Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2736,3,Mod(721,2736)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2736, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("2736.721");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 2736.o (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(74.5506003290\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 4 x^{19} + 80 x^{18} - 152 x^{17} + 4326 x^{16} - 10096 x^{15} + 70116 x^{14} - 93436 x^{13} + \cdots + 36100 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{29}]\) |
Coefficient ring index: | \( 2^{37} \) |
Twist minimal: | no (minimal twist has level 456) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 721.20 | ||
Root | \(4.05338 - 7.02066i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2736.721 |
Dual form | 2736.3.o.r.721.19 |
$q$-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 \(\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times\).
\(n\) | \(1009\) | \(1217\) | \(1711\) | \(2053\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 8.20492 | 1.64098 | 0.820492 | − | 0.571658i | \(-0.193700\pi\) | ||||
0.820492 | + | 0.571658i | \(0.193700\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 8.00860 | 1.14409 | 0.572043 | − | 0.820224i | \(-0.306151\pi\) | ||||
0.572043 | + | 0.820224i | \(0.306151\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 7.74291 | 0.703901 | 0.351950 | − | 0.936019i | \(-0.385519\pi\) | ||||
0.351950 | + | 0.936019i | \(0.385519\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 7.64699i | 0.588230i | 0.955770 | + | 0.294115i | \(0.0950248\pi\) | ||||
−0.955770 | + | 0.294115i | \(0.904975\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −11.4841 | −0.675537 | −0.337769 | − | 0.941229i | \(-0.609672\pi\) | ||||
−0.337769 | + | 0.941229i | \(0.609672\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −17.5525 | + | 7.27380i | −0.923818 | + | 0.382831i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 22.9620 | 0.998347 | 0.499173 | − | 0.866502i | \(-0.333637\pi\) | ||||
0.499173 | + | 0.866502i | \(0.333637\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 42.3207 | 1.69283 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 17.5778i | 0.606132i | 0.952970 | + | 0.303066i | \(0.0980103\pi\) | ||||
−0.952970 | + | 0.303066i | \(0.901990\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 52.3102i | − | 1.68742i | −0.536796 | − | 0.843712i | \(-0.680365\pi\) | ||
0.536796 | − | 0.843712i | \(-0.319635\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 65.7099 | 1.87743 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 40.7090i | 1.10024i | 0.835084 | + | 0.550122i | \(0.185419\pi\) | ||||
−0.835084 | + | 0.550122i | \(0.814581\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 36.2297i | 0.883650i | 0.897101 | + | 0.441825i | \(0.145669\pi\) | ||||
−0.897101 | + | 0.441825i | \(0.854331\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 52.5407 | 1.22188 | 0.610938 | − | 0.791678i | \(-0.290792\pi\) | ||||
0.610938 | + | 0.791678i | \(0.290792\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.90967 | 0.0831844 | 0.0415922 | − | 0.999135i | \(-0.486757\pi\) | ||||
0.0415922 | + | 0.999135i | \(0.486757\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 15.1376 | 0.308931 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 49.8052i | 0.939720i | 0.882741 | + | 0.469860i | \(0.155696\pi\) | ||||
−0.882741 | + | 0.469860i | \(0.844304\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 63.5299 | 1.15509 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 46.6932i | 0.791410i | 0.918378 | + | 0.395705i | \(0.129500\pi\) | ||||
−0.918378 | + | 0.395705i | \(0.870500\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 40.8276 | 0.669305 | 0.334652 | − | 0.942342i | \(-0.391381\pi\) | ||||
0.334652 | + | 0.942342i | \(0.391381\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 62.7429i | 0.965276i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 35.0230i | − | 0.522731i | −0.965240 | − | 0.261365i | \(-0.915827\pi\) | ||
0.965240 | − | 0.261365i | \(-0.0841727\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 106.718i | 1.50307i | 0.659694 | + | 0.751535i | \(0.270686\pi\) | ||||
−0.659694 | + | 0.751535i | \(0.729314\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 113.791 | 1.55878 | 0.779392 | − | 0.626537i | \(-0.215528\pi\) | ||||
0.779392 | + | 0.626537i | \(0.215528\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 62.0098 | 0.805322 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 116.271i | − | 1.47178i | −0.677099 | − | 0.735892i | \(-0.736763\pi\) | ||
0.677099 | − | 0.735892i | \(-0.263237\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 48.3546 | 0.582585 | 0.291293 | − | 0.956634i | \(-0.405915\pi\) | ||||
0.291293 | + | 0.956634i | \(0.405915\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −94.2264 | −1.10855 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 24.3444i | − | 0.273532i | −0.990603 | − | 0.136766i | \(-0.956329\pi\) | ||
0.990603 | − | 0.136766i | \(-0.0436708\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 61.2416i | 0.672985i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −144.017 | + | 59.6809i | −1.51597 | + | 0.628220i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 85.7882i | 0.884414i | 0.896913 | + | 0.442207i | \(0.145804\pi\) | ||||
−0.896913 | + | 0.442207i | \(0.854196\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −166.786 | −1.65135 | −0.825674 | − | 0.564148i | \(-0.809205\pi\) | ||||
−0.825674 | + | 0.564148i | \(0.809205\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 159.516i | − | 1.54870i | −0.632758 | − | 0.774349i | \(-0.718077\pi\) | ||
0.632758 | − | 0.774349i | \(-0.281923\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 99.9199i | − | 0.933830i | −0.884302 | − | 0.466915i | \(-0.845365\pi\) | ||
0.884302 | − | 0.466915i | \(-0.154635\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 152.435i | − | 1.39849i | −0.714883 | − | 0.699244i | \(-0.753520\pi\) | ||
0.714883 | − | 0.699244i | \(-0.246480\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 58.3110i | − | 0.516026i | −0.966141 | − | 0.258013i | \(-0.916932\pi\) | ||
0.966141 | − | 0.258013i | \(-0.0830678\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 188.401 | 1.63827 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −91.9718 | −0.772872 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −61.0474 | −0.504524 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 142.115 | 1.13692 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 110.826i | 0.872649i | 0.899789 | + | 0.436325i | \(0.143720\pi\) | ||||
−0.899789 | + | 0.436325i | \(0.856280\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 93.5498 | 0.714120 | 0.357060 | − | 0.934081i | \(-0.383779\pi\) | ||||
0.357060 | + | 0.934081i | \(0.383779\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −140.571 | + | 58.2529i | −1.05693 | + | 0.437992i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 80.4035 | 0.586887 | 0.293443 | − | 0.955976i | \(-0.405199\pi\) | ||||
0.293443 | + | 0.955976i | \(0.405199\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −205.954 | −1.48168 | −0.740841 | − | 0.671680i | \(-0.765573\pi\) | ||||
−0.740841 | + | 0.671680i | \(0.765573\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 59.2099i | 0.414055i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 144.225i | 0.994653i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −97.8024 | −0.656392 | −0.328196 | − | 0.944610i | \(-0.606441\pi\) | ||||
−0.328196 | + | 0.944610i | \(0.606441\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 37.3870i | − | 0.247596i | −0.992307 | − | 0.123798i | \(-0.960492\pi\) | ||
0.992307 | − | 0.123798i | \(-0.0395075\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 429.201i | − | 2.76904i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −270.158 | −1.72075 | −0.860375 | − | 0.509662i | \(-0.829770\pi\) | ||||
−0.860375 | + | 0.509662i | \(0.829770\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 183.893 | 1.14219 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 67.0137 | 0.411127 | 0.205563 | − | 0.978644i | \(-0.434097\pi\) | ||||
0.205563 | + | 0.978644i | \(0.434097\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 188.784i | − | 1.13044i | −0.824939 | − | 0.565222i | \(-0.808791\pi\) | ||
0.824939 | − | 0.565222i | \(-0.191209\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 110.524 | 0.653986 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 316.740i | 1.83086i | 0.402472 | + | 0.915432i | \(0.368151\pi\) | ||||
−0.402472 | + | 0.915432i | \(0.631849\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 338.930 | 1.93674 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 254.460i | 1.42156i | 0.703413 | + | 0.710781i | \(0.251658\pi\) | ||||
−0.703413 | + | 0.710781i | \(0.748342\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 199.320i | − | 1.10122i | −0.834763 | − | 0.550609i | \(-0.814396\pi\) | ||
0.834763 | − | 0.550609i | \(-0.185604\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 334.014i | 1.80548i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −88.9205 | −0.475511 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 103.088 | 0.539728 | 0.269864 | − | 0.962898i | \(-0.413021\pi\) | ||||
0.269864 | + | 0.962898i | \(0.413021\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 291.262i | 1.50913i | 0.656225 | + | 0.754565i | \(0.272152\pi\) | ||||
−0.656225 | + | 0.754565i | \(0.727848\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 246.923 | 1.25342 | 0.626709 | − | 0.779254i | \(-0.284402\pi\) | ||||
0.626709 | + | 0.779254i | \(0.284402\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −17.5380 | −0.0881307 | −0.0440653 | − | 0.999029i | \(-0.514031\pi\) | ||||
−0.0440653 | + | 0.999029i | \(0.514031\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 140.774i | 0.693467i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 297.261i | 1.45006i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −135.908 | + | 56.3203i | −0.650276 | + | 0.269475i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 300.813i | − | 1.42565i | −0.701341 | − | 0.712826i | \(-0.747415\pi\) | ||
0.701341 | − | 0.712826i | \(-0.252585\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 431.092 | 2.00508 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 418.931i | − | 1.93056i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 87.8190i | − | 0.397371i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 118.853i | − | 0.532971i | −0.963839 | − | 0.266486i | \(-0.914138\pi\) | ||
0.963839 | − | 0.266486i | \(-0.0858625\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 50.4628i | − | 0.222303i | −0.993803 | − | 0.111152i | \(-0.964546\pi\) | ||
0.993803 | − | 0.111152i | \(-0.0354539\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 109.997 | 0.480337 | 0.240168 | − | 0.970731i | \(-0.422797\pi\) | ||||
0.240168 | + | 0.970731i | \(0.422797\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 18.8197 | 0.0807711 | 0.0403855 | − | 0.999184i | \(-0.487141\pi\) | ||||
0.0403855 | + | 0.999184i | \(0.487141\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 32.0785 | 0.136504 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −43.6319 | −0.182560 | −0.0912802 | − | 0.995825i | \(-0.529096\pi\) | ||||
−0.0912802 | + | 0.995825i | \(0.529096\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 114.931i | 0.476893i | 0.971156 | + | 0.238447i | \(0.0766382\pi\) | ||||
−0.971156 | + | 0.238447i | \(0.923362\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 124.203 | 0.506951 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −55.6226 | − | 134.224i | −0.225193 | − | 0.543417i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 120.802 | 0.481281 | 0.240641 | − | 0.970614i | \(-0.422643\pi\) | ||||
0.240641 | + | 0.970614i | \(0.422643\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 177.792 | 0.702737 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 463.010i | − | 1.80160i | −0.434238 | − | 0.900798i | \(-0.642982\pi\) | ||
0.434238 | − | 0.900798i | \(-0.357018\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 326.022i | 1.25877i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 87.4806 | 0.332626 | 0.166313 | − | 0.986073i | \(-0.446814\pi\) | ||||
0.166313 | + | 0.986073i | \(0.446814\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 408.648i | 1.54207i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 396.728i | 1.47482i | 0.675443 | + | 0.737412i | \(0.263952\pi\) | ||||
−0.675443 | + | 0.737412i | \(0.736048\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −328.002 | −1.21034 | −0.605169 | − | 0.796097i | \(-0.706894\pi\) | ||||
−0.605169 | + | 0.796097i | \(0.706894\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 327.685 | 1.19158 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −332.247 | −1.19945 | −0.599724 | − | 0.800207i | \(-0.704723\pi\) | ||||
−0.599724 | + | 0.800207i | \(0.704723\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 0.472892i | − | 0.00168289i | −1.00000 | 0.000841445i | \(-0.999732\pi\) | |||
1.00000 | 0.000841445i | \(-0.000267840\pi\) | ||||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 56.6305 | 0.200108 | 0.100054 | − | 0.994982i | \(-0.468098\pi\) | ||||
0.100054 | + | 0.994982i | \(0.468098\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 290.149i | 1.01097i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −157.115 | −0.543650 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 456.196i | − | 1.55698i | −0.627656 | − | 0.778491i | \(-0.715985\pi\) | ||
0.627656 | − | 0.778491i | \(-0.284015\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 383.114i | 1.29869i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 175.590i | 0.587257i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 420.777 | 1.39793 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 334.987 | 1.09832 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 223.200i | 0.727037i | 0.931587 | + | 0.363519i | \(0.118425\pi\) | ||||
−0.931587 | + | 0.363519i | \(0.881575\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −423.534 | −1.36185 | −0.680924 | − | 0.732354i | \(-0.738421\pi\) | ||||
−0.680924 | + | 0.732354i | \(0.738421\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 276.738 | 0.884148 | 0.442074 | − | 0.896979i | \(-0.354243\pi\) | ||||
0.442074 | + | 0.896979i | \(0.354243\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 580.133i | − | 1.83007i | −0.403370 | − | 0.915037i | \(-0.632161\pi\) | ||
0.403370 | − | 0.915037i | \(-0.367839\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 136.104i | 0.426657i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 201.576 | − | 83.5332i | 0.624073 | − | 0.258617i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 323.626i | 0.995772i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 31.3109 | 0.0951700 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 387.001i | 1.16919i | 0.811326 | + | 0.584594i | \(0.198746\pi\) | ||||
−0.811326 | + | 0.584594i | \(0.801254\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 287.361i | − | 0.857793i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 318.289i | − | 0.944478i | −0.881471 | − | 0.472239i | \(-0.843446\pi\) | ||
0.881471 | − | 0.472239i | \(-0.156554\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 405.033i | − | 1.18778i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −271.190 | −0.790642 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 439.969 | 1.26792 | 0.633961 | − | 0.773365i | \(-0.281428\pi\) | ||||
0.633961 | + | 0.773365i | \(0.281428\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 350.244 | 1.00356 | 0.501782 | − | 0.864994i | \(-0.332678\pi\) | ||||
0.501782 | + | 0.864994i | \(0.332678\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −104.803 | −0.296891 | −0.148446 | − | 0.988921i | \(-0.547427\pi\) | ||||
−0.148446 | + | 0.988921i | \(0.547427\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 875.612i | 2.46651i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 429.578 | 1.19660 | 0.598298 | − | 0.801273i | \(-0.295844\pi\) | ||||
0.598298 | + | 0.801273i | \(0.295844\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 255.184 | − | 255.347i | 0.706880 | − | 0.707333i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 933.648 | 2.55794 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 83.5313 | 0.227606 | 0.113803 | − | 0.993503i | \(-0.463697\pi\) | ||||
0.113803 | + | 0.993503i | \(0.463697\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 398.870i | 1.07512i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 306.430i | 0.821528i | 0.911742 | + | 0.410764i | \(0.134738\pi\) | ||||
−0.911742 | + | 0.410764i | \(0.865262\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −134.417 | −0.356545 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 1.09504i | − | 0.00288929i | −0.999999 | − | 0.00144465i | \(-0.999540\pi\) | ||
0.999999 | − | 0.00144465i | \(-0.000459845\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 521.642i | 1.36199i | 0.732289 | + | 0.680994i | \(0.238452\pi\) | ||||
−0.732289 | + | 0.680994i | \(0.761548\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 508.786 | 1.32152 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 282.146 | 0.725311 | 0.362655 | − | 0.931923i | \(-0.381870\pi\) | ||||
0.362655 | + | 0.931923i | \(0.381870\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −263.698 | −0.674420 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 953.994i | − | 2.41517i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 541.473 | 1.36391 | 0.681955 | − | 0.731394i | \(-0.261130\pi\) | ||||
0.681955 | + | 0.731394i | \(0.261130\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 118.923i | 0.296566i | 0.988945 | + | 0.148283i | \(0.0473746\pi\) | ||||
−0.988945 | + | 0.148283i | \(0.952625\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 400.015 | 0.992593 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 315.206i | 0.774462i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 289.380i | − | 0.707531i | −0.935334 | − | 0.353765i | \(-0.884901\pi\) | ||
0.935334 | − | 0.353765i | \(-0.115099\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 373.947i | 0.905440i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 396.746 | 0.956013 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 478.095 | 1.14104 | 0.570519 | − | 0.821284i | \(-0.306742\pi\) | ||||
0.570519 | + | 0.821284i | \(0.306742\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 446.855i | − | 1.06141i | −0.847555 | − | 0.530707i | \(-0.821926\pi\) | ||
0.847555 | − | 0.530707i | \(-0.178074\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −486.017 | −1.14357 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 326.972 | 0.765742 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 281.363i | 0.652815i | 0.945229 | + | 0.326408i | \(0.105838\pi\) | ||||
−0.945229 | + | 0.326408i | \(0.894162\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 273.831i | 0.632405i | 0.948692 | + | 0.316203i | \(0.102408\pi\) | ||||
−0.948692 | + | 0.316203i | \(0.897592\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −403.041 | + | 167.021i | −0.922291 | + | 0.382198i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 746.505i | − | 1.70047i | −0.526405 | − | 0.850234i | \(-0.676460\pi\) | ||
0.526405 | − | 0.850234i | \(-0.323540\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −101.138 | −0.228301 | −0.114151 | − | 0.993463i | \(-0.536415\pi\) | ||||
−0.114151 | + | 0.993463i | \(0.536415\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 199.743i | − | 0.448862i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 617.400i | − | 1.37506i | −0.726158 | − | 0.687528i | \(-0.758696\pi\) | ||
0.726158 | − | 0.687528i | \(-0.241304\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 280.523i | 0.622002i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 502.483i | 1.10436i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 40.5778 | 0.0887917 | 0.0443959 | − | 0.999014i | \(-0.485864\pi\) | ||||
0.0443959 | + | 0.999014i | \(0.485864\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −409.282 | −0.887814 | −0.443907 | − | 0.896073i | \(-0.646408\pi\) | ||||
−0.443907 | + | 0.896073i | \(0.646408\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 642.547 | 1.38779 | 0.693895 | − | 0.720076i | \(-0.255893\pi\) | ||||
0.693895 | + | 0.720076i | \(0.255893\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −787.885 | −1.68712 | −0.843560 | − | 0.537035i | \(-0.819544\pi\) | ||||
−0.843560 | + | 0.537035i | \(0.819544\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 280.485i | − | 0.598049i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 406.818 | 0.860080 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −742.836 | + | 307.832i | −1.56387 | + | 0.648068i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −329.344 | −0.687566 | −0.343783 | − | 0.939049i | \(-0.611708\pi\) | ||||
−0.343783 | + | 0.939049i | \(0.611708\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −311.301 | −0.647196 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 703.885i | 1.45131i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 172.055i | 0.353296i | 0.984274 | + | 0.176648i | \(0.0565254\pi\) | ||||
−0.984274 | + | 0.176648i | \(0.943475\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −768.359 | −1.56489 | −0.782443 | − | 0.622723i | \(-0.786026\pi\) | ||||
−0.782443 | + | 0.622723i | \(0.786026\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 201.866i | − | 0.409465i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 854.661i | 1.71964i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −704.745 | −1.41232 | −0.706158 | − | 0.708055i | \(-0.749573\pi\) | ||||
−0.706158 | + | 0.708055i | \(0.749573\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −621.881 | −1.23634 | −0.618172 | − | 0.786043i | \(-0.712126\pi\) | ||||
−0.618172 | + | 0.786043i | \(0.712126\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1368.47 | −2.70984 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 334.039i | 0.656265i | 0.944632 | + | 0.328133i | \(0.106419\pi\) | ||||
−0.944632 | + | 0.328133i | \(0.893581\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 911.308 | 1.78338 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 1308.82i | − | 2.54139i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 30.2722 | 0.0585535 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 439.593i | 0.843749i | 0.906654 | + | 0.421875i | \(0.138628\pi\) | ||||
−0.906654 | + | 0.421875i | \(0.861372\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 624.484i | − | 1.19404i | −0.802226 | − | 0.597021i | \(-0.796351\pi\) | ||
0.802226 | − | 0.597021i | \(-0.203649\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 600.737i | 1.13992i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.74751 | −0.00330342 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −277.048 | −0.519789 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 819.834i | − | 1.53240i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 117.209 | 0.217457 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −641.553 | −1.18586 | −0.592932 | − | 0.805252i | \(-0.702030\pi\) | ||||
−0.592932 | + | 0.805252i | \(0.702030\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 1250.72i | − | 2.29490i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 118.198i | − | 0.216084i | −0.994146 | − | 0.108042i | \(-0.965542\pi\) | ||
0.994146 | − | 0.108042i | \(-0.0344581\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −127.858 | − | 308.536i | −0.232046 | − | 0.559956i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 931.167i | − | 1.68385i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 992.629 | 1.78210 | 0.891049 | − | 0.453907i | \(-0.149970\pi\) | ||||
0.891049 | + | 0.453907i | \(0.149970\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 401.778i | 0.718744i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 171.881i | − | 0.305295i | −0.988281 | − | 0.152648i | \(-0.951220\pi\) | ||
0.988281 | − | 0.152648i | \(-0.0487800\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 478.437i | − | 0.846791i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 353.453i | 0.621182i | 0.950544 | + | 0.310591i | \(0.100527\pi\) | ||||
−0.950544 | + | 0.310591i | \(0.899473\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −178.222 | −0.312122 | −0.156061 | − | 0.987747i | \(-0.549880\pi\) | ||||
−0.156061 | + | 0.987747i | \(0.549880\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 971.767 | 1.69003 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −988.498 | −1.71317 | −0.856584 | − | 0.516008i | \(-0.827417\pi\) | ||||
−0.856584 | + | 0.516008i | \(0.827417\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 387.252 | 0.666527 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 385.637i | 0.661470i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −448.477 | −0.764014 | −0.382007 | − | 0.924159i | \(-0.624767\pi\) | ||||
−0.382007 | + | 0.924159i | \(0.624767\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 380.493 | + | 918.176i | 0.645999 | + | 1.55887i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −869.085 | −1.46557 | −0.732787 | − | 0.680458i | \(-0.761781\pi\) | ||||
−0.732787 | + | 0.680458i | \(0.761781\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −754.621 | −1.26827 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 187.244i | 0.312594i | 0.987710 | + | 0.156297i | \(0.0499556\pi\) | ||||
−0.987710 | + | 0.156297i | \(0.950044\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 353.316i | − | 0.587881i | −0.955824 | − | 0.293940i | \(-0.905033\pi\) | ||
0.955824 | − | 0.293940i | \(-0.0949667\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −500.889 | −0.827916 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 60.7690i | − | 0.100114i | −0.998746 | − | 0.0500569i | \(-0.984060\pi\) | ||
0.998746 | − | 0.0500569i | \(-0.0159403\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 29.8972i | 0.0489315i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 774.683 | 1.26376 | 0.631878 | − | 0.775067i | \(-0.282284\pi\) | ||||
0.631878 | + | 0.775067i | \(0.282284\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 379.362 | 0.614849 | 0.307424 | − | 0.951573i | \(-0.400533\pi\) | ||||
0.307424 | + | 0.951573i | \(0.400533\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −428.108 | −0.691612 | −0.345806 | − | 0.938306i | \(-0.612394\pi\) | ||||
−0.345806 | + | 0.938306i | \(0.612394\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 194.964i | − | 0.312944i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 108.025 | 0.172840 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 467.508i | − | 0.743255i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −878.002 | −1.39145 | −0.695723 | − | 0.718310i | \(-0.744916\pi\) | ||||
−0.695723 | + | 0.718310i | \(0.744916\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 909.322i | 1.43200i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 115.757i | 0.181722i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 1234.82i | − | 1.92640i | −0.268785 | − | 0.963200i | \(-0.586622\pi\) | ||
0.268785 | − | 0.963200i | \(-0.413378\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 43.6391 | 0.0678680 | 0.0339340 | − | 0.999424i | \(-0.489196\pi\) | ||||
0.0339340 | + | 0.999424i | \(0.489196\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0.0739040 | 0.000114226 | 5.71128e−5 | − | 1.00000i | \(-0.499982\pi\) | ||||
5.71128e−5 | 1.00000i | \(0.499982\pi\) | ||||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 361.541i | 0.557074i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 468.859 | 0.718008 | 0.359004 | − | 0.933336i | \(-0.383116\pi\) | ||||
0.359004 | + | 0.933336i | \(0.383116\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 767.568 | 1.17186 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 153.264i | 0.232571i | 0.993216 | + | 0.116286i | \(0.0370988\pi\) | ||||
−0.993216 | + | 0.116286i | \(0.962901\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 670.154i | − | 1.01385i | −0.861991 | − | 0.506924i | \(-0.830782\pi\) | ||
0.861991 | − | 0.506924i | \(-0.169218\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1153.38 | + | 477.960i | −1.73440 | + | 0.718737i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 403.622i | 0.605130i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 316.124 | 0.471124 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 819.498i | − | 1.21768i | −0.793294 | − | 0.608839i | \(-0.791635\pi\) | ||
0.793294 | − | 0.608839i | \(-0.208365\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 842.863i | 1.24500i | 0.782621 | + | 0.622498i | \(0.213882\pi\) | ||||
−0.782621 | + | 0.622498i | \(0.786118\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 687.043i | 1.01185i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1286.00i | 1.88286i | 0.337205 | + | 0.941431i | \(0.390518\pi\) | ||||
−0.337205 | + | 0.941431i | \(0.609482\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 659.704 | 0.963071 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −380.860 | −0.552771 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −154.537 | −0.223642 | −0.111821 | − | 0.993728i | \(-0.535668\pi\) | ||||
−0.111821 | + | 0.993728i | \(0.535668\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1689.83 | −2.43142 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 416.066i | − | 0.596938i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 934.984 | 1.33379 | 0.666893 | − | 0.745153i | \(-0.267624\pi\) | ||||
0.666893 | + | 0.745153i | \(0.267624\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −296.109 | − | 714.547i | −0.421208 | − | 1.01643i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1335.72 | −1.88928 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 616.444 | 0.869455 | 0.434728 | − | 0.900562i | \(-0.356845\pi\) | ||||
0.434728 | + | 0.900562i | \(0.356845\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 1201.14i | − | 1.68463i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 485.813i | 0.679458i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1116.28 | 1.55255 | 0.776273 | − | 0.630397i | \(-0.217108\pi\) | ||||
0.776273 | + | 0.630397i | \(0.217108\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 1277.50i | − | 1.77184i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 743.907i | 1.02608i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −457.431 | −0.629203 | −0.314602 | − | 0.949224i | \(-0.601871\pi\) | ||||
−0.314602 | + | 0.949224i | \(0.601871\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −603.384 | −0.825423 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −747.874 | −1.02029 | −0.510146 | − | 0.860088i | \(-0.670409\pi\) | ||||
−0.510146 | + | 0.860088i | \(0.670409\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 271.180i | − | 0.367950i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1211.75 | 1.63971 | 0.819855 | − | 0.572571i | \(-0.194054\pi\) | ||||
0.819855 | + | 0.572571i | \(0.194054\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 354.724i | 0.477422i | 0.971091 | + | 0.238711i | \(0.0767248\pi\) | ||||
−0.971091 | + | 0.238711i | \(0.923275\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −802.461 | −1.07713 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 800.218i | − | 1.06838i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 946.440i | 1.26024i | 0.776498 | + | 0.630120i | \(0.216994\pi\) | ||||
−0.776498 | + | 0.630120i | \(0.783006\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 306.757i | − | 0.406301i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −378.745 | −0.500324 | −0.250162 | − | 0.968204i | \(-0.580484\pi\) | ||||
−0.250162 | + | 0.968204i | \(0.580484\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −827.308 | −1.08713 | −0.543567 | − | 0.839366i | \(-0.682926\pi\) | ||||
−0.543567 | + | 0.839366i | \(0.682926\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 1220.79i | − | 1.59999i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −357.062 | −0.465531 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −674.940 | −0.877686 | −0.438843 | − | 0.898564i | \(-0.644612\pi\) | ||||
−0.438843 | + | 0.898564i | \(0.644612\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1468.47i | 1.89971i | 0.312693 | + | 0.949854i | \(0.398769\pi\) | ||||
−0.312693 | + | 0.949854i | \(0.601231\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 2213.80i | − | 2.85652i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −263.527 | − | 635.923i | −0.338289 | − | 0.816332i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 826.307i | 1.05801i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2216.62 | −2.82372 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 1121.86i | − | 1.42548i | −0.701427 | − | 0.712742i | \(-0.747453\pi\) | ||
0.701427 | − | 0.712742i | \(-0.252547\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 466.989i | − | 0.590378i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 312.208i | 0.393705i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 161.200i | − | 0.202258i | −0.994873 | − | 0.101129i | \(-0.967755\pi\) | ||
0.994873 | − | 0.101129i | \(-0.0322455\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −44.8991 | −0.0561941 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 881.074 | 1.09723 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1508.83 | 1.87432 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1304.40 | −1.61236 | −0.806181 | − | 0.591669i | \(-0.798469\pi\) | ||||
−0.806181 | + | 0.591669i | \(0.798469\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 990.315i | − | 1.22110i | −0.791976 | − | 0.610552i | \(-0.790948\pi\) | ||
0.791976 | − | 0.610552i | \(-0.209052\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 549.842 | 0.674653 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −922.223 | + | 382.170i | −1.12879 | + | 0.467773i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −11.1570 | −0.0135896 | −0.00679479 | − | 0.999977i | \(-0.502163\pi\) | ||||
−0.00679479 | + | 0.999977i | \(0.502163\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1108.14 | −1.34646 | −0.673232 | − | 0.739432i | \(-0.735094\pi\) | ||||
−0.673232 | + | 0.739432i | \(0.735094\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 412.437i | − | 0.498715i | −0.968412 | − | 0.249357i | \(-0.919781\pi\) | ||
0.968412 | − | 0.249357i | \(-0.0802194\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1123.73i | 1.35552i | 0.735282 | + | 0.677761i | \(0.237050\pi\) | ||||
−0.735282 | + | 0.677761i | \(0.762950\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −173.842 | −0.208694 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 1548.96i | − | 1.85504i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 351.722i | − | 0.419216i | −0.977785 | − | 0.209608i | \(-0.932781\pi\) | ||
0.977785 | − | 0.209608i | \(-0.0672188\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 532.020 | 0.632604 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 906.837 | 1.07318 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −488.904 | −0.577218 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 934.760i | 1.09842i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1698.58 | 1.99130 | 0.995649 | − | 0.0931811i | \(-0.0297036\pi\) | ||||
0.995649 | + | 0.0931811i | \(0.0297036\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1684.15i | 1.96517i | 0.185816 | + | 0.982585i | \(0.440507\pi\) | ||||
−0.185816 | + | 0.982585i | \(0.559493\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 828.579 | 0.964585 | 0.482293 | − | 0.876010i | \(-0.339804\pi\) | ||||
0.482293 | + | 0.876010i | \(0.339804\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 841.313i | − | 0.974870i | −0.873159 | − | 0.487435i | \(-0.837933\pi\) | ||
0.873159 | − | 0.487435i | \(-0.162067\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2598.82i | 3.00442i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 900.275i | − | 1.03599i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 267.820 | 0.307486 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1138.14 | 1.30073 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 274.890i | − | 0.313443i | −0.987643 | − | 0.156722i | \(-0.949907\pi\) | ||
0.987643 | − | 0.156722i | \(-0.0500926\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1175.79 | −1.33460 | −0.667302 | − | 0.744787i | \(-0.732551\pi\) | ||||
−0.667302 | + | 0.744787i | \(0.732551\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 213.071 | 0.241303 | 0.120652 | − | 0.992695i | \(-0.461502\pi\) | ||||
0.120652 | + | 0.992695i | \(0.461502\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 1091.62i | − | 1.23069i | −0.788259 | − | 0.615344i | \(-0.789017\pi\) | ||
0.788259 | − | 0.615344i | \(-0.210983\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 887.564i | 0.998385i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −68.6246 | + | 28.4381i | −0.0768472 | + | 0.0318456i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2087.82i | 2.33276i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 919.499 | 1.02280 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 571.969i | − | 0.634816i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 1635.41i | − | 1.80708i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 178.701i | 0.197024i | 0.995136 | + | 0.0985120i | \(0.0314083\pi\) | ||||
−0.995136 | + | 0.0985120i | \(0.968592\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 709.200i | − | 0.778485i | −0.921135 | − | 0.389242i | \(-0.872737\pi\) | ||
0.921135 | − | 0.389242i | \(-0.127263\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 374.405 | 0.410082 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 749.202 | 0.817014 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −577.167 | −0.628038 | −0.314019 | − | 0.949417i | \(-0.601676\pi\) | ||||
−0.314019 | + | 0.949417i | \(0.601676\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −816.071 | −0.884150 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1722.83i | 1.86252i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −474.299 | −0.510547 | −0.255274 | − | 0.966869i | \(-0.582166\pi\) | ||||
−0.255274 | + | 0.966869i | \(0.582166\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −265.704 | + | 110.108i | −0.285396 | + | 0.118268i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −729.586 | −0.780306 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −895.322 | −0.955520 | −0.477760 | − | 0.878490i | \(-0.658551\pi\) | ||||
−0.477760 | + | 0.878490i | \(0.658551\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 702.877i | − | 0.746947i | −0.927641 | − | 0.373473i | \(-0.878167\pi\) | ||
0.927641 | − | 0.373473i | \(-0.121833\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 831.905i | 0.882189i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 189.972 | 0.200604 | 0.100302 | − | 0.994957i | \(-0.468019\pi\) | ||||
0.100302 | + | 0.994957i | \(0.468019\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 870.160i | 0.916923i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 1018.27i | − | 1.06849i | −0.845329 | − | 0.534247i | \(-0.820595\pi\) | ||
0.845329 | − | 0.534247i | \(-0.179405\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 845.830 | 0.885686 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 643.919 | 0.671448 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1775.35 | −1.84740 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2389.78i | 2.47646i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 569.922 | 0.589371 | 0.294686 | − | 0.955594i | \(-0.404785\pi\) | ||||
0.294686 | + | 0.955594i | \(0.404785\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 98.6776i | 0.101625i | 0.998708 | + | 0.0508123i | \(0.0161810\pi\) | ||||
−0.998708 | + | 0.0508123i | \(0.983819\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1649.40 | −1.69517 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 859.441i | 0.879674i | 0.898078 | + | 0.439837i | \(0.144964\pi\) | ||||
−0.898078 | + | 0.439837i | \(0.855036\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 188.496i | − | 0.192539i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 1014.55i | − | 1.03210i | −0.856559 | − | 0.516049i | \(-0.827402\pi\) | ||
0.856559 | − | 0.516049i | \(-0.172598\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2025.99 | 2.05684 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1206.44 | 1.21986 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 803.940i | − | 0.811241i | −0.914042 | − | 0.405621i | \(-0.867055\pi\) | ||
0.914042 | − | 0.405621i | \(-0.132945\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −143.898 | −0.144621 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −865.263 | −0.867867 | −0.433933 | − | 0.900945i | \(-0.642875\pi\) | ||||
−0.433933 | + | 0.900945i | \(0.642875\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2736.3.o.r.721.20 | 20 | ||
3.2 | odd | 2 | 912.3.o.e.721.11 | 20 | |||
4.3 | odd | 2 | 1368.3.o.c.721.20 | 20 | |||
12.11 | even | 2 | 456.3.o.a.265.1 | ✓ | 20 | ||
19.18 | odd | 2 | inner | 2736.3.o.r.721.19 | 20 | ||
57.56 | even | 2 | 912.3.o.e.721.1 | 20 | |||
76.75 | even | 2 | 1368.3.o.c.721.19 | 20 | |||
228.227 | odd | 2 | 456.3.o.a.265.11 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
456.3.o.a.265.1 | ✓ | 20 | 12.11 | even | 2 | ||
456.3.o.a.265.11 | yes | 20 | 228.227 | odd | 2 | ||
912.3.o.e.721.1 | 20 | 57.56 | even | 2 | |||
912.3.o.e.721.11 | 20 | 3.2 | odd | 2 | |||
1368.3.o.c.721.19 | 20 | 76.75 | even | 2 | |||
1368.3.o.c.721.20 | 20 | 4.3 | odd | 2 | |||
2736.3.o.r.721.19 | 20 | 19.18 | odd | 2 | inner | ||
2736.3.o.r.721.20 | 20 | 1.1 | even | 1 | trivial |