Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1792,2,Mod(895,1792)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1792, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1792.895");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1792 = 2^{8} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1792.e (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: | \(14.3091920422\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.12745506816.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 23x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 896) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 895.6 | ||
Root | \(0.323042 + 0.323042i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1792.895 |
Dual form | 1792.2.e.e.895.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1792\mathbb{Z}\right)^\times\).
\(n\) | \(1023\) | \(1025\) | \(1541\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | 0.646084i | 0.373017i | 0.982453 | + | 0.186508i | \(0.0597171\pi\) | ||||
−0.982453 | + | 0.186508i | \(0.940283\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.646084 | 0.288937 | 0.144469 | − | 0.989509i | \(-0.453853\pi\) | ||||
0.144469 | + | 0.989509i | \(0.453853\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.44949 | + | 1.00000i | −0.925820 | + | 0.377964i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.58258 | 0.860859 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.58258 | −1.08019 | −0.540094 | − | 0.841605i | \(-0.681611\pi\) | ||||
−0.540094 | + | 0.841605i | \(0.681611\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.54506 | 1.53792 | 0.768962 | − | 0.639295i | \(-0.220774\pi\) | ||||
0.768962 | + | 0.639295i | \(0.220774\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.417424i | 0.107778i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 6.19115i | − | 1.50157i | −0.660545 | − | 0.750787i | \(-0.729675\pi\) | ||
0.660545 | − | 0.750787i | \(-0.270325\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 6.83723i | − | 1.56857i | −0.620402 | − | 0.784284i | \(-0.713030\pi\) | ||
0.620402 | − | 0.784284i | \(-0.286970\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.646084 | − | 1.58258i | −0.140987 | − | 0.345346i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 5.58258i | − | 1.16405i | −0.813172 | − | 0.582024i | \(-0.802261\pi\) | ||
0.813172 | − | 0.582024i | \(-0.197739\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.58258 | −0.916515 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.60681i | 0.694131i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.00000i | 1.11417i | 0.830455 | + | 0.557086i | \(0.188081\pi\) | ||||
−0.830455 | + | 0.557086i | \(0.811919\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.19115 | 1.11196 | 0.555981 | − | 0.831195i | \(-0.312343\pi\) | ||||
0.555981 | + | 0.831195i | \(0.312343\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 2.31464i | − | 0.402928i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.58258 | + | 0.646084i | −0.267504 | + | 0.109208i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 2.00000i | − | 0.328798i | −0.986394 | − | 0.164399i | \(-0.947432\pi\) | ||
0.986394 | − | 0.164399i | \(-0.0525685\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.58258i | 0.573671i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.29217i | 0.201803i | 0.994896 | + | 0.100901i | \(0.0321726\pi\) | ||||
−0.994896 | + | 0.100901i | \(0.967827\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.58258 | 0.546338 | 0.273169 | − | 0.961966i | \(-0.411928\pi\) | ||||
0.273169 | + | 0.961966i | \(0.411928\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.66856 | 0.248734 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.19115 | 0.903072 | 0.451536 | − | 0.892253i | \(-0.350876\pi\) | ||||
0.451536 | + | 0.892253i | \(0.350876\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.00000 | − | 4.89898i | 0.714286 | − | 0.699854i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.00000 | 0.560112 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.16515i | 1.25893i | 0.777029 | + | 0.629465i | \(0.216726\pi\) | ||||
−0.777029 | + | 0.629465i | \(0.783274\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.31464 | −0.312107 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.41742 | 0.585102 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.54506i | 0.721906i | 0.932584 | + | 0.360953i | \(0.117548\pi\) | ||||
−0.932584 | + | 0.360953i | \(0.882452\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.4440 | 1.33722 | 0.668611 | − | 0.743612i | \(-0.266889\pi\) | ||||
0.668611 | + | 0.743612i | \(0.266889\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.32599 | + | 2.58258i | −0.797000 | + | 0.325374i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.58258 | 0.444364 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.41742 | 0.539674 | 0.269837 | − | 0.962906i | \(-0.413030\pi\) | ||||
0.269837 | + | 0.962906i | \(0.413030\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.60681 | 0.434209 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 9.16515i | − | 1.08770i | −0.839181 | − | 0.543852i | \(-0.816965\pi\) | ||
0.839181 | − | 0.543852i | \(-0.183035\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 7.48331i | − | 0.875856i | −0.899010 | − | 0.437928i | \(-0.855713\pi\) | ||
0.899010 | − | 0.437928i | \(-0.144287\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 2.96073i | − | 0.341875i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 8.77548 | − | 3.58258i | 1.00006 | − | 0.408272i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 2.00000i | − | 0.225018i | −0.993651 | − | 0.112509i | \(-0.964111\pi\) | ||
0.993651 | − | 0.112509i | \(-0.0358886\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.41742 | 0.601936 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.646084i | 0.0709169i | 0.999371 | + | 0.0354585i | \(0.0112891\pi\) | ||||
−0.999371 | + | 0.0354585i | \(0.988711\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 4.00000i | − | 0.433861i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.87650 | −0.415605 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 7.48331i | − | 0.793230i | −0.917985 | − | 0.396615i | \(-0.870185\pi\) | ||
0.917985 | − | 0.396615i | \(-0.129815\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −13.5826 | + | 5.54506i | −1.42384 | + | 0.581281i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.00000i | 0.414781i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 4.41742i | − | 0.453218i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 18.5734i | − | 1.88585i | −0.333009 | − | 0.942924i | \(-0.608064\pi\) | ||
0.333009 | − | 0.942924i | \(-0.391936\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −9.25227 | −0.929888 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.96073 | 0.294603 | 0.147302 | − | 0.989092i | \(-0.452941\pi\) | ||||
0.147302 | + | 0.989092i | \(0.452941\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.29217 | −0.127321 | −0.0636605 | − | 0.997972i | \(-0.520277\pi\) | ||||
−0.0636605 | + | 0.997972i | \(0.520277\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.417424 | − | 1.02248i | −0.0407364 | − | 0.0997835i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.5826 | 1.50642 | 0.753212 | − | 0.657778i | \(-0.228503\pi\) | ||||
0.753212 | + | 0.657778i | \(0.228503\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.16515i | 0.494732i | 0.968922 | + | 0.247366i | \(0.0795650\pi\) | ||||
−0.968922 | + | 0.247366i | \(0.920435\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.29217 | 0.122647 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −13.5826 | −1.27774 | −0.638871 | − | 0.769314i | \(-0.720598\pi\) | ||||
−0.638871 | + | 0.769314i | \(0.720598\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 3.60681i | − | 0.336337i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 14.3205 | 1.32393 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.19115 | + | 15.1652i | 0.567542 | + | 1.39019i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.83485 | 0.166804 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.834849 | −0.0752758 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.19115 | −0.553753 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.5826i | 1.56020i | 0.625654 | + | 0.780101i | \(0.284832\pi\) | ||||
−0.625654 | + | 0.780101i | \(0.715168\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.31464i | 0.203793i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.85971i | 0.686706i | 0.939206 | + | 0.343353i | \(0.111563\pi\) | ||||
−0.939206 | + | 0.343353i | \(0.888437\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.83723 | + | 16.7477i | 0.592863 | + | 1.45221i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.33030i | 0.200561i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.16515 | 0.0995456 | 0.0497728 | − | 0.998761i | \(-0.484150\pi\) | ||||
0.0497728 | + | 0.998761i | \(0.484150\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 19.2195i | − | 1.63018i | −0.579335 | − | 0.815089i | \(-0.696688\pi\) | ||
0.579335 | − | 0.815089i | \(-0.303312\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.00000i | 0.336861i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −19.8656 | −1.66125 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.87650i | 0.321926i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.16515 | + | 3.23042i | 0.261057 | + | 0.266440i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 1.16515i | − | 0.0954529i | −0.998860 | − | 0.0477265i | \(-0.984802\pi\) | ||
0.998860 | − | 0.0477265i | \(-0.0151976\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.41742i | 0.196727i | 0.995151 | + | 0.0983636i | \(0.0313608\pi\) | ||||
−0.995151 | + | 0.0983636i | \(0.968639\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 15.9891i | − | 1.29264i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.00000 | 0.321288 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.96073 | 0.236292 | 0.118146 | − | 0.992996i | \(-0.462305\pi\) | ||||
0.118146 | + | 0.992996i | \(0.462305\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.92146 | −0.469602 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.58258 | + | 13.6745i | 0.439969 | + | 1.07770i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.58258 | 0.280609 | 0.140304 | − | 0.990108i | \(-0.455192\pi\) | ||||
0.140304 | + | 0.990108i | \(0.455192\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − | 1.49545i | − | 0.116421i | ||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11.0901 | 0.858180 | 0.429090 | − | 0.903262i | \(-0.358834\pi\) | ||||
0.429090 | + | 0.903262i | \(0.358834\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 17.7477 | 1.36521 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 17.6577i | − | 1.35032i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −16.6352 | −1.26475 | −0.632375 | − | 0.774662i | \(-0.717920\pi\) | ||||
−0.632375 | + | 0.774662i | \(0.717920\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 11.2250 | − | 4.58258i | 0.848528 | − | 0.346410i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.58258 | −0.269283 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 7.58258 | 0.566748 | 0.283374 | − | 0.959009i | \(-0.408546\pi\) | ||||
0.283374 | + | 0.959009i | \(0.408546\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.52259 | −0.336161 | −0.168081 | − | 0.985773i | \(-0.553757\pi\) | ||||
−0.168081 | + | 0.985773i | \(0.553757\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.74773i | 0.498806i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 1.29217i | − | 0.0950021i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 22.1803i | 1.62198i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.60681 | − | 8.83485i | −0.262357 | − | 0.642641i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 21.1652i | − | 1.53146i | −0.643164 | − | 0.765728i | \(-0.722379\pi\) | ||
0.643164 | − | 0.765728i | \(-0.277621\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.58258 | 0.689769 | 0.344884 | − | 0.938645i | \(-0.387918\pi\) | ||||
0.344884 | + | 0.938645i | \(0.387918\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.31464i | 0.165755i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 18.0000i | − | 1.28245i | −0.767354 | − | 0.641223i | \(-0.778427\pi\) | ||
0.767354 | − | 0.641223i | \(-0.221573\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.29217 | 0.0915993 | 0.0457997 | − | 0.998951i | \(-0.485416\pi\) | ||||
0.0457997 | + | 0.998951i | \(0.485416\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.85403i | 0.201307i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6.00000 | − | 14.6969i | −0.421117 | − | 1.03152i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.834849i | 0.0583084i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 14.4174i | − | 1.00208i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 24.4949i | 1.69435i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −25.9129 | −1.78392 | −0.891958 | − | 0.452118i | \(-0.850669\pi\) | ||||
−0.891958 | + | 0.452118i | \(0.850669\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.92146 | 0.405731 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.31464 | 0.157857 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −15.1652 | + | 6.19115i | −1.02948 | + | 0.420282i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.83485 | 0.326709 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 34.3303i | − | 2.30931i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.58434 | −0.173060 | −0.0865299 | − | 0.996249i | \(-0.527578\pi\) | ||||
−0.0865299 | + | 0.996249i | \(0.527578\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −11.8348 | −0.788990 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.7587i | 0.846824i | 0.905937 | + | 0.423412i | \(0.139168\pi\) | ||||
−0.905937 | + | 0.423412i | \(0.860832\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.66856 | −0.110262 | −0.0551308 | − | 0.998479i | \(-0.517558\pi\) | ||||
−0.0551308 | + | 0.998479i | \(0.517558\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.31464 | + | 5.66970i | 0.152292 | + | 0.373039i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.16515 | −0.0763316 | −0.0381658 | − | 0.999271i | \(-0.512152\pi\) | ||||
−0.0381658 | + | 0.999271i | \(0.512152\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.00000 | 0.260931 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.29217 | 0.0839353 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 25.5826i | 1.65480i | 0.561614 | + | 0.827400i | \(0.310181\pi\) | ||||
−0.561614 | + | 0.827400i | \(0.689819\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 6.19115i | − | 0.398807i | −0.979917 | − | 0.199403i | \(-0.936100\pi\) | ||
0.979917 | − | 0.199403i | \(-0.0639004\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.3205i | 0.918663i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.23042 | − | 3.16515i | 0.206384 | − | 0.202214i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 37.9129i | − | 2.41234i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.417424 | −0.0264532 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.4440i | 0.659222i | 0.944117 | + | 0.329611i | \(0.106918\pi\) | ||||
−0.944117 | + | 0.329611i | \(0.893082\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 20.0000i | 1.25739i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.58434 | 0.161837 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 9.79796i | 0.611180i | 0.952163 | + | 0.305590i | \(0.0988537\pi\) | ||||
−0.952163 | + | 0.305590i | \(0.901146\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.00000 | + | 4.89898i | 0.124274 | + | 0.304408i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 15.4955i | 0.959145i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.83485i | 0.421455i | 0.977545 | + | 0.210727i | \(0.0675832\pi\) | ||||
−0.977545 | + | 0.210727i | \(0.932417\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.92146i | 0.363752i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.83485 | 0.295888 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −23.8488 | −1.45409 | −0.727044 | − | 0.686591i | \(-0.759106\pi\) | ||||
−0.727044 | + | 0.686591i | \(0.759106\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.5510 | −1.06615 | −0.533073 | − | 0.846070i | \(-0.678963\pi\) | ||||
−0.533073 | + | 0.846070i | \(0.678963\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.58258 | − | 8.77548i | −0.216827 | − | 0.531116i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 16.4174 | 0.990008 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.33030i | 0.500519i | 0.968179 | + | 0.250260i | \(0.0805160\pi\) | ||||
−0.968179 | + | 0.250260i | \(0.919484\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 15.9891 | 0.957243 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.0000 | 0.596550 | 0.298275 | − | 0.954480i | \(-0.403589\pi\) | ||||
0.298275 | + | 0.954480i | \(0.403589\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 20.2420i | 1.20326i | 0.798774 | + | 0.601631i | \(0.205482\pi\) | ||||
−0.798774 | + | 0.601631i | \(0.794518\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.85403 | 0.169058 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.29217 | − | 3.16515i | −0.0762742 | − | 0.186833i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −21.3303 | −1.25472 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.0000 | 0.703452 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.66856 | −0.0974783 | −0.0487392 | − | 0.998812i | \(-0.515520\pi\) | ||||
−0.0487392 | + | 0.998812i | \(0.515520\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.58258i | 0.208586i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 12.9217i | − | 0.749792i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 30.9557i | − | 1.79022i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.77548 | + | 3.58258i | −0.505810 | + | 0.206496i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.91288i | 0.109892i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.74773 | 0.386374 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 24.1185i | − | 1.37652i | −0.725466 | − | 0.688258i | \(-0.758376\pi\) | ||
0.725466 | − | 0.688258i | \(-0.241624\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 0.834849i | − | 0.0474929i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.269691 | 0.0152928 | 0.00764639 | − | 0.999971i | \(-0.497566\pi\) | ||||
0.00764639 | + | 0.999971i | \(0.497566\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.0901i | 0.626851i | 0.949613 | + | 0.313426i | \(0.101477\pi\) | ||||
−0.949613 | + | 0.313426i | \(0.898523\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.08712 | + | 1.66856i | −0.230283 | + | 0.0940127i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.33030i | 0.467876i | 0.972251 | + | 0.233938i | \(0.0751613\pi\) | ||||
−0.972251 | + | 0.233938i | \(0.924839\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 21.4955i | − | 1.20351i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 10.0677i | 0.561921i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −42.3303 | −2.35532 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −25.4107 | −1.40953 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.33712 | −0.184543 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −15.1652 | + | 6.19115i | −0.836082 | + | 0.341329i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.4174 | 1.34210 | 0.671052 | − | 0.741411i | \(-0.265843\pi\) | ||||
0.671052 | + | 0.741411i | \(0.265843\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 5.16515i | − | 0.283049i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.85403 | 0.155932 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.74773 | 0.476519 | 0.238260 | − | 0.971202i | \(-0.423423\pi\) | ||||
0.238260 | + | 0.971202i | \(0.423423\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 8.77548i | − | 0.476619i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −22.1803 | −1.20113 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.34847 | + | 17.0000i | −0.396780 | + | 0.917914i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.33030 | 0.125459 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −26.7477 | −1.43589 | −0.717947 | − | 0.696098i | \(-0.754918\pi\) | ||||
−0.717947 | + | 0.696098i | \(0.754918\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.93825 | −0.103752 | −0.0518761 | − | 0.998654i | \(-0.516520\pi\) | ||||
−0.0518761 | + | 0.998654i | \(0.516520\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 20.0000i | 1.06752i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 17.0116i | 0.905435i | 0.891654 | + | 0.452718i | \(0.149545\pi\) | ||||
−0.891654 | + | 0.452718i | \(0.850455\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 5.92146i | − | 0.314278i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −9.79796 | + | 4.00000i | −0.518563 | + | 0.211702i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 13.5826i | − | 0.716861i | −0.933556 | − | 0.358430i | \(-0.883312\pi\) | ||
0.933556 | − | 0.358430i | \(-0.116688\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −27.7477 | −1.46041 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.18547i | 0.0622208i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 4.83485i | − | 0.253068i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 29.3939 | 1.53435 | 0.767174 | − | 0.641439i | \(-0.221662\pi\) | ||||
0.767174 | + | 0.641439i | \(0.221662\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.33712i | 0.173724i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9.16515 | − | 22.4499i | −0.475831 | − | 1.16554i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 28.3303i | − | 1.46689i | −0.679750 | − | 0.733444i | \(-0.737912\pi\) | ||
0.679750 | − | 0.733444i | \(-0.262088\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 4.00000i | − | 0.206559i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 33.2704i | 1.71351i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −29.9129 | −1.53652 | −0.768261 | − | 0.640137i | \(-0.778878\pi\) | ||||
−0.768261 | + | 0.640137i | \(0.778878\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −11.3598 | −0.581981 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 23.7421 | 1.21317 | 0.606583 | − | 0.795020i | \(-0.292540\pi\) | ||||
0.606583 | + | 0.795020i | \(0.292540\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.66970 | − | 2.31464i | 0.288955 | − | 0.117965i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 9.25227 | 0.470319 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 2.00000i | − | 0.101404i | −0.998714 | − | 0.0507020i | \(-0.983854\pi\) | ||
0.998714 | − | 0.0507020i | \(-0.0161459\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −34.5625 | −1.74790 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.07803 | −0.256153 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 1.29217i | − | 0.0650160i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 22.8263 | 1.14562 | 0.572811 | − | 0.819688i | \(-0.305853\pi\) | ||||
0.572811 | + | 0.819688i | \(0.305853\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −10.8204 | + | 4.41742i | −0.541699 | + | 0.221148i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.41742 | −0.320471 | −0.160235 | − | 0.987079i | \(-0.551225\pi\) | ||||
−0.160235 | + | 0.987079i | \(0.551225\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 34.3303 | 1.71011 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.50011 | 0.173922 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.16515i | 0.355163i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 31.2254i | 1.54400i | 0.635624 | + | 0.771999i | \(0.280743\pi\) | ||||
−0.635624 | + | 0.771999i | \(0.719257\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.752785i | 0.0371322i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −5.54506 | − | 13.5826i | −0.272855 | − | 0.668355i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.417424i | 0.0204906i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 12.4174 | 0.608084 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 27.9950i | 1.36765i | 0.729648 | + | 0.683823i | \(0.239684\pi\) | ||||
−0.729648 | + | 0.683823i | \(0.760316\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 31.4955i | − | 1.53499i | −0.641052 | − | 0.767497i | \(-0.721502\pi\) | ||
0.641052 | − | 0.767497i | \(-0.278498\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 15.9891 | 0.777417 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 28.3714i | 1.37622i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −25.5826 | + | 10.4440i | −1.23803 | + | 0.505423i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 12.8348i | − | 0.619672i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 4.74773i | − | 0.228690i | −0.993441 | − | 0.114345i | \(-0.963523\pi\) | ||
0.993441 | − | 0.114345i | \(-0.0364769\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 10.8204i | − | 0.519997i | −0.965609 | − | 0.259998i | \(-0.916278\pi\) | ||
0.965609 | − | 0.259998i | \(-0.0837221\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.50455 | −0.120084 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −38.1694 | −1.82589 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −19.8656 | −0.948134 | −0.474067 | − | 0.880489i | \(-0.657215\pi\) | ||||
−0.474067 | + | 0.880489i | \(0.657215\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 12.9129 | − | 12.6520i | 0.614899 | − | 0.602475i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 22.7477 | 1.08078 | 0.540389 | − | 0.841416i | \(-0.318277\pi\) | ||||
0.540389 | + | 0.841416i | \(0.318277\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 4.83485i | − | 0.229194i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0.752785 | 0.0356055 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −35.4955 | −1.67513 | −0.837567 | − | 0.546335i | \(-0.816023\pi\) | ||||
−0.837567 | + | 0.546335i | \(0.816023\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 4.62929i | − | 0.217985i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.56186 | −0.0733825 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −8.77548 | + | 3.58258i | −0.411401 | + | 0.167954i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.74773 | 0.222089 | 0.111045 | − | 0.993815i | \(-0.464580\pi\) | ||||
0.111045 | + | 0.993815i | \(0.464580\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 22.3303 | 1.04229 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −24.1185 | −1.12331 | −0.561655 | − | 0.827371i | \(-0.689835\pi\) | ||||
−0.561655 | + | 0.827371i | \(0.689835\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.1652i | 0.797732i | 0.917009 | + | 0.398866i | \(0.130596\pi\) | ||||
−0.917009 | + | 0.398866i | \(0.869404\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.58434i | 0.119846i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 36.2311i | − | 1.67658i | −0.545228 | − | 0.838288i | \(-0.683557\pi\) | ||
0.545228 | − | 0.838288i | \(-0.316443\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.8204 | + | 4.41742i | −0.499641 | + | 0.203978i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.91288i | 0.0881408i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −12.8348 | −0.590147 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 31.3321i | 1.43762i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 23.6697i | 1.08376i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −15.9891 | −0.730561 | −0.365280 | − | 0.930898i | \(-0.619027\pi\) | ||||
−0.365280 | + | 0.930898i | \(0.619027\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 11.0901i | − | 0.505666i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −8.83485 | + | 3.60681i | −0.402000 | + | 0.164116i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 12.0000i | − | 0.544892i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 7.25227i | − | 0.328632i | −0.986408 | − | 0.164316i | \(-0.947458\pi\) | ||
0.986408 | − | 0.164316i | \(-0.0525417\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.31464i | 0.104672i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.58258 | 0.161679 | 0.0808397 | − | 0.996727i | \(-0.474240\pi\) | ||||
0.0808397 | + | 0.996727i | \(0.474240\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 37.1469 | 1.67301 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.97774 | −0.268680 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9.16515 | + | 22.4499i | 0.411113 | + | 1.00702i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11.5826 | 0.518507 | 0.259254 | − | 0.965809i | \(-0.416523\pi\) | ||||
0.259254 | + | 0.965809i | \(0.416523\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7.16515i | 0.320115i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −25.0343 | −1.11622 | −0.558112 | − | 0.829766i | \(-0.688474\pi\) | ||||
−0.558112 | + | 0.829766i | \(0.688474\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.91288 | 0.0851220 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 11.4665i | 0.509246i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −36.5008 | −1.61787 | −0.808935 | − | 0.587898i | \(-0.799955\pi\) | ||||
−0.808935 | + | 0.587898i | \(0.799955\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.48331 | + | 18.3303i | 0.331042 | + | 0.810885i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 24.6606 | 1.08879 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.834849 | −0.0367878 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −22.1803 | −0.975486 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 10.7477i | − | 0.471773i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 20.8881i | 0.915124i | 0.889178 | + | 0.457562i | \(0.151277\pi\) | ||||
−0.889178 | + | 0.457562i | \(0.848723\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.915775i | 0.0400440i | 0.999800 | + | 0.0200220i | \(0.00637363\pi\) | ||||
−0.999800 | + | 0.0200220i | \(0.993626\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.96073 | + | 7.25227i | 0.129217 | + | 0.316515i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 38.3303i | − | 1.66969i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.16515 | −0.355007 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 14.3205i | 0.621459i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.16515i | 0.310357i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10.0677 | 0.435262 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.89898i | 0.211407i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −17.9129 | + | 17.5510i | −0.771562 | + | 0.755974i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.8348i | 0.809773i | 0.914367 | + | 0.404887i | \(0.132689\pi\) | ||||
−0.914367 | + | 0.404887i | \(0.867311\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 2.92197i | − | 0.125394i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.33712i | 0.142947i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11.5826 | 0.495235 | 0.247618 | − | 0.968858i | \(-0.420352\pi\) | ||||
0.247618 | + | 0.968858i | \(0.420352\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 26.9725 | 1.15116 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 41.0234 | 1.74765 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.00000 | + | 4.89898i | 0.0850487 | + | 0.208326i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.834849 | 0.0354373 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 27.4955i | 1.16502i | 0.812824 | + | 0.582510i | \(0.197929\pi\) | ||||
−0.812824 | + | 0.582510i | \(0.802071\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 19.8656 | 0.840226 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −14.3303 | −0.605026 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 1.66856i | − | 0.0703214i | −0.999382 | − | 0.0351607i | \(-0.988806\pi\) | ||
0.999382 | − | 0.0351607i | \(-0.0111943\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.77548 | −0.369187 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −13.2699 | + | 5.41742i | −0.557284 | + | 0.227510i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −17.5826 | −0.737100 | −0.368550 | − | 0.929608i | \(-0.620146\pi\) | ||||
−0.368550 | + | 0.929608i | \(0.620146\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.58258 | 0.149926 | 0.0749631 | − | 0.997186i | \(-0.476116\pi\) | ||||
0.0749631 | + | 0.997186i | \(0.476116\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 13.6745 | 0.571259 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 25.5826i | 1.06687i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 34.5625i | − | 1.43886i | −0.694566 | − | 0.719429i | \(-0.744404\pi\) | ||
0.694566 | − | 0.719429i | \(-0.255596\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.19115i | 0.257295i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.646084 | − | 1.58258i | −0.0268041 | − | 0.0656563i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 32.8348i | − | 1.35988i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 9.25227 | 0.382534 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 6.83723i | − | 0.282203i | −0.989995 | − | 0.141101i | \(-0.954936\pi\) | ||
0.989995 | − | 0.141101i | \(-0.0450643\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 42.3303i | − | 1.74419i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 11.6295 | 0.478374 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 5.16867i | − | 0.212252i | −0.994353 | − | 0.106126i | \(-0.966155\pi\) | ||
0.994353 | − | 0.106126i | \(-0.0338447\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.00000 | + | 9.79796i | 0.163984 | + | 0.401677i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0.834849i | 0.0341681i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10.0000i | 0.408589i | 0.978909 | + | 0.204294i | \(0.0654900\pi\) | ||||
−0.978909 | + | 0.204294i | \(0.934510\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 19.8656i | − | 0.810335i | −0.914242 | − | 0.405168i | \(-0.867213\pi\) | ||
0.914242 | − | 0.405168i | \(-0.132787\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 11.4083 | 0.464583 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.18547 | 0.0481960 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 27.3489 | 1.11006 | 0.555029 | − | 0.831831i | \(-0.312707\pi\) | ||||
0.555029 | + | 0.831831i | \(0.312707\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 9.49545 | − | 3.87650i | 0.384775 | − | 0.157084i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 34.3303 | 1.38886 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 21.1652i | 0.854852i | 0.904050 | + | 0.427426i | \(0.140580\pi\) | ||||
−0.904050 | + | 0.427426i | \(0.859420\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.539382 | −0.0217500 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.41742 | −0.0973218 | −0.0486609 | − | 0.998815i | \(-0.515495\pi\) | ||||
−0.0486609 | + | 0.998815i | \(0.515495\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 29.2872i | − | 1.17715i | −0.808442 | − | 0.588575i | \(-0.799689\pi\) | ||
0.808442 | − | 0.588575i | \(-0.200311\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 20.1353 | 0.808002 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.48331 | + | 18.3303i | 0.299813 | + | 0.734388i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 18.9129 | 0.756515 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −15.8258 | −0.632020 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −12.3823 | −0.493714 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.66970i | 0.146088i | 0.997329 | + | 0.0730442i | \(0.0232714\pi\) | ||||
−0.997329 | + | 0.0730442i | \(0.976729\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 16.7419i | − | 0.665430i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 11.3598i | 0.450801i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 27.7253 | − | 27.1652i | 1.09852 | − | 1.07632i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 23.6697i | − | 0.936359i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −20.7477 | −0.819486 | −0.409743 | − | 0.912201i | \(-0.634382\pi\) | ||||
−0.409743 | + | 0.912201i | \(0.634382\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 24.3882i | − | 0.961777i | −0.876782 | − | 0.480888i | \(-0.840314\pi\) | ||
0.876782 | − | 0.480888i | \(-0.159686\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.49545i | 0.0588835i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −43.0683 | −1.69319 | −0.846596 | − | 0.532237i | \(-0.821352\pi\) | ||||
−0.846596 | + | 0.532237i | \(0.821352\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 19.8656i | − | 0.779793i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.00000 | − | 9.79796i | −0.156772 | − | 0.384012i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 27.4955i | − | 1.07598i | −0.842951 | − | 0.537990i | \(-0.819184\pi\) | ||
0.842951 | − | 0.537990i | \(-0.180816\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.07803i | 0.198415i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 19.3262i | − | 0.753988i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −17.2523 | −0.672053 | −0.336027 | − | 0.941853i | \(-0.609083\pi\) | ||||
−0.336027 | + | 0.941853i | \(0.609083\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 47.8606 | 1.86156 | 0.930781 | − | 0.365577i | \(-0.119128\pi\) | ||||
0.930781 | + | 0.365577i | \(0.119128\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 22.1803 | 0.861410 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.41742 | + | 10.8204i | 0.171300 | + | 0.419598i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 33.4955 | 1.29695 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 1.66970i | − | 0.0645542i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −37.4166 | −1.44445 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 36.3303 | 1.40043 | 0.700215 | − | 0.713932i | \(-0.253087\pi\) | ||||
0.700215 | + | 0.713932i | \(0.253087\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − | 16.5285i | − | 0.636182i | ||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −11.7362 | −0.451059 | −0.225530 | − | 0.974236i | \(-0.572411\pi\) | ||||
−0.225530 | + | 0.974236i | \(0.572411\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 18.5734 | + | 45.4955i | 0.712783 | + | 1.74596i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.24318 | −0.315879 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.417424 | −0.0159723 | −0.00798615 | − | 0.999968i | \(-0.502542\pi\) | ||||
−0.00798615 | + | 0.999968i | \(0.502542\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.752785 | 0.0287625 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 1.07803i | − | 0.0411294i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 50.8213i | 1.93614i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 25.4107i | 0.966668i | 0.875436 | + | 0.483334i | \(0.160574\pi\) | ||||
−0.875436 | + | 0.483334i | \(0.839426\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 22.6633 | − | 9.25227i | 0.860909 | − | 0.351465i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 12.4174i | − | 0.471020i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.00000 | 0.303022 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 0.752785i | − | 0.0284730i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 39.4955i | 1.49172i | 0.666101 | + | 0.745861i | \(0.267962\pi\) | ||||
−0.666101 | + | 0.745861i | \(0.732038\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −13.6745 | −0.515742 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.58434i | 0.0973317i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −7.25227 | + | 2.96073i | −0.272750 | + | 0.111350i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 5.16515i | − | 0.193981i | −0.995285 | − | 0.0969907i | \(-0.969078\pi\) | ||
0.995285 | − | 0.0969907i | \(-0.0309217\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 5.16515i | − | 0.193708i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 34.5625i | − | 1.29438i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12.8348 | −0.479996 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −16.5285 | −0.617268 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −40.7537 | −1.51986 | −0.759928 | − | 0.650007i | \(-0.774766\pi\) | ||||
−0.759928 | + | 0.650007i | \(0.774766\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.16515 | − | 1.29217i | 0.117876 | − | 0.0481228i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4.00000 | 0.148762 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 27.4955i | − | 1.02116i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 31.2254 | 1.15809 | 0.579043 | − | 0.815297i | \(-0.303426\pi\) | ||||
0.579043 | + | 0.815297i | \(0.303426\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 7.00000 | 0.259259 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 22.1803i | − | 0.820366i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.10692 | −0.262500 | −0.131250 | − | 0.991349i | \(-0.541899\pi\) | ||||
−0.131250 | + | 0.991349i | \(0.541899\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.04495 | + | 2.08712i | 0.0754292 | + | 0.0769846i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −15.8258 | −0.582949 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −26.7477 | −0.983931 | −0.491966 | − | 0.870615i | \(-0.663721\pi\) | ||||
−0.491966 | + | 0.870615i | \(0.663721\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 24.4949 | 0.899843 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 40.7477i | 1.49489i | 0.664324 | + | 0.747445i | \(0.268719\pi\) | ||||
−0.664324 | + | 0.747445i | \(0.731281\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 0.752785i | − | 0.0275799i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.66856i | 0.0610494i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −38.1694 | + | 15.5826i | −1.39468 | + | 0.569375i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 11.0780i | − | 0.404243i | −0.979360 | − | 0.202122i | \(-0.935216\pi\) | ||
0.979360 | − | 0.202122i | \(-0.0647836\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −6.74773 | −0.245901 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.56186i | 0.0568419i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 30.8348i | 1.12071i | 0.828252 | + | 0.560356i | \(0.189336\pi\) | ||||
−0.828252 | + | 0.560356i | \(0.810664\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −12.9217 | −0.469027 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 28.6411i | − | 1.03824i | −0.854702 | − | 0.519119i | \(-0.826260\pi\) | ||
0.854702 | − | 0.519119i | \(-0.173740\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.16515 | − | 12.6520i | −0.186991 | − | 0.458033i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − | 10.3303i | − | 0.373493i | ||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 30.7477i | 1.11024i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 35.5850i | 1.28323i | 0.767027 | + | 0.641614i | \(0.221735\pi\) | ||||
−0.767027 | + | 0.641614i | \(0.778265\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.33030 | −0.227980 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 10.4440 | 0.375646 | 0.187823 | − | 0.982203i | \(-0.439857\pi\) | ||||
0.187823 | + | 0.982203i | \(0.439857\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −28.3714 | −1.01913 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3.16515 | + | 1.29217i | −0.113549 | + | 0.0463563i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 8.83485 | 0.316541 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 32.8348i | 1.17492i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −21.6409 | −0.773382 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.91288 | 0.0682736 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8.12940i | 0.289782i | 0.989448 | + | 0.144891i | \(0.0462831\pi\) | ||||
−0.989448 | + | 0.144891i | \(0.953717\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4.41589 | −0.157210 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 33.2704 | − | 13.5826i | 1.18296 | − | 0.482941i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 57.9129 | 2.05655 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.82576 | −0.135686 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5.54506 | 0.196416 | 0.0982081 | − | 0.995166i | \(-0.468689\pi\) | ||||
0.0982081 | + | 0.995166i | \(0.468689\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 38.3303i | − | 1.35603i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 19.3262i | − | 0.682859i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 26.8095i | 0.946088i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.60681 | + | 8.83485i | 0.127123 | + | 0.311387i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 15.4083i | − | 0.542399i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.58258 | −0.0556404 | −0.0278202 | − | 0.999613i | \(-0.508857\pi\) | ||||
−0.0278202 | + | 0.999613i | \(0.508857\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1.93825i | − | 0.0680612i | −0.999421 | − | 0.0340306i | \(-0.989166\pi\) | ||
0.999421 | − | 0.0340306i | \(-0.0108344\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 11.3394i | − | 0.397690i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.31464 | 0.0810784 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 24.4949i | − | 0.856968i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −35.0780 | + | 14.3205i | −1.22573 | + | 0.500400i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 54.6606i | 1.90767i | 0.300334 | + | 0.953834i | \(0.402902\pi\) | ||||
−0.300334 | + | 0.953834i | \(0.597098\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 18.8348i | − | 0.656542i | −0.944584 | − | 0.328271i | \(-0.893534\pi\) | ||
0.944584 | − | 0.328271i | \(-0.106466\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 10.6070i | 0.369289i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −25.9129 | −0.901079 | −0.450540 | − | 0.892756i | \(-0.648768\pi\) | ||||
−0.450540 | + | 0.892756i | \(0.648768\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.98320 | −0.138342 | −0.0691712 | − | 0.997605i | \(-0.522035\pi\) | ||||
−0.0691712 | + | 0.997605i | \(0.522035\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.38207 | −0.186702 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −30.3303 | − | 30.9557i | −1.05088 | − | 1.07255i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.16515 | 0.247960 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 22.3303i | 0.771848i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 20.8881 | 0.721137 | 0.360568 | − | 0.932733i | \(-0.382583\pi\) | ||||
0.360568 | + | 0.932733i | \(0.382583\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.00000 | −0.241379 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 6.46084i | 0.222523i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 11.4665 | 0.394460 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.49444 | + | 1.83485i | −0.154431 | + | 0.0630461i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −13.0780 | −0.448837 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −11.1652 | −0.382736 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 47.3212 | 1.62025 | 0.810124 | − | 0.586258i | \(-0.199400\pi\) | ||||
0.810124 | + | 0.586258i | \(0.199400\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 11.4083i | − | 0.390157i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 3.33712i | − | 0.113994i | −0.998374 | − | 0.0569969i | \(-0.981847\pi\) | ||
0.998374 | − | 0.0569969i | \(-0.0181525\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 13.7812i | − | 0.470207i | −0.971970 | − | 0.235104i | \(-0.924457\pi\) | ||
0.971970 | − | 0.235104i | \(-0.0755429\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.04495 | − | 0.834849i | 0.0696918 | − | 0.0284516i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 14.8348i | − | 0.504984i | −0.967599 | − | 0.252492i | \(-0.918750\pi\) | ||
0.967599 | − | 0.252492i | \(-0.0812502\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −10.7477 | −0.365434 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 13.7812i | − | 0.468033i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.16515i | 0.243061i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 24.4949 | 0.829978 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 47.9673i | − | 1.62345i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 15.1652 | − | 6.19115i | 0.512676 | − | 0.209299i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 32.3303i | 1.09172i | 0.837877 | + | 0.545858i | \(0.183796\pi\) | ||||
−0.837877 | + | 0.545858i | \(0.816204\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 1.07803i | − | 0.0363610i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 35.1019i | − | 1.18261i | −0.806447 | − | 0.591307i | \(-0.798612\pi\) | ||
0.806447 | − | 0.591307i | \(-0.201388\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 13.0780 | 0.440111 | 0.220055 | − | 0.975487i | \(-0.429376\pi\) | ||||
0.220055 | + | 0.975487i | \(0.429376\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.31464 | −0.0778059 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −28.6411 | −0.961674 | −0.480837 | − | 0.876810i | \(-0.659667\pi\) | ||||
−0.480837 | + | 0.876810i | \(0.659667\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −17.5826 | − | 43.0683i | −0.589701 | − | 1.44447i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −19.4083 | −0.650204 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 42.3303i | − | 1.41653i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.89898 | 0.163755 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 20.0000 | 0.667781 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 37.1469i | 1.23892i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 56.7428 | 1.89038 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.31464 | − | 5.66970i | −0.0770265 | − | 0.188676i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.92197 | −0.0971296 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.91288 | −0.196334 | −0.0981670 | − | 0.995170i | \(-0.531298\pi\) | ||||
−0.0981670 | + | 0.995170i | \(0.531298\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7.64630 | 0.253612 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 14.4174i | − | 0.477671i | −0.971060 | − | 0.238835i | \(-0.923234\pi\) | ||
0.971060 | − | 0.238835i | \(-0.0767656\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 2.31464i | − | 0.0766035i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 4.35960i | 0.144124i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −7.85971 | − | 19.2523i | −0.259550 | − | 0.635766i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 13.1652i | 0.434278i | 0.976141 | + | 0.217139i | \(0.0696725\pi\) | ||||
−0.976141 | + | 0.217139i | \(0.930327\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 15.5826 | 0.513463 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 50.8213i | − | 1.67280i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.16515i | 0.301348i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.33712 | −0.109605 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 33.0007i | 1.08272i | 0.840792 | + | 0.541359i | \(0.182090\pi\) | ||||
−0.840792 | + | 0.541359i | \(0.817910\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −33.4955 | − | 34.1862i | −1.09777 | − | 1.12041i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0.174243i | 0.00570446i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 14.3303i | 0.468651i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 6.94393i | − | 0.226848i | −0.993547 | − | 0.113424i | \(-0.963818\pi\) | ||
0.993547 | − | 0.113424i | \(-0.0361819\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7.16515 | −0.233826 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 25.6804 | 0.837156 | 0.418578 | − | 0.908181i | \(-0.362529\pi\) | ||||
0.418578 | + | 0.908181i | \(0.362529\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.21362 | 0.234908 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.33030 | − | 5.70805i | −0.0758048 | − | 0.185683i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 46.7477 | 1.51910 | 0.759549 | − | 0.650451i | \(-0.225420\pi\) | ||||
0.759549 | + | 0.650451i | \(0.225420\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 41.4955i | − | 1.34700i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.38207 | −0.174526 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −8.33030 | −0.269845 | −0.134922 | − | 0.990856i | \(-0.543079\pi\) | ||||
−0.134922 | + | 0.990856i | \(0.543079\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 13.6745i | − | 0.442495i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 13.8879 | 0.448931 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.85403 | + | 1.16515i | −0.0921613 | + | 0.0376247i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.33030 | 0.236461 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 40.2432 | 1.29682 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.19115 | 0.199300 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 47.0780i | 1.51393i | 0.653457 | + | 0.756964i | \(0.273318\pi\) | ||||
−0.653457 | + | 0.756964i | \(0.726682\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 27.3489i | − | 0.878574i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 37.5233i | 1.20418i | 0.798429 | + | 0.602090i | \(0.205665\pi\) | ||||
−0.798429 | + | 0.602090i | \(0.794335\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 19.2195 | + | 47.0780i | 0.616150 | + | 1.50925i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 16.4174i | − | 0.525778i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 31.4955 | 1.00763 | 0.503814 | − | 0.863812i | \(-0.331930\pi\) | ||||
0.503814 | + | 0.863812i | \(0.331930\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 26.8095i | 0.856837i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 13.3394i | 0.425894i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 48.2370 | 1.53852 | 0.769261 | − | 0.638935i | \(-0.220625\pi\) | ||||
0.769261 | + | 0.638935i | \(0.220625\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 11.6295i | − | 0.370547i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4.00000 | − | 9.79796i | −0.127321 | − | 0.311872i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 20.0000i | − | 0.635963i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 16.3303i | − | 0.518749i | −0.965777 | − | 0.259375i | \(-0.916484\pi\) | ||
0.965777 | − | 0.259375i | \(-0.0835164\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 15.7757i | 0.500627i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.834849 | 0.0264665 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.85971 | 0.248919 | 0.124460 | − | 0.992225i | \(-0.460280\pi\) | ||||
0.124460 | + | 0.992225i | \(0.460280\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.21362 | 0.228229 |
(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 | 1792.2.e.e.895.6 | 8 | ||
4.3 | odd | 2 | 1792.2.e.d.895.4 | 8 | |||
7.6 | odd | 2 | inner | 1792.2.e.e.895.3 | 8 | ||
8.3 | odd | 2 | inner | 1792.2.e.e.895.5 | 8 | ||
8.5 | even | 2 | 1792.2.e.d.895.3 | 8 | |||
16.3 | odd | 4 | 896.2.f.d.895.5 | yes | 8 | ||
16.5 | even | 4 | 896.2.f.c.895.6 | yes | 8 | ||
16.11 | odd | 4 | 896.2.f.c.895.4 | yes | 8 | ||
16.13 | even | 4 | 896.2.f.d.895.3 | yes | 8 | ||
28.27 | even | 2 | 1792.2.e.d.895.5 | 8 | |||
56.13 | odd | 2 | 1792.2.e.d.895.6 | 8 | |||
56.27 | even | 2 | inner | 1792.2.e.e.895.4 | 8 | ||
112.13 | odd | 4 | 896.2.f.d.895.6 | yes | 8 | ||
112.27 | even | 4 | 896.2.f.c.895.5 | yes | 8 | ||
112.69 | odd | 4 | 896.2.f.c.895.3 | ✓ | 8 | ||
112.83 | even | 4 | 896.2.f.d.895.4 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
896.2.f.c.895.3 | ✓ | 8 | 112.69 | odd | 4 | ||
896.2.f.c.895.4 | yes | 8 | 16.11 | odd | 4 | ||
896.2.f.c.895.5 | yes | 8 | 112.27 | even | 4 | ||
896.2.f.c.895.6 | yes | 8 | 16.5 | even | 4 | ||
896.2.f.d.895.3 | yes | 8 | 16.13 | even | 4 | ||
896.2.f.d.895.4 | yes | 8 | 112.83 | even | 4 | ||
896.2.f.d.895.5 | yes | 8 | 16.3 | odd | 4 | ||
896.2.f.d.895.6 | yes | 8 | 112.13 | odd | 4 | ||
1792.2.e.d.895.3 | 8 | 8.5 | even | 2 | |||
1792.2.e.d.895.4 | 8 | 4.3 | odd | 2 | |||
1792.2.e.d.895.5 | 8 | 28.27 | even | 2 | |||
1792.2.e.d.895.6 | 8 | 56.13 | odd | 2 | |||
1792.2.e.e.895.3 | 8 | 7.6 | odd | 2 | inner | ||
1792.2.e.e.895.4 | 8 | 56.27 | even | 2 | inner | ||
1792.2.e.e.895.5 | 8 | 8.3 | odd | 2 | inner | ||
1792.2.e.e.895.6 | 8 | 1.1 | even | 1 | trivial |