Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1444,3,Mod(721,1444)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1444, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1444.721");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1444 = 2^{2} \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1444.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: | \(39.3461501736\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 721.3 | ||
Character | \(\chi\) | \(=\) | 1444.721 |
Dual form | 1444.3.c.d.721.22 |
$q$-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 \(\left(\mathbb{Z}/1444\mathbb{Z}\right)^\times\).
\(n\) | \(723\) | \(1085\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | − 4.89235i | − 1.63078i | −0.578910 | − | 0.815391i | \(-0.696522\pi\) | ||||
0.578910 | − | 0.815391i | \(-0.303478\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −9.07521 | −1.81504 | −0.907521 | − | 0.420007i | \(-0.862028\pi\) | ||||
−0.907521 | + | 0.420007i | \(0.862028\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 11.2253 | 1.60361 | 0.801806 | − | 0.597584i | \(-0.203873\pi\) | ||||
0.801806 | + | 0.597584i | \(0.203873\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −14.9351 | −1.65945 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.07525 | −0.461386 | −0.230693 | − | 0.973027i | \(-0.574099\pi\) | ||||
−0.230693 | + | 0.973027i | \(0.574099\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 2.03857i | − 0.156813i | −0.996921 | − | 0.0784064i | \(-0.975017\pi\) | ||||
0.996921 | − | 0.0784064i | \(-0.0249832\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 44.3991i | 2.95994i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −15.6174 | −0.918672 | −0.459336 | − | 0.888263i | \(-0.651913\pi\) | ||||
−0.459336 | + | 0.888263i | \(0.651913\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 54.9180i | − 2.61514i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −19.4729 | −0.846649 | −0.423324 | − | 0.905978i | \(-0.639137\pi\) | ||||
−0.423324 | + | 0.905978i | \(0.639137\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 57.3594 | 2.29438 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 29.0364i | 1.07542i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.45784i | 0.0502703i | 0.999684 | + | 0.0251351i | \(0.00800160\pi\) | ||||
−0.999684 | + | 0.0251351i | \(0.991998\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 44.7102i | 1.44226i | 0.692798 | + | 0.721132i | \(0.256378\pi\) | ||||
−0.692798 | + | 0.721132i | \(0.743622\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 24.8299i | 0.752420i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −101.872 | −2.91062 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 34.8762i | 0.942600i | 0.881973 | + | 0.471300i | \(0.156215\pi\) | ||||
−0.881973 | + | 0.471300i | \(0.843785\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −9.97338 | −0.255728 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 60.8205i | 1.48343i | 0.670717 | + | 0.741713i | \(0.265987\pi\) | ||||
−0.670717 | + | 0.741713i | \(0.734013\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.1884 | 0.260194 | 0.130097 | − | 0.991501i | \(-0.458471\pi\) | ||||
0.130097 | + | 0.991501i | \(0.458471\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 135.539 | 3.01197 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −14.7027 | −0.312823 | −0.156412 | − | 0.987692i | \(-0.549993\pi\) | ||||
−0.156412 | + | 0.987692i | \(0.549993\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 77.0071 | 1.57157 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 76.4058i | 1.49815i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 16.7970i | 0.316925i | 0.987365 | + | 0.158463i | \(0.0506538\pi\) | ||||
−0.987365 | + | 0.158463i | \(0.949346\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 46.0589 | 0.837435 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.20357i | 0.105145i | 0.998617 | + | 0.0525727i | \(0.0167421\pi\) | ||||
−0.998617 | + | 0.0525727i | \(0.983258\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 71.3685 | 1.16998 | 0.584988 | − | 0.811042i | \(-0.301099\pi\) | ||||
0.584988 | + | 0.811042i | \(0.301099\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −167.650 | −2.66112 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 18.5004i | 0.284622i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 65.0771i | − 0.971300i | −0.874153 | − | 0.485650i | \(-0.838583\pi\) | ||||
0.874153 | − | 0.485650i | \(-0.161417\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 95.2683i | 1.38070i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 108.429i | − 1.52716i | −0.645711 | − | 0.763582i | \(-0.723439\pi\) | ||||
0.645711 | − | 0.763582i | \(-0.276561\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −35.3311 | −0.483987 | −0.241994 | − | 0.970278i | \(-0.577801\pi\) | ||||
−0.241994 | + | 0.970278i | \(0.577801\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 280.622i | − 3.74163i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −56.9711 | −0.739885 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 113.483i | 1.43649i | 0.695788 | + | 0.718247i | \(0.255055\pi\) | ||||
−0.695788 | + | 0.718247i | \(0.744945\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.64040 | 0.0943260 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 28.8906 | 0.348079 | 0.174040 | − | 0.984739i | \(-0.444318\pi\) | ||||
0.174040 | + | 0.984739i | \(0.444318\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 141.731 | 1.66743 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.13225 | 0.0819799 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 60.0053i | − 0.674217i | −0.941466 | − | 0.337109i | \(-0.890551\pi\) | ||||
0.941466 | − | 0.337109i | \(-0.109449\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 22.8835i | − 0.251467i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 218.738 | 2.35202 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 29.7750i | 0.306959i | 0.988152 | + | 0.153479i | \(0.0490479\pi\) | ||||
−0.988152 | + | 0.153479i | \(0.950952\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 75.7991 | 0.765648 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 194.467 | 1.92541 | 0.962707 | − | 0.270548i | \(-0.0872047\pi\) | ||||
0.962707 | + | 0.270548i | \(0.0872047\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 122.285i | − 1.18723i | −0.804748 | − | 0.593617i | \(-0.797699\pi\) | ||||
0.804748 | − | 0.593617i | \(-0.202301\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 498.392i | 4.74659i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.47576i | 0.0137922i | 0.999976 | + | 0.00689609i | \(0.00219511\pi\) | ||||
−0.999976 | + | 0.00689609i | \(0.997805\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 64.3521i | − 0.590386i | −0.955438 | − | 0.295193i | \(-0.904616\pi\) | ||||
0.955438 | − | 0.295193i | \(-0.0953840\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 170.626 | 1.53717 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 105.595i | 0.934468i | 0.884134 | + | 0.467234i | \(0.154749\pi\) | ||||
−0.884134 | + | 0.467234i | \(0.845251\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 176.721 | 1.53670 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 30.4461i | 0.260223i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −175.310 | −1.47319 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −95.2419 | −0.787123 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 297.555 | 2.41915 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −293.669 | −2.34935 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 167.771i | 1.32103i | 0.750811 | + | 0.660517i | \(0.229663\pi\) | ||||
−0.750811 | + | 0.660517i | \(0.770337\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − 54.7373i | − 0.424320i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.7733 | 0.112773 | 0.0563865 | − | 0.998409i | \(-0.482042\pi\) | ||||
0.0563865 | + | 0.998409i | \(0.482042\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − 263.511i | − 1.95193i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 111.662 | 0.815052 | 0.407526 | − | 0.913194i | \(-0.366392\pi\) | ||||
0.407526 | + | 0.913194i | \(0.366392\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −213.252 | −1.53418 | −0.767092 | − | 0.641537i | \(-0.778297\pi\) | ||||
−0.767092 | + | 0.641537i | \(0.778297\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 71.9307i | 0.510147i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 10.3462i | 0.0723513i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − 13.2302i | − 0.0912426i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 376.745i | − 2.56289i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 63.5403 | 0.426445 | 0.213223 | − | 0.977004i | \(-0.431604\pi\) | ||||
0.213223 | + | 0.977004i | \(0.431604\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 27.9116i | 0.184845i | 0.995720 | + | 0.0924225i | \(0.0294610\pi\) | ||||
−0.995720 | + | 0.0924225i | \(0.970539\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 233.247 | 1.52449 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 405.754i | − 2.61777i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 229.427 | 1.46132 | 0.730660 | − | 0.682742i | \(-0.239213\pi\) | ||||
0.730660 | + | 0.682742i | \(0.239213\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 82.1770 | 0.516836 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −218.589 | −1.35770 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13.9039 | −0.0853000 | −0.0426500 | − | 0.999090i | \(-0.513580\pi\) | ||||
−0.0426500 | + | 0.999090i | \(0.513580\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 225.336i | − 1.36567i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 174.780i | 1.04659i | 0.852153 | + | 0.523293i | \(0.175297\pi\) | ||||
−0.852153 | + | 0.523293i | \(0.824703\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 164.844 | 0.975410 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 326.690i | − 1.88838i | −0.329400 | − | 0.944190i | \(-0.606847\pi\) | ||||
0.329400 | − | 0.944190i | \(-0.393153\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 643.876 | 3.67929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 30.3500 | 0.171469 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 244.659i | 1.36681i | 0.730039 | + | 0.683406i | \(0.239502\pi\) | ||||
−0.730039 | + | 0.683406i | \(0.760498\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 288.840i | − 1.59580i | −0.602789 | − | 0.797900i | \(-0.705944\pi\) | ||||
0.602789 | − | 0.797900i | \(-0.294056\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 349.160i | − 1.90798i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 316.509i | − 1.71086i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 79.2623 | 0.423862 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 325.941i | 1.72456i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 105.373 | 0.551691 | 0.275846 | − | 0.961202i | \(-0.411042\pi\) | ||||
0.275846 | + | 0.961202i | \(0.411042\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 200.893i | 1.04090i | 0.853893 | + | 0.520449i | \(0.174235\pi\) | ||||
−0.853893 | + | 0.520449i | \(0.825765\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 90.5105 | 0.464156 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 112.050 | 0.568782 | 0.284391 | − | 0.958708i | \(-0.408209\pi\) | ||||
0.284391 | + | 0.958708i | \(0.408209\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −278.028 | −1.39713 | −0.698564 | − | 0.715548i | \(-0.746177\pi\) | ||||
−0.698564 | + | 0.715548i | \(0.746177\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −318.380 | −1.58398 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 16.3646i | 0.0806140i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 551.959i | − 2.69248i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 290.829 | 1.40497 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 114.046i | 0.540503i | 0.962790 | + | 0.270252i | \(0.0871069\pi\) | ||||
−0.962790 | + | 0.270252i | \(0.912893\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −530.470 | −2.49047 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −101.537 | −0.472264 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 501.885i | 2.31283i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 172.852i | 0.789278i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 31.8372i | 0.144060i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 247.579i | 1.11022i | 0.831777 | + | 0.555109i | \(0.187324\pi\) | ||||
−0.831777 | + | 0.555109i | \(0.812676\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −856.666 | −3.80741 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 86.1442i | 0.379490i | 0.981833 | + | 0.189745i | \(0.0607661\pi\) | ||||
−0.981833 | + | 0.189745i | \(0.939234\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −125.448 | −0.547808 | −0.273904 | − | 0.961757i | \(-0.588315\pi\) | ||||
−0.273904 | + | 0.961757i | \(0.588315\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 278.722i | 1.20659i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −34.0856 | −0.146290 | −0.0731451 | − | 0.997321i | \(-0.523304\pi\) | ||||
−0.0731451 | + | 0.997321i | \(0.523304\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 133.430 | 0.567787 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 555.198 | 2.34261 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −325.140 | −1.36042 | −0.680210 | − | 0.733017i | \(-0.738111\pi\) | ||||
−0.680210 | + | 0.733017i | \(0.738111\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 319.265i | 1.32475i | 0.749171 | + | 0.662376i | \(0.230452\pi\) | ||||
−0.749171 | + | 0.662376i | \(0.769548\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 223.948i | 0.921595i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −698.856 | −2.85247 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − 141.343i | − 0.567642i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −219.505 | −0.874521 | −0.437260 | − | 0.899335i | \(-0.644051\pi\) | ||||
−0.437260 | + | 0.899335i | \(0.644051\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 98.8299 | 0.390632 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − 693.399i | − 2.71921i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 148.555i | 0.578035i | 0.957324 | + | 0.289018i | \(0.0933286\pi\) | ||||
−0.957324 | + | 0.289018i | \(0.906671\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 391.495i | 1.51156i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 21.7729i | − 0.0834210i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 223.824 | 0.851043 | 0.425522 | − | 0.904948i | \(-0.360091\pi\) | ||||
0.425522 | + | 0.904948i | \(0.360091\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − 152.437i | − 0.575233i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −293.567 | −1.09950 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 351.687i | 1.30739i | 0.756760 | + | 0.653693i | \(0.226781\pi\) | ||||
−0.756760 | + | 0.653693i | \(0.773219\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 98.1840 | 0.362303 | 0.181151 | − | 0.983455i | \(-0.442018\pi\) | ||||
0.181151 | + | 0.983455i | \(0.442018\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −111.954 | −0.410088 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −291.113 | −1.05859 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 222.229 | 0.802271 | 0.401136 | − | 0.916019i | \(-0.368616\pi\) | ||||
0.401136 | + | 0.916019i | \(0.368616\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − 667.749i | − 2.39337i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 445.385i | 1.58500i | 0.609872 | + | 0.792500i | \(0.291221\pi\) | ||||
−0.609872 | + | 0.792500i | \(0.708779\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 269.677 | 0.952924 | 0.476462 | − | 0.879195i | \(-0.341919\pi\) | ||||
0.476462 | + | 0.879195i | \(0.341919\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 682.728i | 2.37884i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −45.0963 | −0.156043 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 145.670 | 0.500583 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 128.310i | 0.437917i | 0.975734 | + | 0.218959i | \(0.0702660\pi\) | ||||
−0.975734 | + | 0.218959i | \(0.929734\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 56.2987i | − 0.190843i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 147.367i | − 0.496184i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 39.6969i | 0.132765i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 125.593 | 0.417251 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 951.399i | − 3.13993i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −647.684 | −2.12356 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 246.087i | − 0.801586i | −0.916169 | − | 0.400793i | \(-0.868735\pi\) | ||||
0.916169 | − | 0.400793i | \(-0.131265\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −598.261 | −1.93612 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 383.981 | 1.23467 | 0.617333 | − | 0.786702i | \(-0.288213\pi\) | ||||
0.617333 | + | 0.786702i | \(0.288213\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −212.369 | −0.678495 | −0.339247 | − | 0.940697i | \(-0.610172\pi\) | ||||
−0.339247 | + | 0.940697i | \(0.610172\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1521.46 | 4.83004 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 250.664i | 0.790738i | 0.918522 | + | 0.395369i | \(0.129383\pi\) | ||||
−0.918522 | + | 0.395369i | \(0.870617\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 7.39889i | − 0.0231940i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.21995 | 0.0224921 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 116.931i | − 0.359788i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −314.833 | −0.962791 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −165.042 | −0.501647 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 99.5337i | − 0.300706i | −0.988632 | − | 0.150353i | \(-0.951959\pi\) | ||||
0.988632 | − | 0.150353i | \(-0.0480410\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 520.878i | − 1.56420i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 590.588i | 1.76295i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 654.811i | 1.94306i | 0.236915 | + | 0.971530i | \(0.423864\pi\) | ||||
−0.236915 | + | 0.971530i | \(0.576136\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 516.607 | 1.52391 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 226.915i | − 0.665441i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 314.388 | 0.916583 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − 864.580i | − 2.50603i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −220.584 | −0.635690 | −0.317845 | − | 0.948143i | \(-0.602959\pi\) | ||||
−0.317845 | + | 0.948143i | \(0.602959\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −196.974 | −0.564396 | −0.282198 | − | 0.959356i | \(-0.591064\pi\) | ||||
−0.282198 | + | 0.959356i | \(0.591064\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 59.1926 | 0.168640 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 105.146 | 0.297864 | 0.148932 | − | 0.988847i | \(-0.452416\pi\) | ||||
0.148932 | + | 0.988847i | \(0.452416\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 984.012i | 2.77186i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 857.677i | 2.40246i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −107.507 | −0.299463 | −0.149731 | − | 0.988727i | \(-0.547841\pi\) | ||||
−0.149731 | + | 0.988727i | \(0.547841\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 465.956i | 1.28363i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 320.637 | 0.878458 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 413.447 | 1.12656 | 0.563280 | − | 0.826266i | \(-0.309539\pi\) | ||||
0.563280 | + | 0.826266i | \(0.309539\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − 908.358i | − 2.46167i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 188.552i | 0.508226i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 309.835i | 0.830656i | 0.909672 | + | 0.415328i | \(0.136333\pi\) | ||||
−0.909672 | + | 0.415328i | \(0.863667\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1436.73i | 3.83128i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.97190 | 0.00788302 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 381.191i | 1.00578i | 0.864350 | + | 0.502890i | \(0.167730\pi\) | ||||
−0.864350 | + | 0.502890i | \(0.832270\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 820.795 | 2.15432 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 674.771i | 1.76180i | 0.473300 | + | 0.880902i | \(0.343063\pi\) | ||||
−0.473300 | + | 0.880902i | \(0.656937\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 517.025 | 1.34292 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −167.099 | −0.431780 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −72.7428 | −0.186999 | −0.0934997 | − | 0.995619i | \(-0.529805\pi\) | ||||
−0.0934997 | + | 0.995619i | \(0.529805\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 304.117 | 0.777792 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 72.2759i | − 0.183908i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 1029.88i | − 2.60730i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −764.241 | −1.92504 | −0.962520 | − | 0.271210i | \(-0.912576\pi\) | ||||
−0.962520 | + | 0.271210i | \(0.912576\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 119.673i | − 0.298437i | −0.988804 | − | 0.149218i | \(-0.952324\pi\) | ||||
0.988804 | − | 0.149218i | \(-0.0476757\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 91.1447 | 0.226166 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −69.3383 | −0.171206 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 177.005i | − 0.434902i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − 623.899i | − 1.52542i | −0.646738 | − | 0.762712i | \(-0.723867\pi\) | ||||
0.646738 | − | 0.762712i | \(-0.276133\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 546.290i | − 1.32917i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 69.6369i | 0.168612i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −262.188 | −0.631779 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1043.30i | 2.50192i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −805.018 | −1.92128 | −0.960642 | − | 0.277791i | \(-0.910398\pi\) | ||||
−0.960642 | + | 0.277791i | \(0.910398\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 449.818i | 1.06845i | 0.845342 | + | 0.534225i | \(0.179397\pi\) | ||||
−0.845342 | + | 0.534225i | \(0.820603\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 219.586 | 0.519115 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −895.806 | −2.10778 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 801.133 | 1.87619 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 50.6174 | 0.117989 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 505.775i | − 1.17349i | −0.809771 | − | 0.586746i | \(-0.800409\pi\) | ||||
0.809771 | − | 0.586746i | \(-0.199591\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 394.512i | 0.911113i | 0.890207 | + | 0.455556i | \(0.150560\pi\) | ||||
−0.890207 | + | 0.455556i | \(0.849440\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −64.7266 | −0.148797 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.1333i | 0.0230827i | 0.999933 | + | 0.0115414i | \(0.00367381\pi\) | ||||
−0.999933 | + | 0.0115414i | \(0.996326\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1150.11 | −2.60795 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 554.992 | 1.25280 | 0.626402 | − | 0.779500i | \(-0.284527\pi\) | ||||
0.626402 | + | 0.779500i | \(0.284527\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 544.561i | 1.22373i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 310.861i | − 0.695439i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 533.512i | 1.18822i | 0.804383 | + | 0.594112i | \(0.202496\pi\) | ||||
−0.804383 | + | 0.594112i | \(0.797504\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 308.679i | − 0.684433i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 136.553 | 0.301442 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 207.673i | 0.456423i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −29.4713 | −0.0644886 | −0.0322443 | − | 0.999480i | \(-0.510265\pi\) | ||||
−0.0322443 | + | 0.999480i | \(0.510265\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 453.473i | − 0.987958i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −20.6073 | −0.0447012 | −0.0223506 | − | 0.999750i | \(-0.507115\pi\) | ||||
−0.0223506 | + | 0.999750i | \(0.507115\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −833.016 | −1.79917 | −0.899586 | − | 0.436744i | \(-0.856131\pi\) | ||||
−0.899586 | + | 0.436744i | \(0.856131\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1985.09 | −4.26901 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 123.523 | 0.264503 | 0.132251 | − | 0.991216i | \(-0.457779\pi\) | ||||
0.132251 | + | 0.991216i | \(0.457779\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 730.509i | − 1.55759i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − 1122.44i | − 2.38309i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −56.7837 | −0.120050 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 250.865i | − 0.525922i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 107.182 | 0.223762 | 0.111881 | − | 0.993722i | \(-0.464313\pi\) | ||||
0.111881 | + | 0.993722i | \(0.464313\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 71.0975 | 0.147812 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1069.41i | 2.21411i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 270.214i | − 0.557143i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 573.209i | − 1.17702i | −0.808490 | − | 0.588510i | \(-0.799715\pi\) | ||||
0.808490 | − | 0.588510i | \(-0.200285\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 68.0227i | 0.139106i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 247.257 | 0.503579 | 0.251789 | − | 0.967782i | \(-0.418981\pi\) | ||||
0.251789 | + | 0.967782i | \(0.418981\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 22.7677i | − 0.0461819i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −687.893 | −1.38968 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 1217.14i | − 2.44898i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −321.230 | −0.643747 | −0.321874 | − | 0.946783i | \(-0.604313\pi\) | ||||
−0.321874 | + | 0.946783i | \(0.604313\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 855.084 | 1.70675 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 160.877 | 0.319835 | 0.159917 | − | 0.987130i | \(-0.448877\pi\) | ||||
0.159917 | + | 0.987130i | \(0.448877\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1764.83 | −3.49471 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 806.475i | − 1.59068i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 95.9149i | 0.188438i | 0.995552 | + | 0.0942189i | \(0.0300354\pi\) | ||||
−0.995552 | + | 0.0942189i | \(0.969965\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −396.602 | −0.776128 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1109.76i | 2.15488i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 74.6198 | 0.144332 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1598.28 | −3.07954 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 818.234i | − 1.57051i | −0.619175 | − | 0.785253i | \(-0.712533\pi\) | ||||
0.619175 | − | 0.785253i | \(-0.287467\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 198.802i | − 0.380119i | −0.981773 | − | 0.190059i | \(-0.939132\pi\) | ||||
0.981773 | − | 0.190059i | \(-0.0608681\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 3150.06i | − 6.00012i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 698.258i | − 1.32497i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −149.805 | −0.283186 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 92.6507i | − 0.174483i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 123.987 | 0.232620 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 13.3929i | − 0.0250334i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1196.96 | 2.22897 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −390.830 | −0.725102 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −908.860 | −1.67996 | −0.839982 | − | 0.542615i | \(-0.817434\pi\) | ||||
−0.839982 | + | 0.542615i | \(0.817434\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1413.11 | −2.60240 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 584.009i | 1.07158i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 252.201i | 0.461062i | 0.973065 | + | 0.230531i | \(0.0740463\pi\) | ||||
−0.973065 | + | 0.230531i | \(0.925954\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1065.89 | −1.94152 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1273.88i | 2.30358i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1548.47 | −2.79004 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −576.073 | −1.03424 | −0.517121 | − | 0.855912i | \(-0.672996\pi\) | ||||
−0.517121 | + | 0.855912i | \(0.672996\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 22.8082i | − 0.0408018i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − 387.778i | − 0.691227i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 407.673i | 0.724109i | 0.932157 | + | 0.362054i | \(0.117925\pi\) | ||||
−0.932157 | + | 0.362054i | \(0.882075\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 958.296i | − 1.69610i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 85.7657 | 0.151262 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 773.395i | 1.35922i | 0.733575 | + | 0.679609i | \(0.237850\pi\) | ||||
−0.733575 | + | 0.679609i | \(0.762150\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 678.192 | 1.18773 | 0.593863 | − | 0.804566i | \(-0.297602\pi\) | ||||
0.593863 | + | 0.804566i | \(0.297602\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 515.521i | − 0.899688i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1116.96 | −1.94253 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 634.074 | 1.09891 | 0.549457 | − | 0.835522i | \(-0.314835\pi\) | ||||
0.549457 | + | 0.835522i | \(0.314835\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 982.840 | 1.69748 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 324.305 | 0.558185 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 85.2492i | − 0.146225i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − 276.305i | − 0.472316i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −86.6998 | −0.147700 | −0.0738499 | − | 0.997269i | \(-0.523529\pi\) | ||||
−0.0738499 | + | 0.997269i | \(0.523529\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − 548.188i | − 0.927560i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 942.791 | 1.58987 | 0.794933 | − | 0.606697i | \(-0.207506\pi\) | ||||
0.794933 | + | 0.606697i | \(0.207506\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1590.98 | 2.67391 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1360.21i | 2.27841i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 510.991i | 0.853074i | 0.904470 | + | 0.426537i | \(0.140267\pi\) | ||||
−0.904470 | + | 0.426537i | \(0.859733\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − 684.427i | − 1.13881i | −0.822056 | − | 0.569407i | \(-0.807173\pi\) | ||||
0.822056 | − | 0.569407i | \(-0.192827\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 971.930i | 1.61182i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 864.340 | 1.42866 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 82.6292i | 0.136127i | 0.997681 | + | 0.0680636i | \(0.0216821\pi\) | ||||
−0.997681 | + | 0.0680636i | \(0.978318\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 80.0615 | 0.131464 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 29.9724i | 0.0490547i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −784.108 | −1.27913 | −0.639566 | − | 0.768736i | \(-0.720886\pi\) | ||||
−0.639566 | + | 0.768736i | \(0.720886\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2700.37 | −4.39085 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 470.095 | 0.761905 | 0.380952 | − | 0.924595i | \(-0.375596\pi\) | ||||
0.380952 | + | 0.924595i | \(0.375596\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −267.534 | −0.432204 | −0.216102 | − | 0.976371i | \(-0.569334\pi\) | ||||
−0.216102 | + | 0.976371i | \(0.569334\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 565.423i | − 0.910504i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 673.577i | − 1.08118i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1231.12 | 1.96979 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 544.676i | − 0.865940i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −757.403 | −1.20032 | −0.600161 | − | 0.799879i | \(-0.704897\pi\) | ||||
−0.600161 | + | 0.799879i | \(0.704897\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 557.954 | 0.881443 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 1522.56i | − 2.39773i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 156.984i | − 0.246443i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1619.39i | 2.53425i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 328.219i | − 0.512042i | −0.966671 | − | 0.256021i | \(-0.917588\pi\) | ||||
0.966671 | − | 0.256021i | \(-0.0824116\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 430.818 | 0.670012 | 0.335006 | − | 0.942216i | \(-0.391262\pi\) | ||||
0.335006 | + | 0.942216i | \(0.391262\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 496.753i | 0.770159i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 102.322 | 0.158148 | 0.0790740 | − | 0.996869i | \(-0.474804\pi\) | ||||
0.0790740 | + | 0.996869i | \(0.474804\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − 31.4847i | − 0.0485126i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2455.39 | 3.77173 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −269.405 | −0.412565 | −0.206283 | − | 0.978492i | \(-0.566137\pi\) | ||||
−0.206283 | + | 0.978492i | \(0.566137\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −134.070 | −0.204688 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 527.672 | 0.803153 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 38.7277i | 0.0587674i | 0.999568 | + | 0.0293837i | \(0.00935446\pi\) | ||||
−0.999568 | + | 0.0293837i | \(0.990646\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 967.272i | − 1.46335i | −0.681655 | − | 0.731674i | \(-0.738740\pi\) | ||||
0.681655 | − | 0.731674i | \(-0.261260\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 155.758 | 0.234930 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 28.3884i | − 0.0425613i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1211.24 | 1.81052 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −362.213 | −0.539811 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 478.524i | 0.711031i | 0.934670 | + | 0.355515i | \(0.115695\pi\) | ||||
−0.934670 | + | 0.355515i | \(0.884305\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1665.51i | 2.46742i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 409.627i | 0.605062i | 0.953140 | + | 0.302531i | \(0.0978316\pi\) | ||||
−0.953140 | + | 0.302531i | \(0.902168\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 334.233i | 0.492243i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 421.447 | 0.618865 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 327.446i | 0.479423i | 0.970844 | + | 0.239711i | \(0.0770528\pi\) | ||||
−0.970844 | + | 0.239711i | \(0.922947\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1013.36 | −1.47935 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 613.735i | 0.893356i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 34.2419 | 0.0496980 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −280.087 | −0.405336 | −0.202668 | − | 0.979248i | \(-0.564961\pi\) | ||||
−0.202668 | + | 0.979248i | \(0.564961\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 850.867 | 1.22780 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1935.30 | 2.78461 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 949.859i | − 1.36278i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 166.759i | 0.238568i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −448.669 | −0.640041 | −0.320020 | − | 0.947411i | \(-0.603690\pi\) | ||||
−0.320020 | + | 0.947411i | \(0.603690\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − 652.786i | − 0.925937i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2182.95 | 3.08762 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −91.6498 | −0.129266 | −0.0646332 | − | 0.997909i | \(-0.520588\pi\) | ||||
−0.0646332 | + | 0.997909i | \(0.520588\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − 1694.88i | − 2.38379i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 870.638i | − 1.22109i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 93.8942i | − 0.131321i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1590.70i | 2.21855i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 420.498 | 0.584837 | 0.292418 | − | 0.956290i | \(-0.405540\pi\) | ||||
0.292418 | + | 0.956290i | \(0.405540\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − 1372.69i | − 1.90386i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1561.96 | 2.16038 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 83.6207i | 0.115339i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −908.205 | −1.24925 | −0.624625 | − | 0.780925i | \(-0.714748\pi\) | ||||
−0.624625 | + | 0.780925i | \(0.714748\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1164.39 | 1.59725 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −174.733 | −0.239033 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 138.411 | 0.188828 | 0.0944139 | − | 0.995533i | \(-0.469902\pi\) | ||||
0.0944139 | + | 0.995533i | \(0.469902\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3419.04i | 4.65176i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 330.282i | 0.448144i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 40.6514 | 0.0550087 | 0.0275044 | − | 0.999622i | \(-0.491244\pi\) | ||||
0.0275044 | + | 0.999622i | \(0.491244\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 119.656i | − 0.161045i | −0.996753 | − | 0.0805223i | \(-0.974341\pi\) | ||||
0.996753 | − | 0.0805223i | \(-0.0256588\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −576.642 | −0.774016 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −431.483 | −0.577621 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 16.5659i | 0.0221173i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 114.859i | − 0.152942i | −0.997072 | − | 0.0764709i | \(-0.975635\pi\) | ||||
0.997072 | − | 0.0764709i | \(-0.0243652\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1073.89i | 1.42615i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 253.304i | − 0.335501i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.91689 | −0.00517423 | −0.00258711 | − | 0.999997i | \(-0.500824\pi\) | ||||
−0.00258711 | + | 0.999997i | \(0.500824\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − 483.510i | − 0.637036i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1013.16 | 1.33135 | 0.665677 | − | 0.746240i | \(-0.268143\pi\) | ||||
0.665677 | + | 0.746240i | \(0.268143\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 722.371i | − 0.946751i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2116.77 | −2.76701 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 12.6464 | 0.0164881 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −504.992 | −0.656687 | −0.328343 | − | 0.944558i | \(-0.606490\pi\) | ||||
−0.328343 | + | 0.944558i | \(0.606490\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 726.783 | 0.942650 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 291.252i | 0.376782i | 0.982094 | + | 0.188391i | \(0.0603272\pi\) | ||||
−0.982094 | + | 0.188391i | \(0.939673\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2564.55i | 3.30910i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1915.33 | 2.46503 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 550.302i | 0.704612i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −42.3303 | −0.0540617 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2082.10 | −2.65236 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 804.654i | − 1.02243i | −0.859452 | − | 0.511216i | \(-0.829195\pi\) | ||||
0.859452 | − | 0.511216i | \(-0.170805\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 1095.03i | − 1.38787i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1185.33i | 1.49852i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 145.490i | − 0.183467i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −745.773 | −0.938080 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 860.780i | − 1.08002i | −0.841657 | − | 0.540012i | \(-0.818420\pi\) | ||||
0.841657 | − | 0.540012i | \(-0.181580\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 229.618 | 0.287382 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 896.183i | 1.11883i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 179.314 | 0.223305 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1983.74 | 2.46428 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1720.57 | 2.13206 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 996.810 | 1.23215 | 0.616075 | − | 0.787687i | \(-0.288722\pi\) | ||||
0.616075 | + | 0.787687i | \(0.288722\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 165.611i | − 0.204205i | −0.994774 | − | 0.102103i | \(-0.967443\pi\) | ||||
0.994774 | − | 0.102103i | \(-0.0325570\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 480.350i | − 0.590837i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 126.181 | 0.154823 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 341.766i | 0.417297i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1109.72 | −1.35167 | −0.675835 | − | 0.737053i | \(-0.736217\pi\) | ||||
−0.675835 | + | 0.737053i | \(0.736217\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 542.480 | 0.659150 | 0.329575 | − | 0.944129i | \(-0.393095\pi\) | ||||
0.329575 | + | 0.944129i | \(0.393095\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1424.23i | 1.72634i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 192.451i | 0.232710i | 0.993208 | + | 0.116355i | \(0.0371211\pi\) | ||||
−0.993208 | + | 0.116355i | \(0.962879\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 973.999i | − 1.17491i | −0.809257 | − | 0.587454i | \(-0.800130\pi\) | ||||
0.809257 | − | 0.587454i | \(-0.199870\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − 1087.22i | − 1.30833i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1202.65 | −1.44376 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 1586.16i | − 1.89960i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1298.22 | −1.55104 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 772.253i | 0.920445i | 0.887804 | + | 0.460223i | \(0.152230\pi\) | ||||
−0.887804 | + | 0.460223i | \(0.847770\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 838.875 | 0.997473 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2178.98 | 2.58479 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1496.00 | −1.77041 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1069.12 | −1.26224 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − 1319.36i | − 1.55401i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 679.141i | − 0.798051i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −184.691 | −0.216520 | −0.108260 | − | 0.994123i | \(-0.534528\pi\) | ||||
−0.108260 | + | 0.994123i | \(0.534528\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 948.525i | 1.10680i | 0.832916 | + | 0.553399i | \(0.186669\pi\) | ||||
−0.832916 | + | 0.553399i | \(0.813331\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 32.0045 | 0.0372579 | 0.0186289 | − | 0.999826i | \(-0.494070\pi\) | ||||
0.0186289 | + | 0.999826i | \(0.494070\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3340.14 | 3.87937 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1146.52i | 1.32852i | 0.747500 | + | 0.664262i | \(0.231254\pi\) | ||||
−0.747500 | + | 0.664262i | \(0.768746\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2964.78i | 3.42749i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 220.627i | 0.254471i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 575.955i | − 0.662779i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −132.664 | −0.152312 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 444.691i | − 0.509383i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3296.51 | −3.76744 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 187.762i | 0.214096i | 0.994254 | + | 0.107048i | \(0.0341399\pi\) | ||||
−0.994254 | + | 0.107048i | \(0.965860\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 627.736 | 0.714148 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 635.725 | 0.721594 | 0.360797 | − | 0.932644i | \(-0.382505\pi\) | ||||
0.360797 | + | 0.932644i | \(0.382505\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 807.361 | 0.914339 | 0.457170 | − | 0.889380i | \(-0.348863\pi\) | ||||
0.457170 | + | 0.889380i | \(0.348863\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −275.433 | −0.311224 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 1208.85i | − 1.36286i | −0.731885 | − | 0.681429i | \(-0.761359\pi\) | ||||
0.731885 | − | 0.681429i | \(-0.238641\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1883.28i | 2.11843i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −38.7769 | −0.0435207 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 2220.33i | − 2.48082i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 194.211 | 0.216511 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −65.1802 | −0.0725030 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 262.326i | − 0.291150i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 614.442i | − 0.680445i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2621.28i | 2.89645i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1364.17i | 1.50404i | 0.659138 | + | 0.752022i | \(0.270921\pi\) | ||||
−0.659138 | + | 0.752022i | \(0.729079\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2904.37 | −3.19513 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 492.916i | 0.541071i | 0.962710 | + | 0.270536i | \(0.0872008\pi\) | ||||
−0.962710 | + | 0.270536i | \(0.912799\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −146.627 | −0.160599 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3168.70i | 3.46306i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 165.834 | 0.180844 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −516.342 | −0.561852 | −0.280926 | − | 0.959729i | \(-0.590641\pi\) | ||||
−0.280926 | + | 0.959729i | \(0.590641\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1203.94 | −1.30721 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −221.039 | −0.239479 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2000.48i | 2.16268i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1826.33i | 1.97016i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1347.03 | −1.44998 | −0.724988 | − | 0.688761i | \(-0.758155\pi\) | ||||
−0.724988 | + | 0.688761i | \(0.758155\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 1878.57i | − 2.01347i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −719.322 | −0.769328 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −179.032 | −0.191069 | −0.0955346 | − | 0.995426i | \(-0.530456\pi\) | ||||
−0.0955346 | + | 0.995426i | \(0.530456\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1038.98i | 1.10648i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1000.60i | 1.06333i | 0.846953 | + | 0.531667i | \(0.178434\pi\) | ||||
−0.846953 | + | 0.531667i | \(0.821566\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 1184.35i | − 1.25594i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − 2957.99i | − 3.13014i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1345.81 | −1.42113 | −0.710564 | − | 0.703633i | \(-0.751560\pi\) | ||||
−0.710564 | + | 0.703633i | \(0.751560\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 72.0248i | 0.0758955i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1226.33 | 1.28952 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 466.625i | − 0.489638i | −0.969569 | − | 0.244819i | \(-0.921271\pi\) | ||||
0.969569 | − | 0.244819i | \(-0.0787286\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −956.282 | −1.00134 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −36.1979 | −0.0378244 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1253.44 | 1.30703 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1038.00 | −1.08013 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 22.0406i | − 0.0228875i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 1823.15i | − 1.88927i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1033.54 | −1.06881 | −0.534406 | − | 0.845228i | \(-0.679465\pi\) | ||||
−0.534406 | + | 0.845228i | \(0.679465\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 1360.16i | − 1.40078i | −0.713761 | − | 0.700390i | \(-0.753010\pi\) | ||||
0.713761 | − | 0.700390i | \(-0.246990\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2393.81 | −2.46024 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −572.067 | −0.586735 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1085.93i | 1.11150i | 0.831350 | + | 0.555749i | \(0.187569\pi\) | ||||
−0.831350 | + | 0.555749i | \(0.812431\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 304.542i | 0.311075i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 961.102i | 0.979717i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 716.409i | − 0.728799i | −0.931243 | − | 0.364399i | \(-0.881274\pi\) | ||||
0.931243 | − | 0.364399i | \(-0.118726\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1016.88 | −1.03236 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 807.443i | 0.818078i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −217.870 | −0.220293 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 514.771i | 0.519446i | 0.965683 | + | 0.259723i | \(0.0836312\pi\) | ||||
−0.965683 | + | 0.259723i | \(0.916369\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −486.953 | −0.490386 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2523.17 | 2.53584 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1037.25 | 1.04037 | 0.520187 | − | 0.854053i | \(-0.325862\pi\) | ||||
0.520187 | + | 0.854053i | \(0.325862\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1012.68 | −1.01369 |
(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 | 1444.3.c.d.721.3 | ✓ | 24 | |
19.18 | odd | 2 | inner | 1444.3.c.d.721.22 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1444.3.c.d.721.3 | ✓ | 24 | 1.1 | even | 1 | trivial | |
1444.3.c.d.721.22 | yes | 24 | 19.18 | odd | 2 | inner |