Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1568,3,Mod(97,1568)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1568, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1568.97");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1568 = 2^{5} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1568.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(42.7249054517\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 36x^{14} + 522x^{12} + 3644x^{10} + 12219x^{8} + 15156x^{6} + 15478x^{4} - 10992x^{2} + 11025 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{28} \) |
Twist minimal: | no (minimal twist has level 224) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 97.10 | ||
Root | \(0.707107 + 0.358323i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1568.97 |
Dual form | 1568.3.c.h.97.7 |
$q$-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 \(\left(\mathbb{Z}/1568\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(1471\) | \(1473\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 0.506745i | 0.168915i | 0.996427 | + | 0.0844575i | \(0.0269157\pi\) | ||||
−0.996427 | + | 0.0844575i | \(0.973084\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5.30261i | 1.06052i | 0.847835 | + | 0.530261i | \(0.177906\pi\) | ||||
−0.847835 | + | 0.530261i | \(0.822094\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 8.74321 | 0.971468 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −17.0900 | −1.55363 | −0.776817 | − | 0.629727i | \(-0.783167\pi\) | ||||
−0.776817 | + | 0.629727i | \(0.783167\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 21.4744i | 1.65187i | 0.563762 | + | 0.825937i | \(0.309353\pi\) | ||||
−0.563762 | + | 0.825937i | \(0.690647\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.68707 | −0.179138 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 24.0168i | − 1.41276i | −0.707835 | − | 0.706378i | \(-0.750328\pi\) | ||||
0.707835 | − | 0.706378i | \(-0.249672\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 12.2203i | 0.643175i | 0.946880 | + | 0.321588i | \(0.104216\pi\) | ||||
−0.946880 | + | 0.321588i | \(0.895784\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −40.2929 | −1.75186 | −0.875932 | − | 0.482435i | \(-0.839752\pi\) | ||||
−0.875932 | + | 0.482435i | \(0.839752\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.11765 | −0.124706 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 8.99128i | 0.333010i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −26.0770 | −0.899209 | −0.449604 | − | 0.893228i | \(-0.648435\pi\) | ||||
−0.449604 | + | 0.893228i | \(0.648435\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 25.2635i | − 0.814953i | −0.913216 | − | 0.407477i | \(-0.866409\pi\) | ||||
0.913216 | − | 0.407477i | \(-0.133591\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 8.66025i | − 0.262432i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 12.9625 | 0.350339 | 0.175169 | − | 0.984538i | \(-0.443953\pi\) | ||||
0.175169 | + | 0.984538i | \(0.443953\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −10.8820 | −0.279026 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 33.8721i | − 0.826150i | −0.910697 | − | 0.413075i | \(-0.864455\pi\) | ||||
0.910697 | − | 0.413075i | \(-0.135545\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 29.9958 | 0.697576 | 0.348788 | − | 0.937202i | \(-0.386593\pi\) | ||||
0.348788 | + | 0.937202i | \(0.386593\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 46.3618i | 1.03026i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 55.7476i | 1.18612i | 0.805159 | + | 0.593060i | \(0.202080\pi\) | ||||
−0.805159 | + | 0.593060i | \(0.797920\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 12.1704 | 0.238636 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.72723 | −0.164665 | −0.0823324 | − | 0.996605i | \(-0.526237\pi\) | ||||
−0.0823324 | + | 0.996605i | \(0.526237\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 90.6214i | − 1.64766i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.19259 | −0.108642 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 49.9862i | − 0.847224i | −0.905844 | − | 0.423612i | \(-0.860762\pi\) | ||||
0.905844 | − | 0.423612i | \(-0.139238\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 3.93621i | − 0.0645281i | −0.999479 | − | 0.0322640i | \(-0.989728\pi\) | ||||
0.999479 | − | 0.0322640i | \(-0.0102717\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −113.870 | −1.75185 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −105.885 | −1.58038 | −0.790189 | − | 0.612864i | \(-0.790018\pi\) | ||||
−0.790189 | + | 0.612864i | \(0.790018\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 20.4182i | − 0.295916i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −35.0232 | −0.493285 | −0.246642 | − | 0.969107i | \(-0.579327\pi\) | ||||
−0.246642 | + | 0.969107i | \(0.579327\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 46.6166i | 0.638584i | 0.947656 | + | 0.319292i | \(0.103445\pi\) | ||||
−0.947656 | + | 0.319292i | \(0.896555\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 1.57985i | − 0.0210647i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 86.9995 | 1.10126 | 0.550630 | − | 0.834750i | \(-0.314388\pi\) | ||||
0.550630 | + | 0.834750i | \(0.314388\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 74.1326 | 0.915217 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 64.0079i | − 0.771180i | −0.922670 | − | 0.385590i | \(-0.873998\pi\) | ||||
0.922670 | − | 0.385590i | \(-0.126002\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 127.352 | 1.49826 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 13.2144i | − 0.151890i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 42.9863i | − 0.482992i | −0.970402 | − | 0.241496i | \(-0.922362\pi\) | ||||
0.970402 | − | 0.241496i | \(-0.0776381\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 12.8022 | 0.137658 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −64.7996 | −0.682101 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 28.7493i | 0.296384i | 0.988959 | + | 0.148192i | \(0.0473454\pi\) | ||||
−0.988959 | + | 0.148192i | \(0.952655\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −149.421 | −1.50930 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 61.4690i | − 0.608604i | −0.952576 | − | 0.304302i | \(-0.901577\pi\) | ||||
0.952576 | − | 0.304302i | \(-0.0984232\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 59.7284i | − 0.579887i | −0.957044 | − | 0.289944i | \(-0.906363\pi\) | ||||
0.957044 | − | 0.289944i | \(-0.0936366\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −131.676 | −1.23062 | −0.615308 | − | 0.788287i | \(-0.710968\pi\) | ||||
−0.615308 | + | 0.788287i | \(0.710968\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −37.8091 | −0.346872 | −0.173436 | − | 0.984845i | \(-0.555487\pi\) | ||||
−0.173436 | + | 0.984845i | \(0.555487\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.56870i | 0.0591774i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −46.4443 | −0.411012 | −0.205506 | − | 0.978656i | \(-0.565884\pi\) | ||||
−0.205506 | + | 0.978656i | \(0.565884\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 213.657i | − 1.85789i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 187.755i | 1.60474i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 171.067 | 1.41378 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 17.1645 | 0.139549 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 116.034i | 0.928268i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.7816 | 0.100642 | 0.0503211 | − | 0.998733i | \(-0.483976\pi\) | ||||
0.0503211 | + | 0.998733i | \(0.483976\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 15.2002i | 0.117831i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 1.07311i | − 0.00819166i | −0.999992 | − | 0.00409583i | \(-0.998696\pi\) | ||||
0.999992 | − | 0.00409583i | \(-0.00130375\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −47.6772 | −0.353165 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −66.8659 | −0.488072 | −0.244036 | − | 0.969766i | \(-0.578472\pi\) | ||||
−0.244036 | + | 0.969766i | \(0.578472\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 221.071i | − 1.59044i | −0.606322 | − | 0.795219i | \(-0.707356\pi\) | ||||
0.606322 | − | 0.795219i | \(-0.292644\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −28.2498 | −0.200353 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 366.996i | − 2.56641i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − 138.276i | − 0.953630i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −39.5212 | −0.265243 | −0.132621 | − | 0.991167i | \(-0.542339\pi\) | ||||
−0.132621 | + | 0.991167i | \(0.542339\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −222.725 | −1.47500 | −0.737499 | − | 0.675348i | \(-0.763994\pi\) | ||||
−0.737499 | + | 0.675348i | \(0.763994\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 209.984i | − 1.37245i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 133.963 | 0.864275 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 202.166i | − 1.28768i | −0.765160 | − | 0.643840i | \(-0.777340\pi\) | ||||
0.765160 | − | 0.643840i | \(-0.222660\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − 4.42248i | − 0.0278144i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.63017 | 0.0161360 | 0.00806802 | − | 0.999967i | \(-0.497432\pi\) | ||||
0.00806802 | + | 0.999967i | \(0.497432\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 45.9219 | 0.278315 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 133.004i | − 0.796434i | −0.917291 | − | 0.398217i | \(-0.869629\pi\) | ||||
0.917291 | − | 0.398217i | \(-0.130371\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −292.148 | −1.72869 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 106.845i | 0.624824i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 97.0857i | − 0.561189i | −0.959826 | − | 0.280594i | \(-0.909468\pi\) | ||||
0.959826 | − | 0.280594i | \(-0.0905316\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 25.3303 | 0.143109 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −84.0371 | −0.469481 | −0.234740 | − | 0.972058i | \(-0.575424\pi\) | ||||
−0.234740 | + | 0.972058i | \(0.575424\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 214.347i | 1.18424i | 0.805851 | + | 0.592119i | \(0.201708\pi\) | ||||
−0.805851 | + | 0.592119i | \(0.798292\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.99466 | 0.0108998 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 68.7352i | 0.371542i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 410.447i | 2.19490i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −54.7374 | −0.286583 | −0.143292 | − | 0.989681i | \(-0.545769\pi\) | ||||
−0.143292 | + | 0.989681i | \(0.545769\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −348.300 | −1.80466 | −0.902332 | − | 0.431042i | \(-0.858146\pi\) | ||||
−0.902332 | + | 0.431042i | \(0.858146\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 57.7031i | − 0.295913i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 161.606 | 0.820337 | 0.410169 | − | 0.912010i | \(-0.365470\pi\) | ||||
0.410169 | + | 0.912010i | \(0.365470\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 137.624i | 0.691579i | 0.938312 | + | 0.345789i | \(0.112389\pi\) | ||||
−0.938312 | + | 0.345789i | \(0.887611\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − 53.6568i | − 0.266949i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 179.611 | 0.876150 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −352.289 | −1.70188 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 208.845i | − 0.999258i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −101.563 | −0.481341 | −0.240670 | − | 0.970607i | \(-0.577367\pi\) | ||||
−0.240670 | + | 0.970607i | \(0.577367\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 17.7478i | − 0.0833232i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 159.056i | 0.739795i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −23.6227 | −0.107866 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 515.747 | 2.33370 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 180.573i | 0.809744i | 0.914373 | + | 0.404872i | \(0.132684\pi\) | ||||
−0.914373 | + | 0.404872i | \(0.867316\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −27.2582 | −0.121148 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 50.7082i | − 0.223384i | −0.993743 | − | 0.111692i | \(-0.964373\pi\) | ||||
0.993743 | − | 0.111692i | \(-0.0356270\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 199.533i | 0.871323i | 0.900111 | + | 0.435661i | \(0.143486\pi\) | ||||
−0.900111 | + | 0.435661i | \(0.856514\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −177.158 | −0.760335 | −0.380167 | − | 0.924918i | \(-0.624134\pi\) | ||||
−0.380167 | + | 0.924918i | \(0.624134\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −295.608 | −1.25790 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 44.0866i | 0.186019i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −135.694 | −0.567756 | −0.283878 | − | 0.958860i | \(-0.591621\pi\) | ||||
−0.283878 | + | 0.958860i | \(0.591621\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 316.241i | 1.31220i | 0.754673 | + | 0.656101i | \(0.227795\pi\) | ||||
−0.754673 | + | 0.656101i | \(0.772205\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 118.488i | 0.487604i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −262.424 | −1.06244 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 32.4357 | 0.130264 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 40.1231i | − 0.159853i | −0.996801 | − | 0.0799265i | \(-0.974531\pi\) | ||||
0.996801 | − | 0.0799265i | \(-0.0254686\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 688.603 | 2.72175 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 64.5349i | 0.253078i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 173.673i | 0.675771i | 0.941187 | + | 0.337886i | \(0.109712\pi\) | ||||
−0.941187 | + | 0.337886i | \(0.890288\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −227.997 | −0.873552 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 364.581 | 1.38624 | 0.693120 | − | 0.720822i | \(-0.256236\pi\) | ||||
0.693120 | + | 0.720822i | \(0.256236\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − 46.2771i | − 0.174631i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 21.7831 | 0.0815846 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 17.4215i | 0.0647638i | 0.999476 | + | 0.0323819i | \(0.0103093\pi\) | ||||
−0.999476 | + | 0.0323819i | \(0.989691\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 130.264i | 0.480680i | 0.970689 | + | 0.240340i | \(0.0772590\pi\) | ||||
−0.970689 | + | 0.240340i | \(0.922741\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 53.2805 | 0.193747 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −249.190 | −0.899601 | −0.449801 | − | 0.893129i | \(-0.648505\pi\) | ||||
−0.449801 | + | 0.893129i | \(0.648505\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − 220.885i | − 0.791701i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −197.454 | −0.702684 | −0.351342 | − | 0.936247i | \(-0.614275\pi\) | ||||
−0.351342 | + | 0.936247i | \(0.614275\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 214.330i | − 0.757350i | −0.925530 | − | 0.378675i | \(-0.876380\pi\) | ||||
0.925530 | − | 0.378675i | \(-0.123620\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 32.8369i | − 0.115217i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −287.809 | −0.995879 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −14.5685 | −0.0500637 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 71.8385i | 0.245182i | 0.992457 | + | 0.122591i | \(0.0391204\pi\) | ||||
−0.992457 | + | 0.122591i | \(0.960880\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 265.057 | 0.898499 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 153.661i | − 0.517376i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 865.263i | − 2.89386i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 31.1491 | 0.102802 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 20.8722 | 0.0684334 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 507.046i | 1.65162i | 0.563951 | + | 0.825808i | \(0.309281\pi\) | ||||
−0.563951 | + | 0.825808i | \(0.690719\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 30.2671 | 0.0979516 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 310.718i | − 0.999092i | −0.866287 | − | 0.499546i | \(-0.833500\pi\) | ||||
0.866287 | − | 0.499546i | \(-0.166500\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 548.907i | − 1.75370i | −0.480767 | − | 0.876848i | \(-0.659642\pi\) | ||||
0.480767 | − | 0.876848i | \(-0.340358\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 141.930 | 0.447730 | 0.223865 | − | 0.974620i | \(-0.428133\pi\) | ||||
0.223865 | + | 0.974620i | \(0.428133\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 445.656 | 1.39704 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − 66.7261i | − 0.207869i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 293.494 | 0.908649 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 66.9495i | − 0.205998i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 19.1596i | − 0.0585919i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 36.8650 | 0.111375 | 0.0556873 | − | 0.998448i | \(-0.482265\pi\) | ||||
0.0556873 | + | 0.998448i | \(0.482265\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 113.334 | 0.340343 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 561.468i | − 1.67602i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −541.604 | −1.60713 | −0.803567 | − | 0.595214i | \(-0.797067\pi\) | ||||
−0.803567 | + | 0.595214i | \(0.797067\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 23.5354i | − 0.0694260i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 431.753i | 1.26614i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 108.270 | 0.313825 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 244.402 | 0.704328 | 0.352164 | − | 0.935938i | \(-0.385446\pi\) | ||||
0.352164 | + | 0.935938i | \(0.385446\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 190.205i | 0.545001i | 0.962156 | + | 0.272501i | \(0.0878507\pi\) | ||||
−0.962156 | + | 0.272501i | \(0.912149\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −193.082 | −0.550091 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 394.767i | 1.11832i | 0.829060 | + | 0.559160i | \(0.188876\pi\) | ||||
−0.829060 | + | 0.559160i | \(0.811124\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 185.714i | − 0.523139i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 296.325 | 0.825418 | 0.412709 | − | 0.910863i | \(-0.364583\pi\) | ||||
0.412709 | + | 0.910863i | \(0.364583\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 211.664 | 0.586326 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 86.6873i | 0.238808i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −247.190 | −0.677232 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 602.598i | 1.64196i | 0.570960 | + | 0.820978i | \(0.306571\pi\) | ||||
−0.570960 | + | 0.820978i | \(0.693429\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − 296.151i | − 0.802578i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 107.000 | 0.286862 | 0.143431 | − | 0.989660i | \(-0.454186\pi\) | ||||
0.143431 | + | 0.989660i | \(0.454186\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −58.7994 | −0.156798 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 559.988i | − 1.48538i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −539.901 | −1.42454 | −0.712270 | − | 0.701906i | \(-0.752333\pi\) | ||||
−0.712270 | + | 0.701906i | \(0.752333\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.47699i | 0.0170000i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 133.620i | − 0.348878i | −0.984668 | − | 0.174439i | \(-0.944189\pi\) | ||||
0.984668 | − | 0.174439i | \(-0.0558112\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 262.259 | 0.677673 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −571.255 | −1.46852 | −0.734260 | − | 0.678868i | \(-0.762471\pi\) | ||||
−0.734260 | + | 0.678868i | \(0.762471\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 967.707i | 2.47495i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.543792 | 0.00138369 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 461.324i | 1.16791i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 199.373i | 0.502198i | 0.967961 | + | 0.251099i | \(0.0807919\pi\) | ||||
−0.967961 | + | 0.251099i | \(0.919208\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 634.422 | 1.58210 | 0.791050 | − | 0.611752i | \(-0.209535\pi\) | ||||
0.791050 | + | 0.611752i | \(0.209535\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 542.519 | 1.34620 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 393.096i | 0.970608i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −221.529 | −0.544298 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − 689.821i | − 1.68661i | −0.537439 | − | 0.843303i | \(-0.680608\pi\) | ||||
0.537439 | − | 0.843303i | \(-0.319392\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 33.8840i | − 0.0824428i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 339.409 | 0.817853 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 112.027 | 0.268649 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 43.8224i | 0.104588i | 0.998632 | + | 0.0522940i | \(0.0166533\pi\) | ||||
−0.998632 | + | 0.0522940i | \(0.983347\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −357.611 | −0.849433 | −0.424717 | − | 0.905326i | \(-0.639626\pi\) | ||||
−0.424717 | + | 0.905326i | \(0.639626\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 487.413i | 1.15228i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 74.8761i | 0.176179i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 185.973 | 0.433505 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 286.518 | 0.664774 | 0.332387 | − | 0.943143i | \(-0.392146\pi\) | ||||
0.332387 | + | 0.943143i | \(0.392146\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 407.880i | 0.941986i | 0.882137 | + | 0.470993i | \(0.156104\pi\) | ||||
−0.882137 | + | 0.470993i | \(0.843896\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 70.0708 | 0.161082 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 492.392i | − 1.12675i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 54.0687i | 0.123163i | 0.998102 | + | 0.0615817i | \(0.0196145\pi\) | ||||
−0.998102 | + | 0.0615817i | \(0.980386\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 316.995 | 0.715564 | 0.357782 | − | 0.933805i | \(-0.383533\pi\) | ||||
0.357782 | + | 0.933805i | \(0.383533\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 227.940 | 0.512224 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 20.0272i | − 0.0448035i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 544.261 | 1.21216 | 0.606081 | − | 0.795403i | \(-0.292741\pi\) | ||||
0.606081 | + | 0.795403i | \(0.292741\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 578.874i | 1.28353i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 112.865i | − 0.249149i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −687.416 | −1.50419 | −0.752096 | − | 0.659053i | \(-0.770957\pi\) | ||||
−0.752096 | + | 0.659053i | \(0.770957\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 215.942 | 0.470462 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 676.260i | 1.46694i | 0.679721 | + | 0.733470i | \(0.262101\pi\) | ||||
−0.679721 | + | 0.733470i | \(0.737899\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 559.738 | 1.20894 | 0.604469 | − | 0.796629i | \(-0.293385\pi\) | ||||
0.604469 | + | 0.796629i | \(0.293385\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 67.8849i | 0.145989i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 369.373i | 0.790948i | 0.918477 | + | 0.395474i | \(0.129420\pi\) | ||||
−0.918477 | + | 0.395474i | \(0.870580\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 102.447 | 0.217509 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −512.627 | −1.08378 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 38.0987i | − 0.0802077i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −76.3040 | −0.159967 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 312.187i | 0.651747i | 0.945413 | + | 0.325874i | \(0.105658\pi\) | ||||
−0.945413 | + | 0.325874i | \(0.894342\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 278.362i | 0.578715i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −152.446 | −0.314322 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 280.389 | 0.575748 | 0.287874 | − | 0.957668i | \(-0.407052\pi\) | ||||
0.287874 | + | 0.957668i | \(0.407052\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.33283i | 0.00272562i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 423.804 | 0.863145 | 0.431573 | − | 0.902078i | \(-0.357959\pi\) | ||||
0.431573 | + | 0.902078i | \(0.357959\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 626.288i | 1.27036i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − 792.322i | − 1.60065i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −166.049 | −0.332763 | −0.166381 | − | 0.986061i | \(-0.553208\pi\) | ||||
−0.166381 | + | 0.986061i | \(0.553208\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 67.3993 | 0.134530 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 632.164i | 1.25679i | 0.777896 | + | 0.628393i | \(0.216287\pi\) | ||||
−0.777896 | + | 0.628393i | \(0.783713\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 325.946 | 0.645438 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 148.045i | − 0.292001i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 310.676i | 0.610365i | 0.952294 | + | 0.305183i | \(0.0987175\pi\) | ||||
−0.952294 | + | 0.305183i | \(0.901283\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −109.876 | −0.214184 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 316.716 | 0.614983 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 952.725i | − 1.84279i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 49.1977 | 0.0947932 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 67.0382i | 0.128672i | 0.997928 | + | 0.0643361i | \(0.0204930\pi\) | ||||
−0.997928 | + | 0.0643361i | \(0.979507\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 534.301i | 1.02161i | 0.859697 | + | 0.510804i | \(0.170652\pi\) | ||||
−0.859697 | + | 0.510804i | \(0.829348\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −606.751 | −1.15133 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1094.51 | 2.06902 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 437.040i | − 0.823051i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 727.383 | 1.36470 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 698.226i | − 1.30509i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 42.5854i | − 0.0793023i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 151.341 | 0.279744 | 0.139872 | − | 0.990170i | \(-0.455331\pi\) | ||||
0.139872 | + | 0.990170i | \(0.455331\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −108.619 | −0.200035 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 200.487i | − 0.367865i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 775.543 | 1.41781 | 0.708906 | − | 0.705303i | \(-0.249189\pi\) | ||||
0.708906 | + | 0.705303i | \(0.249189\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 34.4151i | − 0.0626869i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 318.670i | − 0.578349i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −34.8312 | −0.0627590 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 64.4399 | 0.115691 | 0.0578455 | − | 0.998326i | \(-0.481577\pi\) | ||||
0.0578455 | + | 0.998326i | \(0.481577\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 644.140i | 1.15231i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −207.992 | −0.370752 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 911.853i | 1.61963i | 0.586683 | + | 0.809816i | \(0.300433\pi\) | ||||
−0.586683 | + | 0.809816i | \(0.699567\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 246.276i | − 0.435887i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 236.004 | 0.414770 | 0.207385 | − | 0.978259i | \(-0.433505\pi\) | ||||
0.207385 | + | 0.978259i | \(0.433505\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 829.540 | 1.45278 | 0.726392 | − | 0.687280i | \(-0.241196\pi\) | ||||
0.726392 | + | 0.687280i | \(0.241196\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 27.7379i | − 0.0484082i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 125.619 | 0.218468 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 439.047i | 0.760914i | 0.924799 | + | 0.380457i | \(0.124233\pi\) | ||||
−0.924799 | + | 0.380457i | \(0.875767\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 176.499i | − 0.304835i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 149.148 | 0.255829 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −995.591 | −1.70186 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 871.738i | 1.48507i | 0.669805 | + | 0.742537i | \(0.266378\pi\) | ||||
−0.669805 | + | 0.742537i | \(0.733622\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 308.729 | 0.524158 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 81.8933i | 0.138567i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 765.147i | − 1.29030i | −0.764056 | − | 0.645149i | \(-0.776795\pi\) | ||||
0.764056 | − | 0.645149i | \(-0.223205\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −69.7404 | −0.116818 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −292.799 | −0.488813 | −0.244407 | − | 0.969673i | \(-0.578593\pi\) | ||||
−0.244407 | + | 0.969673i | \(0.578593\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − 748.440i | − 1.24532i | −0.782491 | − | 0.622662i | \(-0.786051\pi\) | ||||
0.782491 | − | 0.622662i | \(-0.213949\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −925.777 | −1.53529 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 907.101i | 1.49934i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 62.0541i | 0.102231i | 0.998693 | + | 0.0511154i | \(0.0162776\pi\) | ||||
−0.998693 | + | 0.0511154i | \(0.983722\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1197.14 | −1.95932 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 44.6560 | 0.0728482 | 0.0364241 | − | 0.999336i | \(-0.488403\pi\) | ||||
0.0364241 | + | 0.999336i | \(0.488403\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 91.0168i | 0.147995i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −832.160 | −1.34872 | −0.674360 | − | 0.738403i | \(-0.735580\pi\) | ||||
−0.674360 | + | 0.738403i | \(0.735580\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 249.870i | 0.403668i | 0.979420 | + | 0.201834i | \(0.0646901\pi\) | ||||
−0.979420 | + | 0.201834i | \(0.935310\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 362.284i | − 0.583389i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −693.221 | −1.10915 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 105.831 | 0.168790 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 311.319i | − 0.494943i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26.0372 | 0.0412634 | 0.0206317 | − | 0.999787i | \(-0.493432\pi\) | ||||
0.0206317 | + | 0.999787i | \(0.493432\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 51.4665i | − 0.0813056i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 67.7756i | 0.106733i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −306.215 | −0.479210 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 470.391 | 0.733839 | 0.366920 | − | 0.930253i | \(-0.380412\pi\) | ||||
0.366920 | + | 0.930253i | \(0.380412\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 668.123i | 1.03907i | 0.854449 | + | 0.519536i | \(0.173895\pi\) | ||||
−0.854449 | + | 0.519536i | \(0.826105\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −80.6007 | −0.124962 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1068.22i | 1.65104i | 0.564374 | + | 0.825519i | \(0.309117\pi\) | ||||
−0.564374 | + | 0.825519i | \(0.690883\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 854.263i | 1.31628i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −779.835 | −1.19423 | −0.597117 | − | 0.802154i | \(-0.703687\pi\) | ||||
−0.597117 | + | 0.802154i | \(0.703687\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.69027 | 0.00868743 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 407.579i | 0.620363i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1017.20 | −1.54355 | −0.771774 | − | 0.635897i | \(-0.780630\pi\) | ||||
−0.771774 | + | 0.635897i | \(0.780630\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 945.931i | − 1.43106i | −0.698582 | − | 0.715530i | \(-0.746185\pi\) | ||||
0.698582 | − | 0.715530i | \(-0.253815\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 261.352i | 0.394196i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1050.72 | 1.57529 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −91.5044 | −0.136778 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 67.2697i | 0.100253i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −76.8911 | −0.114251 | −0.0571256 | − | 0.998367i | \(-0.518194\pi\) | ||||
−0.0571256 | + | 0.998367i | \(0.518194\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 28.0316i | − 0.0415284i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 641.045i | − 0.946891i | −0.880823 | − | 0.473445i | \(-0.843010\pi\) | ||||
0.880823 | − | 0.473445i | \(-0.156990\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 25.6961 | 0.0377329 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1022.92 | −1.49769 | −0.748845 | − | 0.662745i | \(-0.769391\pi\) | ||||
−0.748845 | + | 0.662745i | \(0.769391\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 354.564i | − 0.517611i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −101.112 | −0.147180 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 187.412i | − 0.272006i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 690.043i | − 0.998615i | −0.866425 | − | 0.499307i | \(-0.833588\pi\) | ||||
0.866425 | − | 0.499307i | \(-0.166412\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1172.25 | 1.68669 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −813.502 | −1.16715 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 89.7739i | − 0.128432i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −361.922 | −0.516294 | −0.258147 | − | 0.966106i | \(-0.583112\pi\) | ||||
−0.258147 | + | 0.966106i | \(0.583112\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 158.406i | 0.225329i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − 149.798i | − 0.212479i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 521.904 | 0.736113 | 0.368056 | − | 0.929804i | \(-0.380023\pi\) | ||||
0.368056 | + | 0.929804i | \(0.380023\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 760.655 | 1.06984 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1017.94i | 1.42769i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1946.04 | 2.72173 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 68.7621i | − 0.0959025i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 661.810i | 0.920459i | 0.887800 | + | 0.460230i | \(0.152233\pi\) | ||||
−0.887800 | + | 0.460230i | \(0.847767\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −160.253 | −0.221651 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 81.2990 | 0.112137 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 1169.62i | − 1.60882i | −0.594071 | − | 0.804412i | \(-0.702480\pi\) | ||||
0.594071 | − | 0.804412i | \(-0.297520\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 607.150 | 0.832854 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 720.404i | − 0.985505i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 452.412i | 0.617206i | 0.951191 | + | 0.308603i | \(0.0998614\pi\) | ||||
−0.951191 | + | 0.308603i | \(0.900139\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1809.58 | 2.45533 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.50756 | −0.00745272 | −0.00372636 | − | 0.999993i | \(-0.501186\pi\) | ||||
−0.00372636 | + | 0.999993i | \(0.501186\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 132.982i | − 0.179463i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −866.020 | −1.16557 | −0.582786 | − | 0.812626i | \(-0.698037\pi\) | ||||
−0.582786 | + | 0.812626i | \(0.698037\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − 209.565i | − 0.281296i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 559.635i | − 0.749176i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 460.842 | 0.613638 | 0.306819 | − | 0.951768i | \(-0.400735\pi\) | ||||
0.306819 | + | 0.951768i | \(0.400735\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 20.3322 | 0.0270016 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 1181.02i | − 1.56427i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −547.987 | −0.723893 | −0.361946 | − | 0.932199i | \(-0.617888\pi\) | ||||
−0.361946 | + | 0.932199i | \(0.617888\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 348.946i | 0.459745i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1303.88i | 1.71338i | 0.515830 | + | 0.856691i | \(0.327484\pi\) | ||||
−0.515830 | + | 0.856691i | \(0.672516\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1113.46 | 1.45551 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1073.42 | 1.39951 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 771.004i | 1.00261i | 0.865272 | + | 0.501303i | \(0.167146\pi\) | ||||
−0.865272 | + | 0.501303i | \(0.832854\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −88.0080 | −0.114148 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 1065.32i | − 1.37816i | −0.724685 | − | 0.689080i | \(-0.758015\pi\) | ||||
0.724685 | − | 0.689080i | \(-0.241985\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 78.7628i | 0.101629i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 413.929 | 0.531359 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 598.546 | 0.766384 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 234.466i | − 0.299446i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1072.01 | 1.36561 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 944.631i | − 1.20029i | −0.799890 | − | 0.600147i | \(-0.795109\pi\) | ||||
0.799890 | − | 0.600147i | \(-0.204891\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 184.750i | 0.234157i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 84.5277 | 0.106592 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 23.4507 | 0.0294977 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1245.89i | 1.56322i | 0.623765 | + | 0.781612i | \(0.285602\pi\) | ||||
−0.623765 | + | 0.781612i | \(0.714398\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1338.88 | 1.67570 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − 375.838i | − 0.469211i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 796.676i | − 0.992125i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −8.82824 | −0.0109396 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −177.307 | −0.219168 | −0.109584 | − | 0.993978i | \(-0.534952\pi\) | ||||
−0.109584 | + | 0.993978i | \(0.534952\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1212.71i | 1.49532i | 0.664079 | + | 0.747662i | \(0.268824\pi\) | ||||
−0.664079 | + | 0.747662i | \(0.731176\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −66.0108 | −0.0811941 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 13.9468i | 0.0171126i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 366.558i | 0.448664i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1064.51 | −1.29660 | −0.648298 | − | 0.761387i | \(-0.724519\pi\) | ||||
−0.648298 | + | 0.761387i | \(0.724519\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 285.647 | 0.347081 | 0.173540 | − | 0.984827i | \(-0.444479\pi\) | ||||
0.173540 | + | 0.984827i | \(0.444479\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 26.9996i | 0.0327268i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1182.30 | −1.42962 | −0.714811 | − | 0.699317i | \(-0.753487\pi\) | ||||
−0.714811 | + | 0.699317i | \(0.753487\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 720.994i | 0.869715i | 0.900499 | + | 0.434857i | \(0.143201\pi\) | ||||
−0.900499 | + | 0.434857i | \(0.856799\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − 126.276i | − 0.151956i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 705.270 | 0.844635 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 227.152 | 0.271388 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 548.052i | − 0.653221i | −0.945159 | − | 0.326610i | \(-0.894094\pi\) | ||||
0.945159 | − | 0.326610i | \(-0.105906\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −160.988 | −0.191424 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 100.059i | − 0.118694i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 1549.15i | − 1.83331i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 108.611 | 0.127928 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −522.297 | −0.613745 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 1110.62i | − 1.30201i | −0.759072 | − | 0.651007i | \(-0.774347\pi\) | ||||
0.759072 | − | 0.651007i | \(-0.225653\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −566.556 | −0.662639 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 145.165i | − 0.169388i | −0.996407 | − | 0.0846939i | \(-0.973009\pi\) | ||||
0.996407 | − | 0.0846939i | \(-0.0269912\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1335.32i | 1.55450i | 0.629189 | + | 0.777252i | \(0.283387\pi\) | ||||
−0.629189 | + | 0.777252i | \(0.716613\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −562.851 | −0.652203 | −0.326101 | − | 0.945335i | \(-0.605735\pi\) | ||||
−0.326101 | + | 0.945335i | \(0.605735\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 514.807 | 0.595153 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 145.846i | − 0.168219i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1486.82 | −1.71095 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 2273.82i | − 2.61059i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 251.361i | 0.287928i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −906.537 | −1.03368 | −0.516840 | − | 0.856082i | \(-0.672892\pi\) | ||||
−0.516840 | + | 0.856082i | \(0.672892\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −36.4038 | −0.0414150 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 422.614i | 0.479698i | 0.970810 | + | 0.239849i | \(0.0770979\pi\) | ||||
−0.970810 | + | 0.239849i | \(0.922902\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 310.036 | 0.351116 | 0.175558 | − | 0.984469i | \(-0.443827\pi\) | ||||
0.175558 | + | 0.984469i | \(0.443827\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 134.316i | 0.151770i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 1135.83i | − 1.28053i | −0.768154 | − | 0.640265i | \(-0.778825\pi\) | ||||
0.768154 | − | 0.640265i | \(-0.221175\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1266.92 | −1.42191 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −681.254 | −0.762882 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 445.616i | − 0.497895i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 438.468 | 0.488816 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 658.799i | 0.732813i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 209.601i | 0.232631i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1136.60 | −1.25591 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 80.9267 | 0.0892246 | 0.0446123 | − | 0.999004i | \(-0.485795\pi\) | ||||
0.0446123 | + | 0.999004i | \(0.485795\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 537.436i | − 0.591239i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1285.92 | −1.41155 | −0.705774 | − | 0.708437i | \(-0.749401\pi\) | ||||
−0.705774 | + | 0.708437i | \(0.749401\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1093.89i | 1.19813i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 10.5769i | 0.0115594i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1712.82 | −1.86379 | −0.931894 | − | 0.362732i | \(-0.881844\pi\) | ||||
−0.931894 | + | 0.362732i | \(0.881844\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −256.943 | −0.278983 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 752.101i | − 0.814845i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −40.4126 | −0.0436893 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 522.218i | − 0.563342i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 1361.04i | − 1.46506i | −0.680733 | − | 0.732531i | \(-0.738339\pi\) | ||||
0.680733 | − | 0.732531i | \(-0.261661\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 157.455 | 0.168762 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2176.44 | −2.32774 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 314.858i | 0.336028i | 0.985785 | + | 0.168014i | \(0.0537354\pi\) | ||||
−0.985785 | + | 0.168014i | \(0.946265\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 278.156 | 0.296226 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 301.753i | − 0.320673i | −0.987062 | − | 0.160336i | \(-0.948742\pi\) | ||||
0.987062 | − | 0.160336i | \(-0.0512579\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1364.81i | 1.44730i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1453.18 | 1.53450 | 0.767252 | − | 0.641346i | \(-0.221624\pi\) | ||||
0.767252 | + | 0.641346i | \(0.221624\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1001.06 | −1.05486 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 71.9225i | 0.0756282i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 977.784 | 1.02601 | 0.513003 | − | 0.858387i | \(-0.328533\pi\) | ||||
0.513003 | + | 0.858387i | \(0.328533\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 290.251i | − 0.303928i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 225.834i | 0.235981i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 322.753 | 0.335851 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1151.27 | −1.19550 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 1846.90i | − 1.91389i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 181.044 | 0.187222 | 0.0936109 | − | 0.995609i | \(-0.470159\pi\) | ||||
0.0936109 | + | 0.995609i | \(0.470159\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 148.726i | 0.153484i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 243.030i | − 0.250289i | −0.992139 | − | 0.125144i | \(-0.960061\pi\) | ||||
0.992139 | − | 0.125144i | \(-0.0399394\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 33.9263 | 0.0347962 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1431.73 | 1.46543 | 0.732717 | − | 0.680533i | \(-0.238252\pi\) | ||||
0.732717 | + | 0.680533i | \(0.238252\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 734.635i | 0.750393i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −330.573 | −0.336975 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 444.483i | 0.452170i | 0.974108 | + | 0.226085i | \(0.0725927\pi\) | ||||
−0.974108 | + | 0.226085i | \(0.927407\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 856.936i | 0.869985i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1208.62 | −1.22206 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1804.72 | −1.82111 | −0.910553 | − | 0.413391i | \(-0.864344\pi\) | ||||
−0.910553 | + | 0.413391i | \(0.864344\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 18.6812i | 0.0188128i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −729.767 | −0.733434 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1904.31i | 1.91004i | 0.296548 | + | 0.955018i | \(0.404165\pi\) | ||||
−0.296548 | + | 0.955018i | \(0.595835\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 116.550i | 0.116666i |
(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 | 1568.3.c.h.97.10 | 16 | ||
4.3 | odd | 2 | inner | 1568.3.c.h.97.8 | 16 | ||
7.4 | even | 3 | 224.3.s.a.33.5 | yes | 16 | ||
7.5 | odd | 6 | 224.3.s.a.129.5 | yes | 16 | ||
7.6 | odd | 2 | inner | 1568.3.c.h.97.7 | 16 | ||
28.11 | odd | 6 | 224.3.s.a.33.4 | ✓ | 16 | ||
28.19 | even | 6 | 224.3.s.a.129.4 | yes | 16 | ||
28.27 | even | 2 | inner | 1568.3.c.h.97.9 | 16 | ||
56.5 | odd | 6 | 448.3.s.g.129.4 | 16 | |||
56.11 | odd | 6 | 448.3.s.g.257.5 | 16 | |||
56.19 | even | 6 | 448.3.s.g.129.5 | 16 | |||
56.53 | even | 6 | 448.3.s.g.257.4 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
224.3.s.a.33.4 | ✓ | 16 | 28.11 | odd | 6 | ||
224.3.s.a.33.5 | yes | 16 | 7.4 | even | 3 | ||
224.3.s.a.129.4 | yes | 16 | 28.19 | even | 6 | ||
224.3.s.a.129.5 | yes | 16 | 7.5 | odd | 6 | ||
448.3.s.g.129.4 | 16 | 56.5 | odd | 6 | |||
448.3.s.g.129.5 | 16 | 56.19 | even | 6 | |||
448.3.s.g.257.4 | 16 | 56.53 | even | 6 | |||
448.3.s.g.257.5 | 16 | 56.11 | odd | 6 | |||
1568.3.c.h.97.7 | 16 | 7.6 | odd | 2 | inner | ||
1568.3.c.h.97.8 | 16 | 4.3 | odd | 2 | inner | ||
1568.3.c.h.97.9 | 16 | 28.27 | even | 2 | inner | ||
1568.3.c.h.97.10 | 16 | 1.1 | even | 1 | trivial |