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 | 97.9 | ||
Root | \(-0.707107 - 0.358323i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1568.97 |
Dual form | 1568.3.c.h.97.8 |
$q$-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 | \(-0.822094\pi\) | ||||
0.847835 | − | 0.530261i | \(-0.177906\pi\) | |||||||
\(6\) | 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 | \(-0.216833\pi\) | ||||
0.776817 | + | 0.629727i | \(0.216833\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 21.4744i | − 1.65187i | −0.563762 | − | 0.825937i | \(-0.690647\pi\) | ||||
0.563762 | − | 0.825937i | \(-0.309353\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.68707 | 0.179138 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 24.0168i | 1.41276i | 0.707835 | + | 0.706378i | \(0.249672\pi\) | ||||
−0.707835 | + | 0.706378i | \(0.750328\pi\) | |||||||
\(18\) | 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 | \(-0.160248\pi\) | ||||
0.875932 | + | 0.482435i | \(0.160248\pi\) | |||||||
\(24\) | 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 | \(0.135545\pi\) | ||||
−0.910697 | + | 0.413075i | \(0.864455\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −29.9958 | −0.697576 | −0.348788 | − | 0.937202i | \(-0.613407\pi\) | ||||
−0.348788 | + | 0.937202i | \(0.613407\pi\) | |||||||
\(44\) | 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 | \(0.0102717\pi\) | ||||
−0.999479 | + | 0.0322640i | \(0.989728\pi\) | |||||||
\(62\) | 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 | \(-0.209982\pi\) | ||||
0.790189 | + | 0.612864i | \(0.209982\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 20.4182i | 0.295916i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 35.0232 | 0.493285 | 0.246642 | − | 0.969107i | \(-0.420673\pi\) | ||||
0.246642 | + | 0.969107i | \(0.420673\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 46.6166i | − 0.638584i | −0.947656 | − | 0.319292i | \(-0.896555\pi\) | ||||
0.947656 | − | 0.319292i | \(-0.103445\pi\) | |||||||
\(74\) | 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 | \(-0.685612\pi\) | ||||
−0.550630 | + | 0.834750i | \(0.685612\pi\) | |||||||
\(80\) | 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 | \(0.0776381\pi\) | ||||
−0.970402 | + | 0.241496i | \(0.922362\pi\) | |||||||
\(90\) | 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 | \(-0.952655\pi\) | ||||
0.988959 | − | 0.148192i | \(-0.0473454\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 149.421 | 1.50930 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 61.4690i | 0.608604i | 0.952576 | + | 0.304302i | \(0.0984232\pi\) | ||||
−0.952576 | + | 0.304302i | \(0.901577\pi\) | |||||||
\(102\) | 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 | \(-0.289032\pi\) | ||||
0.615308 | + | 0.788287i | \(0.289032\pi\) | |||||||
\(108\) | 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 | \(-0.516024\pi\) | ||||
−0.0503211 | + | 0.998733i | \(0.516024\pi\) | |||||||
\(128\) | 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 | \(-0.236006\pi\) | ||||
0.737499 | + | 0.675348i | \(0.236006\pi\) | |||||||
\(152\) | 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 | \(0.222660\pi\) | ||||
−0.765160 | + | 0.643840i | \(0.777340\pi\) | |||||||
\(158\) | 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 | \(-0.502568\pi\) | ||||
−0.00806802 | + | 0.999967i | \(0.502568\pi\) | |||||||
\(164\) | 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 | \(0.0905316\pi\) | ||||
−0.959826 | + | 0.280594i | \(0.909468\pi\) | |||||||
\(174\) | 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 | \(-0.424576\pi\) | ||||
0.234740 | + | 0.972058i | \(0.424576\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 214.347i | − 1.18424i | −0.805851 | − | 0.592119i | \(-0.798292\pi\) | ||||
0.805851 | − | 0.592119i | \(-0.201708\pi\) | |||||||
\(182\) | 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 | \(-0.454231\pi\) | ||||
0.143292 | + | 0.989681i | \(0.454231\pi\) | |||||||
\(192\) | 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 | \(-0.422633\pi\) | ||||
0.240670 | + | 0.970607i | \(0.422633\pi\) | |||||||
\(212\) | 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 | \(-0.856514\pi\) | ||||
0.900111 | − | 0.435661i | \(-0.143486\pi\) | |||||||
\(230\) | 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 | \(-0.408379\pi\) | ||||
0.283878 | + | 0.958860i | \(0.408379\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − 316.241i | − 1.31220i | −0.754673 | − | 0.656101i | \(-0.772205\pi\) | ||||
0.754673 | − | 0.656101i | \(-0.227795\pi\) | |||||||
\(242\) | 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 | \(-0.890288\pi\) | ||||
0.941187 | − | 0.337886i | \(-0.109712\pi\) | |||||||
\(258\) | 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 | \(-0.743764\pi\) | ||||
−0.693120 | + | 0.720822i | \(0.743764\pi\) | |||||||
\(264\) | 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 | \(-0.989691\pi\) | ||||
0.999476 | − | 0.0323819i | \(-0.0103093\pi\) | |||||||
\(270\) | 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 | \(-0.960880\pi\) | ||||
0.992457 | − | 0.122591i | \(-0.0391204\pi\) | |||||||
\(294\) | 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 | \(0.340358\pi\) | ||||
−0.480767 | + | 0.876848i | \(0.659642\pi\) | |||||||
\(314\) | 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 | \(-0.517735\pi\) | ||||
−0.0556873 | + | 0.998448i | \(0.517735\pi\) | |||||||
\(332\) | 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 | \(-0.614554\pi\) | ||||
−0.352164 | + | 0.935938i | \(0.614554\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 190.205i | − 0.545001i | −0.962156 | − | 0.272501i | \(-0.912149\pi\) | ||||
0.962156 | − | 0.272501i | \(-0.0878507\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 193.082 | 0.550091 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 394.767i | − 1.11832i | −0.829060 | − | 0.559160i | \(-0.811124\pi\) | ||||
0.829060 | − | 0.559160i | \(-0.188876\pi\) | |||||||
\(354\) | 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 | \(-0.635417\pi\) | ||||
−0.412709 | + | 0.910863i | \(0.635417\pi\) | |||||||
\(360\) | 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 | \(-0.247667\pi\) | ||||
0.712270 | + | 0.701906i | \(0.247667\pi\) | |||||||
\(380\) | 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 | \(-0.919208\pi\) | ||||
0.967961 | − | 0.251099i | \(-0.0807919\pi\) | |||||||
\(398\) | 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 | \(0.319392\pi\) | ||||
−0.537439 | + | 0.843303i | \(0.680608\pi\) | |||||||
\(410\) | 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 | \(-0.607854\pi\) | ||||
−0.332387 | + | 0.943143i | \(0.607854\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 407.880i | − 0.941986i | −0.882137 | − | 0.470993i | \(-0.843896\pi\) | ||||
0.882137 | − | 0.470993i | \(-0.156104\pi\) | |||||||
\(434\) | 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 | \(-0.616467\pi\) | ||||
−0.357782 | + | 0.933805i | \(0.616467\pi\) | |||||||
\(444\) | 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 | \(-0.737899\pi\) | ||||
0.679721 | − | 0.733470i | \(-0.262101\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −559.738 | −1.20894 | −0.604469 | − | 0.796629i | \(-0.706615\pi\) | ||||
−0.604469 | + | 0.796629i | \(0.706615\pi\) | |||||||
\(464\) | 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 | \(-0.592948\pi\) | ||||
−0.287874 | + | 0.957668i | \(0.592948\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − 1.33283i | − 0.00272562i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −423.804 | −0.863145 | −0.431573 | − | 0.902078i | \(-0.642041\pi\) | ||||
−0.431573 | + | 0.902078i | \(0.642041\pi\) | |||||||
\(492\) | 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 | \(-0.446792\pi\) | ||||
0.166381 | + | 0.986061i | \(0.446792\pi\) | |||||||
\(500\) | 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 | \(-0.901283\pi\) | ||||
0.952294 | − | 0.305183i | \(-0.0987175\pi\) | |||||||
\(510\) | 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 | \(-0.979507\pi\) | ||||
0.997928 | − | 0.0643361i | \(-0.0204930\pi\) | |||||||
\(522\) | 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 | \(-0.750811\pi\) | ||||
−0.708906 | + | 0.705303i | \(0.750811\pi\) | |||||||
\(548\) | 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 | \(-0.758804\pi\) | ||||
−0.726392 | + | 0.687280i | \(0.758804\pi\) | |||||||
\(572\) | 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 | \(-0.875767\pi\) | ||||
0.924799 | − | 0.380457i | \(-0.124233\pi\) | |||||||
\(578\) | 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 | \(0.223205\pi\) | ||||
−0.764056 | + | 0.645149i | \(0.776795\pi\) | |||||||
\(594\) | 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 | \(-0.421407\pi\) | ||||
0.244407 | + | 0.969673i | \(0.421407\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 748.440i | 1.24532i | 0.782491 | + | 0.622662i | \(0.213949\pi\) | ||||
−0.782491 | + | 0.622662i | \(0.786051\pi\) | |||||||
\(602\) | 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 | \(-0.506568\pi\) | ||||
−0.0206317 | + | 0.999787i | \(0.506568\pi\) | |||||||
\(632\) | 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 | \(-0.219370\pi\) | ||||
0.771774 | + | 0.635897i | \(0.219370\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 945.931i | 1.43106i | 0.698582 | + | 0.715530i | \(0.253815\pi\) | ||||
−0.698582 | + | 0.715530i | \(0.746185\pi\) | |||||||
\(662\) | 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 | \(0.156990\pi\) | ||||
−0.880823 | + | 0.473445i | \(0.843010\pi\) | |||||||
\(678\) | 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 | \(-0.230609\pi\) | ||||
0.748845 | + | 0.662745i | \(0.230609\pi\) | |||||||
\(684\) | 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 | \(-0.900139\pi\) | ||||
0.951191 | − | 0.308603i | \(-0.0998614\pi\) | |||||||
\(734\) | 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 | \(-0.498814\pi\) | ||||
0.00372636 | + | 0.999993i | \(0.498814\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 132.982i | 0.179463i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 866.020 | 1.16557 | 0.582786 | − | 0.812626i | \(-0.301963\pi\) | ||||
0.582786 | + | 0.812626i | \(0.301963\pi\) | |||||||
\(744\) | 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 | \(-0.599265\pi\) | ||||
−0.306819 | + | 0.951768i | \(0.599265\pi\) | |||||||
\(752\) | 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 | \(-0.672516\pi\) | ||||
0.515830 | − | 0.856691i | \(-0.327484\pi\) | |||||||
\(762\) | 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 | \(-0.832854\pi\) | ||||
0.865272 | − | 0.501303i | \(-0.167146\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 88.0080 | 0.114148 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1065.32i | 1.37816i | 0.724685 | + | 0.689080i | \(0.241985\pi\) | ||||
−0.724685 | + | 0.689080i | \(0.758015\pi\) | |||||||
\(774\) | 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 | \(-0.714398\pi\) | ||||
0.623765 | − | 0.781612i | \(-0.285602\pi\) | |||||||
\(798\) | 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 | \(-0.555521\pi\) | ||||
−0.173540 | + | 0.984827i | \(0.555521\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − 26.9996i | − 0.0327268i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1182.30 | 1.42962 | 0.714811 | − | 0.699317i | \(-0.246513\pi\) | ||||
0.714811 | + | 0.699317i | \(0.246513\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 720.994i | − 0.869715i | −0.900499 | − | 0.434857i | \(-0.856799\pi\) | ||||
0.900499 | − | 0.434857i | \(-0.143201\pi\) | |||||||
\(830\) | 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 | \(0.225653\pi\) | ||||
−0.759072 | + | 0.651007i | \(0.774347\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 566.556 | 0.662639 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 145.165i | 0.169388i | 0.996407 | + | 0.0846939i | \(0.0269912\pi\) | ||||
−0.996407 | + | 0.0846939i | \(0.973009\pi\) | |||||||
\(858\) | 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 | \(-0.394265\pi\) | ||||
0.326101 | + | 0.945335i | \(0.394265\pi\) | |||||||
\(864\) | 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 | \(-0.922902\pi\) | ||||
0.970810 | − | 0.239849i | \(-0.0770979\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −310.036 | −0.351116 | −0.175558 | − | 0.984469i | \(-0.556173\pi\) | ||||
−0.175558 | + | 0.984469i | \(0.556173\pi\) | |||||||
\(884\) | 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 | \(-0.514205\pi\) | ||||
−0.0446123 | + | 0.999004i | \(0.514205\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 537.436i | 0.591239i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1285.92 | 1.41155 | 0.705774 | − | 0.708437i | \(-0.250599\pi\) | ||||
0.705774 | + | 0.708437i | \(0.250599\pi\) | |||||||
\(912\) | 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 | \(-0.118156\pi\) | ||||
0.931894 | + | 0.362732i | \(0.118156\pi\) | |||||||
\(920\) | 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 | \(0.261661\pi\) | ||||
−0.680733 | + | 0.732531i | \(0.738339\pi\) | |||||||
\(930\) | 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 | \(-0.946265\pi\) | ||||
0.985785 | − | 0.168014i | \(-0.0537354\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −278.156 | −0.296226 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 301.753i | 0.320673i | 0.987062 | + | 0.160336i | \(0.0512579\pi\) | ||||
−0.987062 | + | 0.160336i | \(0.948742\pi\) | |||||||
\(942\) | 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 | \(-0.778376\pi\) | ||||
−0.767252 | + | 0.641346i | \(0.778376\pi\) | |||||||
\(948\) | 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 | \(-0.529841\pi\) | ||||
−0.0936109 | + | 0.995609i | \(0.529841\pi\) | |||||||
\(968\) | 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 | \(-0.135656\pi\) | ||||
0.910553 | + | 0.413391i | \(0.135656\pi\) | |||||||
\(992\) | 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 | \(-0.595835\pi\) | ||||
0.296548 | − | 0.955018i | \(-0.404165\pi\) | |||||||
\(998\) | 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.97.9 | 16 | ||
4.3 | odd | 2 | inner | 1568.3.c.h.97.7 | 16 | ||
7.2 | even | 3 | 224.3.s.a.129.4 | yes | 16 | ||
7.3 | odd | 6 | 224.3.s.a.33.4 | ✓ | 16 | ||
7.6 | odd | 2 | inner | 1568.3.c.h.97.8 | 16 | ||
28.3 | even | 6 | 224.3.s.a.33.5 | yes | 16 | ||
28.23 | odd | 6 | 224.3.s.a.129.5 | yes | 16 | ||
28.27 | even | 2 | inner | 1568.3.c.h.97.10 | 16 | ||
56.3 | even | 6 | 448.3.s.g.257.4 | 16 | |||
56.37 | even | 6 | 448.3.s.g.129.5 | 16 | |||
56.45 | odd | 6 | 448.3.s.g.257.5 | 16 | |||
56.51 | odd | 6 | 448.3.s.g.129.4 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
224.3.s.a.33.4 | ✓ | 16 | 7.3 | odd | 6 | ||
224.3.s.a.33.5 | yes | 16 | 28.3 | even | 6 | ||
224.3.s.a.129.4 | yes | 16 | 7.2 | even | 3 | ||
224.3.s.a.129.5 | yes | 16 | 28.23 | odd | 6 | ||
448.3.s.g.129.4 | 16 | 56.51 | odd | 6 | |||
448.3.s.g.129.5 | 16 | 56.37 | even | 6 | |||
448.3.s.g.257.4 | 16 | 56.3 | even | 6 | |||
448.3.s.g.257.5 | 16 | 56.45 | odd | 6 | |||
1568.3.c.h.97.7 | 16 | 4.3 | odd | 2 | inner | ||
1568.3.c.h.97.8 | 16 | 7.6 | odd | 2 | inner | ||
1568.3.c.h.97.9 | 16 | 1.1 | even | 1 | trivial | ||
1568.3.c.h.97.10 | 16 | 28.27 | even | 2 | inner |