Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [288,8,Mod(145,288)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(288, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("288.145");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 288 = 2^{5} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 288.d (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(89.9668873394\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} - 10x^{4} - 24x^{3} - 320x^{2} - 3072x + 32768 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{30} \) |
Twist minimal: | no (minimal twist has level 8) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 145.4 | ||
Root | \(0.776001 + 5.60338i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 288.145 |
Dual form | 288.8.d.b.145.3 |
$q$-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 \(\left(\mathbb{Z}/288\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(65\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(5\) | 184.916i | 0.661574i | 0.943705 | + | 0.330787i | \(0.107314\pi\) | ||||
−0.943705 | + | 0.330787i | \(0.892686\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1051.96 | −1.15919 | −0.579595 | − | 0.814905i | \(-0.696789\pi\) | ||||
−0.579595 | + | 0.814905i | \(0.696789\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4324.35i | 0.979596i | 0.871836 | + | 0.489798i | \(0.162929\pi\) | ||||
−0.871836 | + | 0.489798i | \(0.837071\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 11253.2i | − 1.42061i | −0.703892 | − | 0.710307i | \(-0.748556\pi\) | ||||
0.703892 | − | 0.710307i | \(-0.251444\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 21746.4 | 1.07354 | 0.536768 | − | 0.843730i | \(-0.319645\pi\) | ||||
0.536768 | + | 0.843730i | \(0.319645\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 45466.5i | − 1.52074i | −0.649492 | − | 0.760368i | \(-0.725019\pi\) | ||||
0.649492 | − | 0.760368i | \(-0.274981\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4414.37 | 0.0756522 | 0.0378261 | − | 0.999284i | \(-0.487957\pi\) | ||||
0.0378261 | + | 0.999284i | \(0.487957\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 43931.2 | 0.562320 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 23687.1i | − 0.180351i | −0.995926 | − | 0.0901756i | \(-0.971257\pi\) | ||||
0.995926 | − | 0.0901756i | \(-0.0287428\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −72941.9 | −0.439755 | −0.219878 | − | 0.975527i | \(-0.570566\pi\) | ||||
−0.219878 | + | 0.975527i | \(0.570566\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 194523.i | − 0.766890i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 483338.i | 1.56872i | 0.620307 | + | 0.784359i | \(0.287008\pi\) | ||||
−0.620307 | + | 0.784359i | \(0.712992\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 411040. | 0.931410 | 0.465705 | − | 0.884940i | \(-0.345801\pi\) | ||||
0.465705 | + | 0.884940i | \(0.345801\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 96165.3i | 0.184450i | 0.995738 | + | 0.0922250i | \(0.0293979\pi\) | ||||
−0.995738 | + | 0.0922250i | \(0.970602\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −156171. | −0.219411 | −0.109705 | − | 0.993964i | \(-0.534991\pi\) | ||||
−0.109705 | + | 0.993964i | \(0.534991\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 283070. | 0.343722 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 686962.i | 0.633822i | 0.948455 | + | 0.316911i | \(0.102646\pi\) | ||||
−0.948455 | + | 0.316911i | \(0.897354\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −799641. | −0.648075 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.79961e6i | 1.14077i | 0.821378 | + | 0.570384i | \(0.193206\pi\) | ||||
−0.821378 | + | 0.570384i | \(0.806794\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 1.36394e6i | − 0.769379i | −0.923046 | − | 0.384690i | \(-0.874308\pi\) | ||||
0.923046 | − | 0.384690i | \(-0.125692\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.08090e6 | 0.939841 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.08853e6i | 0.442160i | 0.975256 | + | 0.221080i | \(0.0709582\pi\) | ||||
−0.975256 | + | 0.221080i | \(0.929042\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.60830e6 | −1.85963 | −0.929816 | − | 0.368025i | \(-0.880034\pi\) | ||||
−0.929816 | + | 0.368025i | \(0.880034\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 21698.7 | 0.00652837 | 0.00326418 | − | 0.999995i | \(-0.498961\pi\) | ||||
0.00326418 | + | 0.999995i | \(0.498961\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 4.54903e6i | − 1.13554i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.34010e6 | −0.533998 | −0.266999 | − | 0.963697i | \(-0.586032\pi\) | ||||
−0.266999 | + | 0.963697i | \(0.586032\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 882169.i | − 0.169347i | −0.996409 | − | 0.0846736i | \(-0.973015\pi\) | ||||
0.996409 | − | 0.0846736i | \(-0.0269848\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.02125e6i | 0.710223i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.34738e6 | 0.202594 | 0.101297 | − | 0.994856i | \(-0.467701\pi\) | ||||
0.101297 | + | 0.994856i | \(0.467701\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.18379e7i | 1.64676i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 8.40746e6 | 1.00608 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.32798e6 | 0.815236 | 0.407618 | − | 0.913153i | \(-0.366360\pi\) | ||||
0.407618 | + | 0.913153i | \(0.366360\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.66027e6i | 0.932963i | 0.884531 | + | 0.466482i | \(0.154479\pi\) | ||||
−0.884531 | + | 0.466482i | \(0.845521\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.38659e7 | 1.25031 | 0.625154 | − | 0.780501i | \(-0.285036\pi\) | ||||
0.625154 | + | 0.780501i | \(0.285036\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.88354e7i | 1.48638i | 0.669078 | + | 0.743192i | \(0.266689\pi\) | ||||
−0.669078 | + | 0.743192i | \(0.733311\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.60619e6i | 0.636529i | 0.948002 | + | 0.318265i | \(0.103100\pi\) | ||||
−0.948002 | + | 0.318265i | \(0.896900\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.31340e7 | 0.856292 | 0.428146 | − | 0.903709i | \(-0.359167\pi\) | ||||
0.428146 | + | 0.903709i | \(0.359167\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 816286.i | 0.0500495i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.28763e7 | −1.24443 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 787128. | 0.0403921 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.25701e7i | 1.03359i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.18768e7 | −1.38090 | −0.690449 | − | 0.723381i | \(-0.742587\pi\) | ||||
−0.690449 | + | 0.723381i | \(0.742587\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 1.17050e7i | − 0.454905i | −0.973789 | − | 0.227453i | \(-0.926960\pi\) | ||||
0.973789 | − | 0.227453i | \(-0.0730397\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.78288e7i | 1.76282i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.79174e7 | −1.25984 | −0.629921 | − | 0.776659i | \(-0.716913\pi\) | ||||
−0.629921 | + | 0.776659i | \(0.716913\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.80300e7i | 0.885260i | 0.896704 | + | 0.442630i | \(0.145955\pi\) | ||||
−0.896704 | + | 0.442630i | \(0.854045\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.86630e7 | 1.39163 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.38012e6 | 0.119316 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 6.82083e6i | − 0.168922i | −0.996427 | − | 0.0844608i | \(-0.973083\pi\) | ||||
0.996427 | − | 0.0844608i | \(-0.0269168\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.62068e7 | 1.80125 | 0.900626 | − | 0.434595i | \(-0.143109\pi\) | ||||
0.900626 | + | 0.434595i | \(0.143109\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 1.34881e7i | − 0.290931i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.28737e7i | 0.884183i | 0.896970 | + | 0.442092i | \(0.145763\pi\) | ||||
−0.896970 | + | 0.442092i | \(0.854237\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.64373e6 | −0.0876952 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.12127e7i | 0.745374i | 0.927957 | + | 0.372687i | \(0.121563\pi\) | ||||
−0.927957 | + | 0.372687i | \(0.878437\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.41703e7 | 0.401582 | 0.200791 | − | 0.979634i | \(-0.435649\pi\) | ||||
0.200791 | + | 0.979634i | \(0.435649\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.38869e7 | −1.01814 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.90454e7i | 0.867011i | 0.901151 | + | 0.433505i | \(0.142723\pi\) | ||||
−0.901151 | + | 0.433505i | \(0.857277\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.62137e7 | −0.651835 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.20311e8i | 1.56791i | 0.620819 | + | 0.783954i | \(0.286800\pi\) | ||||
−0.620819 | + | 0.783954i | \(0.713200\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.21539e6i | 0.0403049i | 0.999797 | + | 0.0201525i | \(0.00641517\pi\) | ||||
−0.999797 | + | 0.0201525i | \(0.993585\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8.93768e7 | −1.03782 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.40392e7i | 1.05163i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.04122e7 | 0.731191 | 0.365596 | − | 0.930774i | \(-0.380865\pi\) | ||||
0.365596 | + | 0.930774i | \(0.380865\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.17861e7 | 0.118010 | 0.0590050 | − | 0.998258i | \(-0.481207\pi\) | ||||
0.0590050 | + | 0.998258i | \(0.481207\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.97008e7i | 0.835920i | 0.908465 | + | 0.417960i | \(0.137255\pi\) | ||||
−0.908465 | + | 0.417960i | \(0.862745\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.98955e7 | 0.358871 | 0.179436 | − | 0.983770i | \(-0.442573\pi\) | ||||
0.179436 | + | 0.983770i | \(0.442573\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.49178e7i | 0.209061i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.60078e7i | 0.616197i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.96613e8 | 1.48971 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.63604e7i | 0.486318i | 0.969986 | + | 0.243159i | \(0.0781837\pi\) | ||||
−0.969986 | + | 0.243159i | \(0.921816\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.77825e7 | −0.122027 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.67317e7 | 0.509760 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 2.44718e8i | − 1.52508i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.57269e8 | 0.949675 | 0.474837 | − | 0.880074i | \(-0.342507\pi\) | ||||
0.474837 | + | 0.880074i | \(0.342507\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 1.95129e8i | − 1.10721i | −0.832778 | − | 0.553607i | \(-0.813251\pi\) | ||||
0.832778 | − | 0.553607i | \(-0.186749\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 6.95136e7i | − 0.382512i | −0.981540 | − | 0.191256i | \(-0.938744\pi\) | ||||
0.981540 | − | 0.191256i | \(-0.0612561\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.81872e7 | 0.197776 | 0.0988878 | − | 0.995099i | \(-0.468472\pi\) | ||||
0.0988878 | + | 0.995099i | \(0.468472\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 2.88785e7i | − 0.145157i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.63549e8 | −1.24873 | −0.624366 | − | 0.781132i | \(-0.714643\pi\) | ||||
−0.624366 | + | 0.781132i | \(0.714643\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.21337e8 | 0.558386 | 0.279193 | − | 0.960235i | \(-0.409933\pi\) | ||||
0.279193 | + | 0.960235i | \(0.409933\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.23441e7i | 0.227398i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.11645e8 | −2.16038 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.62042e7i | 0.144511i | 0.997386 | + | 0.0722555i | \(0.0230197\pi\) | ||||
−0.997386 | + | 0.0722555i | \(0.976980\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.90893e7i | 0.0741085i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.75550e8 | −0.645111 | −0.322555 | − | 0.946551i | \(-0.604542\pi\) | ||||
−0.322555 | + | 0.946551i | \(0.604542\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 5.08451e8i | − 1.81844i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.10733e8 | −0.375348 | −0.187674 | − | 0.982231i | \(-0.560095\pi\) | ||||
−0.187674 | + | 0.982231i | \(0.560095\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.27030e8 | −0.419320 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.07561e8i | 0.963382i | 0.876341 | + | 0.481691i | \(0.159977\pi\) | ||||
−0.876341 | + | 0.481691i | \(0.840023\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.86036e8 | 0.873027 | 0.436513 | − | 0.899698i | \(-0.356213\pi\) | ||||
0.436513 | + | 0.899698i | \(0.356213\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.89974e8i | 0.550846i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 3.15642e8i | − 0.892309i | −0.894956 | − | 0.446155i | \(-0.852793\pi\) | ||||
0.894956 | − | 0.446155i | \(-0.147207\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.50451e8 | 0.673366 | 0.336683 | − | 0.941618i | \(-0.390695\pi\) | ||||
0.336683 | + | 0.941618i | \(0.390695\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 3.47387e7i | − 0.0911088i | −0.998962 | − | 0.0455544i | \(-0.985495\pi\) | ||||
0.998962 | − | 0.0455544i | \(-0.0145054\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.32397e8 | −1.07968 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.25676e7 | 0.152478 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 5.34336e8i | − 1.24102i | −0.784200 | − | 0.620508i | \(-0.786926\pi\) | ||||
0.784200 | − | 0.620508i | \(-0.213074\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.32777e8 | −0.754703 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 4.96760e7i | − 0.107472i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 1.01162e8i | − 0.213813i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.52214e8 | 0.509002 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 1.68851e8i | − 0.333057i | −0.986037 | − | 0.166529i | \(-0.946744\pi\) | ||||
0.986037 | − | 0.166529i | \(-0.0532558\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.99677e8 | 1.31897 | 0.659487 | − | 0.751716i | \(-0.270774\pi\) | ||||
0.659487 | + | 0.751716i | \(0.270774\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.06345e8 | 0.933343 | 0.466671 | − | 0.884431i | \(-0.345453\pi\) | ||||
0.466671 | + | 0.884431i | \(0.345453\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 4.78996e8i | − 0.844548i | −0.906468 | − | 0.422274i | \(-0.861232\pi\) | ||||
0.906468 | − | 0.422274i | \(-0.138768\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.02431e8 | 0.176671 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 9.88733e8i | − 1.63256i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 4.94369e8i | − 0.798839i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.64285e8 | 0.254339 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.20825e8i | 0.637828i | 0.947784 | + | 0.318914i | \(0.103318\pi\) | ||||
−0.947784 | + | 0.318914i | \(0.896682\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.01287e8 | −0.292522 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.02987e9 | −1.46580 | −0.732902 | − | 0.680334i | \(-0.761835\pi\) | ||||
−0.732902 | + | 0.680334i | \(0.761835\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 3.15427e8i | − 0.430782i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.68554e8 | 0.760751 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.31496e8i | 0.682883i | 0.939903 | + | 0.341442i | \(0.110915\pi\) | ||||
−0.939903 | + | 0.341442i | \(0.889085\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 1.31436e9i | − 1.65511i | −0.561385 | − | 0.827555i | \(-0.689731\pi\) | ||||
0.561385 | − | 0.827555i | \(-0.310269\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.42031e9 | −1.71858 | −0.859291 | − | 0.511486i | \(-0.829095\pi\) | ||||
−0.859291 | + | 0.511486i | \(0.829095\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 1.03706e9i | − 1.23028i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7.59524e8 | 0.866385 | 0.433193 | − | 0.901301i | \(-0.357387\pi\) | ||||
0.433193 | + | 0.901301i | \(0.357387\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.17333e9 | −1.31264 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.01244e6i | 0.00431900i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.76159e8 | −0.397228 | −0.198614 | − | 0.980078i | \(-0.563644\pi\) | ||||
−0.198614 | + | 0.980078i | \(0.563644\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 7.22655e8i | − 0.734720i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 4.57130e8i | − 0.456099i | −0.973650 | − | 0.228049i | \(-0.926765\pi\) | ||||
0.973650 | − | 0.228049i | \(-0.0732347\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.66557e8 | −0.256209 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 1.91565e9i | − 1.80750i | −0.428056 | − | 0.903752i | \(-0.640801\pi\) | ||||
0.428056 | − | 0.903752i | \(-0.359199\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.57853e9 | 1.43568 | 0.717839 | − | 0.696209i | \(-0.245131\pi\) | ||||
0.717839 | + | 0.696209i | \(0.245131\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.41187e8 | 0.751243 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.21214e9i | 1.90541i | 0.303890 | + | 0.952707i | \(0.401715\pi\) | ||||
−0.303890 | + | 0.952707i | \(0.598285\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.59967e7 | 0.0812153 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 4.32721e8i | − 0.353279i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.30879e9i | 1.04979i | 0.851167 | + | 0.524896i | \(0.175896\pi\) | ||||
−0.851167 | + | 0.524896i | \(0.824104\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.04514e8 | −0.0809413 | −0.0404706 | − | 0.999181i | \(-0.512886\pi\) | ||||
−0.0404706 | + | 0.999181i | \(0.512886\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.20832e8i | 0.624722i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.09013e9 | −1.53671 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.94107e9 | 1.40284 | 0.701421 | − | 0.712747i | \(-0.252549\pi\) | ||||
0.701421 | + | 0.712747i | \(0.252549\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 1.89312e9i | − 1.32237i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.63127e8 | 0.112036 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.96429e9i | 1.30454i | 0.757989 | + | 0.652268i | \(0.226182\pi\) | ||||
−0.757989 | + | 0.652268i | \(0.773818\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.33176e9i | 1.52299i | 0.648174 | + | 0.761493i | \(0.275533\pi\) | ||||
−0.648174 | + | 0.761493i | \(0.724467\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 9.55346e8 | 0.603670 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.43480e9i | 0.891857i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.72745e8 | 0.103929 | 0.0519643 | − | 0.998649i | \(-0.483452\pi\) | ||||
0.0519643 | + | 0.998649i | \(0.483452\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.71381e9 | −1.60647 | −0.803233 | − | 0.595665i | \(-0.796889\pi\) | ||||
−0.803233 | + | 0.595665i | \(0.796889\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 2.00706e8i | − 0.115047i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.73808e8 | 0.154461 | 0.0772307 | − | 0.997013i | \(-0.475392\pi\) | ||||
0.0772307 | + | 0.997013i | \(0.475392\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 2.72048e9i | − 1.48673i | −0.668886 | − | 0.743365i | \(-0.733229\pi\) | ||||
0.668886 | − | 0.743365i | \(-0.266771\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.49152e8i | 0.134031i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.69111e9 | −0.881675 | −0.440837 | − | 0.897587i | \(-0.645318\pi\) | ||||
−0.440837 | + | 0.897587i | \(0.645318\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.77748e9i | 0.912406i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.18902e9 | −1.08945 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.15773e8 | −0.0567413 | −0.0283706 | − | 0.999597i | \(-0.509032\pi\) | ||||
−0.0283706 | + | 0.999597i | \(0.509032\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.34713e8i | 0.444350i | 0.975007 | + | 0.222175i | \(0.0713156\pi\) | ||||
−0.975007 | + | 0.222175i | \(0.928684\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.91738e9 | −0.897790 | −0.448895 | − | 0.893584i | \(-0.648182\pi\) | ||||
−0.448895 | + | 0.893584i | \(0.648182\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.65838e9i | 0.753485i | 0.926318 | + | 0.376742i | \(0.122956\pi\) | ||||
−0.926318 | + | 0.376742i | \(0.877044\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 1.14509e9i | − 0.512548i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4.15853e8 | −0.180686 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 1.99740e9i | − 0.855140i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.09755e9 | 1.70353 | 0.851766 | − | 0.523923i | \(-0.175532\pi\) | ||||
0.851766 | + | 0.523923i | \(0.175532\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.43912e9 | 2.22854 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.35506e9i | 0.539339i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.24167e9 | 1.27180 | 0.635898 | − | 0.771773i | \(-0.280630\pi\) | ||||
0.635898 | + | 0.771773i | \(0.280630\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.16351e9i | 0.824847i | 0.910992 | + | 0.412423i | \(0.135318\pi\) | ||||
−0.910992 | + | 0.412423i | \(0.864682\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 5.15110e8i | − 0.193613i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.89969e9 | 2.15567 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.16713e9i | 0.780787i | 0.920648 | + | 0.390394i | \(0.127661\pi\) | ||||
−0.920648 | + | 0.390394i | \(0.872339\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.58480e9 | −0.905606 | −0.452803 | − | 0.891611i | \(-0.649576\pi\) | ||||
−0.452803 | + | 0.891611i | \(0.649576\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.78633e9 | −0.617224 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.11747e9i | 0.711712i | 0.934541 | + | 0.355856i | \(0.115811\pi\) | ||||
−0.934541 | + | 0.355856i | \(0.884189\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.28261e7 | −0.00756762 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.56402e9i | 0.827172i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 6.75339e8i | − 0.214934i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.34354e9 | 0.726006 | 0.363003 | − | 0.931788i | \(-0.381751\pi\) | ||||
0.363003 | + | 0.931788i | \(0.381751\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.26155e9i | 0.996939i | 0.866907 | + | 0.498470i | \(0.166104\pi\) | ||||
−0.866907 | + | 0.498470i | \(0.833896\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.58622e9 | −0.472093 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.38534e9 | −0.994277 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 4.62554e9i | − 1.32317i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.48296e9 | −0.983354 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.22409e9i | 0.336709i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.24638e9i | 1.96757i | 0.179344 | + | 0.983787i | \(0.442603\pi\) | ||||
−0.179344 | + | 0.983787i | \(0.557397\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.59142e9 | −0.421111 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.41460e9i | 1.67577i | 0.545848 | + | 0.837884i | \(0.316207\pi\) | ||||
−0.545848 | + | 0.837884i | \(0.683793\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.07697e9 | −0.274267 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.46168e9 | 0.619005 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.76223e9i | 0.432085i | 0.976384 | + | 0.216042i | \(0.0693149\pi\) | ||||
−0.976384 | + | 0.216042i | \(0.930685\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.08217e9 | 0.262032 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 2.33270e9i | − 0.550909i | −0.961314 | − | 0.275454i | \(-0.911172\pi\) | ||||
0.961314 | − | 0.275454i | \(-0.0888283\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.42868e9i | 0.566501i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.53591e9 | −1.25978 | −0.629892 | − | 0.776683i | \(-0.716901\pi\) | ||||
−0.629892 | + | 0.776683i | \(0.716901\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.70890e9i | 0.833717i | 0.908971 | + | 0.416858i | \(0.136869\pi\) | ||||
−0.908971 | + | 0.416858i | \(0.863131\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.93929e8 | 0.0425407 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.63713e9 | 0.788212 | 0.394106 | − | 0.919065i | \(-0.371054\pi\) | ||||
0.394106 | + | 0.919065i | \(0.371054\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9.28003e8i | 0.196306i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.97067e9 | −0.620889 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.04311e9i | 0.416926i | 0.978030 | + | 0.208463i | \(0.0668461\pi\) | ||||
−0.978030 | + | 0.208463i | \(0.933154\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.31641e9i | 0.668752i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5.74764e9 | 1.13187 | 0.565937 | − | 0.824448i | \(-0.308514\pi\) | ||||
0.565937 | + | 0.824448i | \(0.308514\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 4.23018e9i | − 0.823284i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.14564e8 | 0.0598020 | 0.0299010 | − | 0.999553i | \(-0.490481\pi\) | ||||
0.0299010 | + | 0.999553i | \(0.490481\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.49586e9 | −0.468985 | −0.234493 | − | 0.972118i | \(-0.575343\pi\) | ||||
−0.234493 | + | 0.972118i | \(0.575343\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.45552e8i | 0.0267224i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.81126e9 | 0.510200 | 0.255100 | − | 0.966915i | \(-0.417892\pi\) | ||||
0.255100 | + | 0.966915i | \(0.417892\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.75743e9i | 0.311698i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 2.34343e9i | − 0.410904i | −0.978667 | − | 0.205452i | \(-0.934134\pi\) | ||||
0.978667 | − | 0.205452i | \(-0.0658664\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.26737e8 | 0.107420 | 0.0537102 | − | 0.998557i | \(-0.482895\pi\) | ||||
0.0537102 | + | 0.998557i | \(0.482895\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 8.90879e9i | − 1.50974i | −0.655876 | − | 0.754869i | \(-0.727700\pi\) | ||||
0.655876 | − | 0.754869i | \(-0.272300\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.41739e9 | −0.234845 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.41437e8 | −0.121477 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.05109e10i | 1.68407i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.21942e9 | 0.351671 | 0.175835 | − | 0.984420i | \(-0.443737\pi\) | ||||
0.175835 | + | 0.984420i | \(0.443737\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 5.89451e9i | − 0.913566i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 3.18545e9i | − 0.488296i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.58104e9 | −1.28688 | −0.643438 | − | 0.765498i | \(-0.722493\pi\) | ||||
−0.643438 | + | 0.765498i | \(0.722493\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 7.71279e9i | − 1.14412i | −0.820210 | − | 0.572062i | \(-0.806144\pi\) | ||||
0.820210 | − | 0.572062i | \(-0.193856\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.18898e10 | 1.72587 | 0.862935 | − | 0.505316i | \(-0.168624\pi\) | ||||
0.862935 | + | 0.505316i | \(0.168624\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.78217e9 | −1.11749 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 2.00345e9i | − 0.281567i | −0.990040 | − | 0.140784i | \(-0.955038\pi\) | ||||
0.990040 | − | 0.140784i | \(-0.0449622\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.16443e9 | 0.300954 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 7.66944e9i | − 1.04391i | −0.852972 | − | 0.521957i | \(-0.825202\pi\) | ||||
0.852972 | − | 0.521957i | \(-0.174798\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 4.04041e9i | − 0.544152i | −0.962276 | − | 0.272076i | \(-0.912290\pi\) | ||||
0.962276 | − | 0.272076i | \(-0.0877103\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −8.84429e9 | −1.16624 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 1.04564e8i | − 0.0136440i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.89816e9 | 0.753681 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.11138e9 | 0.519918 | 0.259959 | − | 0.965620i | \(-0.416291\pi\) | ||||
0.259959 | + | 0.965620i | \(0.416291\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 1.12671e10i | − 1.39557i | −0.716305 | − | 0.697787i | \(-0.754168\pi\) | ||||
0.716305 | − | 0.697787i | \(-0.245832\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.70872e9 | −0.945014 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8.00228e9i | 0.961039i | 0.876984 | + | 0.480520i | \(0.159552\pi\) | ||||
−0.876984 | + | 0.480520i | \(0.840448\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 7.01151e9i | − 0.833479i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7.73055e9 | 0.900416 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.24716e9i | 0.835593i | 0.908541 | + | 0.417797i | \(0.137197\pi\) | ||||
−0.908541 | + | 0.417797i | \(0.862803\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5.18318e9 | −0.585665 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.93865e9 | 0.999902 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 4.68293e8i | − 0.0513458i | −0.999670 | − | 0.0256729i | \(-0.991827\pi\) | ||||
0.999670 | − | 0.0256729i | \(-0.00817283\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.19757e10 | 2.38561 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 1.01622e10i | − 1.08148i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.08926e10i | 1.14781i | 0.818923 | + | 0.573903i | \(0.194571\pi\) | ||||
−0.818923 | + | 0.573903i | \(0.805429\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.21992e8 | −0.0332684 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.99855e9i | 0.920664i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7.40284e9 | −0.742758 | −0.371379 | − | 0.928481i | \(-0.621115\pi\) | ||||
−0.371379 | + | 0.928481i | \(0.621115\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.45863e10 | −1.44935 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 1.04060e9i | − 0.101415i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.04295e10 | −1.00668 | −0.503342 | − | 0.864087i | \(-0.667897\pi\) | ||||
−0.503342 | + | 0.864087i | \(0.667897\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.09125e9i | 0.198014i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 1.55538e10i | − 1.45873i | −0.684127 | − | 0.729363i | \(-0.739816\pi\) | ||||
0.684127 | − | 0.729363i | \(-0.260184\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.70720e9 | −0.433138 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 1.07140e10i | − 0.976554i | −0.872689 | − | 0.488277i | \(-0.837626\pi\) | ||||
0.872689 | − | 0.488277i | \(-0.162374\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5.46982e9 | −0.489229 | −0.244615 | − | 0.969620i | \(-0.578661\pi\) | ||||
−0.244615 | + | 0.969620i | \(0.578661\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.26128e9 | 0.111754 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 1.98140e10i | − 1.72300i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.68185e9 | −0.489497 | −0.244749 | − | 0.969587i | \(-0.578705\pi\) | ||||
−0.244749 | + | 0.969587i | \(0.578705\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.40918e10i | 1.19166i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 5.38304e9i | − 0.451016i | −0.974241 | − | 0.225508i | \(-0.927596\pi\) | ||||
0.974241 | − | 0.225508i | \(-0.0724043\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.28593e9 | 0.270279 | 0.135139 | − | 0.990827i | \(-0.456852\pi\) | ||||
0.135139 | + | 0.990827i | \(0.456852\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 9.05334e9i | − 0.737858i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.02515e10 | 1.62059 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.10914e9 | 0.563735 | 0.281868 | − | 0.959453i | \(-0.409046\pi\) | ||||
0.281868 | + | 0.959453i | \(0.409046\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.08690e10i | 0.846370i | 0.906043 | + | 0.423185i | \(0.139088\pi\) | ||||
−0.906043 | + | 0.423185i | \(0.860912\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.20443e9 | −0.247283 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 1.86886e10i | − 1.41643i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 2.42523e10i | − 1.82169i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.92802e9 | −0.584953 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 1.94246e10i | − 1.42050i | −0.703951 | − | 0.710248i | \(-0.748583\pi\) | ||||
0.703951 | − | 0.710248i | \(-0.251417\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.38164e10 | −0.992606 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.53487e10 | −1.09299 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.30309e10i | 1.61141i | 0.592314 | + | 0.805707i | \(0.298214\pi\) | ||||
−0.592314 | + | 0.805707i | \(0.701786\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.39616e9 | −0.235545 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9.38331e7i | 0.00639516i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 8.58697e8i | − 0.0580169i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.50546e10 | 0.999656 | 0.499828 | − | 0.866125i | \(-0.333397\pi\) | ||||
0.499828 | + | 0.866125i | \(0.333397\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 1.98821e10i | − 1.30885i | −0.756128 | − | 0.654424i | \(-0.772911\pi\) | ||||
0.756128 | − | 0.654424i | \(-0.227089\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7.62086e9 | −0.493120 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.37230e9 | 0.280500 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 2.29870e10i | − 1.44971i | −0.688901 | − | 0.724855i | \(-0.741907\pi\) | ||||
0.688901 | − | 0.724855i | \(-0.258093\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.46696e10 | −0.917316 | −0.458658 | − | 0.888613i | \(-0.651670\pi\) | ||||
−0.458658 | + | 0.888613i | \(0.651670\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 1.26591e9i | − 0.0778277i | −0.999243 | − | 0.0389138i | \(-0.987610\pi\) | ||||
0.999243 | − | 0.0389138i | \(-0.0123898\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.49778e10i | 1.52270i | 0.648342 | + | 0.761349i | \(0.275463\pi\) | ||||
−0.648342 | + | 0.761349i | \(0.724537\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.15576e9 | 0.368998 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.46947e9i | 0.265676i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −3.09477e10 | −1.80909 | −0.904547 | − | 0.426373i | \(-0.859791\pi\) | ||||
−0.904547 | + | 0.426373i | \(0.859791\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.66888e10 | 0.967473 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 1.18137e10i | − 0.673577i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.28024e8 | −0.0468221 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.13363e9i | 0.118677i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 1.86385e10i | − 1.02823i | −0.857723 | − | 0.514113i | \(-0.828121\pi\) | ||||
0.857723 | − | 0.514113i | \(-0.171879\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.37366e10 | 1.28821 | 0.644103 | − | 0.764939i | \(-0.277231\pi\) | ||||
0.644103 | + | 0.764939i | \(0.277231\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.46268e10i | 1.32566i | 0.748770 | + | 0.662830i | \(0.230645\pi\) | ||||
−0.748770 | + | 0.662830i | \(0.769355\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.50051e10 | 1.32431 | 0.662157 | − | 0.749365i | \(-0.269641\pi\) | ||||
0.662157 | + | 0.749365i | \(0.269641\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.09184e10 | −0.573592 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 1.01194e10i | − 0.523102i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.22495e10 | 0.628139 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 2.37428e10i | − 1.19813i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.07280e10i | 0.537057i | 0.963272 | + | 0.268528i | \(0.0865373\pi\) | ||||
−0.963272 | + | 0.268528i | \(0.913463\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −5.94499e9 | −0.292911 | −0.146455 | − | 0.989217i | \(-0.546786\pi\) | ||||
−0.146455 | + | 0.989217i | \(0.546786\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.60870e10i | 0.786342i | 0.919465 | + | 0.393171i | \(0.128622\pi\) | ||||
−0.919465 | + | 0.393171i | \(0.871378\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.61884e10 | −1.26001 | −0.630007 | − | 0.776589i | \(-0.716948\pi\) | ||||
−0.630007 | + | 0.776589i | \(0.716948\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.35330e10 | 1.60072 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.10056e9i | 0.333666i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.22474e10 | −1.03729 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.72778e9i | 0.0793104i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.49390e10i | 0.680430i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5.94575e8 | −0.0266647 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 1.79753e9i | − 0.0799929i | −0.999200 | − | 0.0399964i | \(-0.987265\pi\) | ||||
0.999200 | − | 0.0399964i | \(-0.0127347\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.70021e10 | 1.62148 | 0.810740 | − | 0.585406i | \(-0.199065\pi\) | ||||
0.810740 | + | 0.585406i | \(0.199065\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.81481e9 | 0.165892 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.23131e10i | 0.527322i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.44812e10 | 1.04047 | 0.520234 | − | 0.854024i | \(-0.325845\pi\) | ||||
0.520234 | + | 0.854024i | \(0.325845\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.31115e10i | 2.64182i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.12336e10i | 0.882121i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 6.19981e9 | 0.253702 | 0.126851 | − | 0.991922i | \(-0.459513\pi\) | ||||
0.126851 | + | 0.991922i | \(0.459513\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 1.28702e10i | − 0.522711i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.73893e10 | −0.695732 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.78747e10 | −1.10693 | −0.553466 | − | 0.832871i | \(-0.686695\pi\) | ||||
−0.553466 | + | 0.832871i | \(0.686695\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.45921e10i | 1.35336i | 0.736277 | + | 0.676680i | \(0.236582\pi\) | ||||
−0.736277 | + | 0.676680i | \(0.763418\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.81448e9 | 0.0704632 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 2.20475e10i | − 0.843598i | −0.906689 | − | 0.421799i | \(-0.861399\pi\) | ||||
0.906689 | − | 0.421799i | \(-0.138601\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 2.44181e8i | − 0.00927429i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.95876e9 | 0.148161 | 0.0740805 | − | 0.997252i | \(-0.476398\pi\) | ||||
0.0740805 | + | 0.997252i | \(0.476398\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.30203e10i | 0.483737i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.98874e10 | 1.46040 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.21921e10 | −0.806615 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.17943e9i | 0.0780724i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9.76598e9 | 0.347315 | 0.173657 | − | 0.984806i | \(-0.444441\pi\) | ||||
0.173657 | + | 0.984806i | \(0.444441\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.15553e10i | 0.755589i | 0.925889 | + | 0.377795i | \(0.123317\pi\) | ||||
−0.925889 | + | 0.377795i | \(0.876683\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 2.94863e10i | − 1.02619i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −5.24340e10 | −1.79880 | −0.899398 | − | 0.437131i | \(-0.855995\pi\) | ||||
−0.899398 | + | 0.437131i | \(0.855995\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.82657e9i | 0.198460i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.85116e10 | −0.957380 | −0.478690 | − | 0.877984i | \(-0.658888\pi\) | ||||
−0.478690 | + | 0.877984i | \(0.658888\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.65871e10 | −0.553023 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.24509e8i | 0.0139540i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.72290e10 | 0.888738 | 0.444369 | − | 0.895844i | \(-0.353428\pi\) | ||||
0.444369 | + | 0.895844i | \(0.353428\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7.37731e9i | 0.237420i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.30057e10i | 0.415624i | 0.978169 | + | 0.207812i | \(0.0666343\pi\) | ||||
−0.978169 | + | 0.207812i | \(0.933366\pi\) | |||||||
\(998\) | 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 | 288.8.d.b.145.4 | 6 | ||
3.2 | odd | 2 | 32.8.b.a.17.4 | 6 | |||
4.3 | odd | 2 | 72.8.d.b.37.4 | 6 | |||
8.3 | odd | 2 | 72.8.d.b.37.3 | 6 | |||
8.5 | even | 2 | inner | 288.8.d.b.145.3 | 6 | ||
12.11 | even | 2 | 8.8.b.a.5.3 | ✓ | 6 | ||
24.5 | odd | 2 | 32.8.b.a.17.3 | 6 | |||
24.11 | even | 2 | 8.8.b.a.5.4 | yes | 6 | ||
48.5 | odd | 4 | 256.8.a.q.1.4 | 6 | |||
48.11 | even | 4 | 256.8.a.r.1.3 | 6 | |||
48.29 | odd | 4 | 256.8.a.q.1.3 | 6 | |||
48.35 | even | 4 | 256.8.a.r.1.4 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8.8.b.a.5.3 | ✓ | 6 | 12.11 | even | 2 | ||
8.8.b.a.5.4 | yes | 6 | 24.11 | even | 2 | ||
32.8.b.a.17.3 | 6 | 24.5 | odd | 2 | |||
32.8.b.a.17.4 | 6 | 3.2 | odd | 2 | |||
72.8.d.b.37.3 | 6 | 8.3 | odd | 2 | |||
72.8.d.b.37.4 | 6 | 4.3 | odd | 2 | |||
256.8.a.q.1.3 | 6 | 48.29 | odd | 4 | |||
256.8.a.q.1.4 | 6 | 48.5 | odd | 4 | |||
256.8.a.r.1.3 | 6 | 48.11 | even | 4 | |||
256.8.a.r.1.4 | 6 | 48.35 | even | 4 | |||
288.8.d.b.145.3 | 6 | 8.5 | even | 2 | inner | ||
288.8.d.b.145.4 | 6 | 1.1 | even | 1 | trivial |