − | 6.32100e8i | −0.855474 | − | 0.940768i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.05318e9 | 1.49194 | 0.745971 | − | 0.665979i | \(-0.231986\pi\) | ||||
0.745971 | + | 0.665979i | \(0.231986\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 1.05696e9i | − | 1.35891i | −0.733715 | − | 0.679457i | \(-0.762215\pi\) | ||
0.733715 | − | 0.679457i | \(-0.237785\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.03193e8 | 0.862041 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 1.68924e9i | − | 1.88585i | −0.333008 | − | 0.942924i | \(-0.608064\pi\) | ||
0.333008 | − | 0.942924i | \(-0.391936\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.32568e8 | − | 3.65726e8i | −0.354591 | − | 0.389946i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 7.98123e8 | 0.777424 | 0.388712 | − | 0.921359i | \(-0.372920\pi\) | ||||
0.388712 | + | 0.921359i | \(0.372920\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.63968e8i | 0.804977i | 0.915425 | + | 0.402489i | \(0.131855\pi\) | ||||
−0.915425 | + | 0.402489i | \(0.868145\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 1.41804e9i | − | 1.21060i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 3.25702e8i | − | 0.266351i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.85383e8 | 0.665270 | 0.332635 | − | 0.943056i | \(-0.392062\pi\) | ||||
0.332635 | + | 0.943056i | \(0.392062\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.84525e9 | 1.32992 | 0.664960 | − | 0.746879i | \(-0.268449\pi\) | ||||
0.664960 | + | 0.746879i | \(0.268449\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.23099e8 | −0.280916 | −0.140458 | − | 0.990087i | \(-0.544858\pi\) | ||||
−0.140458 | + | 0.990087i | \(0.544858\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.11852e8i | 0.326387i | 0.986594 | + | 0.163193i | \(0.0521794\pi\) | ||||
−0.986594 | + | 0.163193i | \(0.947821\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.14575e9 | + | 1.25999e9i | 0.674692 | + | 0.741962i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.60018e8 | −0.203849 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 1.09854e9i | − | 0.575744i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.28727e8 | 0.367650 | 0.183825 | − | 0.982959i | \(-0.441152\pi\) | ||||
0.183825 | + | 0.982959i | \(0.441152\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 3.80205e8i | − | 0.177936i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.14980e9 | − | 1.04555e9i | 0.518540 | − | 0.471527i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.77270e8 | −0.241997 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 2.96999e9i | − | 1.20098i | −0.799632 | − | 0.600490i | \(-0.794972\pi\) | ||
0.799632 | − | 0.600490i | \(-0.205028\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.60001e9i | 1.73243i | 0.499674 | + | 0.866213i | \(0.333453\pi\) | ||||
−0.499674 | + | 0.866213i | \(0.666547\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.13006e9i | 1.13818i | 0.822275 | + | 0.569090i | \(0.192704\pi\) | ||||
−0.822275 | + | 0.569090i | \(0.807296\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.12300e9 | −0.381026 | −0.190513 | − | 0.981685i | \(-0.561015\pi\) | ||||
−0.190513 | + | 0.981685i | \(0.561015\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.85095e9 | −1.26269 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.01010e9 | 1.84200 | 0.921002 | − | 0.389559i | \(-0.127373\pi\) | ||||
0.921002 | + | 0.389559i | \(0.127373\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 3.33451e9i | − | 0.988470i | −0.869328 | − | 0.494235i | \(-0.835448\pi\) | ||
0.869328 | − | 0.494235i | \(-0.164552\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.46666e9 | + | 2.34788e8i | 0.684612 | + | 0.0651645i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.94703e9 | −0.523100 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 6.31335e9i | − | 1.59061i | −0.606206 | − | 0.795307i | \(-0.707309\pi\) | ||
0.606206 | − | 0.795307i | \(-0.292691\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.12981e9 | −0.519827 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.72277e9i | 1.31182i | 0.754839 | + | 0.655910i | \(0.227715\pi\) | ||||
−0.754839 | + | 0.655910i | \(0.772285\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.32924e9 | − | 5.86058e9i | −1.18431 | − | 1.30239i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.52582e9 | −0.527935 | −0.263967 | − | 0.964532i | \(-0.585031\pi\) | ||||
−0.263967 | + | 0.964532i | \(0.585031\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.26241e9i | 0.864315i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.83838e9i | 0.351096i | 0.984471 | + | 0.175548i | \(0.0561698\pi\) | ||||
−0.984471 | + | 0.175548i | \(0.943830\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.32017e9i | 0.244768i | 0.992483 | + | 0.122384i | \(0.0390539\pi\) | ||||
−0.992483 | + | 0.122384i | \(0.960946\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.23228e9 | −0.215467 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.31304e9 | 0.732595 | 0.366298 | − | 0.930498i | \(-0.380625\pi\) | ||||
0.366298 | + | 0.930498i | \(0.380625\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.61995e9 | −1.06177 | −0.530884 | − | 0.847444i | \(-0.678140\pi\) | ||||
−0.530884 | + | 0.847444i | \(0.678140\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 4.71632e9i | − | 0.735288i | −0.929967 | − | 0.367644i | \(-0.880165\pi\) | ||
0.929967 | − | 0.367644i | \(-0.119835\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.48791e9 | + | 1.35301e9i | −0.219306 | + | 0.199422i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.01461e9 | 0.575509 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 6.03696e8i | − | 0.0819121i | −0.999161 | − | 0.0409561i | \(-0.986960\pi\) | ||
0.999161 | − | 0.0409561i | \(-0.0130404\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.33646e9 | −0.704637 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.77484e9i | 0.472296i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.42888e9 | − | 1.57134e9i | −0.174072 | − | 0.191428i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.07530e9 | −0.124260 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.43825e10i | 1.61913i | 0.587029 | + | 0.809566i | \(0.300297\pi\) | ||||
−0.587029 | + | 0.809566i | \(0.699703\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.44388e9i | 1.00951i | 0.863264 | + | 0.504753i | \(0.168416\pi\) | ||||
−0.863264 | + | 0.504753i | \(0.831584\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.60438e10i | 1.67159i | 0.549039 | + | 0.835797i | \(0.314994\pi\) | ||||
−0.549039 | + | 0.835797i | \(0.685006\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.74781e9 | −0.470171 | −0.235086 | − | 0.971975i | \(-0.575537\pi\) | ||||
−0.235086 | + | 0.971975i | \(0.575537\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.24542e9 | 0.409976 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9.98744e9 | −0.917580 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.18408e9i | 0.195765i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.59155e10 | + | 1.44725e10i | −1.35843 | + | 1.23527i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.46168e9 | 0.788236 | 0.394118 | − | 0.919060i | \(-0.371050\pi\) | ||||
0.394118 | + | 0.919060i | \(0.371050\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 1.25659e10i | − | 0.997734i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.10076e8 | 0.00853438 | 0.00426719 | − | 0.999991i | \(-0.498642\pi\) | ||||
0.00426719 | + | 0.999991i | \(0.498642\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 3.87415e9i | − | 0.286522i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.10768e10 | − | 8.29978e9i | 0.800271 | − | 0.599639i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.97560e9 | 0.136264 | 0.0681320 | − | 0.997676i | \(-0.478296\pi\) | ||||
0.0681320 | + | 0.997676i | \(0.478296\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.57684e10i | 1.73694i | 0.495741 | + | 0.868470i | \(0.334896\pi\) | ||||
−0.495741 | + | 0.868470i | \(0.665104\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.67150e10i | 1.07648i | 0.842790 | + | 0.538242i | \(0.180912\pi\) | ||||
−0.842790 | + | 0.538242i | \(0.819088\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.90548e9i | 0.434791i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.99902e10 | −1.80552 | −0.902759 | − | 0.430146i | \(-0.858462\pi\) | ||||
−0.902759 | + | 0.430146i | \(0.858462\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.67023e10 | −0.983441 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.93570e9 | 0.109060 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 6.86910e9i | − | 0.378648i | −0.981915 | − | 0.189324i | \(-0.939370\pi\) | ||
0.981915 | − | 0.189324i | \(-0.0606296\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.60189e10 | + | 1.76161e10i | 0.845546 | + | 0.929850i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.47622e10 | −1.79586 | −0.897929 | − | 0.440140i | \(-0.854929\pi\) | ||||
−0.897929 | + | 0.440140i | \(0.854929\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 7.52452e9i | − | 0.372489i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.56196e9 | 0.172636 | 0.0863181 | − | 0.996268i | \(-0.472490\pi\) | ||||
0.0863181 | + | 0.996268i | \(0.472490\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 2.68874e10i | − | 1.24955i | −0.780805 | − | 0.624774i | \(-0.785191\pi\) | ||
0.780805 | − | 0.624774i | \(-0.214809\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.56993e9 | − | 4.15560e9i | 0.208002 | − | 0.189143i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.38727e10 | −0.605845 | −0.302923 | − | 0.953015i | \(-0.597962\pi\) | ||||
−0.302923 | + | 0.953015i | \(0.597962\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.93633e10i | 0.828463i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.91731e10i | 0.787595i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 4.21587e10i | − | 1.69717i | −0.529061 | − | 0.848584i | \(-0.677456\pi\) | ||
0.529061 | − | 0.848584i | \(-0.322544\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.47182e10 | 0.955960 | 0.477980 | − | 0.878371i | \(-0.341369\pi\) | ||||
0.477980 | + | 0.878371i | \(0.341369\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.86648e9 | −0.260324 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.97468e10 | −0.719645 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 4.86302e10i | − | 1.73785i | −0.494941 | − | 0.868926i | \(-0.664810\pi\) | ||
0.494941 | − | 0.868926i | \(-0.335190\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.20550e10 | + | 2.00554e10i | −0.758064 | + | 0.689335i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.53942e9 | −0.254182 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 1.62633e10i | − | 0.527659i | −0.964569 | − | 0.263830i | \(-0.915014\pi\) | ||
0.964569 | − | 0.263830i | \(-0.0849856\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.58983e9 | −0.114274 | −0.0571368 | − | 0.998366i | \(-0.518197\pi\) | ||||
−0.0571368 | + | 0.998366i | \(0.518197\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.12034e10i | 0.343395i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.44409e9 | + | 4.04117e9i | −0.133682 | + | 0.121561i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.73438e10 | 1.37200 | 0.686000 | − | 0.727601i | \(-0.259365\pi\) | ||||
0.686000 | + | 0.727601i | \(0.259365\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.17783e10i | 0.619543i | 0.950811 | + | 0.309772i | \(0.100253\pi\) | ||||
−0.950811 | + | 0.309772i | \(0.899747\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.53092e10i | 1.79081i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.08680e10i | 0.292611i | 0.989239 | + | 0.146305i | \(0.0467382\pi\) | ||||
−0.989239 | + | 0.146305i | \(0.953262\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.16237e10 | 1.60005 | 0.800024 | − | 0.599968i | \(-0.204820\pi\) | ||||
0.800024 | + | 0.599968i | \(0.204820\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.25383e9 | 0.0574754 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.33484e10 | 1.06657 | 0.533283 | − | 0.845937i | \(-0.320958\pi\) | ||||
0.533283 | + | 0.845937i | \(0.320958\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.01340e9i | 0.121179i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −7.36532e9 | − | 8.09967e9i | −0.171849 | − | 0.188983i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.42235e10 | −0.326094 | −0.163047 | − | 0.986618i | \(-0.552132\pi\) | ||||
−0.163047 | + | 0.986618i | \(0.552132\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 3.44851e10i | − | 0.763532i | −0.924259 | − | 0.381766i | \(-0.875316\pi\) | ||
0.924259 | − | 0.381766i | \(-0.124684\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.18685e10 | 0.911095 | 0.455548 | − | 0.890211i | \(-0.349444\pi\) | ||||
0.455548 | + | 0.890211i | \(0.349444\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.41461e10i | 0.297420i | 0.988881 | + | 0.148710i | \(0.0475120\pi\) | ||||
−0.988881 | + | 0.148710i | \(0.952488\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.72249e10 | − | 5.19334e10i | −0.976067 | − | 1.07339i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.29451e9 | −0.105775 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.77872e10i | 0.742284i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 7.79025e10i | − | 1.47982i | −0.672705 | − | 0.739910i | \(-0.734868\pi\) | ||
0.672705 | − | 0.739910i | \(-0.265132\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.49988e10i | 0.653843i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.87596e10 | −0.519775 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.13869e10 | 1.44690 | 0.723450 | − | 0.690376i | \(-0.242555\pi\) | ||||
0.723450 | + | 0.690376i | \(0.242555\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.21353e10 | 0.208796 | 0.104398 | − | 0.994536i | \(-0.466708\pi\) | ||||
0.104398 | + | 0.994536i | \(0.466708\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 3.85976e10i | − | 0.653390i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.59520e10 | + | 2.85395e10i | 0.425349 | + | 0.467758i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.31179e10 | 1.01801 | 0.509003 | − | 0.860765i | \(-0.330014\pi\) | ||||
0.509003 | + | 0.860765i | \(0.330014\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 1.26002e11i | − | 1.96836i | −0.177160 | − | 0.984182i | \(-0.556691\pi\) | ||
0.177160 | − | 0.984182i | \(-0.443309\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.20557e10 | −0.185364 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 9.14104e10i | − | 1.36183i | −0.732360 | − | 0.680917i | \(-0.761581\pi\) | ||
0.732360 | − | 0.680917i | \(-0.238419\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.00003e9 | − | 7.27471e9i | 0.117330 | − | 0.106692i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7.06684e9 | −0.100461 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.36260e10i | 0.750608i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.69946e9i | 0.0502097i | 0.999685 | + | 0.0251048i | \(0.00799196\pi\) | ||||
−0.999685 | + | 0.0251048i | \(0.992008\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 9.10568e10i | − | 1.21704i | −0.793538 | − | 0.608521i | \(-0.791763\pi\) | ||
0.793538 | − | 0.608521i | \(-0.208237\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.52221e10 | −0.456639 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.83085e10 | 0.616880 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.88567e9 | 0.110099 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 9.98142e10i | − | 1.21836i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.26951e9 | − | 3.43492e10i | 0.0387372 | − | 0.406969i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.28845e9 | 0.0967575 | 0.0483787 | − | 0.998829i | \(-0.484595\pi\) | ||||
0.0483787 | + | 0.998829i | \(0.484595\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.57930e9i | 0.0972447i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.46698e10 | 0.722358 | 0.361179 | − | 0.932497i | \(-0.382374\pi\) | ||||
0.361179 | + | 0.932497i | \(0.382374\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 1.30183e11i | − | 1.41237i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.20557e10 | + | 7.92400e10i | 0.770492 | + | 0.847313i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.02550e11 | 1.06541 | 0.532705 | − | 0.846301i | \(-0.321175\pi\) | ||||
0.532705 | + | 0.846301i | \(0.321175\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.38392e9i | 0.0961030i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 1.46724e11i | − | 1.46038i | −0.683244 | − | 0.730191i | \(-0.739431\pi\) | ||
0.683244 | − | 0.730191i | \(-0.260569\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 3.27785e10i | − | 0.321659i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.15957e11 | −1.10623 | −0.553116 | − | 0.833104i | \(-0.686561\pi\) | ||||
−0.553116 | + | 0.833104i | \(0.686561\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.40905e11 | −1.32551 | −0.662753 | − | 0.748838i | \(-0.730612\pi\) | ||||
−0.662753 | + | 0.748838i | \(0.730612\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.32606e10 | 0.670192 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.35313e11i | 1.22078i | 0.792103 | + | 0.610388i | \(0.208986\pi\) | ||||
−0.792103 | + | 0.610388i | \(0.791014\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.11595e10 | + | 2.83345e10i | −0.273455 | + | 0.248663i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.93558e10 | 0.513794 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5.72362e10i | 0.482079i | 0.970515 | + | 0.241039i | \(0.0774883\pi\) | ||||
−0.970515 | + | 0.241039i | \(0.922512\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.18798e11 | −0.987071 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.06242e11i | 0.859167i | 0.903027 | + | 0.429584i | \(0.141340\pi\) | ||||
−0.903027 | + | 0.429584i | \(0.858660\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.77809e10 | − | 4.15479e10i | −0.301443 | − | 0.331498i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.89779e11 | 1.47415 | 0.737073 | − | 0.675813i | \(-0.236207\pi\) | ||||
0.737073 | + | 0.675813i | \(0.236207\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 9.88010e9i | − | 0.0757292i | −0.999283 | − | 0.0378646i | \(-0.987944\pi\) | ||
0.999283 | − | 0.0378646i | \(-0.0120556\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7.67370e10i | 0.572774i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.22612e10i | 0.311306i | 0.987812 | + | 0.155653i | \(0.0497481\pi\) | ||||
−0.987812 | + | 0.155653i | \(0.950252\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.50459e10 | 0.681975 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.42522e11 | 1.00935 | 0.504675 | − | 0.863310i | \(-0.331612\pi\) | ||||
0.504675 | + | 0.863310i | \(0.331612\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.43687e10 | 0.0991463 | 0.0495731 | − | 0.998770i | \(-0.484214\pi\) | ||||
0.0495731 | + | 0.998770i | \(0.484214\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 1.28847e11i | − | 0.877632i | −0.898577 | − | 0.438816i | \(-0.855398\pi\) | ||
0.898577 | − | 0.438816i | \(-0.144602\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 9.31483e9 | − | 8.47030e9i | 0.0618333 | − | 0.0562272i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.97771e10 | −0.195147 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.79529e11i | 1.14692i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.12007e10 | 0.386046 | 0.193023 | − | 0.981194i | \(-0.438171\pi\) | ||||
0.193023 | + | 0.981194i | \(0.438171\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 2.43348e9i | − | 0.0149669i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.08800e10 | − | 5.79484e9i | −0.369757 | − | 0.0351952i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.27354e10 | −0.253137 | −0.126569 | − | 0.991958i | \(-0.540396\pi\) | ||||
−0.126569 | + | 0.991958i | \(0.540396\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 3.10685e11i | − | 1.81751i | −0.417332 | − | 0.908754i | \(-0.637035\pi\) | ||
0.417332 | − | 0.908754i | \(-0.362965\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.02430e11i | 0.584532i | 0.956337 | + | 0.292266i | \(0.0944092\pi\) | ||||
−0.956337 | + | 0.292266i | \(0.905591\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.43124e10i | 0.418873i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.30695e11 | −1.26878 | −0.634389 | − | 0.773014i | \(-0.718748\pi\) | ||||
−0.634389 | + | 0.773014i | \(0.718748\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.57531e10 | 0.302903 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.41191e11 | 1.27885 | 0.639425 | − | 0.768853i | \(-0.279172\pi\) | ||||
0.639425 | + | 0.768853i | \(0.279172\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.04104e11i | 0.545333i | 0.962109 | + | 0.272666i | \(0.0879055\pi\) | ||||
−0.962109 | + | 0.272666i | \(0.912094\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.27429e11 | − | 1.40134e11i | −0.651599 | − | 0.716566i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.52395e11 | −1.27520 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.49740e10i | 0.0738666i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.69473e11 | −0.826116 | −0.413058 | − | 0.910705i | \(-0.635539\pi\) | ||||
−0.413058 | + | 0.910705i | \(0.635539\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.96573e11i | 0.935770i | 0.883789 | + | 0.467885i | \(0.154984\pi\) | ||||
−0.883789 | + | 0.467885i | \(0.845016\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.18860e11 | + | 1.08084e11i | −0.559186 | + | 0.508488i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.25604e11 | 1.03673 | 0.518363 | − | 0.855161i | \(-0.326542\pi\) | ||||
0.518363 | + | 0.855161i | \(0.326542\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 1.41913e11i | − | 0.644557i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 1.05201e11i | − | 0.466815i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 2.41724e11i | − | 1.06025i | −0.847920 | − | 0.530125i | \(-0.822145\pi\) | ||
0.847920 | − | 0.530125i | \(-0.177855\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −8.79971e10 | −0.377163 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.55797e10 | 0.193126 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.33717e11 | −0.967875 | −0.483937 | − | 0.875103i | \(-0.660794\pi\) | ||||
−0.483937 | + | 0.875103i | \(0.660794\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.05521e11i | 2.47918i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.98247e10 | + | 4.53074e10i | −0.199419 | + | 0.181339i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.42622e9 | 0.0254314 | 0.0127157 | − | 0.999919i | \(-0.495952\pi\) | ||||
0.0127157 | + | 0.999919i | \(0.495952\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.30322e11i | 0.891205i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.72912e10 | −0.104423 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.71193e11i | 1.01476i | 0.861722 | + | 0.507380i | \(0.169386\pi\) | ||||
−0.861722 | + | 0.507380i | \(0.830614\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.92064e10 | + | 2.65584e10i | −0.108078 | + | 0.0982792i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.46033e11 | −0.528565 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 3.67678e11i | − | 1.31622i | −0.752920 | − | 0.658111i | \(-0.771356\pi\) | ||
0.752920 | − | 0.658111i | \(-0.228644\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.81355e10i | 0.168576i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.48520e11i | 1.90010i | 0.312099 | + | 0.950050i | \(0.398968\pi\) | ||||
−0.312099 | + | 0.950050i | \(0.601032\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.74985e11 | −0.593106 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.70662e10 | 0.0907504 | 0.0453752 | − | 0.998970i | \(-0.485552\pi\) | ||||
0.0453752 | + | 0.998970i | \(0.485552\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5.45102e11 | −1.78864 | −0.894319 | − | 0.447429i | \(-0.852340\pi\) | ||||
−0.894319 | + | 0.447429i | \(0.852340\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 6.99438e10i | − | 0.227051i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.75119e11 | − | 4.12520e11i | −1.19191 | − | 1.31074i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.15475e11 | −0.677388 | −0.338694 | − | 0.940897i | \(-0.609985\pi\) | ||||
−0.338694 | + | 0.940897i | \(0.609985\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7.35508e10i | 0.226360i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.21637e11 | 0.674930 | 0.337465 | − | 0.941338i | \(-0.390431\pi\) | ||||
0.337465 | + | 0.941338i | \(0.390431\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.70134e11i | 1.10362i | 0.833970 | + | 0.551810i | \(0.186063\pi\) | ||||
−0.833970 | + | 0.551810i | \(0.813937\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.22425e10 | + | 3.54572e10i | 0.0951329 | + | 0.104618i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.31710e11 | 0.380573 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.51630e11i | 0.719543i | 0.933040 | + | 0.359772i | \(0.117145\pi\) | ||||
−0.933040 | + | 0.359772i | \(0.882855\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 8.76043e10i | − | 0.245362i | −0.992446 | − | 0.122681i | \(-0.960851\pi\) | ||
0.992446 | − | 0.122681i | \(-0.0391492\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.33262e11i | 0.369402i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.53733e11 | 0.417461 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.61615e10 | 0.258462 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.02474e11 | −0.269857 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.92202e11i | 1.28305i | 0.767101 | + | 0.641526i | \(0.221698\pi\) | ||||
−0.767101 | + | 0.641526i | \(0.778302\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.23187e11 | − | 1.35470e11i | −0.314673 | − | 0.346048i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.65397e10 | 0.0671125 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 7.26288e11i | 1.80001i | 0.435877 | + | 0.900006i | \(0.356438\pi\) | ||||
−0.435877 | + | 0.900006i | \(0.643562\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.87545e11 | 1.19627 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 2.69554e10i | − | 0.0648312i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.71687e11 | + | 2.47055e11i | −0.646972 | + | 0.588315i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.13737e11 | −0.732439 | −0.366219 | − | 0.930529i | \(-0.619348\pi\) | ||||
−0.366219 | + | 0.930529i | \(0.619348\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 5.18509e11i | − | 1.19860i | −0.800526 | − | 0.599298i | \(-0.795447\pi\) | ||
0.800526 | − | 0.599298i | \(-0.204553\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 4.52674e11i | − | 1.02602i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.62353e11i | 0.364394i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.87453e11 | −1.29300 | −0.646502 | − | 0.762912i | \(-0.723769\pi\) | ||||
−0.646502 | + | 0.762912i | \(0.723769\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.98317e11 | 1.30416 | 0.652082 | − | 0.758149i | \(-0.273896\pi\) | ||||
0.652082 | + | 0.758149i | \(0.273896\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5.41942e11 | 1.15859 | 0.579296 | − | 0.815117i | \(-0.303328\pi\) | ||||
0.579296 | + | 0.815117i | \(0.303328\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 3.02398e11i | − | 0.640266i | −0.947373 | − | 0.320133i | \(-0.896272\pi\) | ||
0.947373 | − | 0.320133i | \(-0.103728\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.12288e11 | − | 2.97250e10i | −0.648598 | − | 0.0617366i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.54298e11 | −0.934533 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.67906e11i | 0.338859i | 0.985542 | + | 0.169430i | \(0.0541925\pi\) | ||||
−0.985542 | + | 0.169430i | \(0.945807\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.86008e9 | 0.00571734 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 3.02244e11i | − | 0.592831i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.88391e11 | + | 3.17145e11i | 0.560335 | + | 0.616203i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.17397e12 | 2.23840 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.12501e10i | 0.0212501i | 0.999944 | + | 0.0106250i | \(0.00338212\pi\) | ||||
−0.999944 | + | 0.0106250i | \(0.996618\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 2.60609e11i | − | 0.483132i | −0.970384 | − | 0.241566i | \(-0.922339\pi\) | ||
0.970384 | − | 0.241566i | \(-0.0776611\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 5.95207e11i | − | 1.09319i | −0.837397 | − | 0.546595i | \(-0.815924\pi\) | ||
0.837397 | − | 0.546595i | \(-0.184076\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −7.81026e11 | −1.40806 | −0.704032 | − | 0.710168i | \(-0.748619\pi\) | ||||
−0.704032 | + | 0.710168i | \(0.748619\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.26063e11 | −1.29691 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.66993e11 | 0.468188 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.10141e11i | 0.538874i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.55444e11 | + | 4.14151e11i | −0.776967 | + | 0.706524i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −8.87976e11 | −1.50108 | −0.750539 | − | 0.660827i | \(-0.770206\pi\) | ||||
−0.750539 | + | 0.660827i | \(0.770206\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.50548e11i | 1.24588i | 0.782271 | + | 0.622938i | \(0.214061\pi\) | ||||
−0.782271 | + | 0.622938i | \(0.785939\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.39811e11 | −0.723474 | −0.361737 | − | 0.932280i | \(-0.617816\pi\) | ||||
−0.361737 | + | 0.932280i | \(0.617816\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 2.20334e11i | − | 0.355948i | −0.984035 | − | 0.177974i | \(-0.943046\pi\) | ||
0.984035 | − | 0.177974i | \(-0.0569543\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.14543e9 | − | 1.00573e10i | −0.0146419 | − | 0.0161017i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.64440e12 | 2.58585 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 3.43046e11i | − | 0.534639i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 4.59109e11i | − | 0.702873i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 5.39638e11i | − | 0.818848i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.71348e11 | 0.553588 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.62985e11 | 0.831894 | 0.415947 | − | 0.909389i | \(-0.363450\pi\) | ||||
0.415947 | + | 0.909389i | \(0.363450\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.03509e12 | 1.50281 | 0.751405 | − | 0.659841i | \(-0.229377\pi\) | ||||
0.751405 | + | 0.659841i | \(0.229377\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.04989e11i | 0.151099i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.30421e11 | − | 2.09530e11i | 0.325870 | − | 0.296325i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.60972e11 | 1.20706 | 0.603528 | − | 0.797342i | \(-0.293761\pi\) | ||||
0.603528 | + | 0.797342i | \(0.293761\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 1.70435e11i | − | 0.234829i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.79243e11 | 0.927808 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5.60419e11i | 0.752403i | 0.926538 | + | 0.376201i | \(0.122770\pi\) | ||||
−0.926538 | + | 0.376201i | \(0.877230\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.05329e12 | − | 1.00257e11i | −1.40201 | − | 0.133450i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.39992e11 | −0.183171 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 1.18541e12i | − | 1.53783i | −0.639349 | − | 0.768916i | \(-0.720796\pi\) | ||
0.639349 | − | 0.768916i | \(-0.279204\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.11841e12i | 1.42641i | 0.700956 | + | 0.713204i | \(0.252757\pi\) | ||||
−0.700956 | + | 0.713204i | \(0.747243\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 2.98052e11i | − | 0.376916i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −8.43072e11 | −1.04825 | −0.524125 | − | 0.851641i | \(-0.675607\pi\) | ||||
−0.524125 | + | 0.851641i | \(0.675607\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.77754e10 | −0.0589033 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.08227e11 | −0.131209 | −0.0656047 | − | 0.997846i | \(-0.520898\pi\) | ||||
−0.0656047 | + | 0.997846i | \(0.520898\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 3.80552e11i | − | 0.457510i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.33335e11 | − | 5.86511e11i | −0.630559 | − | 0.693429i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.33933e11 | 0.508779 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 7.93118e11i | − | 0.914594i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.22545e12 | −1.40149 | −0.700746 | − | 0.713410i | \(-0.747150\pi\) | ||||
−0.700746 | + | 0.713410i | \(0.747150\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 8.37376e10i | − | 0.0941984i | −0.998890 | − | 0.0470992i | \(-0.985002\pi\) | ||
0.998890 | − | 0.0470992i | \(-0.0149977\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.63681e11 | + | 3.30708e11i | −0.405761 | + | 0.368972i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.20619e12 | 1.32385 | 0.661923 | − | 0.749572i | \(-0.269740\pi\) | ||||
0.661923 | + | 0.749572i | \(0.269740\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 3.13855e10i | − | 0.0341664i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 1.48704e12i | − | 1.59260i | −0.604900 | − | 0.796301i | \(-0.706787\pi\) | ||
0.604900 | − | 0.796301i | \(-0.293213\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.81855e11i | 0.193188i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.14764e11 | 0.329003 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.38578e12 | 1.43682 | 0.718408 | − | 0.695622i | \(-0.244871\pi\) | ||||
0.718408 | + | 0.695622i | \(0.244871\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.20002e11 | 0.224458 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 7.07167e11i | − | 0.715717i | −0.933776 | − | 0.357859i | \(-0.883507\pi\) | ||
0.933776 | − | 0.357859i | \(-0.116493\pi\) | |||||||
\(998\) | 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.d.d.181.3 | 10 | ||
3.2 | odd | 2 | 84.9.d.a.13.4 | ✓ | 10 | ||
7.6 | odd | 2 | inner | 252.9.d.d.181.8 | 10 | ||
12.11 | even | 2 | 336.9.f.a.97.9 | 10 | |||
21.20 | even | 2 | 84.9.d.a.13.7 | yes | 10 | ||
84.83 | odd | 2 | 336.9.f.a.97.2 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.9.d.a.13.4 | ✓ | 10 | 3.2 | odd | 2 | ||
84.9.d.a.13.7 | yes | 10 | 21.20 | even | 2 | ||
252.9.d.d.181.3 | 10 | 1.1 | even | 1 | trivial | ||
252.9.d.d.181.8 | 10 | 7.6 | odd | 2 | inner | ||
336.9.f.a.97.2 | 10 | 84.83 | odd | 2 | |||
336.9.f.a.97.9 | 10 | 12.11 | even | 2 |