Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9,76,Mod(1,9)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 76, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9.1");
S:= CuspForms(chi, 76);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9 = 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 76 \) |
Character orbit: | \([\chi]\) | \(=\) | 9.a (trivial) |
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: | yes |
Analytic conductor: | \(320.605553540\) |
Analytic rank: | \(1\) |
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: | \( x^{6} - 3 x^{5} + \cdots - 67\!\cdots\!50 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | multiple of \( 2^{58}\cdot 3^{36}\cdot 5^{7}\cdot 7^{3}\cdot 11\cdot 13\cdot 19 \) |
Twist minimal: | no (minimal twist has level 1) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(5.23553e9\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.67444e11 | −1.89046 | −0.945229 | − | 0.326409i | \(-0.894161\pi\) | ||||
−0.945229 | + | 0.326409i | \(0.894161\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 9.72365e22 | 2.57383 | ||||||||
\(5\) | −2.43619e26 | −1.49739 | −0.748697 | − | 0.662912i | \(-0.769320\pi\) | ||||
−0.748697 | + | 0.662912i | \(0.769320\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.21530e31 | 0.247460 | 0.123730 | − | 0.992316i | \(-0.460514\pi\) | ||||
0.123730 | + | 0.992316i | \(0.460514\pi\) | |||||||
\(8\) | −2.18473e34 | −2.97525 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 8.95165e37 | 2.83076 | ||||||||
\(11\) | 5.65037e38 | 0.501016 | 0.250508 | − | 0.968115i | \(-0.419402\pi\) | ||||
0.250508 | + | 0.968115i | \(0.419402\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.30382e40 | 0.0894774 | 0.0447387 | − | 0.998999i | \(-0.485754\pi\) | ||||
0.0447387 | + | 0.998999i | \(0.485754\pi\) | |||||||
\(14\) | −4.46553e42 | −0.467813 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.35419e45 | 3.05076 | ||||||||
\(17\) | −1.14821e45 | −0.0828300 | −0.0414150 | − | 0.999142i | \(-0.513187\pi\) | ||||
−0.0414150 | + | 0.999142i | \(0.513187\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.24645e48 | 1.38808 | 0.694042 | − | 0.719935i | \(-0.255828\pi\) | ||||
0.694042 | + | 0.719935i | \(0.255828\pi\) | |||||||
\(20\) | −2.36887e49 | −3.85404 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.07620e50 | −0.947149 | ||||||||
\(23\) | −8.02205e50 | −0.691022 | −0.345511 | − | 0.938415i | \(-0.612294\pi\) | ||||
−0.345511 | + | 0.938415i | \(0.612294\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.28805e52 | 1.24219 | ||||||||
\(26\) | −1.94886e52 | −0.169153 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.18171e54 | 0.636920 | ||||||||
\(29\) | −8.53673e54 | −1.23415 | −0.617073 | − | 0.786906i | \(-0.711682\pi\) | ||||
−0.617073 | + | 0.786906i | \(0.711682\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.18737e55 | −0.733572 | −0.366786 | − | 0.930305i | \(-0.619542\pi\) | ||||
−0.366786 | + | 0.930305i | \(0.619542\pi\) | |||||||
\(32\) | −7.74555e56 | −2.79208 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.21904e56 | 0.156587 | ||||||||
\(35\) | −2.96069e57 | −0.370546 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.98766e58 | −0.932594 | −0.466297 | − | 0.884628i | \(-0.654412\pi\) | ||||
−0.466297 | + | 0.884628i | \(0.654412\pi\) | |||||||
\(38\) | −4.58002e59 | −2.62411 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 5.32243e60 | 4.45513 | ||||||||
\(41\) | 5.32628e60 | 1.76616 | 0.883079 | − | 0.469224i | \(-0.155466\pi\) | ||||
0.883079 | + | 0.469224i | \(0.155466\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.59254e61 | 1.44098 | 0.720489 | − | 0.693466i | \(-0.243917\pi\) | ||||
0.720489 | + | 0.693466i | \(0.243917\pi\) | |||||||
\(44\) | 5.49422e61 | 1.28953 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.94766e62 | 1.30635 | ||||||||
\(47\) | 5.76440e62 | 1.14047 | 0.570236 | − | 0.821481i | \(-0.306852\pi\) | ||||
0.570236 | + | 0.821481i | \(0.306852\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.26417e63 | −0.938763 | ||||||||
\(50\) | −1.20818e64 | −2.34831 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5.15725e63 | 0.230299 | ||||||||
\(53\) | −5.92558e63 | −0.129535 | −0.0647673 | − | 0.997900i | \(-0.520630\pi\) | ||||
−0.0647673 | + | 0.997900i | \(0.520630\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.37654e65 | −0.750219 | ||||||||
\(56\) | −2.65510e65 | −0.736257 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.13677e66 | 2.33310 | ||||||||
\(59\) | −2.82712e66 | −1.10763 | −0.553814 | − | 0.832640i | \(-0.686828\pi\) | ||||
−0.553814 | + | 0.832640i | \(0.686828\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.43239e66 | 0.609708 | 0.304854 | − | 0.952399i | \(-0.401392\pi\) | ||||
0.304854 | + | 0.952399i | \(0.401392\pi\) | |||||||
\(62\) | 2.27352e67 | 1.38679 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.20109e68 | 2.22755 | ||||||||
\(65\) | −1.29211e67 | −0.133983 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.61376e68 | −0.869883 | −0.434941 | − | 0.900459i | \(-0.643231\pi\) | ||||
−0.434941 | + | 0.900459i | \(0.643231\pi\) | |||||||
\(68\) | −1.11648e68 | −0.213190 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.08789e69 | 0.700501 | ||||||||
\(71\) | −1.78760e67 | −0.00676213 | −0.00338106 | − | 0.999994i | \(-0.501076\pi\) | ||||
−0.00338106 | + | 0.999994i | \(0.501076\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.09051e70 | −1.45554 | −0.727770 | − | 0.685821i | \(-0.759443\pi\) | ||||
−0.727770 | + | 0.685821i | \(0.759443\pi\) | |||||||
\(74\) | 2.20013e70 | 1.76303 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.21201e71 | 3.57269 | ||||||||
\(77\) | 6.86687e69 | 0.123981 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.49375e71 | −1.03101 | −0.515504 | − | 0.856887i | \(-0.672395\pi\) | ||||
−0.515504 | + | 0.856887i | \(0.672395\pi\) | |||||||
\(80\) | −1.06076e72 | −4.56820 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.95711e72 | −3.33885 | ||||||||
\(83\) | −3.39100e71 | −0.367197 | −0.183599 | − | 0.983001i | \(-0.558775\pi\) | ||||
−0.183599 | + | 0.983001i | \(0.558775\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.79727e71 | 0.124029 | ||||||||
\(86\) | −9.52613e72 | −2.72411 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.23446e73 | −1.49065 | ||||||||
\(89\) | −2.45405e72 | −0.193981 | −0.0969905 | − | 0.995285i | \(-0.530922\pi\) | ||||
−0.0969905 | + | 0.995285i | \(0.530922\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.44571e71 | 0.0221421 | ||||||||
\(92\) | −7.80036e73 | −1.77857 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.11810e74 | −2.15601 | ||||||||
\(95\) | −3.03660e74 | −2.07851 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.36838e74 | 0.428811 | 0.214405 | − | 0.976745i | \(-0.431219\pi\) | ||||
0.214405 | + | 0.976745i | \(0.431219\pi\) | |||||||
\(98\) | 8.31957e74 | 1.77469 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.19719e75 | 3.19719 | ||||||||
\(101\) | 2.90130e74 | 0.199775 | 0.0998875 | − | 0.994999i | \(-0.468152\pi\) | ||||
0.0998875 | + | 0.994999i | \(0.468152\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.39725e74 | 0.145139 | 0.0725696 | − | 0.997363i | \(-0.476880\pi\) | ||||
0.0725696 | + | 0.997363i | \(0.476880\pi\) | |||||||
\(104\) | −1.15874e75 | −0.266218 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.17732e75 | 0.244879 | ||||||||
\(107\) | 1.61246e76 | 1.27526 | 0.637629 | − | 0.770344i | \(-0.279915\pi\) | ||||
0.637629 | + | 0.770344i | \(0.279915\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.51780e76 | −1.38924 | −0.694620 | − | 0.719376i | \(-0.744428\pi\) | ||||
−0.694620 | + | 0.719376i | \(0.744428\pi\) | |||||||
\(110\) | 5.05802e76 | 1.41826 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 5.29163e76 | 0.754942 | ||||||||
\(113\) | 3.77510e76 | 0.385911 | 0.192955 | − | 0.981208i | \(-0.438193\pi\) | ||||
0.192955 | + | 0.981208i | \(0.438193\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.95433e77 | 1.03473 | ||||||||
\(116\) | −8.30081e77 | −3.17648 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.03881e78 | 2.09392 | ||||||||
\(119\) | −1.39542e76 | −0.0204971 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.52628e77 | −0.748983 | ||||||||
\(122\) | −1.99610e78 | −1.15263 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −6.01638e78 | −1.88809 | ||||||||
\(125\) | −1.56178e78 | −0.362656 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.76725e78 | 0.738464 | 0.369232 | − | 0.929337i | \(-0.379621\pi\) | ||||
0.369232 | + | 0.929337i | \(0.379621\pi\) | |||||||
\(128\) | −1.48716e79 | −1.41900 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 4.74780e78 | 0.253289 | ||||||||
\(131\) | 1.75382e79 | 0.701960 | 0.350980 | − | 0.936383i | \(-0.385849\pi\) | ||||
0.350980 | + | 0.936383i | \(0.385849\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.51481e79 | 0.343495 | ||||||||
\(134\) | 9.60412e79 | 1.64448 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.50854e79 | 0.246440 | ||||||||
\(137\) | 2.46770e80 | 1.84192 | 0.920961 | − | 0.389654i | \(-0.127405\pi\) | ||||
0.920961 | + | 0.389654i | \(0.127405\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.49076e79 | 0.324691 | 0.162346 | − | 0.986734i | \(-0.448094\pi\) | ||||
0.162346 | + | 0.986734i | \(0.448094\pi\) | |||||||
\(140\) | −2.87887e80 | −0.953721 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 6.56845e78 | 0.0127835 | ||||||||
\(143\) | 2.99686e79 | 0.0448296 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.07971e81 | 1.84800 | ||||||||
\(146\) | 4.00704e81 | 2.75164 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −5.82219e81 | −2.40034 | ||||||||
\(149\) | −3.07560e81 | −0.985020 | −0.492510 | − | 0.870307i | \(-0.663920\pi\) | ||||
−0.492510 | + | 0.870307i | \(0.663920\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.13847e81 | −0.221151 | −0.110575 | − | 0.993868i | \(-0.535269\pi\) | ||||
−0.110575 | + | 0.993868i | \(0.535269\pi\) | |||||||
\(152\) | −2.72317e82 | −4.12990 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.52319e81 | −0.234382 | ||||||||
\(155\) | 1.50736e82 | 1.09845 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.14834e82 | 0.967979 | 0.483989 | − | 0.875074i | \(-0.339187\pi\) | ||||
0.483989 | + | 0.875074i | \(0.339187\pi\) | |||||||
\(158\) | 5.48870e82 | 1.94908 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.88696e83 | 4.18085 | ||||||||
\(161\) | −9.74916e81 | −0.171000 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.14457e83 | 1.26359 | 0.631795 | − | 0.775135i | \(-0.282318\pi\) | ||||
0.631795 | + | 0.775135i | \(0.282318\pi\) | |||||||
\(164\) | 5.17909e83 | 4.54579 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.24600e83 | 0.694171 | ||||||||
\(167\) | −3.68869e83 | −1.64061 | −0.820304 | − | 0.571928i | \(-0.806196\pi\) | ||||
−0.820304 | + | 0.571928i | \(0.806196\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.48546e83 | −0.991994 | ||||||||
\(170\) | −1.02784e83 | −0.234472 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.52089e84 | 3.70883 | ||||||||
\(173\) | −4.14388e83 | −0.490544 | −0.245272 | − | 0.969454i | \(-0.578877\pi\) | ||||
−0.245272 | + | 0.969454i | \(0.578877\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.99596e83 | 0.307393 | ||||||||
\(176\) | 2.46028e84 | 1.52848 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 9.01729e83 | 0.366713 | ||||||||
\(179\) | −1.08783e84 | −0.358570 | −0.179285 | − | 0.983797i | \(-0.557378\pi\) | ||||
−0.179285 | + | 0.983797i | \(0.557378\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.20049e84 | −0.478161 | −0.239080 | − | 0.971000i | \(-0.576846\pi\) | ||||
−0.239080 | + | 0.971000i | \(0.576846\pi\) | |||||||
\(182\) | −2.36844e83 | −0.0418587 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.75260e85 | 2.05596 | ||||||||
\(185\) | 1.45871e85 | 1.39646 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.48783e83 | −0.0414992 | ||||||||
\(188\) | 5.60510e85 | 2.93538 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.11578e86 | 3.92933 | ||||||||
\(191\) | 8.56878e84 | 0.247838 | 0.123919 | − | 0.992292i | \(-0.460454\pi\) | ||||
0.123919 | + | 0.992292i | \(0.460454\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.83853e85 | 0.555513 | 0.277756 | − | 0.960652i | \(-0.410409\pi\) | ||||
0.277756 | + | 0.960652i | \(0.410409\pi\) | |||||||
\(194\) | −5.02802e85 | −0.810648 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.20160e86 | −2.41622 | ||||||||
\(197\) | 1.39395e86 | 1.26405 | 0.632024 | − | 0.774949i | \(-0.282224\pi\) | ||||
0.632024 | + | 0.774949i | \(0.282224\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.12515e86 | 0.698587 | 0.349294 | − | 0.937013i | \(-0.386422\pi\) | ||||
0.349294 | + | 0.937013i | \(0.386422\pi\) | |||||||
\(200\) | −7.18352e86 | −3.69583 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.06607e86 | −0.377666 | ||||||||
\(203\) | −1.03746e86 | −0.305402 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.29758e87 | −2.64464 | ||||||||
\(206\) | −1.61574e86 | −0.274379 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.30939e86 | 0.272974 | ||||||||
\(209\) | 7.04292e86 | 0.695452 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.53042e87 | 1.05735 | 0.528675 | − | 0.848824i | \(-0.322689\pi\) | ||||
0.528675 | + | 0.848824i | \(0.322689\pi\) | |||||||
\(212\) | −5.76182e86 | −0.333400 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −5.92490e87 | −2.41082 | ||||||||
\(215\) | −6.31591e87 | −2.15771 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.51948e86 | −0.181530 | ||||||||
\(218\) | 1.29260e88 | 2.62630 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.33850e88 | −1.93093 | ||||||||
\(221\) | −6.08992e85 | −0.00741142 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.54993e87 | −0.481787 | −0.240893 | − | 0.970552i | \(-0.577440\pi\) | ||||
−0.240893 | + | 0.970552i | \(0.577440\pi\) | |||||||
\(224\) | −9.41313e87 | −0.690929 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.38714e88 | −0.729548 | ||||||||
\(227\) | 5.62742e87 | 0.250807 | 0.125403 | − | 0.992106i | \(-0.459977\pi\) | ||||
0.125403 | + | 0.992106i | \(0.459977\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.39160e86 | −0.0172937 | −0.00864684 | − | 0.999963i | \(-0.502752\pi\) | ||||
−0.00864684 | + | 0.999963i | \(0.502752\pi\) | |||||||
\(230\) | −7.18106e88 | −1.95612 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.86505e89 | 3.67190 | ||||||||
\(233\) | 1.05527e89 | 1.76814 | 0.884072 | − | 0.467351i | \(-0.154791\pi\) | ||||
0.884072 | + | 0.467351i | \(0.154791\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.40432e89 | −1.70774 | ||||||||
\(236\) | −2.74899e89 | −2.85085 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 5.12738e87 | 0.0387490 | ||||||||
\(239\) | 1.07654e89 | 0.695201 | 0.347600 | − | 0.937643i | \(-0.386997\pi\) | ||||
0.347600 | + | 0.937643i | \(0.386997\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.81853e89 | 1.80409 | 0.902043 | − | 0.431647i | \(-0.142067\pi\) | ||||
0.902043 | + | 0.431647i | \(0.142067\pi\) | |||||||
\(242\) | 3.50038e89 | 1.41592 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 5.28226e89 | 1.56928 | ||||||||
\(245\) | 5.51595e89 | 1.40570 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.61097e88 | 0.124202 | ||||||||
\(248\) | 1.35178e90 | 2.18256 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 5.73868e89 | 0.685586 | ||||||||
\(251\) | 4.93768e89 | 0.507877 | 0.253939 | − | 0.967220i | \(-0.418274\pi\) | ||||
0.253939 | + | 0.967220i | \(0.418274\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.53276e89 | −0.346213 | ||||||||
\(254\) | −2.11915e90 | −1.39603 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 9.26877e89 | 0.455012 | ||||||||
\(257\) | −3.14677e90 | −1.33467 | −0.667334 | − | 0.744759i | \(-0.732565\pi\) | ||||
−0.667334 | + | 0.744759i | \(0.732565\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.27678e89 | −0.230780 | ||||||||
\(260\) | −1.25641e90 | −0.344849 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −6.44433e90 | −1.32702 | ||||||||
\(263\) | 4.16943e90 | 0.744279 | 0.372140 | − | 0.928177i | \(-0.378624\pi\) | ||||
0.372140 | + | 0.928177i | \(0.378624\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.44358e90 | 0.193964 | ||||||||
\(266\) | −5.56608e90 | −0.649363 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2.54153e91 | −2.23893 | ||||||||
\(269\) | −1.97317e91 | −1.51166 | −0.755829 | − | 0.654769i | \(-0.772766\pi\) | ||||
−0.755829 | + | 0.654769i | \(0.772766\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.23482e91 | 1.29686 | 0.648432 | − | 0.761273i | \(-0.275425\pi\) | ||||
0.648432 | + | 0.761273i | \(0.275425\pi\) | |||||||
\(272\) | −4.99954e90 | −0.252695 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −9.06743e91 | −3.48208 | ||||||||
\(275\) | 1.85787e91 | 0.622358 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.38744e91 | 0.864729 | 0.432365 | − | 0.901699i | \(-0.357679\pi\) | ||||
0.432365 | + | 0.901699i | \(0.357679\pi\) | |||||||
\(278\) | −2.75244e91 | −0.613815 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 6.46833e91 | 1.10247 | ||||||||
\(281\) | 7.17828e91 | 1.07037 | 0.535184 | − | 0.844735i | \(-0.320242\pi\) | ||||
0.535184 | + | 0.844735i | \(0.320242\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.11121e92 | 1.27000 | 0.635000 | − | 0.772512i | \(-0.281000\pi\) | ||||
0.635000 | + | 0.772512i | \(0.281000\pi\) | |||||||
\(284\) | −1.73820e90 | −0.0174046 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.10118e91 | −0.0847484 | ||||||||
\(287\) | 6.47300e91 | 0.437054 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.90844e92 | −0.993139 | ||||||||
\(290\) | −7.64178e92 | −3.49357 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.06038e93 | −3.74631 | ||||||||
\(293\) | −4.84927e91 | −0.150709 | −0.0753547 | − | 0.997157i | \(-0.524009\pi\) | ||||
−0.0753547 | + | 0.997157i | \(0.524009\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.88741e92 | 1.65856 | ||||||||
\(296\) | 1.30815e93 | 2.77470 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.13011e93 | 1.86214 | ||||||||
\(299\) | −4.25476e91 | −0.0618308 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.15070e92 | 0.356585 | ||||||||
\(302\) | 4.18326e92 | 0.418076 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 5.42729e93 | 4.23471 | ||||||||
\(305\) | −1.32343e93 | −0.912974 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.53608e92 | −0.298891 | −0.149446 | − | 0.988770i | \(-0.547749\pi\) | ||||
−0.149446 | + | 0.988770i | \(0.547749\pi\) | |||||||
\(308\) | 6.67710e92 | 0.319107 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −5.53872e93 | −2.07657 | ||||||||
\(311\) | 3.84755e93 | 1.27841 | 0.639204 | − | 0.769037i | \(-0.279264\pi\) | ||||
0.639204 | + | 0.769037i | \(0.279264\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.85920e93 | 0.747019 | 0.373509 | − | 0.927626i | \(-0.378154\pi\) | ||||
0.373509 | + | 0.927626i | \(0.378154\pi\) | |||||||
\(314\) | −7.89395e93 | −1.82992 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.45247e94 | −2.65364 | ||||||||
\(317\) | 7.23036e92 | 0.117338 | 0.0586688 | − | 0.998278i | \(-0.481314\pi\) | ||||
0.0586688 | + | 0.998278i | \(0.481314\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.82357e93 | −0.618327 | ||||||||
\(320\) | −2.92609e94 | −3.33552 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3.58228e93 | 0.323269 | ||||||||
\(323\) | −1.43119e93 | −0.114975 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.74393e93 | 0.111148 | ||||||||
\(326\) | −4.20565e94 | −2.38876 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.16365e95 | −5.25477 | ||||||||
\(329\) | 7.00545e93 | 0.282221 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.94545e94 | −0.624409 | −0.312205 | − | 0.950015i | \(-0.601067\pi\) | ||||
−0.312205 | + | 0.950015i | \(0.601067\pi\) | |||||||
\(332\) | −3.29729e94 | −0.945102 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.35539e95 | 3.10150 | ||||||||
\(335\) | 6.36762e94 | 1.30256 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.36785e94 | −1.04201 | −0.521005 | − | 0.853554i | \(-0.674443\pi\) | ||||
−0.521005 | + | 0.853554i | \(0.674443\pi\) | |||||||
\(338\) | 1.28071e95 | 1.87532 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.71996e94 | 0.319230 | ||||||||
\(341\) | −3.49610e94 | −0.367531 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5.68276e94 | −0.479767 | ||||||||
\(344\) | −5.66400e95 | −4.28728 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.52264e95 | 0.927353 | ||||||||
\(347\) | −2.45590e94 | −0.134232 | −0.0671160 | − | 0.997745i | \(-0.521380\pi\) | ||||
−0.0671160 | + | 0.997745i | \(0.521380\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.80433e94 | 0.123559 | 0.0617796 | − | 0.998090i | \(-0.480322\pi\) | ||||
0.0617796 | + | 0.998090i | \(0.480322\pi\) | |||||||
\(350\) | −1.46829e95 | −0.581113 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4.37652e95 | −1.39888 | ||||||||
\(353\) | −3.99820e95 | −1.14898 | −0.574491 | − | 0.818511i | \(-0.694800\pi\) | ||||
−0.574491 | + | 0.818511i | \(0.694800\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.35495e93 | 0.0101256 | ||||||||
\(356\) | −2.38624e95 | −0.499274 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.99718e95 | 0.677860 | ||||||||
\(359\) | −7.73805e95 | −1.18192 | −0.590962 | − | 0.806699i | \(-0.701252\pi\) | ||||
−0.590962 | + | 0.806699i | \(0.701252\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.47301e95 | 0.926777 | ||||||||
\(362\) | 8.08560e95 | 0.903942 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 6.26758e94 | 0.0569899 | ||||||||
\(365\) | 2.65670e96 | 2.17952 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.77357e95 | 0.385893 | 0.192946 | − | 0.981209i | \(-0.438196\pi\) | ||||
0.192946 | + | 0.981209i | \(0.438196\pi\) | |||||||
\(368\) | −3.49296e96 | −2.10814 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −5.35995e96 | −2.63995 | ||||||||
\(371\) | −7.20132e94 | −0.0320546 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.37386e96 | 1.22757 | 0.613784 | − | 0.789474i | \(-0.289646\pi\) | ||||
0.613784 | + | 0.789474i | \(0.289646\pi\) | |||||||
\(374\) | 2.38392e95 | 0.0784524 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.25937e97 | −3.39319 | ||||||||
\(377\) | −4.52773e95 | −0.110428 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.66618e96 | −0.733235 | −0.366618 | − | 0.930372i | \(-0.619484\pi\) | ||||
−0.366618 | + | 0.930372i | \(0.619484\pi\) | |||||||
\(380\) | −2.95268e97 | −5.34973 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −3.14855e96 | −0.468527 | ||||||||
\(383\) | 7.65115e96 | 1.03222 | 0.516111 | − | 0.856522i | \(-0.327379\pi\) | ||||
0.516111 | + | 0.856522i | \(0.327379\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.67290e96 | −0.185649 | ||||||||
\(386\) | −1.04300e97 | −1.05017 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.33056e97 | 1.10368 | ||||||||
\(389\) | −2.43483e97 | −1.83383 | −0.916913 | − | 0.399087i | \(-0.869327\pi\) | ||||
−0.916913 | + | 0.399087i | \(0.869327\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.21102e95 | 0.0572373 | ||||||||
\(392\) | 4.94661e97 | 2.79306 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −5.12199e97 | −2.38963 | ||||||||
\(395\) | 3.63906e97 | 1.54383 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.68145e96 | 0.199441 | 0.0997207 | − | 0.995015i | \(-0.468205\pi\) | ||||
0.0997207 | + | 0.995015i | \(0.468205\pi\) | |||||||
\(398\) | −4.13431e97 | −1.32065 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.43168e98 | 3.78963 | ||||||||
\(401\) | 2.25071e97 | 0.542507 | 0.271254 | − | 0.962508i | \(-0.412562\pi\) | ||||
0.271254 | + | 0.962508i | \(0.412562\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.28167e96 | −0.0656381 | ||||||||
\(404\) | 2.82112e97 | 0.514187 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.81211e97 | 0.577349 | ||||||||
\(407\) | −3.38325e97 | −0.467245 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.79631e97 | 0.551168 | 0.275584 | − | 0.961277i | \(-0.411129\pi\) | ||||
0.275584 | + | 0.961277i | \(0.411129\pi\) | |||||||
\(410\) | 4.76790e98 | 4.99957 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 4.27573e97 | 0.373563 | ||||||||
\(413\) | −3.43579e97 | −0.274094 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.26113e97 | 0.549839 | ||||||||
\(416\) | −4.10810e97 | −0.249828 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2.58788e98 | −1.31472 | ||||||||
\(419\) | −2.11564e98 | −0.982688 | −0.491344 | − | 0.870966i | \(-0.663494\pi\) | ||||
−0.491344 | + | 0.870966i | \(0.663494\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.18038e97 | −0.0847137 | −0.0423569 | − | 0.999103i | \(-0.513487\pi\) | ||||
−0.0423569 | + | 0.999103i | \(0.513487\pi\) | |||||||
\(422\) | −5.62345e98 | −1.99887 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.29458e98 | 0.385398 | ||||||||
\(425\) | −3.77539e97 | −0.102891 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.60196e97 | 0.150878 | ||||||||
\(428\) | 1.56790e99 | 3.28229 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.32075e99 | 4.07907 | ||||||||
\(431\) | 3.92051e98 | 0.631605 | 0.315802 | − | 0.948825i | \(-0.397726\pi\) | ||||
0.315802 | + | 0.948825i | \(0.397726\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.09183e98 | −1.23128 | −0.615638 | − | 0.788029i | \(-0.711102\pi\) | ||||
−0.615638 | + | 0.788029i | \(0.711102\pi\) | |||||||
\(434\) | 2.76299e98 | 0.343174 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.42058e99 | −3.57567 | ||||||||
\(437\) | −9.99911e98 | −0.959196 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.19604e98 | −0.743330 | −0.371665 | − | 0.928367i | \(-0.621213\pi\) | ||||
−0.371665 | + | 0.928367i | \(0.621213\pi\) | |||||||
\(440\) | 3.00737e99 | 2.23209 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.23771e97 | 0.0140110 | ||||||||
\(443\) | −3.04060e99 | −1.74912 | −0.874561 | − | 0.484915i | \(-0.838850\pi\) | ||||
−0.874561 | + | 0.484915i | \(0.838850\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.97855e98 | 0.290466 | ||||||||
\(446\) | 2.03929e99 | 0.910798 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.45968e99 | 0.551229 | ||||||||
\(449\) | −1.16326e99 | −0.404055 | −0.202027 | − | 0.979380i | \(-0.564753\pi\) | ||||
−0.202027 | + | 0.979380i | \(0.564753\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.00955e99 | 0.884873 | ||||||||
\(452\) | 3.67077e99 | 0.993268 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2.06776e99 | −0.474140 | ||||||||
\(455\) | −1.57030e98 | −0.0331555 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.88576e99 | 0.516895 | 0.258447 | − | 0.966025i | \(-0.416789\pi\) | ||||
0.258447 | + | 0.966025i | \(0.416789\pi\) | |||||||
\(458\) | 1.98111e98 | 0.0326929 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.90032e100 | 2.66322 | ||||||||
\(461\) | 8.99071e99 | 1.16147 | 0.580737 | − | 0.814092i | \(-0.302765\pi\) | ||||
0.580737 | + | 0.814092i | \(0.302765\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.13924e98 | 0.0454604 | 0.0227302 | − | 0.999742i | \(-0.492764\pi\) | ||||
0.0227302 | + | 0.999742i | \(0.492764\pi\) | |||||||
\(464\) | −3.71706e100 | −3.76509 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.87754e100 | −3.34260 | ||||||||
\(467\) | −1.66999e99 | −0.132840 | −0.0664202 | − | 0.997792i | \(-0.521158\pi\) | ||||
−0.0664202 | + | 0.997792i | \(0.521158\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.17649e99 | −0.215261 | ||||||||
\(470\) | 5.16009e100 | 3.22840 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 6.17651e100 | 3.29548 | ||||||||
\(473\) | 1.46488e100 | 0.721953 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.09840e100 | 1.72427 | ||||||||
\(476\) | −1.35685e99 | −0.0527561 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −3.95570e100 | −1.31425 | ||||||||
\(479\) | 3.76475e99 | 0.115652 | 0.0578262 | − | 0.998327i | \(-0.481583\pi\) | ||||
0.0578262 | + | 0.998327i | \(0.481583\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.17575e99 | −0.0834461 | ||||||||
\(482\) | −1.40310e101 | −3.41055 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −9.26302e100 | −1.92775 | ||||||||
\(485\) | −3.33363e100 | −0.642099 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.27929e100 | −0.706376 | −0.353188 | − | 0.935552i | \(-0.614902\pi\) | ||||
−0.353188 | + | 0.935552i | \(0.614902\pi\) | |||||||
\(488\) | −1.18683e101 | −1.81404 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.02681e101 | −2.65741 | ||||||||
\(491\) | −7.91421e100 | −0.961284 | −0.480642 | − | 0.876917i | \(-0.659596\pi\) | ||||
−0.480642 | + | 0.876917i | \(0.659596\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.80198e99 | 0.102224 | ||||||||
\(494\) | −2.42916e100 | −0.234799 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.69410e101 | −2.23795 | ||||||||
\(497\) | −2.17247e98 | −0.00167336 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.93019e101 | 1.27888 | 0.639441 | − | 0.768840i | \(-0.279166\pi\) | ||||
0.639441 | + | 0.768840i | \(0.279166\pi\) | |||||||
\(500\) | −1.51862e101 | −0.933415 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1.81432e101 | −0.960120 | ||||||||
\(503\) | 3.34549e101 | 1.64308 | 0.821542 | − | 0.570147i | \(-0.193114\pi\) | ||||
0.821542 | + | 0.570147i | \(0.193114\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.06813e100 | −0.299142 | ||||||||
\(506\) | 1.66554e101 | 0.654500 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 5.60787e101 | 1.90068 | ||||||||
\(509\) | −2.90608e101 | −0.914935 | −0.457467 | − | 0.889226i | \(-0.651243\pi\) | ||||
−0.457467 | + | 0.889226i | \(0.651243\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.32530e101 | −0.360188 | ||||||||
\(512\) | 2.21256e101 | 0.558819 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1.15626e102 | 2.52313 | ||||||||
\(515\) | −1.07125e101 | −0.217331 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.25710e101 | 0.571394 | ||||||||
\(518\) | 2.67381e101 | 0.436280 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2.82292e101 | 0.398634 | ||||||||
\(521\) | −9.37841e101 | −1.23230 | −0.616148 | − | 0.787631i | \(-0.711308\pi\) | ||||
−0.616148 | + | 0.787631i | \(0.711308\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.17575e101 | 0.816684 | 0.408342 | − | 0.912829i | \(-0.366107\pi\) | ||||
0.408342 | + | 0.912829i | \(0.366107\pi\) | |||||||
\(524\) | 1.70536e102 | 1.80672 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.53203e102 | −1.40703 | ||||||||
\(527\) | 7.10442e100 | 0.0607618 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.04150e101 | −0.522489 | ||||||||
\(530\) | −5.30437e101 | −0.366681 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.47295e102 | 0.884098 | ||||||||
\(533\) | 2.82497e101 | 0.158031 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.92827e102 | −1.90956 | ||||||||
\(536\) | 5.71037e102 | 2.58812 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 7.25030e102 | 2.85773 | ||||||||
\(539\) | −1.27934e102 | −0.470335 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.17380e102 | −1.33547 | −0.667734 | − | 0.744400i | \(-0.732736\pi\) | ||||
−0.667734 | + | 0.744400i | \(0.732736\pi\) | |||||||
\(542\) | −8.21173e102 | −2.45167 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 8.89354e101 | 0.231268 | ||||||||
\(545\) | 8.57004e102 | 2.08024 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.04913e102 | 1.06830 | 0.534148 | − | 0.845391i | \(-0.320633\pi\) | ||||
0.534148 | + | 0.845391i | \(0.320633\pi\) | |||||||
\(548\) | 2.39951e103 | 4.74079 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −6.82665e102 | −1.17654 | ||||||||
\(551\) | −1.06406e103 | −1.71310 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.81535e102 | −0.255133 | ||||||||
\(554\) | −1.24470e103 | −1.63473 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 7.28375e102 | 0.835700 | ||||||||
\(557\) | −2.22240e102 | −0.238371 | −0.119185 | − | 0.992872i | \(-0.538028\pi\) | ||||
−0.119185 | + | 0.992872i | \(0.538028\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.37504e102 | 0.128935 | ||||||||
\(560\) | −1.28914e103 | −1.13045 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2.63762e103 | −2.02349 | ||||||||
\(563\) | 2.54936e103 | 1.82964 | 0.914822 | − | 0.403858i | \(-0.132331\pi\) | ||||
0.914822 | + | 0.403858i | \(0.132331\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.19687e102 | −0.577861 | ||||||||
\(566\) | −4.08307e103 | −2.40088 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.90544e101 | 0.0201191 | ||||||||
\(569\) | 6.38673e102 | 0.308013 | 0.154006 | − | 0.988070i | \(-0.450782\pi\) | ||||
0.154006 | + | 0.988070i | \(0.450782\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.66278e103 | 1.12585 | 0.562925 | − | 0.826508i | \(-0.309676\pi\) | ||||
0.562925 | + | 0.826508i | \(0.309676\pi\) | |||||||
\(572\) | 2.91404e102 | 0.115384 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2.37847e103 | −0.826231 | ||||||||
\(575\) | −2.63769e103 | −0.858381 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.56700e103 | 0.447689 | 0.223844 | − | 0.974625i | \(-0.428139\pi\) | ||||
0.223844 | + | 0.974625i | \(0.428139\pi\) | |||||||
\(578\) | 7.01247e103 | 1.87749 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2.02224e104 | 4.75644 | ||||||||
\(581\) | −4.12107e102 | −0.0908667 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.34817e102 | −0.0648988 | ||||||||
\(584\) | 2.38248e104 | 4.33060 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.78184e103 | 0.284910 | ||||||||
\(587\) | −8.05760e102 | −0.120858 | −0.0604292 | − | 0.998172i | \(-0.519247\pi\) | ||||
−0.0604292 | + | 0.998172i | \(0.519247\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.71227e103 | −1.01826 | ||||||||
\(590\) | −2.53074e104 | −3.13543 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.60714e104 | −2.84512 | ||||||||
\(593\) | 6.05490e103 | 0.620234 | 0.310117 | − | 0.950698i | \(-0.399632\pi\) | ||||
0.310117 | + | 0.950698i | \(0.399632\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.39951e102 | 0.0306923 | ||||||||
\(596\) | −2.99061e104 | −2.53527 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.56339e103 | 0.116889 | ||||||||
\(599\) | −2.34648e104 | −1.64782 | −0.823912 | − | 0.566718i | \(-0.808213\pi\) | ||||
−0.823912 | + | 0.566718i | \(0.808213\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.86432e104 | −1.15539 | −0.577693 | − | 0.816254i | \(-0.696047\pi\) | ||||
−0.577693 | + | 0.816254i | \(0.696047\pi\) | |||||||
\(602\) | −1.15771e104 | −0.674108 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.10701e104 | −0.569203 | ||||||||
\(605\) | 2.32078e104 | 1.12152 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.83308e104 | −0.782718 | −0.391359 | − | 0.920238i | \(-0.627995\pi\) | ||||
−0.391359 | + | 0.920238i | \(0.627995\pi\) | |||||||
\(608\) | −9.65446e104 | −3.87564 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4.86288e104 | 1.72594 | ||||||||
\(611\) | 3.05734e103 | 0.102046 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.12669e104 | −0.923244 | −0.461622 | − | 0.887077i | \(-0.652732\pi\) | ||||
−0.461622 | + | 0.887077i | \(0.652732\pi\) | |||||||
\(614\) | 2.03420e104 | 0.565041 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.50023e104 | −0.368876 | ||||||||
\(617\) | 2.66517e103 | 0.0616640 | 0.0308320 | − | 0.999525i | \(-0.490184\pi\) | ||||
0.0308320 | + | 0.999525i | \(0.490184\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.58700e103 | 0.0325220 | 0.0162610 | − | 0.999868i | \(-0.494824\pi\) | ||||
0.0162610 | + | 0.999868i | \(0.494824\pi\) | |||||||
\(620\) | 1.46571e105 | 2.82721 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1.41376e105 | −2.41677 | ||||||||
\(623\) | −2.98240e103 | −0.0480026 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.89860e104 | −0.699152 | ||||||||
\(626\) | −1.05060e105 | −1.41221 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.08897e105 | 2.49141 | ||||||||
\(629\) | 6.87511e103 | 0.0772468 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.59377e105 | 1.58974 | 0.794868 | − | 0.606782i | \(-0.207540\pi\) | ||||
0.794868 | + | 0.606782i | \(0.207540\pi\) | |||||||
\(632\) | 3.26345e105 | 3.06751 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −2.65675e104 | −0.221822 | ||||||||
\(635\) | −1.40501e105 | −1.10577 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.20088e104 | −0.0839981 | ||||||||
\(638\) | 1.77239e105 | 1.16892 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 3.62300e105 | 2.12480 | ||||||||
\(641\) | −1.17862e105 | −0.651925 | −0.325962 | − | 0.945383i | \(-0.605688\pi\) | ||||
−0.325962 | + | 0.945383i | \(0.605688\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.50923e105 | −1.23489 | −0.617447 | − | 0.786612i | \(-0.711833\pi\) | ||||
−0.617447 | + | 0.786612i | \(0.711833\pi\) | |||||||
\(644\) | −9.47974e104 | −0.440125 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5.25884e104 | 0.217355 | ||||||||
\(647\) | −4.06698e105 | −1.58621 | −0.793107 | − | 0.609082i | \(-0.791538\pi\) | ||||
−0.793107 | + | 0.609082i | \(0.791538\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.59743e105 | −0.554940 | ||||||||
\(650\) | −6.40796e104 | −0.210121 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.11294e106 | 3.25226 | ||||||||
\(653\) | 3.54682e105 | 0.978576 | 0.489288 | − | 0.872122i | \(-0.337257\pi\) | ||||
0.489288 | + | 0.872122i | \(0.337257\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.27265e105 | −1.05111 | ||||||||
\(656\) | 2.31917e106 | 5.38813 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2.57411e105 | −0.533527 | ||||||||
\(659\) | −1.86786e105 | −0.365714 | −0.182857 | − | 0.983140i | \(-0.558535\pi\) | ||||
−0.182857 | + | 0.983140i | \(0.558535\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.71414e105 | 1.17337 | 0.586686 | − | 0.809815i | \(-0.300432\pi\) | ||||
0.586686 | + | 0.809815i | \(0.300432\pi\) | |||||||
\(662\) | 7.14843e105 | 1.18042 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 7.40843e105 | 1.09251 | ||||||||
\(665\) | −3.69036e105 | −0.514348 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.84821e105 | 0.852822 | ||||||||
\(668\) | −3.58675e106 | −4.22264 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2.33975e106 | −2.46243 | ||||||||
\(671\) | 3.06950e105 | 0.305473 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.00080e106 | −1.78090 | −0.890448 | − | 0.455086i | \(-0.849609\pi\) | ||||
−0.890448 | + | 0.455086i | \(0.849609\pi\) | |||||||
\(674\) | 2.33983e106 | 1.96987 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3.38914e106 | −2.55322 | ||||||||
\(677\) | −7.19375e105 | −0.512720 | −0.256360 | − | 0.966581i | \(-0.582523\pi\) | ||||
−0.256360 | + | 0.966581i | \(0.582523\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.66298e105 | 0.106114 | ||||||||
\(680\) | −6.11128e105 | −0.369019 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.28462e106 | 0.694802 | ||||||||
\(683\) | −2.35846e106 | −1.20740 | −0.603700 | − | 0.797211i | \(-0.706308\pi\) | ||||
−0.603700 | + | 0.797211i | \(0.706308\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.01180e106 | −2.75809 | ||||||||
\(686\) | 2.08810e106 | 0.906978 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.12884e107 | 4.39608 | ||||||||
\(689\) | −3.14282e104 | −0.0115904 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.49985e105 | −0.115777 | −0.0578885 | − | 0.998323i | \(-0.518437\pi\) | ||||
−0.0578885 | + | 0.998323i | \(0.518437\pi\) | |||||||
\(692\) | −4.02936e106 | −1.26258 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 9.02408e105 | 0.253760 | ||||||||
\(695\) | −1.82489e106 | −0.486191 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.11571e105 | −0.146291 | ||||||||
\(698\) | −1.03043e106 | −0.233583 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 3.88553e106 | 0.791176 | ||||||||
\(701\) | −1.66052e106 | −0.320493 | −0.160247 | − | 0.987077i | \(-0.551229\pi\) | ||||
−0.160247 | + | 0.987077i | \(0.551229\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.46334e106 | −1.29452 | ||||||||
\(704\) | 6.78661e106 | 1.11604 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.46912e107 | 2.17210 | ||||||||
\(707\) | 3.52594e105 | 0.0494364 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.35084e107 | −1.70361 | −0.851805 | − | 0.523858i | \(-0.824492\pi\) | ||||
−0.851805 | + | 0.523858i | \(0.824492\pi\) | |||||||
\(710\) | −1.60020e105 | −0.0191420 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 5.36146e106 | 0.577143 | ||||||||
\(713\) | 4.96354e106 | 0.506914 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.30092e105 | −0.0671276 | ||||||||
\(716\) | −1.05777e107 | −0.922896 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 2.84330e107 | 2.23438 | ||||||||
\(719\) | 1.69563e107 | 1.26473 | 0.632364 | − | 0.774671i | \(-0.282085\pi\) | ||||
0.632364 | + | 0.774671i | \(0.282085\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.34395e105 | 0.0359162 | ||||||||
\(722\) | −2.74591e107 | −1.75203 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2.13968e107 | −1.23070 | ||||||||
\(725\) | −2.80692e107 | −1.53305 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.53639e107 | −1.74189 | −0.870944 | − | 0.491382i | \(-0.836492\pi\) | ||||
−0.870944 | + | 0.491382i | \(0.836492\pi\) | |||||||
\(728\) | −1.40822e106 | −0.0658784 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −9.76191e107 | −4.12029 | ||||||||
\(731\) | −2.97678e106 | −0.119356 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.06459e107 | 0.385286 | 0.192643 | − | 0.981269i | \(-0.438294\pi\) | ||||
0.192643 | + | 0.981269i | \(0.438294\pi\) | |||||||
\(734\) | −2.12147e107 | −0.729514 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.21352e107 | 1.92939 | ||||||||
\(737\) | −1.47687e107 | −0.435825 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.41863e107 | −0.378184 | −0.189092 | − | 0.981959i | \(-0.560554\pi\) | ||||
−0.189092 | + | 0.981959i | \(0.560554\pi\) | |||||||
\(740\) | 1.41840e108 | 3.59425 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.64609e106 | 0.0605979 | ||||||||
\(743\) | −5.02005e107 | −1.09302 | −0.546510 | − | 0.837453i | \(-0.684044\pi\) | ||||
−0.546510 | + | 0.837453i | \(0.684044\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.49276e107 | 1.47496 | ||||||||
\(746\) | −1.23971e108 | −2.32067 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −6.30854e106 | −0.106812 | ||||||||
\(749\) | 1.95962e107 | 0.315575 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.03488e107 | −1.02508 | −0.512541 | − | 0.858663i | \(-0.671296\pi\) | ||||
−0.512541 | + | 0.858663i | \(0.671296\pi\) | |||||||
\(752\) | 2.50993e108 | 3.47931 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.66369e107 | 0.208760 | ||||||||
\(755\) | 2.77354e107 | 0.331150 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.78445e108 | −1.92934 | −0.964670 | − | 0.263461i | \(-0.915136\pi\) | ||||
−0.964670 | + | 0.263461i | \(0.915136\pi\) | |||||||
\(758\) | 1.34712e108 | 1.38615 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 6.63416e108 | 6.18409 | ||||||||
\(761\) | −1.13160e108 | −1.00408 | −0.502041 | − | 0.864844i | \(-0.667417\pi\) | ||||
−0.502041 | + | 0.864844i | \(0.667417\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.27517e107 | −0.343782 | ||||||||
\(764\) | 8.33197e107 | 0.637892 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.81137e108 | −1.95137 | ||||||||
\(767\) | −1.49946e107 | −0.0991077 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.36032e107 | 0.261385 | 0.130692 | − | 0.991423i | \(-0.458280\pi\) | ||||
0.130692 | + | 0.991423i | \(0.458280\pi\) | |||||||
\(770\) | 6.14698e107 | 0.350962 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2.76008e108 | 1.42979 | ||||||||
\(773\) | −1.42158e108 | −0.701518 | −0.350759 | − | 0.936466i | \(-0.614076\pi\) | ||||
−0.350759 | + | 0.936466i | \(0.614076\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.03444e108 | −0.911237 | ||||||||
\(776\) | −2.98954e108 | −1.27582 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 8.94664e108 | 3.46677 | ||||||||
\(779\) | 6.63896e108 | 2.45158 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.01006e106 | −0.00338793 | ||||||||
\(782\) | −3.38454e107 | −0.108205 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −9.85864e108 | −2.86394 | ||||||||
\(785\) | −5.23377e108 | −1.44945 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.52484e108 | 0.635597 | 0.317799 | − | 0.948158i | \(-0.397056\pi\) | ||||
0.317799 | + | 0.948158i | \(0.397056\pi\) | |||||||
\(788\) | 1.35543e109 | 3.25344 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1.33715e109 | −2.91854 | ||||||||
\(791\) | 4.58786e107 | 0.0954975 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.88124e107 | 0.0545551 | ||||||||
\(794\) | −2.08762e108 | −0.377035 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.09406e109 | 1.79804 | ||||||||
\(797\) | 3.24886e108 | 0.509383 | 0.254691 | − | 0.967022i | \(-0.418026\pi\) | ||||
0.254691 | + | 0.967022i | \(0.418026\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.61876e107 | −0.0944653 | ||||||||
\(800\) | −2.54678e109 | −3.46830 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −8.27011e108 | −1.02559 | ||||||||
\(803\) | −6.16182e108 | −0.729249 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.37508e108 | 0.256055 | ||||||||
\(806\) | 1.20583e108 | 0.124086 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −6.33857e108 | −0.594382 | ||||||||
\(809\) | −7.50813e108 | −0.672144 | −0.336072 | − | 0.941836i | \(-0.609099\pi\) | ||||
−0.336072 | + | 0.941836i | \(0.609099\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.73314e108 | −0.631065 | −0.315533 | − | 0.948915i | \(-0.602183\pi\) | ||||
−0.315533 | + | 0.948915i | \(0.602183\pi\) | |||||||
\(812\) | −1.00879e109 | −0.786052 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.24316e109 | 0.883306 | ||||||||
\(815\) | −2.78839e109 | −1.89209 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.23147e109 | 2.00020 | ||||||||
\(818\) | −1.76238e109 | −1.04196 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.26173e110 | −6.80684 | ||||||||
\(821\) | 3.36586e109 | 1.73471 | 0.867356 | − | 0.497689i | \(-0.165818\pi\) | ||||
0.867356 | + | 0.497689i | \(0.165818\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.81695e109 | 0.854768 | 0.427384 | − | 0.904070i | \(-0.359435\pi\) | ||||
0.427384 | + | 0.904070i | \(0.359435\pi\) | |||||||
\(824\) | −9.60681e108 | −0.431826 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.26246e109 | 0.518163 | ||||||||
\(827\) | 2.22688e109 | 0.873454 | 0.436727 | − | 0.899594i | \(-0.356138\pi\) | ||||
0.436727 | + | 0.899594i | \(0.356138\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.37867e109 | −0.493931 | −0.246965 | − | 0.969024i | \(-0.579433\pi\) | ||||
−0.246965 | + | 0.969024i | \(0.579433\pi\) | |||||||
\(830\) | −3.03551e109 | −1.03945 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 6.37037e108 | 0.199315 | ||||||||
\(833\) | 2.59975e108 | 0.0777578 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.98636e109 | 2.45664 | ||||||||
\(836\) | 6.84829e109 | 1.78997 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 7.77379e109 | 1.85773 | ||||||||
\(839\) | 4.92096e109 | 1.12454 | 0.562272 | − | 0.826953i | \(-0.309928\pi\) | ||||
0.562272 | + | 0.826953i | \(0.309928\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.50293e109 | 0.523116 | ||||||||
\(842\) | 8.01169e108 | 0.160148 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.48813e110 | 2.72144 | ||||||||
\(845\) | 8.49126e109 | 1.48541 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.15772e109 | −0.185343 | ||||||||
\(848\) | −2.58011e109 | −0.395179 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.38724e109 | 0.194511 | ||||||||
\(851\) | 4.80334e109 | 0.644443 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.45733e110 | −1.79048 | −0.895239 | − | 0.445587i | \(-0.852995\pi\) | ||||
−0.895239 | + | 0.445587i | \(0.852995\pi\) | |||||||
\(854\) | −2.42585e109 | −0.285229 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.52280e110 | −3.79422 | ||||||||
\(857\) | −1.15609e109 | −0.119182 | −0.0595910 | − | 0.998223i | \(-0.518980\pi\) | ||||
−0.0595910 | + | 0.998223i | \(0.518980\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.68941e110 | 1.59585 | 0.797924 | − | 0.602758i | \(-0.205932\pi\) | ||||
0.797924 | + | 0.602758i | \(0.205932\pi\) | |||||||
\(860\) | −6.14137e110 | −5.55359 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.44057e110 | −1.19402 | ||||||||
\(863\) | −6.04075e109 | −0.479386 | −0.239693 | − | 0.970849i | \(-0.577047\pi\) | ||||
−0.239693 | + | 0.970849i | \(0.577047\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.00953e110 | 0.734538 | ||||||||
\(866\) | 3.34074e110 | 2.32767 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −7.31168e109 | −0.467227 | ||||||||
\(869\) | −8.44025e109 | −0.516551 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.38629e109 | −0.0778348 | ||||||||
\(872\) | 7.68546e110 | 4.13334 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 3.67412e110 | 1.81332 | ||||||||
\(875\) | −1.89803e109 | −0.0897430 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.52884e107 | −0.00283368 | −0.00141684 | − | 0.999999i | \(-0.500451\pi\) | ||||
−0.00141684 | + | 0.999999i | \(0.500451\pi\) | |||||||
\(878\) | 3.37904e110 | 1.40523 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −5.99372e110 | −2.28874 | ||||||||
\(881\) | −3.50306e110 | −1.28189 | −0.640946 | − | 0.767586i | \(-0.721458\pi\) | ||||
−0.640946 | + | 0.767586i | \(0.721458\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.71634e110 | −0.912973 | −0.456487 | − | 0.889730i | \(-0.650892\pi\) | ||||
−0.456487 | + | 0.889730i | \(0.650892\pi\) | |||||||
\(884\) | −5.92162e108 | −0.0190757 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.11725e111 | 3.30664 | ||||||||
\(887\) | 1.19560e110 | 0.339194 | 0.169597 | − | 0.985513i | \(-0.445753\pi\) | ||||
0.169597 | + | 0.985513i | \(0.445753\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.00892e109 | 0.182740 | ||||||||
\(890\) | −2.19678e110 | −0.549114 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −5.39655e110 | −1.24004 | ||||||||
\(893\) | 7.18505e110 | 1.58307 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.65017e110 | 0.536920 | ||||||||
\(896\) | −1.80733e110 | −0.351146 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 4.27434e110 | 0.763848 | ||||||||
\(899\) | 5.28199e110 | 0.905335 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.80382e108 | 0.0107293 | ||||||||
\(902\) | −1.10584e111 | −1.67281 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −8.24759e110 | −1.14818 | ||||||||
\(905\) | 5.36083e110 | 0.715995 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.20263e111 | 1.47863 | 0.739315 | − | 0.673359i | \(-0.235149\pi\) | ||||
0.739315 | + | 0.673359i | \(0.235149\pi\) | |||||||
\(908\) | 5.47190e110 | 0.645534 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 5.76998e109 | 0.0626790 | ||||||||
\(911\) | −1.56417e111 | −1.63059 | −0.815297 | − | 0.579042i | \(-0.803427\pi\) | ||||
−0.815297 | + | 0.579042i | \(0.803427\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.91604e110 | −0.183972 | ||||||||
\(914\) | −1.06036e111 | −0.977168 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5.24260e109 | −0.0445109 | ||||||||
\(917\) | 2.13141e110 | 0.173707 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.97001e111 | 1.47957 | 0.739787 | − | 0.672841i | \(-0.234926\pi\) | ||||
0.739787 | + | 0.672841i | \(0.234926\pi\) | |||||||
\(920\) | −4.26968e111 | −3.07859 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −3.30359e111 | −2.19571 | ||||||||
\(923\) | −9.48114e107 | −0.000605058 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.96878e111 | −1.15846 | ||||||||
\(926\) | −1.52094e110 | −0.0859409 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 6.61216e111 | 3.44583 | ||||||||
\(929\) | 5.85098e110 | 0.292846 | 0.146423 | − | 0.989222i | \(-0.453224\pi\) | ||||
0.146423 | + | 0.989222i | \(0.453224\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.82218e111 | −1.30308 | ||||||||
\(932\) | 1.02611e112 | 4.55090 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 6.13628e110 | 0.251129 | ||||||||
\(935\) | 1.58056e110 | 0.0621406 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.05778e111 | 1.47249 | 0.736247 | − | 0.676713i | \(-0.236596\pi\) | ||||
0.736247 | + | 0.676713i | \(0.236596\pi\) | |||||||
\(938\) | 1.16718e111 | 0.406942 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.36551e112 | −4.39542 | ||||||||
\(941\) | −3.76642e111 | −1.16498 | −0.582489 | − | 0.812839i | \(-0.697921\pi\) | ||||
−0.582489 | + | 0.812839i | \(0.697921\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.27277e111 | −1.22045 | ||||||||
\(944\) | −1.23098e112 | −3.37911 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5.38262e111 | −1.36482 | ||||||||
\(947\) | 1.55286e111 | 0.378450 | 0.189225 | − | 0.981934i | \(-0.439403\pi\) | ||||
0.189225 | + | 0.981934i | \(0.439403\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.78390e110 | −0.130238 | ||||||||
\(950\) | −1.50594e112 | −3.25965 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 3.04862e110 | 0.0609842 | ||||||||
\(953\) | −3.52427e111 | −0.677775 | −0.338887 | − | 0.940827i | \(-0.610051\pi\) | ||||
−0.338887 | + | 0.940827i | \(0.610051\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.08752e111 | −0.371111 | ||||||||
\(956\) | 1.04679e112 | 1.78933 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.38334e111 | −0.218636 | ||||||||
\(959\) | 2.99899e111 | 0.455803 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.28586e111 | −0.461872 | ||||||||
\(962\) | 1.16691e111 | 0.157751 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 3.71300e112 | 4.64341 | ||||||||
\(965\) | −6.91520e111 | −0.831822 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.78672e111 | −0.644080 | −0.322040 | − | 0.946726i | \(-0.604369\pi\) | ||||
−0.322040 | + | 0.946726i | \(0.604369\pi\) | |||||||
\(968\) | 2.08124e112 | 2.22841 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1.22492e112 | 1.21386 | ||||||||
\(971\) | 1.04108e111 | 0.0992577 | 0.0496288 | − | 0.998768i | \(-0.484196\pi\) | ||||
0.0496288 | + | 0.998768i | \(0.484196\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.10348e110 | 0.0803482 | ||||||||
\(974\) | 1.57240e112 | 1.33537 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.36537e112 | 1.86007 | ||||||||
\(977\) | −1.54003e111 | −0.116542 | −0.0582711 | − | 0.998301i | \(-0.518559\pi\) | ||||
−0.0582711 | + | 0.998301i | \(0.518559\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.38663e111 | −0.0971875 | ||||||||
\(980\) | 5.36352e112 | 3.61803 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 2.90803e112 | 1.81727 | ||||||||
\(983\) | 9.94251e110 | 0.0598052 | 0.0299026 | − | 0.999553i | \(-0.490480\pi\) | ||||
0.0299026 | + | 0.999553i | \(0.490480\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.39593e112 | −1.89278 | ||||||||
\(986\) | −3.60168e111 | −0.193251 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 6.42827e111 | 0.319675 | ||||||||
\(989\) | −2.07975e112 | −0.995748 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.08266e112 | −0.924392 | −0.462196 | − | 0.886778i | \(-0.652938\pi\) | ||||
−0.462196 | + | 0.886778i | \(0.652938\pi\) | |||||||
\(992\) | 4.79246e112 | 2.04819 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 7.98261e109 | 0.00316341 | ||||||||
\(995\) | −2.74108e112 | −1.04606 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.02320e112 | 0.362152 | 0.181076 | − | 0.983469i | \(-0.442042\pi\) | ||||
0.181076 | + | 0.983469i | \(0.442042\pi\) | |||||||
\(998\) | −7.09239e112 | −2.41767 | ||||||||
\(999\) | 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 | 9.76.a.c.1.1 | 6 | ||
3.2 | odd | 2 | 1.76.a.a.1.6 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.76.a.a.1.6 | ✓ | 6 | 3.2 | odd | 2 | ||
9.76.a.c.1.1 | 6 | 1.1 | even | 1 | trivial |