Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1568,3,Mod(97,1568)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1568, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1568.97");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1568 = 2^{5} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1568.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(42.7249054517\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 26 x^{14} - 16 x^{13} + 469 x^{12} + 144 x^{11} - 4526 x^{10} + 4440 x^{9} + 32608 x^{8} + \cdots + 208849 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{28}\cdot 7^{2} \) |
Twist minimal: | no (minimal twist has level 224) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 97.14 | ||
Root | \(2.08703 + 2.02145i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1568.97 |
Dual form | 1568.3.c.g.97.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1568\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(1471\) | \(1473\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 3.98546i | 1.32849i | 0.747516 | + | 0.664244i | \(0.231246\pi\) | ||||
−0.747516 | + | 0.664244i | \(0.768754\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 9.01776i | 1.80355i | 0.432204 | + | 0.901776i | \(0.357736\pi\) | ||||
−0.432204 | + | 0.901776i | \(0.642264\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −6.88390 | −0.764878 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 16.5618 | 1.50561 | 0.752807 | − | 0.658241i | \(-0.228699\pi\) | ||||
0.752807 | + | 0.658241i | \(0.228699\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 0.446263i | − 0.0343279i | −0.999853 | − | 0.0171640i | \(-0.994536\pi\) | ||||
0.999853 | − | 0.0171640i | \(-0.00546373\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −35.9399 | −2.39599 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.95177i | 0.408928i | 0.978874 | + | 0.204464i | \(0.0655451\pi\) | ||||
−0.978874 | + | 0.204464i | \(0.934455\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 12.7440i | 0.670735i | 0.942087 | + | 0.335367i | \(0.108860\pi\) | ||||
−0.942087 | + | 0.335367i | \(0.891140\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −26.5742 | −1.15540 | −0.577701 | − | 0.816248i | \(-0.696050\pi\) | ||||
−0.577701 | + | 0.816248i | \(0.696050\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −56.3199 | −2.25280 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 8.43362i | 0.312356i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 26.4655 | 0.912603 | 0.456301 | − | 0.889825i | \(-0.349174\pi\) | ||||
0.456301 | + | 0.889825i | \(0.349174\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 25.1303i | − 0.810656i | −0.914171 | − | 0.405328i | \(-0.867157\pi\) | ||||
0.914171 | − | 0.405328i | \(-0.132843\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 66.0062i | 2.00019i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −63.3984 | −1.71347 | −0.856735 | − | 0.515757i | \(-0.827511\pi\) | ||||
−0.856735 | + | 0.515757i | \(0.827511\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.77857 | 0.0456042 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 0.519795i | − 0.0126779i | −0.999980 | − | 0.00633896i | \(-0.997982\pi\) | ||||
0.999980 | − | 0.00633896i | \(-0.00201777\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −25.5364 | −0.593870 | −0.296935 | − | 0.954898i | \(-0.595964\pi\) | ||||
−0.296935 | + | 0.954898i | \(0.595964\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 62.0774i | − 1.37950i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 68.6455i | 1.46054i | 0.683157 | + | 0.730272i | \(0.260607\pi\) | ||||
−0.683157 | + | 0.730272i | \(0.739393\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −27.7060 | −0.543255 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.17014 | −0.135286 | −0.0676429 | − | 0.997710i | \(-0.521548\pi\) | ||||
−0.0676429 | + | 0.997710i | \(0.521548\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 149.350i | 2.71545i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −50.7906 | −0.891062 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 75.4237i | 1.27837i | 0.769054 | + | 0.639184i | \(0.220728\pi\) | ||||
−0.769054 | + | 0.639184i | \(0.779272\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 46.0559i | − 0.755014i | −0.926007 | − | 0.377507i | \(-0.876781\pi\) | ||||
0.926007 | − | 0.377507i | \(-0.123219\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.02429 | 0.0619122 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 42.8097 | 0.638951 | 0.319476 | − | 0.947595i | \(-0.396493\pi\) | ||||
0.319476 | + | 0.947595i | \(0.396493\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 105.911i | − 1.53494i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 60.0281 | 0.845466 | 0.422733 | − | 0.906254i | \(-0.361071\pi\) | ||||
0.422733 | + | 0.906254i | \(0.361071\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 46.7938i | − 0.641011i | −0.947247 | − | 0.320505i | \(-0.896147\pi\) | ||||
0.947247 | − | 0.320505i | \(-0.103853\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 224.461i | − 2.99281i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −54.3077 | −0.687439 | −0.343720 | − | 0.939072i | \(-0.611687\pi\) | ||||
−0.343720 | + | 0.939072i | \(0.611687\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −95.5670 | −1.17984 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 11.4213i | 0.137606i | 0.997630 | + | 0.0688028i | \(0.0219179\pi\) | ||||
−0.997630 | + | 0.0688028i | \(0.978082\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −62.6894 | −0.737522 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 105.477i | 1.21238i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 61.4132i | − 0.690036i | −0.938596 | − | 0.345018i | \(-0.887873\pi\) | ||||
0.938596 | − | 0.345018i | \(-0.112127\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 100.156 | 1.07695 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −114.922 | −1.20970 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 20.3570i | − 0.209866i | −0.994479 | − | 0.104933i | \(-0.966537\pi\) | ||||
0.994479 | − | 0.104933i | \(-0.0334629\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −114.010 | −1.15161 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 179.252i | − 1.77477i | −0.461027 | − | 0.887386i | \(-0.652519\pi\) | ||||
0.461027 | − | 0.887386i | \(-0.347481\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 68.1553i | 0.661702i | 0.943683 | + | 0.330851i | \(0.107336\pi\) | ||||
−0.943683 | + | 0.330851i | \(0.892664\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 127.131 | 1.18814 | 0.594072 | − | 0.804412i | \(-0.297519\pi\) | ||||
0.594072 | + | 0.804412i | \(0.297519\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −21.5704 | −0.197894 | −0.0989468 | − | 0.995093i | \(-0.531547\pi\) | ||||
−0.0989468 | + | 0.995093i | \(0.531547\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − 252.672i | − 2.27632i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 82.1812 | 0.727267 | 0.363634 | − | 0.931542i | \(-0.381536\pi\) | ||||
0.363634 | + | 0.931542i | \(0.381536\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 239.640i | − 2.08383i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.07203i | 0.0262567i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 153.292 | 1.26687 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.07162 | 0.0168425 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 282.436i | − 2.25949i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 42.9545 | 0.338225 | 0.169112 | − | 0.985597i | \(-0.445910\pi\) | ||||
0.169112 | + | 0.985597i | \(0.445910\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − 101.774i | − 0.788948i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 192.812i | 1.47185i | 0.677063 | + | 0.735925i | \(0.263252\pi\) | ||||
−0.677063 | + | 0.735925i | \(0.736748\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −76.0523 | −0.563351 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 146.249 | 1.06751 | 0.533754 | − | 0.845640i | \(-0.320781\pi\) | ||||
0.533754 | + | 0.845640i | \(0.320781\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 101.042i | − 0.726921i | −0.931610 | − | 0.363460i | \(-0.881595\pi\) | ||||
0.931610 | − | 0.363460i | \(-0.118405\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −273.584 | −1.94031 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 7.39090i | − 0.0516846i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 238.659i | 1.64593i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −191.108 | −1.28261 | −0.641303 | − | 0.767287i | \(-0.721606\pi\) | ||||
−0.641303 | + | 0.767287i | \(0.721606\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −28.7170 | −0.190179 | −0.0950893 | − | 0.995469i | \(-0.530314\pi\) | ||||
−0.0950893 | + | 0.995469i | \(0.530314\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 47.8553i | − 0.312780i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 226.619 | 1.46206 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 126.133i | 0.803397i | 0.915772 | + | 0.401698i | \(0.131580\pi\) | ||||
−0.915772 | + | 0.401698i | \(0.868420\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − 28.5763i | − 0.179725i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 254.251 | 1.55982 | 0.779911 | − | 0.625890i | \(-0.215264\pi\) | ||||
0.779911 | + | 0.625890i | \(0.215264\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −595.228 | −3.60744 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 1.71028i | − 0.0102412i | −0.999987 | − | 0.00512059i | \(-0.998370\pi\) | ||||
0.999987 | − | 0.00512059i | \(-0.00162994\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 168.801 | 0.998822 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 87.7282i | − 0.513030i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 100.654i | − 0.581815i | −0.956751 | − | 0.290907i | \(-0.906043\pi\) | ||||
0.956751 | − | 0.290907i | \(-0.0939571\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −300.598 | −1.69830 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 227.284 | 1.26974 | 0.634872 | − | 0.772617i | \(-0.281053\pi\) | ||||
0.634872 | + | 0.772617i | \(0.281053\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 27.1608i | 0.150060i | 0.997181 | + | 0.0750298i | \(0.0239052\pi\) | ||||
−0.997181 | + | 0.0750298i | \(0.976095\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 183.554 | 1.00303 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 571.711i | − 3.09033i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 115.133i | 0.615687i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 55.3123 | 0.289593 | 0.144797 | − | 0.989461i | \(-0.453747\pi\) | ||||
0.144797 | + | 0.989461i | \(0.453747\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −222.565 | −1.15319 | −0.576594 | − | 0.817031i | \(-0.695618\pi\) | ||||
−0.576594 | + | 0.817031i | \(0.695618\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 16.0387i | 0.0822496i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −15.2516 | −0.0774191 | −0.0387095 | − | 0.999251i | \(-0.512325\pi\) | ||||
−0.0387095 | + | 0.999251i | \(0.512325\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 44.2879i | − 0.222552i | −0.993790 | − | 0.111276i | \(-0.964506\pi\) | ||||
0.993790 | − | 0.111276i | \(-0.0354938\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 170.617i | 0.848838i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.68738 | 0.0228653 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 182.935 | 0.883742 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 211.062i | 1.00987i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −138.721 | −0.657446 | −0.328723 | − | 0.944426i | \(-0.606618\pi\) | ||||
−0.328723 | + | 0.944426i | \(0.606618\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 239.240i | 1.12319i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 230.281i | − 1.07107i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 186.495 | 0.851575 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.10232 | 0.0140376 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 53.1564i | − 0.238370i | −0.992872 | − | 0.119185i | \(-0.961972\pi\) | ||||
0.992872 | − | 0.119185i | \(-0.0380281\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 387.701 | 1.72312 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 400.609i | 1.76480i | 0.470501 | + | 0.882399i | \(0.344073\pi\) | ||||
−0.470501 | + | 0.882399i | \(0.655927\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 380.550i | 1.66179i | 0.556430 | + | 0.830895i | \(0.312171\pi\) | ||||
−0.556430 | + | 0.830895i | \(0.687829\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −333.003 | −1.42920 | −0.714598 | − | 0.699535i | \(-0.753391\pi\) | ||||
−0.714598 | + | 0.699535i | \(0.753391\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −619.029 | −2.63417 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 216.441i | − 0.913255i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 123.781 | 0.517912 | 0.258956 | − | 0.965889i | \(-0.416622\pi\) | ||||
0.258956 | + | 0.965889i | \(0.416622\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − 83.2837i | − 0.345575i | −0.984959 | − | 0.172788i | \(-0.944723\pi\) | ||||
0.984959 | − | 0.172788i | \(-0.0552774\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 304.976i | − 1.25505i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.68716 | 0.0230249 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −45.5190 | −0.182807 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 403.749i | − 1.60856i | −0.594250 | − | 0.804281i | \(-0.702551\pi\) | ||||
0.594250 | − | 0.804281i | \(-0.297449\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −440.116 | −1.73959 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − 249.846i | − 0.979788i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 258.268i | 1.00493i | 0.864596 | + | 0.502467i | \(0.167574\pi\) | ||||
−0.864596 | + | 0.502467i | \(0.832426\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −182.186 | −0.698030 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −393.857 | −1.49756 | −0.748778 | − | 0.662821i | \(-0.769359\pi\) | ||||
−0.748778 | + | 0.662821i | \(0.769359\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − 64.6586i | − 0.243995i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 244.760 | 0.916704 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 53.8363i | 0.200135i | 0.994981 | + | 0.100067i | \(0.0319059\pi\) | ||||
−0.994981 | + | 0.100067i | \(0.968094\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 47.5133i | 0.175326i | 0.996150 | + | 0.0876629i | \(0.0279398\pi\) | ||||
−0.996150 | + | 0.0876629i | \(0.972060\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −932.757 | −3.39184 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −243.918 | −0.880569 | −0.440285 | − | 0.897858i | \(-0.645122\pi\) | ||||
−0.440285 | + | 0.897858i | \(0.645122\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 172.995i | 0.620053i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 173.857 | 0.618709 | 0.309355 | − | 0.950947i | \(-0.399887\pi\) | ||||
0.309355 | + | 0.950947i | \(0.399887\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 52.5435i | − 0.185666i | −0.995682 | − | 0.0928330i | \(-0.970408\pi\) | ||||
0.995682 | − | 0.0928330i | \(-0.0295923\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 458.017i | − 1.60708i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 240.673 | 0.832778 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 81.1322 | 0.278805 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 321.060i | − 1.09577i | −0.836554 | − | 0.547885i | \(-0.815433\pi\) | ||||
0.836554 | − | 0.547885i | \(-0.184567\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −680.153 | −2.30560 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 139.676i | 0.470288i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 11.8591i | 0.0396626i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 714.402 | 2.35776 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 415.321 | 1.36171 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 568.177i | 1.85074i | 0.379066 | + | 0.925370i | \(0.376245\pi\) | ||||
−0.379066 | + | 0.925370i | \(0.623755\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −271.630 | −0.879063 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 48.1978i | 0.154977i | 0.996993 | + | 0.0774884i | \(0.0246901\pi\) | ||||
−0.996993 | + | 0.0774884i | \(0.975310\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 81.4683i | − 0.260282i | −0.991495 | − | 0.130141i | \(-0.958457\pi\) | ||||
0.991495 | − | 0.130141i | \(-0.0415430\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 396.581 | 1.25104 | 0.625522 | − | 0.780206i | \(-0.284886\pi\) | ||||
0.625522 | + | 0.780206i | \(0.284886\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 438.315 | 1.37403 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 506.678i | 1.57844i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −88.5930 | −0.274282 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 25.1335i | 0.0773339i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 85.9680i | − 0.262899i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −474.236 | −1.43274 | −0.716369 | − | 0.697722i | \(-0.754197\pi\) | ||||
−0.716369 | + | 0.697722i | \(0.754197\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 436.428 | 1.31060 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 386.048i | 1.15238i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 234.392 | 0.695526 | 0.347763 | − | 0.937583i | \(-0.386941\pi\) | ||||
0.347763 | + | 0.937583i | \(0.386941\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 327.530i | 0.966165i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 416.203i | − 1.22054i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 955.076 | 2.76834 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 224.989 | 0.648384 | 0.324192 | − | 0.945991i | \(-0.394908\pi\) | ||||
0.324192 | + | 0.945991i | \(0.394908\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 414.621i | 1.18802i | 0.804456 | + | 0.594012i | \(0.202457\pi\) | ||||
−0.804456 | + | 0.594012i | \(0.797543\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.76362 | 0.0107226 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 200.599i | 0.568268i | 0.958785 | + | 0.284134i | \(0.0917060\pi\) | ||||
−0.958785 | + | 0.284134i | \(0.908294\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 541.319i | 1.52484i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −149.929 | −0.417630 | −0.208815 | − | 0.977955i | \(-0.566961\pi\) | ||||
−0.208815 | + | 0.977955i | \(0.566961\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 198.591 | 0.550115 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 610.939i | 1.68303i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 421.975 | 1.15610 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 485.835i | 1.32380i | 0.749592 | + | 0.661900i | \(0.230250\pi\) | ||||
−0.749592 | + | 0.661900i | \(0.769750\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.57822i | 0.00969706i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −162.047 | −0.434442 | −0.217221 | − | 0.976122i | \(-0.569699\pi\) | ||||
−0.217221 | + | 0.976122i | \(0.569699\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1125.64 | 3.00170 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 11.8106i | − 0.0313278i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 388.817 | 1.02590 | 0.512951 | − | 0.858418i | \(-0.328552\pi\) | ||||
0.512951 | + | 0.858418i | \(0.328552\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 171.194i | 0.449327i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 28.2666i | 0.0738031i | 0.999319 | + | 0.0369015i | \(0.0117488\pi\) | ||||
−0.999319 | + | 0.0369015i | \(0.988251\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 175.790 | 0.454238 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 606.292 | 1.55859 | 0.779296 | − | 0.626656i | \(-0.215577\pi\) | ||||
0.779296 | + | 0.626656i | \(0.215577\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 184.738i | − 0.472476i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −768.446 | −1.95533 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 489.734i | − 1.23983i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 610.769i | − 1.53846i | −0.638971 | − | 0.769231i | \(-0.720640\pi\) | ||||
0.638971 | − | 0.769231i | \(-0.279360\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −214.109 | −0.533938 | −0.266969 | − | 0.963705i | \(-0.586022\pi\) | ||||
−0.266969 | + | 0.963705i | \(0.586022\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −11.2148 | −0.0278282 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 861.800i | − 2.12790i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1049.99 | −2.57983 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 238.496i | 0.583120i | 0.956553 | + | 0.291560i | \(0.0941742\pi\) | ||||
−0.956553 | + | 0.291560i | \(0.905826\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 582.869i | 1.41817i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −102.994 | −0.248179 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 402.699 | 0.965705 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 126.446i | 0.301779i | 0.988551 | + | 0.150890i | \(0.0482138\pi\) | ||||
−0.988551 | + | 0.150890i | \(0.951786\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −113.097 | −0.268639 | −0.134319 | − | 0.990938i | \(-0.542885\pi\) | ||||
−0.134319 | + | 0.990938i | \(0.542885\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 472.549i | − 1.11714i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 391.523i | − 0.921231i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 29.4562 | 0.0686624 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −689.184 | −1.59903 | −0.799517 | − | 0.600643i | \(-0.794911\pi\) | ||||
−0.799517 | + | 0.600643i | \(0.794911\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 600.031i | 1.38575i | 0.721057 | + | 0.692876i | \(0.243657\pi\) | ||||
−0.721057 | + | 0.692876i | \(0.756343\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −951.167 | −2.18659 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 338.661i | − 0.774968i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 165.206i | 0.376324i | 0.982138 | + | 0.188162i | \(0.0602530\pi\) | ||||
−0.982138 | + | 0.188162i | \(0.939747\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −204.833 | −0.462377 | −0.231189 | − | 0.972909i | \(-0.574261\pi\) | ||||
−0.231189 | + | 0.972909i | \(0.574261\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 553.810 | 1.24452 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 761.655i | − 1.70393i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −112.007 | −0.249458 | −0.124729 | − | 0.992191i | \(-0.539806\pi\) | ||||
−0.124729 | + | 0.992191i | \(0.539806\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 8.60871i | − 0.0190881i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 114.450i | − 0.252650i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 165.235 | 0.361564 | 0.180782 | − | 0.983523i | \(-0.442137\pi\) | ||||
0.180782 | + | 0.983523i | \(0.442137\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −58.6286 | −0.127731 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 187.790i | 0.407353i | 0.979038 | + | 0.203677i | \(0.0652891\pi\) | ||||
−0.979038 | + | 0.203677i | \(0.934711\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 678.682 | 1.46584 | 0.732918 | − | 0.680317i | \(-0.238158\pi\) | ||||
0.732918 | + | 0.680317i | \(0.238158\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 903.183i | 1.94233i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 15.9116i | 0.0340720i | 0.999855 | + | 0.0170360i | \(0.00542299\pi\) | ||||
−0.999855 | + | 0.0170360i | \(0.994577\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −502.699 | −1.06730 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −422.928 | −0.894139 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 717.739i | − 1.51103i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 49.3586 | 0.103477 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 553.743i | − 1.15604i | −0.816023 | − | 0.578020i | \(-0.803826\pi\) | ||||
0.816023 | − | 0.578020i | \(-0.196174\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 28.2924i | 0.0588199i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 183.575 | 0.378505 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −393.559 | −0.808129 | −0.404065 | − | 0.914730i | \(-0.632403\pi\) | ||||
−0.404065 | + | 0.914730i | \(0.632403\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1013.31i | 2.07220i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −96.8828 | −0.197317 | −0.0986586 | − | 0.995121i | \(-0.531455\pi\) | ||||
−0.0986586 | + | 0.995121i | \(0.531455\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 183.982i | 0.373188i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − 1028.11i | − 2.07699i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −154.872 | −0.310366 | −0.155183 | − | 0.987886i | \(-0.549597\pi\) | ||||
−0.155183 | + | 0.987886i | \(0.549597\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.81624 | 0.0136053 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 710.432i | 1.41239i | 0.708018 | + | 0.706194i | \(0.249590\pi\) | ||||
−0.708018 | + | 0.706194i | \(0.750410\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1616.45 | 3.20089 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 672.749i | 1.32692i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 85.0058i | 0.167005i | 0.996508 | + | 0.0835027i | \(0.0266107\pi\) | ||||
−0.996508 | + | 0.0835027i | \(0.973389\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −107.478 | −0.209508 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −614.608 | −1.19341 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1136.89i | 2.19902i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 401.152 | 0.772933 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 480.680i | 0.922610i | 0.887242 | + | 0.461305i | \(0.152619\pi\) | ||||
−0.887242 | + | 0.461305i | \(0.847381\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 532.458i | − 1.01808i | −0.860742 | − | 0.509042i | \(-0.830000\pi\) | ||||
0.860742 | − | 0.509042i | \(-0.170000\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 174.700 | 0.331500 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 177.190 | 0.334954 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 519.210i | − 0.977796i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.231965 | −0.000435207 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1146.44i | 2.14288i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 905.832i | 1.68684i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −827.485 | −1.52955 | −0.764774 | − | 0.644299i | \(-0.777149\pi\) | ||||
−0.764774 | + | 0.644299i | \(0.777149\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −108.248 | −0.199352 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 194.517i | − 0.356911i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 665.687 | 1.21698 | 0.608489 | − | 0.793562i | \(-0.291776\pi\) | ||||
0.608489 | + | 0.793562i | \(0.291776\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 317.044i | 0.577494i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 337.275i | 0.612114i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2278.53 | 4.10547 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −18.8463 | −0.0338353 | −0.0169177 | − | 0.999857i | \(-0.505385\pi\) | ||||
−0.0169177 | + | 0.999857i | \(0.505385\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11.3960i | 0.0203863i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −458.860 | −0.817932 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 512.440i | − 0.910196i | −0.890441 | − | 0.455098i | \(-0.849604\pi\) | ||||
0.890441 | − | 0.455098i | \(-0.150396\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 741.090i | 1.31166i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −631.779 | −1.11033 | −0.555166 | − | 0.831740i | \(-0.687345\pi\) | ||||
−0.555166 | + | 0.831740i | \(0.687345\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 916.717 | 1.60546 | 0.802729 | − | 0.596344i | \(-0.203380\pi\) | ||||
0.802729 | + | 0.596344i | \(0.203380\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 220.445i | 0.384721i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1496.66 | 2.60289 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 184.769i | 0.320223i | 0.987099 | + | 0.160111i | \(0.0511854\pi\) | ||||
−0.987099 | + | 0.160111i | \(0.948815\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 887.025i | − 1.53199i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −118.750 | −0.203688 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −27.7029 | −0.0473553 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 141.805i | 0.241575i | 0.992678 | + | 0.120788i | \(0.0385420\pi\) | ||||
−0.992678 | + | 0.120788i | \(0.961458\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 320.260 | 0.543735 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − 60.7845i | − 0.102850i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 567.422i | − 0.956867i | −0.878124 | − | 0.478433i | \(-0.841205\pi\) | ||||
0.878124 | − | 0.478433i | \(-0.158795\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 176.508 | 0.295658 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 448.906 | 0.749426 | 0.374713 | − | 0.927141i | \(-0.377741\pi\) | ||||
0.374713 | + | 0.927141i | \(0.377741\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − 939.633i | − 1.56345i | −0.623623 | − | 0.781725i | \(-0.714340\pi\) | ||||
0.623623 | − | 0.781725i | \(-0.285660\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −294.698 | −0.488720 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1382.35i | 2.28487i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 218.704i | 0.360303i | 0.983639 | + | 0.180151i | \(0.0576588\pi\) | ||||
−0.983639 | + | 0.180151i | \(0.942341\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 30.6340 | 0.0501375 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 283.223 | 0.462028 | 0.231014 | − | 0.972950i | \(-0.425796\pi\) | ||||
0.231014 | + | 0.972950i | \(0.425796\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 18.6814i | 0.0303762i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1099.79 | −1.78247 | −0.891236 | − | 0.453539i | \(-0.850161\pi\) | ||||
−0.891236 | + | 0.453539i | \(0.850161\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 598.401i | − 0.966722i | −0.875421 | − | 0.483361i | \(-0.839416\pi\) | ||||
0.875421 | − | 0.483361i | \(-0.160584\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 224.117i | − 0.360897i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1138.94 | 1.82230 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −841.181 | −1.34160 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 440.731i | − 0.700685i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1056.45 | 1.67425 | 0.837127 | − | 0.547008i | \(-0.184233\pi\) | ||||
0.837127 | + | 0.547008i | \(0.184233\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 552.868i | − 0.873409i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 387.353i | 0.610005i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −413.228 | −0.646679 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 598.958 | 0.934412 | 0.467206 | − | 0.884149i | \(-0.345261\pi\) | ||||
0.467206 | + | 0.884149i | \(0.345261\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 707.781i | 1.10075i | 0.834918 | + | 0.550374i | \(0.185515\pi\) | ||||
−0.834918 | + | 0.550374i | \(0.814485\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 917.776 | 1.42291 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 488.067i | 0.754353i | 0.926141 | + | 0.377177i | \(0.123105\pi\) | ||||
−0.926141 | + | 0.377177i | \(0.876895\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1249.15i | 1.92473i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 355.995 | 0.545168 | 0.272584 | − | 0.962132i | \(-0.412122\pi\) | ||||
0.272584 | + | 0.962132i | \(0.412122\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1738.74 | −2.65456 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 322.124i | 0.490295i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1182.36 | 1.79418 | 0.897088 | − | 0.441852i | \(-0.145678\pi\) | ||||
0.897088 | + | 0.441852i | \(0.145678\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 87.8710i | − 0.132936i | −0.997789 | − | 0.0664682i | \(-0.978827\pi\) | ||||
0.997789 | − | 0.0664682i | \(-0.0211731\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 12.3642i | 0.0186488i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −703.300 | −1.05442 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 211.853 | 0.316671 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 762.766i | − 1.13676i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 939.720 | 1.39631 | 0.698157 | − | 0.715944i | \(-0.254004\pi\) | ||||
0.698157 | + | 0.715944i | \(0.254004\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 474.981i | − 0.703676i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 84.8451i | − 0.125325i | −0.998035 | − | 0.0626626i | \(-0.980041\pi\) | ||||
0.998035 | − | 0.0626626i | \(-0.0199592\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1596.61 | −2.34451 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 303.080 | 0.443748 | 0.221874 | − | 0.975075i | \(-0.428783\pi\) | ||||
0.221874 | + | 0.975075i | \(0.428783\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1318.84i | 1.92531i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1516.67 | −2.20767 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.19977i | 0.00464408i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 255.450i | − 0.369682i | −0.982768 | − | 0.184841i | \(-0.940823\pi\) | ||||
0.982768 | − | 0.184841i | \(-0.0591770\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 911.172 | 1.31104 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.61349 | 0.00518435 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 1327.17i | − 1.89867i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −560.333 | −0.799333 | −0.399667 | − | 0.916661i | \(-0.630874\pi\) | ||||
−0.399667 | + | 0.916661i | \(0.630874\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 807.947i | − 1.14928i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − 2467.12i | − 3.49945i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 822.738 | 1.16042 | 0.580210 | − | 0.814467i | \(-0.302970\pi\) | ||||
0.580210 | + | 0.814467i | \(0.302970\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 373.849 | 0.525807 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 667.820i | 0.936634i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 66.6494 | 0.0932159 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 493.324i | 0.688039i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1242.96i | 1.72874i | 0.502859 | + | 0.864368i | \(0.332281\pi\) | ||||
−0.502859 | + | 0.864368i | \(0.667719\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 331.924 | 0.459092 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1490.53 | −2.05591 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 1025.14i | − 1.41010i | −0.709156 | − | 0.705052i | \(-0.750924\pi\) | ||||
0.709156 | − | 0.705052i | \(-0.249076\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 355.367 | 0.487472 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 177.523i | − 0.242850i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 768.426i | 1.04833i | 0.851617 | + | 0.524165i | \(0.175622\pi\) | ||||
−0.851617 | + | 0.524165i | \(0.824378\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 709.004 | 0.962014 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 880.474 | 1.19144 | 0.595720 | − | 0.803192i | \(-0.296867\pi\) | ||||
0.595720 | + | 0.803192i | \(0.296867\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 22.6660i | 0.0305883i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −984.949 | −1.32564 | −0.662819 | − | 0.748780i | \(-0.730640\pi\) | ||||
−0.662819 | + | 0.748780i | \(0.730640\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − 1723.37i | − 2.31325i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 78.6228i | − 0.105251i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −333.968 | −0.444697 | −0.222349 | − | 0.974967i | \(-0.571372\pi\) | ||||
−0.222349 | + | 0.974967i | \(0.571372\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1609.13 | 2.13695 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 258.963i | − 0.342997i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −964.869 | −1.27460 | −0.637298 | − | 0.770617i | \(-0.719948\pi\) | ||||
−0.637298 | + | 0.770617i | \(0.719948\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − 1754.07i | − 2.31102i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 885.964i | − 1.16421i | −0.813113 | − | 0.582105i | \(-0.802229\pi\) | ||||
0.813113 | − | 0.582105i | \(-0.197771\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 431.547 | 0.564114 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 33.6588 | 0.0438838 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − 416.779i | − 0.541976i | −0.962583 | − | 0.270988i | \(-0.912650\pi\) | ||||
0.962583 | − | 0.270988i | \(-0.0873503\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1029.32 | −1.33504 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 66.9101i | − 0.0865590i | −0.999063 | − | 0.0432795i | \(-0.986219\pi\) | ||||
0.999063 | − | 0.0432795i | \(-0.0137806\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1415.34i | 1.82624i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.62424 | 0.00850352 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 994.171 | 1.27295 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 223.200i | 0.285057i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1137.44 | −1.44897 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1223.31i | 1.55439i | 0.629258 | + | 0.777196i | \(0.283359\pi\) | ||||
−0.629258 | + | 0.777196i | \(0.716641\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 1569.70i | − 1.98948i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −20.5530 | −0.0259181 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 257.694 | 0.324144 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 578.768i | − 0.726184i | −0.931753 | − | 0.363092i | \(-0.881721\pi\) | ||||
0.931753 | − | 0.363092i | \(-0.118279\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −477.208 | −0.597256 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 422.763i | 0.527794i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 774.987i | − 0.965115i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −214.562 | −0.265877 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −892.128 | −1.10275 | −0.551377 | − | 0.834256i | \(-0.685897\pi\) | ||||
−0.551377 | + | 0.834256i | \(0.685897\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 200.724i | 0.247502i | 0.992313 | + | 0.123751i | \(0.0394925\pi\) | ||||
−0.992313 | + | 0.123751i | \(0.960508\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −189.362 | −0.232918 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2292.77i | 2.81322i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 325.435i | − 0.398329i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 632.629 | 0.770559 | 0.385280 | − | 0.922800i | \(-0.374105\pi\) | ||||
0.385280 | + | 0.922800i | \(0.374105\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.81646 | −0.00463726 | −0.00231863 | − | 0.999997i | \(-0.500738\pi\) | ||||
−0.00231863 | + | 0.999997i | \(0.500738\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − 3717.47i | − 4.50602i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1174.97 | −1.42076 | −0.710382 | − | 0.703817i | \(-0.751478\pi\) | ||||
−0.710382 | + | 0.703817i | \(0.751478\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 744.824i | − 0.898461i | −0.893416 | − | 0.449230i | \(-0.851698\pi\) | ||||
0.893416 | − | 0.449230i | \(-0.148302\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − 972.125i | − 1.16983i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 15.4229 | 0.0184705 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 211.940 | 0.253214 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1124.03i | 1.33973i | 0.742485 | + | 0.669863i | \(0.233647\pi\) | ||||
−0.742485 | + | 0.669863i | \(0.766353\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −140.579 | −0.167156 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 692.902i | 0.821947i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1522.21i | 1.80143i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 209.410 | 0.246655 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1684.76 | 1.97975 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 96.2021i | 0.112781i | 0.998409 | + | 0.0563905i | \(0.0179592\pi\) | ||||
−0.998409 | + | 0.0563905i | \(0.982041\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 791.112 | 0.925277 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 856.417i | 0.999319i | 0.866222 | + | 0.499660i | \(0.166542\pi\) | ||||
−0.866222 | + | 0.499660i | \(0.833458\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 1676.12i | − 1.95125i | −0.219443 | − | 0.975625i | \(-0.570424\pi\) | ||||
0.219443 | − | 0.975625i | \(-0.429576\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −283.249 | −0.328215 | −0.164107 | − | 0.986442i | \(-0.552474\pi\) | ||||
−0.164107 | + | 0.986442i | \(0.552474\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 907.672 | 1.04933 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 959.193i | 1.10634i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −899.431 | −1.03502 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 19.1044i | − 0.0219339i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 140.136i | 0.160522i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −832.492 | −0.949250 | −0.474625 | − | 0.880188i | \(-0.657416\pi\) | ||||
−0.474625 | + | 0.880188i | \(0.657416\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1279.57 | 1.45572 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 890.282i | 1.01054i | 0.862962 | + | 0.505268i | \(0.168606\pi\) | ||||
−0.862962 | + | 0.505268i | \(0.831394\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 322.429 | 0.365152 | 0.182576 | − | 0.983192i | \(-0.441556\pi\) | ||||
0.182576 | + | 0.983192i | \(0.441556\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 2710.72i | − 3.06296i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 542.546i | 0.611665i | 0.952085 | + | 0.305832i | \(0.0989347\pi\) | ||||
−0.952085 | + | 0.305832i | \(0.901065\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1582.76 | −1.77638 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −874.816 | −0.979637 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2049.59i | 2.29005i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −47.2640 | −0.0526912 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 665.087i | − 0.739807i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 49.8452i | − 0.0553221i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −244.929 | −0.270640 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1455.95 | −1.60524 | −0.802619 | − | 0.596493i | \(-0.796560\pi\) | ||||
−0.802619 | + | 0.596493i | \(0.796560\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1233.95i | 1.35748i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −336.756 | −0.369655 | −0.184828 | − | 0.982771i | \(-0.559173\pi\) | ||||
−0.184828 | + | 0.982771i | \(0.559173\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 189.156i | 0.207181i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1655.24i | 1.80901i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −980.740 | −1.06718 | −0.533591 | − | 0.845743i | \(-0.679158\pi\) | ||||
−0.533591 | + | 0.845743i | \(0.679158\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2264.45 | −2.45868 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 26.7883i | − 0.0290231i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3570.59 | 3.86010 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 469.175i | − 0.506121i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 414.270i | 0.445931i | 0.974826 | + | 0.222965i | \(0.0715737\pi\) | ||||
−0.974826 | + | 0.222965i | \(0.928426\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −192.090 | −0.205885 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1038.25 | −1.11042 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1323.89i | 1.41290i | 0.707764 | + | 0.706449i | \(0.249704\pi\) | ||||
−0.707764 | + | 0.706449i | \(0.750296\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 324.689 | 0.345781 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 950.630i | 1.01023i | 0.863051 | + | 0.505117i | \(0.168551\pi\) | ||||
−0.863051 | + | 0.505117i | \(0.831449\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13.8132i | 0.0146481i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1160.49 | 1.22543 | 0.612717 | − | 0.790302i | \(-0.290077\pi\) | ||||
0.612717 | + | 0.790302i | \(0.290077\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −20.8823 | −0.0220046 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1580.56i | 1.66200i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1025.81 | −1.07640 | −0.538201 | − | 0.842816i | \(-0.680896\pi\) | ||||
−0.538201 | + | 0.842816i | \(0.680896\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 498.793i | 0.522297i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1746.89i | 1.82538i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 329.466 | 0.342836 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −875.161 | −0.908786 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 2007.04i | − 2.07983i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −648.379 | −0.670505 | −0.335253 | − | 0.942128i | \(-0.608822\pi\) | ||||
−0.335253 | + | 0.942128i | \(0.608822\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − 353.084i | − 0.364380i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 731.698i | 0.753551i | 0.926305 | + | 0.376776i | \(0.122967\pi\) | ||||
−0.926305 | + | 0.376776i | \(0.877033\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −100.169 | −0.102737 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −777.446 | −0.795749 | −0.397874 | − | 0.917440i | \(-0.630252\pi\) | ||||
−0.397874 | + | 0.917440i | \(0.630252\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 1017.11i | − 1.03893i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 148.489 | 0.151364 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 1359.09i | − 1.38260i | −0.722570 | − | 0.691298i | \(-0.757039\pi\) | ||||
0.722570 | − | 0.691298i | \(-0.242961\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − 137.535i | − 0.139629i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 678.611 | 0.686158 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 705.097 | 0.711500 | 0.355750 | − | 0.934581i | \(-0.384225\pi\) | ||||
0.355750 | + | 0.934581i | \(0.384225\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 1890.05i | − 1.90337i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 399.377 | 0.401384 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 1245.74i | − 1.24949i | −0.780829 | − | 0.624745i | \(-0.785203\pi\) | ||||
0.780829 | − | 0.624745i | \(-0.214797\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − 534.678i | − 0.535213i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1568.3.c.g.97.14 | 16 | ||
4.3 | odd | 2 | inner | 1568.3.c.g.97.4 | 16 | ||
7.4 | even | 3 | 224.3.s.b.33.7 | yes | 16 | ||
7.5 | odd | 6 | 224.3.s.b.129.7 | yes | 16 | ||
7.6 | odd | 2 | inner | 1568.3.c.g.97.3 | 16 | ||
28.11 | odd | 6 | 224.3.s.b.33.2 | ✓ | 16 | ||
28.19 | even | 6 | 224.3.s.b.129.2 | yes | 16 | ||
28.27 | even | 2 | inner | 1568.3.c.g.97.13 | 16 | ||
56.5 | odd | 6 | 448.3.s.h.129.2 | 16 | |||
56.11 | odd | 6 | 448.3.s.h.257.7 | 16 | |||
56.19 | even | 6 | 448.3.s.h.129.7 | 16 | |||
56.53 | even | 6 | 448.3.s.h.257.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
224.3.s.b.33.2 | ✓ | 16 | 28.11 | odd | 6 | ||
224.3.s.b.33.7 | yes | 16 | 7.4 | even | 3 | ||
224.3.s.b.129.2 | yes | 16 | 28.19 | even | 6 | ||
224.3.s.b.129.7 | yes | 16 | 7.5 | odd | 6 | ||
448.3.s.h.129.2 | 16 | 56.5 | odd | 6 | |||
448.3.s.h.129.7 | 16 | 56.19 | even | 6 | |||
448.3.s.h.257.2 | 16 | 56.53 | even | 6 | |||
448.3.s.h.257.7 | 16 | 56.11 | odd | 6 | |||
1568.3.c.g.97.3 | 16 | 7.6 | odd | 2 | inner | ||
1568.3.c.g.97.4 | 16 | 4.3 | odd | 2 | inner | ||
1568.3.c.g.97.13 | 16 | 28.27 | even | 2 | inner | ||
1568.3.c.g.97.14 | 16 | 1.1 | even | 1 | trivial |