Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [392,2,Mod(177,392)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(392, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("392.177");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 392 = 2^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 392.i (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.13013575923\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 361.1 | ||
Root | \(-0.707107 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 392.361 |
Dual form | 392.2.i.h.177.1 |
$q$-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 \(\left(\mathbb{Z}/392\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(295\) | \(297\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.707107 | + | 1.22474i | −0.408248 | + | 0.707107i | −0.994694 | − | 0.102882i | \(-0.967194\pi\) |
0.586445 | + | 0.809989i | \(0.300527\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.41421 | − | 2.44949i | −0.632456 | − | 1.09545i | −0.987048 | − | 0.160424i | \(-0.948714\pi\) |
0.354593 | − | 0.935021i | \(-0.384620\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.500000 | + | 0.866025i | 0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.00000 | + | 5.19615i | −0.904534 | + | 1.56670i | −0.0829925 | + | 0.996550i | \(0.526448\pi\) |
−0.821541 | + | 0.570149i | \(0.806886\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.65685 | −1.56893 | −0.784465 | − | 0.620174i | \(-0.787062\pi\) | ||||
−0.784465 | + | 0.620174i | \(0.787062\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.00000 | 1.03280 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.707107 | + | 1.22474i | −0.171499 | + | 0.297044i | −0.938944 | − | 0.344070i | \(-0.888194\pi\) |
0.767445 | + | 0.641114i | \(0.221528\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.12132 | + | 3.67423i | 0.486664 | + | 0.842927i | 0.999882 | − | 0.0153309i | \(-0.00488018\pi\) |
−0.513218 | + | 0.858258i | \(0.671547\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.00000 | − | 3.46410i | −0.417029 | − | 0.722315i | 0.578610 | − | 0.815604i | \(-0.303595\pi\) |
−0.995639 | + | 0.0932891i | \(0.970262\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.50000 | + | 2.59808i | −0.300000 | + | 0.519615i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.65685 | −1.08866 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.00000 | −1.11417 | −0.557086 | − | 0.830455i | \(-0.688081\pi\) | ||||
−0.557086 | + | 0.830455i | \(0.688081\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.41421 | + | 2.44949i | −0.254000 | + | 0.439941i | −0.964623 | − | 0.263631i | \(-0.915080\pi\) |
0.710623 | + | 0.703573i | \(0.248413\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.24264 | − | 7.34847i | −0.738549 | − | 1.27920i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.00000 | − | 1.73205i | −0.164399 | − | 0.284747i | 0.772043 | − | 0.635571i | \(-0.219235\pi\) |
−0.936442 | + | 0.350823i | \(0.885902\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.00000 | − | 6.92820i | 0.640513 | − | 1.10940i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.41421 | −0.220863 | −0.110432 | − | 0.993884i | \(-0.535223\pi\) | ||||
−0.110432 | + | 0.993884i | \(0.535223\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.0000 | 1.52499 | 0.762493 | − | 0.646997i | \(-0.223975\pi\) | ||||
0.762493 | + | 0.646997i | \(0.223975\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.41421 | − | 2.44949i | 0.210819 | − | 0.365148i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.41421 | + | 2.44949i | 0.206284 | + | 0.357295i | 0.950541 | − | 0.310599i | \(-0.100530\pi\) |
−0.744257 | + | 0.667893i | \(0.767196\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.00000 | − | 1.73205i | −0.140028 | − | 0.242536i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.00000 | − | 1.73205i | 0.137361 | − | 0.237915i | −0.789136 | − | 0.614218i | \(-0.789471\pi\) |
0.926497 | + | 0.376303i | \(0.122805\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 16.9706 | 2.28831 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.00000 | −0.794719 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.707107 | + | 1.22474i | −0.0920575 | + | 0.159448i | −0.908377 | − | 0.418153i | \(-0.862678\pi\) |
0.816319 | + | 0.577601i | \(0.196011\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.24264 | + | 7.34847i | 0.543214 | + | 0.940875i | 0.998717 | + | 0.0506406i | \(0.0161263\pi\) |
−0.455502 | + | 0.890235i | \(0.650540\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 8.00000 | + | 13.8564i | 0.992278 | + | 1.71868i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.00000 | + | 3.46410i | −0.244339 | + | 0.423207i | −0.961946 | − | 0.273241i | \(-0.911904\pi\) |
0.717607 | + | 0.696449i | \(0.245238\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.65685 | 0.681005 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.0000 | −1.42414 | −0.712069 | − | 0.702109i | \(-0.752242\pi\) | ||||
−0.712069 | + | 0.702109i | \(0.752242\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.94975 | − | 8.57321i | 0.579324 | − | 1.00342i | −0.416233 | − | 0.909258i | \(-0.636650\pi\) |
0.995557 | − | 0.0941608i | \(-0.0300168\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.12132 | − | 3.67423i | −0.244949 | − | 0.424264i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.00000 | + | 3.46410i | 0.225018 | + | 0.389742i | 0.956325 | − | 0.292306i | \(-0.0944227\pi\) |
−0.731307 | + | 0.682048i | \(0.761089\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.50000 | − | 4.33013i | 0.277778 | − | 0.481125i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.41421 | 0.155230 | 0.0776151 | − | 0.996983i | \(-0.475269\pi\) | ||||
0.0776151 | + | 0.996983i | \(0.475269\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.00000 | 0.433861 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.24264 | − | 7.34847i | 0.454859 | − | 0.787839i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.12132 | + | 3.67423i | 0.224860 | + | 0.389468i | 0.956277 | − | 0.292462i | \(-0.0944744\pi\) |
−0.731418 | + | 0.681930i | \(0.761141\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.00000 | − | 3.46410i | −0.207390 | − | 0.359211i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.00000 | − | 10.3923i | 0.615587 | − | 1.06623i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.7279 | 1.29232 | 0.646162 | − | 0.763200i | \(-0.276373\pi\) | ||||
0.646162 | + | 0.763200i | \(0.276373\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.00000 | −0.603023 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.41421 | − | 2.44949i | 0.140720 | − | 0.243733i | −0.787048 | − | 0.616891i | \(-0.788392\pi\) |
0.927768 | + | 0.373158i | \(0.121725\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.07107 | + | 12.2474i | 0.696733 | + | 1.20678i | 0.969593 | + | 0.244723i | \(0.0786971\pi\) |
−0.272860 | + | 0.962054i | \(0.587970\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.00000 | − | 3.46410i | −0.193347 | − | 0.334887i | 0.753010 | − | 0.658009i | \(-0.228601\pi\) |
−0.946357 | + | 0.323122i | \(0.895268\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.00000 | − | 8.66025i | 0.478913 | − | 0.829502i | −0.520794 | − | 0.853682i | \(-0.674364\pi\) |
0.999708 | + | 0.0241802i | \(0.00769755\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.82843 | 0.268462 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.00000 | 0.376288 | 0.188144 | − | 0.982141i | \(-0.439753\pi\) | ||||
0.188144 | + | 0.982141i | \(0.439753\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.65685 | + | 9.79796i | −0.527504 | + | 0.913664i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.82843 | − | 4.89898i | −0.261488 | − | 0.452911i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −12.5000 | − | 21.6506i | −1.13636 | − | 1.96824i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.00000 | − | 1.73205i | 0.0901670 | − | 0.156174i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.65685 | −0.505964 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.00000 | −0.709885 | −0.354943 | − | 0.934888i | \(-0.615500\pi\) | ||||
−0.354943 | + | 0.934888i | \(0.615500\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.07107 | + | 12.2474i | −0.622573 | + | 1.07833i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.6066 | − | 18.3712i | −0.926703 | − | 1.60510i | −0.788799 | − | 0.614651i | \(-0.789297\pi\) |
−0.137904 | − | 0.990446i | \(-0.544037\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 8.00000 | + | 13.8564i | 0.688530 | + | 1.19257i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.00000 | − | 3.46410i | 0.170872 | − | 0.295958i | −0.767853 | − | 0.640626i | \(-0.778675\pi\) |
0.938725 | + | 0.344668i | \(0.112008\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −21.2132 | −1.79928 | −0.899640 | − | 0.436632i | \(-0.856171\pi\) | ||||
−0.899640 | + | 0.436632i | \(0.856171\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.00000 | −0.336861 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 16.9706 | − | 29.3939i | 1.41915 | − | 2.45804i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.48528 | + | 14.6969i | 0.704664 | + | 1.22051i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.00000 | + | 5.19615i | 0.245770 | + | 0.425685i | 0.962348 | − | 0.271821i | \(-0.0876260\pi\) |
−0.716578 | + | 0.697507i | \(0.754293\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.00000 | + | 6.92820i | −0.325515 | + | 0.563809i | −0.981617 | − | 0.190864i | \(-0.938871\pi\) |
0.656101 | + | 0.754673i | \(0.272204\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.41421 | −0.114332 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.00000 | 0.642575 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.48528 | + | 14.6969i | −0.677199 | + | 1.17294i | 0.298622 | + | 0.954372i | \(0.403473\pi\) |
−0.975821 | + | 0.218572i | \(0.929860\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.41421 | + | 2.44949i | 0.112154 | + | 0.194257i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.00000 | − | 1.73205i | −0.0783260 | − | 0.135665i | 0.824202 | − | 0.566296i | \(-0.191624\pi\) |
−0.902528 | + | 0.430632i | \(0.858291\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −12.0000 | + | 20.7846i | −0.934199 | + | 1.61808i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.82843 | −0.218870 | −0.109435 | − | 0.993994i | \(-0.534904\pi\) | ||||
−0.109435 | + | 0.993994i | \(0.534904\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 19.0000 | 1.46154 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.12132 | + | 3.67423i | −0.162221 | + | 0.280976i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.00000 | − | 1.73205i | −0.0751646 | − | 0.130189i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.0000 | + | 17.3205i | −0.747435 | + | 1.29460i | 0.201613 | + | 0.979465i | \(0.435382\pi\) |
−0.949048 | + | 0.315130i | \(0.897952\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.9706 | 1.26141 | 0.630706 | − | 0.776022i | \(-0.282765\pi\) | ||||
0.630706 | + | 0.776022i | \(0.282765\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −12.0000 | −0.887066 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.82843 | + | 4.89898i | −0.207950 | + | 0.360180i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.24264 | − | 7.34847i | −0.310253 | − | 0.537373i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.00000 | + | 3.46410i | 0.144715 | + | 0.250654i | 0.929267 | − | 0.369410i | \(-0.120440\pi\) |
−0.784552 | + | 0.620063i | \(0.787107\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.00000 | + | 13.8564i | −0.575853 | + | 0.997406i | 0.420096 | + | 0.907480i | \(0.361996\pi\) |
−0.995948 | + | 0.0899262i | \(0.971337\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −22.6274 | −1.62038 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.0000 | 1.28245 | 0.641223 | − | 0.767354i | \(-0.278427\pi\) | ||||
0.641223 | + | 0.767354i | \(0.278427\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.7279 | + | 22.0454i | −0.902258 | + | 1.56276i | −0.0777029 | + | 0.996977i | \(0.524759\pi\) |
−0.824556 | + | 0.565781i | \(0.808575\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.82843 | − | 4.89898i | −0.199502 | − | 0.345547i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.00000 | + | 3.46410i | 0.139686 | + | 0.241943i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.00000 | − | 3.46410i | 0.139010 | − | 0.240772i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −25.4558 | −1.76082 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.0000 | 0.826114 | 0.413057 | − | 0.910705i | \(-0.364461\pi\) | ||||
0.413057 | + | 0.910705i | \(0.364461\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8.48528 | − | 14.6969i | 0.581402 | − | 1.00702i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −14.1421 | − | 24.4949i | −0.964486 | − | 1.67054i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 7.00000 | + | 12.1244i | 0.473016 | + | 0.819288i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.00000 | − | 6.92820i | 0.269069 | − | 0.466041i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.3137 | 0.757622 | 0.378811 | − | 0.925474i | \(-0.376333\pi\) | ||||
0.378811 | + | 0.925474i | \(0.376333\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.00000 | −0.200000 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.94975 | + | 8.57321i | −0.328526 | + | 0.569024i | −0.982220 | − | 0.187735i | \(-0.939885\pi\) |
0.653693 | + | 0.756760i | \(0.273219\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4.00000 | − | 6.92820i | −0.262049 | − | 0.453882i | 0.704737 | − | 0.709468i | \(-0.251065\pi\) |
−0.966786 | + | 0.255586i | \(0.917731\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.00000 | − | 6.92820i | 0.260931 | − | 0.451946i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −5.65685 | −0.367452 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.00000 | −0.258738 | −0.129369 | − | 0.991596i | \(-0.541295\pi\) | ||||
−0.129369 | + | 0.991596i | \(0.541295\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.707107 | − | 1.22474i | 0.0455488 | − | 0.0788928i | −0.842352 | − | 0.538927i | \(-0.818830\pi\) |
0.887901 | + | 0.460035i | \(0.152163\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −4.94975 | − | 8.57321i | −0.317526 | − | 0.549972i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −12.0000 | − | 20.7846i | −0.763542 | − | 1.32249i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.00000 | + | 1.73205i | −0.0633724 | + | 0.109764i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.41421 | 0.0892644 | 0.0446322 | − | 0.999003i | \(-0.485788\pi\) | ||||
0.0446322 | + | 0.999003i | \(0.485788\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 24.0000 | 1.50887 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.82843 | + | 4.89898i | −0.177123 | + | 0.306786i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.36396 | + | 11.0227i | 0.396973 | + | 0.687577i | 0.993351 | − | 0.115126i | \(-0.0367273\pi\) |
−0.596378 | + | 0.802704i | \(0.703394\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.00000 | − | 5.19615i | −0.185695 | − | 0.321634i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.00000 | − | 3.46410i | 0.123325 | − | 0.213606i | −0.797752 | − | 0.602986i | \(-0.793977\pi\) |
0.921077 | + | 0.389380i | \(0.127311\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.65685 | −0.347498 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.00000 | −0.367194 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −14.1421 | + | 24.4949i | −0.862261 | + | 1.49348i | 0.00747990 | + | 0.999972i | \(0.497619\pi\) |
−0.869741 | + | 0.493508i | \(0.835714\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.65685 | + | 9.79796i | 0.343629 | + | 0.595184i | 0.985104 | − | 0.171961i | \(-0.0550103\pi\) |
−0.641474 | + | 0.767144i | \(0.721677\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −9.00000 | − | 15.5885i | −0.542720 | − | 0.940019i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.00000 | + | 12.1244i | −0.420589 | + | 0.728482i | −0.995997 | − | 0.0893846i | \(-0.971510\pi\) |
0.575408 | + | 0.817867i | \(0.304843\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.82843 | −0.169334 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −32.0000 | −1.90896 | −0.954480 | − | 0.298275i | \(-0.903589\pi\) | ||||
−0.954480 | + | 0.298275i | \(0.903589\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.6066 | − | 18.3712i | 0.630497 | − | 1.09205i | −0.356953 | − | 0.934122i | \(-0.616184\pi\) |
0.987450 | − | 0.157931i | \(-0.0504822\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 8.48528 | + | 14.6969i | 0.502625 | + | 0.870572i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.50000 | + | 12.9904i | 0.441176 | + | 0.764140i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9.00000 | + | 15.5885i | −0.527589 | + | 0.913812i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.82843 | 0.165238 | 0.0826192 | − | 0.996581i | \(-0.473671\pi\) | ||||
0.0826192 | + | 0.996581i | \(0.473671\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.00000 | 0.232889 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 16.9706 | − | 29.3939i | 0.984732 | − | 1.70561i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 11.3137 | + | 19.5959i | 0.654289 | + | 1.13326i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.00000 | + | 3.46410i | 0.114897 | + | 0.199007i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 12.0000 | − | 20.7846i | 0.687118 | − | 1.19012i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.41421 | −0.0807134 | −0.0403567 | − | 0.999185i | \(-0.512849\pi\) | ||||
−0.0403567 | + | 0.999185i | \(0.512849\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −20.0000 | −1.13776 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.65685 | − | 9.79796i | 0.320771 | − | 0.555591i | −0.659877 | − | 0.751374i | \(-0.729391\pi\) |
0.980647 | + | 0.195783i | \(0.0627248\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.6066 | − | 18.3712i | −0.599521 | − | 1.03840i | −0.992892 | − | 0.119020i | \(-0.962025\pi\) |
0.393371 | − | 0.919380i | \(-0.371309\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 11.0000 | + | 19.0526i | 0.617822 | + | 1.07010i | 0.989882 | + | 0.141890i | \(0.0453179\pi\) |
−0.372061 | + | 0.928208i | \(0.621349\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 18.0000 | − | 31.1769i | 1.00781 | − | 1.74557i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.65685 | 0.315735 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.00000 | −0.333849 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.48528 | − | 14.6969i | 0.470679 | − | 0.815239i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 7.07107 | + | 12.2474i | 0.391031 | + | 0.677285i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.00000 | + | 12.1244i | 0.384755 | + | 0.666415i | 0.991735 | − | 0.128302i | \(-0.0409527\pi\) |
−0.606980 | + | 0.794717i | \(0.707619\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.00000 | − | 1.73205i | 0.0547997 | − | 0.0949158i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 11.3137 | 0.618134 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.0000 | −0.762629 | −0.381314 | − | 0.924445i | \(-0.624528\pi\) | ||||
−0.381314 | + | 0.924445i | \(0.624528\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.82843 | + | 4.89898i | −0.153619 | + | 0.266076i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.48528 | − | 14.6969i | −0.459504 | − | 0.795884i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −8.00000 | − | 13.8564i | −0.430706 | − | 0.746004i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.00000 | + | 8.66025i | −0.268414 | + | 0.464907i | −0.968452 | − | 0.249198i | \(-0.919833\pi\) |
0.700038 | + | 0.714105i | \(0.253166\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.9706 | 0.908413 | 0.454207 | − | 0.890896i | \(-0.349923\pi\) | ||||
0.454207 | + | 0.890896i | \(0.349923\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 32.0000 | 1.70803 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −12.0208 | + | 20.8207i | −0.639803 | + | 1.10817i | 0.345672 | + | 0.938355i | \(0.387651\pi\) |
−0.985476 | + | 0.169817i | \(0.945682\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 16.9706 | + | 29.3939i | 0.900704 | + | 1.56007i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.00000 | + | 6.92820i | 0.211112 | + | 0.365657i | 0.952063 | − | 0.305903i | \(-0.0989582\pi\) |
−0.740951 | + | 0.671559i | \(0.765625\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.500000 | − | 0.866025i | 0.0263158 | − | 0.0455803i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 35.3553 | 1.85567 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −28.0000 | −1.46559 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.82843 | + | 4.89898i | −0.147643 | + | 0.255725i | −0.930356 | − | 0.366658i | \(-0.880502\pi\) |
0.782713 | + | 0.622383i | \(0.213835\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.707107 | − | 1.22474i | −0.0368105 | − | 0.0637577i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13.0000 | − | 22.5167i | −0.673114 | − | 1.16587i | −0.977016 | − | 0.213165i | \(-0.931623\pi\) |
0.303902 | − | 0.952703i | \(-0.401711\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.00000 | − | 6.92820i | 0.206559 | − | 0.357771i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 33.9411 | 1.74806 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.00000 | −0.102733 | −0.0513665 | − | 0.998680i | \(-0.516358\pi\) | ||||
−0.0513665 | + | 0.998680i | \(0.516358\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.65685 | − | 9.79796i | 0.289809 | − | 0.501965i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.07107 | − | 12.2474i | −0.361315 | − | 0.625815i | 0.626863 | − | 0.779130i | \(-0.284339\pi\) |
−0.988177 | + | 0.153314i | \(0.951005\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.00000 | + | 8.66025i | 0.254164 | + | 0.440225i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 15.0000 | − | 25.9808i | 0.760530 | − | 1.31728i | −0.182047 | − | 0.983290i | \(-0.558272\pi\) |
0.942578 | − | 0.333987i | \(-0.108394\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.65685 | 0.286079 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 30.0000 | 1.51330 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.65685 | − | 9.79796i | 0.284627 | − | 0.492989i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14.1421 | − | 24.4949i | −0.709773 | − | 1.22936i | −0.964941 | − | 0.262467i | \(-0.915464\pi\) |
0.255168 | − | 0.966897i | \(-0.417869\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.00000 | + | 15.5885i | 0.449439 | + | 0.778450i | 0.998350 | − | 0.0574304i | \(-0.0182907\pi\) |
−0.548911 | + | 0.835881i | \(0.684957\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.00000 | − | 13.8564i | 0.398508 | − | 0.690237i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −14.1421 | −0.702728 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 12.0000 | 0.594818 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.12132 | − | 3.67423i | 0.104893 | − | 0.181679i | −0.808802 | − | 0.588081i | \(-0.799883\pi\) |
0.913694 | + | 0.406402i | \(0.133217\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.82843 | + | 4.89898i | 0.139516 | + | 0.241649i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.00000 | − | 3.46410i | −0.0981761 | − | 0.170046i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 15.0000 | − | 25.9808i | 0.734553 | − | 1.27228i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 32.5269 | 1.58904 | 0.794522 | − | 0.607236i | \(-0.207722\pi\) | ||||
0.794522 | + | 0.607236i | \(0.207722\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −18.0000 | −0.877266 | −0.438633 | − | 0.898666i | \(-0.644537\pi\) | ||||
−0.438633 | + | 0.898666i | \(0.644537\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.41421 | + | 2.44949i | −0.0687614 | + | 0.119098i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.12132 | − | 3.67423i | −0.102899 | − | 0.178227i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 24.0000 | + | 41.5692i | 1.15873 | + | 2.00698i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −18.0000 | + | 31.1769i | −0.867029 | + | 1.50174i | −0.00201168 | + | 0.999998i | \(0.500640\pi\) |
−0.865018 | + | 0.501741i | \(0.832693\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −15.5563 | −0.747590 | −0.373795 | − | 0.927511i | \(-0.621944\pi\) | ||||
−0.373795 | + | 0.927511i | \(0.621944\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −24.0000 | −1.15071 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.48528 | − | 14.6969i | 0.405906 | − | 0.703050i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.48528 | + | 14.6969i | 0.404980 | + | 0.701447i | 0.994319 | − | 0.106439i | \(-0.0339450\pi\) |
−0.589339 | + | 0.807886i | \(0.700612\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −18.0000 | − | 31.1769i | −0.855206 | − | 1.48126i | −0.876454 | − | 0.481486i | \(-0.840097\pi\) |
0.0212481 | − | 0.999774i | \(-0.493236\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.00000 | − | 10.3923i | 0.284427 | − | 0.492642i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −8.48528 | −0.401340 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.00000 | −0.0943858 | −0.0471929 | − | 0.998886i | \(-0.515028\pi\) | ||||
−0.0471929 | + | 0.998886i | \(0.515028\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.24264 | − | 7.34847i | 0.199778 | − | 0.346026i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.65685 | − | 9.79796i | −0.265782 | − | 0.460348i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12.0000 | + | 20.7846i | 0.561336 | + | 0.972263i | 0.997380 | + | 0.0723376i | \(0.0230459\pi\) |
−0.436044 | + | 0.899925i | \(0.643621\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.00000 | − | 6.92820i | 0.186704 | − | 0.323381i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −22.6274 | −1.05386 | −0.526932 | − | 0.849907i | \(-0.676658\pi\) | ||||
−0.526932 | + | 0.849907i | \(0.676658\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.0000 | −0.743583 | −0.371792 | − | 0.928316i | \(-0.621256\pi\) | ||||
−0.371792 | + | 0.928316i | \(0.621256\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.65685 | + | 9.79796i | −0.262330 | + | 0.454369i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10.6066 | + | 18.3712i | 0.490815 | + | 0.850117i | 0.999944 | − | 0.0105737i | \(-0.00336576\pi\) |
−0.509129 | + | 0.860690i | \(0.670032\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −12.0000 | − | 20.7846i | −0.552931 | − | 0.957704i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −30.0000 | + | 51.9615i | −1.37940 | + | 2.38919i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −12.7279 | −0.583997 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.00000 | 0.0915737 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.89949 | + | 17.1464i | −0.452319 | + | 0.783440i | −0.998530 | − | 0.0542078i | \(-0.982737\pi\) |
0.546210 | + | 0.837648i | \(0.316070\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.65685 | + | 9.79796i | 0.257930 | + | 0.446748i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −18.0000 | − | 31.1769i | −0.817338 | − | 1.41567i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −18.0000 | + | 31.1769i | −0.815658 | + | 1.41276i | 0.0931967 | + | 0.995648i | \(0.470291\pi\) |
−0.908855 | + | 0.417113i | \(0.863042\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.82843 | 0.127906 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 28.0000 | 1.26362 | 0.631811 | − | 0.775122i | \(-0.282312\pi\) | ||||
0.631811 | + | 0.775122i | \(0.282312\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.24264 | − | 7.34847i | 0.191079 | − | 0.330958i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 8.48528 | + | 14.6969i | 0.381385 | + | 0.660578i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.0000 | + | 24.2487i | 0.626726 | + | 1.08552i | 0.988204 | + | 0.153141i | \(0.0489388\pi\) |
−0.361478 | + | 0.932381i | \(0.617728\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.00000 | − | 3.46410i | 0.0893534 | − | 0.154765i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5.65685 | −0.252227 | −0.126113 | − | 0.992016i | \(-0.540250\pi\) | ||||
−0.126113 | + | 0.992016i | \(0.540250\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.00000 | −0.355995 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −13.4350 | + | 23.2702i | −0.596671 | + | 1.03346i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 19.7990 | + | 34.2929i | 0.877575 | + | 1.52000i | 0.853994 | + | 0.520282i | \(0.174173\pi\) |
0.0235804 | + | 0.999722i | \(0.492493\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −12.0000 | − | 20.7846i | −0.529813 | − | 0.917663i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 20.0000 | − | 34.6410i | 0.881305 | − | 1.52647i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −16.9706 | −0.746364 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16.2635 | − | 28.1691i | 0.712515 | − | 1.23411i | −0.251395 | − | 0.967885i | \(-0.580889\pi\) |
0.963910 | − | 0.266228i | \(-0.0857773\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16.2635 | − | 28.1691i | −0.711151 | − | 1.23175i | −0.964425 | − | 0.264356i | \(-0.914841\pi\) |
0.253274 | − | 0.967395i | \(-0.418493\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.00000 | − | 3.46410i | −0.0871214 | − | 0.150899i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.50000 | − | 6.06218i | 0.152174 | − | 0.263573i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.41421 | −0.0613716 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.00000 | 0.346518 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.65685 | + | 9.79796i | −0.244567 | + | 0.423603i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −14.1421 | − | 24.4949i | −0.610278 | − | 1.05703i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.00000 | − | 8.66025i | −0.214967 | − | 0.372333i | 0.738296 | − | 0.674477i | \(-0.235631\pi\) |
−0.953262 | + | 0.302144i | \(0.902298\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −12.0000 | + | 20.7846i | −0.514969 | + | 0.891953i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −28.2843 | −1.21157 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.0000 | 0.598597 | 0.299298 | − | 0.954160i | \(-0.403247\pi\) | ||||
0.299298 | + | 0.954160i | \(0.403247\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.24264 | + | 7.34847i | −0.181071 | + | 0.313625i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −12.7279 | − | 22.0454i | −0.542228 | − | 0.939166i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.00000 | − | 6.92820i | −0.169791 | − | 0.294086i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −9.00000 | + | 15.5885i | −0.381342 | + | 0.660504i | −0.991254 | − | 0.131965i | \(-0.957871\pi\) |
0.609912 | + | 0.792469i | \(0.291205\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −56.5685 | −2.39259 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 12.0000 | 0.506640 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10.6066 | − | 18.3712i | 0.447015 | − | 0.774253i | −0.551175 | − | 0.834390i | \(-0.685820\pi\) |
0.998190 | + | 0.0601369i | \(0.0191537\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.65685 | − | 9.79796i | −0.237986 | − | 0.412203i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 11.0000 | + | 19.0526i | 0.461144 | + | 0.798725i | 0.999018 | − | 0.0443003i | \(-0.0141058\pi\) |
−0.537874 | + | 0.843025i | \(0.680772\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.00000 | − | 8.66025i | 0.209243 | − | 0.362420i | −0.742233 | − | 0.670142i | \(-0.766233\pi\) |
0.951476 | + | 0.307722i | \(0.0995665\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.65685 | −0.236318 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 12.0000 | 0.500435 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10.6066 | + | 18.3712i | −0.441559 | + | 0.764802i | −0.997805 | − | 0.0662152i | \(-0.978908\pi\) |
0.556247 | + | 0.831017i | \(0.312241\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −11.3137 | − | 19.5959i | −0.470182 | − | 0.814379i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.00000 | + | 10.3923i | 0.248495 | + | 0.430405i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −8.00000 | + | 13.8564i | −0.330759 | + | 0.572892i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4.24264 | −0.175113 | −0.0875563 | − | 0.996160i | \(-0.527906\pi\) | ||||
−0.0875563 | + | 0.996160i | \(0.527906\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12.0000 | −0.494451 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12.7279 | + | 22.0454i | −0.523557 | + | 0.906827i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.53553 | − | 6.12372i | −0.145187 | − | 0.251471i | 0.784256 | − | 0.620438i | \(-0.213045\pi\) |
−0.929443 | + | 0.368967i | \(0.879712\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −18.0000 | − | 31.1769i | −0.736691 | − | 1.27599i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 26.8701 | 1.09605 | 0.548026 | − | 0.836461i | \(-0.315379\pi\) | ||||
0.548026 | + | 0.836461i | \(0.315379\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.00000 | −0.162893 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −35.3553 | + | 61.2372i | −1.43740 | + | 2.48965i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −19.7990 | − | 34.2929i | −0.803616 | − | 1.39190i | −0.917221 | − | 0.398378i | \(-0.869573\pi\) |
0.113605 | − | 0.993526i | \(-0.463760\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.00000 | − | 13.8564i | −0.323645 | − | 0.560570i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −21.0000 | + | 36.3731i | −0.848182 | + | 1.46909i | 0.0346469 | + | 0.999400i | \(0.488969\pi\) |
−0.882829 | + | 0.469695i | \(0.844364\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5.65685 | −0.228106 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 22.0000 | 0.885687 | 0.442843 | − | 0.896599i | \(-0.353970\pi\) | ||||
0.442843 | + | 0.896599i | \(0.353970\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.12132 | + | 3.67423i | −0.0852631 | + | 0.147680i | −0.905503 | − | 0.424339i | \(-0.860506\pi\) |
0.820240 | + | 0.572019i | \(0.193840\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 11.3137 | + | 19.5959i | 0.454003 | + | 0.786357i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.5000 | + | 26.8468i | 0.620000 | + | 1.07387i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 18.0000 | − | 31.1769i | 0.718851 | − | 1.24509i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.82843 | 0.112777 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 28.0000 | 1.11466 | 0.557331 | − | 0.830290i | \(-0.311825\pi\) | ||||
0.557331 | + | 0.830290i | \(0.311825\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8.48528 | + | 14.6969i | −0.337260 | + | 0.584151i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 11.3137 | + | 19.5959i | 0.448971 | + | 0.777640i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.00000 | − | 10.3923i | −0.237356 | − | 0.411113i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.00000 | − | 5.19615i | 0.118493 | − | 0.205236i | −0.800678 | − | 0.599095i | \(-0.795527\pi\) |
0.919171 | + | 0.393860i | \(0.128860\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 35.3553 | 1.39428 | 0.697139 | − | 0.716936i | \(-0.254456\pi\) | ||||
0.697139 | + | 0.716936i | \(0.254456\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 40.0000 | 1.57500 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 21.2132 | − | 36.7423i | 0.833977 | − | 1.44449i | −0.0608835 | − | 0.998145i | \(-0.519392\pi\) |
0.894861 | − | 0.446346i | \(-0.147275\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.24264 | − | 7.34847i | −0.166538 | − | 0.288453i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 13.0000 | + | 22.5167i | 0.508729 | + | 0.881145i | 0.999949 | + | 0.0101092i | \(0.00321793\pi\) |
−0.491220 | + | 0.871036i | \(0.663449\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −30.0000 | + | 51.9615i | −1.17220 | + | 2.03030i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 9.89949 | 0.386216 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.00000 | 0.233727 | 0.116863 | − | 0.993148i | \(-0.462716\pi\) | ||||
0.116863 | + | 0.993148i | \(0.462716\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18.3848 | − | 31.8434i | 0.715085 | − | 1.23856i | −0.247842 | − | 0.968801i | \(-0.579721\pi\) |
0.962927 | − | 0.269763i | \(-0.0869453\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.65685 | + | 9.79796i | 0.219694 | + | 0.380521i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12.0000 | + | 20.7846i | 0.464642 | + | 0.804783i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8.00000 | + | 13.8564i | −0.309298 | + | 0.535720i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −50.9117 | −1.96542 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −44.0000 | −1.69608 | −0.848038 | − | 0.529936i | \(-0.822216\pi\) | ||||
−0.848038 | + | 0.529936i | \(0.822216\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 8.48528 | − | 14.6969i | 0.326599 | − | 0.565685i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 16.9706 | + | 29.3939i | 0.652232 | + | 1.12970i | 0.982580 | + | 0.185839i | \(0.0595004\pi\) |
−0.330348 | + | 0.943859i | \(0.607166\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.00000 | − | 12.1244i | −0.268241 | − | 0.464606i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.00000 | + | 3.46410i | −0.0765279 | + | 0.132550i | −0.901750 | − | 0.432259i | \(-0.857717\pi\) |
0.825222 | + | 0.564809i | \(0.191050\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11.3137 | −0.432275 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5.65685 | + | 9.79796i | −0.215509 | + | 0.373273i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21.9203 | − | 37.9671i | −0.833888 | − | 1.44434i | −0.894933 | − | 0.446201i | \(-0.852777\pi\) |
0.0610448 | − | 0.998135i | \(-0.480557\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 30.0000 | + | 51.9615i | 1.13796 | + | 1.97101i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.00000 | − | 1.73205i | 0.0378777 | − | 0.0656061i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 11.3137 | 0.427924 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 38.0000 | 1.43524 | 0.717620 | − | 0.696435i | \(-0.245231\pi\) | ||||
0.717620 | + | 0.696435i | \(0.245231\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.24264 | − | 7.34847i | 0.160014 | − | 0.277153i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5.65685 | + | 9.79796i | 0.213049 | + | 0.369012i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17.0000 | − | 29.4449i | −0.638448 | − | 1.10583i | −0.985773 | − | 0.168080i | \(-0.946243\pi\) |
0.347325 | − | 0.937745i | \(-0.387090\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.00000 | + | 3.46410i | −0.0750059 | + | 0.129914i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 11.3137 | 0.423702 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −96.0000 | −3.59020 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.82843 | − | 4.89898i | 0.105630 | − | 0.182956i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.41421 | + | 2.44949i | 0.0527413 | + | 0.0913506i | 0.891191 | − | 0.453629i | \(-0.149871\pi\) |
−0.838449 | + | 0.544979i | \(0.816537\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.00000 | + | 1.73205i | 0.0371904 | + | 0.0644157i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9.00000 | − | 15.5885i | 0.334252 | − | 0.578941i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −25.4558 | −0.944105 | −0.472052 | − | 0.881570i | \(-0.656487\pi\) | ||||
−0.472052 | + | 0.881570i | \(0.656487\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.0000 | 1.07407 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7.07107 | + | 12.2474i | −0.261533 | + | 0.452988i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.24264 | − | 7.34847i | −0.156706 | − | 0.271422i | 0.776973 | − | 0.629534i | \(-0.216754\pi\) |
−0.933679 | + | 0.358112i | \(0.883421\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −12.0000 | − | 20.7846i | −0.442026 | − | 0.765611i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.00000 | − | 5.19615i | 0.110357 | − | 0.191144i | −0.805557 | − | 0.592518i | \(-0.798134\pi\) |
0.915914 | + | 0.401374i | \(0.131467\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 33.9411 | 1.24686 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −24.0000 | −0.880475 | −0.440237 | − | 0.897881i | \(-0.645106\pi\) | ||||
−0.440237 | + | 0.897881i | \(0.645106\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.48528 | − | 14.6969i | 0.310877 | − | 0.538454i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.707107 | + | 1.22474i | 0.0258717 | + | 0.0448111i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.00000 | + | 10.3923i | 0.218943 | + | 0.379221i | 0.954485 | − | 0.298259i | \(-0.0964058\pi\) |
−0.735542 | + | 0.677479i | \(0.763072\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.00000 | + | 1.73205i | −0.0364420 | + | 0.0631194i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 22.6274 | 0.823496 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22.0000 | −0.799604 | −0.399802 | − | 0.916602i | \(-0.630921\pi\) | ||||
−0.399802 | + | 0.916602i | \(0.630921\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −16.9706 | + | 29.3939i | −0.615992 | + | 1.06693i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13.4350 | + | 23.2702i | 0.487019 | + | 0.843542i | 0.999889 | − | 0.0149244i | \(-0.00475076\pi\) |
−0.512869 | + | 0.858467i | \(0.671417\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.00000 | + | 3.46410i | 0.0723102 | + | 0.125245i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.00000 | − | 6.92820i | 0.144432 | − | 0.250163i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −29.6985 | −1.07095 | −0.535477 | − | 0.844550i | \(-0.679868\pi\) | ||||
−0.535477 | + | 0.844550i | \(0.679868\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18.0000 | −0.648254 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 9.89949 | − | 17.1464i | 0.356060 | − | 0.616714i | −0.631239 | − | 0.775589i | \(-0.717453\pi\) |
0.987299 | + | 0.158874i | \(0.0507865\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.24264 | − | 7.34847i | −0.152400 | − | 0.263965i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.00000 | − | 5.19615i | −0.107486 | − | 0.186171i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 36.0000 | − | 62.3538i | 1.28818 | − | 2.23120i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 33.9411 | 1.21296 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 48.0000 | 1.71319 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16.2635 | − | 28.1691i | 0.579730 | − | 1.00412i | −0.415780 | − | 0.909465i | \(-0.636492\pi\) |
0.995510 | − | 0.0946561i | \(-0.0301751\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.82843 | + | 4.89898i | 0.100695 | + | 0.174408i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −24.0000 | − | 41.5692i | −0.852265 | − | 1.47617i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.00000 | − | 6.92820i | 0.141865 | − | 0.245718i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 39.5980 | 1.40263 | 0.701316 | − | 0.712850i | \(-0.252596\pi\) | ||||
0.701316 | + | 0.712850i | \(0.252596\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.00000 | −0.141510 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.12132 | + | 3.67423i | −0.0749532 | + | 0.129823i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 29.6985 | + | 51.4393i | 1.04804 | + | 1.81525i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −20.0000 | − | 34.6410i | −0.704033 | − | 1.21942i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 16.0000 | − | 27.7128i | 0.562530 | − | 0.974331i | −0.434745 | − | 0.900554i | \(-0.643161\pi\) |
0.997275 | − | 0.0737769i | \(-0.0235053\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.07107 | 0.248299 | 0.124149 | − | 0.992264i | \(-0.460380\pi\) | ||||
0.124149 | + | 0.992264i | \(0.460380\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −16.0000 | −0.561144 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.82843 | + | 4.89898i | −0.0990755 | + | 0.171604i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 21.2132 | + | 36.7423i | 0.742156 | + | 1.28545i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9.00000 | + | 15.5885i | 0.314102 | + | 0.544041i | 0.979246 | − | 0.202674i | \(-0.0649632\pi\) |
−0.665144 | + | 0.746715i | \(0.731630\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 28.0000 | − | 48.4974i | 0.976019 | − | 1.69051i | 0.299487 | − | 0.954100i | \(-0.403185\pi\) |
0.676532 | − | 0.736413i | \(-0.263482\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 25.4558 | 0.886259 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −4.00000 | −0.139094 | −0.0695468 | − | 0.997579i | \(-0.522155\pi\) | ||||
−0.0695468 | + | 0.997579i | \(0.522155\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −12.7279 | + | 22.0454i | −0.442059 | + | 0.765669i | −0.997842 | − | 0.0656587i | \(-0.979085\pi\) |
0.555783 | + | 0.831327i | \(0.312418\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −9.89949 | − | 17.1464i | −0.343410 | − | 0.594803i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.00000 | + | 6.92820i | 0.138426 | + | 0.239760i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.00000 | − | 13.8564i | 0.276520 | − | 0.478947i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −31.1127 | −1.07413 | −0.537065 | − | 0.843541i | \(-0.680467\pi\) | ||||
−0.537065 | + | 0.843541i | \(0.680467\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 22.6274 | − | 39.1918i | 0.779330 | − | 1.34984i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −26.8701 | − | 46.5403i | −0.924358 | − | 1.60104i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 15.0000 | + | 25.9808i | 0.514799 | + | 0.891657i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.00000 | + | 6.92820i | −0.137118 | + | 0.237496i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −16.9706 | −0.581061 | −0.290531 | − | 0.956866i | \(-0.593832\pi\) | ||||
−0.290531 | + | 0.956866i | \(0.593832\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 12.0000 | 0.410391 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.53553 | − | 6.12372i | 0.120772 | − | 0.209182i | −0.799301 | − | 0.600931i | \(-0.794796\pi\) |
0.920072 | + | 0.391749i | \(0.128130\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.77817 | − | 13.4722i | −0.265388 | − | 0.459665i | 0.702277 | − | 0.711904i | \(-0.252167\pi\) |
−0.967665 | + | 0.252238i | \(0.918833\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −22.0000 | − | 38.1051i | −0.748889 | − | 1.29711i | −0.948356 | − | 0.317209i | \(-0.897254\pi\) |
0.199467 | − | 0.979905i | \(-0.436079\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −21.2132 | −0.720438 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −24.0000 | −0.814144 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11.3137 | − | 19.5959i | 0.383350 | − | 0.663982i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6.36396 | + | 11.0227i | 0.215387 | + | 0.373062i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 19.0000 | + | 32.9090i | 0.641584 | + | 1.11126i | 0.985079 | + | 0.172102i | \(0.0550559\pi\) |
−0.343495 | + | 0.939155i | \(0.611611\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.00000 | + | 3.46410i | −0.0674583 | + | 0.116841i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 38.1838 | 1.28644 | 0.643222 | − | 0.765680i | \(-0.277597\pi\) | ||||
0.643222 | + | 0.765680i | \(0.277597\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −28.0000 | −0.942275 | −0.471138 | − | 0.882060i | \(-0.656156\pi\) | ||||
−0.471138 | + | 0.882060i | \(0.656156\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.82843 | + | 4.89898i | −0.0950765 | + | 0.164677i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −18.3848 | − | 31.8434i | −0.617300 | − | 1.06920i | −0.989976 | − | 0.141234i | \(-0.954893\pi\) |
0.372676 | − | 0.927962i | \(-0.378440\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 15.0000 | + | 25.9808i | 0.502519 | + | 0.870388i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6.00000 | + | 10.3923i | −0.200782 | + | 0.347765i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 56.5685 | 1.89088 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −32.0000 | −1.06845 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8.48528 | − | 14.6969i | 0.283000 | − | 0.490170i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.41421 | + | 2.44949i | 0.0471143 | + | 0.0816043i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −24.0000 | − | 41.5692i | −0.797787 | − | 1.38181i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 10.0000 | − | 17.3205i | 0.332045 | − | 0.575118i | −0.650868 | − | 0.759191i | \(-0.725595\pi\) |
0.982913 | + | 0.184073i | \(0.0589282\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.82843 | 0.0938130 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −48.0000 | −1.59031 | −0.795155 | − | 0.606406i | \(-0.792611\pi\) | ||||
−0.795155 | + | 0.606406i | \(0.792611\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.24264 | + | 7.34847i | −0.140411 | + | 0.243199i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 16.9706 | + | 29.3939i | 0.561029 | + | 0.971732i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 16.0000 | + | 27.7128i | 0.527791 | + | 0.914161i | 0.999475 | + | 0.0323936i | \(0.0103130\pi\) |
−0.471684 | + | 0.881768i | \(0.656354\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.00000 | − | 1.73205i | 0.0329511 | − | 0.0570730i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 67.8823 | 2.23437 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.00000 | 0.197279 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7.07107 | + | 12.2474i | −0.232244 | + | 0.402259i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 16.2635 | + | 28.1691i | 0.533587 | + | 0.924199i | 0.999230 | + | 0.0392269i | \(0.0124895\pi\) |
−0.465644 | + | 0.884972i | \(0.654177\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 8.00000 | + | 13.8564i | 0.261908 | + | 0.453638i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −12.0000 | + | 20.7846i | −0.392442 | + | 0.679729i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −21.2132 | −0.693005 | −0.346503 | − | 0.938049i | \(-0.612631\pi\) | ||||
−0.346503 | + | 0.938049i | \(0.612631\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 30.0000 | 0.979013 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 15.5563 | − | 26.9444i | 0.507122 | − | 0.878362i | −0.492844 | − | 0.870118i | \(-0.664043\pi\) |
0.999966 | − | 0.00824396i | \(-0.00262416\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.82843 | + | 4.89898i | 0.0921063 | + | 0.159533i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 21.0000 | + | 36.3731i | 0.682408 | + | 1.18197i | 0.974244 | + | 0.225497i | \(0.0724007\pi\) |
−0.291835 | + | 0.956469i | \(0.594266\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −28.0000 | + | 48.4974i | −0.908918 | + | 1.57429i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −31.1127 | −1.00890 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −26.0000 | −0.842223 | −0.421111 | − | 0.907009i | \(-0.638360\pi\) | ||||
−0.421111 | + | 0.907009i | \(0.638360\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.65685 | − | 9.79796i | 0.183052 | − | 0.317055i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 25.4558 | + | 44.0908i | 0.822871 | + | 1.42525i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11.5000 | + | 19.9186i | 0.370968 | + | 0.642535i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.00000 | − | 3.46410i | 0.0644491 | − | 0.111629i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 45.2548 | 1.45680 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 60.0000 | 1.92947 | 0.964735 | − | 0.263223i | \(-0.0847856\pi\) | ||||
0.964735 | + | 0.263223i | \(0.0847856\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.24264 | − | 7.34847i | 0.136293 | − | 0.236067i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 16.2635 | + | 28.1691i | 0.521919 | + | 0.903990i | 0.999675 | + | 0.0254978i | \(0.00811707\pi\) |
−0.477756 | + | 0.878493i | \(0.658550\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 12.0000 | + | 20.7846i | 0.384308 | + | 0.665640i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −6.00000 | + | 10.3923i | −0.191957 | + | 0.332479i | −0.945899 | − | 0.324462i | \(-0.894817\pi\) |
0.753942 | + | 0.656941i | \(0.228150\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −25.4558 | −0.813572 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.0000 | 0.319275 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −26.8701 | + | 46.5403i | −0.857022 | + | 1.48441i | 0.0177349 | + | 0.999843i | \(0.494355\pi\) |
−0.874757 | + | 0.484562i | \(0.838979\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −25.4558 | − | 44.0908i | −0.811091 | − | 1.40485i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −20.0000 | − | 34.6410i | −0.635963 | − | 1.10152i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.0000 | − | 27.7128i | 0.508257 | − | 0.880327i | −0.491698 | − | 0.870766i | \(-0.663623\pi\) |
0.999954 | − | 0.00956046i | \(-0.00304324\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −19.7990 | −0.628302 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 72.0000 | 2.28255 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.24264 | − | 7.34847i | 0.134366 | − | 0.232728i | −0.790989 | − | 0.611830i | \(-0.790434\pi\) |
0.925355 | + | 0.379102i | \(0.123767\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.65685 | + | 9.79796i | 0.178975 | + | 0.309994i |
(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 | 392.2.i.h.361.1 | 4 | ||
3.2 | odd | 2 | 3528.2.s.bj.361.2 | 4 | |||
4.3 | odd | 2 | 784.2.i.n.753.2 | 4 | |||
7.2 | even | 3 | inner | 392.2.i.h.177.1 | 4 | ||
7.3 | odd | 6 | 392.2.a.g.1.1 | ✓ | 2 | ||
7.4 | even | 3 | 392.2.a.g.1.2 | yes | 2 | ||
7.5 | odd | 6 | inner | 392.2.i.h.177.2 | 4 | ||
7.6 | odd | 2 | inner | 392.2.i.h.361.2 | 4 | ||
21.2 | odd | 6 | 3528.2.s.bj.3313.2 | 4 | |||
21.5 | even | 6 | 3528.2.s.bj.3313.1 | 4 | |||
21.11 | odd | 6 | 3528.2.a.be.1.1 | 2 | |||
21.17 | even | 6 | 3528.2.a.be.1.2 | 2 | |||
21.20 | even | 2 | 3528.2.s.bj.361.1 | 4 | |||
28.3 | even | 6 | 784.2.a.k.1.2 | 2 | |||
28.11 | odd | 6 | 784.2.a.k.1.1 | 2 | |||
28.19 | even | 6 | 784.2.i.n.177.1 | 4 | |||
28.23 | odd | 6 | 784.2.i.n.177.2 | 4 | |||
28.27 | even | 2 | 784.2.i.n.753.1 | 4 | |||
35.4 | even | 6 | 9800.2.a.bv.1.1 | 2 | |||
35.24 | odd | 6 | 9800.2.a.bv.1.2 | 2 | |||
56.3 | even | 6 | 3136.2.a.bp.1.1 | 2 | |||
56.11 | odd | 6 | 3136.2.a.bp.1.2 | 2 | |||
56.45 | odd | 6 | 3136.2.a.bk.1.2 | 2 | |||
56.53 | even | 6 | 3136.2.a.bk.1.1 | 2 | |||
84.11 | even | 6 | 7056.2.a.ct.1.1 | 2 | |||
84.59 | odd | 6 | 7056.2.a.ct.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
392.2.a.g.1.1 | ✓ | 2 | 7.3 | odd | 6 | ||
392.2.a.g.1.2 | yes | 2 | 7.4 | even | 3 | ||
392.2.i.h.177.1 | 4 | 7.2 | even | 3 | inner | ||
392.2.i.h.177.2 | 4 | 7.5 | odd | 6 | inner | ||
392.2.i.h.361.1 | 4 | 1.1 | even | 1 | trivial | ||
392.2.i.h.361.2 | 4 | 7.6 | odd | 2 | inner | ||
784.2.a.k.1.1 | 2 | 28.11 | odd | 6 | |||
784.2.a.k.1.2 | 2 | 28.3 | even | 6 | |||
784.2.i.n.177.1 | 4 | 28.19 | even | 6 | |||
784.2.i.n.177.2 | 4 | 28.23 | odd | 6 | |||
784.2.i.n.753.1 | 4 | 28.27 | even | 2 | |||
784.2.i.n.753.2 | 4 | 4.3 | odd | 2 | |||
3136.2.a.bk.1.1 | 2 | 56.53 | even | 6 | |||
3136.2.a.bk.1.2 | 2 | 56.45 | odd | 6 | |||
3136.2.a.bp.1.1 | 2 | 56.3 | even | 6 | |||
3136.2.a.bp.1.2 | 2 | 56.11 | odd | 6 | |||
3528.2.a.be.1.1 | 2 | 21.11 | odd | 6 | |||
3528.2.a.be.1.2 | 2 | 21.17 | even | 6 | |||
3528.2.s.bj.361.1 | 4 | 21.20 | even | 2 | |||
3528.2.s.bj.361.2 | 4 | 3.2 | odd | 2 | |||
3528.2.s.bj.3313.1 | 4 | 21.5 | even | 6 | |||
3528.2.s.bj.3313.2 | 4 | 21.2 | odd | 6 | |||
7056.2.a.ct.1.1 | 2 | 84.11 | even | 6 | |||
7056.2.a.ct.1.2 | 2 | 84.59 | odd | 6 | |||
9800.2.a.bv.1.1 | 2 | 35.4 | even | 6 | |||
9800.2.a.bv.1.2 | 2 | 35.24 | odd | 6 |