Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,9,Mod(197,252)]
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, 1, 0]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.197");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.c (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: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 4002260 x^{14} + 6534459751956 x^{12} + \cdots + 19\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 2^{32}\cdot 3^{37}\cdot 7^{12} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 197.3 | ||
Root | \(-899.394i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 252.197 |
Dual form | 252.9.c.a.197.14 |
$q$-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 | ||||||||
\(5\) | − 899.394i | − 1.43903i | −0.694477 | − | 0.719515i | \(-0.744364\pi\) | ||||
0.694477 | − | 0.719515i | \(-0.255636\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 907.493 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 21934.5i | 1.49816i | 0.662481 | + | 0.749079i | \(0.269504\pi\) | ||||
−0.662481 | + | 0.749079i | \(0.730496\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 20852.6 | 0.730108 | 0.365054 | − | 0.930986i | \(-0.381051\pi\) | ||||
0.365054 | + | 0.930986i | \(0.381051\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 54914.5i | 0.657493i | 0.944418 | + | 0.328747i | \(0.106626\pi\) | ||||
−0.944418 | + | 0.328747i | \(0.893374\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −112287. | −0.861620 | −0.430810 | − | 0.902443i | \(-0.641772\pi\) | ||||
−0.430810 | + | 0.902443i | \(0.641772\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 364864.i | − 1.30383i | −0.758294 | − | 0.651913i | \(-0.773967\pi\) | ||||
0.758294 | − | 0.651913i | \(-0.226033\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −418285. | −1.07081 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 493187.i | − 0.697299i | −0.937253 | − | 0.348650i | \(-0.886640\pi\) | ||||
0.937253 | − | 0.348650i | \(-0.113360\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −947146. | −1.02558 | −0.512791 | − | 0.858514i | \(-0.671388\pi\) | ||||
−0.512791 | + | 0.858514i | \(0.671388\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 816194.i | − 0.543902i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.31637e6 | −1.23595 | −0.617976 | − | 0.786197i | \(-0.712047\pi\) | ||||
−0.617976 | + | 0.786197i | \(0.712047\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 336127.i | 0.118951i | 0.998230 | + | 0.0594755i | \(0.0189428\pi\) | ||||
−0.998230 | + | 0.0594755i | \(0.981057\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −164303. | −0.0480587 | −0.0240294 | − | 0.999711i | \(-0.507650\pi\) | ||||
−0.0240294 | + | 0.999711i | \(0.507650\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 1.21616e6i | − 0.249229i | −0.992205 | − | 0.124614i | \(-0.960231\pi\) | ||||
0.992205 | − | 0.124614i | \(-0.0397694\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 823543. | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.50757e6i | 0.317797i | 0.987295 | + | 0.158898i | \(0.0507943\pi\) | ||||
−0.987295 | + | 0.158898i | \(0.949206\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.97278e7 | 2.15589 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.27740e7i | 1.05419i | 0.849807 | + | 0.527094i | \(0.176718\pi\) | ||||
−0.849807 | + | 0.527094i | \(0.823282\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.01258e7 | −0.731323 | −0.365661 | − | 0.930748i | \(-0.619157\pi\) | ||||
−0.365661 | + | 0.930748i | \(0.619157\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − 1.87547e7i | − 1.05065i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.53739e6 | 0.374043 | 0.187022 | − | 0.982356i | \(-0.440117\pi\) | ||||
0.187022 | + | 0.982356i | \(0.440117\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.21448e7i | 1.65848i | 0.558892 | + | 0.829240i | \(0.311226\pi\) | ||||
−0.558892 | + | 0.829240i | \(0.688774\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.47745e7 | −1.22453 | −0.612266 | − | 0.790652i | \(-0.709742\pi\) | ||||
−0.612266 | + | 0.790652i | \(0.709742\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.99054e7i | 0.566250i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.95932e6 | 0.0503033 | 0.0251517 | − | 0.999684i | \(-0.491993\pi\) | ||||
0.0251517 | + | 0.999684i | \(0.491993\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.01258e7i | 0.424073i | 0.977262 | + | 0.212037i | \(0.0680096\pi\) | ||||
−0.977262 | + | 0.212037i | \(0.931990\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.93898e7 | 0.946153 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 1.15659e7i | − 0.184341i | −0.995743 | − | 0.0921703i | \(-0.970620\pi\) | ||||
0.995743 | − | 0.0921703i | \(-0.0293804\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.89236e7 | 0.275955 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.00990e8i | 1.23990i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.91217e7 | −1.11965 | −0.559825 | − | 0.828611i | \(-0.689131\pi\) | ||||
−0.559825 | + | 0.828611i | \(0.689131\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 1.13987e8i | − 1.09539i | −0.836679 | − | 0.547694i | \(-0.815506\pi\) | ||||
0.836679 | − | 0.547694i | \(-0.184494\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.40209e8 | −1.24574 | −0.622868 | − | 0.782327i | \(-0.714033\pi\) | ||||
−0.622868 | + | 0.782327i | \(0.714033\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 8.47465e7i | − 0.646527i | −0.946309 | − | 0.323263i | \(-0.895220\pi\) | ||||
0.946309 | − | 0.323263i | \(-0.104780\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.16339e7 | −0.436630 | −0.218315 | − | 0.975878i | \(-0.570056\pi\) | ||||
−0.218315 | + | 0.975878i | \(0.570056\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.48925e8i | 0.913382i | 0.889625 | + | 0.456691i | \(0.150966\pi\) | ||||
−0.889625 | + | 0.456691i | \(0.849034\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.28157e8 | −1.87625 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.98345e7i | 0.248509i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.66765e8 | −1.24448 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.48770e7i | 0.101896i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.37067e8 | 1.68009 | 0.840046 | − | 0.542515i | \(-0.182528\pi\) | ||||
0.840046 | + | 0.542515i | \(0.182528\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.99853e8i | 1.35774i | 0.734261 | + | 0.678868i | \(0.237529\pi\) | ||||
−0.734261 | + | 0.678868i | \(0.762471\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.01900e8 | −0.325662 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.51026e8i | 1.28032i | 0.768240 | + | 0.640161i | \(0.221133\pi\) | ||||
−0.768240 | + | 0.640161i | \(0.778867\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.59839e7 | −0.176758 | −0.0883789 | − | 0.996087i | \(-0.528169\pi\) | ||||
−0.0883789 | + | 0.996087i | \(0.528169\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.57392e8i | 1.09382i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.43569e8 | −1.00344 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.48851e8i | 1.51932i | 0.650319 | + | 0.759662i | \(0.274635\pi\) | ||||
−0.650319 | + | 0.759662i | \(0.725365\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.69152e8 | 1.67181 | 0.835907 | − | 0.548871i | \(-0.184942\pi\) | ||||
0.835907 | + | 0.548871i | \(0.184942\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.51858e8i | 1.47584i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.43252e8 | 0.564956 | 0.282478 | − | 0.959274i | \(-0.408844\pi\) | ||||
0.282478 | + | 0.959274i | \(0.408844\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 3.31112e8i | − 0.492800i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.03494e9 | −1.46610 | −0.733052 | − | 0.680173i | \(-0.761905\pi\) | ||||
−0.733052 | + | 0.680173i | \(0.761905\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.55929e8i | 1.10045i | 0.835015 | + | 0.550227i | \(0.185459\pi\) | ||||
−0.835015 | + | 0.550227i | \(0.814541\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.80900e8 | −0.466943 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 1.21109e9i | − 1.35204i | −0.736882 | − | 0.676021i | \(-0.763703\pi\) | ||||
0.736882 | − | 0.676021i | \(-0.236297\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.79590e8 | −0.404728 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.65570e8i | 0.161276i | 0.996743 | + | 0.0806381i | \(0.0256958\pi\) | ||||
−0.996743 | + | 0.0806381i | \(0.974304\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.87197e9 | −1.74416 | −0.872078 | − | 0.489367i | \(-0.837228\pi\) | ||||
−0.872078 | + | 0.489367i | \(0.837228\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.08333e9i | 1.77857i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.20452e9 | −0.985029 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 5.54193e8i | − 0.416416i | −0.978085 | − | 0.208208i | \(-0.933237\pi\) | ||||
0.978085 | − | 0.208208i | \(-0.0667631\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.65475e9 | −1.91335 | −0.956677 | − | 0.291152i | \(-0.905961\pi\) | ||||
−0.956677 | + | 0.291152i | \(0.905961\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.36750e9i | 1.57190i | 0.618292 | + | 0.785949i | \(0.287825\pi\) | ||||
−0.618292 | + | 0.785949i | \(0.712175\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.24978e9 | 1.43459 | 0.717294 | − | 0.696771i | \(-0.245380\pi\) | ||||
0.717294 | + | 0.696771i | \(0.245380\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 4.47563e8i | − 0.263554i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.02311e8 | 0.171174 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 2.46297e9i | − 1.29084i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.61666e9 | 0.815624 | 0.407812 | − | 0.913066i | \(-0.366292\pi\) | ||||
0.407812 | + | 0.913066i | \(0.366292\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.47773e8i | 0.0691580i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.59528e8 | −0.387633 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.14511e9i | 0.480041i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.03660e9 | −1.63229 | −0.816143 | − | 0.577850i | \(-0.803892\pi\) | ||||
−0.816143 | + | 0.577850i | \(0.803892\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.28153e8i | 0.311894i | 0.987765 | + | 0.155947i | \(0.0498429\pi\) | ||||
−0.987765 | + | 0.155947i | \(0.950157\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.05916e9 | −0.748770 | −0.374385 | − | 0.927273i | \(-0.622146\pi\) | ||||
−0.374385 | + | 0.927273i | \(0.622146\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.06700e9i | 1.04062i | 0.853979 | + | 0.520308i | \(0.174183\pi\) | ||||
−0.853979 | + | 0.520308i | \(0.825817\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.09380e9 | −0.358648 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.90569e9i | 1.19703i | 0.801111 | + | 0.598516i | \(0.204243\pi\) | ||||
−0.801111 | + | 0.598516i | \(0.795757\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.96315e9 | 1.76769 | 0.883847 | − | 0.467775i | \(-0.154944\pi\) | ||||
0.883847 | + | 0.467775i | \(0.154944\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 7.40690e8i | − 0.205576i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.34148e9 | −0.629075 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 2.52021e9i | − 0.634954i | −0.948266 | − | 0.317477i | \(-0.897164\pi\) | ||||
0.948266 | − | 0.317477i | \(-0.102836\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.00312e9 | 1.95334 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 2.17920e8i | − 0.0499533i | −0.999688 | − | 0.0249766i | \(-0.992049\pi\) | ||||
0.999688 | − | 0.0249766i | \(-0.00795114\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.10209e9 | −0.467146 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 3.78536e9i | − 0.791196i | −0.918424 | − | 0.395598i | \(-0.870537\pi\) | ||||
0.918424 | − | 0.395598i | \(-0.129463\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.25529e9 | 0.457320 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.04980e9i | 1.34638i | 0.739469 | + | 0.673190i | \(0.235077\pi\) | ||||
−0.739469 | + | 0.673190i | \(0.764923\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.60874e8 | −0.0298270 | −0.0149135 | − | 0.999889i | \(-0.504747\pi\) | ||||
−0.0149135 | + | 0.999889i | \(0.504747\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 9.17488e9i | − 1.60424i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.44864e9 | 1.60491 | 0.802454 | − | 0.596714i | \(-0.203527\pi\) | ||||
0.802454 | + | 0.596714i | \(0.203527\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 5.14862e9i | − 0.825783i | −0.910780 | − | 0.412891i | \(-0.864519\pi\) | ||||
0.910780 | − | 0.412891i | \(-0.135481\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.72901e9 | −0.737266 | −0.368633 | − | 0.929575i | \(-0.620174\pi\) | ||||
−0.368633 | + | 0.929575i | \(0.620174\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.05033e8i | 0.0449592i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.96016e9 | 0.567703 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 1.31304e9i | − 0.178158i | −0.996025 | − | 0.0890791i | \(-0.971608\pi\) | ||||
0.996025 | − | 0.0890791i | \(-0.0283924\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.14888e10 | 1.51701 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 7.60837e9i | − 0.951934i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.49104e8 | −0.0181645 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 9.10707e9i | 1.05240i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.29371e9 | −0.258217 | −0.129108 | − | 0.991630i | \(-0.541212\pi\) | ||||
−0.129108 | + | 0.991630i | \(0.541212\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 1.29318e10i | − 1.38235i | −0.722687 | − | 0.691176i | \(-0.757093\pi\) | ||||
0.722687 | − | 0.691176i | \(-0.242907\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.63693e10 | −1.70550 | −0.852751 | − | 0.522317i | \(-0.825068\pi\) | ||||
−0.852751 | + | 0.522317i | \(0.825068\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 1.30871e10i | − 1.29601i | −0.761637 | − | 0.648004i | \(-0.775604\pi\) | ||||
0.761637 | − | 0.648004i | \(-0.224396\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.08178e10 | 1.04466 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 6.16619e9i | − 0.566509i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −8.72233e9 | −0.781806 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − 1.10365e9i | − 0.0941996i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.33867e10 | −1.11522 | −0.557611 | − | 0.830102i | \(-0.688282\pi\) | ||||
−0.557611 | + | 0.830102i | \(0.688282\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 6.77908e9i | − 0.538260i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.92070e9 | −0.536575 | −0.268288 | − | 0.963339i | \(-0.586458\pi\) | ||||
−0.268288 | + | 0.963339i | \(0.586458\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 2.07752e10i | − 1.53648i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.47359e8 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 5.48176e9i | − 0.378096i | −0.981968 | − | 0.189048i | \(-0.939460\pi\) | ||||
0.981968 | − | 0.189048i | \(-0.0605402\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.62728e10 | 1.09689 | 0.548443 | − | 0.836188i | \(-0.315221\pi\) | ||||
0.548443 | + | 0.836188i | \(0.315221\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 2.57447e10i | − 1.65802i | −0.559237 | − | 0.829008i | \(-0.688906\pi\) | ||||
0.559237 | − | 0.829008i | \(-0.311094\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.79048e10 | 2.38660 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.68498e9i | 0.342256i | 0.985249 | + | 0.171128i | \(0.0547412\pi\) | ||||
−0.985249 | + | 0.171128i | \(0.945259\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.37515e9 | −0.257611 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.12760e10i | 1.76214i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.12442e10 | 0.619820 | 0.309910 | − | 0.950766i | \(-0.399701\pi\) | ||||
0.309910 | + | 0.950766i | \(0.399701\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.27560e9i | 0.120116i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.82711e10 | 0.943910 | 0.471955 | − | 0.881623i | \(-0.343549\pi\) | ||||
0.471955 | + | 0.881623i | \(0.343549\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 1.02842e10i | − 0.509104i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.30958e10 | 1.11938 | 0.559689 | − | 0.828703i | \(-0.310921\pi\) | ||||
0.559689 | + | 0.828703i | \(0.310921\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.12755e10i | 0.988745i | 0.869250 | + | 0.494372i | \(0.164602\pi\) | ||||
−0.869250 | + | 0.494372i | \(0.835398\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.79028e10 | 0.814852 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 3.68614e9i | − 0.160981i | −0.996755 | − | 0.0804903i | \(-0.974351\pi\) | ||||
0.996755 | − | 0.0804903i | \(-0.0256486\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.00363e10 | 0.857257 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 1.76220e9i | − 0.0723880i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.57692e9 | 0.103738 | 0.0518692 | − | 0.998654i | \(-0.483482\pi\) | ||||
0.0518692 | + | 0.998654i | \(0.483482\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.27654e10i | 0.493693i | 0.969055 | + | 0.246847i | \(0.0793944\pi\) | ||||
−0.969055 | + | 0.246847i | \(0.920606\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.97505e10 | −0.748785 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 5.08085e10i | − 1.85165i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.66538e10 | −0.595142 | −0.297571 | − | 0.954700i | \(-0.596177\pi\) | ||||
−0.297571 | + | 0.954700i | \(0.596177\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.15923e10i | 0.398446i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.81010e10 | 0.610254 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.06318e10i | 0.669391i | 0.942326 | + | 0.334696i | \(0.108633\pi\) | ||||
−0.942326 | + | 0.334696i | \(0.891367\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.94606e10 | −1.89278 | −0.946391 | − | 0.323023i | \(-0.895301\pi\) | ||||
−0.946391 | + | 0.323023i | \(0.895301\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 2.29699e10i | − 0.704050i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9.18907e9 | −0.276414 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 3.73736e10i | − 1.08307i | −0.840679 | − | 0.541534i | \(-0.817844\pi\) | ||||
0.840679 | − | 0.541534i | \(-0.182156\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.44971e10 | −0.981365 | −0.490683 | − | 0.871338i | \(-0.663253\pi\) | ||||
−0.490683 | + | 0.871338i | \(0.663253\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.09696e10i | 1.12340i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.40944e10 | 1.45644 | 0.728222 | − | 0.685341i | \(-0.240347\pi\) | ||||
0.728222 | + | 0.685341i | \(0.240347\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.18604e10i | 0.827249i | 0.910448 | + | 0.413625i | \(0.135737\pi\) | ||||
−0.910448 | + | 0.413625i | \(0.864263\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.04023e10 | −0.265272 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 5.50863e10i | − 1.35537i | −0.735352 | − | 0.677686i | \(-0.762983\pi\) | ||||
0.735352 | − | 0.677686i | \(-0.237017\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.37279e9 | −0.178207 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 1.70198e10i | − 0.397107i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.41618e10 | −1.01247 | −0.506234 | − | 0.862396i | \(-0.668963\pi\) | ||||
−0.506234 | + | 0.862396i | \(0.668963\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.85244e10i | 1.73861i | 0.494280 | + | 0.869303i | \(0.335432\pi\) | ||||
−0.494280 | + | 0.869303i | \(0.664568\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.61686e10 | −1.65750 | −0.828748 | − | 0.559623i | \(-0.810946\pi\) | ||||
−0.828748 | + | 0.559623i | \(0.810946\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.86924e10i | 0.813502i | 0.913539 | + | 0.406751i | \(0.133338\pi\) | ||||
−0.913539 | + | 0.406751i | \(0.866662\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.84013e9 | 0.141375 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 3.60391e9i | − 0.0719996i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.69680e10 | 0.922630 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.21577e9i | 0.0610862i | 0.999533 | + | 0.0305431i | \(0.00972368\pi\) | ||||
−0.999533 | + | 0.0305431i | \(0.990276\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.83024e10 | −0.902378 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.91495e10i | 1.61121i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.36460e10 | −1.13150 | −0.565751 | − | 0.824576i | \(-0.691414\pi\) | ||||
−0.565751 | + | 0.824576i | \(0.691414\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 7.53919e10i | − 1.29717i | −0.761140 | − | 0.648587i | \(-0.775360\pi\) | ||||
0.761140 | − | 0.648587i | \(-0.224640\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.70831e10 | 0.458470 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.82461e10i | 0.626847i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.00879e10 | 0.969136 | 0.484568 | − | 0.874754i | \(-0.338977\pi\) | ||||
0.484568 | + | 0.874754i | \(0.338977\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 7.02391e10i | − 1.09725i | −0.836068 | − | 0.548626i | \(-0.815151\pi\) | ||||
0.836068 | − | 0.548626i | \(-0.184849\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.02519e11 | −1.57630 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7.49035e10i | 1.11591i | 0.829870 | + | 0.557957i | \(0.188415\pi\) | ||||
−0.829870 | + | 0.557957i | \(0.811585\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.15576e10 | −0.462829 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.26103e11i | 1.79265i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.66758e10 | 0.373384 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.53205e10i | 1.15798i | 0.815333 | + | 0.578992i | \(0.196554\pi\) | ||||
−0.815333 | + | 0.578992i | \(0.803446\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.90127e10 | 0.922407 | 0.461203 | − | 0.887294i | \(-0.347418\pi\) | ||||
0.461203 | + | 0.887294i | \(0.347418\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 5.20120e10i | − 0.674313i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.48148e10 | −0.699963 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.00912e9i | 0.0868470i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.62205e10 | −0.930372 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.80640e10i | 0.214023i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.81530e10 | 0.328652 | 0.164326 | − | 0.986406i | \(-0.447455\pi\) | ||||
0.164326 | + | 0.986406i | \(0.447455\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.54332e10i | 0.628324i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.27027e10 | −0.141888 | −0.0709440 | − | 0.997480i | \(-0.522601\pi\) | ||||
−0.0709440 | + | 0.997480i | \(0.522601\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.53785e10i | 0.600807i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.77807e9 | 0.0190129 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9.93534e10i | 1.03220i | 0.856530 | + | 0.516098i | \(0.172616\pi\) | ||||
−0.856530 | + | 0.516098i | \(0.827384\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.42615e9 | −0.0350881 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 1.28318e11i | − 1.27719i | −0.769544 | − | 0.638594i | \(-0.779516\pi\) | ||||
0.769544 | − | 0.638594i | \(-0.220484\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.33942e11 | 1.31438 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9.69562e10i | 0.924968i | 0.886628 | + | 0.462484i | \(0.153042\pi\) | ||||
−0.886628 | + | 0.462484i | \(0.846958\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.85788e10 | 0.456985 | 0.228493 | − | 0.973546i | \(-0.426620\pi\) | ||||
0.228493 | + | 0.973546i | \(0.426620\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.52617e11i | 1.39615i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.00425e11 | −0.906024 | −0.453012 | − | 0.891504i | \(-0.649650\pi\) | ||||
−0.453012 | + | 0.891504i | \(0.649650\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.82640e10i | 0.160285i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.50024e10 | −0.476110 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5.94122e10i | 0.500407i | 0.968193 | + | 0.250203i | \(0.0804975\pi\) | ||||
−0.968193 | + | 0.250203i | \(0.919502\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.06352e11 | 0.883662 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 1.44264e11i | − 1.16665i | −0.812240 | − | 0.583324i | \(-0.801752\pi\) | ||||
0.812240 | − | 0.583324i | \(-0.198248\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.48209e10 | 0.357612 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 4.20875e10i | − 0.326923i | −0.986550 | − | 0.163462i | \(-0.947734\pi\) | ||||
0.986550 | − | 0.163462i | \(-0.0522660\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.91047e10 | −0.682972 | −0.341486 | − | 0.939887i | \(-0.610930\pi\) | ||||
−0.341486 | + | 0.939887i | \(0.610930\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.39927e11i | 1.79084i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.58228e10 | −0.190217 | −0.0951083 | − | 0.995467i | \(-0.530320\pi\) | ||||
−0.0951083 | + | 0.995467i | \(0.530320\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 2.53600e10i | − 0.181964i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.19898e11 | −1.55733 | −0.778663 | − | 0.627442i | \(-0.784102\pi\) | ||||
−0.778663 | + | 0.627442i | \(0.784102\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.21752e10i | 0.429019i | 0.976722 | + | 0.214510i | \(0.0688153\pi\) | ||||
−0.976722 | + | 0.214510i | \(0.931185\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.05984e11 | −1.40304 | −0.701521 | − | 0.712649i | \(-0.747495\pi\) | ||||
−0.701521 | + | 0.712649i | \(0.747495\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 1.04960e10i | − 0.0696742i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.41018e11 | −0.924177 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 1.27202e11i | − 0.812630i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.41366e11 | 0.891715 | 0.445858 | − | 0.895104i | \(-0.352899\pi\) | ||||
0.445858 | + | 0.895104i | \(0.352899\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 3.93095e11i | − 2.41770i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.71730e10 | 0.104301 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.65042e10i | 0.0977605i | 0.998805 | + | 0.0488802i | \(0.0155653\pi\) | ||||
−0.998805 | + | 0.0488802i | \(0.984435\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.08388e10 | −0.297407 | −0.148704 | − | 0.988882i | \(-0.547510\pi\) | ||||
−0.148704 | + | 0.988882i | \(0.547510\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 2.01779e11i | − 1.15149i | −0.817630 | − | 0.575745i | \(-0.804712\pi\) | ||||
0.817630 | − | 0.575745i | \(-0.195288\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.80191e11 | −1.57934 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 4.45752e10i | − 0.245155i | −0.992459 | − | 0.122577i | \(-0.960884\pi\) | ||||
0.992459 | − | 0.122577i | \(-0.0391160\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.59625e11 | 1.95382 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 2.28817e11i | − 1.21324i | −0.794993 | − | 0.606619i | \(-0.792525\pi\) | ||||
0.794993 | − | 0.606619i | \(-0.207475\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.44329e10 | 0.337522 | 0.168761 | − | 0.985657i | \(-0.446023\pi\) | ||||
0.168761 | + | 0.985657i | \(0.446023\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 9.16481e10i | 0.468637i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.79946e11 | −0.909157 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 2.22104e11i | − 1.09564i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.53716e11 | 1.72423 | 0.862114 | − | 0.506715i | \(-0.169140\pi\) | ||||
0.862114 | + | 0.506715i | \(0.169140\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 6.09182e10i | − 0.289996i | −0.989432 | − | 0.144998i | \(-0.953682\pi\) | ||||
0.989432 | − | 0.144998i | \(-0.0463176\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.99523e10 | −0.423188 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6.41129e10i | 0.294620i | 0.989090 | + | 0.147310i | \(0.0470615\pi\) | ||||
−0.989090 | + | 0.147310i | \(0.952938\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.05650e11 | 1.84242 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.22894e10i | 0.232026i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.88610e11 | 0.827280 | 0.413640 | − | 0.910441i | \(-0.364257\pi\) | ||||
0.413640 | + | 0.910441i | \(0.364257\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5.93455e10i | 0.254360i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.84582e10 | −0.0782094 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.73439e11i | 0.718248i | 0.933290 | + | 0.359124i | \(0.116924\pi\) | ||||
−0.933290 | + | 0.359124i | \(0.883076\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.60099e11 | 1.06492 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 1.03442e11i | − 0.414018i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.87397e11 | −1.53310 | −0.766551 | − | 0.642184i | \(-0.778029\pi\) | ||||
−0.766551 | + | 0.642184i | \(0.778029\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.45580e11i | 1.33718i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.11376e11 | 1.57404 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 3.88408e11i | − 1.45336i | −0.686976 | − | 0.726680i | \(-0.741062\pi\) | ||||
0.686976 | − | 0.726680i | \(-0.258938\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.27238e11 | −0.470844 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.06292e11i | 0.746674i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.15997e10 | −0.184718 | −0.0923591 | − | 0.995726i | \(-0.529441\pi\) | ||||
−0.0923591 | + | 0.995726i | \(0.529441\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 9.02263e9i | − 0.0315983i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.68072e11 | 0.582209 | 0.291105 | − | 0.956691i | \(-0.405977\pi\) | ||||
0.291105 | + | 0.956691i | \(0.405977\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.65329e11i | 0.560376i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.48752e11 | 0.834043 | 0.417021 | − | 0.908897i | \(-0.363074\pi\) | ||||
0.417021 | + | 0.908897i | \(0.363074\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 1.00329e11i | − 0.329209i | −0.986360 | − | 0.164605i | \(-0.947365\pi\) | ||||
0.986360 | − | 0.164605i | \(-0.0526348\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.73512e11 | 2.18635 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 7.69068e10i | − 0.244364i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.60192e11 | 1.13233 | 0.566166 | − | 0.824291i | \(-0.308426\pi\) | ||||
0.566166 | + | 0.824291i | \(0.308426\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 7.81710e11i | − 2.40579i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.05727e11 | 0.931000 | 0.465500 | − | 0.885048i | \(-0.345874\pi\) | ||||
0.465500 | + | 0.885048i | \(0.345874\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 4.98951e11i | − 1.48771i | −0.668339 | − | 0.743857i | \(-0.732995\pi\) | ||||
0.668339 | − | 0.743857i | \(-0.267005\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.59323e10 | −0.165031 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.66371e11i | 0.769670i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.27348e11 | −1.50797 | −0.753983 | − | 0.656894i | \(-0.771870\pi\) | ||||
−0.753983 | + | 0.656894i | \(0.771870\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 7.10274e10i | − 0.198933i | −0.995041 | − | 0.0994667i | \(-0.968286\pi\) | ||||
0.995041 | − | 0.0994667i | \(-0.0317137\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.96177e11 | 1.09820 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 3.77427e10i | − 0.102491i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.24426e11 | −2.48467 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 3.08719e11i | − 0.812989i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.06243e10 | −0.105898 | −0.0529489 | − | 0.998597i | \(-0.516862\pi\) | ||||
−0.0529489 | + | 0.998597i | \(0.516862\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.35148e11i | 0.345226i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.11149e11 | −0.533944 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 1.67239e10i | − 0.0414482i | −0.999785 | − | 0.0207241i | \(-0.993403\pi\) | ||||
0.999785 | − | 0.0207241i | \(-0.00659715\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.67846e10 | 0.163866 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 7.62763e11i | − 1.83454i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.97800e11 | −0.709154 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 5.87647e11i | − 1.37190i | −0.727648 | − | 0.685950i | \(-0.759387\pi\) | ||||
0.727648 | − | 0.685950i | \(-0.240613\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.74855e11 | −1.09768 | −0.548842 | − | 0.835926i | \(-0.684931\pi\) | ||||
−0.548842 | + | 0.835926i | \(0.684931\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 9.30819e11i | 2.10977i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.84492e10 | 0.0414084 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 5.95199e11i | − 1.31005i | −0.755605 | − | 0.655027i | \(-0.772657\pi\) | ||||
0.755605 | − | 0.655027i | \(-0.227343\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.88252e11 | 1.50020 | 0.750098 | − | 0.661326i | \(-0.230006\pi\) | ||||
0.750098 | + | 0.661326i | \(0.230006\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 1.12237e11i | − 0.239946i | −0.992777 | − | 0.119973i | \(-0.961719\pi\) | ||||
0.992777 | − | 0.119973i | \(-0.0382808\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4.65905e11 | −0.986460 | −0.493230 | − | 0.869899i | \(-0.664184\pi\) | ||||
−0.493230 | + | 0.869899i | \(0.664184\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.52244e10i | 0.0939276i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.69818e11 | 1.58359 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 8.26729e11i | − 1.66846i | −0.551418 | − | 0.834229i | \(-0.685913\pi\) | ||||
0.551418 | − | 0.834229i | \(-0.314087\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.57013e11 | 0.513774 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.42579e11i | 0.671945i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.42087e11 | −0.470368 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.45161e11i | 1.61147i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.95037e11 | 0.935064 | 0.467532 | − | 0.883976i | \(-0.345143\pi\) | ||||
0.467532 | + | 0.883976i | \(0.345143\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.44761e11i | 0.639138i | 0.947563 | + | 0.319569i | \(0.103538\pi\) | ||||
−0.947563 | + | 0.319569i | \(0.896462\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.07526e11 | 1.48315 | 0.741573 | − | 0.670872i | \(-0.234080\pi\) | ||||
0.741573 | + | 0.670872i | \(0.234080\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 7.70866e11i | 1.38975i | 0.719132 | + | 0.694873i | \(0.244539\pi\) | ||||
−0.719132 | + | 0.694873i | \(0.755461\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.08924e12 | −1.94563 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.29767e10i | 0.0753623i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.57174e11 | 0.273092 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.25757e10i | 0.0385131i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.63983e11 | −0.953384 | −0.476692 | − | 0.879071i | \(-0.658164\pi\) | ||||
−0.476692 | + | 0.879071i | \(0.658164\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 7.69781e11i | − 1.27780i | −0.769289 | − | 0.638901i | \(-0.779389\pi\) | ||||
0.769289 | − | 0.638901i | \(-0.220611\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.40219e11 | −1.38213 | −0.691066 | − | 0.722792i | \(-0.742859\pi\) | ||||
−0.691066 | + | 0.722792i | \(0.742859\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 1.09144e12i | − 1.76322i | −0.471983 | − | 0.881608i | \(-0.656461\pi\) | ||||
0.471983 | − | 0.881608i | \(-0.343539\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.96635e11 | 0.635015 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.36559e11i | 0.214740i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.48913e11 | 0.232081 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.67120e11i | 0.715137i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.37702e11 | −0.208949 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.68364e12i | 2.50989i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.73121e10 | 0.0255812 | 0.0127906 | − | 0.999918i | \(-0.495929\pi\) | ||||
0.0127906 | + | 0.999918i | \(0.495929\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 1.09440e12i | − 1.58892i | −0.607319 | − | 0.794458i | \(-0.707755\pi\) | ||||
0.607319 | − | 0.794458i | \(-0.292245\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.41450e11 | −0.635329 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.62864e11i | 0.513176i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.09637e12 | −1.53707 | −0.768537 | − | 0.639805i | \(-0.779015\pi\) | ||||
−0.768537 | + | 0.639805i | \(0.779015\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 8.78828e11i | 1.21087i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.68903e11 | 1.32347 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 6.77872e11i | − 0.910090i | −0.890468 | − | 0.455045i | \(-0.849623\pi\) | ||||
0.890468 | − | 0.455045i | \(-0.150377\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.24733e10 | −0.123089 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.08334e12i | 1.41749i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.32341e12 | 1.71687 | 0.858434 | − | 0.512924i | \(-0.171438\pi\) | ||||
0.858434 | + | 0.512924i | \(0.171438\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.32278e11i | 0.678859i | 0.940631 | + | 0.339430i | \(0.110234\pi\) | ||||
−0.940631 | + | 0.339430i | \(0.889766\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.22641e11 | 0.155091 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 3.55370e11i | − 0.441856i | −0.975290 | − | 0.220928i | \(-0.929091\pi\) | ||||
0.975290 | − | 0.220928i | \(-0.0709086\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.25139e11 | −0.894039 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 8.27352e11i | 1.00304i | 0.865146 | + | 0.501520i | \(0.167226\pi\) | ||||
−0.865146 | + | 0.501520i | \(0.832774\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.98438e11 | −0.599236 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.09303e11i | 0.483917i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.41948e10 | 0.0518177 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.38767e12i | 2.75337i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.09343e11 | −0.582511 | −0.291256 | − | 0.956645i | \(-0.594073\pi\) | ||||
−0.291256 | + | 0.956645i | \(0.594073\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.25774e12i | 1.41486i | 0.706784 | + | 0.707429i | \(0.250145\pi\) | ||||
−0.706784 | + | 0.707429i | \(0.749855\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.98799e10 | −0.0668082 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.03465e12i | 1.13557i | 0.823177 | + | 0.567785i | \(0.192199\pi\) | ||||
−0.823177 | + | 0.567785i | \(0.807801\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.53694e11 | 0.276171 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 9.31373e11i | − 0.997492i | −0.866748 | − | 0.498746i | \(-0.833794\pi\) | ||||
0.866748 | − | 0.498746i | \(-0.166206\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.12931e12 | 2.26201 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.99484e10i | 0.0626603i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.90752e11 | −0.819871 | −0.409936 | − | 0.912114i | \(-0.634449\pi\) | ||||
−0.409936 | + | 0.912114i | \(0.634449\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 2.02344e12i | − 2.06442i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.61160e12 | −1.63109 | −0.815543 | − | 0.578696i | \(-0.803562\pi\) | ||||
−0.815543 | + | 0.578696i | \(0.803562\pi\) | |||||||
\(998\) | 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.c.a.197.3 | ✓ | 16 | |
3.2 | odd | 2 | inner | 252.9.c.a.197.14 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.9.c.a.197.3 | ✓ | 16 | 1.1 | even | 1 | trivial | |
252.9.c.a.197.14 | yes | 16 | 3.2 | odd | 2 | inner |